Indoor Air Quality Diagnosis Program for School Multi-Purpose Activity and Office Spaces

Abstract

This study presents a simple indoor air quality diagnosis program for school office spaces, which are occupied for long durations by teachers, and indoor sports facilities, whose utilization has been on the rise in response to high concentrations of pollutants in outdoor air. The proposed program was made with Visual Basic for Applications (VBA) and Microsoft Excel. This program requires inputs which can be easily determined or measured even by nonexperts and can check the current status of indoor air quality such as CO₂ and PM_2.5 concentrations and predict the effect if changes are made. In addition, it is possible to diagnose indoor air quality before and after class and compare it with the initial plan so that if it exceeds the indoor air quality maintenance standard range, it can be improved by using a ventilation system and an air purifier. The development of the program was divided into four stages. First, prior research on the influencing factors was investigated. Second, influencing factors affecting the changes in PM_2.5 and CO₂ concentrations were selected by category to accommodate the various factors, and those selected as input were presented. Third, mass and concentration conservation equations were utilized to derive PM_2.5 and CO₂ concentration prediction equations according to activity and passage of time, and a VBA code was used for constructing the program. For verification of the developed program, the calculation results were compared with the measured data. The mean absolute percentage error (MAPE) was 19.47% for PM_2.5 concentration. In order to improve accuracy, Simulation 2, in which the wind speed and indoor/outdoor air pressure difference are corrected, is presented. The MAPE of PM_2.5 concentration by the corrected Simulation 2 was lowered 5.15%.

1. Introduction

The annual average concentration of fine particulate matter (PM_2.5) in South Korea was 18 µg/m³ in 2021, which was the lowest since 2015 due to seasonal management, main sources management (including industry, power generation, and transportation), the government’s heightened concern about this issue, and the impact of COVID-19 (Figure 1a) [1,2,3]. However, this amount still exceeds the recommended emission level provided by the World Health Organization (WHO) global air quality guidelines on PM_2.5 (Figure 1b) [3,4,5].

Despite active governmental management and regulations, the annual concentration of PM_2.5, which is a representative air pollutant as well as a Group 1 carcinogen causing and worsening respiratory and cardiovascular diseases, has been consistently high (Figure 2a) [6,7,8].

This rise has increased the death rate due to respiratory and cardiovascular diseases both worldwide and in South Korea, negatively affecting the daily lives of children, who are particularly vulnerable to air pollutants (Figure 2b) [9,10,11,12].

Because the daily lives of children and the elderly are affected by the rise in the concentration of PM, the South Korean government has classified children, students, and the elderly as vulnerable to PM [13]. In particular, the respiratory volume of children is high due to their body structure and behavioral and developmental characteristics, causing them to inhale a relatively high amount of air pollutants [14,15].

Figure 2. (a) Increases in death rate by disease according to the rising PM₁₀ and PM_2.5 concentrations [10]. (b) Application rate for each method of coping with PM in the elderly and children [12].

Figure 2. (a) Increases in death rate by disease according to the rising PM₁₀ and PM_2.5 concentrations [10]. (b) Application rate for each method of coping with PM in the elderly and children [12].

To protect children, South Korean authorities are updating guidelines and standards for dealing with fine dust in schools each year in preparation for the increase in fine dust concentration [13,16,17]. According to the Air Pollution Response Manual, schools, including kindergartens, should prepare and implement an alternative plan for outdoor classes considering the situation of high outdoor concentrations of PM, consider shortened classes upon air quality alerts based on high PM levels, and hold outdoor physical education classes in indoor sports facilities [6,13,16,17].

The School Health Act was updated with special cases concerning the Maintenance and Management of Air Quality in Articles 4-2 and 4-3 in April 2019 in response to the increased utilization of indoor school facilities [18]. These newly established standards are dedicated to classrooms, providing no detailed rules regarding other spaces, such as the offices of teachers, principals, and administrators, which are occupied for long periods, as well as indoor sport facilities, where respiratory volume increases due to multiple people engaging in physical activity [19,20].

Furthermore, the indoor air quality should be monitored by analyzing the characteristics of spaces, as the concentration of each pollutant, despite being similar when outdoors, varies depending on the configuration of the space and facility conditions [21,22,23].

Analyses of indoor air quality in South Korea are conducted based mainly on an air quality measurement methods that utilize measuring devices and a method that predicts the indoor air quality of spaces using the Computational Fluid Dynamic (CFD) program. Because this measurement and program require user proficiency, they are difficult for nonexperts, such as teachers or school managers, to utilize [24,25,26,27].

Currently, a lot of research is being conducted on indoor air quality monitoring programs and indoor air quality prediction diagnostic programs. In the case of the program and monitoring system of previous studies, it is a program that analyzes one pollutant, and it is difficult for non-experts to directly operate it [28,29,30]. Therefore, there is a need for a program that allows nonexperts to diagnose indoor air quality by identifying the characteristics of the space when planning the space before class. In addition, if the maintenance standard range of indoor air pollutants is exceeded during diagnosis, a tool that can diagnose compared to the initial plan is needed so that improvements can be made using ventilation facilities, etc.

Thus, this study developed an indoor air quality diagnosis program for office and multipurpose activity spaces at schools that enables nonexperts to accessibly determine the change in pollutants in these spaces. The program proposed in this study was made with Visual Basic for Applications (VBA) and the Microsoft Excel program, which nonexperts such as teachers and school managers can easily access and use to predict indoor air quality. This study presented a tool that can be compared with the initial plan so that nonexperts can diagnose the indoor air quality before and after class and improve it by using ventilation equipment, such as an air purifier, when it exceeds the indoor air quality maintenance standard range.

In addition, the necessary information is presented as optional factors (maximum, minimum, median, etc.) in consideration of input factors that are difficult for nonexperts to grasp when predicting indoor air quality.

2. Methods

This program was designed with VBA and executed with Microsoft Excel. Figure 3 shows the research process of this study for diagnosing changes in pollutant levels depending on the space and activities conducted in it.

This research process was divided into four stages, and PM_2.5 and CO₂ were selected as the pollutants for indoor air quality diagnosis.

First, the prior research of the influencing factors to be selected for the Input sheet was investigated through analyses of architectural drawings and experimental data. In particular, the major factors of changes in PM_2.5 and CO₂ concentrations were identified through experimental data analysis. Second, factors affecting PM_2.5 and CO₂ concentration changes were selected. The selected influencing factors were used as input conditions that the user could input or select during program operation [29,31]. Third, input conditions (space volume, number of occupants, air volume, etc.) were applied to the mass and concentration conservation equations. The equations derived from these serve as the final predictions of PM_2.5 and CO₂, which change with time. In addition, the program was configured by inputting VBA code to run it for each instructional schedule (number of occupants, hours of use, operation of air purification facilities, etc.) input by the user. Finally, to verify the accuracy of the simple indoor air quality diagnosis program, the calculated results were compared with the measured data.

3. Prior Research

Prior to the development of the indoor air quality program, research was conducted to identify various variables, such as spatial, facility, and environmental factors, affecting changes in PM_2.5 and CO₂ concentrations [21,22,23,25,31,32,33]. First, the completed school facility drawings were examined to analyze the architectural elements and applied facilities of the office and multipurpose activity spaces [21,22,23,25,29,33]. Second, indoor air quality experiments were conducted to analyze the characteristics of changes in PM_2.5 and CO₂ concentrations depending on the number of occupants, air purification facilities, and activities in the office and multipurpose activity spaces [21,22,23,25,29,33].

3.1. Architectural Drawing Analysis

To analyze the application statuses of the architectural and equipment elements, the spaces in the drawings were classified and defined depending on function, and 10 drawings were analyzed based on floor area, ceiling height, window type, and air purification facility application status.

3.1.1. Definition of Spaces by Function

Prior to analyzing the current statuses of office and multipurpose activity spaces, this study defined the functions of the office and multipurpose activity spaces described on the architectural drawings, as shown in

Table 1. Definitions of the functions of office and multipurpose activity spaces.

Space Type	Definition
Office	Space for teachers and school administrators to prepare for class and conduct business (Examples: principal’s office, teachers’ offices, and administration office)
Multipurpose activity	Space for various classroom activities and school events (Examples: multipurpose room, auditorium, and indoor gymnasium)

[34,35,36].

3.1.2. Architectural Elements and Application Statuses of Air Purification Facilities

This study conducted architectural drawing analysis on 10 office spaces, which revealed an average floor area of 75 m² and an average ceiling height of 2.6 m. The sliding window type was applied to most schools, while the awning window type was applied to new school buildings or administrative offices of universities. The consideration of ventilation depending on opening angles is necessary due to the various angles available for awning windows [37,38].

The average floor area of multipurpose activity spaces was 607 m², and the average ceiling height was 10.5 m. The window type was sliding window for all 10 schools [33].

This study further analyzed the application statuses of air purification facilities, which affect the change in concentrations of indoor air pollutants [39,40,41,42]. Six of the office spaces and four of the multipurpose activity spaces lacked air purification facilities (

Table 2. Application statuses of air purification facilities in office and multipurpose activity spaces at 10 schools.

Name of School	Office	Multipurpose Activity Space
A	X	O (Jet fan)
B	X	X
C	X	O (Jet fan)
D	X	O (Jet fan)
E	X	X
F	O (HRV)	O (Jet fan)
G	O (HRV)	O (Jet fan)
H	O (ERV)	X
I	X	X
J	O (ERV)	O (Jet fan)

HRV: Heat Recovery Ventilator. ERV: Energy Recovery Ventilator.

).

Thus, the architectural drawing analysis showed that there are various sizes, window types, and available air purification facilities for office and multipurpose activity spaces. In consideration of these elements, this study added the calculation of input conditions that allow users to directly input information or select various types of information in the air quality diagnosis program.

3.2. Indoor Air Quality Tests

To determine the changes in PM_2.5 and CO₂ concentrations depending on the number of occupants, air purification facilities, and activities in office and multipurpose activity spaces, this study compared and analyzed the data from the indoor air quality test regarding office and multipurpose activity spaces at three locations.

As shown in Figure 4, the indoor air quality measurement data of three spaces were analyzed. Figure 4a is an office space located in a school facility, Figure 4b is a multipurpose activity space, and Figure 4c is a department office located in a school facility.

The measuring devices were a Sensirion SPS30 (which is certified for monitoring by the U.K. Environment Agency), an IAQ160, and a SCD40 for the PM_2.5 concentration and a Testo 400 for the CO₂ concentration (Figure 5) [32].

3.2.1. Analysis of the Characteristics of PM_2.5 and CO₂: Outdoors and in Hallways

The indoor air quality test data, which were collected on 12 August 2021, were utilized to analyze the changes in air quality concentrations in an indoor space depending on the changes in PM_2.5 and CO₂ concentrations outdoors and in hallways. This space was an office space capable of accommodating a maximum of 15 people with a floor area of 60.43 m² [32]. Points 1 and 2 were measured at the 1.2 m level by considering the respiration height [32,33,43].

Figure 6 is a graph of PM_2.5 and CO₂ concentrations measured from 10:00 to 16:00 on 12 August. As shown in Figure 6a, the PM_2.5 concentration of Point 2 was measured at a maximum of 22 µg/m³ between 13:45 and 14:00, while the hallway PM_2.5 concentration maximum was 28 µg/m³ at the same time interval. Figure 6b is the analysis result of the CO₂ concentration. The CO₂ concentration of Point 2 increased to a maximum of 860 ppm at 16:00 due to an increased number of occupants after lunchtime. However, the outdoor and hallway CO₂ concentrations remained below approximately 500 ppm.

The data analysis shows that the factors affecting indoor PM_2.5 and CO₂ concentrations differ, thereby suggesting that indoor PM_2.5 concentration is affected by the outdoor PM_2.5 concentration and that CO₂ concentration is affected by the number of occupants.

3.2.2. Analysis of the Characteristics of PM_2.5 and CO₂: Windows, Doors, and Air Purification Facilities

The indoor air quality test data collected on 18 November 2020 were utilized to analyze the change in concentrations of PM_2.5 and CO₂ in the indoor space depending on the opening and closing of doors and windows as well as the availability of ventilation facilities. This space was a multipurpose activity space that is utilized as an auditorium and sports facility and has a floor area of 616.14 m² [33]. Points 1 and 2 were measured at the 1.2 m level by considering the respiration height [32,33,43].

Figure 7 shows the indoor air quality measurement data from 8:45 to 15:30 on 18 November. As shown in Figure 7a, the indoor PM_2.5 concentration decreased by approximately 3.02 µg/m³ between 10:15 and 11:45, which was when the jet fan was in operation. In addition, the PM_2.5 concentration in the hallway decreased from 25.19 to 15.10 µg/m³ between 14:30 and 15:00, which was when the door between the hallway and the multipurpose activity space was open, while the concentration in the multipurpose activity space increased from 9.8 to 10.94 µg/m³.

The CO₂ concentration remained below 250 ppm from 8:45 to 10:15 and increased to a maximum of 450 ppm from 10:15 to 11:45, at the start time of the occupants’ activities. As shown in Figure 7b, the concentration was measured to be 370 ppm or less after 15:00, when there was no change in the number of occupants.

In addition, the indoor air quality data measured on 20 August 2020 were utilized to analyze the changes in PM_2.5 and CO₂ concentrations according to the opening and closing of windows as well as the operation of air purifiers. This space was being used as administrative offices and had a floor area of 48.79 m².

As shown in Figure 8, the air purifier was in operation from 9:30 to 13:00, and the initial PM_2.5 concentration at Point 2 decreased from 18.15 µg/m³ at 9:30 to 2.25 µg/m³ at 10:55. Moreover, when the window was open between 12:11 and 12:22, the concentration of Point 1 increased by approximately 2.67 µg/m³, from 3.07 to 5.74 µg/m³.

Through the data analysis of Figure 4, Figure 5 and Figure 6, each influencing factor of PM_2.5 and CO₂ was identified. The data analysis showed that a jet fan, which brings in outside air through an air purification facility, decreases PM_2.5 and CO₂ concentrations during its operation. In addition, the results indicated that the air purifier decreased the PM_2.5 concentration. They further showed that the opening of windows and doors affected the PM_2.5 and CO₂ concentrations in the indoor space, as the PM_2.5 and CO₂ of the adjacent space flowed into the indoor space.

3.2.3. Analysis of the Characteristics of PM_2.5 and CO₂: Regions

This study utilized Our Neighborhood’s Atmospheric Information and the Annual Report of Air Quality in Korea 2020 provided by the Korea Environment Corporation to check the changes and deviations in PM_2.5 concentrations depending on regional location [44,45]. The data from Our Neighborhood’s Atmospheric Information were utilized to analyze the standard deviation of PM_2.5 concentration based on the three locations where the previous measurement experiment was conducted (two in Seoul and one in Pyeongtaek, Gyeonggi-do). The standard deviation analysis was conducted based on data gathered in January, when the number of days with a high PM_2.5 concentration by year is high in South Korea [46]. The average deviation of PM_2.5 concentration in January 2021 in the three regions was 2.07 µg/m³, and as shown in Figure 9, the highest deviation was 6.02 µg/m³ on 13 January.

This study utilized the Annual Report of Air Quality in Korea 2020 to check the annual average PM_2.5 concentrations by city and province [45]. As a result, the PM_2.5 concentration in the Chungcheongbuk-do region in 2018 and 2019 was the highest, while that in Jeju was the lowest. Furthermore, the average annual PM_2.5 concentrations in South Korea were 23 µg/m³ and 18 µg/m³ in 2018 and in 2019 and 2020, respectively, indicating a decreasing trend in the annual PM_2.5 concentration (Figure 10).

The outdoor CO₂ concentration was obtained from Lee et al. [32], who reported an average annual CO₂ concentration of 420 ppm in 2020.

The prior research has identified the increasing and decreasing factors of PM_2.5 and CO₂ concentrations through indoor air quality experiments and analyzed the annual average change in PM_2.5 concentration by region. These factors have further been utilized to derive the correlations and concentration prediction equation for each influencing factor for predicting PM_2.5 and CO₂ concentrations over time, which comprise the core of the simple indoor air quality diagnosis program for office and multipurpose activity spaces at schools.

4. General Structure of the Proposed Program

To calculate the predicted concentrations to be presented as output of the simple diagnostic program, this study separated PM_2.5 and CO₂ to provide the influencing factors by category by referring to the increasing and decreasing factors obtained from the prior research in addition to selecting input influencing factors to allow users to select or input values. Moreover, an equation for predicting PM_2.5 and CO₂ concentrations was derived using the mass conservation equation [32,47].

4.1. Prediction of PM_2.5 Concentration

To predict PM_2.5 concentration depending on user input and selection in the simple diagnostic program, this study derived the influencing factors as input conditions and utilized Equation (1) to derive the change rate of PM_2.5 concentration.

4.1.1. Factors Influencing PM_2.5

For the classification of influencing factors, factors increasing or decreasing PM_2.5 concentrations in the prior research were divided into large and intermediate categories, as shown in

Table 3. Category selection according to the classification of factors affecting changes in PM_2.5 concentration.

Large Category	Intermediate Category	Small Category
Architectural elements	Space	Floor area
		Ceiling height
		Window effective opening area
		Door area (indoor/outdoor)
		Door area (indoor/adjacent space)
		Rate of air changes
Equipment elements	Air purifier	Number of machines
		Supply/exhaust air flow rates
		Filter type and efficiency
		Operation time
	Mechanical ventilation system	Number of machines
		Supply/exhaust air volume
		Filter type and efficiency
		Operation time
		Indoor PM2.5 concentration
	External	Outdoor PM2.5 concentration
		Adjacent PM2.5 concentration
		Pressure difference (indoor/outdoor)
		Pressure difference (indoor/adjacent space)

, and the factors applied as input factors in the Input sheet for program users were selected as belonging to the small category.

4.1.2. Input Conditions for Factors Influencing PM_2.5

For the small category of factors influencing PM_2.5, the factors were further divided into two types: user input conditions, in which a user directly inputs the factor applied to a building, and optional input conditions, in which the program allows a user to select input items. The information on optional input conditions was obtained from a literature review, as shown in

Table 4. Input conditions for PM_2.5 influencing factors.

Small Category (Input Condition)	References
Window effective opening area ratio (Sliding: 0.5/Pivot horizontal: 0.26/Pivot vertical: 0.26/Awning: 0.13/Projected: 0.13)	[37,38,48]
Outdoor PM2.5 concentration (PM2.5 concentration by city and month)	[45]
Air change per hour (New school: 0.1/h/Normal school: 0.37/h/Old school: 1/h)	[48,49,50,51]
Air purifier efficiency (Pre: η = 0.28/Medium: η = 0.59/Hepa: η = 0.98)	[42,52,53]

.

4.1.3. Derivation of the PM_2.5 Concentration Prediction Equation

The PM_2.5 concentration prediction equation depending on occupancy time was derived using the previously derived input values and the mass conservation equation [32,47]. Furthermore, the PM_2.5 concentration, unlike the CO₂ concentration, decreases with air purifier operation and is affected by deposition over time. Thus, the PM_2.5 prediction equation was derived considering the deposition rate presented by Ji et al. [54].

In addition, the indoor PM_2.5 concentration changes depend on the degree to which the windows and doors are opened. The air volume caused by the opening of the windows and doors was derived using Equations (1) and (2) [32,47].

Equation (1) is the air velocity flowing into the indoor space through a window [32,47].

$$V_w=\sqrt{ \frac{2\Delta P}{{\rho }_{air}}}$$

(1)

The variables in Equation (1) are defined as follows:

$V_w$: Wind speed through the window (m/s);

$\Delta P$: Indoor and outdoor pressure difference (Pa);

${\rho }_{air}$: Air density (kg/m³).

The pressure difference applied in Equation (1) differs depending on the position of the window and door. In the input condition, the input value was created so that the user could input by dividing the indoor and outdoor pressure difference by the indoor and adjacent space pressure difference.

Equation (2) is the volume of air entering through the window of the indoor working space.

$${\dot{V}}_w={\dot{A}}_w{V}_w·3600$$

(2)

The variables in Equation (2) are defined as follows:

$V_w$: Wind speed through the window (m/s);

${\dot{V}}_w$: Air flow rate through the window (m³/h);

${\dot{A}}_w$: Window opening area (m²).

To obtain the air volume of the door, one can input the area of the door and the wind speed of the air flowing in from the door into the equation. Equation (3) shows the prediction of indoor PM_2.5 concentration changes depending on activity and other factors using Equation (2) and the previously derived input values.

The prediction of indoor PM_2.5 concentration change depending on activity and other factors is given by Equation (3) [32,47,54].

$$\begin{array}{cc}\hfill V\frac{d{C}_{PM2.5, in}}{dt}& =\{(1-{\eta }_{erv}){\dot{V}}_{erv}{C}_{PM2.5, out}+{\dot{V}}_w{C}_{PM2.5, out}+{\dot{V}}_{inf,out}{C}_{PM2.5, out}\hfill \\ & + {\dot{V}}_{inf,hall}{C}_{PM2.5,hall}+{\dot{V}}_{d,out}{C}_{PM2.5,out}+{\dot{V}}_{d,hall}{C}_{PM2.5,hall}\}\hfill \\ & - C_{PM2.5, in}({\dot{V}}_{erv}+{\dot{V}}_w+{\dot{V}}_{inf,out}+{\dot{V}}_{inf,hall}+{\dot{V}}_{d,out}+{\dot{V}}_{d,hall}\hfill \\ & + {\lambda }_{PM2.5}\Sigma A+{\dot{V}}_p{\eta }_p)\hfill \end{array}$$

(3)

The variables in Equation (3) are defined as follows:

V: Volume of the room (m³);

$t$: Time (h);

$C_{PM2.5,\mathit{in}}$: Indoor PM_2.5 concentration (µg/m³);

${\eta }_{erv}$: Mechanical ventilation system filter efficiency;

${\dot{V}}_{erv}$: ERV supply flow rate (m³/h);

$C_{PM2.5,out}$: Outdoor PM_2.5 concentration (µg/m³);

${\dot{V}}_{window}$: Air flow rate through the window (m³/h);

${\dot{V}}_{inf,out}$: Infiltration flow rate from outdoor air (m³/h);

${\dot{V}}_{inf,hall}$: Infiltration flow rate from adjacent space air (m³/h);

$C_{PM2.5,hall}$: Concentration of PM_2.5 in adjacent spaces (µg/m³);

${\dot{V}}_{d,out}$: Air flow rate through the external door opening (m³/h);

${\dot{V}}_{d,hall}$: Air flow rate through the adjacent door opening (m³/h);

${\lambda }_{PM2.5, d}$: PM_2.5 deposition rate (m/h);

$\Sigma A$: Surface area of the space (m²);

${\dot{V}}_p$: Air purifier flow rate (m³/h);

${\eta }_p$: Air purifier filter efficiency.

4.2. Prediction of CO₂ Concentration

To predict CO₂ concentration depending on user input and selection in the simple diagnostic program, this study derived the influencing factors as input conditions and utilized Equation (2) to derive the CO₂ concentration change per hour.

4.2.1. Factors Influencing CO₂

For the classification of influencing factors, factors increasing and decreasing CO₂ concentrations in the prior research were divided into large and intermediate categories, as shown in

Table 5. Category selection according to the classification of factors affecting changes in CO₂ concentration.

Large Category	Intermediate Category	Small Category
Architectural elements	Space	Floor area
		Ceiling height
		Window effective opening area
		Door area (indoor/outdoor)
		Door area (indoor/adjacent space)
Equipment elements	Mechanical ventilation system	Number of machines
		Supply/exhaust air flow rate
		Operation time
Environmental factors	Indoor	Rate of air changes
		Indoor CO2 concentration
	External	Outdoor CO2 concentration
		Adjacent CO2 concentration
		Pressure difference (indoor/outdoor)
		Pressure difference (indoor/adjacent space)
	Occupant characteristics	Number of occupants
		Age
		Activity type

, and those applied as input factors in the Input sheet for program users were selected as belonging to the small category.

4.2.2. Input Conditions for Factors Influencing CO₂

For the small category of factors influencing CO₂, the factors were further divided into two types: user input conditions, in which a user directly inputs the factor applied to a building, and optional input conditions, in which the program allows a user to select input items. The information on optional input conditions was obtained from a literature review, as shown in

Table 6. Input conditions for factors influencing CO₂.

Small Category (Input Condition)	References
CO2 emission by occupant (Calculation of CO2 emissions by age/activity of occupants)	[31,32,33,43,55,56,57]
Outdoor CO2 concentration	[58]

.

4.2.3. Derivation of the CO₂ Concentration Prediction Equation

The CO₂ concentration prediction equation depending on occupancy time was derived using the previously derived input values [32,47,52]. In addition, CO₂ concentration, unlike PM_2.5 concentration, is subject to significant change based on the number of occupants, and its increase rate varies depending on the type of activities performed by the occupants [31,32,33,55,56,57].

The CO₂ emissions per person per hour, taking into account the size of the body of students and adults, are as shown in Equation (4) [32,43,56,57].

$${\dot{C}}_{a\left(or s\right)}=RQ \frac{0.0276A_{D}M}{\left(0.23RQ+0.77\right)} ·3600$$

(4)

The variables in Equation (4) are defined as follows:

${\dot{C}}_{a\left(or s\right)}$: The amount of CO₂ per person per hour for each activity (ℓ/h);

$RQ$: Respiratory quotient (0.83);

A_D: Occupant’s surface area (m²);

$M$: Met level.

Equation (5) predicts changes in indoor CO₂ concentration according to activity and other factors using Equations (1), (2) and (4).

The prediction of indoor CO₂ concentration change depending on activity and other factors is given by Equation (5) [32,47,55,56,57].

$$\begin{array}{cc}\hfill V\frac{d{C}_{CO2, in}}{dt}& =(N_a{\dot{C}}_a+N_s{\dot{C}}_s+{\dot{V}}_{erv}{C}_{CO2, out}+{\dot{V}}_w{C}_{CO2,out}+ {\dot{V}}_{inf,out}{C}_{CO2, out}\hfill \\ & + {\dot{V}}_{inf,hall}{C}_{CO2, hall}+{\dot{V}}_{d,out}{C}_{CO2, out}+{\dot{V}}_{d,hall}{C}_{CO2, hall})\hfill \\ & - C_{CO2,in}({\dot{V}}_{erv}+{\dot{V}}_w+{\dot{V}}_{inf,out}+{\dot{V}}_{inf,hall}+{\dot{V}}_{d,out}+{\dot{V}}_{d,hall})\hfill \end{array}$$

(5)

The variables in Equation (5) are defined as follows:

V: Volume of the room (m³);

$t$: Time (h);

$C_{CO2,in}$: Indoor CO₂ concentration (ppm);

$N_a$: Number of adults;

$N_s$: Number of students;

$\dot{C_a}$: CO₂ emissions by adult (ℓ/h);

$\dot{C_s}$: CO₂ emissions by student (ℓ/h);

${\dot{V}}_{erv}$: ERV supply flow rate (m³/h);

$C_{CO2,out}$: Outdoor CO₂ concentration (ppm);

${\dot{V}}_{window}$: Air flow rate through the window (m³/h);

${\dot{V}}_{inf,out}$: Infiltration flow rate of outdoor air (m³/h);

${\dot{V}}_{inf,hall}$: Infiltration flow rate of adjacent space air (m³/h);

$C_{CO2,hall}$: Concentration of CO₂ in the adjacent space (ppm);

${\dot{V}}_{d,out}$: Air flow rate through the external door opening (m³/h);

${\dot{V}}_{d,hall}$: Air flow rate through the adjacent door opening (m³/h).

4.3. The Simple Diagnosis Program for Indoor Air Quality

The PM_2.5 and CO₂ concentration prediction equations were utilized to produce a simple diagnostic program that enables a user to check the indoor air quality by either directly inputting values or selecting each element. This program was created using Microsoft Excel.

4.3.1. Implementation of the Concentration Prediction Equation for Each Class Period

This study constructed a period checklist for the simple diagnosis program for indoor air quality, as shown in Figure 11, which allows users to input or modify conditions subject to change by period by considering the characteristics of school facilities utilized in each class period. For the modification of input conditions for each period, an icon was added using a macro function, which is a development tool of Microsoft Excel. Furthermore, as shown in Figure 11, the input conditions for the architectural, equipment, and environmental elements selected in Input were utilized to declare and assign variables through VBA in Microsoft Excel, and the equation utilizing the concentration prediction equation that was previously derived was applied to present the output for each class period with VBA coding.

4.3.2. Coding of the Simple Diagnosis Program

The simple diagnosis program for indoor air quality consists largely of two sheets. First, the Input sheet is a sheet in which the user inputs space information. As shown in Figure 12, the parameters in the Input sheet are architectural, equipment, and environmental factors, and their ranges can be determined by either user input or optional selection. Moreover, this program, in consideration of the characteristics of school operation, offers a period checklist, which enables variable conditions to be modified or added for each period; the “Show Result” button allows users to move to the result window.

The diagnosis program, as shown in Figure 13, was configured to allow users to read the PM_2.5 and CO₂ concentrations predicted by the input into the Input sheet. The Result sheet provides the prediction information in graphical form to determine the PM_2.5 and CO₂ concentration per hour. The Result sheet was further configured to show the occupant schedule per hour, the air purifier operation schedule, and the mechanical ventilation operation schedule for improving air quality in the diagnosis space in addition to the predicted concentration. Finally, this program offers a “Return to Input” button, which allows users to return to the input conditions to enhance user convenience.

5. Validation and Results

To improve the reliability of the prediction results on PM_2.5 and CO₂ concentrations calculated by the simple diagnosis program, this study conducted a comparative analysis on the measured data and the result data from the simple diagnosis program. For the measured data to be compared, an indoor air quality test was conducted for a single-person office space, which is capable of the smooth control of external environmental factors, using the measurement devices presented in Section 4.2 (Figure 5).

The floor area of the space was approximately 28.10 m², and the measurement was performed from 9 February to 22 February 2022. As shown in Figure 14a, the measurement of PM_2.5 and CO₂ was performed at the 1.6 m level in height on three measurement points. The measurement data presented in Figure 13 and Figure 14 represent the average concentrations of the three measurement points.

Figure 15 shows the comparison result with PM_2.5 data on 15 February, which includes the activities of opening and closing windows during the occupancy of one male adult doing light office work. Simulations 1 and 2 refer to the results before and after correction, respectively.

To ensure the reliability and accuracy of the comparative analysis between the measured data and those from the simple diagnostic program, root mean square error (RMSE) and mean absolute percentage error (MAPE) statistical analyses were conducted to determine the error range [32,59,60,61,62,63].

RMSE (root mean square error) is the most used measure when dealing with the difference between the predicted value and the actual measured value in simulation. MAPE (mean absolute percentage error) is one of the numerical measures that measures the relative proportion of the error to the actual value by dividing the difference between the actual measured value and the predicted value by the actual measured value [32,59,60,61,62,63]. In addition, the RMSE percentage was analyzed for PM_2.5 data [32,59].

Table 7. PM_2.5 concentration test and prediction tool RMSE and MAPE results.

Pollutant	Simulation	RMSE (µg/m3)	RMSE Percentage (%)	MAPE Percentage (%)
PM2.5	1(a)	4.21	27.10	23.78
	1(b)	1.63	15.59	15.15
	Average	2.92	21.35	19.47
	2(a)	0.86	5.49	3.82
	2(b)	0.65	6.19	6.48
	Average	0.76	5.84	5.15

shows the results of RMSE and MAPE assays for PM2.5 concentrations. In Simulation 1 before correction, the wind speed formula for the opening was reflected by setting the difference in air pressure between indoors and outdoors to 0.6 Pa, as shown in Figure 12 [64,65]. As shown, the corrected Simulation 2 represents the results with an average wind speed of 0.08 m/s measured through Testo 400 using the anemometer, as shown in Figure 14b, and with the in-door/outdoor pressure difference set to 0.1 Pa [66,67].

According to the comparison between the PM_2.5 measurement results and those from Simulation 1, as shown in Table 7, the average RMSE was 2.92 µg/m³, and the RMSE and MAPE percentages were relatively high at 21.35% and 19.47%, respectively. According to the comparison between the PM_2.5 measurement results and those from Simulation 2, the average RMSE was 0.76 µg/m³, and the RMSE and MAPE percentages became 5.84% and 5.15%, respectively, which are much lower than those of Simulation 1.

Figure 16 presents the comparison results between the measured data and simulation data for CO₂ concentration, displaying Simulation 1, the simulation results before correction, and Simulation 2, those after correction.

Table 8. CO₂ concentration test and prediction tool RMSE and MAPE results.

Pollutant	Simulation	RMSE (ppm)	RMSE Percentage (%)	MAPE Percentage (%)
CO2	1(a)	173.28	24.69	19.29
	1(b)	134.94	17.65	16.38
	Average	154.11	21.17	17.84
	2(a)	32.39	4.61	3.48
	2(b)	18.92	2.48	2.11
	Average	25.61	3.55	2.80

shows the results from RMSE and MAPE analyses for CO₂ concentration. Simulation 1 reflects the wind speed formula through the opening [64], which was obtained by setting the indoor/outdoor pressure difference to 0.6 Pa in consideration of the wind pressure coefficient [65]. Simulation 2 is the result of applying the correction factor of 0.5 to the wind speed formula through the opening [64] and changing the indoor/outdoor pressure difference to 0.1 Pa [66,67].

According to the comparison between the CO₂ measurement results and those from Simulation 1, as shown in Table 8, the average RMSE was 154.11 ppm, and the percentages were relatively high at 21.17% and 17.84%, respectively. According to the comparison between the CO₂ measurement results and those from Simulation 2, the average RMSE was 25.61 ppm, and the percentages became 3.55% and 2.80%, respectively, which are much lower than those of Simulation 1. The RMSE percentage of Simulation 2 was 17.6% lower than that of Simulation 1, showing better accuracy.

Therefore, this study proposes Simulation 2 as the final program, as its accuracy was shown to be better than that of Simulation 1 through RMSE and MAPE analyses.

6. Discussion

There may be errors in the results from the comparison between the program prediction results and the measured data due to various variables affecting the indoor air quality. Thus, the error range could be reduced by comparing the program prediction results with those from actual measurements of more diverse spaces and by further utilizing the correction factor. In particular, in the case of the PM_2.5 category reflected in this study, there are insufficient parts that do not reflect the characteristics of changes in PM_2.5 concentration due to occupant activities. Therefore, it is necessary to conduct experiments and corrections related to the characteristics of floating fine dust and deposition according to time.

Furthermore, a deep learning model trained through various interpretations using the actual measurement data, in addition to the actual measurement model, could be utilized to minimize the errors by upgrading the presented program.

7. Conclusions

This study proposed a simple indoor air quality diagnosis program for office spaces and indoor sports facilities, whose utilization has been on the rise in response to high concentrations of outdoor PM and other air pollutants. The program proposed in this study was made with VBA and the Microsoft Excel program, which nonexperts such as teachers and school managers can easily access and utilize to predict indoor air quality. In addition, the necessary information is presented as optional factors (maximum, minimum, median, etc.) in consideration of input factors that are difficult for nonexperts to grasp when predicting indoor air quality.

In particular, the program presented in this study was constructed based on PM_2.5 and CO₂, and it provides a concentration prediction equation by classifying the influencing factors for each pollutant through analyses of experimental data in various spaces. In addition, to increase the accuracy and reliability of the results of the simple indoor air quality diagnosis program, this study conducted verification through comparative analyses with measured data. The main contents and results of the simple indoor air quality diagnosis program are described below:

• Prior research was conducted to analyze the influencing factors to be selected for the Input sheet. Among them, the analysis of measurement data from 12 August 2021 confirmed a sharp increase in CO₂ concentration. The CO₂ concentration of Point 2, an office space with a total floor area of 60.43 m², increased to a maximum of 860 ppm after 13:30, when the number of occupants rose. From the data results, it was inferred that the number of occupants influenced the increase in indoor CO₂ concentration.
• The input conditions for the simple indoor air quality diagnosis program selected through previous research are as follows. In the program, input conditions for PM_2.5 and CO₂ were selected as floor area, ceiling height, and effective window area. In addition, in the case of PM_2.5 input conditions, 10 categories, including the rate of air changes, outdoor PM_2.5 concentration, and adjacent PM_2.5 concentration, were additionally included because the PM_2.5 concentration is greatly affected by external environmental factors. In the case of CO₂ input conditions, eight categories, including the number and age of occupants and activity type, were additionally included because the CO₂ concentration is greatly affected by the number and activity of occupants.
• The simple indoor air quality diagnosis program proposed in this study uses the equation derived using the mass and concentration conservation equation so that PM_2.5 and CO₂ concentrations can be predicted by the input conditions using Excel. Additionally, the program was configured by inputting the VBA code for each instructional schedule (number of people, hours of use, operation of air purification facilities, etc.) input by the user.
• To verify the accuracy of the simple indoor air quality diagnosis program, Simulation 1, which contained the program result data, was compared with the measured data. The average RMSE was 2.92 µg/m³, and the RMSE percentage was 21.35% according to the comparative analysis of the PM_2.5 concentration of the measured data with those of Simulation 1. The RMSE was 154.11 ppm, and the RMSE percentage was 21.17% according to the comparative analysis of the CO₂ concentration of the measured data with those of Simulation 1.
• In order to improve accuracy, Simulation 2, in which the wind speed and indoor/outdoor air pressure difference are corrected, was presented. The RMSE was 0.76 µg/m³, and the RMSE percentage was 5.84% in the PM_2.5 by Simulation 2. In the case of CO₂ concentration, the RMSE was 25.61 ppm, and the RMSE percentage was 3.55%.

This study proposes a simple indoor air quality diagnosis program for office and multipurpose activity spaces at schools in the form of Excel VBA, which can be utilized by nonexperts, in place of the CFD program and the air quality measurement method, which are currently the main indoor air quality diagnosis methods. Further studies will be conducted to find a method of reducing the margin of error in consideration of the diversity of both spatial sizes and variables, thereby enhancing user convenience and program accuracy through comparison with various simulations.

In addition, after completing the process of calibrating the program through comparison to various measurement cases, we plan to make this software available in a web network so that it can be easily accessed and used by any experts or nonexperts who are interested in diagnosing and improving the indoor air quality of various spaces.