Indoor Air Quality Evaluation in Rural Houses Using Different Heating Methods in Northern Shanxi, China

Abstract

It has been shown that heating methods have a large impact on rural indoor air quality. Previous studies on indoor air quality in rural houses involved a limited number of heating methods and lacked comprehensive comparative research on the three heating methods: coal-fired boiler radiator heating, air-source heat pump radiator heating, and Chinese stove–kang heating. In this paper, subjective surveys and objective tests were conducted on indoor air quality in rural houses using these three heating methods in northern Shanxi, China. The gray relational analysis method and the comprehensive index method were used to evaluate the indoor air pollution levels of the three heating methods. The results were as follows: The subjective evaluations of most rural residents were overly optimistic about the indoor air quality of coal-fired boiler radiator heating and Chinese stove–kang heating. The indoor TVOC concentrations from these two heating methods far exceeded the standard limit of 0.6 mg/m³ at night. The indoor PM_2.5 and PM₁₀ concentrations from Chinese stove–kang heating varied greatly over a day and showed intermittent peak fluctuations that far exceeded the standard limits in the initial period of fuel combustion. The pollution levels from coal-fired boiler radiator heating, air-source heat pump radiator heating, and Chinese stove–kang heating were evaluated as light pollution, non-pollution, and medium or heavy pollution, respectively.

1. Introduction

The worldwide community has stepped up its efforts to lessen the impact of air pollution and global warming in recent years [1]. In 2020, China proposed carbon peaking and carbon neutrality goals [2]. Due to this, China’s northern rural areas have accelerated the promotion of clean heating projects, some of which have already realized clean heating. However, some rural areas still use traditional heating methods that mainly include Chinese kang, firewall, domestic coal-fired stoves, and “Tu Nuanqi” [3,4,5]. The fuel for these heating methods is usually coal or biomass. The toxic pollutants from coal and biomass fuel combustion pose a great threat to the health of rural residents [6,7,8,9]. With the continuous progress of society, people are becoming more and more concerned about indoor air quality [10,11]. It has been found that heating methods have a large impact on rural indoor air quality [12,13,14]. Therefore, it is necessary to conduct an in-depth study of the indoor air quality of different heating methods in rural areas to know the current situation and provide a reference for the improvement of indoor air quality in these areas.

The common heating methods in rural houses in northern Shanxi, China, are coal-fired boiler radiator heating, air-source heat pump radiator heating, and Chinese stove–kang heating. Many households in other rural areas of northern China also use these three heating methods for heating. However, there is no comprehensive comparative study on these three heating methods. The poor indoor air quality in rural residential buildings in northern China is in urgent need of improvement. The research on the effect of heating methods on indoor air quality is conducive to the control and improvement of indoor environmental quality in rural areas, which in turn is beneficial to the health and life of the residents. This study had two primary aims: 1. To evaluate indoor air quality in rural houses using these three heating methods. 2. To investigate the changing characteristics of indoor pollutant concentrations throughout the day.

Given the need for research, this study conducted subjective surveys and objective tests on indoor air quality in rural houses using the three heating methods mentioned above in northern Shanxi. The indoor concentrations of PM_2.5, PM₁₀, TVOC, and CO₂ were measured for a short period of time in 300 rural houses. In addition, three typical rural houses using these three heating methods were selected for 24 hours of continuous monitoring. The gray relational analysis method and the comprehensive index method were used to evaluate the indoor air pollution levels of the three heating methods. This research provides a reference for the selection of heating methods and the improvement of indoor air quality in rural houses.

2. Literature Review

In the 1970s, the energy crisis caused air-conditioned buildings to strengthen the airtightness of their envelopes, which exacerbated the deterioration of the indoor air environment and the sick building syndrome ensued [15]. People began to pay attention to the problem of indoor air quality. Studies on urban indoor air quality were conducted earlier than studies on rural indoor air quality. In recent years, more and more scholars have begun to conduct research on rural indoor air quality.

The results of foreign studies on indoor air quality in rural buildings are broadly polarized. Indoor air pollution levels are low in middle- and high-income neighborhoods of developed countries. However, the levels are high in low-income neighborhoods of developed countries as well as neighborhoods of some developing countries, such as South Africa [16], Nigeria [17], and Senegal [18]. Health risks associated with poor air quality are not randomly distributed in the population but are negatively correlated with socioeconomic status [19]. Walker Ethan S et al. [20] tested PM_2.5 in rural US homes and found that using good quality cookers and regular chimney cleaning helped to improve indoor air quality. Maksimul et al. [21] assessed the effects of stove-use patterns and kitchen chimneys on indoor air quality in rural India. The results showed that stoves using liquefied petroleum gas were more effective at reducing indoor PM_2.5 concentrations compared with traditional solid fuel stoves and improved biomass stoves. Kitchen chimneys were also effective at improving indoor air quality. Yucheng He et al. [22] studied indoor PM_2.5 emissions from stoves with chimneys in rural areas and found that the contribution of outdoor infiltration to indoor PM_2.5 concentrations increased with higher packing density and ventilation rate. For highly packed communities, fugitive concentration accounted for ~90% of the total exposure. Foster and Poston [23] assessed the occupant’s views and experiences of their kitchen environments, including indoor air quality in low-energy social and affordable housing in Scotland. Enlai Wan et al. [24] used laser-induced breakdown spectroscopy technology and single-particle aerosol mass spectrometer technology to detect indoor air pollution caused by electronic welding operations. The results showed that the main components in the smoke were Pb and Sn.

Some Chinese scholars have conducted comprehensive evaluations of indoor air pollution levels in rural China. In 2016, Wang Zhaojun et al. [25] evaluated indoor air pollution levels in rural houses near Harbin and found that, compared with the non-heating period, indoor air pollution levels in rural houses were higher during the heating period. In 2020, Wang Dongji et al. [26] evaluated the indoor environments of several clean heating methods in rural houses in Tianjin. The results showed that the clean heating methods greatly improved indoor air quality compared to traditional heating methods. In the same year, Li Jinping et al. [27] studied the indoor air quality of four heating methods in rural areas of Northwest China and found that the indoor air pollution level of solar radiant floor heating was non-pollution, that of boiler heating was medium pollution, and that of new hanging kang heating and floor kang heating was heavy pollution. In 2021, Huibo Zhang et al. [28] studied indoor air quality in old rural houses with open boiler heating in severely cold areas. The result showed that most of them were exposed to air pollution and PM_2.5 was the most dominant indoor air pollutant, with relatively high PM_2.5 concentrations when cooking. In 2022, Xiaoying Li et al. [29] measured indoor and community air quality in rural Beijing before, during, and after the COVID-19 lockdown. The results showed that household energy choice and indoor smoking had a greater impact on indoor air quality than the COVID-19 lockdown in rural China. In 2024, Shengming Dong et al. [30] investigated indoor air quality in coal-heating rural residential buildings in northern China and found that indoor PM_2.5 mainly originated from indoor activities and that CO₂ was positively correlated with formaldehyde and PM_2.5 in most households.

Overall, it has been shown that most rural residential buildings in northern China have poor indoor air quality in winter, with different levels of indoor air pollution based on different heating methods. Currently, there is no comprehensive comparative study on the three common heating methods: coal-fired boiler radiator heating, air-source heat pump radiator heating, and Chinese stove–kang heating.

Recent research methods used to study indoor air quality in rural areas are mostly a combination of subjective questionnaires and objective tests [10]. There is no unified comprehensive evaluation method for indoor air quality [31]. The relatively commonly used methods are the gray relational analysis method [32], the fuzzy comprehensive evaluation method [33], the decibel index method [34], and the comprehensive index method [35]. Wang Zhaojun et al. [25] used the gray relational analysis method and the fuzzy comprehensive evaluation method to evaluate indoor air quality in rural houses in Harbin China and concluded that the resolution of the gray relational analysis method was significantly higher than that of the fuzzy comprehensive evaluation method. Zhou Zhiping et al. [35] evaluated the indoor air quality of four residential buildings in China using the comprehensive index method and the decibel index method and concluded that the comprehensive index method was more reasonable than the decibel index method. Shu Aixia et al. [36] evaluated the indoor air quality of a residential district in Handan China using the comprehensive index method and the fuzzy comprehensive evaluation method and concluded that the comprehensive index method was superior to the fuzzy comprehensive evaluation method. Based on the above, it can be seen that the gray relational method and the comprehensive index method are, currently, the two superior methods for evaluating indoor air quality. Therefore, this study used the gray relational analysis method and the comprehensive index method to evaluate the research objects.

There are two main indoor air quality standards in China: “Standard for Indoor Environmental Pollution Control of Civil Building Engineering” (GB50325-2020) [37] and “Standards for Indoor Air Quality” (GB/T18883-2022) [38]. The former is a mandatory standard, the latter is a recommended standard. The former applies to civil buildings under construction in China while the latter applies to residential and office buildings in use in China. The former specifies 5 parameters (4 chemical + 1 radiological); the latter specifies 19 parameters (4 physical + 13 chemical + 1 radiological + 1 biological). Due to the second point above, the criterion referenced in this study is the “Standards for Indoor Air Quality” (GB/T18883-2022).

3. Materials and Methods

3.1. Research Area

As shown in Figure 1, the research area is northern Shanxi (110.9° E to 114.6° E and 38.1° N to 40.7° N). Northern Shanxi is located in the north of China, which is a severely cold region with a long heating time. This region has a temperate continental monsoon climate. Winters are long, cold, and dry, with average temperatures of around −10 °C and lows of −20 °C in January. Summers are short, hot, and rainy, with average temperatures of around 24 °C and highs of 35 °C in July. Coal-fired boiler radiator heating, air-source heat pump radiator heating, and Chinese stove–kang heating are three common heating methods in the area. Rural houses in northern Shanxi are usually single-story buildings of relatively regular plan, with the main living area being a row of rooms facing south, as shown in Figure 2. The building structures are generally brick and wood, with wooden flat roofs, brick and clay exterior walls (outer layer of brick, inner layer of clay), and adobe interior walls. In order to keep warm in winter, the doors and windows of the rural houses are closed all the time, except when residents go in and out of the houses. In addition, due to economic constraints, they are not fitted with fresh air systems or air purifiers.

3.2. Introduction to the Three Heating Methods

The heat source for the coal-fired boiler radiator heating is the boiler. The pollution source of this heating method is also the boiler. The boiler is usually installed in the kitchen or sunroom and the radiator is usually placed in the living room or bedroom. Residents usually add coal to the boiler every morning and afternoon. The main components of this heating system are the boiler, the radiator, the inlet pipe, the return pipe, and the water container. This heating system utilizes the physical properties of water and gravity to achieve the natural circulation of water in the pipes. The water container connected to the return pipe is installed at the highest point of the system to provide constant water pressure. The inlet and return pipes are installed at a certain slope. Coal is burned in the boiler to produce heat to raise the temperature of the water. After being heated, the water has a lower density and rises along the inlet pipe. Then, the hot water flows into the radiator and releases heat. The radiator heats up, which in turn heats the surrounding air via radiation and convection. After that, the temperature of the water decreases and the density increases. Then, the water drops down along the return pipe and eventually flows back into the boiler for the next cycle. The heating system has flues to vent smoke outside. Before using the boiler, it should be verified that the flues are clear. If the flues are blocked, the smoke will flow backward into the room, degrading the indoor air quality. In addition, too much or too little air intake by the boiler may cause the coal to burn incompletely, resulting in more pollutants leaking into the room. The pollutants escaping indoors from the coal-fired boiler will spread to the living rooms and the bedrooms.

The heat source for the air-source heat pump radiator heating is the air-source heat pump. This heating method has no pollution sources. The air-source heat pump consists of an evaporator, expansion valve, condenser, and compressor. The low-temperature gaseous refrigerant is compressed by the compressor to raise its temperature. Then, the high-temperature and high-pressure gaseous refrigerant passes through the condenser and transfers the heat to the cold water to raise the water temperature. After cooling, the refrigerant becomes liquid. The liquid refrigerant passes through the expansion valve and enters the evaporator. Due to the sudden drop in pressure, the liquid refrigerant in the evaporator quickly absorbs a large amount of heat and becomes gaseous. Under the operation of the fan, a large amount of air flows over the surface of the evaporator, and the heat in the air is absorbed by the evaporator. After that, the refrigerant returns to the compressor for the next cycle. The hot water is piped into the radiators to heat the rooms. The heating system does not require any fuel but rather only a small amount of electricity to operate, hence it does not produce any pollutants. It also allows residents to set the water temperature on their own to regulate the indoor temperature.

The heat source for Chinese stove–kang heating is the stove and the kang. The pollution source of this heating method is the stove and the cooking stove of the kang system, as shown in Figure 2c. The stove and the kang system are two separate parts of this heating method. Both are located in the same room. This room has the functions of a bedroom, kitchen, and living room, which is the main living space for local residents. The stove is in the center and the kang is on one side of it. Burning coal in the stove produces heat that raises the temperature of the external surface of the stove, which then heats the room via radiation. The smoke generated is discharged to the outside through a flue. The kang system consists of a cooking stove, the kang body, and a chimney. Wood and corn cobs are burned in the cooking stove. The high-temperature flue gas from combustion flows into the kang body, raising its surface temperature. Finally, the flue gas is released to the outside through the chimney. Some fraction of the pollutants leaks directly into the indoor air from the stove and the cooking stove. The flue structure inside the kang body can affect the flow resistance of smoke significantly; the larger the flow resistance, the better the heat exchange performance a kang has. However, a large flow resistance may lead to a backflow of the smoke and result in poor indoor air quality.

3.3. Subjective Survey

Due to individual differences, the perception of indoor air quality varies from person to person. To understand the local residents’ true evaluation of indoor air quality, this study concurrently involved subjective questionnaire surveys and parameter measurements. The coldest month of the year in northern Shanxi is January, which is the month with the highest heating energy consumption during the heating period, and correspondingly, the month with the largest heating pollutant emission during the heating period. Therefore, in January 2023 and January 2024, indoor air quality questionnaire surveys were administered in rural households in northern Shanxi using the three heating methods mentioned above.

The method used for the questionnaire survey was simple random sampling. Using Formula (1) [39] and taking the margin of error ($d$) as 0.1, the number of households to be surveyed for each heating method was calculated to be 96. In this study, 100 questionnaires were distributed to households using each heating method.

$$n=\frac{{Z_{\alpha /2}}^2(1-P)P}{d^2}$$

(1)

where $n$ is the minimum sample size, $Z_{\alpha /2}$ is the normal standard distribution ($Z_{\alpha /2}$ = 1.96) at a confidence level of 95% and $\alpha$ = 0.05, $P$ is the prevalence/population proportion, usually taking a value of 0.5, and $d$ is the tolerable margin of error.

Six villages in northern Shanxi were randomly selected for the questionnaire survey. Their geographic locations are shown in Figure 1. A list of households and heating methods was obtained from village committees. The total sample size was allocated proportionally to the six villages based on the number of households with each heating method in each village. The names of the villages and the number of allocations are shown in

Table 1. The names of the villages surveyed and the number of allocations.

Village Name	Coal-Fired Boiler Radiator Heating	Air-Source Heat Pump Radiator Heating	Chinese Stove–Kang Heating
Daiyuedian Village	3	10	4
Qijiayan Village	15	12	30
Shahukou Village	30	20	15
Balitai Village	24	26	22
Zhijiao Village	22	24	24
Dongjie Village	6	8	5

. Finally, 100 households with each heating method were selected using simple random sampling, and a total of 300 questionnaires were distributed. Before filling in the questionnaire, the researcher explained the questions in the questionnaire in detail to the residents and assisted them in interpreting the questions correctly. The age range of the participants was 19–55 years old, with a male-to-female ratio of 1:1.04. Questionnaires with smokers in the surveyed households were invalid and the rest were valid. A total of 286 valid questionnaires were returned. Among them, 94 questionnaires were valid for coal-fired boiler radiator heating, 97 questionnaires were valid for air-source heat pump radiator heating, and 95 questionnaires were valid for Chinese stove–kang heating.

The questionnaire content included resident information, building information, and residents’ subjective evaluation of indoor air quality. More specifically, the subjective evaluation included residents’ responses to indoor odors, circulation conditions, dust amounts, and overall satisfaction with the indoor air quality. Following the requirements of the ASHRAE 55–2013 standard [40], the satisfaction vote used a 5-level scale. Detailed information about the questionnaire content can be found in Appendix A.

3.4. Objective Test

The objective test consisted of two parts. One part was on-site tracking tests and the other part was all-day continuous tests. Due to the wide variety of pollutants released by combustion heating systems, it was impossible to monitor each pollutant. Constrained by the realistic conditions, four representative pollutants, PM_2.5, PM₁₀, TVOC, and CO₂, which had a significant impact on the health and comfort of residents, were selected as the monitoring and evaluation factors in this study.

PM_2.5 refers to particulate matter in ambient air with an aerodynamic equivalent diameter of less than or equal to 2.5 μm, which can enter human lungs. PM₁₀ refers to particulate matter in ambient air with an aerodynamic equivalent diameter of less than or equal to 10 μm, which can enter the respiratory tract of human beings. TVOC is short for total volatile organic compounds, which are usually in the form of vapor in the air at room temperature. CO₂ is short for carbon dioxide, which mainly originates from the combustion of various types of fuels as well as from human respiration.

The limits of PM_2.5, PM₁₀, TVOC, and CO₂ in the standard [38] are 50 μg/m³ (daily average), 100 μg/m³ (daily average), 0.6 mg/m³ (8 h average), and 1000 ppm (hourly average). The measuring instrument was the JT-IAQ-50 Indoor Air Quality and Thermal Comfort Tester with the relevant sensor parameters shown in

Table 2. Sensor parameters.

Sensor Name	Parameter Name	Basic Parameters
PM2.5	Test range	0–9999 μg/m3
	Measurement accuracy	±10% of reading
PM10	Test range	0–9999 μg/m3
	Measurement accuracy	±10% of reading
TVOC	Test range	125–600 ppb
	Measurement accuracy	——
CO2	Test range	0–5000 ppm
	Measurement accuracy	±30 ppm

. The sensors were calibrated monthly. Since the outdoor air in the research area is clean, the indoor air quality in rural houses in the research area is mainly influenced by indoor pollution sources. Thus, this study focused on testing and analyzing indoor pollutants. The reference standard [38] stipulates that one measurement point should be set in the center of a room less than 25 m². The rooms measured in this study were heating rooms, which were bedrooms or living rooms. They all had an area of less than 25 m², hence one measurement point was set at their centers. The height of the measurement point should be consistent with the height of the human respiratory zone, which is 0.5–1.5 m above the ground [38]. The actual heights used ranged between 0.7 and 1 m, as shown in Figure 3.

The on-site tracking test was conducted simultaneously with the questionnaire survey, both in January, the coldest month of the year. A total of 300 rural houses were tested, with 100 tested for each heating method. The heating system was in normal operation during the test. The tester used in the study was capable of monitoring indoor pollutants in real time. Due to the limited time and large sample size, each household was tested for only 30 min, which could reflect the indoor air pollution status when the heating system was in normal operation. All pollutants were recorded once every 10 min. The average value for the 30 min was recorded as one sample data. For each house, four pollutants were considered and four sample data were obtained. A total of 1200 sample data were obtained from the on-site tracking test.

The continuous test conducted throughout the day involved selecting one typical rural house for each heating method to test for 24 h to understand the characteristics of dynamic changes in indoor pollutant concentrations in a day. Each pollutant was measured every 10 min for 24 h. The plans for the three typical houses are shown in Figure 2, and demonstrate the locations of measurement points and heating equipment. The structure and material of the selected houses were similar.

3.5. Data Analysis Using the Gray Relational Analysis Method

The gray system theory is a system science founded by a Chinese scholar, Professor Deng Julong, in the early 1980s [41]. The basic idea of gray relational analysis in gray system theory is to judge whether the sequences are closely related based on the similarity between their curves. The closer the curves are and the more similar the shapes are, the greater the association between the corresponding sequences, and vice versa [42].

The following are the calculation steps followed for the gray comprehensive evaluation method.

In the first step, the reference sequences and the comparison sequences are determined, where the ones reflecting system behavior characteristics are the reference sequences and the ones consisting of the factors affecting the system behavior are the comparison sequences. In this study, the reference sequences are the sequences of indoor air quality evaluation criteria: $X_i,i\in M=\left\{\mathrm{1,2},\cdots \cdots ,m\right\}$, and the comparison sequences are the measured data from on-site tracking tests: $Y_j,j\in N=\left\{\mathrm{1,2},\cdots \cdots ,n\right\}$.

In the second step, the reference and comparison sequences are made dimensionless because the factors in the system have different physical meanings and their values may be so different that it is not convenient to compare them. Equation (2) [42] is the dimensionless reference sequence and Equation (3) [42] is the dimensionless comparison sequence.

$$X_i=\left\{x_i\left(1\right), x_i\left(2\right),\cdots \cdots ,x_i\left(k\right),\cdots \cdots x_i\left(u\right)\right\},k\in U=\left\{\mathrm{1,2},\cdots \cdots u\right\}$$

(2)

$$Y_j=\left\{y_j\left(1\right),y_j\left(2\right),\cdots \cdots ,y_j\left(k\right),\cdots \cdots y_j\left(u\right)\right\},k\in U=\left\{\mathrm{1,2},\cdots \cdots u\right\}$$

(3)

In the third step, the grey correlation coefficients and the relational degrees between the reference sequences and the comparison sequences are calculated to obtain the association matrix composed of the relational degrees.

In the fourth step, the relational degrees in the association matrix are compared and analyzed.

3.6. Data Analysis Using the Comprehensive Index Method

The comprehensive index method is used to assess indoor air quality using an organic combination of pollutant sub-indices. The pollutant sub-index is the ratio of the pollutant’s measured value to its standard limit value [43]. In this study, the pollutant’s measured value came from the on-site tracking test. The composite index $I$ takes into account the average and maximum sub-indices [35]. The grading and description of the composite index are shown in

Table 3. Composite index grading and description.

Composite Index I	Grade	Feature
≤0.49	Clean	Suitable for human life
0.50~0.99	Non-pollution	All pollutant indexes within standard limits; human life is normal
1.00~1.49	Light pollution	At least one excessive pollutant; except for sensitive people, usually no acute and chronic poisoning occurs
1.50~1.99	Medium pollution	Usually 2–3 excessive pollutants; the health of the population suffers, and sensitive persons suffer even more
≥2.00	Heavy pollution	Usually 3–4 excessive pollutants; the health of the population is severely damaged, and sensitive persons may be at risk of death

[44].

4. Results and Discussion

4.1. Analysis of Subjective Survey Results

The results of the subjective research are as follows. In terms of indoor air circulation conditions, air-source heat pump radiator heating was the best and the remaining two heating methods had a relatively large proportion of “average” or “stuffy” (Figure 4a). As for indoor odor, residents using air-source heat pump radiator heating felt that there was no odor in the room. For the residents using Chinese stove–kang heating, about 9% found the indoor odor unbearable and about 45% found the indoor odor slight. In addition, 20–30% of the residents using coal-fired boiler radiator heating found the indoor odor slight (Figure 4b). In terms of indoor dust amount, the air-source heat pump radiator heating had the largest proportion of “not at all” or “little”, while the Chinese stove–kang heating had the largest proportion of “much” (Figure 4c). As for overall satisfaction with indoor air quality, about 18% of the residents using Chinese stove–kang heating were “dissatisfied”, while residents using the other two heating methods were all “very satisfied”, “satisfied” or “basically satisfied” with their indoor air quality (Figure 4d). Taken together, the residents’ subjective perception of indoor air quality was that the air-source heat pump radiator heating was the best, followed by the coal-fired boiler radiator heating, while the Chinese stove–kang heating was the worst.

4.2. Analysis of Objective Test Results

4.2.1. On-Site Tracking Test Results

Sample data from rural houses with people smoking indoors during the test period were invalid and excluded. Sample data were excluded from three rural houses with coal-fired boiler radiator heating, two houses with air-source heat pump radiator heating, and three houses with Chinese stove–kang heating. Sample data from 97, 98, and 97 rural houses were valid for coal-fired boiler radiator heating, air-source heat pump radiator heating, and Chinese stove–kang heating. Exceedance rate is defined as the percentage of the data that exceeds the standard limit in the total data for each pollutant. The statistical results of the exceedance rate obtained from the on-site tracking tests are shown in

Table 4. Exceedance rates of indoor pollutants.

	PM2.5	PM10	TVOC	CO2
Coal-fired boiler radiator heating	64%	37%	58%	22%
Air-source heat pump radiator heating	0%	0%	17%	6%
Chinese stove–kang heating	85%	76%	63%	38%

. The coal-fired boiler radiator heating had relatively high PM_2.5 and TVOC exceedance rates of 64% and 58%, respectively. The air-source heat pump radiator heating had a low exceedance rate of each indoor pollutant. The Chinese stove–kang heating had high PM_2.5, PM_10, and TVOC exceedance rates of 85%, 76%, and 63%, respectively.

As can be seen from Figure 5a, the overall PM_2.5 concentrations from air-source heat pump radiator heating were lower than the standard limit of 50 μg/m³ [38], and the data distribution was relatively concentrated. The average PM_2.5 concentration from Chinese stove–kang heating was higher than the standard limit of 50 μg/m³ [38], and the data distribution was relatively decentralized, which was presumed to be due to the different fuel combustion statuses of different households during the on-site tracking tests. The average concentration of PM_2.5 from coal-fired boiler radiator heating was slightly higher than the standard limit of 50 μg/m³ [38], and the overall concentrations were much lower than those of Chinese stove–kang heating. This was mainly because the coal-fired boiler was not placed in the heating room and the fuel was only coal, while the stove and the kang were located directly in the heating room and the fuels included coal and biomass. As can be seen from Figure 5a,b, the distributions of PM₁₀ and PM_2.5 concentrations were approximately the same. The average PM₁₀ concentrations from coal-fired boiler radiator heating and air-source heat pump radiator heating were both lower than the standard limit of 100 μg/m³ [38] while that of Chinese stove–kang heating was higher than the standard limit of 100 μg/m³ [38]. As can be seen from Figure 5c, the average TVOC concentration from coal-fired boiler radiator heating was relatively close to that of Chinese stove–kang heating, and both were higher than the standard limit of 0.6mg/m³ [38]. However, compared with coal-fired boiler radiator heating, Chinese stove–kang heating had a much higher maximum TVOC concentration. The average TVOC concentration from air-source heat pump radiator heating was lower than the standard limit of 0.6mg/m³ [38], and the maximum concentration was slightly higher than the standard limit. Although this heating method used clean energy, a few rural houses with TVOC concentrations still exceeded the standard limit due to interior decorations. As can be seen in Figure 5d, the average CO₂ concentrations from the three heating methods did not exceed the standard limit of 1000 ppm [38], and the distributions of the concentrations were relatively decentralized. This was presumably because, in addition to the effect of fuel combustion, the number of people indoors also affected the indoor CO₂ concentration.

4.2.2. All-Day Continuous Test Results

As can be seen from Figure 6a,b, the PM_2.5 and PM₁₀ concentrations from air-source heat pump radiator heating varied very little over a day and stayed below the standard limits. The PM_2.5 and PM₁₀ concentrations from Chinese stove–kang heating varied greatly within the day and showed intermittent peak fluctuations, which were related to the intermittent fuel-adding behavior of the residents. The PM_2.5 concentration fluctuated in the range of 13–1355 μg/m³ and the PM₁₀ concentration fluctuated in the range of 14–1387 μg/m³, which far exceeded the standard limits in the initial period of fuel combustion. Therefore, it was necessary to ventilate appropriately to reduce the PM_2.5 and PM₁₀ concentrations during this period. The lower levels of PM_2.5 and PM₁₀ pollution of coal-fired boiler radiator heating were presumably due to the fact that the coal-fired boiler was placed far away from the tested room. This was consistent with the findings of Xudong Xie et al. [45] who found that placing the coal-fired boiler far away from the heating rooms could significantly reduce the concentration of particulate matter. As can be seen from Figure 6c, the all-day fluctuation ranges in TVOC concentrations from Chinese stove–kang heating and coal-fired boiler radiator heating were approximately the same, ranging from 0.3 mg/m³ to 2.6 mg/m³. Throughout the night, the TVOC concentrations from the two heating methods were maintained at comparatively high levels, far exceeding the TVOC standard limit of 0.6 mg/m³ [38]. This was presumably because doors and windows were closed at night while fuel continued to burn inside the building. The TVOC concentrations from air-source heat pump radiator heating gradually increased from 10:00 a.m. to 2:00 p.m., which was associated with the residents’ cooking behavior. As can be seen from Figure 6d, the CO₂ concentrations from coal-fired boiler radiator heating and Chinese stove–kang heating exceeded the standard limit of 1000 ppm [38] during the night. This was because the doors and windows were closed tightly at night and a lot of CO₂ was produced from breathing and fuel combustion. The CO₂ concentrations from air-source heat pump radiator heating were roughly below the standard limit throughout the day and remained at a low level during the night presumably because only one person was sleeping in the tested household and there was no fuel to burn.

4.3. Evaluation Using the Gray Relational Analysis Method

According to the above indoor air quality classification criteria (Table 3), the evaluation of indoor air quality in rural houses was divided into five classes. The values for the clean class were the background concentrations of indoor air pollutants, and the values for the light pollution class were the standard limits in the reference standard [38]. The proposed evaluation criteria for indoor air quality in rural houses are shown in

Table 5. Evaluation criteria for indoor air quality.

Parameter	Clean	Non-Pollution	Light Pollution	Medium Pollution	Heavy Pollution
PM2.5/(mg/m3)	0.01	0.025	0.05	0.075	0.15
PM10/(mg/m3)	0.04	0.065	0.1	0.15	0.3
TVOC/(mg/m3)	0.06	0.24	0.6	1.8	3.6
CO2/ppm	400	650	1000	1800	3600

.

Similar to noise, the logarithmic conversion is consistent with the human body’s perception of odor intensity, thus the logarithmic method was used for the dimensionless processing of different pollutants [35]. The formula for the calculation was proposed as follows:

$$L=p\log \frac{n}{n_0}$$

(4)

where $L$ is the pollution intensity, $n$ is the measured pollutant concentration value (

Table 6. Measured values of indoor air quality.

Heating Methods	PM2.5/(μg/m3)	PM10/(μg/m3)	TVOC/(mg/m3)	CO2/ppm
Coal-fired boiler radiator heating	58.524	65.540	1.120	774.434
Air-source heat pump radiator heating	12.194	16.543	0.480	539.547
Chinese stove–kang heating	165.640	176.135	1.050	888.730

), $n_0$ is the background concentration of the pollutant, and $p$ is the pollutant constant.

In order to obtain the specific value $p \mathrm{f}\mathrm{o}\mathrm{r} \mathrm{e}\mathrm{a}\mathrm{c}\mathrm{h} \mathrm{p}\mathrm{o}\mathrm{l}\mathrm{l}\mathrm{u}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{t}$, the value $L$ for each pollutant’s light pollution level was taken as 2 [25] and the background concentration value $n_0$ (i.e., the value of the clean level mentioned above) and the value $n$ of the light pollution level were inserted into Equation (4) [42] according to the data in Table 5. This ensured that the $p$ value and the equation for each pollutant could be obtained. After preprocessing the evaluation criteria (Table 5) and measured values (Table 6) for each pollutant using Formula (4) [42], the elements of each sequence became dimensionless, as shown in

Table 7. Dimensionless indoor air quality evaluation criteria.

Parameter	Clean	Non-Pollution	Light Pollution	Medium Pollution	Heavy Pollution
PM2.5	0.00	1.14	2.00	2.50	3.37
PM10	0.00	1.06	2.00	2.89	4.40
TVOC	0.00	1.20	2.00	2.95	3.56
CO2	0.00	1.06	2.00	3.28	4.80

and

Table 8. Dimensionless indoor pollutant measured values.

Heating Methods	PM2.5	PM10	TVOC	CO2
Coal-fired boiler radiator heating	2.196	1.078	2.543	1.442
Air-source heat pump radiator heating	0.246	−1.928	1.805	0.653
Chinese stove–kang heating	3.488	3.236	2.486	1.743

.

$${∆}_{ij}\left(k\right)=\left|x_i\left(k\right)-y_j\left(k\right)\right|$$

(5)

$${∆}_{max}=\underset{i}{\max }\underset{j}{\max }\underset{k}{\max }{∆}_{ij}\left(k\right)$$

(6)

$${∆}_{min}=\underset{i}{\min }\underset{j}{\min }\underset{k}{\min }{∆}_{ij}\left(k\right)$$

(7)

Using Equations (5)–(7) [42], ${∆}_{max}$ and ${∆}_{min}$ can be obtained using Equations (8) and (9) [42].

$${∆}_{max}=\underset{i}{\max }\underset{j}{\max }\underset{k}{\max }\left|x_i\left(k\right)-y_j\left(k\right)\right|=6.328$$

(8)

$${∆}_{min}=\underset{i}{\min }\underset{j}{\min }\underset{k}{\min }\left|x_i\left(k\right)-y_j\left(k\right)\right|=0.018$$

(9)

After that, the gray correlation coefficients between the reference sequences and the comparison sequences were calculated using Equation (10) [42], and then the relational degrees were calculated using Equation (11) [42]. The association matrix of Equation (12) [42], composed of the relational degrees, is shown in

Table 9. Association matrix of indoor air quality for different heating methods.

Heating Methods	Clean	Non-Pollution	Light Pollution	Medium Pollution	Heavy Pollution	Grade
Coal-fired boiler radiator heating	0.648	0.839	0.860	0.771	0.618	Light pollution
Air-source heat pump radiator heating	0.758	0.759	0.687	0.568	0.481	Non-pollution
Chinese stove–kang heating	0.547	0.679	0.802	0.807	0.742	Medium pollution

.

$${\mathsf{\xi }}_{ij}\left(k\right)=\frac{{∆}_{min}+\rho {∆}_{max}}{{∆}_{ij}\left(k\right)+\rho {∆}_{max}}$$

(10)

$$r_{ij}=\frac{1}{u}{\sum }_{k=1}^u{\mathsf{\xi }}_{ij}\left(k\right),\rho \in \left(0, 1\right),i\in M,j\in N,k\in U$$

(11)

where ${\mathsf{\xi }}_{ij}\left(k\right)$ is the correlation coefficient, reflecting the integrity of the system; $\rho \left(0<\rho <1\right)$ is the discrimination coefficient, usually taking a value of 0.5; and $r_{ij}$ is the relational degree between $X_i$ and $Y_j,$ reflecting the degree of similarity between $X_i$ and $Y_j$ sequence curves. A larger $r_{ij}$ value indicates a closer relationship between $X_i$ and $Y_j$.

An $m\times n$ order association matrix is formed by the relational degrees $r_{ij}, i\in M, j\in N$:

$$R=\left[\begin{array}{ccc}{r}_{11}& \cdots & r_{m1}\\ ⋮& \ddots & ⋮\\ r_{1n}& \cdots & r_{mn}\end{array}\right]$$

(12)

In the association matrix $R$, the elements of each row are the grey relational degrees between an object to be evaluated and different indoor air quality levels. The level corresponding to the maximum relational degree is the indoor air quality level of the object. The elements of each column in $R$ are the grey relational degrees between an indoor air quality level and the corresponding objects [25].

The relational degrees between each heating method and the five evaluation levels were compared; the level corresponding to the maximum value is the pollution level for that heating method. As shown in Table 8, coal-fired boiler radiator heating was light pollution, air-source heat pump radiator heating was non-pollution, and Chinese stove–kang heating was medium pollution. In order of indoor air quality, from best to worst, air-source heat pump radiator heating ranked first, coal-fired boiler radiator heating ranked second, and Chinese stove–kang heating ranked last.

4.4. Evaluation Using the Comprehensive Index Method

The indoor pollutant subindices and composite indices of different heating methods determined using Equation (13) [43] are shown in

Table 10. Indoor pollutant subindices and composite indices.

Heating Methods	PM2.5	PM10	TVOC	CO2	$\mathbf{Composite} \mathbf{Index} \mathit{I}$	Grade
Coal-fired boiler radiator heating	1.170	0.655	1.869	0.774	1.445	Light pollution
Air-source heat pump radiator heating	0.244	0.165	0.799	0.540	0.591	Non-pollution
Chinese stove–kang heating	3.313	1.761	1.750	0.889	2.527	Heavy pollution

.

$$I=\sqrt{\left(\mathrm{m}\mathrm{a}\mathrm{x}\left|\frac{C_1}{S_1},\frac{C_1}{S_1},\cdots \frac{C_n}{S_n}\right|\right) ·\left(\frac{1}{n}\sum \frac{C_i}{S_i}\right)}$$

(13)

where $C_i$ is the measured concentration of the indoor pollutant,$S_i$ is the national standard limit value of the indoor pollutant, and $C_i/S_i$ is the subindex of the indoor pollutant.

The evaluation results using the comprehensive index method showed that the coal-fired boiler radiator heating resulted in light pollution, the air-source heat pump radiator heating resulted in non-pollution, and the Chinese stove–kang heating resulted in heavy pollution. In order of indoor air quality, from best to worst, air-source heat pump radiator heating ranked first, coal-fired boiler radiator heating ranked second, and Chinese stove–kang heating ranked last.

Taken together, there was little difference between the results of the gray relational analysis method and the comprehensive index method. Thus, coal-fired boiler radiator heating could be classified as light pollution, air-source heat pump radiator heating as non-pollution, and Chinese stove–kang heating as medium or heavy pollution.

4.5. Comparison of Subjective and Objective Evaluation Results

As can be seen from Figure 3d of the overall satisfaction with indoor air quality, only 18% of the respondents were “dissatisfied” with Chinese stove–kang heating, and all the respondents were “very satisfied”, “more satisfied” or “basically satisfied” with coal-fired boiler radiator heating. Compared with the objective evaluation results, the subjective evaluations of most rural residents were overly optimistic about the indoor air quality of coal-fired boiler radiator heating and Chinese stove–kang heating. Their perception of indoor pollutants was weak.

In this study, the tests were not conducted in summer for the following reasons. In summer, the rural residents in northern Shanxi do not use the heating systems and often open windows for ventilation. Therefore, indoor air is more affected by outdoor air. In winter, the windows and doors of the local rural houses are basically closed all the time, and indoor air is less affected by outdoor air. The rooms tested were similar in size and were all rectangular in shape. Therefore, the factors of room size, room shape, and residents’ habits regarding the use of doors and windows had little influence on the results of this study.

5. Conclusions

This study evaluated the indoor air pollution levels of three heating methods used in rural houses in northern Shanxi and analyzed the changes in the characteristics of indoor pollutants. The conclusions were as follows:

(1)

For indoor air quality, the rural residents subjectively felt that air-source heat pump radiator heating was the best, coal-fired boiler radiator heating was the second best, and Chinese stove–kang heating was the worst. Compared with the objective test results, the subjective evaluations of most rural residents about the indoor air quality of coal-fired boiler radiator heating and Chinese stove–kang heating were overly optimistic.

(2)

According to the statistical results of the on-site tracking tests for 300 rural houses in northern Shanxi, the exceedance rates of PM_2.5, PM₁₀, TVOC, and CO₂ of coal-fired boiler radiator heating were 64%, 37%, 58%, and 22%, respectively. The exceedance rates of PM_2.5, PM₁₀, TVOC, and CO₂ of air-source heat pump radiator heating were 0%, 0%, 17%, and 6%, respectively. The exceedance rates of PM_2.5, PM₁₀, TVOC, and CO₂ of Chinese stove–kang heating were 85%, 76%, 63%, and 38%, respectively, and the data distribution for each indoor pollutant was relatively decentralized.

(3)

The indoor PM_2.5 and PM₁₀ concentrations from Chinese stove–kang heating varied greatly within the day and showed intermittent peak fluctuations that far exceeded the standard limits in the initial period of fuel combustion. Coal-fired boiler radiator heating had lower PM_2.5 and PM₁₀ pollution levels compared to Chinese stove–kang heating. The PM_2.5 and PM₁₀ concentrations from the air-source heat pump radiator heating varied very little within the day and remained below the standard limits. The indoor TVOC concentrations from coal-fired boiler radiator heating and Chinese stove–kang heating were maintained at comparatively high levels throughout the night, far exceeding the limit of 0.6 mg/m³ stipulated in the referenced standard [38]. With doors and windows closed tightly at night, the indoor CO₂ concentrations from these two heating methods exceeded the standard limit of 1000 ppm [38].

(4)

The evaluation results using the gray relational analysis method showed that coal-fired boiler radiator heating was associated with light pollution, the air-source heat pump radiator heating was associated with non-pollution, and the Chinese stove–kang heating was associated with medium pollution. Evaluation results using the comprehensive index method showed that the coal-fired boiler radiator heating was associated with light pollution, the air-source heat pump radiator heating was associated with non-pollution, and the Chinese stove–kang heating was associated with heavy pollution. Thus, coal-fired boiler radiator heating could be classified as light pollution, air-source heat pump radiator heating could be classified as non-pollution, and Chinese stove–kang heating could be classified as medium or heavy pollution.

This study provides an important supplement to the field of rural indoor air quality research. The results can help residents make choices about heating methods. In addition, based on the changing characteristics of indoor pollutants, residents can make human-initiated interventions during high pollution periods, such as opening windows and ventilating. Due to the constraints of experimental conditions and time, this study only investigated indoor pollution conditions in the coldest month of the year. Comparative analysis of different months during the heating periods can be conducted in future research. Furthermore, subsequent research should be undertaken to explore specific improvement strategies for high-pollution periods in rural houses.