*Article* **Indoor Air Quality and Health Outcomes in Employees Working from Home during the COVID-19 Pandemic: A Pilot Study**

**Taehyun Roh 1, Alejandro Moreno-Rangel 2, Juha Baek 3, Alexander Obeng 4, Nishat Tasnim Hasan <sup>1</sup> and Genny Carrillo 4,5,\***


**Abstract:** Indoor air quality (IAQ) has a substantial impact on public health. Since the beginning of the COVID-19 pandemic, more employees have worked remotely from home to minimize in-person contacts. This pilot study aims to measure the difference in workplace IAQ before and during the pandemic and its impact on employees' health. The levels of fine particulate matter (PM2.5) and total volatile organic chemicals (tVOC) were measured in the employees' offices before the COVID-19 pandemic and at homes while working from home during the pandemic using Foobot air monitors. The frequencies of six sick building syndrome (SBS) symptoms were evaluated at each period of monitoring. The result showed PM2.5 levels in households while working from home were significantly higher than in offices while working at the office for all participants (*p* < 0.05). The PM2.5 levels in all households exceeded the health-based annual mean standard (12 μg/m3), whereas 90% of offices were in compliance. The tVOC levels were all below the standard (500 μg/m3). We also found a higher frequency of SBS symptoms were observed while working from home as the IAQ was worse at home. This study suggested that working from home might have a detrimental health impact due to poor IAQ and providing interventions to remote employees should be considered.

**Keywords:** indoor air quality; air monitor; particulate matter 2.5; COVID-19; employee health; remote work

#### **1. Introduction**

Indoor air pollution has been classified as one of the top five environmental health hazards. In the United States (US), the average person spends nearly 90% of their time indoors, where air quality is estimated two to five times worse than outdoors [1]. Indoor air quality (IAQ) is affected by outdoor factors (i.e., motor vehicle and industry), indoor activities (i.e., cooking and smoking) and building-related factors (i.e., ventilation and air conditioning systems) [2].

Outdoor chemicals, including fine particulate matter (PM2.5), volatile organic compounds (VOCs), ozone (O3), carbon monoxide (CO), and radon could affect IAQ. However, there are a variety of additional sources for indoor air pollution in offices and homes. In offices, most indoor pollutants are related to building materials and human activities such as carpet and other office furniture, cleaning agents, air fresheners, paints, adhesives, printers,

**Citation:** Roh, T.; Moreno-Rangel, A.; Baek, J.; Obeng, A.; Hasan, N.T.; Carrillo, G. Indoor Air Quality and Health Outcomes in Employees Working from Home during the COVID-19 Pandemic: A Pilot Study. *Atmosphere* **2021**, *12*, 1665. https:// doi.org/10.3390/atmos12121665

Academic Editors: Ashok Kumar, M Amirul I Khan, Alejandro Moreno Rangel and Michał Piasecki

Received: 30 November 2021 Accepted: 9 December 2021 Published: 11 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

pesticides, and biological contaminants from poor ventilation systems or water-damaged walls [3–6]. A study conducted by Serafin et al. prioritized the indoor air pollutants in office buildings and found formaldehyde, acetaldehyde, benzene, PM2.5, and PM10 as priority pollutants [7]. In households, activities performed by individuals including cooking, laundry, smoking, and the use of chemicals for cleaning and hobbies increase indoor air pollution [8]. The primary indoor air pollutants include particulate matter, volatile organic compounds (VOCs), semi-volatile organic compounds (SVOCs), ozone, asbestos, tobacco smoke, nonpolar volatile organic compounds, allergens, and mold [9,10].

Modern buildings are designed to be airtight, eliminating natural ventilation as they are controlled by heating, ventilation, and air conditioning (HVAC) systems that recirculate a high percentage of the air with minimal fresh air replacement, maintaining constant IAQ across seasons [10–12]. HVAC systems have a critical role in keeping people inside buildings comfortable and healthy, and they are intended to provide an air supply to the room and have an exhaust system to remove dirty air from indoor spaces [13]. Nonresidential buildings like offices usually have an mechanical ventilation for outdoor air change, with less natural ventilation or infiltration contribution, maintaining constant IAQ over seasons [14]. It is recommended to install filters (F7 grade or above) to filter fresh air to the unit to protect HVAC units and limit the ingress of outdoor particles. However, inadequate system installation and poorly maintained air ducts and filters diminish the air quality [15]. Biological particles such as bacteria, fungi, and viruses correlated with respiratory health conditions can float in the air and linger longer in poorly ventilated indoor spaces [16–18].

IAQ is a significant concern because it could adversely impact human health, comfort, well-being, and productivity [19]. Acute and chronic health effects are associated with exposure to indoor air pollutants in office environments. Sick building syndrome (SBS) is a group of acute adverse health experiences related to IAQ, including headache, eye irritation, dry cough, and itching skin for occupants of a building related to the time spent in the building [20,21]. According to a multi-country study in Europe, the most prevalence adverse health outcomes were dry eyes and headache, accounting for one-third of the office workers [22]. In the US, SBS could be responsible for an overall loss in productivity, leading to costs up to \$75 billion per year [23]. Poor IAQ also increases the risk of chronic health problems including cardiovascular disease, chronic obstructive and pulmonary disease, and lung cancer [24]. Among indoor air pollutants, PM2.5 has become a major public health hazard because it penetrates deeply into the respiratory trat, entering the circulatory system and causing oxidative stress and inflammation [25–28]. Among indoor air pollutants, PM2.5 is a dominant indoor air pollutant causing 4000 DALYs (disability-adjusted life years) per one million population, which is 80% of the total annual burden of diseases related to indoor exposure [29].

The development of information and communication technologies have changed the work environment, increasing the adaptation of remote work in diverse occupations including managers, educators, and those working in computers, finance, and law [30,31]. In Europe, the proportion of teleworkers was less than 10% in normal times, which increased up to 31% during the COVID-19 pandemic [32]. In the US, the percentage of employees who had ever worked remotely increased from 9% in 1995 to 37% in 2015 and the average number of days working remotely per month was 2.3 [33]. The advantages of remote work include flexibility, cost and time savings on commuting, and more time with family [34,35]. In contrast, it also has negative aspects such as loss of social interaction and self-discipline and unfavorable physical conditions, leading to productivity reduction and psychological and psychological distress [36–38].

In December 2019, the COVID-19, caused by a new coronavirus, SARS-CoV-2, was first detected in Wuhan, China [39]. The World Health Organization (WHO) proclaimed the COVID-19 outbreak to be the sixth global public health emergency on 30 January 2020 [40,41]. Due to the highly contagious nature of the disease, governments decided to implement "social distancing" measures, closing businesses and enacting stay-at-home

orders [42]. Some sectors of occupations such as healthcare, farm, construction, and service workers could not be carried out remotely, and therefore had higher risks of contracting COVID-19 [43]. In contrast, many employees in fields including management, education, and information technology worked remotely during 2020 and half of 2021 [31,44–46]. In the US, approximately 30% of employees changed to working from home between February and May 2020 [47]. In Canada, the percentage of remote workers increased from 13% to 39% during March 2020 [48]. In the Netherlands, 6% of workers worked from home before the pandemic, but the percentage increased to 39% during the pandemic [49]. However, the domestic spaces became offices without consideration of environmental infrastructures such as ventilation systems and subsequent indoor air quality, posing health risks to employees [50].

This study aims to evaluate the IAQ in the office before the COVID-19 pandemic and at home while working remotely from home during the pandemic and compare the health outcomes in employees between those two periods.

#### **2. Materials and Methods**

#### *2.1. Participants and Study Design*

This pilot study was conducted in McAllen, South Texas, during May–July 2019 in employees' offices before the COVID-19 pandemic and during June–September 2020 at their households while employees worked from home during the pandemic. A total of eight staff members working in the same building in an academic organization participated in the study. The study protocol was reviewed and approved by Texas A&M University's Institutional Review Boards. The methodology presented here was adapted to comply with the COVID-19 regulation from a previous study from our research group [51].

#### *2.2. Air Quality Assessment*

This study used a low-cost consumer monitor called Foobot® Air Monitor (Model# FBT0002100, AirBoxLab, San Francisco, CA, USA) to assess the IAQ in the offices and households. The performance and accuracy of the Foobot monitor were assessed and determined to be a reliable tool for measuring indoor pollution levels [52,53]. The Foobots (low-cost air monitors) were used in the offices and homes (bedroom, kitchen, and living room), where occupants stay for a longer time [54]. As suggested in previous studies, calibration equations, data quality, and data corroboration were followed by comparison [55,56]. The IAQ was measured according to the ASTM D7297-14. The Foobot monitors (air temperature (−40–125 ◦C), relative humidity (0–100%), PM2.5 (0–1300 <sup>μ</sup>g/m3), and tVOC (100–1000 ppb) were installed in each office on top of a bookshelf (5–6 feet). The Foobot air monitors collected data at 5-minute intervals for two months in each office. The same procedure was done in households to avoid any accidents with children living at the house. We used hotspots in both locations to have a stable WiFi connection throughout the study periods. The data was stored automatically every five minutes in a protected online storage and were safely saved in an encrypted computer.

The outdoor temperature and PM2.5 levels in the study area during the same periods of IAQ measurements were retrieved from the Texas Air Monitoring Information System (TAMIS), a database maintained by the Texas Commission on Environmental Quality (TCEQ). The outdoor tVOC levels were not collected because data were not available.

#### *2.3. Health Outcomes Assessment*

A brief version of the modified Office Environment Survey (OES) was implemented for all participants to assess six SBS symptoms while they were working in the office before the COVID pandemic and at home during the pandemic as well as the characteristics of residential environment and behaviors in the participants' homes [57]. The selected six SBS symptoms included in this study were: dry eyes, itchy or watery eyes, blocked or stuffy nose, dry throat, headache, and dry or irritated skin, as these were identified as more dominant and prevalent from previous studies [56–59]. The frequencies of these symptoms were assessed using a Likert scale, and scores for each symptom were assigned by the frequency of symptoms: 0 (not at all), 1 (less often), 2 (every 2–3 weeks), 3 (1–2 days each week), 4 (3–4 days each week) and 5 (every day). The surveys were conducted online via Qualtrics.

#### *2.4. Statistical Analysis*

The least-square geometric means (LSGMs) for PM2.5 and tVOC levels were calculated from the data collected at 5-minute intervals for each monitoring period in the offices and the three locations (bedroom, kitchen, and living room) within the homes. After adjusting for temperature and relative humidity, the generalized linear model was fitted to estimate LSGMs and 95% confidence intervals (CIs) of PM2.5 and tVOC levels and compare those levels in the offices while working at the office before the COVID-19 pandemic and at homes working from home during the pandemic in each participant and overall. The differences in levels of those pollutants among locations within the houses were assessed using Tukey's post hoc test. However, for health outcomes, statistical analyses could not be conducted for their associations with IAQ due to the small sample size. Instead, the direction of changes in IAQ and frequencies of health outcomes were manually compared between the two periods for each participant. All statistical analyses were conducted using SAS version 9.4 (SAS Institute Inc., Cary, NC, USA). A *p*-value less than 0.05 was considered statistically significant.

#### **3. Results**

In our study, eight female academic staff members aged 23 to 67 years old (average 36.1, standard deviation 13.1) participated. All participants lived in single-family detached houses with central air conditioning systems and electric heaters. All households had electric dryers vented outside and kitchen fans, and none of their family members smoked or worked with hazardous materials on the job. Table 1 summarizes other characteristics of the residential environment and behaviors in the participants' home. The average numbers of rooms and people living in the house were 3.3 and 3.4. Six homes had furry pets and non-carpeted floors at their homes. Seven families used electronic stoves and bathroom fans, and three households had air purifiers. Most households rarely opened windows for ventilation and only three households cleaned their floors regularly using a vacuum cleaner. Five houses used chemicals for lawn care. The averages of indoor temperature and relative humidity measured at homes during the study period were 24.6 ◦C (range: 23.6–26.9) and 52.8% (range: 46.3–57.5), which are within the recommended ranges of indoor temperature (23–27 ◦C) and relative humidity (30–60%) [60,61].



<sup>1</sup> Frequency per one month.

Table 2 shows the averages of PM2.5 levels in the offices before the COVID-19 pandemic and at homes during the pandemic for each participant. The results showed that the averages of indoor PM2.5 levels ranged from 5.6–12.2 μg/m<sup>3</sup> for offices and 11.2–45.7 μg/m3 for homes in our participants. The PM2.5 concentration levels at homes during the pandemic were significantly higher than those in the offices before the pandemic for each participant. Six homes had levels higher than the current health-based standard (12 μg/m3) of the National Ambient Air Quality Standards (NAAQS) [62], whereas one office had PM2.5

levels higher than this level. Only one participant had PM2.5 levels higher than the national standard in both the office and home.

**Table 2.** Averages of indoor PM2.5 levels (μg/m3) in the offices before the COVID-19 pandemic and at homes during the pandemic (LSGMs, 95% CI).


\* PM2.5 level in the household was significantly higher than the office at *p* < 0.05.

Table 3 describes the mean PM2.5 levels for different locations such as the bedroom, kitchen, and living room in each home. Bedroom PM2.5 levels ranged from 9.95–94.51 μg/m3 compared to 10.87–22.58 μg/m3 for kitchens and 8.89–29.71 μg/m3 for living rooms. In four homes (50%), the PM2.5 levels were highest in the bedrooms compared to the kitchens and living rooms of the same home. The levels of PM2.5 were highest in the kitchen (participants 6 and 8) and the living room (participant 5) compared to the other two locations within the same home. At homes of six participants (75%), the levels of PM2.5 in the living room were significantly lower than in other locations.

**Table 3.** Averages of PM2.5 levels (μg/m3) at different locations in the households (LSGMs and 95% CI).


\* PM2.5 level at the location was significantly higher than other locations at *p* < 0.05. † PM2.5 level at the location was significantly lower than other locations at *p* < 0.05.

Table 4 describes the average tVOC levels in the offices and homes for all participants. The average tVOC levels ranged from 151.65–215.08 μg/m3 for offices and 152.87–279.86 μg/m3 for homes. The tVOC levels were significantly higher at homes than in the offices for all participants. However, all the tVOC levels in the offices and homes were much lower than the acceptable maximum tVOC level of 500 μg/m3 [63].

Additional analyses showed that the average tVOC levels within the house ranged from 159.4–305.2 μg/m3 in the bedrooms, 151.1–286.1 μg/m3 in the kitchens, and 148.9– 273.8 μg/m3 in the living rooms (Table 5). The tVOC levels at all locations within homes were much lower than the acceptable maximum level of 500 μg/m3 [63]. In four homes (50%), the tVOC levels were highest in the bedrooms compared to the kitchens and living rooms of the same home. The tVOC levels were highest in the kitchen (participants 1, 3, and 5) and the living room (participants 2 and 7) compared to the other two locations within the same home.


**Table 4.** Averages of indoor tVOC levels (μg/m3) in the offices before the COVID-19 pandemic and at homes during the pandemic (LSGMs, 95% CI).

\* The tVOC level in the household was significantly higher than the office at *p* < 0.05.

**Table 5.** Averages of tVOC levels (μg/m3) at different locations in the households (LSGMs and 95% CI).


\* The tVOC level at the location was significantly higher than other locations at *p* < 0.05. † The tVOC level at the location was significantly lower than other locations at *p* < 0.05.

Table 6 shows the changes in the frequency of six SBS symptoms associated with poor air quality that participants reported. Among six participants who completed the health survey at both periods, four subjects reported higher frequency of multiple symptoms while working at home than while working in the office. The PM2.5 level while working at home during COVID-19 (greater than the standard 12 μg/m3) was higher than at the office before the COVID-19 pandemic (less than the standard 12 μg/m3). However, in participants 5 and 7, despite the statistically significant difference, both office and home PM2.5 levels were lower or higher than the standard 12 μg/m3, and the frequencies of symptoms in these participants were stable between the two different time periods.

**Table 6.** Frequencies of experiencing six SBS symptoms while working in the office before COVID-19 pandemic and working at home during the pandemic.


Each score means the frequency of symptoms: 0 (not at all), 1 (less often), 2 (every 2–3 weeks), 3 (1–2 days each week), 4 (3–4 days each week), and 5 (every day). \* Change in the frequencies of the symptoms while working from home during the COVID-19 pandemic, compared to those while working in the office before the pandemic.

> Table 7 displays the averages of outdoor temperatures and PM2.5 levels in the study area before and during the COVID-19 pandemic for the same periods of office and home IAQ measurements for each participant. In all participants, outdoor air quality while working at home during the pandemic was significantly better than in the office before the pandemic. The outdoor PM2.5 levels before the pandemic were significantly higher than

the current national standard of 12 μg/m3, whereas those during the pandemic were below the standard. The outdoor temperatures during the pandemic were lower than those before the pandemic. Study participants' homes and offices were in the same or neighboring areas, and therefore there was no difference in outdoor air conditions among the participants.

**Table 7.** Averages of outdoor temperature (◦C) and PM2.5 levels (μg/m3) in the study area while working in the office before the COVID-19 pandemic and working from home during the pandemic (LSGMs and 95% CI).


\* The values during the COVID-19 pandemic were significantly lower than the office at *p* < 0.05.

#### **4. Discussion**

The advent of COVID-19 caused the shift of working pattern to work from home remotely for many employees. However, homes may not be a good working environment, compared to conventional office settings with better air conditioning and ventilation systems [4]. In addition, activities performed by individuals at homes may increase indoor air pollution, contributing to more negative health issues [8]. Therefore, in this pilot study, IAQ in the offices before the COVID-19 pandemic and at homes during the pandemic and employees' health status in both periods were compared to assess the impact of working from home on employees' health during the pandemic. Our study found that the IAQ in households during the pandemic was worse than that in the office before the pandemic in all participants, and participants experienced higher frequency of SBS symptoms while working from home. Specifically, home IAQ was worse than the outdoor air quality, and the PM2.5 levels in all households while working from home were greater than the health-based standard 12 μg/m3.

The interest in studying the impact of COVID-19 in different settings has led to higher scrutiny of the IAQ at homes during the lockdown. A recent study conducted in Northern Italy estimated the average indoor PM2.5 levels ranged from 8.6 to 18.7 μg/m3, which were higher than the outdoor PM2.5 levels (7.4–15.4 μg/m3) for a two-week study period in summer during the lockdown [4]. In a study conducted in Norway, the IAQ in home offices were evaluated for up to two weeks, and levels of CO2 and other pollutants higher than health-based standards were detected [50]. Our findings were consistent with previous studies to investigate the IAQ at homes during the COVID-19 pandemic. However, previous studies only focused on home IAQ during the pandemic without comparing with IAQ in the office before the pandemic and the IAQ was measured for shorter time periods (2 weeks) than our study (2 months), and the health impact was not evaluated directly from the participants.

One of the strengths of our study is that evaluating IAQ in the office before the pandemic and that at home during the pandemic in the same individuals in the same season enabled us to compare personal exposure to air pollutants. In addition, their health status during those two different periods was directly assessed in each individual to investigate the negative health impact of the COVID-19 pandemic. Another strength of this study is the utilization of a low-cost Foobot air monitor, for which reliability and accuracy in collecting temporal and spatial IAQ data were validated in previous studies [51–53]. This monitor provides real-time data and was helpful to monitor multiple locations at home simultaneously, allowing longitudinal monitoring for months in each period. In addition, the user-friendly interface requiring low maintenance and power consumption allows participants to install it quickly without a researcher's visit to their homes when social distancing was in place.

There are several limitations to our study. First, due to the small sample size, we could not conduct a statistical analysis to investigate the comprehensive association between IAQ and health outcomes, adjust for characteristics of residential environments and behavioral factors, and differentiate the influences of multiple factors on health complaints. Although the changes of frequencies of health outcomes were in the same direction and degree of changes of PM2.5, larger sample sizes should be considered to perform statistical analyses in future studies. However, the IAQ was measured at 5-minute intervals for 2 months at each location before and during the pandemic, and there were enough numbers of measurements for statistical analyses, demonstrating a significantly worse air quality at homes of all individual subjects during the pandemic, regardless of home environments. Second, the Foobot air monitor did not measure the outdoor air pollutants simultaneously because this monitor is not suitable for outdoor measurements. However, we collected the daily outdoor temperature and PM2.5 data in our study area from TCEQ during the study periods. We found the outdoor PM2.5 levels were significantly lower while working from home during the pandemic, which is consistent with other studies showing the reduction of ambient air pollution globally during the pandemic [64]. This indicates that the outdoor PM2.5 levels did not confound the exacerbation of symptoms caused by home IAQ. Third, IAQ measurements were not conducted during the whole year and seasonal and temporal changes could not be addressed. In South Texas, the PM2.5 levels were highest in summer, due to the hot and humid climate, and lowest in winter, and residents may experience more symptoms in summer and less in winter [65]. However, the seasonal difference could be excluded by assessing and comparing IAQ and health complaints in the same season. Fourth, the health outcome was assessed by self-report surveys, leading to recall biases. Finally, the effects of other behavioral factors could affect our findings. For example, some symptoms such as headache or dry eyes could be related to the increased screen time from telework [66], and other studies proposed that increased sedentary behaviors and reduced physical activity may increase the susceptibility to adverse health outcomes [46,67].

Despite these limitations, IAQ and health outcomes were measured in the office and household of the same participants, providing a unique opportunity to gather some limited but essential information, allowing the comparison of two different work environments. Especially, our findings provided us with information on whether employers need to provide a healthy place at home for a remote worker and such intervention will be possible with reasonable costs to protect and improve the health of all employees. Further large-scale studies should be conducted by addressing the limitations discussed earlier.

#### **5. Conclusions**

This pilot study assessed workplace IAQ and SBS symptoms before and during the COVID-19 pandemic in academic administrative staff members whose workplace changed from office to home due to the pandemic. Low-cost sensors were found suitable for in situ and continuous IAQ monitoring due to their simplicity, speed, and data accessibility. This study found that working from home may cause greater health issues for employees due to poor home IAQ, emphasizing the importance of the interventions to improve the home IAQ. One of the recommendations to enhance IAQ at homes can be achieved through behavioral changes such as opening windows and doors unless the outdoor air quality is harmful. Another approach is to provide remote workers with portable air purifiers with HEPA filters, particularly in locations where appropriate ventilation is difficult to attain. Lastly, integrating these strategies with smart building technologies would maximize the health and wellness of building occupants.

**Author Contributions:** Study design and conceptualization, G.C.; data analysis and interpretation, T.R., A.M.-R., A.O., and J.B.; writing—original draft preparation, T.R., A.O., J.B., N.T.H., and G.C.; writing–review and editing, A.M.-R., J.B., T.R., N.T.H., and G.C.; project administration and funding acquisition, G.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Research England's Expanding Excellence in England (E3) Fund, the National Institute of Environmental Health Sciences (P30 ES029067), and the State of Texas's legislative action to establish and support the Healthy South Texas Initiative. Funds were administered through Texas A&M University Health Science Center (grant number 23-183000).

**Institutional Review Board Statement:** The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by the Institutional Review Board of Texas A&M University's Institutional Review Boards reviewed and approved the study protocol.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The data used to support the findings of this study are available from the corresponding author upon request.

**Acknowledgments:** The authors thank Lucy Conner for coordinating the fieldwork. AirBoxLab (Foobot) partially funded this study by offering a discount on the air monitors used in this research.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **A Study on the Measurement of Unregulated Pollutants in Korean Residential Environments**

**Hyuntae Kim 1,\*, Taewoo Kim <sup>2</sup> and Sihwan Lee <sup>3</sup>**


**Abstract:** This study investigated the pollution caused by unregulated chemical substances in Korean residential environments. A TA tube was used for indoor air collection, and Gas Chromatography– Mass Spectrometry was used for the analysis of chemical substances. According to the results of this study, 13 substances out of the 16 analyzed chemicals were detected and, among them, the concentrations of phenol, α-pinene, and limonene within the indoor air were high. The average concentration of phenol was 32.7 μg/m3. α-pinene and limonene were detected, of which the highest concentrations were as 598.2 μg/m<sup>3</sup> and 652.5 μg/m3, respectively. The maximum concentrations of these three substances exceeded the levels of the lowest concentration of interest. Notably, α-pinene and limonene were released from the wood itself. Wood has been widely used indoors as a natural building material and as furniture. Therefore, it was considered that this was the reason for the high the concentrations of the two substances in indoor air. However, we do not argue that the usage of wood should be reduced because of the results obtained in this study. Instead, we sμggest that it is important to reduce the emissions of α-pinene and limonene throμgh the processing of the wood, extending its drying period, and determining the most appropriate time of use.

**Keywords:** sick house syndrome; indoor air quality; volatile organic compounds; pollutants; chemical substances

#### **1. Introduction**

In Korea, sick house syndrome has been a significant issue since the 1990s owing to the chemical contamination of indoor air [1–3]. Modern-day people spend more than 90% of their time indoors, and indoor air quality can affect their health, comfort, and intellectual productivity [4–6]. Volatile organic compounds (VOCs) such as formaldehyde, benzene, and toluene are representative chemicals that contaminate indoor air [7–10]. Hazardous chemicals in the living environment are emitted from interior finishes, such as wallpaper, flooring, and paint, and household items, such as televisions, sofas, and closets [11–13]. In addition, indoor heating appliances and smoking by occupants can further deteriorate the indoor air quality [14–16]. As the social interest in indoor pollutants has increased, in 2003, the Ministry of Environment of Korea implemented the indoor air quality management act for new apartment complexes and, in 2005, the guidelines for indoor air quality for new apartment complexes were published [17,18]. Furthermore, the presence of a mechanical ventilation system was mandated to ensure indoor ventilation. In the case of formaldehyde, the Healthy Building Mark (HB Mark) is displayed according to the amount of emission to empower consumers or construction workers to select lowemission building materials [19]. In December 2010, the Ministry of Land, Infrastructure and Transport in Korea (2010) announced, and has since enforced, construction standards

**Citation:** Kim, H.; Kim, T.; Lee, S. A Study on the Measurement of Unregulated Pollutants in Korean Residential Environments. *Buildings* **2022**, *12*, 243. https://doi.org/ 10.3390/buildings12020243

Academic Editors: Ashok Kumar, M Amirul I Khan, Alejandro Moreno Rangel and Michał Piasecki

Received: 28 January 2022 Accepted: 16 February 2022 Published: 19 February 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

for clean and healthy houses [20]. The aim of this policy was to solve sick house syndrome. However, despite the establishment of guidelines for improving indoor air quality and new revisions of construction standards, residents have recently complained about indoor air quality. Residents are concerned about the contamination of indoor air by unregulated chemicals as the use of alternative chemicals and new building materials increases [21,22].

Therefore, this study measured the concentrations of unregulated pollutant chemicals in Korean houses to analyze new indoor pollutants that could cause sick house syndrome.

#### **2. Method**

#### *2.1. Houses to Be Measured and Air Collection*

Table 1 presents an overview of the houses to be measured. Table 2 lists the finishing materials and singularities in the houses. In this study, eleven houses were measured: seven apartment houses in Daegu, three houses for apartments in Busan, and one apartment in Andong City. The targeted houses were evaluated for indoor air quality at the request of the residents and construction companies. In Korea, for apartment houses with more than 100 households, it is required to make the results of the indoor air quality measurements known, and the construction method incorporating the HB Mark is applied only to apartment houses with more than 500 households. The A to G houses measured in Daegu are houses that are not regulated by the Korean government for the improvement of indoor air quality (non-regulated house: Non-RH). However, the four houses measured in both Busan and Andong were built using a construction method that included the indoor air quality improvement method proposed by the Korean government (regulated house: RH). In accordance with the official experimental method promulgated by the South Korean Ministry of Environment (2003), the indoor air quality for each house was measured [17]. Before collecting indoor air, all doors and windows contacted with the outside air were opened. In addition, all internal doors and furniture doors were opened, and the house was left to ventilate for 30 min. Thereafter, all the windows and doors connected to the outside were closed, while the furniture doors and the lower kitchen sink cupboards were left open. The house was left in this state for 5 h. During this 5 h period in which the house was sealed, indoor air was sampled for 30 min under this condition. The air-sampling pump used was a SIBATA (Japan) MP-Σ30H. The VOCs were sampled using a Tenax TA tube. The indoor air sampling was performed at the center of the room, 1.2 m from the floor. A travel blank (TB) was used to confirm the contamination of the sampler.


**Table 1.** The overview of the houses.


#### **Table 2.** Finishing materials and singularities in the house.

#### *2.2. Measured Substances*

Saito reported on the frequency and concentrations of unregulated chemicals in houses, and mentioned that some chemicals are associated with sick house syndrome [21,22]. Therefore, in this study, we decided to select and measure chemicals with high detection frequencies and high concentrations that were mentioned in previous studies. In this study, 16 chemicals were analyzed. A Tenax TA tube containing an adsorbent was used to collect the air in the room. The chemical analysis system consists of an Automatic Thermal Desorption (ATD) mechanism that heats the TA tube, and a Gas Chromatography–Mass Spectrometer (GC/MS) for the qualitative and quantitative analysis of chemicals. The ATD device desorbs the chemicals collected in the TA tube, and the desorbed chemicals are injected into the column. Depending on the temperature of the GC oven and the kinds of column, each chemical is separated, enabling the qualitative analysis of the chemical.

The temperature range of the GC oven is from 35 to 250 ◦C. The temperature change of the GC oven is increased by 15 ◦C per minute from 35 ◦C to 95 ◦C; by 2.5 ◦C per minute from 95 ◦C to 105 ◦C; and by 5 ◦C per minute from 105 ◦C to 250 ◦C. The column selectively delays each chemical and separates it according to the difference in arrival time to the detector. The column used in this study was HP-VOC 60 m × 0.32 mm, df = 1.8 μm. The change in the GC oven temperature served to separate the mixed chemicals inside the column. The detection limit was <5 ng. Table 3 shows the conditions of the GC/MS analysis.

**Table 3.** The conditions of GC/MS.


#### **3. Results**

#### *3.1. Concentration of Unregulated Chemicals*

Figure 1 show the concentrations of chemical substances measured in the air. In this study, the concentration range of acetone in the air was 31.0–83.4 μg/m<sup>3</sup> and the average value was 58.8 μg/m3. The average concentration of 2-butanone was 279.4 μg/m3 and the highest concentration was 402.5 μg/m3, which was found in House B in Daegu. The concentration of 2-ethyl-1-hexanol was in the range of 15.3–163.5 μg/m3 and the results demonstrated that the concentration of this material differed significantly depending on the housing. The average concentration of 2-ethyl-1-hexanol was 128.8 μg/m3. The concentrations of Texanol and TXIB within the indoor air were 1.1–1.8 μg/m3 and <1.0 μg/m3, respectively, which were low. The concentration of 2-(2-butoxyethoxy) ethanol was in the range of 2.0–6.1 μg/m<sup>3</sup> and its average concentration was 3.9 μg/m3. The average concentration of phenol was 32.7 μg/m3 and it ranged from 7.9 to 50.2 μg/m3, showing differences in concentration depending on the housing. The concentration of α-pinene in terpenes was in the range of 16.4–598.2 μg/m3 and the D house in Daegu had the highest concentration. The average concentration of α-pinene was 317.2 μg/m3. The average concentration of limonene was 414.1 μg/m<sup>3</sup> and the range was 120.4–652.5 μg/m3. The concentration of camphene among terpenes was in the range of 1.1–4.2 μg/m3 and its average concentration was 2.5 μg/m3. Notably, the concentration of 3-caren was found to be at a very low concentration of <1.0 μg/m3. The concentration of dichloromethane was detected in the range of 8.7–67.2 μg/m<sup>3</sup> and its average concentration was 3.1 μg/m3. The results showed that the concentration of methylcyclohexane was in the range of 8.78–67.2 μg/m<sup>3</sup> and its average concentration was 45.9 μg/m3. The concentration of tridecane was in the range of 1.2–6.1 μg/m3 and its average concentration was 4.2 μg/m3. Lastly, the concentration of 1,2,4-trimethylbenzene was in the range of 1.4–4.6 μg/m3 and its average concentration was 2.9 μg/m3. The concentration of p-cymene was <1.0 μg/m3.

#### *3.2. Indoor Air Quality Evaluation*

Table 4 presents a comparison between the measurement results and the lowest concentration of interest (LCI). The LCIs within indoor air were determined in a European theoretical R&D cooperation [23]. The LCI value is defined as the minimum concentration that irritates organs such as the skin and eyes in humans. Because the unregulated chemical substances measured in this study do not have guidelines for indoor air quality, the measurement results of this study were compared with the LCI values. Among the 16 chemicals measured in this study, the substances exceeding the LCI value were phenol, α-pinene, and limonene. The average concentration of phenol was 1.637 times its LCI, and the maximum concentration of phenol was measured to be 2.510 times higher than its LCI. The maximum concentration of α-pinene and limonene were 2.39 and 2.18 times higher than their LCIs, respectively. The average concentration of α-pinene and limonene were 1.269 and 1.380 times higher than their LCIs, respectively. In contrast, the maximum concentrations of other chemicals were assessed to be 0.01–0.4 times lower than their LCIs. The maximum concentration of Texanol, TXIB, 3-caren, di-chloromethane, methylcyclohexane, tridecane, and p-cymene were found to be 0.008 times their LCI concentrations.

**Figure 1.** The concentrations of chemical substances measured in the air.


**Table 4.** Comparison between measurement results and LCI (lowest concentration of interest).

\*: Maximum concentration in this study, \*\*: lowest concentration of interest.

#### **4. Discussion**

According to the results of this study, 13 of the 16 chemicals analyzed were detected. The chemicals that exceeded their LCI levels were phenol, α-pinene, and limonene.

Phenol is widely used in many industries for various purposes. Phenol is a commonly used disinfectant and has been proven to be an effective antibacterial, antifungal, and antiviral substance. In addition, it is also used in the wood industry as a preservative to protect the wood from infestations of microorganisms such as bacteria and mold [27,28]. Phenol is produced during the thermal decomposition of organic substances. Thus, it is a constituent of motor vehicle exhaust gases, wood smoke, cigarette smoke, and smoked foods. In the general human, approximately two-thirds of phenol intake may be from air exposure [29].

According to the results of this study, phenol concentration in the air was high in the houses measured in the Daegu area. What is important to note is that within the houses in Daegu, the sinks, tables, and furniture were made of synthetic wood. Althoμgh formalin was widely used as an antimicrobial agent in wood building finishes and wooden furniture, its use declined after formaldehyde was included in air quality guidelines. Therefore, it is considered that phenol is likely to be used as a substitute for formalin. In the houses measured in the Daegu area, it was not considered that phenol was generated from the activities of daily life, such as cooking, because the residents have not yet moved in.

It is well known that α-pinene and limonene are substances that are emitted from wood [30]. In this study, α-pinene and limonene were detected at high concentrations. These two chemicals belong to the class of terpenes and have been reported to cause eye irritation and respiratory problems [31,32]. For α-pinene, 4 out of 11 houses exceeded the LCI values and for limonene, 5 out of 11 houses exceeded the LCI values. In particular, the concentrations of α-pinene and limonene were found to be high in houses using synthetic

wood furniture. However, the concentrations from houses with wooden furniture and wooden flooring did not exceed the LCI levels. The most probable reason for this is that the houses in Busan and Andong that had wooden furniture have been around for more than two years from the date of construction, and the furniture was also purchased more than two years ago. However, about a year has passed since the construction of the houses in the Daegu area and the residents have not moved in.

Approximately 20 years have passed since the Korean government promulgated the indoor air quality guidelines to improve indoor air quality. Recently, the concentration of VOCs, such as formaldehyde, toluene, styrene, and benzene, within the air in the general residential environment was found to be remarkably low. However, as the use of alternative chemicals and vinyl chloride-based interior finishing materials has increased, indoor contamination of unregulated chemicals has become a concern.

In particular, phthalate is a representative contaminant of plastics, as they are the plasticizers used in plastic products [33,34]. The plasticizer emitted from the interior finishing material attaches to household dust and interior surfaces, and it is reportedly related to atopic dermatitis and asthma in children [35–37].

Therefore, in recent years, there has been a trend in the use of synthetic wood and wood as interior finishing materials to reduce the amount of plastic products used indoors. The same is also true for furniture. This study showed that the α-pinene and limonene emitted from wood were measured at high concentrations indoors. In spite of this, the amount of wood used indoors has been increased in the construction market.

This does not sμggest that we should reduce the amount of wood used indoors; instead, we propose using wood more safely indoors. As shown in this study, even if the floor finishing material is wood and the furniture is made of wood, the air concentrations of α-pinene and limonene are sometimes measured as low. This result is thoμght to be related to the construction period and the period of use of the furniture. If the processing and drying period of wood are adjusted, the amount of terpenes emitted from the wood can be reduced [38] and, even if the amount of wood used indoors increases, the air quality will not be greatly affected.

#### **5. Conclusions**

This study evaluated the contamination of unregulated chemicals in Korean houses. Of the 16 analyzed chemicals, 13 unregulated chemicals were detected. Among them, the average concentrations of phenol (32.7 μg/m3), α-pinene (317.2 μg/m3), and limonene (414.1 μg/m3) were higher than their LCI concentrations, and the maximum concentrations of chemicals were found to be more than twice their LCI levels. According to this study, these chemicals should be noted as new pollutants present in the air within a house. However, althoμgh α-pinene and limonene are emitted from wood, there is no need to limit the use of wood indoors. Instead, this study sμggests reducing the amount of chemical substances emitted from wood throμgh the processing method and drying period of the wood, which would be the ways to use wood more safely indoors.

**Author Contributions:** The three authors contributed equally to this research. Conceptualization, H.K. and T.K.; methodology, H.K., T.K. and S.L.; validation, T.K. and S.L.; Analysis, H.K.; investigation, T.K.; data curation, T.K. and S.L.; writing—original draft preparation, H.K.; writing—review and editing, T.K.; visualization, S.L.; project administration, H.K.; funding acquisition, H.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by KAKENHI, Grant-in-Aid for Scientific Research(C)20K04809.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** Thanks to the people who participated in the measurement. Additionally, I would like to express my gratitude to H.Tanaka of MC Evolve Technologies Corporation, who analyzed the chemical substances.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Performance of Modern Passive Stack Ventilation in a Retrofitted Nordic Apartment Building**

**Ilia Kravchenko 1,\*, Risto Kosonen 1,2,3, Juha Jokisalo 1,3 and Simo Kilpeläinen <sup>1</sup>**


**\*** Correspondence: ilia.kravchenko@aalto.fi

**Abstract:** The paper analyses the performance of a five-storey apartment building equipped with modern passive stack ventilation in Nordic conditions. The passive stack ventilation system was retrofitted in 2019, and novel self-regulating air inlet devices with filters were equipped. The building was simulated with IDA ICE software, where the model of the self-regulating terminal units was developed using manufacturer product data. Several case scenarios were created to analyze the effects of poor maintenance, improved airtightness, and window opening on the system performance. For the analysis, one-room and three-room apartments on the second and fifth floors have been chosen. The CO2 concentration and indoor air temperature were analyzed and compared with EN 16798-1 standard guidelines. The results show a significant effect of poor maintenance and possibility to open windows on the CO2 concentration. The results also show a trend for the one-room apartments to overheat despite having a higher air change rate than the three-room apartments. The threeroom apartments tolerate over-heating, although they are much more sensitive to poor maintenance. Furthermore, the apartments on the fifth floor are even more sensitive to poor maintenance, and three-room apartments there showed warning levels of CO2. Improving the envelope airtightness does not benefit the IAQ of the apartments.

**Keywords:** natural ventilation; Nordic climate; apartment building; building overheating; indoor climate; retrofitting

#### **1. Introduction**

The general function of the building ventilation system is to provide occupants with enough fresh air while maintaining high energy efficiency. According to the WHO, IAQ is one of the most important determinants of human health and well-being, thus playing a significant role in the indoor environment of the building [1]. In the European Union (EU), most countries have their national building codes and normative documentation for the building design, which are binding [2]. The preferable indoor air quality and airflow rates are presented in the EU directives, binding for EU countries and standards. They are presented in such documents as Energy performance of buildings directive with levels of Energy performance Certification, EN 16798-1 standard in general, and EN 15214 in specific for the IAQ (indoor air quality) [3–5]. Most recommendations and buildings codes consider the minimum airflow rate, temperature level and CO2 concentration. In Finland, the building stock ventilation construction and design requirements are provided by the Ministry of Environment [3,6,7]. The documents consider new and retrofitted buildings separately as buildings of different ages present the stock [8].

Mainly, in Finland, the residential building stock is presented by 85% of all buildings. Blocks of flats represent only 4% of this number. However, they account for approximately 30% of the total floor area of the residential building stock and around 1.3 million occupants

**Citation:** Kravchenko, I.; Kosonen, R.; Jokisalo, J.; Kilpeläinen, S. Performance of Modern Passive Stack Ventilation in a Retrofitted Nordic Apartment Building. *Buildings* **2022**, *12*, 96. https://doi.org/10.3390/ buildings12020096

Academic Editors: Ashok Kumar, M. Amirul I. Khan, Alejandro Moreno Rangel and Michał Piasecki

Received: 29 November 2021 Accepted: 13 January 2022 Published: 20 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

for the buildings with four floors or higher [9]. The buildings constructed before the 1950s are mostly equipped with passive stack ventilation. After the 1960s and until the 2000s, apartment buildings were typically equipped with mechanical exhaust ventilation thanks to the reliable and predictable airflow rates. New apartment buildings are mostly equipped with balanced mechanical ventilation [10].

The new buildings are required to follow strict heat losses standards, calculated with the compensation principle [7]. Although, starting from 2018, the requirements have changed, making it possible to utilize natural ventilation systems in buildings in certain conditions. After renovation and retrofitting, if a ventilation system is changed in an old building, it should have at least 45% heat recovery. However, if only the envelope is retrofitted, the ventilation system could remain the same [10,11]. Additionally, in the case of protected buildings, energy performance requirements are not applied instead of following the standard requirements for major renovation often require separate permission for retrofitting from the Finnish Heritage Agency. In practice, it creates a building stock equipped with natural ventilation presented with a passive stack ventilation system that operates in Nordic conditions.

Overall, natural ventilation utilizes the wind driving forces and thermal buoyancy forces to provide airflow [12]. The basic wind-induced ventilation concept is windows opening ventilation with single or crossflow. This approach is widely used in detached houses and apartment buildings in warm climates [13–15]. However, these systems are likely to create draughts and are not applicable in cold climates. Wind towers and windcatchers have been introduced to further the advancement of technology in cold climates. This approach gives a centralized source of airflow, which may be distributed and used to create systems with heat recovery and regulated airflow rate. These systems have limitations applied to the residential apartment buildings though, such as building height, floor number and local weather conditions [13,16].

On the other hand, natural ventilation can also be realized by thermally induced ventilation. The passive stack ventilation systems often present a basic ventilation strategy of this type. This approach is widely used in the cold climate to create underpressure in the apartments, thus enabling ventilation by infiltration through the envelope. However, these systems are strongly dependent on the outdoor conditions and the indoor-outdoor temperature difference [17]. The advancement of this technology includes solar chimneys and double skin facades. The solar chimneys create a centralized air distribution that is also controllable. However, this technology requires a significant amount of solar radiation throughout the year [18–20]. The double-skin facades create buoyancy-driven airflow between internal and external envelopes or between external and internal glazing. This airflow may be controlled and utilized for heat recovery. These systems are energy-efficient but sophisticated and mainly utilized in office buildings [21–23].

In practice, old buildings are usually equipped with passive stack ventilation systems with windows opening ventilation for the warm period of the year [24]. Some of these buildings are also equipped with self-regulating inlet devices. The inlet devices maintain the designed airflow rate by different means: indoor-outdoor pressure difference, outdoor temperature, or manually controlling the slot size [25,26]. The devices with pressure control show a reliable constant airflow rate in laboratory measurements [27]. Component performance field studies for warm and mild climates show a predictable performance for cases with a 10 Pa pressure difference or higher, thus, the airflow characteristics depend on the opening degree of the slot [28]. The system simulation studies of different types of buildings with mechanical exhaust ventilation and passive stack ventilation with selfregulating inlet devices in Belgium indicate poor IAQ conditions for low-pressure indoor to outdoor difference and possible draft issues [29]. The field studies with occupant surveys in Portugal assessed the IAQ in social buildings with partly natural ventilation, introduced by self-regulated inlets. It is reported that the average air change rate is 0.6–0.7 ACH and thermal comfort, presented with PMV and PPD in class B [4,30]. However, it is also reported that self-regulated inlets had been sealed in 40% of apartments due to draft

issues and cold sensations during the winter [31]. Further laboratory device testing and investigation showed malfunction of pressure-control inlets due to the membrane, leading to an inconsistent airflow rate that differs from manufacturer data [32]. Another field study in Porto of 40 social residential buildings showed an air change rate level of 0.35 ACH in winter, best-case scenario, and around 0.1 ACH in August, in the worst-case scenario. Some of the inlets were also sealed by the occupants [33]. A study in the UK has identified that, for a significant period of time, the supply of outdoor air via the inlet devices will not provide a Category A according to the UK building regulation [30] perceived indoor air quality index [34].

In the Nordic climate, the interest in implementing such devices is presented in retrofitting protected or heritage buildings. These buildings have limited or no access to the retrofit of the envelope and ventilation system. Some retrofitted apartment multi-storey buildings in Finland are equipped with self-regulating inlets with outdoor temperature control to preserve a natural passive stack ventilation system. The ventilation system is designed for the nominal conditions; however, natural ventilation performance depends on the outdoor conditions, and yearly performance has not been assessed. Some studies have investigated the performance of the self-regulated inlet devices in cold climate via CFD analysis [35,36]; yet, no studies regarding the building ventilation system performance in Nordic climate were found. Another investigated performance of slot-controlled or pressure-controlled inlet devices, although the self-regulating inlet device with outdoor temperature control, which works on reducing the inlet area when the outdoor temperature decreases, was not assessed or simulated in the literature.

The paper novelty comes from the performance assessment of a multi-storey apartment building with natural ventilation retrofitted with self-regulated air inlets in Nordic climate. The building presents old heritage and protected building stock with limited or no access to the ventilation system reconstruction, demanding to be retrofitted to perform according to the EN energy and IAQ standards [37,38]. The importance of renovation and decarbonization of old stock buildings also empathizes with the recent European renovation wave strategy [39]. Natural ventilation systems performance depends on outdoor and weather conditions and may significantly vary during the year, making it essential to make a simulation to meet the requirements. The building performance simulation reflects various cases with the effect of poor maintenance, different retrofit strategies such as the implementation of shading and improved envelope airtightness, and effect of buildings user behaviour. Such a ventilation system has individual filters for each apartment, making maintenance demanding. The poor maintenance cases investigate the influence of dirty inlet device filter, passive stack duct, and a combination of those. The different airtightness cases describe the influence of envelope retrofitting. The air movement is also provided by infiltration and exfiltration through the building envelope; thus, the airtightness of the building might also influence the ventilation system performance. The occupant behaviour cases describe different schedules for opening windows and doors as the occupants operate doors, possibly creating additional airflow resistance. The research evaluates the impact of these factors on the system performance, along with weather conditions and building height. In this study, a building model was created in IDA ICE with a custom component to describe the temperature-dependent self-regulating inlet. The IAQ parameters were calculated and evaluated concerning requirements and legislation. The internal airflows were also calculated for various periods and assessed. The main research question is if the ventilation system with modern passive stack ventilation has sufficient performance in a multi-storey building in the Nordic climate.

#### **2. Materials and Methods**

#### *2.1. Target Values*

The chosen parameters reflect such metrics as CO2—the direct IAQ indicator and reflection of the EN standards, temperature—thermal comfort and overheating indicator, internal airflow and air change rate as an indicator of IAQ, internal airflow patterns and reflection pf EN standards. The target values used in this paper are based on national Finnish building codes, legislations and European standards EN 16798-1 [38] and EN 15251 [37] for the IAQ parameters, the CO2 concentration in residential apartments in specific.

The requirements forced by the Ministry of the Environment define overheating in the living spaces of the buildings as apartments being more than 150 ◦Ch over 27 ◦C [7]. This requirement applies to the simulated indoor temperature from June to August in the design phase of the new building, and the simulation input data required by the building code are used. In this paper, this rule is used to evaluate overheating risk and thermal comfort. However, it is not applicable to fulfil this requirement due to the different building code input data. Additionally, the requirement by the Ministry of Social Affairs and Health of Finland for all the existing residential buildings or other living spaces is 30 ◦C as the maximum health-related temperature for the elderly people who are cared for in the residential living spaces and 32 ◦C as the overall maximum indoor air temperature [40].

The guidelines suggested by EN 15251 are applied for CO2 concentration analysis. The CO2 concentration is presented for the I to IV indoor air categories with a base concentration assumed to be 430 ppm [41]. The categories from I to III present acceptable CO2 levels, also referring to the apartment airflow rates. The IV category presents all other possible cases allowed in the apartments only for a limited period of the year.

All the data are presented in hourly mean values. The degree hours are also calculated with hourly mean values.

#### *2.2. Building Description*

For the purpose of analysis, an apartment building with passive stack ventilation in Southern Finland, Helsinki, has been chosen. The building was constructed in 1951 and recently renovated during 2016–2018. The building is located close to the city centre and is sheltered from direct wind by an adjacent apartment building. During the renovation, it was equipped with self-regulating air inlet devices with filters. The building consists of 5 floors and have 600 m2 of net floor area. The ground floor is non-residential. The four residential floors have the same apartment and room layout, shown in Figure 1.

**Figure 1.** The building natural passive stack ventilation system design with openable windows and self-regulating inlet devices with an outdoor temperature-dependent airflow rate.

Three-room and one-room apartments on the second and fifth floor in one staircase have been chosen for the analysis and presented in Figure 2.

**Figure 2.** The building simulation model for the three and one-room apartments on the second and fifth floors connected with stairwell.

The outdoor air in apartments is supplied into bedrooms and living rooms through the inlet devices and the envelope. The separated exhaust stack ducts are located in the kitchen and WC. The apartment room layout and ventilation design are presented in Figure 3.

The envelope properties, window properties and other building structure properties are set according to the common practice of the construction year and shown in Table 1. The load-bearing structures of the building are massive concrete, external walls are two rows of burnt bricks with insulation layers, internal walls between the apartments are brick walls, and internal walls between rooms are lightweight structures with an air gap. The envelope airtightness was set according to the building year for the reference case, and the air leakage rate (n50) equals 2.4 L/h at a pressure difference of 50 Pa [24].

The internal doors have a gap at the floor level of 2 cm. The windows are 2 panes glazed with a U-value of 2 W/m2K and are equipped with integrated shading with blinds between panels. The window blinds are manually controlled according to the occupation profile and the intensity of solar radiation (>100 W/m2). In three-room apartments, all windows besides the ones in the kitchen are openable. In one-room apartments, all windows are openable. The openable windows area is 10% of a window.

The water radiators carry out space heating with a dimensioning temperature of 70/40 ◦C, and the heat distribution efficiency is 80%. The design powers are 100 W/floor-m2 on the top floor and 60 W/floor-m2 on the middle floor. The temperature setpoint of space heating is 21 ◦C in the apartments. In the staircase and basement floor, the setpoint of space heating is 17 ◦C. The annual net heating demand of domestic hot water (DHW) is 35 kWh/m2 per heated net floor area. It is assumed that DHW consumption is constant with time. Heat losses of the DHW circuit are 0.56 W/m2, and 50% of the heat losses were assumed to end up as internal heat gains in the zones.

**Figure 3.** The building floor level ventilation system design and airflow rates at nominal conditions of 5 Pa pressure difference over the inlet device and outdoor temperature of 15 ◦C.

**Table 1.** The structural building details and properties of windows.


#### *2.3. Inlet Device*

The self-regulating inlet devices are installed in the living rooms and bedrooms of the apartments. The inlet device regulates airflow based on the outdoor temperature. The minimum opening is 4 mm, and the maximum is 16 mm for −5 ◦C and lower, and +15 ◦C and higher, respectively, and the settings are linear. The inlet device flow characteristics are presented in Figure 4. The bedrooms are equipped with a 160 mm diameter inlet device with a nominal setting of 9.3 L/s at a pressure difference of 5 Pa. The living rooms are equipped with 100 mm diameter inlet devices with a nominal setting of 5.1 L/s at a pressure difference of 5 Pa. The flow characteristics are presented in Table 2.

**Figure 4.** The inlet device product scheme (**a**); The inlet device opening as a function of outdoor temperature (**b**).


**Table 2.** The inlet device airflow rate at different pressure differences and opening degree. Nominal conditions 5 Pa, 15 ◦C outdoor air temperature.

\* nominal conditions 5 Pa, 15 ◦C outdoor air temperature.

#### *2.4. The Building Usage*

Household equipment's total annual electricity consumption is 21.0 kWh/m<sup>2</sup> per heated net floor area [7]. The appliances are used every day between 9:00 and 22:00. The total annual electricity consumption of indoor lighting is 7.9 kWh/m2, per the building's total heated net floor area [7]. The electric lighting power is assumed to be evenly distributed by the floor area of all the simulated zones in the apartments and by the floor area of the staircase. The usage time of the lights is between 21:00 and 23:00 from May to August and 7:00–9:00 and 15:00–23:00 from September to April [10].

• The occupational patterns for the rooms and the apartment occupant number are presented in Table 3.


**Table 3.** The apartment occupancy and occupancy patterns.


#### *2.5. Weather Data*

The weather data are presented with typical climatological conditions at the Helsinki-Vantaa weather station in southern Finland for the 2012 reference year [42,43]. The data consist of hourly outdoor air temperature, relative humidity, direct and diffused insolation, wind speed and direction. The temperature and wind speed are presented in Figure 5. Heating degree days at indoor temperature +17 ◦C annually are 3952 ◦Kd in the reference year.

**Figure 5.** The yearly outdoor temperature and wind velocity of the reference year with chosen example weeks.

For the purpose of the air change rate and airflow rate analyses, three weeks have been chosen. The week with the lowest outdoor temperature in winter, a week with outdoor temperature close to average 2 ◦C and high average wind velocity in spring, and the week with the highest outdoor temperature in summer. The outdoor conditions for chosen weeks are presented in Table 4.


**Table 4.** The example weeks outdoor temperature and wind data.

#### *2.6. IDA ICE Simulation Tool*

The model of the building has been created with the IDA ICE dynamic building simulation tool [42,44]. The software allows the modelling of multi-zone buildings and provides simultaneous dynamic simulation of heat transfer and airflows, considering flows between zones, building envelope and windows. It calculates the interactions between building structures, HVAC systems, operational and occupancy schedules of the building, and outdoor climate conditions. The infiltration airflows are calculated by wind pressure on each façade combined with zones stack effects.

#### 2.6.1. Façade Pressure Calculation

Wind pressure distribution around the house is simulated using the normal assumption in building engineering that the wind flow is horizontal and an atmospheric boundary layer is neutral without vertical airflow. The wind conditions of the environment were approximated using the wind profile equation reported in [34], see Equation (1).

Wind pressure on facades corresponds to the LBL model wind profile:

$$\mathcal{U}I(h) = \mathcal{U}\_{\mathfrak{m}} \cdot k \cdot \left(\frac{h}{h\_{\mathfrak{m}}}\right)^{a} \,. \tag{1}$$

where *U*(*h*) is the wind speed at height *h* (m/s), *Um* is the wind speed measured on open ground at the weather station (m/s), *h* is the height from the surface of the ground (m), *hm* is the height of the measurement equipment (10 m), and parameters *k* and *a* are terrain-dependent constants.

The simulated building is located in a typical Finnish city center area with closely built houses where the height of adjacent houses is approximately the same as the simulated one.

However, this study simplified the calculation of wind conditions, and wind pressure coefficients were not measured nor simulated.

The values of the wind pressure coefficients are approximated values for low-rise buildings surrounded by obstacles equal to the height and size of the house. The shape of the building being studied is more complicated, so the simulated wind pressure distribution around the building was also simplified.

The wind pressure outside the building facades *Pw* is determined by Equation (2):

$$P\_w = c\_p \cdot \frac{1}{2} \rho\_{out} \cdot \mathcal{U}^2 \,, \tag{2}$$

where *ρout* is the outdoor air density (kg/m3), *Cp* is the wind pressure coefficient, and *U* is the local wind velocity defined by Equation (1).

Because of the square dependence of the wind velocity in Equation (2), wind velocity has a more significant effect on wind pressure than the value of the wind pressure coefficient. The local outside surface pressure *Ps* on the building facades is:

$$P\_s = P\_{out} - \rho\_{out} \cdot \mathbf{g} \cdot \mathbf{h} + P\_{\text{lv}\_f} \tag{3}$$

where *Pout* is the outdoor air pressure at ground level (Pa), *ρout* is the outdoor air density (kg/m3), and *g* is the acceleration of gravity (m/s2).

The pressure difference between the zone and outdoor air is calculated as:

$$
\Delta P = P\_{\rm in} - \rho\_{\rm in} \cdot \lg \cdot h\_{\rm in} - P\_{\rm s} \tag{4}
$$

where *Pin* is the indoor air pressure at floor level (Pa), *ρin* is the indoor air density (kg/m3), and *hin* is the height from floor level (m).

#### 2.6.2. Internal Flows Calculation

IDA ICE calculates the internal flows for each zone, where large vertical openings such as an open door between the zones are simulated as bi-directional flows. The vertical flow profile in the opening depends on the density differences between the adjusted zones. If the densities are equal, the flow profile is flat. Otherwise, it is slanted. In the case of a flat velocity profile, the air mass flow between the zones is calculated with the standard orifice flow equation:

$$Q = \mathbb{C}\_d \cdot A \sqrt{2\rho \cdot \Delta P},\tag{5}$$

where *Cd* is a discharge coefficient and *A* is the area of the opening (m2). In the case of a slanted profile, the airflow between the zones is simultaneously bi-directional.


#### 2.6.3. Passive Stack

The passive stack ventilation is implemented with the standard IDA ICE chimney model with stacks of different heights according to the floor. The chimney model considers the inlet and outlet loss coefficient, duct roughness, duct shape and height. The model calculates bi-directional flow.

#### 2.6.4. Inlet Device

The self-regulating inlet device was created as a custom model based on the infiltration model with temperature-dependent power-law k-factor and exponent equal 0.5. The model has a simultaneous single direction flow.

The k-values for the inlet device and filter were calculated from the manufacturer product data for designed airflows. The following equation was used for the volumetric airflow rate:

$$\mathbf{q}\_{\rm v} = \mathbf{k} \cdot \sqrt{\Delta p} \,, \tag{6}$$

where qv is volumetric airflow rate and Δ*p* is component pressure drop.

The k-value has been calculated for the given inlet device positions and linearly interpolated between the data points. The k-value has been coupled with outdoor temperature and presented as a function in Figure 6.

The calculated function for the bedroom and living room inlet devices has been used in the simulation model to calculate the airflow according to the pressure difference and outdoor temperature. Dirty filters were simulated by decreasing k-values twice, assuming that the filter had been working for the year without maintenance [46].

#### *2.7. The Simulation Case Description*

The CO2 level during the year and indoor air temperature during the summer have been chosen to assess the IAQ. The CO2 level is used as an indirect indicator for the room and personal airflow rate and compared against standards [7,10]. The indoor air temperature has been used to assess the influence of the airflow rate in apartments and occupant personal conditions.

The apartments on the second and fifth floors were chosen to represent the influence of the height on the stack effect. One and three-room apartments were selected to represent the influence of different floor areas and inlet supply ventilation system configuration.

**Figure 6.** The inlet device flow characteristics via k-value against outdoor temperature: (**a**) bedroom inlet device; (**b**) living room inlet device.

The three time periods have been chosen to address the most critical weather conditions for the passive stack ventilation: the coldest week during the winter, a week with an average outdoor temperature of 2 ◦C combined with the highest average wind during spring and a week with warmest outdoor air temperature. The results during the cold week present the influence of a significant pressure difference. The spring conditions represent the case with a low pressure difference and the absence of additional windows opening ventilation. The summer case has the lowest pressure difference and influence of additional windows opening ventilation. The apartment air change rates have been calculated to present the apartment airflow rates for the chosen time. For the reference case, internal airflows and their direction have also been calculated.

A range of cases, descriptions, and abbreviations have been created to assess the chosen parameters, shown in Tables 5 and 6.


**Table 5.** The simulation case scenarios, name and abbreviation cross-dependency.


**Table 6.** The building simulation case scenarios.

The reference case represents the case where the inlet devices and passive stack duct are clean, and only the bedroom doors are closed at night. The windows shading is realized with blinds and operated according to the solar insolation. The windows are closed for the cold period from September to April for most of the day and open for half an hour, 22.00–22.30. In the summertime, windows are always opened if the outdoor temperature is higher than 12 ◦C and indoor higher than 22 ◦C, Table 6. The stack duct has the summed pressure loss coefficient of passive stack equal to 15. In the best-case scenario, all the doors are always opened.

The cases with dirty inlet device filters (M1) and passive stack ducts (M2) are created to represent poor maintenance cases, where the filters and duct are not serviced for more than 1 year. [46] The dirty filter is described as in the reference case presented in inlet device characteristics but with half the standard k-value. The stack duct has the summed pressure loss coefficient of the passive stack increased to 40. In these cases, the roles of the inlet device and the passive stack are assessed. The case with improved airtightness (M3) represents a building with better envelope insulation, and thus higher airtightness of 1.5 L/h to assess the influence of the infiltration airflow change on the indoor conditions. The case with no windows shading (M4) represents no integrated blinds between glazing. The cases with non-openable windows (M5) describe the ventilation only via infiltration and inlet devices, and represent the scenario where windows are not operated for some reason, such as occupant inability to do it. The worst-case scenario (M6) describes the case with closed doors due to the occupant's possible preference or draught issues.

#### **3. Results**

#### *3.1. Apartment Indoor Temperature Overheating Analysis Results*

The apartment overheating was assessed based on the indoor air temperature results. The results are presented for three-room and one-room apartments on the second and fifth floor to consider the size of apartments and height factor influences. The results are shown for the summer period, June to August, as figures, duration curves, and tables with degree hours, in Figures 7 and 8 and Tables 7 and 8, respectively. The results are presented first for the three-room apartments and then for one-room apartments for each described case. The colours for the figures are used consistently throughout the paper to show the correlations.

**Figure 7.** The indoor air temperature duration curves for the three-room apartments on the second and fifth floors from June to August.

The simulation shows the significant influence of the poor maintenance and ability to open the windows on the overheating possibility. The indoor air temperatures in the three-room apartments on the second and fifth floors are shown in Table 7 and in Figure 7. The reference case, best case, and cases with poor maintenance (M1, M2) show acceptable performance on both floors. The case with no integrated window blinds (M4) shows a warning performance level on the second floor and is unacceptable for new buildings on the fifth floor with more than 150 ◦Ch above 27 ◦C. The cases with no window opening (M5, M6) show a poor level of performance with most hours spent above 27 ◦C and around 300 ◦Ch above 32 ◦C for the first floor. For the fifth floor, more than 1000 ◦Ch are spent above 32 ◦C, which is above health legislation [40].

Overall, the higher floor shows lower performance due to more insolation, and results indicate lower airflow rates in the apartments.

The indoor air temperatures in the one-room apartments on the second and fifth floors are shown in Table 8 and in Figure 8. The results have the same trend as three-room apartments with indoor air overheating in the cases with no windows shading (M4) and non-openable windows (M5, M6). Smaller apartments have higher indoor air temperatures during the summer and are more likely to overheat, resulting in a dangerous level of performance with most hours spent above 32 ◦C and more than 1000 ◦Ch and 3800 ◦Ch for the first and fifth floor in the cases with no window opening (M5, M6). Time spent above 32 ◦C is an overall health warning level and 30 ◦C is a health risk for the elderly people.

#### *3.2. The Indoor Air Quality Results*

The results are presented for three-room and one-room apartments on the second and fifth floors. The results are presented separately for the winter and summer periods to present the influence of the opening window ventilation and to make the results comparable to the overheating analysis. The winter period is from January to April, and the summer period is from May to August to consider the heating period.

**Figure 8.** The indoor air temperature duration curves for the one-room apartments on the second and fifth floors from June to August.


**Table 7.** The three-room apartment on the second and fifth floor overheating results—number of degree hours above 27 ◦C, 30 ◦C and 32 ◦C during the year.


**Table 8.** The one-room apartment on the second and fifth floor overheating results—number of degree hours over 27 ◦C, 30 ◦C and 32 ◦C during the year.

3.2.1. Apartment Bedroom Average CO2 Concentration Analysis Results

The CO2 concentration in the three-room apartments on the second floor is shown in Table 9 and Figure 9. In winter, in the best-case scenario, the occupants spend more than 40% of the time in indoor air categories II and III and in I [37] for the rest, and the concentration is around 720 ppm on average. The reference case shows a significant effect of the occupant and door schedules, transitioning to more than 50% in the II and III categories and 890 ppm on average. Cases with maintenance issues (M1, M2) show the effects of dirty inlet device filter and passive stack duct, further deteriorating the IAQ to 25% and 35% at the IV category for the dirty filter and its combination with stack duct, with the concentrations at 960 ppm and 1200 ppm on average. High airtightness (M3) and nonopenable window (M4) cases show the worst performance, with an average of around 45% of the time in the IV category and 1350 ppm.

**Table 9.** The three-room apartment on the second floor CO2 level results. Percentage of hours in each indoor air quality category (I–IV) during the year.


**Figure 9.** The duration curves of CO2 level in the three-room apartment on the second floor for different cases for winter and summer with indoor air quality reference levels.

In summer, the additional opening ventilation significantly improves cases with maintenance issues, with only around 12% and 13% of the time spent in the IV category and about 670 ppm on average. The case with high airtightness (M3) shows the same performance as the previous ones. The case with non-openable windows (M5) show the worst performance, most of the time in the IV category and around 1600 ppm on average.

The CO2 concentration in the three-room apartments on the fifth floor has the same trend as on the first floor, although the average level is much higher, as shown in Table 10 and Figure 10. Compared to the first floor, occupants spend more time in the III and IV category and only around 20% and 10% in I and II in reference, best and M1 cases. The average concentrations are around 1000 ppm. Other cases in winter (M2–M5) are presented only in the time spent in II, but mostly in III and IV categories with about 4%, 10% and 85%, respectively, with average concentrations of about 2400 ppm.

**Table 10.** The three-room apartment on the fifth floor IAQ results. Time spent in each indoor air category in percent.


**Figure 10.** The duration curves of CO2 level in the three-room apartment on the fifth floor for different cases for winter and summer periods with indoor air quality reference levels.

In summer, the additional opening ventilation significantly affects cases with openable windows (Ref., Best, M1–M4) showing better performance, with only around 16% and 18% of the time in the IV category and about 1000 ppm on average. Although, the case with non-openable windows (M5) shows the worse performance, with most of the time in the IV category and around 2600 ppm on average as the stack effect is lower in summer and the stack duct length in fifth floor apartments is also about three times shorter.

The CO2 concentration in the one-room apartments on the second floor is shown in Table 11 and Figure 11. Overall, in winter, most of the time is spent in the I and II categories. In the best, reference and case with dirty inlet device filter (M1), at around 100% of time spent in the I category. All other cases have comparable performance with around 60% and 30% in the I and II categories with 700 ppm on average.

**Table 11.** The one-room apartment on the second floor IAQ results. Time spent in each indoor air category in percent.


**Figure 11.** The duration curves of CO2 level in the one-room apartment on the second floor for different cases for winter and summer with indoor air quality reference levels.

In summer, the performance has the same trends as in the three-room apartments. The average time spent in the I category for all cases slightly decreased for the best reference and case with a dirty inlet device filter (M1). However, more maintenance issues (M2) and improved envelope airtightness (M3) showed better performance due to the additional airflow through the windows. The performance of the worst-case scenario is around 20%, 30% and 50% at the III, II, and I categories and indicates the significance of the additional airflow through the windows.

The CO2 concentration in the one-room apartments on the fifth floor has the same trend as on the first floor and the same, as three-room apartments on the fifth floor. Overall, the average level is between three-room apartments on the first and fifth floor. The results are shown in Figure 12 and Table 12.

In the best case, around 90% of the time is spent in the I category in winter. The rest of the time is spent in the II category. The average CO2 concentration is 650 ppm. The reference case shows a significant effect of the occupant and door schedules, transitioning to more than 25% in the IV category and 790 ppm on average. Case with dirty inlet device filter (M1) shows further deterioration of the IAQ to around 25% in the IV category. The combination of dirty inlet filter and stack duct (M2) shows mostly the same performance as with additional combination with high airtightness (M3) and non-openable windows (M5) with around 45% time in IV category and 1470 ppm on average. The worst-case (M5) with non-openable windows shows the worst performance with 45% in the IV category.

In the summer case, the additional opening ventilation significantly affects all cases, showing better performance. The best reference and cases with maintenance issues (M1, M2) show around 80% in the I and II categories with only around 2%, 4%, 12%, and 13% of the time in the IV category for reference case, cases with maintenance issues (M1, M2) and

case high airtightness (M3). The case with non-openable windows (M5) shows the worst performance with 50% in the IV category.

**Figure 12.** The duration curves of CO2 level in the one-room apartment on the fifth floor for different cases for winter and summer with indoor air quality reference levels.



3.2.2. Apartment Internal Airflow and Air Change Analysis Results

The results for the internal airflow rate and air change rates for the apartments are presented in Figure 13 and Table 13. The airflow and air change rates are average during the chosen weeks in winter, spring and summer. The nominal air change rate shows rate at 15 ◦C as a nominal conditions. In figures, arrows represent the average airflow direction through envelope and windows and between the rooms through doors. Additionally, the mail slot is taken into consideration as a connection to the stairwell. Tables show the average airflow rate for each room. Table 13 shows air change rates for the reference case, for the cases with poor maintenance and the worst-case scenario to show the overall influence of factors on the air change rates of the apartments. The ventilation air change rate was calculated for the exhaust airflow rate through the passive stack. The total air

change rate was calculated for the exhaust airflow rate through the passive stack, envelope and windows, considering all outcoming airflow rates.

**Figure 13.** The building simulation airflow directions pattern and rate values for the one-room apartments on the second floor (**a**); And on the fifth floor (**b**), where red arrows are external airflows and blue are internal.

**Table 13.** Apartment average ventilation and total air change rates for the second and fifth floor apartments during the example weeks.


\* nominal airflow rate.

Results show the trend for the apartments air change rate. The apartments on the second floor have a higher air change rate of around 15% than apartments on the fifth floor due to the higher buoyancy effect. The ventilation air change rate deteriorates from winter to summer in all cases in percentage from 20% to 50% compared to winter cases. The total ventilation air change rate deteriorates from winter to spring around 20% compared to the winter case. The total air change rate is highest in summer due to the additional airflow through windows opening, around 20% higher than the winter case.

The one-room apartment on the fifth floor shows the highest air change rates across the apartments. However, cases show increasing deterioration from reference to the worst case at around 15%, 30%, 40% and 50% between summer and spring ventilation air change, respectively. The combination of maintenance issues shows the most significant relative

effect on the air change rate. In summer, the trend is the same with 5%, 23%, 29% and 30% reductions, respectively.

The one-room apartment on the fifth floor shows less significant relative deterioration from reference case to worst case. Although, the overall air change rate is much lower. The deterioration is around 6%, 25%, 31%, and 31% for the summer case. The air change rate plummets in the spring by about 13%, 37%, 43%, and 47%, respectively. The combination of maintenance issues shows the most significant relative effect on the air change rate. In summer the trend is the same with 5%, 23%, 29% and 30% reductions.

The three-room apartment on the second floor shows a lower air change rate than both one-room apartments. Additionally, the deterioration trend from reference to worst case stays the same with around 4%, 50%, 57%, and 64% for summer. The air change rate is the same for reference case and M1 in the spring but plummets by about 52%, 57%, and 57%, respectively. The dirty inlet filter and passive stack duct combination (M2) shows the most significant relative effect on the air change rate. The trend is the same in summer with no change for the M1 case and 62% for the rest, respectively.

The three-room apartment on the fifth floor shows the lowest air change rate across the simulated apartments. The overall trend is the same. However, the case with a dirty inlet device filter also affects the results. The simulation shows deterioration from reference case to worst case of around 13%, 52%, 57% and 57% for summer. In the spring, the air change rate plummets by about 20%, 40%, 33% and 33%, respectively. The combination of maintenance issues shows the most significant relative effect on the air change rate. In summer the trend is the same with 23% for the M1 case and 62% and for the rest, respectively.

The apartment airflow rate in the one-room apartments on the fifth floor is shown in Figure 14. Due to the vertical location differences of second and fifth floors the airflow rate is lower by around 20%. The infiltration airflow rate in the bedroom is mostly equal to the inlet device airflow rate in winter and spring cases. In summer, the windows opening ventilation combined with infiltration accounts for around 80% of outdoor airflow.

The lowest apartment total supply airflow rates are presented during the springtime on both floors, with 27 L/s and 17 L/s for the second and fifth floors, respectively. In winter, the apartment total airflow rate is around 32 L/s and 25 L/s. The total apartment and supply airflows are the highest in summer, around 45 L/s and 28 L/s, respectively. During the summer, the reversed airflow may occur due to the apartment overheating. This also indicates a low apartment airflow rate in that period. Although, a low average reverse airflow rate indicates that it is a rare occurrence.

The apartment airflow rate in the three-room apartments has the same trend as in one-room apartments and shown in Figure 14, with the fifth floor lower by around 30% than the second floor due to the vertical position difference. The infiltration airflow rate in the bedroom is also almost equal to the inlet device airflow rate in winter and spring cases. In summer, the windows opening ventilation combined with infiltration accounts for around 75% of supply airflow.

The lowest apartment total supply airflow rates are presented during the springtime on both floors, with 44 L/s and 27 L/s for the second and fifth floors, respectively. In winter, the apartment total airflow rate is around 50 L/s and 42 L/s. The total supply airflow is the highest in summer, around 79 L/s and 72 L/s, respectively.

During the summer, the reversed airflow is also presented due to the apartment overheating. This also indicates a low apartment airflow rate in that period. Although, low average reverse airflow rate indicates that it is a rare occurrence.

**Figure 14.** The building simulation airflow directions pattern and airflow rates for the three-room apartments on the second floor (**a**); And fifth floor (**b**), where red arrows are external airflows and blue are internal.

#### **4. Discussion**

Apartment retrofitting requires a simple but efficient solution to provide adequate IAQ, energy performance, and retrofit costs. It is particularly important for protected or heritage buildings with natural passive stack ventilation and no or limited access to the building envelope or ventilation system changes. One of the solutions is the implementation of self-regulating inlet devices to preserve the initial ventilation system and envelope and provide designed airflow rates and low costs as it is commonly assumed that natural ventilation does not have much maintenance. However, modern self-regulating inlet devices have filters that require at least yearly maintenance, which should be done by the service company or by occupants. The results clearly show that maintenance of the modern passive stack system with openable apartment windows is essential. These results are to consider, as if it is the occupant responsibility to do maintenance, it might be a challenge doing that without much experience. On the other hand, if the service company does it, it requires labour and the ability to visit apartments to be carried out. Additionally, the maintenance of the passive stack duct should be carefully planned to prevent its clogging.

It is also crucial to avoid overheating in the cases of a group of vulnerable people, such as elderly people who have openable windows but cannot operate them. Otherwise, the apartment temperature exceeds 30 ◦C, which is a health risk for elderly people. In some cases, the temperature exceeds 32 ◦C, which is a health limit for other occupants.

The three-room and one-room apartments, both equipped with the same exhaust system, consist of two passive stacks in the bathroom and kitchen. The difference is the number of rooms with inlet devices and an external surface for infiltration, thus lowering system resistance. In general, it means that three-room apartments are more sensible for the passive stack ventilation system poor maintenance than one-room apartments. Therefore, three-room apartments on the fifth floor with a low buoyancy effect show a CO2 level higher than 4000 ppm. On the other hand, improved airtightness in such apartments does not benefit the ventilation system and IAQ performance.

It is presented in the simulation of the reference case that the CO2 level in one-room apartments is lower than in three-room apartments. However, they are much more likely to overheat. Although, this is partly mitigated by the fact that the air movement rate in a one-room apartment is higher, creating more pleasant indoor thermal conditions.

In cases with poor maintenance, with dirty inlet devices and passive stack, the most crucial effect is shown on the fifth-floor apartments for the CO2 level, which rises due to the significantly lower passive stack exhaust rates. The case with improved airtightness restricts infiltration and exfiltration airflow rate in all the apartments. It leads to significant overheating in the one-room apartments with an indoor air temperature of 30 ◦C and higher. The additional airflow rate of the windows opening ventilation shows a crucial effect with a much lower CO2 level in summer. However, the window opening ventilation has its limitation due to the outdoor airborne and noise pollution, and it is preferable not to be utilized in the cities with high population density, near roads and traffic lines.

The limitations of the study are mostly presented with physical model limitations and case-specific input data. This simulation analysis assesses the average airflow and air change rates calculated via hourly average outdoor conditions. However, the momentary airflow rate may be significantly different. The building simulation model considers building design and structure, device parameters, occupant behaviour, and lighting and heating schedule, but it still has some limitations. The simulation model is created with separate nodes for each room, but each node represents the entire room. All the nodes are calculated to be in balance. The distribution of the parameters within each node is calculated only for the boundary elements, such as inlets, doors and windows. As the distribution in each node, room, is even as for the mixed model, the calculated values are average, but local values are needed to analyze draught. This means that cold draughts, airflow patterns etc., may be calculated indirectly and may significantly change the occupant thermal comfort sensations. The case-specific input is presented with the Nordic climate weather and outdoor conditions. The façade wind pressure coefficients and building structure materials

were assumed according to the building age. Furthermore, the inlet device model is created based on the design manufacturer data, representing its theoretical performance and placed according to the building documentation. The pressure drop in filters and stack ducts in cases of poor maintenance has been assumed based on literature. The case building is presented with five floors; thus, the simulation results for high-rise buildings might differ due to the significant effect of the wind pressure.

The simulation results of ACH may be compared against previous experimental studies of passive stack ventilation. The study was conducted in the warm climate of Portugal and showed a good correlation. The average air change rate was 0.6–0.7 ACH with window opening ventilation [31] and the air change level of 0.35 ACH in winter, best-case scenario, and around 0.1 ACH in August, in the worst-case scenario for the cases without opening ventilation [33]. Additionally, the results agree with previous field studies in Nordic climate, Helsinki, where the mean air-exchange rates in apartments had a high variation (average 0.6 L/h, range 0.1–1.2 L/h) [47]. The ASHRAE minimum value of 0.35 L/h was not achieved in 28% of all dwellings, and the average air change rate in the naturally ventilated apartments is 0.64 L/h [47]. Some previous studies assessed the CO2 in the cold climate, Beijing, in bedrooms, concluding the necessity of additional windows opening ventilation. The maximum CO2 level was observed at around 4000 to 5000 ppm [48].

Natural ventilation advancements present the trend of making systems less dependent on outdoor weather conditions and having reliable and constant airflow rates. In practice, one of the most demanding paths is the building stock retrofit, which requires high IAQ, but simple solutions, presented with such devices as self-controlled air inlets or passive stack outlets and wise windows opening strategies. The results and highlighted points may be considered in the renovation design for the buildings with passive stack ventilation in the Nordic conditions to ensure good IAQ and prevent apartment overheating, especially in homes of vulnerable groups of people.

#### **5. Conclusions**

The regulations and standards are developed to ensure high indoor environment quality in the building stock, and that the classification of the IAQ parameters reflects the desirable level in residential buildings. In practice, the lowest level considers the effect of health; thus, renovation and retrofit of the old buildings should aim to provide a high IAQ level. The paper analyses the performance of a retrofitted five-storey apartment building equipped with modern passive stack ventilation in Nordic conditions. The passive stack ventilation system was retrofitted in 2018, and novel self-regulating air inlet devices with filters were equipped. The building was simulated with IDA ICE software, where the model of the self-regulating inlet devices was developed using manufacturer product data. Several case scenarios were created to analyze the effect of poor maintenance, improved airtightness, and window opening on the system performance. For the analysis, one-room and three-room apartments on the second and fifth floors were chosen. The CO2 levels and indoor air temperature were analyzed and compared with EN 16798-1 to assess the IAQ. The results are separated for the winter and summer to show the influence of additional airflow from opening ventilation. The apartment air change rate and internal airflow patterns were assessed and compared case by case.

The results show a trend for the one-room apartment to overheat, despite having a higher air change rate than the three-room apartments. The three-room apartments tolerate overheating, although they are much more sensible considering the poor maintenance. Improving the envelope airtightness does not benefit the IAQ of the apartments. The results show a significant effect of poor maintenance and window opening possibility on the CO2 concentration. Furthermore, the apartments on the fifth floor are more sensitive to poor maintenance, and three-room apartments situated there showed warning levels of CO2. The case with non-openable windows showed more than 150 ◦Ch over 32 ◦C in all apartments.

Filter replacement is essential for the desired operation of the modern passive stack ventilation system. Additionally, the maintenance of the passive stack duct should be carefully planned to prevent its clogging. It is crucial to prevent overheating due to windows being left closed. Otherwise, the temperature in the apartments can reach above 32 ◦C, which is a health risk.

The results and highlighted points are crucial as the protected and heritage buildings with natural ventilation and limited or no access to the envelope or ventilation system reconstruction require retrofit to meet current building codes requirements. The results may be applied to retrofit the buildings with passive stack ventilation in the Nordic conditions to ensure good IAQ and prevent apartment overheating, especially in the homes of vulnerable groups of people.

**Author Contributions:** Conceptualization, I.K., R.K., J.J., S.K.; methodology, I.K., J.J., R.K.; software, I.K., J.J.; validation, I.K., J.J., S.K.; formal analysis, I.K.; investigation, I.K., J.J.; resources, I.K.; data curation, I.K.; writing—original draft preparation, I.K.; writing—review and editing, R.K., J.J., S.K.; visualization, I.K.; supervision, R.K.; project administration, R.K.; funding acquisition, R.K., J.J. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by HEATCLIM (Heat and health in the changing climate, Grant No. 329306) funded by the Academy of Finland within the CLIHE (Climate change and health) program. SUREFIT (Sustainable solutions for affordable retrofit of domestic buildings) funded by the European Union (Horizon 2020 program, Grant No. 894511).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** The authors would like to acknowledge Mika Vuolle from Equa Simulation Finland Ltd. for developing the inlet device model, IDA ICE software support and cooperation.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **A Time-Varying Model for Predicting Formaldehyde Emission Rates in Homes**

**Haoran Zhao \*, Iain S. Walker, Michael D. Sohn and Brennan Less**

Residential Building Systems Group and Indoor Environment Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA; iswalker@lbl.gov (I.S.W.); mdsohn@lbl.gov (M.D.S.); bdless@lbl.gov (B.L.) **\*** Correspondence: haoranzhao@lbl.gov; Tel.: +1-(312)-804-8091

**Abstract:** Recent studies have succeeded in relating emissions of various volatile organic compounds to material mass diffusion transfer using detailed empirical characteristics of each of the individual emitting materials. While significant, the resulting models are often scenario specific and/or require a host of individual component parameters to estimate emission rates. This study developed an approach to estimate aggregated emissions rates based on a wide number of field measurements. We used a multi-parameter regression model based on previous mass transfer models to predict formaldehyde emission rate for a whole dwelling using field-measured, time-resolved formaldehyde concentrations, air exchange rates, and indoor environmental parameters in 63 California singlefamily houses built between 2011 and 2017. The resulting model provides time-varying formaldehyde emission rates, normalized by floor area, for each study home, assuming a well-mixed mass balance transport model of the home, and a well-mixed layer transport model of indoor surfaces. The surface layer model asserts an equilibrium concentration within the surface layer of the emitted materials that is a function of temperature and *RH*; the dwelling ventilation rate serves as a surrogate for indoor concentration. We also developed a more generic emission model that is suitable for broad prediction of emission for a population of buildings. This model is also based on measurements aggregated from 27 homes from the same study. We showed that errors in predicting household formaldehyde concentrations using this approach were substantially less than those using a traditional constant emission rate model, despite requiring less unique building information.

**Keywords:** formaldehyde; indoor air quality; emission rate; new homes; field measured data; temperature; humidity; modeling; simulation

#### **1. Introduction**

Formaldehyde emission rates have most commonly been estimated as fixed values based on materials and house characteristics that are invariant with temperature, humidity or air change rate [1,2]. However, previous field measurements and modeling studies have shown that these environmental factors influence indoor formaldehyde emissions. The objective of this study was to develop an improved calculation procedure to estimate the emission rate of formaldehyde for modeling indoor air quality in residential buildings. Rather than a fixed emission rate, we developed an emission rate model that varies in time depending on environmental parameters. The model-development procedure was based on using measured field data to estimate emission rates and to correlate the emission rate with various commonly known indoor parameters: temperature, humidity, ventilation rate, and floor area. The intent was that the emission rate estimates could be used to determine formaldehyde concentrations in indoor air in homes under dynamic environmental and ventilation conditions. Some previous studies have used similar physical models, but were based on coefficients from test chamber samples rather than emissions in real homes requiring considerable assumptions, to convert emissions from samples to emissions from all the sources in a home. In order to remove these assumptions, the current study used

**Citation:** Zhao, H.; Walker, I.S.; Sohn, M.D.; Less, B. A Time-Varying Model for Predicting Formaldehyde Emission Rates in Homes. *Int. J. Environ. Res. Public Health* **2022**, *19*, 6603. https://doi.org/10.3390/ ijerph19116603

Academic Editors: Paul B. Tchounwou, Ashok Kumar, Michał Piasecki, M Amirul I Khan and Alejandro Moreno Rangel

Received: 30 March 2022 Accepted: 26 May 2022 Published: 28 May 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

measured data from a group of homes to investigate home-to-home emission rate variability. The value of accurate, time-varying emission estimates for formaldehyde in dwellings is that we can improve our ability to predict changes in formaldehyde exposures associated with changes in the building code, dwelling ventilation rates or controls.

Estimation of formaldehyde concentrations in homes is important, because indoor exposures are associated with substantial public health burdens, as quantified by Disability Adjusted Life Years (DALYs) [3]. Formaldehyde is found in many common building materials, such as engineered wood products, cabinetry, and flooring. Acute exposure to formaldehyde can cause nose, eye, and throat irritation [4,5]. Indoor chronic exposure to formaldehyde can cause respiratory symptoms and cancer [6,7].

Previous studies have found that formaldehyde concentrations in new and existing residences routinely exceed health relevant thresholds. In a study of 105 California homes built in 2002–2005 [8], formaldehyde concentrations measured over 24-h exceeded the California Office of Environmental Health Hazards Assessment (OEHHA) chronic and 8-h reference exposure levels of 9 μg/m3 (7.3 ppb) [9] in 98% of homes, and exceeded the World Health Organization 30-min exposure guideline of 0.1 mg/m3 [4] in 5% of the homes. In a more recent study in California of newly built homes with low-emitting materials, weekly average formaldehyde concentrations exceeded the California OEHHA chronic and 8-h reference exposure levels in all 68 homes [10]. In another large-scale study of 352 existing California homes, the average indoor formaldehyde concentration was lower (14 μg/m3), but 95% homes still exceeded the California OEHHA chronic and 8-h reference exposure levels [11]. In a study investigating 398 existing US homes, the mean indoor formaldehyde concentration was 21.6 μg/m<sup>3</sup> [12]. Two recent surveys conducted in Canada found formaldehyde concentrations (averaged over 24-h) exceeded the Health Canada residential indoor air quality 8-h exposure guideline of 50 μg/m<sup>3</sup> [13] in 16 out of 59 homes (27%) in Prince Edward Island [14], and in 11 out of 96 homes (11%) in Quebec City [15].

There are two key engineering control measures for limiting formaldehyde concentrations in residences: source control through use of low-emitting materials and ventilation with outside air.

Formaldehyde emissions from engineered wood products were first regulated in the US by the State of California beginning in 2007. National regulations based on the California requirements (Formaldehyde Standards for Composite Wood Products Act of 2010—Code of Federal Regulations 40 CFR Part 770) [16] were legislated in 2010 and came into force in March of 2019. These standards limit formaldehyde emissions by prescribing maximum allowable equilibrium concentrations measured in laboratory chamber tests of product samples under standard conditions. The effectiveness of these regulations in reducing formaldehyde concentrations has been demonstrated in field studies [17]. However, the emission rates are not measured or regulated directly by the standard. The actual emission rate of the emitting materials in homes is dominated by the maximum allowable equilibrium concentration, but also affected by environmental conditions, such as temperature and relative humidity, which will be described in the later sections. The whole house equilibrium concentration is highly variable because the type and quantity of the materials in homes remain unknown. Thus, the model we developed in this study will focus on a specific group of homes with low- emitting materials. The whole house equilibrium concentration was estimated as a coefficient to represent house to house variance.

Ventilation with outside air can reduce the concentration of formaldehyde in residences via dilution and removal. Quantitative studies have demonstrated how formaldehyde concentrations decrease as air change rates increase cross-sectionally for populations of homes [17–20]. Based on formaldehyde emission factors, one study estimated that an air change rate (ACH) of 0.5 h−<sup>1</sup> would maintain formaldehyde concentrations below 50 ppb in typical new North American houses [21]. A study in Canadian homes found that an ACH of 0.35 h−<sup>1</sup> appears sufficient to ensure a formaldehyde concentration lower than the 50 μg/m3 Health Canada guideline in most homes [15].

Increasing ventilation rate would increase the concentration gradient between material air surface layer and the room air, leading to an increment of whole house formaldehyde emission rate, as suggested by previous studies [17,22–26]. Specifically, ventilation has been shown to increase formaldehyde emissions, while still providing a net-reduction in indoor concentrations. Hult et al. reported measurements in nine new homes in which they systematically achieved three different ventilation rates [17]. As ventilation rates were increased, they compared observed reductions in formaldehyde concentrations versus expected reductions based a fixed emission rate assumption. They found that up to 60% of the benefit of increased ventilation (assuming fixed emissions) was lost due to corresponding increases in formaldehyde emission rates. Liu et al. performed a time-resolved assessment of VOC emission rates (including formaldehyde) in a Northern California residence, and they found that emission rates increased with household ventilation rates and with temperature [25]. Offermann et al. tested three ventilation rates in a CA home (0.21, 0.41 and 0.64 h−1), and observed formaldehyde emissions increase from 17 to 24 to 31 μg/m3/h [26].

Several studies have measured changes in formaldehyde concentrations associated with temperature and humidity conditions, from which changes in emission rates are inferred. Andersen et al. measured an increase in temperature of 7 ◦C doubled the formaldehyde equilibrium concentration in a chamber and the change of 40% relative humidity also doubled the formaldehyde concentration [27]. Salthammer et al. measured an increase of 6 μg/m<sup>3</sup> per Celsius degree increase in temperature and 2 μg/m<sup>3</sup> for every 1% increase in relative humidity [19]. Poppendieck et al. found almost a factor of 2.6 increase in VOCs for an 8 ◦C increase in temperature [22]. Another study measured four homes during winter and summer and found changes of about three to five ppb per ◦C [23]. A study measuring formaldehyde concentrations in environmental chamber tests [28] found formaldehyde concentrations were positively correlated with temperature and absolute humidity, but were poorly correlated with relative humidity.

Studies using material mass diffusion transfer analytical models to predict the volatile organic compound (VOC) emission rates from multiple building materials have demonstrated that VOC emission rates are dominated by three factors: the initial emittable concentration (C0), a mass diffusion coefficient for the compound in building materials (Dm), and the material-air partition coefficient (Kp) [29–31]. Chamber studies have shown that Kp and Dm are strongly influenced by temperature [32–34] and Co is driven by both temperature and humidity [35]. By including the factors mentioned above, previous studies have used measured emission rates of material samples from test chambers to determine the parameters for mass diffusion transfer (C0, Dm, and Kp), and, in turn, to develop physics-based emission models to predict the emission rate for materials, such as a particleboard, plywood paneling, or hard wood piece with UF coating [29–31]. The studies investigating physical models have provided referenced parameters for estimating the mass transfer and the relationship between these parameters and environmental conditions. However, to utilize the chamber measured parameters to predict a whole house emission rate, the quantities of each type of emitting materials in the house need to be characterized, including structural materials, furniture, cabinetry, and other indoor sources. For example, in a previous case study in an unfurnished net-zero house [36], the investigator characterized the surface area of the emitting surfaces and determined the corresponding mass transfer dynamic parameters (C0, Dm, and Kp) from previous chamber studies. The whole house VOC emission rate was estimated using a physics-based model combined with measured temperature and humidity. A similar study by Bourdin et al. used a simplified surface mass transfer model to estimate formaldehyde emission rate in a classroom [37]. The mass transfer coefficient (Dm) was estimated using an empirical equation and the concentration at the surface layer of each type of material was measured in a chamber. With an accurately measured surface area of each piece of emitting material in the room, the dynamic formaldehyde emission rate was estimated. Generally, it is very difficult and impractical to measure the required input data for the physics-based models for each

emitting material in each home. The characterization of emitting materials in real homes during field test is impracticable due to limit amount of time, specifically the mixture of quantities and material types present in any given home.

Data-driven approaches, such as partial linear regression, machine learning, and deep learning, have been previously developed to predict indoor air pollutant concentrations such as CO2 and PM2.5 [38]. Those data-drive approaches were expanded for predicting formaldehyde emission rate and/or concentrations for certain materials in the chamber or a whole building in recent studies. Akyüz et al. presented an implantation of artificial neural networks (ANN) for modeling the formaldehyde emission from particleboard based on manufacturing variables, including wood-glue moisture content, density of board, and pressing temperature [39]. Ouaret et al. developed an approach using Fourier transform and two nonlinear model: threshold autoregressive (TAR) and Chaos dynamics models to forecast the formaldehyde concentration 12 h ahead in a regularly occupied office with diurnal pattern [40]. Zhang et al. recently applied an artificial neural networks (ANN) approach to predict gas-phase VOC concentrations from four kinds of furniture in a chamber [41]. The ANN approach used VOC concentration at the previous timestep, temperature, relative humidity, and ventilation rate as inputs for training the model, and the method was validated by predicting predict VOC concentrations for different environmental conditions. Zhang et al. also developed another approach using deep learning model and tested it in an occupied classroom [42]. Similarly, Mohammadshirazi et al. also used a LSTM deep learning approach to predict formaldehyde concentration in an occupied office based on historical measured data [43] and compared to other three forecasting models: rolling average, Random Forest, and Gradient Boosting. The datadriven methods do not require detailed mass transfer parameters of the emitting materials, but the approaches typically need massive data for training and the approaches have not been applied to any residential buildings, where the environmental and occupancy pattern are more complex than commercial buildings. In addition, it is unknown how well these models trained for an individual building or room would predict emission rates or concentrations in other spaces. In our study we want to develop a model that could be applied beyond an individual home where the measurements were made. Therefore, we developed an empirical model derived from physics-based model in order to bypass characterizing mass transfer parameters as well as involving the emission rate variability due to environmental conditions.

In indoor environments, formaldehyde mass transport from building materials has been modeled by assuming the concentration in a thin layer of air near the emitting material (*Ceq*) is in equilibrium with the contaminant concentration in the surface layer of the storage medium (*Cmaterial*). *Cmaterial* remains constant because internal transport within the material is rapid enough to replenish the surface layer as it emits into the air above the surface. At any given moment, the formaldehyde emission is governed by transport from air surface layer to bulk air at a constant rate (*k*), as shown in Equation (1) [17,31,44–46].

$$E = k \left( \mathbb{C}\_{\text{eq}} - \mathbb{C}\_{\text{in}} \right) A\_m \tag{1}$$

where *E* is the whole-house formaldehyde emission rate (μg/s) at certain temperature and humidity; *Ceq* is the concentration within the air surface layer, which is equal to the bulk air concentration when the ventilation rate is zero (μg/m3) at that condition; *Cin* is the concentration in the bulk air (μg/m3) (i.e., the indoor formaldehyde concentration); *k* is the mass transfer constant (m/s); and *Am* is the effective surface area of the emitting materials indoors (m2). The values of *k, Ceq*, and *Cin* are treated as whole-house values that include all the emitting surfaces in the home. This simplified concentration-dependent emission model has been validated in chamber studies [44,45], and the implications of indoor formaldehyde concentration on emission rate were discussed in a previous study [46]. Under this model, the changes in temperature and humidity will influence *Ceq*, which has been investigated in previous studies [27,47,48]. The indoor air exchange rate will influence *Cin*. Changes of indoor temperature and air velocity caused by changing air change rate will also influence

the mass transfer rate (k), but this is assumed to be negligible in this study, because the variations of indoor temperature and surface air velocity are small.

The focus of this paper is to develop a simplified emission model for predicting formaldehyde emission rates in homes that vary with the key variables explored above. This is a top-down approach that does not rely on the availability of highly specific details about emitting materials in each home. Instead, we focused on estimating whole-house emission rates across a group of sample homes using three predictor variables: temperature, humidity, and air change rate. We used field measured, time-resolved formaldehyde concentrations together with coincident temperature and relative humidity in 63 California single-family homes built in 2011–2017 with low-emitting materials (i.e., materials regulated by the California Air Resources Board). Estimates of time-resolved ventilation rates were used in a mass balance to estimate the time-varying formaldehyde emission rates. A multivariate regression was used to develop a predictive model for emission rate as a function of temperature, humidity, and air change rate. The resulting emission model was evaluated by using it to predict the concentrations in the same homes used to generate the emission model, and then comparing the resulting predicted concentrations against those measured in the field. This evaluation was performed for individual model coefficients specific to each home, as well as for coefficients averaged over the cohort of homes.

#### **2. Materials and Methods**

#### *2.1. Data Collection Overview*

The data used to estimate formaldehyde emission rates were collected from a recent field study of ventilation and indoor air quality in new California homes. The Healthy, Efficient New Gas Homes (HENGH) study [49] collected data in 2016–2018 in 70 singlefamily, detached houses that were constructed between 2011 and 2017. These homes were built using composite wood products required in California to have low formaldehyde emissions. All homes had dwelling unit mechanical ventilation systems installed to meet state building code requirements. The homes also had natural gas cooking appliances with venting range hoods and bathroom exhaust fans. Each home was monitored for a six-to-nine-day period. Residents were asked to keep windows closed and the dwelling unit mechanical ventilation system operating. This allowed us to make good estimates of the ventilation rate, because the homes were dominated by the air flow through mechanical ventilation systems, for which airflows and operation were measured and recorded in the study. We included estimates of natural infiltration, based on air leakage tests of the homes, local weather conditions (from the nearest publicly available weather station) and the enhanced ventilation model from ASHRAE Handbook of Fundamentals [50] and Walker and Wilson [51]. The total ventilation rate combining the mechanical fan and natural infiltration flows was determined using the superposition method from ASHRAE Standard 62.2 and a previous study [52].

Measurements in each home included time-integrated indoor and outdoor formaldehyde concentrations, and additional time-resolved measurements were made indoors. The outdoor formaldehyde concentrations were measured using SKC Umex-100 passive samplers at each site to obtain an average concentration for the whole monitoring period. The time-resolved indoor formaldehyde concentrations were measured at 30-min or 60-min intervals using Shinyei/Graywolf FM-801 photoelectric photometry meters deployed in the living rooms and master bedrooms in most of the homes. The averaged indoor concentrations calculated using the real-time meters were compared against UMEx-100 passive samplers deployed at the same location with same duration in 66 test homes that had both types of measurements. Results showed considerable scattering between co-located real-time formaldehyde meters and passive samplers, as shown in Figure 1. The weekly averaged indoor concentrations measured by real-time meters compared to the passive samplers, had a negative bias of 2% and root mean square difference (RMSE) of 6.9 μg/m3. The temperature and relative humidity were also measured in the living rooms and master bedrooms in these houses using ExTech CO2 monitors at 1-min intervals.

**Figure 1.** Weekly averaged formaldehyde concentrations measured by passive samplers and real-time monitors in 66 test houses, concentrations were averaged from both master bedroom and living room.

The airflows of bath and laundry exhaust fans in each home were measured using a TEC Exhaust Fan Flow Meter. Range hood airflows were measured using a balancedpressure flow hood method using a TEC Minneapolis Duct Blaster [53]. The operation of these fans was monitored at 1-min intervals using a logging anemometer (Digisense WD-20250-22) placed at the air inlet or using a motor on-off logger (Onset HOBO UX90-004) placed close to the motor. The air leakage of the building envelope and the forced air heating/cooling system were measured with the DeltaQ test (ASTM-E1554-2013, Method A) using a TEC Minneapolis Blower Door System with DG-700 digital manometer. The test also quantifies air leakage of the forced air heating/cooling system to outside of the living space under normal operating conditions. Building envelope air leakage was converted to air changes per hour at 50 Pa indoor-outdoor pressure difference (ACH50) using the estimated home volume. Not all of the 70 homes in the original study were included in the analysis. Two houses had instrumentation failure, four homes did not have measured envelope air leakage (so we could not estimate air change rates), and one did not have temperature or relative humidity (*RH*) measured, leaving 63 homes to be evaluated.

#### *2.2. Time-Resolved Formaldehyde Emission Rate Calculation*

For a well-mixed home, a mass balance can be used to describe the indoor formaldehyde concentrations, as shown in Equation (2). A discretized version of Equation (2) is shown in Equation (3).

$$\frac{d\text{Cin}}{dt} = a\text{Cout} - a\text{Cin} + \frac{E}{V} \tag{2}$$

$$E\_t = \frac{V}{dt}(\text{Cin}\_{t+1} - \text{Cin}\_t) + a\_t \text{Cin}\_t V - a\_t V \text{Cout} \tag{3}$$

where *Et* is the formaldehyde net emission rate at the time step (μg/s); *dt* is the time step (1 h = 3600 s); *Cint* and *Cint+*<sup>1</sup> are formaldehyde concentrations at this time step and one-time step after (μg/m3); *Cout* is the average outdoor formaldehyde concentration (μg/m3); *V* is the total volume of the house (m3); and *at* is the air exchange rate (AER) (1/s). Indoor formaldehyde is both absorbed as well as emitted (in a reversible way) by building surfaces [54], therefore, in our method, the time-resolved emission rates in each home were the net-emission rate, representing both desorption and absorption processes. For most of

the time, the net-emission was positive, because the combined emission and desorption were much larger than adsorption.

A key assumption of this approach is that we can use a single concentration for the whole home, and that the concentration is conditional to the whole home ventilation rates in our calculations. To investigate the validity of this approach, the well-mixed condition for formaldehyde in the test houses was evaluated by comparing the weekly average formaldehyde concentrations measured in the master bedroom and in the living room of each home, as shown in Figure 2. A linear regression fit was performed to the weekly averaged concentrations, showing reasonable correlation (R-squared of 0.64, a slope of 1.05 and an intercept of 2.4 μg/m3). The RMSE was 7.1 μg/m3. Given the instrument accuracy is 4.9 μg/m3 (4 ppb) or 10% of the reading (whichever is larger), these results indicate that the assumption of uniform formaldehyde concentrations was reasonable overall, but the situation varies home-by-home. We also calculated the absolute difference of the hourly measured formaldehyde concentrations between the master bedroom and living room at each home. The average absolute difference across all homes was 5.3 μg/m3 (4.3 ppb), which is close to the instrument accuracy. The mean absolute differences between bedroom and living room were larger than the instrument accuracy in 21 homes. Of these 21 homes, 19 had two-stories. These results indicate that our assumption of uniform concentration within a home is generally acceptable.

**Figure 2.** Weekly averaged formaldehyde concentrations measured in the master bedroom and living room in 63 test houses with both locations measured.

These concentrations are lower than those measured in new California homes built in 2002–2005 in a similar study [8], where the mean indoor concentration was 43 μg/m3. They are also lower than the formaldehyde concentrations measured in studies from more than ten years ago, such as 32.2 μg/m3 from 162 French homes [55] and about 30 μg/m3 from 96 Canadian homes [15]. Possible reasons for the lower concentrations in this set of homes is that the sample homes were all built with lower-emitting materials and mechanical ventilation as required by California building regulations.

#### *2.3. Predictors for Formaldehyde Emission Rate*

Formaldehyde is emitted from building materials, fittings, and furnishings, therefore, the emission rate scales with the quantities of these elements in a home. To be useful for

future modeling purposes, the emission rates need to be normalized to account for this. A direct approach is to assume that the quantity of emitting materials scales with floor area/volume and to use floor area to normalize the emission rates. It might be that this is not an exact correlation, because the sources of formaldehyde may not scale exactly with floor area. For example, a larger house might not have proportionally more furnishings, cabinetry, etc. Furthermore, formaldehyde emissions are associated with effective surface area that is emitting formaldehyde, and the formaldehyde content of the materials present in the home varies greatly between homes. For the purposes of this study, we performed a simple analysis to verify that normalizing by floor area is a reasonable assumption, which is discussed in the results section.

Previous studies have demonstrated that *Ceq* varies with temperature and relative humidity [48]. The temperature and *RH* varied within each home during the sampling period. These parameters also varied cross-sectionally, since the homes were sampled in different seasons, had different thermostat setpoints, different occupancies, and other changes that would impact temperature and *RH*. In order to account for the impacts of temperature and *RH* on the emission rate, an empirical mathematical equation from Myers [48] was used to normalize the equilibrium formaldehyde concentration to a value (*Cst*) at reference condition (i.e., 25 ◦C, 50% *RH*), as shown in Equation (4).

$$\mathcal{C}\_{eq} = \mathcal{C}\_{st} \exp\left[A\left(\frac{1}{T} - \frac{1}{298}\right)\right] \times \left[1 + B(RH - 50)\right] \tag{4}$$

For indoor environments when the variation of temperature is small, a simple linear form is often used:

$$\mathcal{C}\_{\text{eq}} = \mathcal{C}\_{\text{st}} \left[ 1 + A(T - 25) \right] \times \left[ 1 + B(RH - 50) \right] \tag{5}$$

Applying Equation (5) to Equation (1), the time-varying concentration-dependent emission model corelated with temperature and relative humidity is shown in Equation (6).

$$\frac{E\_l}{A\_f} = kL\{\mathbb{C}\_{st}[1 + A(T\_l - 25)] \times [1 + B(RH\_l - 50)] - \mathbb{C}in\_t\} \times H \tag{6}$$

where *A*, *B*, and *Cst* are the fitted parameters. *L* is the effective emitting material loading rate in the house (*Am/V*, m2/m3). *Tt* and *RHt* are the average temperature and relative humidity of the rooms with a formaldehyde monitor (in this case, the living room and a bedroom of each home) at the time step. Et and Cint are the emission rate and indoor formaldehyde concentration at the time step. *Af* is the floor area and *H* is the ceiling height. We did try using the Equation (6) and the field measured hourly formaldehyde concentrations to develop our model but the performance of this model to estimate timeresolved concentrations was dissatisfying. A main problem with this approach was that it used the concentration from a previous time step to estimate the emission rate for the current time step because the current concentration is unknown. To improve the modeling accuracy for predicting time-resolved concentrations, we developed an approach to use hourly air exchange rate as a surrogate for the concentration in the bulk room air, which has been used in previous studies [14,38–40].

In our measured data, the indoor formaldehyde concentrations were sampled hourly, and the differences between consecutive hours (i.e., *Cint+*<sup>1</sup> − *Cint*) were typically very small. Similarly, the temperature and *RH* varied slowly with time. Air exchange rate could change suddenly due to mechanical ventilation operation, but the duration of the fan usage was typically short, leading the hourly variation of the total air exchange rate to be relatively small. Therefore, we assume that the measured formaldehyde concentration at each hour can be considered to be a pseudo-steady-state concentration under the corresponding temperature, *RH*, and AER conditions. The calculated hourly emission rate was, therefore, also a pseudo-steady-state emission rate. For a given well-mixed home, the steady-state

indoor concentration (*Cinss*) under certain temperature, relative humidity, and air exchange conditions can be expressed using Equation (7).

$$\text{Cin}\_{\text{ss}} = \text{Cout} + \frac{E}{aV} \tag{7}$$

Replacing Equation (1) with a pseudo-steady-state emission rate and concentration yields Equation (8).

$$E = (\mathbb{C}\_{\text{eq}} - \text{Count}) \frac{akL}{a+kL} V \tag{8}$$

In our measured data, the average outdoor formaldehyde concentration is 2.2 μg/m3. This suggests the outdoor term is an order of magnitude smaller than the indoor term. Ignoring the outdoor term and combining with Equation (5), the hourly pseudo-steadystate emission rate was correlated to the hourly average measured temperature, *RH* with modeling coefficients (*A* and *B*) and equilibrium concentration at reference condition (*Cst*) through a multi-parameter model, along with hourly air exchange rates, mass transport coefficient, and loading rate as other independent inputs (Equation (9)).

$$\frac{E\_t}{A\_f} = \frac{C\_{st} \times (1 + A(T\_t - 25))(1 + B(RH\_t - 50))}{\frac{1}{a\_t} + \frac{1}{kL}} \times H \tag{9}$$

In the analysis of the measured data, we used one-hour averages for all the measured parameters and corresponding one-hour averaged emission rates calculated using Equation (3). This avoided the issue generated by small step changes in some parameters—such as air change rate—from one time-step to another. The one-hour pseudosteady-state emission rate may not be appropriate in some homes settings due to sudden changes in AER, temperature, and humidity caused by occupancy activities or mechanical equipment operation. Such cases resulted in "outlier" emission rates at the time-step with sudden changes. To eliminate these sudden large changes in emission rate, we examined an option that excluded the hourly emission rates that were greater than the 95th percentile and smaller than the 5th percentile for each home prior to fitting the regression model in Equation (9). We also investigated an approach that applied an eight-hour running average to the measured formaldehyde concentration, air exchange rate, temperature and *RH*. Given the average air exchange rate across all homes was 0.35 h−<sup>1</sup> and the ventilation was the only effective loss term for indoor formaldehyde, a home would generally achieve steady-state within about eight hours after any changes in emission and ventilation. The multi-parameter regressions were compared using the running 8-h and 1-h inputs. The approach was used to check whether hourly emission rates could be assumed to be pseudo-steady-state.

The constant *kL* is the product of the transport coefficient *k* and the loading factor *L*. Measurements of loading factor *L* from another study [56] were found to be relatively stable, ranging from 0.5 to 1 m2/m3, and the *k* value ranged from 0.011 to 3.6 m/h. Based on measurements in single-family and mobile homes, Myers reported *k* between 0.19 and 2.7 m/h [45]. Homes likely contain a range of formaldehyde-containing materials, but the fastest timescales (higher *kL*) will tend to dominate the effective value for a home [46]. In our model, we use the average value from Sherman and Hult which reported *kL* values from 0.05 to 0.62 in nine low-emitting US houses (most in California) with average of 0.29/h−<sup>1</sup> [46]. We did attempt to also include *kL* as a fitted parameter in our model, but this resulted in unstable model values, with large variations in *kL* that also drove large changes in the other three coefficients that were out of the range of common building materials reported by Myers. This is likely caused by limited data in each home, where we only have a small range of temperature, *RH*, and AER, resulting in least square regression results with large uncertainties. Due to this result, we chose to fix the value of *kL* based on those found in the literature described above.

A multi-parameter, least square non-linear regression fit was applied to Equation (9) for each house. The independent inputs of the regression fit were the measured temperature, *RH* and air exchange rate, either by hourly step or 8-h running average. The *kL* was assumed constant. The dependent input of the regression was the floor area normalized emission rate for each home, either by hourly step or 8-h running average. The regression fits resulted in 63 sets of least squares fitted coefficients: *A*, *B*, and *Cst* for each home. We have considered multiple statistical approaches used in the previous studies for indoor air quality model evaluation [57,58]. The commonly-used parameters for model performance evaluation include standard deviation of observations and predictions, least square slope and intercept regression statistics, Quantile–Quantile (Q-Q) plots, etc. By considering all of the statistical approaches, two criteria were selected to carefully evaluate the predictor sets:


$$\text{Cin}\_{\text{est},t+1} = \text{Cin}\_{\text{est},t} + \left(\frac{E\_{\text{est},t}}{V} - a\_I \text{Cin}\_{\text{est},t} + a\_I \text{Cout}\right)dt\tag{10}$$

where *Cinest,t* is the estimated formaldehyde concentration at current time; *Cinest,t+1* is the predicted concentration for next time step; *Eest,t* is the emission rate predicted using the three coefficients for each home; and *dt* is the length of the time step (one-hour in this case). The accuracy of the prediction was evaluated by calculating the Normalized Root Mean Square errors (NRMSE) for all the measurements (where *N* is the number of measurements, typically 160 over the week of testing for each home), as shown in Equation (11).

$$\text{Normalized RMS Error} \left( \% \right) = \frac{\sqrt[2]{\sum\_{0}^{N} \frac{\left( \text{Cin}\_{l} - \text{Cin}\_{\text{ref},l} \right)^{2}}{N}}}{\overline{\text{Cin}}} \tag{11}$$

#### **3. Results and Discussion**

We begin by describing the emission rate estimates produced from our calculation procedure, and we compare these against previously reported measurements. Next, we present a summary of the regression models used to estimate emission rates and the accuracy of the predicted concentrations using those same emission estimates in each home. Finally, a generalized regression model is presented that combines the model parameter coefficients from each individual study home into a generic model for future modeling efforts.

#### *3.1. Emission Rate Estimation*

The mean emission rate across the 63 houses calculated using Equation (3) was 1.3 μg/s with a standard deviation of 0.6 μg/s. The distribution of weekly averaged emission rates ranked by emission rate for each home is shown Figure 3. The distribution is fairly uniform between 1 and 3 μg/s, with no significant grouping at any particular emission rate. This indicates a wide range of formaldehyde sources in these homes, even though they represent a very specific subset of homes because they were selected to be new, single-family homes from California that should be compliant with State standard requiring low formaldehyde emission products to be used in their construction.

**Figure 3.** Weekly average formaldehyde emission rate (marker) for 63 new California single-family homes; shading area presents the 25th and 75th of the hourly emission rate for each home, *x*-axis rank ordered by average emission rate.

It may be useful to normalize emission rates by floor area to account for differences in emission rates for different sized homes. There is a weak general trend that emission rate increased with floor area in the study homes, with a Spearman correlation rank of 0.34 (*p*-value < 0.01) and Pearson rank of 0.31 (*p*-value = 0.016). This suggests that normalizing the emission rate by floor area can slightly improve emission rate estimates.

The distribution of floor area normalized emission rates is shown in Figure 4 with a mean (±s.d.) of 19.6 ± 10.4 <sup>μ</sup>g/h/m2. The value is comparable to the emission rate calculated using the concentration measured by co-located passive samplers, that had a mean of 17.4 μg/h/m2. This is greater than the emission rate of 6.7 μg/h/m<sup>2</sup> previously reported in a home designed and constructed to be low-emitting [22], but it is lower than the mean emission rate of 23 μg/h/m2 measured in 13 homes in another study intended to have low-emitting materials [17]. It is also lower than the average emission rate of 29 μg/h/m2 reported by a previous study in 99 California homes built prior to formaldehyde emission limits for building materials and that generally did not have mechanical ventilation [8]. The value is also much lower than those in older studies, such as Hodgson et al., who reported emission rates of 45 μg/h/m2 for manufactured homes [59].

**Figure 4.** Distribution of weekly averaged formaldehyde emission rate (marker) normalized by floor area; shading area presents the 25th and 75th of the hourly normalized emission rate for each home, *x*-axis rank ordered by average normalized emission rate.

#### *3.2. Formaldehyde Emission Rate Model and Concentration Prediction*

We carefully reviewed the 63 sets of regression coefficients, and we noticed that some homes had regression coefficients of *A* < 0 or *B* < 0. We consider these to be nonphysical results, because emission rates should positively correlate with temperature and *RH* according to previous studies. Table 1 summarizes the degree of correlation and the remaining errors from the multi-parameter models (r-squared and relative RMSE of the regression fits), comparing the model-predicted emission rates against those derived from the measured data. Table 1 also summarizes the accuracy and consistency of the predicted emission rates for estimating indoor formaldehyde concentrations, which are shown as the normalized RMS errors between estimated indoor formaldehyde concentrations using the predicted emission rate and the measured concentrations. Two variations on the regression models were assessed: (1) applying an eight-hour running average to the measured data, and (2) excluding hourly emission rates outside of the 5th–95th percentile range. Both of these variations improved the fitness of the multi-parameter regression, with higher r-squared values and lower relative RMSE. The improvements are expected, because both approaches intentionally eliminate the outliers of the hourly emission rate and/or decrease the noise in the data used for the regression.


**Table 1.** Summary of regression performance results.

<sup>1</sup> NRMSE between estimated 8-h running average indoor concentration and 8-h running average measured data.

<sup>2</sup> NRMSE between estimated hourly indoor concentration and hourly measured data.

While using running mean inputs and removing outliers improved emission rate predictions, they did not meaningfully improve the accuracy for estimating indoor concentrations. All three methods gave the similar results for estimating indoor concentrations using the predicted emission rates. This indicates that our original approach using one-hour average data and our assumption that the hourly emission rate was a pseudo-steady-state emission rate are reasonable.

For all three approaches, the formaldehyde concentration predictions were poor in some remaining homes. The reasons for this were unclear, but may include poor indoor mixing; unexpected ventilation (e.g., if windows or doors were opened); high emitting materials concentrated in one place (the area normalized emission assumption may not applicable); large variations in formaldehyde concentrations, temperature, *RH*, and AER between adjacent hours caused by occupant activity (the steady-state assumptions may not applicable); different loading rate and mass transport coefficients in some home (assumption of *kL* = 0.29 may not applicable); and other possible measurement errors for temperature, *RH* and AER. Illustrative examples of qualitatively poor and good predictions are shown in the time-series of measured and estimated formaldehyde concentrations in Figure 5a (poor predictions in home 46) and in Figure 5b (good predictions in home 31). In Figure 5a, some very low formaldehyde concentrations were measured without any obvious changes in other parameters, such as the air exchange rate, which might be caused by window opening by occupants. In fact, actual concentrations in Home 46 appear to be positively correlated with the ventilation rate, such that increased outside airflow leads to higher indoor concentrations. This further supports the potential for errors in the ventilation rate calculation method for this home. The good prediction in Home 31 shows agreement in both the magnitude and timing of changes in the indoor formaldehyde concentrations, with notable short-term spikes in the ventilation rate followed by temporarily reduced formaldehyde concentrations.

**Figure 5.** Examples of (**a**) a poor predictor and (**b**) a good predictor, by plotting time-resolved measured and estimated formaldehyde concentrations along with the air exchange rate per hour.

Our intent is to develop a working relationship that results in reasonable predictions of emission rates and the resulting indoor formaldehyde concentrations. Accordingly, we decided that the emission predictions that gave the poorest estimates on either emission rate or indoor concentration would not be used. Firstly, we removed a quarter of the homes with lowest r-square values from multi-parameter regression models using Equation (9). These homes were considered not applicable to the generalized multi-parameter regression model, because the emission rates were not well-correlated with indoor temperature, *RH*, or AER. Then, by calculating average relative difference using Equation (11) for each home, we removed the homes that had greater than 20% average relative difference, unless the average was affected by some extreme data points. This filtering process left 27 sets of estimates of predictors for the formaldehyde emission rate when using the original 1-h average approach, 27 sets for the 8-h running average approach and 26 sets for the approach excluding outliers. Most selected homes with good estimates were the same homes irrespective of the method used, but there were three to four selected homes may vary by approaches.

The estimated concentrations using the predicted emission rates based on house specific coefficients by one-hour average method for 27 selected homes with good estimators are compared to the measured formaldehyde concentrations in those same homes in Figure 6a. These results show an overall bias of prediction of less than 0.1% (slope = 0.9993). An RMSE of 3.2 μg/m3 (2.5 ppb) and r-square of 0.88 indicate that the general prediction is consistent, and that the fitted coefficients are also reasonable at predicting the changes in concentration as the parameters vary. For comparison, we also plot estimated concentrations using a fixed weekly average emission rate of each home versus the measured concentrations in Figure 6b. The RMSE is substantially higher (8.6 vs. 3.2) and r-square is substantially lower (0.45 vs. 0.88) when using weekly averaged emission rates compared to the dynamic emission rates predicted by temperature, *RH*, and air exchange rates. Similar comparisons are performed for the method excluding outliners (Figure 6c,d), and method using 8-h running average (Figure 6e,f). Generally, all three methods show similar improvement in predicting indoor concentrations compared to single, fixed weekly average emission rates from each home. The methods using 8-h running averages and those excluding outliers slightly underestimated overall concentrations (slopes of 0.99 and 0.98). This is expected because both alternative methods filter out very high concentrations/emission rates before applying to the regression model, and the resulting coefficient estimators are more accurate for mid-range concentrations. We've considered multiple guidelines that have been used for indoor air quality model evaluation [57]. The ideal IAQ model should have the observed value and predicted value plotted along the 1:1 line, with relatively smaller MSE between observations and predictions. Thus, the original 1-hr average approach was selected for further analysis.

Our overall estimate of an area normalized emission rate model for a generic house was determined by averaging the *A*, *B*, *Cst* model coefficients for each of the selected homes. Coefficients were averaged together, because they were linearly correlated with the emission rate (i.e., the value of *A* for use in generic predictions is the average of the 27 values of *A* from the 27 homes). The resulting generic regression coefficients and variance in selected homes for each approach are shown in Table 2. The coefficients resulting from the regression model for temperature, *RH*, and equilibrium concentration are also compared to those in the previous studies. Overall, the coefficients we found from the selected homes are comparable to effects observed in previous studies.

**Figure 6.** Predicted HCHO concentrations versus measured concentrations in selected houses using (**a**) emission rates predicted by the home-specific coefficients for each home using hourly averaged method, (**b**) corresponding constant emission rates by weekly average for each home using hourly averaged method, (**c**) emission rates predicted by the home-specific coefficients for each home using excluding outliner method, (**d**) corresponding constant emission rates by weekly average for each selected home using excluding outliner method, (**e**) emission rates predicted by the corresponding coefficients for each individual home using 8-hr average method, and (**f**) corresponding constant emission rates by weekly average for each selected home using 8-hr average method.


**Table 2.** Summary of regression coefficients in selected homes.

An additional analysis was performed to evaluate the overall estimate of an area normalized emission rate model using the average *A*, *B*, *Cst* model coefficients. The estimated concentrations in 27 selected homes using the predicted emission rates based on averaged model coefficients (*A*, *B*, *Cst*) in Table 2 with 1-hr average method are compared to measured hourly concentrations in Figure 7a. Figure 7b shows the estimated concentrations using a single fixed floor area normalized emission rate that averaged across 27 selected homes (i.e., 23.6 μg/h/m2) versus the measured hourly concentrations. Significant improvement is presented when using the proposed time-varying model with averaged coefficients, which gives an overall slope of 0.98, r-square value of 0.67 and a root mean square error of 5.6 μg/m3 (3.9 ppb). While using an averaged fixed floor area normalized emission rate, the root mean square error between estimated and measured concentration is doubled, with a value of 11.6 μg/m3 (9.3 ppb) with a poor r-square value of 0.06, though the overall slope is 0.99. The overall variation of time-resolved formaldehyde concentrations in a group of homes consists of three dimensions: (1) within-home variation due to environmental condition changes during the measured week; (2) cross-home variation due to house to house environmental condition (e.g., one home may have higher indoor humidity than the other, even though same emitting materials were furnished in the two home); and (3) cross-home variation due to different emitting materials across homes. Figure 7a used the proposed model with averaged model coefficients for the whole dataset that predicted the time-resolved concentration with emission rates to account for the temperature, humidity, and air change rate variability within home and cross homes. Conversely, the results in Figure 7b, which used a fixed floor area normalized emission rate to predict time-resolved concentrations for each home in the group, did not capture any temperature, humidity, and air change rate variations. Estimated concentrations by both approaches resulted in overall slopes close to one when comparing to measured values, which indicates that the time-averaged estimated concentrations for homes by either approach would show little difference compared to averaged measured concentrations. However, using a single average the floor area normalized emission rate for all homes omits the variations of emission rates due to environmental condition changes within a home and across homes, leading to larger differences when comparing to time-resolved hourly data. We note here that the overall fit in Figure 7a is worse than Figure 6 left panel, because we used a single set of model coefficients that averaged coefficients over 27 homes to predict the time-resolved concentrations for the whole group of houses. The variation that is caused by the difference emitting materials across homes was not accounted for, leading to the estimated values having great variation across the 1:1 line. Thus, this set of averaged model coefficient would preferably be used as a predictive/comparative tool in future modeling work, rather than as a forecasting model for a specific house.

**Figure 7.** Predicted HCHO concentrations versus measured concentrations in 27 selected houses using (**a**) estimated emission rate by the proposed model with averaged coefficients across homes and (**b**) estimated emission rate by a traditional approach that using a fixed floor area normalized emission rate averaged across 27 homes.

#### **4. Limitations**

The most important limitation of this study is the unknown bias associated with the sample of homes used to estimate the emission rates compared with any particular home (or group of homes) one may want to model. The homes where the measurements were made were relatively newly constructed (built since 2011) in California, and they were required to use low-emitting products and install mechanical ventilation. This group of 27 homes cannot be assumed to represent conditions in all homes throughout the state, let alone the US. The average temperature, humidity, and air exchange rates across the sample of homes ranged from 18–27 ◦C, 28–63% and 0.08–1.14 h<sup>−</sup>1. All regression results, therefore, must be regarded as exploratory and suggestive, and we caution their use beyond similar houses within similar environmental conditions. Our model can be improved by having a larger dataset of measurements in real homes. We are collecting more data in about 120 houses across the US. Future studies will refine the current model and improve the accuracy. The data-driven approaches will be also tested to compare the performance in real homes.

An additional source of potentially meaningful error in these emission rate estimates are the air exchange rates used to determine emission factors from measured concentrations. The air exchange rates were estimated from building leakage measurements, weather data and fan operation logging, and these estimates are subject to errors in accounting, measurement, and the models used to combine natural and mechanical flows. In addition, window and door operation cannot be ruled out as contributing to the measured concentrations, while not being reflected in air exchange rate estimates.

Finally, the accuracy of the time-resolved formaldehyde concentrations is an important source of error. Comparing one-week average concentrations for the real-time data used in this study to time averaging sensors showed across all test homes the RMSE was 6.9 μg/m3. The error may be larger for measuring time resolved data.

#### **5. Conclusions**

The intent of this work was to develop a modeling approach to determine formaldehyde emission rates in dwellings that is suitable for estimating indoor formaldehyde concentrations based on variations in indoor temperature, humidity and air change rate. This study applied an empirical model based on previous study to correlate emission rates with temperature, relative humidity, and air change rate in 63 new houses in California. Compared to the approaches using physics-based models, the method herein does not

require detailed model coefficients for every emitting material to predict a dynamic whole house formaldehyde emission rate. The proposed model also provides a simplified approach to investigate emission rate variability due to environmental condition changes for a group of reprehensive homes built with low-emitting materials. In total, 27 homes with acceptable regression results were selected with resulting uncertainty in the predicted indoor formaldehyde concentrations of about 3.2 μg/m3 (13%). These results indicate that the simplified functional form and parameterization of the emission rate prediction is a reasonable approach. Obvious accuracy improvement was found for predicting indoor formaldehyde concentrations using the derived emission rate models, compared to using constant emission rates averaged weekly for each individual house. We caution that this likely would not be the case if this model were used to predict concentrations in any individual home, rather than using it as a predictive/comparative tool.

**Author Contributions:** Conceptualization, I.S.W.; methodology, H.Z., I.S.W., and M.D.S.; validation, H.Z., I.S.W., and B.L.; formal analysis, H.Z.; investigation, H.Z., I.S.W., and M.D.S.; resources, I.S.W.; data curation, H.Z.; writing—original draft preparation, H.Z.; writing—review and editing, I.S.W., M.D.S., and B.L.; visualization, H.Z. and B.L.; supervision, I.S.W.; funding acquisition, I.S.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the California Energy Commission through Contract PIR-14-007 and the U.S. Department of Energy Building America Program via Contract DE-AC02-9 05CH11231.

**Institutional Review Board Statement:** The field study contributing data to this research were approved by LBNL's institutional review board following US government regulations for research involving human subjects; the house study was protocol 318H003 approved 5/12/2015 and the apartment study was protocol 280H013 approved 11/19/2018.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Model to Balance an Acceptable Radon Level Indoors**

**Torben Valdbjørn Rasmussen \* and Thomas Cornelius**

Department of Civil Engineering and Construction Management, BUILD, Aalborg University, A.C. Meyers Vænge 15, 2450 Copenhagen, Denmark; tcb@build.aau.dk

**\*** Correspondence: tvr@build.aau.dk

**Abstract:** A theoretical model is presented for balancing an acceptable radon concentration in indoor air. The infiltration of radon from the ground to the indoor air can be controlled by barriers or by lowering the air pressure at the lower zone of the ground slab. Indoor air with a radon concentration higher than that of outdoor air can further be controlled through the effective dilution of indoor air with outdoor air. The theory estimates the allowed radon infiltration from the ground to balance radon at an acceptable level indoors for a given ventilation rate, considering the radon contribution to the indoor air from indoor materials, building materials and the interior. A method using this theory is presented, identifying the necessary airtightness required for a radon barrier to balance the acceptable radon concentration for a building. Barriers include commercially used system solutions, such as bitumen-based radon blockers, wet-room membranes, reinforced fixed mortar pastes, and polyethene membranes. An acceptable indoor radon concentration of between 100 and 300 Bq/m3 in indoor air is used. Barriers are evaluated by their ability to prevent soil gas penetration from the ground in combination with their effect on the building durability, as barriers may create a far more vulnerable building.

**Keywords:** model; radon; soil gas; indoor materials; penetration; ventilation; indoor air quality

#### **1. Introduction**

Radon-222 develops from the radioactive decay of radium-226 and has a half-life of 3.8 days. This gas seeps through the soil into buildings to interfere with radon derived from the atmosphere and building materials. If not diluted with outdoor air through ventilation, much higher human exposure levels can occur indoors than outdoors [1,2]. Thus, radon affects occupants through the indoor climate.

Radium is a decay product of uranium. Radium is a solid as uranium. Since uranium is one of the most common radioactive elements on Earth, radon will be present on Earth long into the future despite its short half-life.

The World Health Organization (WHO) recommends that states introduce requirements for the maximum radiation concentration from natural indoor-air sources. After determining that radon is responsible for 3% to 14% of lung cancer cases, the WHO recommended these requirements, depending on the average radon exposure in various countries [3]. The results indicate that radon is the second-leading cause of lung cancer (smoking tobacco is still the primary cause). Therefore, it is crucial to prevent radon from penetrating buildings. Since 2010, Danish building regulations have required that buildings be constructed to ensure that indoor radon levels remain below 100 Bq/m3 [4].

The radon level indoors in Danish dwellings built before 2018 is 105 Bq/m3. For dwellings built before 1995, the radon level is 106 Bq/m3. For dwellings built between 1996 and 2009, the radon level is 93 Bq/m3, and for dwellings built between 2010 and 2018, the radon level is 58 Bq/m3. Approximately 9% of dwellings built before 2018 have a radon level above 200 Bq/m3. In addition, 41% have a radon level above 100 Bq/m3 [5]. In comparison, the radon level in dwellings in Finland is 96 Bq/m3, in Sweden 108 Bq/m3 and in Norway 60 Bq/m3. In addition, the radon level in Germany is 50 Bq/m3, in France

**Citation:** Rasmussen, T.V.; Cornelius, T. Model to Balance an Acceptable Radon Level Indoors. *Buildings* **2022**, *12*, 447. https://doi.org/10.3390/ buildings12040447

Academic Editors: Ashok Kumar, Amirul I Khan, Alejandro Moreno-Rangel and Michał Piasecki

Received: 28 February 2022 Accepted: 31 March 2022 Published: 5 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

66 Bq/m3 and in England 20 Bq/m3, [6]. In Sweden, Norway and Finland, the limit value for radon levels in newly built buildings is 200 Bq/m3. Norway requires that buildings for permanent residence must be able to activate measures to reduce the radon level, if the radon level exceeds 100 Bq/m3. In England (England, Wales, Scotland and Ireland) the authorities apply an action level of 200 Bq/m3 and a target level of 100 Bq/m3. In Germany, the radon level in a workplace must not exceed 300 Bq/m3 [7]. For other buildings, there is no requirement for the radon level in the indoor air [8]. However, new buildings should be planned and constructed so that the radon level does not exceed 100 Bq/m3.

Infiltration of radon from the ground to the indoor air can be prevented by barriers, such as membranes, or by lowering the air pressure at the lower zone of the ground slab or combining them.

Radon originates from the ground. Soil gas penetrates from the ground underneath a building and is the primary radon source in indoor air [9]. However, building materials can also contribute to the radon concentration in indoor air if they contain radium or the chemical elements uranium and thorium (e.g., granite and alum shale). The radon contributions to the indoor air from building materials used indoors are seldomly considered in balancing the radon concentration. Outdoor air and the atmosphere contain a low concentration of radon because the soil gas is diluted when reaching the ground surface.

When using barriers as a system solution to prevent radon from penetrating buildings, it is crucial to determine the airtightness of such barriers. Moreover, the barrier must be sufficiently airtight and have airtight joints at the corners, across floor-level changes, around barrier-penetrating pipes and against floor drains.

This paper presents a theoretical model for balancing an acceptable radon concentration in indoor air for a typical single-family building construction. The presented theory theoretically estimates the allowed radon infiltration from the ground to balance the radon at an acceptable level indoors for a given ventilation rate, considering the radon contribution to the indoor air from indoor materials, such as building materials and the interior.

However, the choice of a radon barrier must be made consistently with an acceptable change in the building physics. Using a barrier to prevent radon gas penetration from soil often causes a change in the building physics related to the moisture level in the building materials from the rising soil moisture.

Ideally, the indoor radon concentration is lowered to a balanced level that meets the national building regulations. However, for existing buildings, a higher indoor radon concentration might be considered acceptable, considering the expense of preventing a rise in the soil moisture level. Therefore, a barrier must be evaluated by its ability to prevent soil gas penetration from the ground and its influence on the overall moisture level in the affected building materials.

This paper demonstrates the theory used in practice to balance the indoor radon concentration at an acceptable level, using several different radon barriers, which were evaluated as single-system solutions. The barriers include system solutions based on various materials, such as bitumen-based radon blockers, wet-room membranes, reinforced fixed mortar pastes, and mortar and polyethene membranes.

The barriers were tested using a modified version of the NBI 167/02 radon membrane airtightness test method [10], which determines the airtightness of a radon barrier used as a system solution. The assessment method was modified by providing a digital stirring and control system and introducing equipment to determine the overall mean air-pressure difference over the barrier. Barriers were identified to balance the indoor radon concentration between 100 and 300 Bq/m3 for a ventilation rate of between 0.5 and 4 h<sup>−</sup>1. For these findings, the model considered a low initial radon contribution from indoor materials of around 40 Bq/m3 and higher contributions of around 1000 Bq/m3. Barriers managed the radon exposure from the ground of up to 800,000 Bq/m3 in the soil gas.

#### **2. Balancing Radon Indoors**

Indoor-air infiltration of radon from the ground must be prevented, and the radon that reaches the indoor air must be diluted to reach a balance of an acceptable radon concentration or a radon concentration at a lower level. An efficient way to avoid radon infiltration in a building is by making the ground slab airtight and lowering the air pressure at the lower zone of the ground slab, either as individual measures or by combining the two measures. If resulting in a higher radon concentration than that of the outdoor air, radon in the indoor air can be diluted with outdoor air and ventilated.

Methods to balance the indoor radon concentration comprise a combination of the three design criteria shown in Figure 1:


The indoor radon concentration can be balanced at an acceptable level using this method [11]. However, in contrast to new buildings, the three design criteria may not be implementable to influence the indoor radon concentration sufficiently for alreadyconstructed buildings.

**Figure 1.** Design criteria to control the radon penetration and radon concentration in indoor air: 1. radon barrier—establishing a barrier preventing soil gas from penetrating from the ground; 2. pressure lowering—lowering the air pressure in the lower zone of the ground slab; and 3. ventilation—diluting indoor air with outdoor air.

#### **3. Model for Balancing Radon Indoors**

The theoretical model is based on a description of a detached single-family house with a ground area denoted by A, a ceiling height h and an air-change rate q. The indoor air is diluted with outdoor air with a radon concentration denoted by r and an indoor-air radon concentration denoted by R, as shown in Figure 2. Soil gas and the contribution from building materials and the interior are assumed to increase the indoor-air radon concentration. Therefore, the maximum penetration of soil gas with radon content (Rg)

and contribution from indoor materials (Rm) to maintain an acceptable indoor radon concentration were found using the equilibrium equation.

**Figure 2.** The equilibrium equation describes the equilibrium between the constant radon concentration in the indoor air (R), and the radon supply from soil gas (Rg), exterior air (r) and indoor materials (Rim) for a constant air-pressure difference between the interior and exterior over time.

Assuming the air-pressure difference between the interior and exterior of the building is constant over time, the equilibrium equation describes the static equilibrium of all internal and external system forces [12]. In the static case, the equilibrium equation is as follows:

$$\mathbf{K} \cdot \mathbf{u} = \mathbf{F},\tag{1}$$

where K denotes the stiffness matrix of the system, u is the vector with nodal displacements and F represents external forces.

The equilibrium equation describes the equilibrium between the constant radon concentration in the indoor air and the radon supply from soil gas, exterior air and indoor materials. The soil gas and exterior air are both assumed to have a constant but different radon concentrations. The contribution from indoor materials is assumed to follow the dilution equation. The radon contribution from indoor materials contributes to the indoor radon concentration and depends on the ventilation rate. The contribution to the indoor radon concentration from indoor materials reduces by 50% when the ventilation rate doubles. The equilibrium is given by Equations (2)–(4):

$$\mathbf{q} \cdot \mathbf{A} \cdot \mathbf{h} \cdot \mathbf{R}\_{\mathbb{P}^\mathbf{V}} = \mathbf{y} \cdot \mathbf{r} + \mathbf{x} \cdot \mathbf{R}\_{\mathbb{B}'} \tag{2}$$

where the indoor-air radon content, denoted as R, is the result of the radon contribution from soil gas, outdoor air (Rpv) and indoor materials (Rm):

$$\mathbf{R} = \mathbf{R}\_{\text{PV}} + \mathbf{R}\_{\text{m.}} \tag{3}$$

The radon contribution from indoor materials (Rm) is described by the function F, where the contribution declines with the ventilation rate following the dilution equation:

$$\mathbf{R\_m} = \mathbf{F} \text{ (\$\mathbf{R\_{im}}\$\_\circ\$ q)},\tag{4}$$

where Rim is the initial radon contribution from indoor materials. The radon content in the air outlet equals the indoor-air radon content provided from the three supply sources: the outdoor air, soil gas and indoor materials.

The equilibrium equation also describes the equilibrium between the indoor-air volume ventilated out of the building and the air supply volume needed from the soil gas and exterior air to stabilize the air-pressure difference over the building envelope over time. The equilibrium is given by Equation (5):

$$\mathbf{x} + \mathbf{y} = \mathbf{q} \cdot \mathbf{A} \cdot \mathbf{h}.\tag{5}$$

The variables x and y are the only undefined variables in these equations (i.e., in Equations (2) and (5)). The air supply from the ventilation and the penetrating soil gas is equal to the building air outlet.

#### **4. Quantifying the Contribution of Indoor Materials**

The radon contribution from indoor materials is well known [13]. The contribution to the indoor-air radon content is related to the specific materials used in a building, contributing to the indoor radon concentration if the materials contain radium or the chemical elements uranium and thorium (e.g., granite and alum shale). The radon contribution to the indoor radon concentration from building materials is seldomly significant in wellventilated buildings. However, if an acceptable indoor-air level of radon concentration is as low as 100 Bq/m3, or even lower, radon contributions from less polluting sources must be considered.

The contribution from indoor materials is theoretically described in this paper by the function F, where the contribution declines with the ventilation rate. The radon concentration from indoor materials is described by an initial contribution (Rim) that declines by 50% every time the ventilation rate is doubled, following the dilution equation [14].

The initial contribution (Rim) from indoor materials (Rm) must be defined. The presented theory defines the initial radon contribution to the indoor-air radon concentration and considers the contribution related to a very low air change q of 0.1 times per hour, as illustrated in Figure 3 and Table 1.

**Table 1.** Decline in the radon contribution to the indoor-air radon concentration from indoor materials. q is the air change per hour.


<sup>1</sup> Rm is calculated for several different ventilation rates ranging from 0.01 h−<sup>1</sup> to 12.8 h−1. Initial radon contributions (Rim) of 40, 100, 500 and 1000 Bq/m3 are shown. The initial radon contribution (Rim) is defined at the air change q equal to 0.1 times per hour.

**Figure 3.** Radon contribution to the indoor-air radon concentration from indoor materials (Rm) described by the function F where the contribution declines by 50% every time the ventilation rate doubles, taking its starting contribution as the initial contribution (Rim) at an air-change rate q of 0.1 times per hour.

Although a ventilation rate of 0.1 h−<sup>1</sup> is low, field studies show measurements of the ventilation rates in new detached single-family houses to be as low as 0.07 h−<sup>1</sup> [15].

#### **5. Balancing Radon Indoors**

The presented theory can be used to determine the related values and requirements for the radon penetration from soil gas, the radon contribution from indoor materials and the radon concentration in outdoor air. The theory can also determine the ventilation rate to balance radon in indoor air at an acceptable level for a specific detached single-family house.

For a detached single-family house, the maximum penetration of soil gas to maintain an acceptable indoor radon concentration of 100 Bq/m3 was determined for several radon exposures from soil gas. The radon concentration in soil gas varied from less than 1000 to 150,000 Bq/m3. The ground area of the house was 100 m2 with a ceiling height of 2.5 m. The air-change rate was 0.5 h−<sup>1</sup> to maintain an acceptable indoor environment, equivalent to changing all the indoor air every two hours.

The initial radon contribution from indoor materials to the indoor radon concentration (Rim) was 40 Bq/m3, resulting in a radon contribution of 8 Bq/m3 from indoor materials (Rm) to the indoor radon concentration (Figure 3 and Table 1). Indoor air was diluted with outdoor air with a radon concentration of 5 Bq/m3. The requirements to balance an acceptable indoor radon concentration R of 100 Bq/m3 for the penetration of soil gas containing radon are listed in Figure 4.

**Figure 4.** Soil gas penetration, balancing an acceptable radon concentration in indoor air of 100, 300, and 600 Bq/m3. Soil gas contains radon. Indoor air was diluted with outdoor air. Outdoor air contains 5 Bq/m<sup>3</sup> radon. The air-change rate was 0.5 h−1. The initial radon contribution from indoor materials (Rim) was 40 Bq/m3, providing a radon contribution from indoor materials (Rm) of 8 Bq/m3 to the radon indoor-air concentration. The house has a ground area of 100 m2 and a ceiling height of 2.5 m.

Additionally, Figure 4 illustrates that the soil gas penetration for the same detached single-family house can increase to balance an acceptable radon indoor-air concentration R of 300 and 600 Bq/m3. Penetration was calculated in liters per minute. Less soil gas may penetrate the indoor air through the ground slab to balance an acceptable radon indoor-air level of 100, 300 and 600 Bq/m<sup>3</sup> to increase the radon concentration in the soil gas. To reach a balance at a higher level of an acceptable radon concentration in the indoor air, a larger amount of radon penetrates indoor air through the ground slab, either through the increased penetration of soil gas or a higher radon concentration in the soil gas.

When balancing an acceptable indoor radon concentration of 100 Bq/m<sup>3</sup> for a house, the maximum penetration of soil gas was found for several radon exposures from soil gas and for several initial radon contributions from indoor materials (Rim) with air-change rates of 0.5, 1.06 and 2.11 h−1. For the initial radon contribution from indoor materials (Rim) of 237 Bq/m3, an indoor radon concentration R of 100 Bq/m3 can be balanced and kept with an air-change rate of 0.5 h−<sup>1</sup> if soil gas penetration containing radon is avoided. To further increase the initial radon contributions from indoor materials, the air-change rate must be increased to balance indoor radon at a concentration of 100 Bq/m3, still avoiding soil gas penetration containing radon. For the initial radon contribution from indoor materials of 500 Bq/m3, an air-change rate of 1.06 h−<sup>1</sup> is needed. For an initial radon contribution from indoor materials of 1000 Bq/m3, an air-change rate of 2.11 h−<sup>1</sup> is needed for balance at an acceptable radon indoor-air concentration R of 100 Bq/m3 (Figure 5). The ground slab must be airtight, and measures must be taken to lower the air pressure at its lower

zone to avoid soil gas penetration of the indoor air through the ground slab of a detached single-family house.

**Figure 5.** The allowed soil gas penetration with a given radon concentration balancing the radon indoor-air concentration at 100 Bq/m3 with increased initial radon contributions from indoor materials and an air-change rate starting from 20 Bq/m3 and 0.5 h<sup>−</sup>1, respectively.

#### **6. Controlling Soil Gas Penetration**

Controlling the radon concentration via soil gas penetration through the ground slab is a key parameter for balancing the radon indoor-air concentration at an acceptable level. Measures that make the ground slab airtight or lower the air pressure at the lower zone of the ground slab can be used individually or combined. Making the ground slab airtight increases the effect of a pressure-lowering measurement at the lower slab zone. A measure reducing radon penetration to a predefined level can be reached using a barrier. The barrier choice depends on its ability to reduce infiltration. Ten radon barriers used as system solutions were tested with the modified version of the NBI 167/02 radon membrane, the airtightness test method [10], which determines the airtightness of a radon barrier used as a system solution.

#### *6.1. Barriers*

Ten barriers were tested as system solutions, which are denoted as Systems A through J, as shown in Table 2.


Figure 6 illustrates mounting the test material inside the mock-up for System B. System B is a firm bitumen-based radon blocker combined with a two-component floating sealant. Figure 7 displays the mounting of the two-component fixed mortar paste combined with edge reinforcements, epoxy and elastic pipe collars, denoted as System E.

**Figure 6.** Mounting the test material inside the mock-up for System B, which is a firm bitumen-based radon blocker (**a**) combined with a two-component floating sealant (**b**).

The barriers were used as delivered, and the manufacturer mounted them inside the mock-up. The tests started 40 h after mounting the barrier to ensure a stress-free barrier and joints. The tests set no specific requirements for the indoor climate at the testing laboratory. However, the laboratory climate should be a dry tempered room with a temperature between 17 ◦C and 25 ◦C with relative humidity between 15% and 65%.

**Figure 7.** Mounting the test material inside the mock-up for System E, which is a two-component fixed mortar paste combined with edge reinforcements, epoxy and elastic pipe collars.

#### *6.2. Test of Air Infiltration*

The test determines the air penetration through a material evaluated for suitability as a radon barrier. The test evaluates how well a barrier prevents soil gas with radon from penetrating the indoor air. The barrier was mounted inside a mock-up, providing a stable basis with penetrating pipes, an elevation, and narrow-angled and wide-angled corners. The airtightness of the barrier was determined as the air penetration through the barrier and its joints for a difference in air pressure of 30 Pa, denoted as q30. The difference in air pressure over the barrier is the difference in the air pressure between the air inside the mock-up (designed as a box) and in the surrounding test laboratory.

#### *6.3. Measurement Setup*

The test was conducted by mounting the test material inside a mock-up. After molding the test material, the mock-up was filled with pressure-firm thermal insulation using mineral wool. On top of the firm insulation, a test-material layer was mounted to seal the mock-up volume that holds the firm insulation enveloped by the test material. The constant airflow from the sealed mock-up was measured. The airflow provides a constant air-pressure difference.

#### *6.4. Equipment*

The barrier was mounted in a mock-up of laminated wooden boards 3.0 m long and wide and 0.3 m high with a notch of 1.0 by 1.0 m, with changed floor levels, penetrating pipes and floor drains (Figure 8). The air was extracted from the volume using a fan. The cavity of the mock-up was filled with pressure-firm thermal insulation material and enveloped by the test barrier material. The coherent airflow values and difference in air pressure between the air inside the mock-up and the surrounding test laboratory were systematically measured and logged.

**Figure 8.** Sketch of mock-up measuring the barrier airtightness.

Using the program TECLOC3 from BlowerDoor Gmbh, the data were logged by connecting a (1) computer to a unit measuring the pressure difference and (2) a fan. The fan was a Minneapolis micro leakage meter, type FD E51-767, which measured the airflow between 0.09 and 79 m3h−1. The fan was mounted on a disc with a circular hole to measure the airflow. Individual discs were mounted, and each had a circular hole of 3.8, 8.0, 20 or 45 mm. A computer controlled the fan to extract the air from the mock-up volume and measure the airflow, introducing predetermined differences in air pressure between the volume within the mock-up and the air in the surrounding test laboratory.

The mean value of the difference in air pressure between the volume within the mockup and the air in the surrounding test laboratory was determined using five air-pressure difference measurement units mounted on the top layer of the test material. These units were used to calibrate the airflow pressure measurements because the air pressure within the mock-up was not homogeneously distributed.

Adding air infiltration through well-defined openings was necessary to measure the airtightness of the barriers with very low airflow in the lower ranges of the capacity of the micro leakage meter. The well-defined openings were added using discs with a 7, 10, 14 or 20 mm diameter. The airflow through the well-defined opening was subtracted from the measured airflow during data processing.

#### *6.5. Processing Results*

The airflow was measured at four air-pressure levels of 30, 50, 70 and 90 Pa controlled by the air-pressure measuring equipment mounted over the barrier system. At each pressure level, four measurements were performed using four different well-defined openings. For all 16 measurements, the opening areas, the individual air-pressure differences in the five air-pressure difference measurement units, and the airflow through the suction point were measured. The measurements were used to calculate the airflow in liters per minute for a 30-Pa mean pressure difference, denoted as q30, over the barrier system, where q30 was determined for the individual barrier systems.

The airflow for a 30-Pa mean pressure difference over the barrier system comprises the soil gas penetration for a one-floor building with a ground area of 100 m<sup>2</sup> with a difference in air pressure over the building envelope of 1 to 4 Pa [4,9,10,16]. The highest allowed soil gas penetrations with a radon concentration not exceeding an acceptable level in the indoor air of 100, 200 and 300 Bq/m3 were determined. Soil gas penetration was determined as the intersection between the air balance indoors, given by the air-change rate and an acceptable radon concentration from Equations (2) and (3), an initial radon contribution from indoor materials of 40 Bq/m<sup>3</sup> and the penetration of soil gas, q30. For the calculations, indoor air was assumed to be diluted with outdoor air with a radon concentration of 5 Bq/m<sup>3</sup> [17]. Additionally, the air-change rate in the building was set at 0.5 h−<sup>1</sup> [18]. Figure 9 presents the soil gas determination with a radon concentration not exceeding acceptable indoor-air levels of 100, 200 and 300 Bq/m3 for the System B and E barriers.

**Figure 9.** Radon barriers for System B and E, where the intersection between the horizontal line indicating the measured airtightness and the curves for reaching an acceptable radon indoor-air level of 100, 200 and 300 Bq/m3 provides the critical radon concentration in soil gas.

Figure 10 displays the soil gas determination with a radon concentration not exceeding an acceptable level in indoor air of 100 Bq/m3 for an air-change rate of 0.5, 1.0, 2.0 and 4.0 h−<sup>1</sup> for the System B and E barriers.

**Figure 10.** Radon barriers for System B and E, where the intersection between the horizontal line measuring the airtightness and the curves for the air-change rates provides the radon concentration in soil gas.

#### **7. Results**

The penetration rates and radon concentration in soil gas (Table 3) should not exceed 100, 200 and 300 Bq/m3 to reach an acceptable radon concentration in indoor air. For Table 3, the air-change rate was 0.5 h−1, and the initial radon contributions from indoor materials (Rim) was 40 Bq/m3. Moreover, the penetration rates and radon concentration in soil gas to not exceed 100 Bq/m3 are listed in Table 4, where the air-change rates were 0.5, 1.0, 2.0 and 4.0 h<sup>−</sup>1, and the initial radon contribution from indoor materials (Rim) was 40 Bq/m3.

**Table 3.** Maximum soil gas penetration to reach an indoor radon concentration of 100, 200 and 300 Bq/m3 for System A to J barriers. The air-change rate was 0.5 h<sup>−</sup>1, and the initial radon contribution from indoor materials (Rim) was 40 Bq/m3. The airflow penetration rate (q30) defines how well a barrier prevents soil gas penetration.


**Table 4.** Maximum soil gas penetration to reach an indoor-air radon concentration of 100 Bq/m<sup>3</sup> for System A to J barriers. The air-change rate was 0.5, 1.0, 2.0 and 4.0 h−1, and the initial radon contribution from indoor materials (Rim) was 40 Bq/m3. The airflow penetration rate (q30) defines how well a barrier prevents soil gas penetration.


#### **8. Moisture Challenges**

A radon barrier can easily be applied during building construction, creating a barrier to increase the ground slap airtightness within or above the ground slab. The barrier can even be mounted in the ground below the slab. This barrier can be applied in numerous ways with suitable fixation onto the materials and surfaces, combined with a moisture barrier that prevents ground moisture from reaching constructions above the foundation or the basement interior. Applying a radon barrier to an already-constructed building can affect the durability of the building, especially for heritage buildings, because measures may create a far more vulnerable building and change its robustness to withstanding moisture and user behavior.

The influence and change in moisture load and content of other building components and constructions must be considered when deciding on a radon barrier mounted on the ground slab or basement wall and floor. Thus, the changed water vapor diffusion and resulting rise in soil moisture load may create a more vulnerable building after mounting a radon barrier for construction. Special attention must be focused on the risk of mold growth, for example, in an air cavity behind a radon barrier that is not bonded to the underlayment.

Through diffusion, radon can penetrate the ground slab or basement wall and floor. The ability of gases, vapors and other minor molecules to penetrate the ground slab, basement wall and floor by diffusion depends on the individual permeability of the ground slab, basement wall and floor.

Diffusion through concrete is considered limited. Fixed mortar paste can reduce diffusion but cannot prevent penetration by diffusion. As the ability to limit diffusion is related to the density of the fixed mortar paste and the thickness of the mortar paste layer, even minor cracks can increase diffusion [19].

Investigations have found that radon diffusion through a typical concrete slab of 150 mm in thickness without cracks contributes to indoor radon by approximately 15 to 20 Bq/m3. For these investigations, an air-change rate of 0.5 h−<sup>1</sup> was provided in the building, and the radon content in the soil gas was 500,000 Bq/m<sup>3</sup> [20].

In Denmark, the general radon content in soil gas is substantially lower, approximately 50,000 Bq/m<sup>3</sup> [21]. In this case, the contribution by radon diffusion into the indoor air is substantially lower at approximately 2 Bq/m3.

Radon penetration through the ground slab, basement wall and floor by diffusion in buildings today represents a limited contribution to the overall indoor-air radon content, and the primary source is soil gas from the ground. However, a high indoor-air radon content can be observed in indoor air where the air-change rate is lower than 0.5 h−<sup>1</sup> due to the accumulation of radon from indoor materials.

#### **9. Discussion**

Soil gas penetrating through the ground slab is the primary source of radon in indoor air in most cases [11]. However, the contribution from indoor materials may affect the indoor-air radon content, resulting in an unacceptable level. Therefore, the (1) geological composition of the ground on which a building is situated, (2) radon concentration in soil gas, (3) soil gas penetration through the ground slab, (4) contribution from indoor materials and (5) air-change rate are used to set the indoor radon concentration level. Radon seeps into a building through soil gas penetration through cracks or other ground construction openings [22] and indoor materials. Therefore, it is essential to control soil gas penetration and balance the radon concentration indoors through ventilation.

Establishing a barrier that prevents soil gas penetration from the ground is an efficient way to prevent radon penetration. By avoiding soil gas penetration and lowering the air pressure in the lower zone of the ground slab, a barrier provides a more effective solution, providing a far better possibility of providing an air-change rate of 0.5 h−<sup>1</sup> that balances the indoor radon concentration at an acceptable level. However, when combining the three mentioned design criteria, (1) making the ground slab airtight, (2) lowering the air pressure at the lower zone of the ground slab and (3) effectively diluting the indoor air with outdoor air, the radon concentration in indoor air can be robustly balanced and maintained at an acceptable level. If the air pressure in the lower zone of the ground slab cannot be lowered, the radon barrier choice is crucial for soil gas penetrating the indoor air.

The presented theory aids in combining the radon barrier choice and related necessary ventilation rate of the indoor air to balance the radon at an acceptable indoor concentration. The theory estimates the allowed radon infiltration from the ground to balance the radon at an acceptable indoor level for a given ventilation rate, considering the radon contribution to the indoor air from indoor materials. However, the moisture-level change in the building components must be considered when choosing the most suitable radon barrier, which depends on individual building physics.

The requirement for the airtightness of a radon barrier, the penetration rate (q30), can be determined from the radon concentration in soil gas underneath a building. In certain cases, a diffusion-tight radon barrier can be used, and in others, a diffusion-open barrier is preferred. The barrier choice depends on the moisture level after mounting. It is crucial to choose a sufficiently airtight radon barrier to meet the requirements while contributing to the building physics.

From the theoretical processing of the test results combined with the radon contribution from indoor materials and the indoor-air ventilation rates, a radon barrier can be chosen based on the indoor radon concentration being balanced at an acceptable level and the radon content in the soil gas underneath a building. The theoretical processing demonstrates that, for an initial radon contribution from indoor materials (Rim) of up to 237 Bq/m3, an acceptable indoor radon concentration of 100 Bq/m3 can be achieved with an air-change rate of 0.5 h−1, controlling the soil gas penetration. However, at a radon contribution from materials of 237 Bq/m3, soil gas penetration containing radon must be avoided. An increased initial radon contribution from indoor materials means an increased ventilation rate is needed, balancing an acceptable indoor radon concentration of 100 Bq/m3. The ventilation rates of 1.06 and 2.11 h−<sup>1</sup> are needed for radon contributions from indoor materials of 500 and 1000 Bq/m3, respectively, balancing an acceptable indoor radon concentration of 100 Bq/m<sup>3</sup> and avoiding soil gas penetration containing radon. Hence, in this study, the radon contribution from indoor materials was determined as the initial contribution at a ventilation rate of 0.1 h−1. Avoiding soil gas penetration into the indoor air through the ground slab requires combined measures, including making the ground slab airtight and lowering the air pressure at the lower zone of the ground slab to a level that is even lower than the air pressure above the ground slab [23].

The theoretical test results indicate that the radon barrier in System B with the penetration rate (q30) of 1.9 L/min can balance an acceptable radon concentration in indoor air that is less than or equal to 100 Bq/m<sup>3</sup> in a building on soil with a radon concentration of less

than or equal to 86,600 Bq/m3. If the soil gas contains a concentration of between 86,600 and 305,800 Bq/m3, an acceptable indoor radon concentration can be balanced between 100 and 300 Bq/m3. For theoretical processing, it was assumed that indoor air was diluted with outdoor air with a radon concentration of 5 Bq/m<sup>3</sup> at an air-change rate of 0.5 h−<sup>1</sup> and an initial radon contribution from indoor materials of 40 Bq/m3. However, by increasing the air-change rate to 1, 2, or 4 h−1, an acceptable radon concentration in indoor air could be kept balanced at 100 Bq/m<sup>3</sup> or less in a building on soil with a radon concentration of 190,800, 399,000 and 817,000 Bq/m3, respectively.

In terms of the testing barriers, it is vital to be aware of how the joints perform. These concerns are based on the performance of Systems G and H and Systems I and J, which are alike except for how the joints perform.

#### **10. Conclusions**

A model for theoretically balancing the radon concentration in indoor air was presented. The theory estimates the allowed radon infiltration from the ground to balance the radon at an acceptable indoor level for a given ventilation rate considering the radon contribution to the indoor air from indoor materials, such as building materials and the interior. The theory is useful for a typical building construction for a single-family house. Furthermore, the paper presents a theoretical processing method to balance the radon concentration indoors by combining the results from an improved testing method for determining the airtightness of a radon barrier assessed as a system solution [10]. Moreover, if appearing in the indoor air, a radon concentration above that of the outdoor air can be lowered by diluting the indoor air using outdoor air and ventilation. The model also demonstrates how the radon contribution from indoor materials influences the measures balancing the radon concentration indoor at an acceptable level.

Using the theoretical processing of the results determining the airtightness of the radon barriers as system solutions made it possible to choose a radon barrier with an acceptable radon concentration in indoor air and soil gas underneath a building with the ventilation rate and radon exposure from indoor materials. However, the acceptable radon concentration in indoor air could be compromised because a suitable radon barrier depends on the moisture-level change in the building after mounting the radon barrier. A radon barrier must contribute to the building physics, creating a more robust building. Further, the needed ventilation rate to achieve an acceptable radon concentration in indoor air could compromise the energy performance of the building.

The presented theory and theoretical processing method assumed that only soil gas, indoor materials and the atmosphere contain radon and that soil gas and indoor materials are the radon sources in indoor air. However, the contribution to the radon concentration in indoor air from indoor building materials is seldom significant. The contribution from indoor building materials is included in the theory, as materials contribute radon if they contain radium or the chemical elements uranium and thorium (e.g., granite and alum shale).

**Author Contributions:** Conceptualization, methodology, validation, formal analysis, investigation, data curation, writing—original draft preparation, writing—review and editing, project administration and funding acquisition: T.V.R.; visualization and lab tests: T.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Realdania a philanthropic association, with the mission of improving quality of life and benefitting the common good by improving the built environment. Its focus is on solving challenges in Danish society in cooperation with the government, the municipalities, foundations, associations, private businesses and local, voluntary enthusiasts.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data are reported in Danish: Rasmussen, T.V. og Buch-Hansen, T.C. (2018). SBI-rapport; Nr. 2018:06. Egnede membransystemer til radonsikring: vurdering af ti membransystemer. 1. udg.: Statens Byggeforskningsinstitut, Aalborg Universitet. København. 28 s. (SBi-Report; No. 2018:06: Membranes for radon protection of buildings; in Danish). Danish Building Research Institute-Aalborg University. Copenhagen. Denmark. The test method is described in Danish: Rasmussen, Torben Valdbjørn & Buch-Hansen, Thomas Cornelius. (2016). Airtightsenes of radon barrier: Testmethod (Lufttæthed af materialer til radonsikring: Testmetode). (SBi, Vol. 2016:21). 1. ed. Copenhagen: SBi. 27 p.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Modeling the Airborne Transmission of SARS-CoV-2 in Public Transport**

**Christina Matheis 1,\*, Victor Norrefeldt 1, Harald Will 1, Tobias Herrmann 2, Ben Noethlichs 2, Michael Eckhardt 3, André Stiebritz 3, Mattias Jansson <sup>3</sup> and Martin Schön <sup>3</sup>**


**Abstract:** This study presents the transmission of SARS-CoV-2 in the main types of public transport vehicles and stations to comparatively assess the relative theoretical risk of infection of travelers. The presented approach benchmarks different measures to reduce potential exposure in public transport and compares the relative risk between different means of transport and situations encountered. Hence, a profound base for the selection of measures by operators, travelers and staff is provided. Zonal modeling is used as the simulation method to estimate the exposure to passengers in the immediate vicinity as well as farther away from the infected person. The level of exposure to passengers depends on parameters such as the duration of stay and travel profile, as well as the ventilation situation and the wearing of different types of masks. The effectiveness of technical and behavioral measures to minimize the infection risk is comparatively evaluated. Putting on FFP2 (N95) masks and refraining from loud speech decreases the inhaled viral load by over 99%. The results show that technical measures, such as filtering the recirculated air, primarily benefit passengers who are a few rows away from the infected person by reducing exposure 84–91%, whereas near-field exposure is only reduced by 30–69%. An exception is exposure in streetcars, which in the near-field is 17% higher due to the reduced air volume caused by the filter. Thus, it can be confirmed that the prevailing measures in public transport protect passengers from a high theoretical infection risk. At stations, the high airflows and the large air volume result in very low exposures (negligible compared to the remaining means of transport) provided that distance between travelers is kept. The comparison of typical means of transport indicates that the inhaled quanta dose depends primarily on the duration of stay in the vehicles and only secondarily on the ventilation of the vehicles. Due to the zonal modeling approach, it can also be shown that the position of infected person relative to the other passengers is decisive in assessing the risk of infection.

**Keywords:** simulation; zonal modeling; SARS-CoV-2; public transport; airborne transmission; risk assessment

## **1. Introduction**

During the spread of SARS-CoV-2, it was found that transmission occurs primarily by virus-bearing particles [1–5]—consider the following three routes of transmission for SARS-CoV-2:


**Citation:** Matheis, C.; Norrefeldt, V.; Will, H.; Herrmann, T.; Noethlichs, B.; Eckhardt, M.; Stiebritz, A.; Jansson, M.; Schön, M. Modeling the Airborne Transmission of SARS-CoV-2 in Public Transport. *Atmosphere* **2022**, *13*, 389. https://doi.org/10.3390/ atmos13030389

Academic Editors: Ashok Kumar, Amirul Khan, Alejandro Moreno Rangel and Michał Piasecki

Received: 18 January 2022 Accepted: 23 February 2022 Published: 25 February 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

3. Transmission by direct contact with the virus through contact with an infected person or through direct contact with contaminated surfaces.

The difference between droplets and aerosols is the particle size or physical properties. While larger particles (>5 μm) sink to the ground more quickly, the smaller aerosols can remain in the air for a longer time and thus disperse in enclosed spaces. For example, a 5 μm aerosol takes 33 min to sink to ground from 1.5 m in resting air. Whether and how long droplets and aerosols remain suspended in the air depends on various factors such as temperature and humidity [2,6].

In the context of the SARS-CoV-2 pandemic, ways to minimize the risk of infection are constantly being sought. A minimum distance of 1.5 m from another person is recommended to minimize the likelihood of coming into contact with virus-containing droplets from a person infected with SARS-CoV-2 [7]. Partly because these distances cannot be maintained during rush hour, many people have health concerns about using public transportation. Despite implemented hygiene concepts, this has led to a significant decline in passenger numbers. Statistical data in the number of sold tickets in Germany reveal a decrease of 40–70% of passengers after the outbreak of SARS-CoV-2 in 2020 [8]. To counteract this effect, the effectiveness of current protective measures, as already elaborated in [9], is to be examined by means of simulations.

In [10], it is also shown that there is a great demand for research in the transport sector worldwide to counteract this effect. This includes some publications on infections with SARS-CoV-2 in public transport in USA, China, Japan and UK [10]. For example, in a Chinese study, a variety of protection measures in public transportation are developed, ranging from institutional requirements to personal protection and knowledge promotion [11]. However, the effect can only be confirmed in general terms. The authors of [12] conduct a systematic literature review on transmission in trains and buses and conclude that an empirical definition of the risk of infection is lacking observational data. Therefore, a model-based estimation of the risk based on the interior air, the travel duration and the passenger density is considered a beneficial approach. In [13], elaborate CFD flow simulations are performed in a car to determine infection risk. It is found that zero-dimensional approaches have limited applicability for an adequate assessment of risk in confined spaces, and that multidimensional approaches are necessary to represent complex fluid dynamics. The detailed consideration, however, does not allow the results to be transferred to other means of transport [13]. An approach to risk assessment in transportation based on simple geometry and the assumption of an ideally mixed space is shown in [14]. Nevertheless, these methods do not allow for a detailed comparison of all occupied areas in public transport taking into account airflows. In an experimental study on a train, [15] concludes that the carriage is not well mixed over its length but rather along its height and width. Hence, the location of a possibly infectious passenger is crucial for the infection risk, and a purely well-mixed assumption is not valid. Similar to these findings, virus exposure is considered locally resolved. The calculated exposures provide the basis for assessing the risk of airborne transmission of SARS-CoV-2 in public transportation and for evaluation of measures and recommendations. Here, the focus lies in understanding the dispersion of SARS-CoV-2 in indoor air and quantifying it assuming a SARS-CoV-2 infected passenger is on a train, bus or in a train station. Scenarios are simulated with adherence to the behavioral recommendations, such as wearing masks, avoiding speech and maintaining distances. The influence of ventilation in respect to fresh air rates and filtration efficiencies will also be investigated. With regard to a return to normality, scenarios without these measures are also considered.

A represented selection of the most important vehicle types of German public transport is being taken into account: long-distance trains and long-distance buses, regional trains, suburban trains, city trains and subway trains, streetcars and city buses. Furthermore, stations and stops are modeled both above and below ground. For model validation, CO2 measurements were used as field measurements in public transport, from which fresh air volumes can be back-calculated and verified against manufacturer data. In a previously

performed literature study, typical vehicle categories, information on possibilities and limitations of the system technology, information on aerosol dispersion, data on passenger numbers before and after start of the pandemic and documented transmissions of SARS-CoV-2 in public transport were determined and used for the simulations [16]. Through this approach, the gap can be closed between cited measurements or simulations for specific coaches and ventilation situations and the broad overview of meta-studies.

#### **2. Materials and Methods**

The applied modeling methodology is based on a zonal model, which is used to describe the indoor airflow [17]. In the model, a passenger infected with SARS-CoV-2 is inserted as a source. Starting from this, the dispersion behavior in different trains, buses and station types is determined. The main features of the modeling approach are presented below.

#### *2.1. Zonal Model*

The "Indoor Environment Simulation Suite" is a toolbox of different sub-models for the rapid simulation of indoor climate. The core of this toolbox is the "Velocity Propagating Zonal Model" (VEPZO) [17], which in many cases is a superior alternative to complex computational fluid dynamics (CFD) simulations. A trade-off between computational effort and level of detail of the result is chosen. It uses similar mathematical theories but divides the space into only 100 to 1000 volume zones [17]. Especially for considerations such as temperature and concentration fields in the interior, zonal modeling can achieve informative value similar to the detailed CFD simulations, but at lower computational cost. Therefore, the zonal modeling approach can be used for parametric studies. The model has been developed in the multi-physics modeling language Modelica [18], and the commercial software Dymola is used for solving of the model equations.

The VEPZO volume model implements the conservation of scalar quantities, such as mass, heat and tracer gas and particle/aerosol concentrations. Neighboring zones are connected by flow models in which the amount of exchanged air is calculated. By arranging the volume and flow models in three dimensions, space is represented zonally (Figure 1) to predict temperature, mass and airflow distribution.

**Figure 1.** Schematic 2D representation of a zonal model: subdivision of the space into zones (cubes) connected by flow models (grey).

A detailed description of the zonal approach comprising the flow and volume models can be found in [17]. In the volume model, the equations for conservation of mass, heat and tracer gases are set up. For mass conservation, the air volumes flowing across the six zonal boundaries (right, left, front, back, down and up) are added. In a steady state, the sum of all inflowing and outflowing air quantities is zero. For heat conservation, the internal loads and the enthalpies flowing across the zone boundaries are summarized in Equation (1) [17]. This results in the transient profile of the enthalpy. The temperature can be determined via the equations of the state of the air:

$$V\_i \cdot \rho\_i \cdot \dot{h}\_i = \sum\_{j=1}^6 \dot{m}\_j \cdot h\_{i/j} + \sum \dot{Q}\_{Source} \tag{1}$$

where *Vi*, *ρi*, . *hi* is volume, density and enthalpy change of zone *<sup>i</sup>*; . *mj* is mass flow from the adjacent zone (positive: inflowing, negative: outflowing); *hi*/*<sup>j</sup>* is enthalpy of zone *i* or *j*, depending on flow direction; . *QSource* is heat flow from sources, e.g., heat emission from persons, convective exchange with enclosing surfaces, etc.

The conservation equations for tracer gases, particles and aerosols in the air are implemented analogously to enthalpy conservation. Since emitted human viral particles have been shown to be capable of remaining airborne for extended periods [19], deposition was not considered in the simulation. This approach is considered conservative. In common zonal models, the airflow between two zones is calculated using the Bernoulli equation. In the VEPZO model, however, the acceleration of the flow in the flow paths is calculated in order to avoid the numerically unstable square root function of velocity vs. pressure difference. To model the losses of the flow, a viscous term is introduced. The flow model takes into account the air fluxes between the neighboring zones and calculates the mass flow to be exchanged via the pressure, momentum, height difference and the viscous loss term. The effective viscosity is a calibration parameter of the model, and it has been concluded that 0.001 provides good results [17]. To calculate the flow velocity, Equation (2) sums up the forces acting on the flow path and determines the resulting acceleration of the flow. The equation underlying the flow path is shown for the x-coordinate but is correspondingly valid for the other Cartesian coordinates:

$$\dot{u} = -\frac{\Delta p\_{i,j} + \Delta \left(u^2\right)\_{i,j} + g \cdot \Delta z\_{i,j}}{\Delta x} + \frac{\mu}{\rho} \cdot \left(\frac{\Delta \frac{\partial u}{\partial y}}{\Delta y} + \frac{\Delta \frac{\partial u}{\partial z}}{\Delta z}\right) \tag{2}$$

where . *u* is acceleration of air in the x-direction (in the steady state 0); Δ*pi*,*j*, Δ *u*2 *<sup>i</sup>*,*<sup>j</sup>* and Δ*zi*,*<sup>j</sup>* are pressure difference, difference of velocity squares and height difference, respectively, between zones *i* and *j*; *g* is 9.81 m/s2; *ρ* is density of flowing air; *μ* is calibration parameter for effective viscosity (0.001).

#### *2.2. Model Development and Evaluation*

The Thermal Model Generation Tool is a self-developed tool used for model generation [20]. Starting from a geometry file of the simulated interior, the zoning in x-, y- and z-directions is defined, and the location of flow sources and sinks as well as heat loads are determined. The tool then automatically generates the Modelica source code of the zonal model. After defining the source intensities and the thermal resistances of enclosures, the exported model is ready for simulation. The described workflow is shown in Figure 2.

The airborne exposure to potentially infectious material inside vehicles and at stations was evaluated in particular. To represent the airborne SARS-CoV-2 spread, the so-called quanta notion was used. This is a description of the amount of virus emitted by a person infected with SARS-CoV-2 and is based on [21,22]. By definition, a vulnerable person has a 63% risk of getting infected after inhaling the dose of one quanta. This definition was set out for the initial SARS-CoV-2 virus, to the best of our knowledge, how mutations change this rate is not defined. The advantage of this approach is that, regardless the dominant mutation of SARS-CoV-2 or any other airborne infectious disease, the general conclusions on protective means and their efficiency remain valid. Therefore, the theoretical risk assessment in this study is based on the inhaled quanta-dose. The calculated quanta concentration is exported as a result for each individual zone and presented as a numerical value. In addition, the concentration predicted in simulation is deposited as a color gradient, as shown in Figure 3, from green (from 0 mili-quanta/m3) to yellow (at 20 mili-quanta/m3) to red (from 50 quanta/m3).

**Figure 2.** Indoor Environment Simulation Suite (IESS) workflow.


**Figure 3.** Example of evaluation/representation of the simulation: shown is the concentration in mili-quanta/m3 in a section through the compartment at breathing height.

The inhaled dose at selected locations is determined by integrating the concentration over the residence time, weighted by the respiratory volume and the protective effect of masks, as shown in Equation (3). The neighboring zone of the emitter with the highest concentration (max. dose) and a zone far away from the emitter (min. dose) are evaluated in each case. As a measure for the dose, the mili-quanta is used, where 1000 mili-quanta correspond to one quanta.

$$Dose = \dot{V}\_{Breatling} \cdot f\_{Mask} \cdot \int\_{t\_{start}}^{t\_{end}} c\_i(t)dt \tag{3}$$

where . *VBreathing* is breathing volume, here 540 L/h (light, sedentary work, [23]); *fMask* is self-protection effect depending on mask type (Section 2.3 Boundary Conditions); *ci*(*t*) is time-resolved course of concentration in the evaluated zone *i*; *tstart* and *tend* are start and end of exposure, respectively.

#### *2.3. Boundary Conditions*

#### 2.3.1. Viral Load

In the following, a theoretical risk of infection is assumed for everyone present in the vehicles without knowledge of personal risk factors. To assess whether an infectious human should be modeled by aerosol, particle or quanta emission rates, a comparison in Figure 4 was performed [16].

**Figure 4.** Relative comparison of approaches to describe the emitter as a quanta, particulate or aerosol source.

Speaking loudly corresponds to 100%. Depending on the observation, breathing equals 2–4% of the emissivity of speaking loudly and talking equivalent to 16–23%. Thus, an approximately constant gradation between activity levels is expected independent of the selected source term. The relative proportions between breathing, talking and speaking loudly are quite close (Table 1). That is, regardless of how the source is modeled, the relative outcome between the different activity levels remains similar.



The quanta doses recorded in different scenarios are compared with the assumption that a higher dose intake always leads to a higher risk. The emission strength is given in quanta/h for different activity levels. An Excel calculation tool [24] fixed the following listed mean emission rates:


These values are implemented as a unidirectional source in the model.

#### 2.3.2. CO2 Emission

For model validation against in situ measurements, it was necessary to use an airborne tracer that is commonly found in transport vehicles. CO2 is a reliable tracer gas emitted by passengers and thus allows, together with the passenger count, an estimation of the fresh airflow rate supplied to the cabin. To measure the CO2 concentration in transport means, a Rotronic CP11, 0–5000 ppm with accuracy of ±30 ppm/±5% was used. Passengers were accurately counted where feasible (especially in long-haul transport) or estimated (e.g., quarter filled, half full, especially in local transport). For model validation an emission rate of 18 L/h is assumed per passenger [28].

#### 2.3.3. Masks

Wearing masks is considered an effective measure to reduce the spread of SARS-CoV-2. A recent review [29] also recommended the wearing of masks in public places. Therefore, the following three mask types were included in simulations:


In each case, the simulation of mask types includes the protective effect during exhalation (i.e., a percentage reduction in the source term) and the protective effect during inhalation (i.e., a reduction in the absorbed dose). Average values for the mask types are considered in the simulations as given in Table 2, however, a higher protective effect [24,30] can be achieved with correct handling. To compare the three different mask types, it is assumed that everyone in the vehicle or on the station wears the same mask type.

**Table 2.** Reduction effect through masks [31].


#### 2.3.4. Ventilation

Depending on the operational condition, different modes of ventilation are implemented in the models. Generally, the supply air in public transport is a mixture of fresh air, which is free of SARS-CoV-2 pathogens, and recirculated air, with the viral load of the return air of the vehicle. Typical filters used today on trains are not of sufficient quality for viral particles. In the case studies, hypothetical filter implementations were considered, taking into account that changing the filter to HEPA in an existing system will lead to reduced flow. In the model, the filter is described as a sink with a certain efficiency, i.e., the viral load downstream is reduced by a factor from the upstream load. The magnitude of flow reduction and realistically achievable filter efficiencies was provided by experts within the research group. Any filtering and purification devices reduce the pathogen concentration in the recirculated air by a certain percentage. For example, if a filtering effect of 80% is assumed, the recirculated air in the model will have a residual pathogen concentration of 20% compared to the exhausted air.

In addition, the air exchange through the open doors is implemented in the model. The main driver for this is the temperature difference between the interior and the outside air. When the door is opened, this causes cool air to enter the cabin through the lower area of the door, while warmer air leaves the cabin through the upper area. The formulas for temperature-driven air exchange at a rectangular opening are derived from [32].

$$\dot{V}\_{dorr} = \frac{1}{3} \cdot \mathbb{C}\_D \cdot B \cdot \sqrt{\frac{\Delta T \cdot \text{g} \cdot H^3}{T\_m}} \tag{4}$$

where . *Vdoor* is volume flow through the open door; *B* is width; *H* is height; Δ*T* is temperature difference; *Tm* is mean temperature; *g* = 9.81 m/s2; *CD* = pressure loss coefficient.

*CD* is the pressure loss coefficient and ultimately describes the flow resistance of the door opening. As a typical, conservative assumption, the value of *CD* is considered as 0.4. The indoor temperature of 23 ◦C, the outdoor temperature of 16.6 ◦C for the summer and 9.1 ◦C for winter (Germany-wide average) is assumed [33]. The outdoor temperature in the subway tunnel was estimated to be 15 ◦C based on measurement (27 January 2021, Munich, Sendlinger Tor subway station). The airflow calculated by Equation (4) during the door opening times serves as input for a ventilation source in the model.

Openable windows were not modeled. Since the infection situation is most critical in winter, windows are usually closed at this time of year for comfort and energy efficiency reasons. If a window is opened in practice, additional air exchange takes place, which results in a lower risk of infection. The simulations thus correspond to a worst-case scenario. In addition, their shape varies greatly, and the actual opening is difficult to model in practice.

#### 2.3.5. Partition Walls

Partition walls as flow obstacles are implemented in the model by reducing the crosssection area of the geometrically closest flow path. In the case of an airtight partition, the corresponding flow path and thus the air exchange between the affected, neighboring zones are removed from the model. Thus, seat surfaces and backrests that affect the airflow are considered in the model.

#### 2.3.6. Occupancy Density

The occupancy density is used as a parameter for heat release in the interior. For air conditioning and ventilation systems operated in fixed-volume flow mode, the occupancy density does not influence the supply airflowrate. In demand-controlled systems (e.g., the high-speed train ICE), the fresh air volume adjusts to the occupancy. For the passenger density at the stations, it is assumed that there is a train on each side of the platform. The number of people is therefore made up of the passengers who get on or off both trains at the same time. A typical capacity utilization of the trains in pandemic periods was applied [16]. Simulations focus on the airborne spread of infectious matter, hence it is intrinsically assumed that the distance between passengers is large enough to inhibit direct particle transmission.

#### *2.4. Determination of Train, Bus and Station Types*

In order to make a representative selection of train types, a survey was carried out on the number and characteristics of the train stock in Germany [16]. Furthermore, the selection was based on the availability of operational data and the possibility to conduct validation measurements on the modeled vehicles. Table 3 shows the selected types and the criteria by which these types where chosen. In cases where no detailed data on ventilation were available, data from these measurements were used and determined using CO2 balancing equations.


**Table 3.** Representative trains, buses and stations based on research and statistical analysis.

If similar ventilation systems are installed for the train types not considered here, the simulated results can also be transferred to these. For this purpose, the fresh and recirculated air volumes, the form of air injection and the driving cycle must be compared with the input data used here.

As an estimate of whether the distance of 1.5 m can be maintained to exclude transmission by large particles, the maximum occupancy density possible for this purpose is determined. A circle of 1.5 m diameter requires an area of 1.76 m2. It corresponds to a maximum occupancy density of 0.56 passengers/m2, neglecting areas that cannot be used by passengers. The number of passengers for the considered means of transport in the pre-pandemic phase was ascertained from German operator data [42–48] and statistical information [8]. The reduction of travelers during the pandemic was determined from [16]. In general, it can be assumed that the minimum distance of 1.5 m can only be maintained in selected cases, such as in low-occupancy vehicles at night or on secondary routes. For this reason, it is deemed necessary to wear a medical mask or mouth-nose protection (MNP). Both terms are used synonymously in the following. Additionally, simulation cases with stronger-filtering FFP2 masks were included to take into account that some regions impose this type of mask.

#### **3. Simulation**

In the simulation, it is assumed that an infected person is present in the transport vehicle or on the platform. Based on this, the exposure in the near field and in the wider environment of the emitter is calculated. The virus is assumed to be airborne. Pathogen transmission through surfaces (smear infection) is not modeled because findings consistently show only low levels of viral load on surfaces [16].

The simulation study included eight different means of public transport and two types of train stations, with the typical travel time determined for the respective means of transport. The typical maximum time spent on the platform (8 to 35 min) was taken from [49]. The models and corresponding input data were validated with existing manufacturer data or by CO2 measurements. In each case, the evaluation is performed concerning the activity (breathing, talking and loud speaking) of the SARS-CoV-2 infected passenger and by mask type (without mask, MNP and FFP2). Then the influence of air filtration and the amount of fresh air is considered. In addition, the heating and cooling scenarios in the respective means of transport are examined to observe a possible influence on the airflow pattern. The effect on exposure of introducing compartments in comparison to the saloon coach was also investigated.

#### *3.1. Input Data*

For zonal modeling, the geometry of the selected means of transport are divided into small zones. Depending on the geometry and interior design, 8–17 zones in the x-direction (longitudinal) and 4–5 zones in the y-direction were created. The height is divided into five zones in each case (cf. Figure 5). In comparison, the zones in the models of stations are significantly larger to represent areas shown in Figure 6. The zones surrounding the emitter are 5 m long in their largest extension.

In heating mode, the air is supplied mainly through the floor area and is extracted through the ceiling. In cooling mode, air is supplied from the ceiling (cf. Figure 5). This results in different flow characteristics in the coaches. Depending on the train type, recirculation air is aspired in a dedicated outlet or from the exhaust air ducting. According to the operators, no distinction is made between heating and cooling cases in buses and tramways.

**Figure 5.** Zonal model of the ICE 4 with sources and sinks for heating (**top**) and cooling (**bottom**) mode: light green arrows, supply air; dark green arrows, exhaust air; red-marked person, emitter.

**Figure 6.** Simulation models of the train hall section (**top**) and an underground station using the example of Munich Central Station and the Odeonsplatz (U3/U6 subway station) in Munich (**bottom**).

For the train station hall, two cases were considered as flow boundary conditions. One case is characterized by the mean wind speed from the direction NW to SW at 3.3 m/s according to reference weather data in Munich [33]; the other case is purely thermally driven, with an assumed temperature difference of 1 K. This is an assumption. However, it is expected that waste heat from trains, lighting and passengers, as well as solar heat input may well lead to an increase in temperature in the building. The formula according to [32] was again used to determine the resulting airflowrate. For the evaluation of a subway station, a mean flow velocity through the two tunnel tubes of 2 m/s was assumed as a boundary condition. This value is the time average of any flows created by the stack effect and the piston ventilation effect that incoming trains have (Z. Kebdani, personal communication, 5 February 2021) [50].

To consider the effects of door opening in the simulations, travel profiles for the various means of transport were derived (Table 4):


**Table 4.** Typical travel profiles and durations of stay in the different means of transport and stations.

#### *3.2. Validation*

The models were validated using measured CO2 concentrations from field measurements. For example, measurement was carried out on the Munich–Erfurt route in an ICE 4 to validate the long-distance train (Figure 7). Shortly before Erfurt, the trains pass through a tunnel, where the fresh air supply is interrupted to avoid the pressure surge in the cabin. Figure 7 shows the measured (black, dashed) and simulated (black, solid) CO2 concentration. Overall, there is good agreement between simulation and measurement, with a maximum deviation of about 150 ppm at time 60 min. Later, it was found that there is also a tunnel at that time, shortly before Nuremberg, which could lead to the measured CO2 peak.

**Figure 7.** Comparison of measured and simulated CO2 concentration on Munich–Erfurt route in an ICE 4.

The validation of the remaining models was performed similarly to the long-distance train. The occupancy in the means of transport during the measurements was estimated based on recordings of the measurement team. The actual amount of fresh air was determined based on CO2 measurements and occupancy. The validation of the zonal model of the regional train and the suburban railroad was carried out based on extensive flow simulations by the manufacturer, Bombardier Transportation. It could be shown in all models that the zonal simulation approach used here is suitable to represent the temperature distribution and thus the indoor climate in the train. For the validation of the above-ground

station, CO2 concentration was measured at the Munich Central Station. However, the measured values were so close to the outside air that a meaningful validation is impossible.

#### *3.3. Main Results of Flow Simulations*

The activity levels of breathing, speaking and speaking loudly, without a mask or with a MNP or FFP2 mask were considered. A concentration profile was created for each simulation. Figure 8 shows an example of the concentration distribution in the horizontal section at head height (approx. 1.1 m) of an ICE large-capacity coach for the case of a speaking infected passenger in the case of HVAC heating at 50% occupancy. It is clear that around the emitter (zone marked with a red oval), there is a higher concentration of up to 32 mili-quanta/m3, while farther away in the wagon it is 13 to 19 mili-quanta/m3. The reason for the presence of some infectious material in the distant field is the shape of recirculated air because of the ventilation in the coach.


**Figure 8.** Example of concentration distribution in mili-quanta per m3 for the case "HVAC heating, 50% occupancy, talking, without mask" in ICE.

Integrating the concentration from Equation (3) throughout the trip yields the determined inhaled dose. For each simulated case, the minimum dose farther away and the maximum dose at the seats adjacent to the infected passenger are evaluated.

Figure 9 represents the results of minimum and maximum inhaling of infectious material in different speaking and mask wearing scenarios after 2.5 h in an ICE. Without wearing masks, the maximum doses are columns 1, 2 and 3 for breathing, speaking and loud speaking, respectively. The worst-case scenario of loud speaking is considered for MNP and FFP2 masks, where the maximum doses are columns 4 and 5, respectively. For the FFP2 mask, the massive reduction in values is due to pathogen filtering during both exhalation and inhalation. These ratios are valid for all types of transport means and stations.

**Figure 9.** Comparison of inhaled dose in mili-quanta after 2.5 h in ICE with an infected person during different activities (breathing, talking or speaking loudly) of the emitter and with different mask types (none, MNP or FFP2): min. dose, minimum dose absorbed farther away from the emitter; max. dose, maximum exposure that is absorbed close to the emitter.

A comparison of the different ventilation scenarios shows in all means of transport that a similar maximum dose is reached in the vicinity of the emitter with the same supply air quantities. Farther away from the infected person, however, the minimum dose increases as the proportion of outdoor air decreases. The Figure 10 shows the inhaled doses at different ventilation rates as an example case for the ICE. Here, for example, a demand-driven reduction in the fresh air rate from 1500 m3/h to 500 m3/h due to lower occupancy results in a 3.4-fold increase in exposure farther away. In contrast, ventilation with pure, fresh air leads to a 90% reduction in exposure farther away from the emitter.

**Figure 10.** Influence of fresh air and recirculated airflowrate on the amount of exposure for the ICE: min. dose, minimum dose absorbed farther away from the emitter; max. dose, maximum exposure that is absorbed close to the emitter.

For the consideration of recirculating filtered air, a filter effectiveness of 80% towards SARS-CoV-2 was assumed in accordance with the current state of technology. As a result of the increased pressure drop across the filter, there is an assumed reduction in air volumes of 10%. Figure 11 shows the reduction of the exposure due to filtration.

**Figure 11.** Influence of filtering on the amount of exposure: min. dose, minimum dose absorbed farther away from the emitter; max. dose, maximum exposure that is absorbed close to the emitter.

In the areas farther away from the infected person, the reduction of the inhaled quanta amount is between 80% and 90% in all cases. In the close-up area, the supply of fresh air has a significant influence on the quanta concentration in the air. The better the area is ventilated, the more the emissions can be diluted and the concentration decreases. In the case of streetcar ventilation, at 34%, the proportion of recirculated air is the lowest in comparison with the other vehicles. Here, the main effect is the lower amount of supply air in case of filtering in the close range of the infected person. The emissions are less diluted, resulting in an increase of the quanta dose in the vicinity.

Table 5 presents the inhaled dose for breathing activity of the emitter in the different means of transport. When speaking loudly, the values from Table 6 are obtained. For the comparison of the individual means of transport, the worst-case heating scenario with minimum fresh air supply was selected. In the case of the train station hall, the unfavorable case of thermal-buoyancy-driven flow bya1K temperature difference is chosen for comparison.


**Table 5.** Absorbed dose in mili-quanta when breathing at close proximity (max. dose) or farther away from the emitter (min. dose) for the assumed durations of stay.

**Table 6.** Absorbed dose in mili-quanta when speaking loudly at close proximity (max. dose) or farther away from the emitter (min. dose) for the assumed durations of stay.


*3.4. Further Simulations*

For a fully occupied long-distance train, the presence of an infected person in a compartment is investigated. For this purpose, walls were introduced in the model around the emitter's seating group. Due to pressure equalization, overflow is possible through joints or gaps, for example, through doors. It is assumed that a fraction of exhaust air from the compartment is supplied to the rest of the coach by the central air recirculation system. Figure 12 shows the concentration distribution when the emitter speaks loudly without a mask in a compartment. Compared with the large-capacity coach, the concentration peak is confined to the compartment. In the area outside the compartment, the recirculating air is the cause of dispersion, and a result similar to the large-capacity coach is obtained. Figure 13 compares the inhaled dose. Other passengers in the compartment are exposed to a dose almost two times higher than in the large-capacity coach. On the other hand, numerically, fewer persons are affected. The optimum protection for persons outside the compartment would theoretically be achieved by a decentralized air recirculation system, but this would mean that each compartment would need its own ventilation system.


**Figure 12.** Concentration distribution in mili-quanta/m<sup>3</sup> for the case "Speaking loudly, without mask" in the ICE with compartment formation around the emitter.

**Figure 13.** Comparison of the absorbed quanta dose in a large-capacity railcar (**left**) versus a compartment (**right**): min. dose, minimum dose absorbed farther away from the emitter; max. dose, maximum exposure that is absorbed close to the emitter.

#### *3.5. Risk Assessment*

In all cases, the highest protective effect is obtained by wearing an FFP2 mask by all passengers. This measure provides both good third-party protection and high selfprotection. In addition, speaking loudly should be avoided. This represents another way of releasing as small an amount of infectious material as possible. Filtered recirculation reduces the emission load farther away from the emitter. In contrast, the load closer to the infected person decreases only slightly or may have a slightly higher concentration peak due to the associated reduction in airflow. Operation with pure fresh air at a lower total flowrate results in a higher concentration peak in the area of the emitter but reduces the exposure to passengers farther away. Since in reality the infected person remains unknown to fellow passengers, the highest possible level of self-protection is advisable for every passenger.

The comparison makes it clear that only the consistent use of an FFP2 mask can achieve values in the near and far range of the emitter in the lower range of the probability of infection with the original SARS-CoV-2 virus reported from the observational study. Speaking loudly significantly increases exposure by a factor of about 28 and thus indirectly increases the theoretical risk of infection. The recommendation to avoid loud talking in all public transport as a risk-reduction measure can be justified because it is expected that this also worsens the fit of the mask [52]. In addition, masks should only be removed as briefly as possible for eating or drinking. Technical measures, such as increasing the fresh air rate or recirculating filtered air limit the area of spread and thus reduce the risk of infection farther away from the emitter.

A direct derivation from the level of exposure to a possible medical risk from the quanta dose determined in each case is not considered possible. However, Ref. [53] gives indications on the risk of infection in Chinese high-speed trains in the period December 2019 to March 2020. The study also distinguishes between exposure in the close range of the emitter and in the more distant range. The assumption is made that the Chinese high-speed trains are ventilated in a basically similar way to the German ICE trains. Thus, the risk of infection in the ICE can at least be classified. Due to cultural customs, it can at best be assumed that people in Chinese trains speak quietly and never loudly. Whether the Chinese passengers were wearing MNP at the time and to what extent cannot be determined. However, wearing MNP in public transport was quite common in Asia even before the pandemic. Therefore, the comparison can only serve as an orientation. Another limitation is that the study refers to the original SARS-CoV-2 variant. Over time, however, the apparently more contagious mutations dominate the infections. With these assumptions and limitations, the probability of infection can be narrowed down for the original SARS-CoV-2 in such a way that the risk of infection lies in the range of 0.14% to 3.5% when 0.6 to 40 mili-quanta are inhaled. For this purpose, the dose range (Figure 14) between "Breathing without MNP" and "Talking with MNP" for the HVAC heating case with high occupancy was colored in the diagram.

**Figure 14.** Comparison of the dose in mili-quanta determined in the simulation in the area farther away from the infected person compared to the determined probability of infection according to Hu et al. [53].

Assuming that the ventilation system is similar to the bus considered here, a comparison with documented contagions during bus trips indicates that a substantial risk of infection may exist. For example, during a 2.5 h bus ride, Ref. [54] described eight additional infections attributable to an infected person. The infected persons were both close to and farther away from the infected person. The authors of [55] investigated infections during a total 1 h 40 min pilgrimage of Buddhist believers in a bus. Here, 24 of 68 passengers later tested positive for SARS-CoV-2. Both studies indicate that the buses were ventilated with a recirculating air component. Since the studies consider individual

cases, it is not possible to make a generalized estimate of risk, as is the case for high-speed trains [53]. The studies do not include averages over several journeys or information on journeys with infected persons without contagions. Moreover, it cannot be excluded that the index persons were super emitters, i.e., their emission is higher by a factor of 10–100 than assumed in the simulations shown here. Thus, the exposure for other passengers would also have been correspondingly higher. Nevertheless, the studies impressively show that contagions cannot be ruled out even for the scenarios simulated here.

#### **4. Results**

Potential exposure to SARS-CoV-2 via aerosols is detailed for each mode of transportation in Section 3. Figures 15–17 compare the cases "breathing without mask", "speaking with MNP" and "speaking loudly with FFP2". The respective times spent in vehicles were estimated due to the lack of available data (Table 4). For the selection, a reference ventilation case or cases actually measured in operation were selected.

Figure 15 shows that, particularly in means of transport with a high proportion of recirculated air, an increased quanta dose can also be absorbed farther away from the emitter (min. dose). Near the emitter, this also applies to means of transport without recirculation. Figure 16 demonstrates that the combination "talking with MNP" leads to an increased exposure compared to "Breathing without mask". Figure 17 shows that even speaking loudly with an FFP2 mask results in a lower dose than breathing without a mask.

A significant reduction of the dose and thus of the risk results from the use of MNP or FFP2 masks, as well as from not speaking loudly. Refraining from loud speech leads to a reduction of the quanta emission of about 80%. The consistent wearing of an FFP2 mask by all passengers causes a reduction of the inhaled dose of 99%. If passengers use MNP, the reduction is only 65%. The zonal modeling approach can also be used to show that the location of the infectious passenger in relation to others plays a major role for the spread and exposure.

In addition, discrepancies between expected and actual ventilation were found in some measurements. The reduced supply of fresh air leads to a significantly higher infection risk, especially in the vicinity of the infected person.

**Figure 15.** Comparison of typical means of transport considered for the case "breathing without mask": min. dose, minimum dose absorbed farther away from the emitter; max. dose, maximum exposure that is absorbed close to the emitter.

**Figure 16.** Comparison of typical means of transport considered for the case "Talking with MNP": min. dose, minimum dose absorbed farther away from the emitter; max. dose, maximum exposure that is absorbed close to the emitter.

**Figure 17.** Comparison of typical means of transport considered for the case "Speaking loudly with FFP2": min. dose, minimum dose absorbed farther away from the emitter; max. dose, maximum exposure that is absorbed close to the emitter.

#### **5. Discussion**

This study deals with the risk of essentially airborne transmission of SARS-CoV-2 in public transport. The simulations allow the assessment of the potential exposure in the near and far field when travelling with an infected passenger. A direct conclusion from the exposure in a coach to a percentage risk, however, is not possible. An analogy comparison between the study from Hu et al. [53] on infections in Chinese high-speed trains and with the simulation results of the ICE from Section 3.3 provides at least an estimate. Through this analogy consideration, it is shown that there is also a risk of infection with SARS-CoV-2 when using rail- and road-passenger transport. This risk is different for different scenarios but can, to a large extent, be mitigated by technical measures such as recirculation air filtration, increased fresh airflow and by personal behavior such as mask wearing and refraining from loud speech. For example, the highest theoretical risk of infection are for routes with a longer duration, no masks and loud speaking, as determined based on the comparatively high quanta dose. More infectious mutations of the Sars-CoV-2 virus and the vaccination or infection of large fractions of the populations have, to some extent, outdated the risk assessed by Hu [53]; nevertheless, the general conclusions of this simulation study remain valid.

For the exposure calculations, the quanta approach was chosen because this term does not attempt to model, for example, the flight dynamics of particles. From these calculations, it is evident that a significantly lower dose is achieved on the platforms of the stations investigated compared to the interior of the respective means of transport. On the one hand, this can be attributed to the relatively short stay of only a few minutes and on the other hand to the good ventilation. In accordance with the current scientific literature (e.g., [56]), no higher theoretical risk of infection is found in outdoor areas, in this case in the area of the train station hall. Provided that the minimum distance can be maintained, it is, therefore, possible to dispense with the wearing of an MNP or an FFP2 mask in outdoor areas.

In the confined areas, and if the required minimum distance cannot be maintained, there is a theoretical risk of infection. In these cases, further measures should be taken to reduce the risk, e.g., wearing a mask to prevent direct droplet infection. FFP2 masks show a higher reduction in both emission and inhaling of infectious material compared with surgical MNP. For this reason, they are more suitable for both third-party and self-protection.

#### *5.1. Influence of Input Parameters*

It should be taken into account that the study described here investigates the mean emission of a SARS-CoV-2 infected person during different activities (breathing, talking or speaking loudly) and using different masks (none, MNP or FFP2/N95). Here, it is always assumed that all passengers wear the same type of mask for the entire trip. Mixtures of mask types give results between the cases considered. So, for example, if the emitter has an MNP and the person taking in the dose has an FFP2 mask, the dose taken in can be expected to be between the "MNP" case and the "FFP2" case.

There are reports of so-called super emitters, who emit up to 100 times more than a normal emitter [57]. In the simulation, this would likewise lead to a factor of 100 higher dose uptake. In the case of the reported infections in public transport, it is unknown whether these are due to "normal" or super emitters. The impact of a super emitter in this simulation would be a factor of 100 higher; the relative ratios of the measures to each other would be unaffected.

#### *5.2. Influence of Compliance*

The simulations assume full compliance of rules by the passengers, i.e., the rules for wearing MNP or FFP2 and refraining from loud speech. Obviously, unruly passengers would lead to a situation closer to the case of no-mask with elevated speech in terms of source intensity and/or infectious matter uptake.

#### *5.3. Influence of Occupancy*

One limitation of this study is that the actual risk of presence of one infected passenger is not known. Thus, even though intuitively a higher occupation will result in higher risk of presence of an infected passenger, this cannot be quantified. Therefore, in demandcontrolled ventilation cases, the trade-off between higher occupancy reducing airborne transmission due to increased ventilation and the increased risk that one of the passengers actually is infected is not possible.

Due to the lack of quantification, the occupancy density in the sense of the probability of the presence of a passenger infected with SARS-CoV-2 as a risk factor is thus not evaluated in this study.

#### **6. Conclusions**

The study investigates the theoretical risk for infection with SARS-CoV-2 in public transport using dispersion modeling in different vehicles and train stations. The actions (breathing, talking and speaking loudly), as well as the preventive measures (masks, filtering recirculating air and fresh air operation), are used to determine the risk assessment based on the definition of an infected passenger in the model. It is shown that the risk is reduced most efficiently if loud speaking is avoided and a FFP2 (N95) mask is worn correctly. Only these two measures create a reduction of the virus load of over 99% for both those in the close range of the infected person and those farther away. Thus, the already known protective measures, such as keeping quiet and using masks, can be confirmed in this study. Technical measures, such as recirculating filtered air further reduce the exposure to other passengers in the close range by 30–69% and farther away in the same vehicle by 80–91% (except in the streetcar/tram, where near-field exposure is increased by 17% due to filter-related reduced airflow). Higher fresh air rates also lead to a decrease in exposures in the broader environment. The study shows that near-field exposure cannot be eliminated, no matter how good the ventilation is. However, the refurbishment of trains and buses with HEPA filters in the recirculation air would lead to a clear reduction of other passengers' exposure. In addition, operators should absolutely avoid decreasing fresh air ventilation rates during operation. More broadly, these findings show that local protection can only be achieved locally (mask wearing), whereas central protection (filtration) mainly is effective more distant from the source. Hence, future research and development should focus on how technical solutions could act locally, for example by using partitions or ionization for the supply air. Analysis of the space needed to comply with the distance rules reveals that the distances cannot be met inside the vehicles. Therefore, the mask requirement should remain in place to protect against transmission by droplets. Compared with the risk inside the means of transport, the exposure on the platforms of the stations is considered minor. Particularly on above-ground platforms and provided that the recommended minimum distance of 1.5 m can be consistently maintained, the wearing of an MNP/FFP2 mask is temporarily dispensable, or an interruption of the mask requirement is justifiable. The inhaled quanta doses in the various means of transport mainly depend on the time spent in the vehicles. The ventilation of the transport vehicles also has an impact but is subordinate to the time component.

Even though new mutations of the SARS-CoV-2 virus and the increased immunity of large fractions of the population have altered the initial risk of infection, the general conclusions in this paper are considered valid.

**Author Contributions:** Conceptualization, C.M., V.N. and H.W.; methodology, V.N.; software, C.M.; validation, C.M.; formal analysis, V.N.; investigation, C.M. and V.N.; resources, T.H., B.N., M.S., A.S., M.E. and M.J.; data curation, T.H., B.N., M.S., A.S., M.E. and M.J.; writing—original draft preparation, C.M.; writing—review and editing, C.M. and V.N.; visualization, C.M. and V.N.; supervision, H.W.; project administration, H.W.; funding acquisition, H.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Deutsches Zentrum für Schienenverkehrsforschung beim Eisenbahnbundesamt grant number 2020-33-S-1202.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** No applicable.

**Acknowledgments:** This study was commissioned by "German Center for Rail Transport Research (DZSF) at the Railroad Federal Office". The authors are responsible for the content of this publication.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

