Sustainable Natural Ventilation Strategies for Acceptable Indoor Air Quality: An Experimental and Simulated Study in a Small Office During the Winter Season

Abstract

This study proposes sustainable natural ventilation strategies using the periodic opening and closing of windows and doors to maintain acceptable indoor air quality in a small office space during the winter season. Field experiments were conducted in a 26.8 m² university office room in Seoul, Korea, measuring the indoor and outdoor temperature, humidity, wind speed, carbon dioxide concentration, and fine dust levels. A simulation model based on a first-order differential equation was developed using EES software (version 9) to predict indoor CO₂ concentrations at one-minute intervals. The simulation results showed good agreement with the experimental data, validating the accuracy of the modeling approach. Based on the validated model, practical ventilation durations and intervals were derived according to the occupant number and room volume, ensuring that indoor CO₂ concentrations remained below the recommended 1000 ppm threshold. The results demonstrate that simple, periodic natural ventilation is effective in maintaining acceptable indoor air quality. As a passive strategy requiring no electrical energy, it offers a sustainable and low-cost solution for creating a healthy indoor environment.

1. Introduction

Recently, the concentration of fine dust has gradually increased compared to the past, becoming a serious environmental problem [1,2,3,4,5]. The International Agency for Research on Cancer (IARC) under the World Health Organization (WHO) classified fine dust as a Group 1 carcinogen [6,7,8,9]. As shown in Figure 1, a comparison of annual PM_2.5 concentrations in Seoul, South Korea, over a seven-year period (2014–2020) indicates that Seoul recorded the second highest levels, following Beijing, China [2,10,11]. According to the ‘2019 World Air Quality Report’ published by Air Visual, a global air pollution research institute, Korea’s annual average fine dust concentration was the highest at 24.8 µg/m³ among OECD member countries in 2019, and 61 Korean cities were included in the world’s top 100 cities with the most severe ultrafine dust pollution [12,13]. As air quality continues to deteriorate, the frequency of ultrafine dust advisories and warnings is on the rise [6,14,15,16,17]. As a result of this air pollution alert system, the public has become increasingly aware of the dangers posed by fine dust and has gradually recognized the importance of proper ventilation [6,18,19,20].

Most people spend over 90% of their time indoors [21,22,23,24,25]. Without adequate ventilation, pollutants generated from human activities and building materials can gradually accumulate, leading to a deterioration in the indoor air quality. In particular, the buildup of fine dust and CO₂ generated from human respiration can pose a significant threat to the health of occupants [26,27,28,29,30,31,32,33,34].

In the case of spaces where mechanical ventilation equipment is installed, the efficiency of filters has increased due to technological advancements, so HEPA filters can filter out more than 98% of ultrafine dust, and fresh outside air can now be introduced without concern, even if it contains high levels of fine dust [35,36,37,38,39]. In the Republic of Korea, the installation of mechanical ventilation systems is mandatory in public housing, such as apartments with more than 100 households, when natural ventilation does not meet the minimum ventilation requirements. This regulation is based on the ‘Rules on Equipment Standards for Buildings’, announced by the Ministry of Land, Infrastructure, and Transport in 2006 [40,41].

However, in relatively small spaces, mechanical ventilation systems are often lacking [42,43]. Recently, as the number of individuals aspiring to start their own businesses has increased, the number of one-person creative enterprises has grown rapidly. Consequently, the demand for single-person offices has also risen [43,44,45]. In such smaller spaces without mechanical ventilation systems, natural ventilation is essential due to health concerns. Since there are no legal regulations regarding ventilation in these spaces, it is imperative to conduct research on appropriate ventilation methods [43,46].

The concentration of CO₂ has been regarded as an essential indicator for measuring and managing indoor air quality. The Ministry of Environment of the Republic of Korea, in the “Enforcement Rule of the Indoor Air Quality Control Act” (hereinafter referred to as the “Indoor Air Quality Maintenance Standards”), mandates that indoor carbon dioxide concentration levels be maintained below 1000 ppm [47]. When the concentration of CO₂ in indoor air exceeds the safety threshold of 1000 ppm, it causes discomfort to occupants, leading to symptoms such as drowsiness, headaches, decreased concentration, and reduced work performance [32,33,34,48,49]. An increase in indoor CO₂ concentration has a negative impact on work productivity from a qualitative perspective, even when the concentration is below the indoor air quality standard of 1000 ppm [31].

Table 1. Standards for indoor air pollutants: domestic and international.

	South Korea	Japan	Hong Kong	Singapore	WHO
Facility Type	Office	Office	Office	Office	Indoor
Fine dust (µg/m3)	150	150	180	150	-
CO2 (ppm)	1000	1000	1000	1000	-
Formaldehyde (µg/m3)	120	100	100	120	100
Airborne bacteria(CFU/m3)	800	-	100	500	-
CO (ppm)	10	10	8.7	9	10
VOCs (CFU/m3)	500	-	600	300

shows the indoor air pollutant standards for offices both domestically and internationally [46].

In the future, as fossil energy sources become increasingly scarce and global climate change mitigation efforts intensify (e.g., under the Paris Agreement and UN Sustainable Development Goals), developing methods to maintain indoor air quality (IAQ) without excessive energy consumption will be essential [50,51,52,53,54,55]. This need is underscored by the building sector’s significant energy and carbon footprint. It currently accounts for roughly 34% of the global final energy demand and about 21% of global greenhouse gas emissions [56]. This considerable share highlights the importance of energy-efficient ventilation strategies for achieving global climate targets, as outlined in international agreements and agendas. While mechanical ventilation systems rely on high-grade energy sources such as electricity, natural ventilation through doors and windows operates without any active energy input [57,58,59]. This passive approach harnesses natural pressure differences between indoor and outdoor environments, making it a more sustainable ventilation strategy for buildings. However, both ventilation methods inevitably introduce outdoor air, which can influence indoor thermal conditions. In particular, during cold winter periods, introducing fresh outdoor air through either mechanical or natural ventilation can lead to heat loss and an increased heating energy demand. The primary difference is that mechanical ventilation actively draws in air using fans, whereas natural ventilation achieves this air exchange passively. Given this fundamental similarity in outcomes, our study focused on the feasibility and effectiveness of natural ventilation as a low-energy strategy, rather than conducting a comparative cost analysis of heating energy requirements.

2. Research Objectives

To propose an appropriate ventilation method for small spaces without mechanical ventilation systems, an experiment was conducted in a small office where people were working. Natural ventilation was achieved through doors and windows, and indoor air quality was analyzed by measuring fine dust and CO₂ concentrations. The experiment was carried out during the winter season when the air exchange rate between the indoors and outdoors is relatively high.

The goal of this study is to provide practical guidelines for individuals in similar environments, particularly those managing natural ventilation in small-scale spaces comparable to the experimental setting by determining how long and how often doors and windows should be opened for effective ventilation. By focusing on spaces with similar external conditions and occupancy patterns, this study aims to propose an appropriate ventilation method tailored for small office spaces. Specifically, a correlation equation and guidelines were developed to predict the appropriate natural ventilation times based on the number of occupants and room volume. Furthermore, a simulation program using EES software(version 9) was developed to predict CO₂ concentrations on a minute-by-minute basis, and a multiple regression analysis was performed to derive an equation that calculates the appropriate ventilation time on an hourly basis, providing a more precise recommendation for when and for how long occupants should ventilate their spaces.

3. Methods

3.1. Space of Test Subject

This study was conducted in a professor’s office within a university building in Seoul, Korea, which was selected as the experimental space. The office is designed for single occupancy. The building has eight floors above ground and one basement level, with the experiment space situated on the 5th floor. The office has a floor area of 26.8 m², a ceiling height of 2.7 m, and a total volume of 72.36 m³. The room features one door and one window; the door connects to a hallway, and the window opens to the outside. The door, which opens inward, has a surface area of 1.908 m², while the window, an awning type, provides an effective open area of 0.324 m². Figure 2 illustrates the experimental space, and the key specifications are summarized in

Table 2. Office information.

Architectural Specifications	Dimensional Parameters	Additional Information
Construction	Reinforced concrete	Completion year 2021
Floor area	26.8 m2	-
Ceiling height	2.7 m	-
Volume	72.36 m3	Actual volume excluding the volume occupied by the furniture, 65.124 m3
Door area	1.91 m2	The door on the north wall opens and closes inward
Window effective open area	0.324 m2	Awning window on the south wall
Window area ratio	1.21%	-

.

3.2. Measurement Method

3.2.1. Measuring Points and Measuring Elements

To analyze the indoor air quality in the experimental space, concentrations of carbon dioxide (CO₂), particulate matter (PM), temperature, and humidity were measured. For CO₂ concentration, Sensirion SEK-SCD41 sensors were positioned at heights of 50, 120, and 190 cm above the floor at each sampling point. The placement strategy was designed to ensure a comprehensive representation of CO₂ distribution throughout the space. Specifically, the sensors were widely distributed to capture the overall concentration levels across the room, minimizing the impact of localized variations and ensuring a more generalized assessment of air quality.

The choice of measurement heights was determined based on the expected dynamics of CO₂ and PM dispersion. Given that the primary source of CO₂ emissions is human respiration, the 120 cm height was selected to correspond with the average breathing height of seated occupants, reflecting realistic exposure levels. Additionally, sensors were positioned at 50 cm and 190 cm, representing lower and upper measurement points, respectively, to assess vertical distribution variations. These heights were selected based on a balanced approach, ensuring a 70 cm interval above and below the primary breathing zone to capture potential stratification effects.

For PM concentration, Sensirion SEK-SPS30 sensors were placed at heights of 50 cm and 160 cm above the floor. This placement considered the possibility of particulate matter suspension in air, as lower positions capture settled or resuspended particles near the floor, while higher positions detect airborne particulates within the breathing zone. By incorporating multiple heights, this study aimed to analyze the distribution of PM across different layers of the indoor environment.

Anemometers were installed on the door and window to measure the air velocity of ventilation airflow. The overall arrangement of the sensors was carefully designed to ensure an even distribution across the experimental space, allowing for a representative assessment of air quality parameters. Horizontally, the measurements were taken at three interior points and two exterior points, as shown in Figure 3a, to observe horizontal variations. Since occupants primarily stay near the center of the room, the three interior points were positioned accordingly near the center. Figure 3 illustrates each measurement location, and

Table 3. Measurement locations and elements.

Measurement Height [cm]	A	B	C	Hall	Door	Window	Out
50	CO2, PM2.5	CO2, PM2.5	PM2.5
120	CO2	CO2
160	PM2.5	PM2.5	PM2.5	CO2, PM2.5
190	CO2	CO2
-					Wind speed	Wind speed	CO2, PM2.5

specifies the measured variables at each point.

3.2.2. Experiment Schedule

The experiment was conducted in February 2022 during the winter season and spanned two consecutive days, allowing for stable conditions under typical winter weather. The first day was designated as Experiment 1 and the second day as Experiment 2. The schedule of Experiment 1 was designed to reflect the average working hours of office employees, with occupancy from 9 a.m. to 12 p.m., a lunch break from 12 p.m. to 1 p.m., and re-occupancy from 1 p.m. to 6 p.m. Natural ventilation was implemented every 50 min of occupancy, followed by a 10 min ventilation period. Experiment 1 involved ventilation through both the door and window, and its data were subsequently compared with simulation results to validate the reliability of the simulation model. In Experiment 2, natural ventilation was performed at two-hour intervals, with 110 min of occupancy followed by 10 min of ventilation. This experiment also included ventilation by simultaneously opening the door and window. The detailed schedule of the experiments is provided in

Table 4. Experiment schedule.

Experiment	Time [Hour:Min]	Number of Occupants	Door Ventilation	Window Ventilation
1	09:00~09:50	1	Close	Close
	09:50~10:00	1	Open	Close
	10:00~10:50	1	Close	Close
	10:50~11:00	1	Open	Close
	11:00~11:50	1	Close	Close
	11:50~12:00	1	Open	Close
	12:00~13:00	0	Close	Close
	13:00~13:50	2	Close	Close
	13:50~14:00	2	Close	Open
	14:00~14:50	1	Close	Close
	14:50~15:00	1	Open	Close
	15:00~15:50	2	Close	Close
	15:50~16:00	2	Close	Open
	16:00~16:50	1	Close	Close
	16:50~17:00	1	Open	Close
	17:00~17:50	2	Close	Close
	17:50~18:00	2	Close	Open
2	09:00~09:50	1	Close	Close
	09:50~10:00	1	Close	Open
	10:00~11:50	2	Close	Close
	11:50~12:00	2	Close	Open
	12:00~13:00	0	Close	Open
	13:00~13:50	2	Close	Close
	13:50~14:00	2	Open	Open
	14:00~14:50	1	Close	Close
	14:50~15:00	1	Open	Open
	15:00~15:50	1	Close	Close
	15:50~16:00	1	Open	Open
	16:00~17:50	2	Close	Close
	17:50~18:00	2	Open	Open

.

The outdoor PM_2.5 concentration during the experiments varied within the range classified as ‘Good’ to ‘Moderate’ based on the standards set by the World Health Organization (WHO). Specifically, during Experiment 1, the average outdoor PM_2.5 concentration was 16.81 µg/m³ (Moderate), while during Experiment 2, it was 8.58 µg/m³ (Good) [60]. These values indicate that the experiments were conducted under representative air quality conditions in which natural ventilation is generally considered viable. Additionally, the average outdoor temperatures were −1.7 °C for Experiment 1 and −4.8 °C for Experiment 2, with corresponding average relative humidity levels of 38.0% and 22.8%, respectively. These conditions align with typical winter environments, where colder temperatures are often accompanied by lower humidity levels. To maintain an optimal indoor temperature of 21 °C during winter, adjustments were made accordingly, resulting in an average indoor temperature of 21.2 °C for Experiment 1 and 20.4 °C for Experiment 2.

Although this study was conducted over two days, the selection of experimental days was based on stable and representative meteorological conditions to ensure the reliability of the results. Given the variability of outdoor air quality and meteorological factors over extended periods, increasing the number of test days could introduce additional variables that might complicate the interpretation of natural ventilation effects. Instead, by conducting the experiments under controlled yet realistic conditions, this study aimed to provide a practical framework for natural ventilation strategies during the winter season. The findings serve as a reference for appropriate ventilation practices under favorable winter air quality conditions, offering insights that can be applied in similar environments.

3.3. Development of a CO₂ Concentration Prediction Simulation Program

3.3.1. A CO₂ Concentration Prediction Simulation Program Based on First-Order Differential Equation

In this study, we developed a CO₂ concentration simulation program based on a mass balance equation to predict indoor CO₂ concentration at one-minute intervals. The change in indoor CO₂ concentration over time can be represented by a first-order differential equation, as shown in Equation (1).

$$V{\displaystyle \frac{{dC}_{{CO}_2}}{dt}}={\dot{V}}_{adj}{C}_{adj}-{\dot{V}}_{adj}{\dot{C}}_{{CO}_2}+{\dot{V}}_{out}{\dot{C}}_{out}-{\dot{V}}_{out}{C}_{{CO}_2}+{\dot{M}}_{adult}{N}_{adult}$$

(1)

Here, $V$, $C_{{CO}_2}$, ${\dot{V}}_{adj}$, $C_{adj}$, ${\dot{V}}_{out}$, $C_{out}$, ${\dot{M}}_{adult}$, and $N_{adult}$ are the volume of the room, indoor CO₂ concentration, volumetric flow rate infiltrating into the adjacent space, CO₂ in the adjacent space, external volumetric flow rate, outdoor CO₂ concentration, outdoor CO₂ concentration, adult CO₂ emission rate, and number of adult occupants, respectively. The conceptual diagram of this equation is shown in Figure 4.

This program predicts indoor CO₂ concentration over time based on inputs such as room volume, the number of occupants and their occupancy duration, CO₂ emission rates per occupant, initial indoor CO₂ concentration, outdoor CO₂ concentration, CO₂ concentration of adjacent spaces, and the method and timing of natural ventilation through a door and window. For the simulation, measured values were used for initial, adjacent, and outdoor CO₂ concentrations.

The experiment was conducted in a single-person office space, which inherently involves fewer occupants and lower levels of physical activity compared to multi-occupant offices. To reflect the realistic conditions of such a workspace, one or two occupants primarily remained seated, performing typical office tasks such as reading documents or working at a desk.

3.3.2. Validation of the Simulation Program

To validate the accuracy of the simulation program, measured CO₂ concentrations were compared with time-based concentration values generated by the simulation. The accuracy was verified using the CV(RMSE)(Coefficient of Variation of the Root Mean Square Error), as recommended in ASHRAE (2014) Guideline 14. According to this guideline, time-series data with a CV(RMSE) within ±30% are considered reliable, with reliability increasing as the value approaches 0% [61]. The CV(RMSE) can be calculated using Equations (2) and (3) [62].

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{\sum _{i=1}^n{(y_{sim,i}-y_i)}^2}{n}}}$$

(2)

$$\mathrm{C}\mathrm{V}(\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E})={\displaystyle \frac{\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}}{\overline{y}}}\times 100$$

(3)

where RMSE is the Root Mean Square Error; $y_{sim,i}$ is simulation based value; $y_i$ is actual measurement value; $n$ is the number of actual measurement value; CV(RMSE) is the Coefficient of Variance of the Root Mean Square Error; and $\overline{y}$ is mean of actual measurement value.

4. Result

4.1. Results of the Simulation Program Reliability Validation

4.1.1. Simulation Verification Through Experiment 1

The measured CO₂ concentrations from Experiment 1 and the predicted values from the simulation program are displayed in Figure 5. The CV(RMSE) for the measured and predicted values in Experiment 1 was calculated to be 4.69%. The CO₂ concentration prediction simulation program developed in this study, based on first-order differential equations, met the reliability criteria proposed in ASHRAE Guideline 14 [61].

4.1.2. Simulation Verification Through Experiment 2

The CV(RMSE) of the predicted values from the simulation program in Experiment 1 satisfies the criteria of ASHRAE Guideline 14. Therefore, the same simulation input conditions applied in Experiment 1 were used in the simulation to compare with the measured data from Experiment 2, conducted the following day. The measured and simulated CO₂ concentrations from Experiment 2 are presented in Figure 6. The CV(RMSE) for Experiment 2 was calculated to be 7.00%. Since both Experiments 1 and 2 satisfy ASHRAE Guideline 14, the reliability of the simulation program for predicting CO₂ concentrations at 1 min intervals is considered to be sufficiently validated. Consequently, the simulation program is deemed fully applicable for predicting indoor CO₂ concentrations during the winter season.

4.1.3. Air Changes per Hour (ACH) Derived from the Simulation Program

The simulation analysis showed that the air change rate through doors was 4.8 ACH, through windows was 5.2 ACH, and for a closed classroom was 0.2 ACH.

4.2. Analysis Results of Appropriate Ventilation Method for Each Case

Based on ASHRAE Guideline 14, an appropriate natural ventilation method for small spaces was proposed using a minute-by-minute CO₂ concentration prediction simulation program that has proven reliability. Since the Ministry of Environment of the Republic of Korea’s “Enforcement Rules for the Indoor Air Quality Management Act” (hereinafter referred to as “Indoor Air Quality Maintenance Standards”) sets the indoor CO₂ concentration to 1000 ppm or less, a ventilation method that does not exceed 1000 ppm was proposed [47]. The initial CO₂ concentration in the room, CO₂ concentration in the adjacent space, and outdoor air concentration were set at 424.7 ppm, which is the monthly average CO₂ concentration in January 2020 according to the “Atmospheric Environment Yearbook 2020” published by the National Institute of Environmental Research of the Republic of Korea [63]. For each of the three ventilation methods, the ventilation time according to the occupancy time in 1 h and 2 h increments was presented when one person was in the room and the ventilation time according to the occupancy time in 1 h and 2 h increments when two people were in the room were presented. The results for each case are shown in Figure 7, and the appropriate ventilation methods are shown in

Table 5. Appropriate natural ventilation time for various natural ventilation methods.

Case	Number of Occupants	Ventilation Method	Time Interval [h]	Residence Time [min]	Ventilation Time [min]
1	1	Door	1	57	3
2		Window		57	3
3		Door + Window		58	2
4		Door	2	113	7
5		Window		114	6
6		Door + Window		117	3
7	2	Door	1	50	10
8		Window		51	9
9		Door + Window		55	5
10		Door	2	83	37
11		Window		84	36
12		Door + Window		92	28

.

Figure 7 shows the results of Cases 1 to 12, which analyzed the natural ventilation method to prevent the indoor CO₂ concentration from exceeding 1000 ppm using a minute-by-minute CO₂ concentration prediction simulation program. Overall, the concentration of CO₂ increased while the occupants were in the room, and CO₂ decreased more rapidly during ventilation through doors and windows than the CO₂ that increased during the occupancy of one or two people.

It was confirmed that in a small space without mechanical ventilation equipment, the CO₂ concentration can be sufficiently maintained below 1000 ppm through natural ventilation.

4.3. Development of Natural Ventilation Time Correlation Equation

4.3.1. Proposal of a Predictive Equation

Based on the results of this study, a correlation equation was developed using the least squares method—one of the most widely used techniques for fitting sample data—through regression analysis to predict the natural ventilation time required for a room [64]. The formula for the least squares method is as shown in Equation (4), and the coefficient value that minimizes the sum of error squares was determined. A regression analysis was performed using the number of occupants and volume as parameters, and the analysis was performed using the least squares method function installed in the EES software(version 9). The first- and second-order expressions of the elements were proposed for the predictive equations, as shown in Equations (5) and (6).

$$S=\sum {(T_{est,i}-T_i)}^2$$

(4)

$$T_{vent}=C_{n}n+C_{V}V+C$$

(5)

$$T_{vent}=C_{1}n+C_2{n}^2+C_{3}nV+C_{4}V+C_5{V}^2+C_6$$

(6)

where $T_{est,i}$ is the estimated ventilation time and $T_i$ is the validated simulation ventilation time.

4.3.2. Case Selection and Analysis Results for Predicting Ventilation Time

To enable a more precise analysis, the simulation program, which originally predicted the CO₂ concentration on a minute-by-minute basis, was modified to predict on a second-by-second basis. The results were then converted back to minute-by-minute values rounded to the first decimal place for analysis. Furthermore, to improve the accuracy of the regression equations, a database of 25 results was constructed for each of the three previously mentioned ventilation methods. The database was created by varying the number of occupants (1, 1.5, 2, 2.5, and 3 persons) and the room volume (1, 1.5, 2, 2.5, and 3 times the experimental volume). The database of ventilation times for the door, window, and door + window ventilations times created from the simulation results is shown in

Table 6. Database generated from simulation results.

Number of Occupants	Volume [m3]	Door		Window		Door + Window
		Residence Time [min]	Ventilation Time [min]	Residence Time [min]	Ventilation Time [min]	Residence Time [min]	Ventilation Time [min]
1	58.53	58.1	1.9	58.2	1.8	59.1	0.9
1.5	58.53	54.8	5.2	55.2	4.8	57.4	2.6
2	58.53	50.9	9.1	51.6	8.4	55.5	4.5
2.5	58.53	46.4	13.6	47.3	12.7	52.9	7.1
3	58.53	41.4	18.9	42.5	17.5	49.4	10.6
1	87.79	59.9	0.1	59.9	0.1	59.9	0.1
1.5	87.79	58.1	1.9	58.2	1.8	59.1	0.9
2	87.79	55.9	4.1	56.2	3.8	58.0	2.0
2.5	87.79	53.6	6.4	54.0	6.0	56.8	3.2
3	87.79	50.9	9.1	51.6	8.4	55.5	4.5
1	117.06	60.0	0.0	60.0	0.0	60.0	0.0
1.5	117.06	59.7	0.3	59.7	0.3	59.8	0.2
2	117.06	58.1	1.9	58.2	1.8	59.1	0.9
2.5	117.06	56.5	3.5	56.7	3.3	58.3	1.7
3	117.06	54.7	5.3	55.1	4.9	57.4	2.6
1	146.33	60.0	0.0	60.0	0.0	60.0	0.0
1.5	146.33	59.9	0.1	59.9	0.1	59.9	0.1
2	146.33	59.4	0.6	59.4	0.6	59.7	0.3
2.5	146.33	58.1	1.9	58.2	1.8	59.1	0.9
3	146.33	56.8	3.2	57.0	30.	58.4	1.6
1	175.59	60.0	0.0	60.0	0.0	60.0	0.0
1.5	175.59	60.0	0.0	60.0	0.0	60.0	0.0
2	175.59	59.9	0.1	59.9	0.1	59.9	0.1
2.5	175.59	59.2	0.8	59.2	0.8	59.6	0.4
3	175.59	58.1	1.9	58	1.8	59.0	1.0

.

4.3.3. Regression Analysis Results

The regression analysis results for the window, door, and door + window ventilation methods in Table 6, using the number of occupants and volume as the parameters, showed that the second-order prediction equation had fewer errors compared to the first-order prediction equation. The results of the multiple regression analysis are presented in Figure 8, and the coefficients for the two equations are shown in

Table 7. First- and second-order correlation constants and standard deviation $\sigma$.

Ventilation Method	$\mathit{T}={\mathit{C}}_{\mathit{n}}\mathit{n}+{\mathit{C}}_{\mathit{V}}\mathit{V}+\mathit{C}$				$\mathit{T}={\mathit{C}}_1\mathit{n}+{\mathit{C}}_2{\mathit{n}}^2+{\mathit{C}}_3\mathit{n}\mathit{V}+{\mathit{C}}_4\mathit{V}+{\mathit{C}}_5{\mathit{n}}^5+{\mathit{C}}_6$
	${\mathit{C}}_{\mathit{n}}$	${\mathit{C}}_{\mathit{V}}$	$\mathit{C}$	$\mathsf{\sigma }$	${\mathit{C}}_1$	${\mathit{C}}_2$	${\mathit{C}}_3$	${\mathit{C}}_4$	${\mathit{C}}_5$	${\mathit{C}}_6$	$\mathsf{\sigma }$
Door	3.66	−0.07353	4.884	140.074	7.309	0.8857	−0.06144	−0.16	0.000894	4.321	14.781
Window	3.4	−0.06806	4.52	119.563	6.832	0.8	−0.5665	−0.1485	0.000827	3.77	12.895
Door + Window	1.924	−0.03841	2.496	46.223	3.669	0.5657	−0.03424	−0.08709	0.0005	2.46	6.866

.

A comparison of the first-order and second-order equations obtained through multiple regression analysis revealed that predictions using the second-order equation had fewer errors than those using the first-order equation. The second-order correlation equations for predicting the ventilation time through doors, windows, and simultaneous door and window ventilation are given as Equations (7), (8), and (9), respectively.

$$T_{d,vent}=7.309n+0.8857n^2-0.06144nV-0.16V+0.000894V^2+4.321$$

(7)

$$T_{w,vent}=6.832n+0.8n^2-0.5665nV-0.1485V+0.000827V^2+3.977$$

(8)

$$T_{dw,vent}=3.669n+0.5657n^2-0.03424nV-0.08709V+0.0005V^2+2.46$$

(9)

This study focused on analyzing CO₂ concentrations and did not primarily address particulate matter. However, during the two-day experiment, the average indoor PM_2.5 concentrations were 13.87 µg/m³ and 8.21 µg/m³, respectively, both of which satisfy the World Health Organization (WHO) guideline of 15 µg/m³ or less for good indoor air quality. The relatively low activity levels typical of office environments likely contributed to the minimal resuspension of the particulate matter.

In Experiment 1, the average outdoor and corridor PM_2.5 concentrations were 16.81 µg/m³ and 15.19 µg/m³, respectively. In Experiment 2, they were 8.58 µg/m³ and 8.51 µg/m³. Since indoor and outdoor PM_2.5 levels were generally low and comparable, natural ventilation did not significantly increase the indoor particulate concentrations. Consequently, indoor PM_2.5 levels in both experiments remained at 13.87 µg/m³ and 8.21 µg/m³, respectively.

Both experiments were conducted under conditions where particulate matter concentrations were within acceptable limits according to WHO guidelines [60], allowing for natural ventilation without the significant deterioration of indoor air quality. Therefore, this study primarily concentrated on CO₂ analysis. Future research will aim to investigate particulate matter dynamics in greater detail and assess their potential effects on indoor air quality during natural ventilation.

5. Conclusions

This study developed a simulation program to predict the indoor CO₂ concentration on a one-minute basis using a mass balance equation. The program was used to propose optimal ventilation times for small spaces without mechanical ventilation systems during winter, focusing on natural ventilation methods using windows, doors, and doors + windows. Additionally, correlation equations for predicting optimal natural ventilation times were developed through multiple linear regression analysis. The experiments were conducted in winter and involved natural ventilation through doors, windows, and the simultaneous use of doors and windows. The reliability of the simulation program was validated based on ASHRAE Guideline 14. Using the validated simulation program, optimal ventilation methods were proposed. Regression analysis was conducted with the number of occupants and the volume as parameters to develop correlation equations for predicting natural ventilation durations. The main findings are as follows.

(1)

In this study, a simulation program was developed to predict indoor CO₂ concentrations based on a mass balance equation. The program’s reliability was validated using ASHRAE Guideline 14 by comparing it with measured values from two experiments, resulting in CV(RMSE) values of 4.69% and 7.00%, respectively, thereby demonstrating its reliability.

(2)

For a single occupant over a 1 h period, it was seen that indoor CO₂ concentration does not exceed 1000 ppm under the following conditions: 57 min of occupancy and 3 min of ventilation using the door, 57 min of occupancy and 3 min of ventilation using the window, or 58 min of occupancy and 2 min of ventilation using both the door and window simultaneously.

(3)

Under the same single-occupant scenario, for a two-hour period, the analysis showed that with ventilation through a door, 113 min of occupancy and 7 min of ventilation, with ventilation through a window, 114 min of occupancy and 6 min of ventilation, and with simultaneous ventilation through both a door and a window, 117 min of occupancy and 3 min of ventilation, the indoor CO₂ concentration does not exceed 1000 ppm.

(4)

For a scenario with two occupants, the analysis revealed that with ventilation through a door, 50 min of occupancy and 10 min of ventilation per hour, with ventilation through a window, 51 min of occupancy and 9 min of ventilation per hour, and with simultaneous ventilation through both a door and a window, 55 min of occupancy and 5 min of ventilation per hour, the indoor CO₂ concentration does not exceed 1000 ppm.

(5)

In the two-occupants scenario for a two-hour interval, the analysis indicated that with ventilation through a door, 83 min of occupancy and 37 min of ventilation, with ventilation through a window, 84 min of occupancy and 36 min of ventilation, and with simultaneous ventilation through both a door and a window, 92 min of occupancy and 28 min of ventilation, the indoor CO₂ concentration does not exceed 1000 ppm.

These results demonstrate that natural ventilation, when properly scheduled, can effectively maintain the indoor air quality without the need for continuous mechanical ventilation systems. This has important implications for reducing building energy use, especially in small-scale office environments where mechanical systems may not be present or efficient. As natural ventilation relies solely on pressure and temperature differences rather than electricity, it serves as a passive and low-energy solution aligned with broader environmental goals to minimize fossil fuel consumption and greenhouse gas emissions.

Future research will address these limitations by considering particulate matter concentrations and room characteristics to propose more generalized ventilation methods. This study aimed to propose natural ventilation methods for small spaces and conducted experiments in a single-person workspace. However, it is limited in that it does not account for the diverse characteristics of various space types under different conditions. This study was carried out in a specific setting, and to improve the reliability of the findings, further validation through repeated experiments under identical conditions across a range0 of space types is necessary. As the workspace size and occupancy increase, the presence of additional furniture and electronic equipment is expected to influence the airflow patterns, CO₂ distribution, and the circulation of other contaminants. In larger work environments, the air temperature tends to be neither uniform nor constant throughout the space, resulting in variations in ventilation effectiveness [65]. These factors were beyond the scope of the present study, but will be addressed in future research to develop ventilation strategies suitable for larger and more complex indoor environments. Future studies will also aim to overcome current limitations by incorporating factors such as particulate matter concentrations and room-specific characteristics, ultimately proposing more generalized and robust natural ventilation methods.