Simulating the Natural Seasonal Ventilation of a Classroom in Poland Based on Measurements of the CO₂ Concentration

Abstract

There are many different factors affecting indoor air quality: environmental ones such as temperature, humidity, human activities within the building, smoking, cooking, and cleaning, but also external pollutants such as particulate matter, biological contaminants, and viruses or allergens. This study investigated the indoor air quality (IAQ) of a primary-school classroom in Cracow, Poland, based only on CO₂ concentration levels exhaled by occupants. In the 1960s, over a thousand schools were built in Poland using similar technology. Most of them are still in use, and in many cases, modernization works are being carried out to improve their building envelope and the comfort of their use. The analyzed school is one of several hundred similar ones in southern Poland. Therefore, analyzing the possibilities of improving IAQ is an important topic, and the results can be used in the modernization process for many other buildings. Measurements indicated that the CO₂ levels significantly exceeded acceptable standards, signaling poor air quality during usage time. This problem was connected mainly with the low efficiency of the natural ventilation system being used in the classroom. It is worth emphasizing that this type of ventilation system is the most commonly used ventilation solution in Polish schools. To address this problem, the classroom environment was simulated using CONTAM software, and the model was validated by comparing the simulated measurement data against the collected measurement data. Next, simulations for the entire heating season in Cracow were conducted, revealing that the IAQ remained consistently poor throughout this period. These findings highlight the persistent problem of inadequate ventilation in the classroom, which can have adverse effects on the health and performance of students and teachers. This article shows the usefulness of CONTAM for modeling not only gravity ventilation but also the window-opening process. The validated CONTAM model will be subsequently utilized to simulate annual IAQ conditions under various ventilation strategies in order to identify the most effective methods for maintaining acceptable IAQ while minimizing energy consumption. In our future analysis, the validated model will be used to test the following systems: demand-controlled ventilation (DCV), exhaust ventilation, and DCV/balanced ventilation with heat recovery.

1. Introduction

Children spend nearly 12% of their lives in classrooms, which is more time than they spend in any building other than their homes [1]. This makes it crucial to ensure good indoor air quality (IAQ) in these spaces. IAQ in schools is a key factor influencing both the health and academic performance of students. Typically, IAQ in classrooms is measured based on the CO₂ concentration, which tends to increase with the number of students and decrease with better ventilation. An oxygen concentration that is too low can cause feelings of breathlessness and headaches and consequently reduce students’ concentration and the effectiveness of learning. Such conclusions have been presented in many scientific studies and works in the literature [2,3,4,5,6,7]. The authors of these studies have proven that an increased concentration of carbon dioxide negatively affects the absorption of knowledge; therefore, when designing ventilation, special attention should be paid to controlling this concentration. Various groups of students and pupils were the subjects of these studies. The results obtained in tests (mathematical tests, reading comprehensions, etc.) taken in a classroom with a controlled concentration of carbon dioxide in the range of 600–5000 ppm (depending on the test being taken) were analyzed. All researchers agreed that at concentrations above 2000–3000 ppm, the results obtained by students are significantly worse compared with the results obtained at concentrations below 1000 ppm [2,6]. The authors of [6], on the basis of their own literature review and research, specified the effects of specific concentration levels of carbon dioxide as follows:

• Carbon dioxide at 1000 ppm—maximum hygienic level;
• Carbon dioxide at 5000 ppm—feelings of fatigue, discomfort;
• Carbon dioxide at 15,000 ppm—breathing disorders;
• Carbon dioxide at 30,000 ppm—dizziness, headaches;
• Carbon dioxide at 50,000 ppm—difficulty breathing, visual disturbances;
• Carbon dioxide at 100,000 ppm—unconsciousness.

Taking into account the research on the correlation between test results and the concentration of carbon dioxide and knowing the effects of an increased CO₂ concentration, it should be stated that the value of this parameter is very important in educational buildings.

Numerous factors impact indoor air quality [8], including environmental, building-related, and occupant-related elements. Environmental factors encompass climatic conditions and seasonal variations, while building-related factors involve airtightness, school location, classroom and window design, ventilation type and rate, internal temperature, window drafts, and room size. Occupant-related influences include CO₂ exhalation rates, occupants’ behavior, system maintenance and operation, operating schedules, the number of occupants, activity levels, and the time spent in the room, as well as occupants’ age and individual thermal comfort preferences [9].

Maintaining healthy indoor air quality is crucial for children’s well-being, as they are particularly sensitive to indoor air pollutants. Consequently, occupant-related factors significantly influence IAQ in primary-school buildings, especially given the potential variability and unpredictability of these factors [8].

There is a significant body of research exploring the impact of classroom conditions on children’s academic performance, driven by the observation that thermal and air quality standards in schools frequently fall below recommended levels. This discrepancy often arises due to limited funding for building maintenance and upgrades, as well as a growing tendency for schools to allow classroom temperatures to exceed the advised winter range of 20–22 °C during warmer periods. Additionally, outdoor air supply rates are often kept low to conserve energy, causing carbon dioxide concentrations to surpass 1000 ppm for extended periods during school hours. These poorly considered energy-saving measures, though cost-free, can negatively affect children’s academic performance by up to 30%. Wargocki provided a comprehensive overview of these studies in [10].

In paper [11], the authors highlight the critical need for on-site measurements of indoor air quality (IAQ) in schools. They point out that children differ from adults in several key aspects, including their higher vulnerability to poor indoor environments. Children not only inhale more air relative to their body weight but are also more sensitive to variations in temperature and humidity, making them more susceptible to adverse conditions that can impede healthy development. A properly maintained educational setting can lower absentee rates, boost test performance, and increase productivity for both students and teachers. This article outlines a roadmap for future improvements in school air quality, advocating for more detailed on-site measurements to better understand the characteristics of contaminants. Additionally, it emphasizes the need for tailored strategies based on the specific locations of schools, such as their proximity to traffic or industrial zones, in order to address region-specific challenges. The socio-economic impacts of children’s health and academic performance should also be considered. Furthermore, there is a pressing need for larger-scale, comprehensive studies that explore the links between environmental health, student outcomes, and indoor comfort.

This paper presents the results of CO₂ concentration measurements taken in the classroom of a primary school located in Cracow, Poland. The results of short time measurements proved to be very unfavorable. The authors conducted the simulations using a specific program to analyze the longer heating season [12].

2. Literature Review

2.1. Indoor Air Quality in Schools

Air quality in school buildings is a significant issue worldwide. The measurements of IAQ parameters, such as temperature, humidity, pollutants and CO₂ concentrations, has been the focus of numerous researchers. Godwin [6] reported findings from IAQ measurements conducted in 64 elementary and middle school classrooms in Michigan (USA). In each classroom, bioaerosols, VOCs, CO₂ levels, relative humidity, and temperature were tracked. Ventilation rates were calculated based on CO₂ levels and occupancy data. Many of the classrooms exhibited inadequate ventilation, with CO₂ concentrations frequently surpassing 1000 ppm and occasionally reaching as high as 3000 ppm. In another study, Godwin [13] presented air quality monitoring data from 85 classrooms and other areas within eight schools in Minnesota, USA. The results indicated insufficient ventilation in rooms within five of the eight schools, as evidenced by elevated CO₂ levels. Paraskevi [14] conducted an analysis of IAQ in nine naturally ventilated primary schools in Athens, Greece, during the spring season. The study examined ventilation rates and pollutant levels during both teaching and non-teaching periods. Average carbon dioxide concentrations across the schools ranged from 893 to 2082 ppm, with most measurements slightly exceeding recommended threshold levels. CO₂ levels showed a positive correlation with the number of students and a negative correlation with ventilation rates. Turanjanin [15] analyzed the indoor air quality in five naturally ventilated Serbian schools during the heating season. CO₂ concentrations were measured both outdoors and in three classrooms over five working days, with ventilation rates calculated using a trace gas decay method. The results indicated insufficient ventilation, with the mean value of carbon dioxide concentration mostly exceeding 1000 ppm. Chang [16] conducted similar measurements in five Hong Kong schools where the CO₂ level were above 1000 ppm for most of the time, reaching a maximum of 5900 ppm when classrooms were fully occupied by students.

Korsavi [17] focused on factors influencing children’s perceptions of IAQ in 29 primary school classrooms in the UK, all naturally ventilated, during non-heating and heating seasons. The study indicated that children’s perceptions of IAQ are influenced by the “at-the-time CO₂ level”, which refers to the CO₂ measurements taken over the last 5 min, as children typically acclimate to the classroom’s air quality within that time frame. It also emphasized that low CO₂ levels alone do not ensure acceptable IAQ if children experience thermal discomfort in the classroom. When the CO₂ concentration exceeds 1000 ppm and the temperature is higher than 23 °C, the conditions are considered unacceptable.

Myhrvold [2] presented the results of a Norwegian project called Indoor Environment in Schools. The aim of the project was to investigate the indoor environment in regard to the pupils’ health, social environment and level of performance. The project included field measurements of eight different schools (35 classrooms) with natural ventilation systems and 800 pupils. The CO₂ concentrations at those schools in the daytime ranged between 601 and 3827 ppm. The health symptoms such as headache, dizziness, tiredness, difficulties in concentration, unpleasant odor, and throat irritation were analyzed using questionnaires and analyzing the results of computer tests analyzing pupils’ reaction times. The results showed strong correlation between student health, student performance and CO₂ concentration.

Simoni [3] described the influence of IAQ on the respiratory health of schoolchildren living in Norway, Sweden, Denmark, France and Italy. The researchers found that many disorders, such as wheezing, dry cough at night and rhinitis, were more prevalent among children in poorly ventilated classrooms. Schoolchildren exposed to CO₂ levels exceeding 1000 ppm had a significantly higher risk for dry cough and rhinitis. In the analyzed schools, children were exposed to CO2 levels greater than 1000 ppm 66% of the time. The authors emphasized the poor IAQ in European classrooms; it is related to respiratory disturbances and affects nasal patency. Gennaro [4] focused on the analysis of IAQ in schools as children have greater susceptibility to some environmental pollutants than adults because they breathe higher volumes of air relative to their body weights, and their tissues and organs are actively growing.

Paper [18] presents findings from IAQ assessments conducted in 64 primary school buildings across five Central European countries (Czech Republic, Hungary, Italy, Poland, and Slovenia). Various factors affecting indoor air quality, including concentrations of volatile organic compounds, aldehydes, PM_2.5 particles, carbon dioxide, radon, and physical parameters, were measured during the heating season of 2017/2018. The study revealed significant disparities in IAQ parameters between the countries. Median indoor/outdoor ratios varied widely, highlighting the need to evaluate each region individually due to differing environmental conditions. A thorough analysis of IAQ in relation to potential health impacts and comfort was conducted. While most hazard quotient values remained below the threshold of 1, one exception was noted. However, 31% of the schools had hazard index values exceeding 1. The maximum cumulative ratio approach suggested that concerns regarding non-carcinogenic health effects were generally low or driven by multiple substances. Notably, around 80% of the schools failed to meet the recommended carbon dioxide concentration limit of 1000 ppm.

Building energy regulations prioritize improving the efficiency of building structures and energy supply systems. As a result, the overall energy consumption linked to building characteristics is being reduced.

Human behavior significantly impacts a building’s energy usage. Actions such as turning on the heating, opening windows, or switching on lights alter the building’s energy balance, directly influencing overall energy consumption [16]. Duton [19,20] described results of measurements and simulations of indoor air quality conducted in two classrooms in the UK, including the impact of window openings. The simulations were conducted in the Energy Plus program. The authors aimed to enhance the prediction of building performance by gaining a deeper understanding of occupant behavior and the factors that shape it. The simulation model was validated by the measurements conducted by the authors. Opening windows significantly improves the air quality and lowers the CO₂ levels; however, due to the low external temperatures or noise levels outside the building, this cannot be considered a suitable solution. Belafi [21] examined the window-opening and closing behavior in two classrooms of a Hungarian school, using surveys and measurements to identify the environmental, contextual, or habitual factors influencing window usage. The study utilized eight-month-long time-series datasets and qualitative interviews with teachers to explore these behaviors. In one classroom, window use was largely driven by habits and time-dependent actions, while in the other, environmental factors played a more significant role. Specifically, indoor temperature emerged as the most reliable predictor for both opening and closing windows. Understanding and assessing such behaviors can help optimize the indoor environment, which is crucial for both energy efficiency and the health of students in school buildings.

Kulis and Muller [22] designed and validated a prototype device aimed at improving indoor air quality by enhancing natural ventilation in buildings. The device, built on a Raspberry Pi single-board computer (SBC) and equipped with optical sensors, utilized a fuzzy logic control algorithm to optimize performance. Its effectiveness in improving indoor air quality was confirmed, suggesting that this device could serve as a viable solution for supporting ventilation systems and enhancing indoor air quality.

IAQ is affected by environmental factors such as temperature, humidity, and air contaminants, as well as human behavior and adaptive approaches to thermal comfort and air quality (Zhang [23]).

Sowa [24] compared the actual state of the environment in classrooms in Poland with accepted requirements and standards, based on indoor environmental measurements in 28 classrooms in Warsaw. Polish regulations on indoor air quality lag behind similar regulations in developed countries; moreover, they are generally not observed. Increasing the ventilation rate would play a key role. Unfortunately, this action requires the use of mechanical ventilation systems to control the air exchange.

Sowa [25,26,27] described the results of simulations of indoor air quality in a school located in Zgierz after conversion of the ventilation system from natural to mechanical ventilation with high-efficiency heat recovery. After the modernization, the ventilation rate increased tenfold (from 3 m³/h per pupil to 30 m³/h per pupil).

2.2. Ventilation of Internal Space

A typical gravitational ventilation system introduces fresh air while removing contaminated, humid air from the indoor spaces. When the air exchange rate is too low, indoor air quality and occupants’ health can be compromised, whereas an excessively high rate can lead to unnecessary energy losses. Ventilation, as a deliberate air exchange process, must be considered in conjunction with infiltration, which occurs naturally due to pressure differences between the indoor and outdoor environments. In gravitational ventilation systems, where usually only exhaust ducts are installed, the fresh air supply is often uncontrolled, entering through infiltration via cracks and leaks in the building’s exterior envelope. The airtightness of this envelope is a crucial factor in determining ventilation intensity and, consequently, indoor air quality. Griffiths [28] examined the impact of trickle ventilators on ventilation rates in classrooms. These ventilators can improve air circulation and reduce CO₂ and contaminant concentrations, though they typically do not reduce them to acceptable levels.

The efficiency of air exchange can be evaluated using the gas tracing method, with carbon dioxide being used as the tracer gas. Since CO₂ is naturally produced by occupants, it can serve as an effective tracer without the need for artificial gas emitters. This approach simplifies and reduces the cost of testing by utilizing the CO₂ already present in the environment. Gas tracing with CO₂ allows for the simultaneous evaluation of air quality, ventilation efficiency, and building airtightness. Many researchers, including Sowa [25,26], Bulińska [29], Kersavi [8], and Persily [30], have used this method, utilizing metabolically produced CO₂ to evaluate ventilation performance and indoor air quality by analyzing CO₂ concentrations within indoor spaces. Zhang [31] and Nowak-Dzieszko [32] applied this technique to dormitories and offices to assess ventilation rates, while Benedettelli [33] and Cichowicz [34] measured ventilation intensity in university facilities. Additionally, Sowa [24,25], Turanjanin [14], Myhrvold [2], and Griffiths [28] employed the method to analyze IAQ in schools. All these studies were conducted using the gas tracer concentration decay method, initially introduced by Sherman [35] and outlined in the ISO standard EN 12569 [36]. This approach is based on measuring the natural decay of tracer gas concentration mixed with indoor air and was also used by the authors to assess the air exchange rate in the studied classroom.

Measuring the increase in CO₂ concentration during the occupancy of a building or room allows determination of the quality of indoor air. This approach has been proposed in Persily [30], Bulinska [29], and Zhang [31]. The results of the air quality analyses based on the level of CO₂ concentration inside classrooms are described in [29,30]. The authors confirm that in rooms with natural ventilation, the level of CO₂ very quickly exceeds the legal limits due to insufficient ventilation exchange.

Lis [37] sought to determine whether natural ventilation could supply enough air to meet the ventilation requirements. The analysis indicated that achieving the minimum ventilation airflow would be impossible without installing additional vents in the rooms or, preferably, implementing mechanical ventilation with heat recovery. The airtightness of the windows alone would not suffice to meet these requirements effectively.

Mijakowski and Narowski [38] compared the energy performance and indoor climate of typical school classrooms using two different ventilation strategies: mechanical balanced ventilation with heat recovery and natural/hybrid ventilation. The primary energy consumption, including heating and electricity for ventilation, in rooms with similar ventilation rates and thermal comfort were analyzed. The study found that while thermal comfort could be maintained with both systems, energy performance and indoor air quality varied significantly between the two strategies. Specifically, classrooms equipped with mechanical ventilation with heat recovery consumed approximately 40% less primary energy for heating and ventilation compared to those with natural/hybrid ventilation. The authors demonstrated that, in a moderate climate such as in Europe and Poland, it is feasible to meet indoor climate requirements and maintain reasonable energy consumption levels with both mechanical ventilation with heat recovery and natural/hybrid ventilation. Additionally, Mijakowski [39] compared the performance of passive stack ventilation and indoor conditions before and after the installation of humidity-sensitive air inlets in a kindergarten building. The analysis revealed that while the humidity-sensitive air inlets did enhance ventilation performance, their effect was insufficient to meet the current Polish and European standards and recommendations.

2.3. Standard Requirements

Polish governmental recommendations do not specify acceptable concentrations of carbon dioxide in rooms intended for permanent occupancy; only permissible concentrations in the working environment are defined, as follows [40]:

• Permissible Exposure Limit (NDS): This is the average concentration level that, when experienced by an employee over an 8-hour workday and an average workweek, should not result in adverse health effects for the employee or their future generations.
• Short-Term Permissible Exposure Limit (NDSCh): This refers to the average concentration level that should not cause harmful effects if present in the work environment for no more than 15 min, and not more than twice during a work shift, with at least a 1-hour interval between exposures.
• Maximum Exposure Limit (NDSP): This is the concentration level that must not be exceeded at any time in the work environment due to potential health or life-threatening risks. According to these regulations, the NDS for carbon dioxide is 5000 ppm (9000 mg/m³), while the NDSCh should not exceed 15,000 ppm (27,000 mg/m³).

Permissible carbon dioxide levels are established by European standards and widely adopted US guidelines, such as ANSI/ASHRAE [41] and ASTM [42]. These regulations specify that CO₂ concentrations in spaces occupied by people for extended periods should not exceed 1000 ppm. To maintain this standard, approximately 27 m³/h of fresh air per person must be supplied each hour [41].

According to the PN-B-03430 standard [42], which has been widely used for years in designing ventilation systems for public utility buildings intended for both permanent and temporary occupancy, the required external air volume flow should be at least 20 m³/h per person. However, in the case of rooms in kindergartens and nurseries where children are present, the standard permits a reduction of the air volume flow to 15 m³/h per child. It should be noted that these rooms are also occupied by adults caring for the children, for whom the stream should be calculated as 20 m³/h per person. An overview of ventilation requirements in other countries can also be found in the study [43]. Detailed guidelines adapted to the age of users in educational buildings are included, among others, in the American ASHRAE 61.1 [41] guidelines. These provide specific information on the required outside air flow, which is calculated as the sum of the airflow per person in the room (based on human activity) and the airflow associated with building materials and room equipment, depending on the area. The guidelines for educational rooms are as follows:

• nursery rooms (for children up to 4 years old)—18 m³/h per person
• classes (for children aged 5–8)—18 m³/h per person
• classes (for children from 9 years of age)—18 m³/h per person
• lecture rooms—13.4 m³/h per person

Permissible levels of carbon dioxide in non-residential spaces are regulated by the standard EN 16798-1 [44], which outlines national requirements. This standard defines four acceptable levels of carbon dioxide concentration depending on the selected level of indoor air quality.

Table 1. Permissible values for carbon dioxide concentration depending on the air quality category, acc. to standard EN 16798-1 [44].

Category of Air Quality in the Room	Increment of CO2 Concentration above CO2 Level in External Air, [ppm]
High quality of air	550
Medium quality of air	800
Moderate quality of air	1350
Low quality of air	1350

shows the permissible values for the carbon dioxide concentration according to the air quality category.

In any enclosed space where people reside, the concentration of carbon dioxide rises due to the consumption of oxygen during breathing. The CO₂ concentration in exhaled air is approximately 40,000 ppm. However, the exact amount of CO₂ produced by the human body can vary based on factors such as body weight and metabolic activity levels [41,42].The exhaled CO₂ stream is related to the amount of oxygen consumed. The amount of oxygen consumed by one person, m³/h, can be determined from Equation (1) [9]:

$$V_{02}=3.6·{\displaystyle \frac{0.00276·A_D·M}{0.23·R_q+0.7}}$$

(1)

where:

• A_D—DuBois surface (surface of human body), [m²]
• M—metabolic rate, [met], (1 met is equal to 58.2 W/m²)
• R_q—a respiratory quotient, [-]

The respiratory quotient can be adjusted based on the intensity of the activity being performed. For an average adult, the DuBois surface area is typically assumed to be 1.8 m². In building design, it is often practical to use standardized average values. According to the European standard EN 16798-1 [44], the indicative CO₂ emission rate is set at 20 L per hour per person.

Persily [9] introduces a method for estimating CO₂ generation rates from building occupants, which is valuable for indoor air quality and ventilation studies. This approach utilizes concepts from human metabolism and exercise physiology, representing a significant advancement in the analysis of IAQ and ventilation. The method provides a robust framework for applying CO₂ data in both practical ventilation applications and simulation models for IAQ research.

3. Methods and Measurements

3.1. Classroom Tested in Cracow

The analyzed classroom is located on the ground floor of a two-story primary school building located on Mackiewicza Street in Cracow, about two kilometers from the old city center (Figure 1a,b). The room can accommodate a maximum of 31 people (30 pupils plus teacher). The room has only one external wall with three large (2.55 m width and 1.8 m height) windows at the west elevation of building. In the room, there is a natural ventilation system with four ventilation ducts measuring 10 cm by 10 cm and located 3.0 m above floor level.

The total floor area of the classroom (Figure 1c) is 51.92 m², and its internal volume is 166.14 m³.The analyzed classroom is free of internal sources of contaminants, including CO₂.

All the measurements were conducted using an iBros set of remote sensors allowing continuous measurements and the registration of CO₂ concentration, temperature and relative humidity. Data were recorded every 30 s, with CO₂ measurement precision of ±50 ppm, temperature precision of ±0.4 °C, and relative humidity precision of ±5% (Figure 1d).

Simultaneous measurements of CO₂, temperature, and humidity were carried out using nine detectors placed at various locations within the tested space. This setup enabled an assessment of the spatial distribution of CO₂, temperature, and fluctuations in momentary concentrations throughout the area. Details of the sensors’ locations are provided in

Table 2. Description of sensors’ locations.

Sensor Number	Sensor Location
Sensor 1	Located on the internal window sill
Sensor 2	Located on the external window sill
Sensor 3	Attached to the entrance door frame, 2.0 m above floor
Sensor 4	Located on the desk next to the wall, opposite the windows
Sensor 5	Located on the desk next to the wall, opposite the windows
Sensor 6	Located on the wardrobe, 1.8 m above floor, next to the ventilation ducts
Sensor 7	Located on the wardrobe, 1.8 m above floor
Sensor 8	Located on the internal window sill
Sensor 9	Located on the projector 20 cm below the soffit

. Prior to the testing, all sensors were calibrated according to the manufacturer’s instructions.

3.2. CO₂ Concentration

Measurements of internal air quality were conducted over 3 days: 4 January 2019, 11 January 2019, and 1 February 2019, during the morning hours while classes were in session. The detailed analysis focused on one representative day (4 January) to highlight the observed phenomena. The trends in the CO₂ and temperature distributions were similar across all days. Figure 2 illustrates the fluctuations in CO₂ levels throughout the school day in the classroom on 4 January, showing both increases and decreases in concentration. The number of users were 21 students plus two adults. Sensor #2 was located on the external window sill.

Figure 3 presents the shorter time range, covering two lessons with a break between them when the windows were opened (average of data collected from 6 sensors on 1 February).

Lessons start at 8:55, and children enter the classroom between 8:40 and 08:50. Each lesson lasts 45 min. The first lesson ends at 9:40, followed by a short 10-min break (9:40–9:50 a.m.). According to Figure 2, the mean CO₂ concentration rises to 2500 ppm by the time the first break occurs and then decreases to 1250 ppm during the break (a 50% reduction) due to the opening of windows. This reduction of 1250 ppm over the 10-min break equates to 125 ppm/min in the studied classroom. However, the breaks are not long enough to bring CO₂ levels below 1000 ppm. After the first break, the children remain in the classroom until the next 10-min break (9:50–10:35). During the second lesson, the peak CO₂ concentration exceeds 3000 ppm, as the initial level was already higher. This trend repeats during the following two lessons. The indoor air quality remains poor throughout each lesson, as shown in Table 1.This pattern of fluctuating CO₂ levels in the schools under study has been documented in numerous other research studies [8,24,27].

The windows are typically kept closed during lessons due to low outdoor temperatures or noise. This is the typical usage scheme in the classrooms in Poland but also in many other countries. Such high concentrations should not be viewed merely as a comfort issue but rather as a significant health risk to occupants. It is worth emphasizing that this classroom could be occupied by 31 individuals (30 pupils plus teacher), which would further exacerbate the conditions.

3.3. Classroom Modeled in CONTAM

In the first simulation step, the results of measurements were used to adjust and validate the CONTAM model. The classroom was modeled as a single zone, with the air flow paths in the envelope representing the ventilation ducts and four external windows (Figure 4).

The following assumptions were used in modeling:

• The occupancy schedule was based on the observations during measurements and aligned with the timing of lessons and breaks between.
• Cracks were modeled using the power law flow model (V = C × DPⁿ) with C = 3.2 × 10⁻⁴ m³/s/Paⁿ per meter of crack and n = 0.67.
• Open windows were modeled as two-way flow according CONTAM, with specified area and an exponent of 0.5.
• Natural ventilation was modeled as being driven by wind speed and temperature difference.
• Users profiles were adjusted according to [9], presented in

  Table 3. User profiles used in the simulations.

  Users	Children	Adults
  Number	25	2
  Weight	45 kg	80 kg
  Height	1.55 m	1.8 m
  DuBois surface area	1.40 m2	1.99 m2
  Respiratory quotient	0.85	0.85
  Metabolic rate	1.6 met	1.6 met
  CO2 generation rate	0.005441 dm3/s 19.59 dm3/h	0.007743 dm3/s 27.88 dm3/h

  .

Figure 5 presents the model’s calibration against the measurement data. The black line represents the simulation curve, which closely follows the measurement results. The probability distribution and density are presented in Figure 6.

After adjusting the model with measurements, the root mean square error was below 185 ppm, and correlation between measurements and calculation had strong correlation (R² = 0.93), Figure 7. This calibrated model was then used for simulating the entire winter period.

3.4. Air Exchange Rate: Gas Tracing

To measure the air exchange rate in the classroom with all windows closed, a gas tracing decay test was conducted on 5 November 2021. The simultaneous CO₂ measurements were conducted using five detectors, which were located at different locations within the tested space. CO₂ was generated from a bottle.

When using the gas tracing method to determine the air exchange rate, the concentration of carbon dioxide in the entire tested area should not vary by more than 10% from the mean concentration value [36]. During the analyzed period, this criterion was met by all five sensors. The average concentration decay data obtained were used to calculate the natural airflow rate using the gas tracing method [36]. The specific airflow rate was calculated by means of a two-point decay method, Equation (2).

$$\overline{N}={\displaystyle \frac{1}{t_2{-t}_1}}{\log }_e{\displaystyle \frac{C\left(t_1\right)}{C\left(t_2\right)}}$$

(2)

where:

• N—time-mean specific airflow rate, [1/h]
• t—time (t₁: measurement start point, t₂: measurement end point), [h].

For the analyzed room, the air exchange rate was determined to be n = 0.27 1/h. However, it is important to note that specific airflow rates are significantly influenced by external climatic conditions, which means there could be substantial differences in values if the tests were conducted under varying environmental conditions. During the analyzed period, the external temperature ranged between 8 °C and 10 °C.

Assuming the total internal volume of the classroom to be 166.14 m³, the average air exchange rate was 44.8 m³/h. With the average of 22 pupils plus teacher (total 23 people) working in the classroom, the air flow per person was 1.95 m³/h. Under maximum occupancy of 31 people (30 pupils plus teacher), this would drop to only 1.44 m³/h. The obtained results do not meet the minimum of 20 m³/h per person required by the standard. The results just confirmed very unfavorable conditions in the analyzed classroom.

Sowa [16,17] applied the same method to calculate airflow rates in 28 classrooms across Warsaw schools. The results showed that most classrooms had an air exchange rate below 1 h⁻¹. When assuming full occupancy (all seats occupied), the airflow rate per person ranged from 1.2 to 9.6 m³.

4. Results—CONTAM Simulations

The aim of the conducted simulations was to analyze the internal CO₂ level in the classroom during the heating season, from 1 November to 31 March under Cracow’s climatic conditions (hourly data). The Christmas break and winter vacations were scheduled in the simulations.

The outdoor temperature and wind speed profiles are shown in Figure 8 and Figure 9, respectively.

CONTAM, developed by the National Institute of Standards and Technology (NIST), is a comprehensive computer program for modeling and analyzing indoor air quality and ventilation. It simulates airflows, including infiltration, exfiltration, and room-to-room movement driven by mechanical systems, wind pressures on the building exterior, and buoyancy effects caused by temperature differences between indoor and outdoor air. Additionally, CONTAM models the dispersal of airborne contaminants, accounting for their transport via these airflows and their transformation through various processes such as chemical reactions, adsorption and desorption with building materials, filtration, and deposition on surfaces [12].

Winter-Time Simulation Results

Since the model accurately reflects real conditions, it was used for the further simulation of CO₂ concentration throughout the heating season in Cracow (1 November thru 31 March). Figure 10 and Figure 11c,d show the variations in CO₂ concentration over the entire five-month period as well as shorter intervals, including five working days and one particular day. When comparing these diagrams with Figure 2, presenting measurement data, a similar trend in changes can be observed across all weeks. Figure 11b,d present the changes in ventilation airflow for five working days and one particular day. The average, maximum and minimum values for both CO₂ concentration level and air flow are listed in

Table 4. Average, minimum, maximum and standard deviation in the analyzed period of time.

	Air Flow [m3/h]	Air Flow for the Occupied Hours [m3/h]	CO2 Concentration [ppm]	CO2 Concentration for the Occupied Hours [ppm]
average	223.6	314.8	717	1726
min	33.8	71.0	500	550
max	2894.4	2894.4	3279	3279
stddev	310.2	487.6	442	554
percentile 90%			1320	2407

.

Based on the average value of the CO₂ concentration during the occupied hours, the indoor air quality, according to [44], was considered low. The maximum concentration reached nearly double the average, at 3279 ppm.

The correlation shown in Figure 12a illustrates the relationship between air flow and outdoor temperature, which is typical for natural ventilation. The data points form three distinct groups: air flow through cracks (the bottom group), air flow through window slightly open (the middle group) and air flow through window fully open (the top group). These trends are further reflected in Figure 11b–d.

The total energy consumption for air heating during the analyzed period of time was 5605 kWh, which gives 33.8 kWh/m².

Figure 13 illustrates the daily concentration profile, while Figure 14 shows the daily ventilation air flow profile for the working days in the analyzed period. The indoor CO₂ concentration, including the minimum values, consistently exceeded 1000ppm, indicating poor indoor air quality.

Figure 15 summarizes the CO₂ concentration issues in the classroom during the winter period. During occupied hours, the CO₂ concentration was below 1000 ppm for only 10% of the time, while concentrations above 1900 ppm (indicating low quality of air according to EN-16798-1 [44]) occurred over more than 40% of the occupied time period.

5. Conclusions

The measurements conducted in the analyzed classroom confirmed the low indoor air quality linked to high levels of metabolically generated CO₂ during occupancy hours. A model developed using the CONTAM software (https://www.nist.gov/services-resources/software/contam, accessed on 29 August 2024) was evaluated against measurement data and is considered a suitable tool for future energy calculations and simulations of various ventilation schedules and systems.

The model was validated with measurement data and used to analyze the internal conditions during the entire heating season in Cracow. The simulations confirmed consistently poor air quality during this period, attributed to the low efficiency of the existing natural ventilation system.

The energy demand of the current inefficient ventilation system is substantial. While implementing mechanical ventilation would enhance indoor air quality, it would also increase energy demand.

Therefore, it is essential to use a mechanical ventilation system with heat recovery to both improve indoor air quality and optimize energy consumption. Future research will incorporate mechanical ventilation into the developed model to conduct annual simulations with different control strategies for mechanical ventilation systems.