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Definition of Optimal Ventilation Rates for Balancing Comfort and Energy Use in Indoor Spaces Using CO_{2} Concentration Data

^{*}

## Abstract

**:**

_{2}concentration variation is presented as a general element for controlling the operation of heating ventilation and air cooling (HVAC) systems. The specific CO

_{2}exhalation rate is estimated using experimental data in some real conditions in university classrooms. A method for the definition of optimal values of air exchange rate is defined, highlighting that the obtained values are much lower than those defined in current technical standards with possibilities of relevant reduction of the total energy consumption.

## 1. Introduction

_{2}concentration, and the authors also estimate the air flow rate profile necessary to maintain a selected CO

_{2}concentration in two different zones of the apartments.

_{2}concentration or the presence/absence of users in the room. In the paper, the strategy based on CO

_{2}monitoring appears to be the most promising one, with energy savings of 62% with respect to constant air volume system. Similar results were found in [6], where the authors compare a constant air volume system and a demand control ventilation system based on CO

_{2}measurements. Simanic et al. [7] present the outcomes of seven monitoring activities in primary schools in Sweden, where variable air volume systems are usually employed. The results show that a low CO

_{2}concentration is achieved by the use of quite high values of ventilation rates (over 0.01 ÷ 0.02 m

^{3}⁄s × occupant).

_{2}concentration.

_{2}are often correlated to metabolic rate, and this is connected to the specific activity [8]. In medical and biological applications, the specific CO

_{2}production rate is an object of a detailed study, even through experimental measurements [9]; the values of those exhalation rates differ from the estimates of engineering applications.

_{2}measurements, excessively high values of carbon dioxide in closed environments can be an indication of malfunctioning of mechanical ventilation systems and an excessive occupancy density, which can lead to undesired issues for users, such as headache and somnolence. Some studies have also reported a reduction of users’ productivity in environments with higher CO

_{2}concentration [10,11]; another work [12] highlights the concept that decrease in users’ performance at school and work is probably due to concurrent effects of both high CO

_{2}concentrations and other adverse conditions (e.g., bad thermal conditions, exposure to other pollutants).

_{2}concentration over 1000–1500 ppm should be avoided [13,14] to maintain good indoor air quality conditions. Strictly speaking, the objectives of maintaining good IAQ with reduced energy use for the operation of an HVAC system is difficult, because the second objective usually requires high ventilation rates, and this has a consequence in terms of increase of the energy necessary for air exchange and for air treatment. A compromise is not simple and would require detailed quantitative knowledge of the link between air quality parameters and operation of thermal and ventilation control systems in the specific building under analysis. This knowledge is not exactly evident from the analysis of the above mentioned references. The problem is particularly relevant for public buildings, where it is estimated that around a third of energy consumption related to thermal control is due to ventilation. In literature, in particular, it is found that the choice of correct ventilation rates is difficult, especially in educational buildings, as considered in two recent papers [15,16].

_{2}concentration in educational buildings is prescribed by various regulatory documents from EU levels down to national design guidelines for educational buildings, but the dynamic control of the air flow rate is not always considered.

_{2}concentration obtained during examinations and lessons in several classrooms within the Engineering School of the University of Pisa, previously presented in [17], are here used to provide a possible correlation between CO

_{2}concentration increase and number of occupants. The experimental analysis was performed in various classrooms of university buildings. The rooms were characterized by different geometrical parameters, such as surface area, volume, and shape, and operating parameters, such as indoor occupation. Then, a multi-objective methodology was proposed to establish optimal profile of demanded controlled ventilation of indoor spaces based on the actual occupation’s profile obtained by monitoring the increase of carbon dioxide concentration with time.

_{2}in order to define a dynamic and demanded controlled ventilation (DCV) strategy that permits one to maintain the required standards of CO

_{2}concentration with minimum energy use, thus pursuing the objective of energy saving while satisfying the occupants’ comfort.

## 2. The Connection of Carbon Dioxide Concentration, Occupation of the Indoor Spaces, and Air Ventilation Rate in Indoor Spaces

_{2}) and for energy efficiency purposes. Due to the relevant energy consumption connected to HVAC system operation, for maintaining temperature and humidity standards and pollutant concentration, a quite accurate estimation of the actual number of users inside a building or of a single room can be useful in order to modulate the operation of the HVAC system, varying the supply temperature to terminal units and an appropriate value of the air exchange rate.

_{2}concentration and its rise appears to be a particularly interesting one. Furthermore, it also solves some of the major issues related to the adoption of the other methods, such as use of video-cameras [19].

_{2}concentration data for estimating the occupants’ number could be less accurate than other technologies (such as video-cameras or counters) for defining the exact number of persons present inside the indoor space; regardless, it can be considered quite useful for an approximate quantitative estimation of a percentage value of occupation without interferences due to other devices or privacy concerns.

_{2}was considered as the only component to be monitored. This component, even if it is not considered a real indoor pollutant, is correlated to IAQ in several studies, and its generation is due to people breathing. As its monitoring is easier than other indoor pollutants (e.g., carbon monoxide, formaldehyde, volatile organic compounds VOCs) thanks to relatively “cheap” sensors, it can be monitored as a “pollutant” of an indoor environment, as reported in other studies in literature.

_{2}can be written, considering valid the following assumptions:

- -
- uniform concentration in the room, assuming a well-mixed model;
- -
- constant value of outdoor CO
_{2}concentration; - -
- well-defined value of the generation rate of the occupants;

_{2}indoor concentration rise can be assumed to be dependent on air ventilation rate, imposed with a mechanical device or dependent on infiltration losses through doors and windows frames, with the following equation:

_{{CO2}}is the indoor concentration of carbon dioxide, V the total volume of the room, n

_{occ}the number of occupants, $\text{}\dot{r}$ the CO

_{2}generation rate per person, $\text{}\dot{\mathrm{m}}$ the air flow rate due to ventilation (mechanical of natural due to infiltration) expressed in m

^{3}/s, and C

_{ext}is the outdoor CO

_{2}concentration. CO

_{2}concentration variation in the room can also be written in explicit form, thus, at time t, it is equal at:

_{2}concentration inside a definite volume. However, these formulas are reported in the literature, such as [15].

_{2}concentration can be easily connected to the number of occupants if the rate of generation and the air exchange rate are exactly known, while the use of such a kind of model is quite difficult if no control on ventilation rate is available.

_{2}concentration and the occupancy profile of the room was analyzed, proposing a linear correlation between the CO

_{2}concentration rise and the specific volume per occupant. It was discussed how, for a specific activity and for a specific category of users (students and young people), the most relevant variables are the volume available for each person, the specific production, and the air exchange rate.

_{2}concentration variation inside the room:

_{2}concentration variation in a given time period, Equation (3) allows for the estimation of the number of occupants in the room, and the estimation of the CO

_{2}production rate per person is an essential element. Furthermore, one can observe a hyperbolic correlation between the CO

_{2}concentration rise and the specific volume per occupant.

_{2}; this air flow rate can be adjusted to reduce energy requirements, thus obtaining an advantageous value for both the objectives.

_{2}concentration and the air volume per occupant based on the application of the model previously exposed in Equation (3) for three different values of CO

_{2}production rate: (i) 0.2 L/min, used as a typical lower value for people sitting or involved in light intensity activities, such as students during teaching lessons (${\dot{r}}_{1}$); (ii) 0.8 L/min, used for people standing and operating a medium physical activity (${\dot{r}}_{2}$); and (iii) 1.5 L/min, used for high intensity physical activities (${\dot{r}}_{3}$). The validity of Equations (2) and (3) was tested using the results of a detailed experimental analysis in several classrooms of educational buildings with different shapes and occupation profiles [17].

## 3. Air Exchange Rate and Direct Correlation with Real Occupation: Data from a Monitoring Activity

_{2}concentration, this last value being a typical pollutant marker in indoor spaces, the operation of HVAC in order to control the environmental parameters has to be correlated with the real occupation of the spaces. In particular, air exchange rate in closed rooms and indoor spaces generally causes relevant additional energy consumption. This is because the air that is circulated from the external environment, usually at lower (in winter) or higher (in summer) temperatures than the environment depending on the season, must be brought to the room temperature. The energy consumption is higher the greater the flow rate of air to exchange (air flow rate volume) and the difference in temperature between the external environment and the room are. The higher the required air exchange rate is, the better the air quality in the indoor space will be, but the ventilation power required and the overall energy consumption will also be higher.

_{2}production rates for each student. The measurements of CO

_{2}concentration together with the measurements of indoor temperature and relative humidity were obtained using up to four different sensors, Chauvin Arnoux C.A 1510, [20]. Concerning the specific problem of CO

_{2}concentration measurement, the sensors permitted us to cover a measurement range 0–5000 ppm with an uncertainty of ± 3% of the reading ± 50 ppm at 25 °C at atmospheric pressure. Even in literature, CO

_{2}measurements are usually carried out through a single sensor placed next to the center of the room, and the uniformity of carbon dioxide concentration in the room must be proven. Thus, in some of the experiences, two or three sensors were placed in different zones of the room at breathing level to check if the assumption of well-mixed indoor volume could be realistic.

_{2}variation (increase) with time are shown in Figure 2 and Figure 3. In Figure 2, the profile is related to an experimental analysis of room 5, where two sensors were used to measure the CO

_{2}concentration increase. Figure 3 provides the CO

_{2}concentration profile within the classroom identified as CL1 (computer lab).

_{2}measurements were found, similar to those provided in the previous Figure 2. Possible differences among the measurement of the sensors were within the error band of the sensors represented by the filled area, thus the hypothesis of well-mixed room was considered valid.

_{2}was overcome. Results show the starting value and an average value of the CO

_{2}concentration increased in each classroom, which was evaluated in the first 10–15 min of monitoring, and an evaluation of the elapsed time between the start of the measurement and the time in with the CO

_{2}threshold value (1500 ppm) was reached. This time duration was used to evaluate the CO

_{2}concentration increase with time. Only in two cases was the threshold limit lower than the initial value, meaning that, during the previous didactic activity, the CO

_{2}concentration increased over the limit, and natural ventilation was not sufficient to have the concentration decreased; in those two cases, the estimation of the CO

_{2}concentration increase with time was done using the concentration at the starting value of the lesson.

_{2}concentration, expressed by the derivative $\frac{{\mathrm{dC}}_{\left\{{\mathrm{CO}}_{2}\right\}}}{\mathrm{dt}}$ estimated in the experimental analysis referred in [17], ranged between 0.1 ppm/s up to 0.7 ppm/s, with maximum occurrence in the range between 0.2 and 0.5 ppm/s.

_{2}concentration with time, according to the model provided in Equations (1)–(3), accurate knowledge of the value of the CO

_{2}production rate per occupant was needed. This value can be obtained with reference to the available literature and technical standards, but it can also be measured. In the present paper, this second path was considered. In particular, the benchmark room was the one identified with label 0 in Table 1.

_{2}was measured in two different point during the first phase of a short duration examination (a test of 30 min). A total number of 20 students were present inside the room at the initial time of the experimental analysis, and the windows were closed. The two sensors measured an almost uniform profile of CO

_{2}increase; the mean values are shown in Figure 4. In the first phase (five minutes), the sensors began to measure; CO

_{2}was almost constant as the classroom was unoccupied. Then, in a few minutes, twenty students entered and sat inside the room for about 30 min. Then, the door was opened, and the majority of the students left the room (phase 3), while only five of them remained inside.

_{2}production rate equal to 0.20 l/min per person could be estimated. The value obtained agreed quite well with the specific activity when compared with CO

_{2}production rates available in the literature [8,9,21,22].

## 4. Correlation of CO_{2} Concentration Rise and Occupation for Defining Optimal Air Exchange Rate

_{2}measurements has been diffusely expressed in the literature and has been object of recent analyses as well [24,25]. On the other hand, a demand controlled ventilation (DCV) strategy within the context of the American Society of Heating Refrigerating and Air-Conditioning Engineers (ASHRAE) Technical Standards is developed in [26] for public buildings using a digital control system.

_{2}concentration. The analysis refers to some of the situations previously tested. The idea of defining a procedure for calculating a value of the air exchange rate, a demand controlled mechanical ventilation rate, has already been developed in the literature, and papers about this specific topic are already available [27,28].

_{2}increase and the specific volume per student in Equation (2) using the results of the specific experimental analysis. The problem in using Equation (3) is that it neglects air change in the room. Some of the results are shown in Figure 4, where the twelve pair of values $\left(\frac{{\mathsf{\Delta}\mathrm{C}}_{\left\{{\mathrm{CO}}_{2}\right\}}}{\mathsf{\Delta}\mathrm{t}},\frac{\mathrm{V}}{{\mathrm{n}}_{\mathrm{occ}}}\right)$ obtained considering the data acquired in twelve specific experimental analyses are reported. Figure 5 also shows a hyperbolic curve, in red, representing the least-squares fitting curve for Equation (3). The value of CO

_{2}production rate per person as evaluated using the least-squares fit,${\text{}\dot{r}}_{ls}$, was $0.20\text{}\mathrm{l}/\mathrm{min}$ and was equal to the estimated value derived after the monitoring of room 0, defined as ${\text{}\dot{r}}_{0}$.

_{2}production among the monitored classrooms, ${\text{}\dot{r}}_{\mathrm{m}}=0.22\mathrm{l}/\mathrm{m}\mathrm{i}\mathrm{n}$, fit exactly the experimental results obtained in the experimental analysis 5#1. The curve is represented in Figure 5 with a black dotted line.

_{2}concentration, $\frac{{\mathsf{\Delta}\mathrm{C}}_{\left\{{\mathrm{CO}}_{2}\right\}}}{\mathsf{\Delta}\mathrm{t}}$, and the volume available for each student, $\frac{\mathrm{V}}{{\mathrm{n}}_{\mathrm{occ}}}$, seemed to fit the results of the experimental analysis quite well. A hyperbolic function was used with model y = a/x, with “x” representing the derivative of CO

_{2}concentration (in ppm/s) and “y” the air volume per student (in m3). The fitting procedure provided the “a” value, generally in the range between three and four (average value equal to 3.33).

_{2}concentration in the room in a given time step (e.g., 10–15 min) in the absence of mechanical ventilation and knowing the volume of the room, it was possible to estimate, with quite good accuracy, the approximate number of occupants. This procedure can be repeated periodically for controlling the operation of the mechanical ventilation system in order to meet the desired target in terms of temperature relative humidity and IAQ.

_{2}concentration inside the room,$\text{}\dot{\mathrm{m}}$, using Equation (2).

^{3,}and several scenarios were assumed with different numbers of persons inside. An indoor steady-state CO

_{2}concentration between 800 ppm and 1500 ppm was considered acceptable for maintaining good IAQ conditions. Thus, for each threshold value, it was possible to estimate the air flow rate values that allowed for maintenance of the CO

_{2}concentration below the imposed value. The result of the application of the methodology is shown in Figure 6, where the thin colored curves represent the lines of equal air flow rate ($\mathrm{iso}-\text{}\dot{\mathrm{m}}$). For example, for a number of occupants equal to 122 (corresponding to a reference value of the volume available for each occupant of $10{\mathrm{m}}^{3}$) and a maximum allowable CO

_{2}concentration of 1000 ppm, an air exchange rate of $0.8{\mathrm{m}}^{3}/\mathrm{s}$ was required.

_{2}concentration can also be correlated with the energy requirements. This value depends on the mass flow rate and on indoor and external temperature; through the following equation (referred to an operating time,$\mathrm{t}$), the energy amount required for ventilation can be calculated:

^{3}/s. For users’ comfort purposes, the indoor air temperature is limited within a given range (e.g., in winter, 18–22 °C and 24–27 °C in summer). Thus, it is possible to display ventilation loads such as in Figure 6, where a combination of curves are shown varying ventilation rate as well as external and indoor temperature. In the figure, the markers represent ventilation loads at the same indoor temperature (i.e., rhomboidal, plus, round, square, and triangular markers refer to five different values of the indoor temperature,${T}_{in}=18-22\xb0C$), while the colorbar on the right side represents the energy consumption for ventilation, expressed in kWh.

_{2}concentration, for example, 1200 ppm). In general, Figure 7 can be used to evaluate, for each couple of T

_{in}and T

_{ext}, the energy required for ventilation, (e.g., for a ${\mathrm{T}}_{\mathrm{int}}=20\text{}\xb0\mathrm{C}$ and ${\mathrm{T}}_{\mathrm{ext}}=0\text{}\xb0\mathrm{C}$, ${\mathrm{Q}}_{\mathrm{v}}=15\text{}\mathrm{kWh}$). If the air exchange rate necessary is at levels of 0.2 m

^{3}/s, the energy used is reduced at 5–6 kWh.

_{2}concentration obtained using the proposed methodology can be used as a dynamic method for ventilation rate control as an alternative to actual regulation solutions, as proposed in the European Union EN 16798 [23]. This technical standard proposes a ventilation rate to dilute bio effluents from the occupants and a ventilation rate to remove pollution produced inside the building. The former term depends on the occupancy, while the latter term depends on the type of building. In particular, the parameters are the maximum number of the persons in the room and consequently the ventilation rate for occupancy per person, expressed in l/(s person), and the floor area, m

^{2}, corresponding to the ventilation rate for emissions from building, l/(s·m

^{2}).

_{floor}is the surface of the room, and q

_{b}is the ventilation rate for emissions from building, expressed in l/(s·m

^{2}). In the technical standards, four categories are presented depending on the level of required IAQ. Here, two methods were considered, conventionally labeled with TS1 and TS2 (Technical Standards 1 and 2), corresponding with the maximum and the minimum values contained in Technical Standard EN 16798 [21] for comparison with the method proposed based on an accurate estimation of the occupation. In particular, the values of q ranged from 2.5 l/s person (category IV) to 10 l/s (category I), while the values of q

_{b}ranged from 0.3 l/(s m

^{2}) for category I up to 1.0 l/(s m

^{2}) in case of category I.

**Method**

**TS1.**The air exchange rate is calculated depending on the maximum number of occupants for the specific classroom under analysis,${n}_{occ,max}$, and on the building type, based on floor surface, using the lowest values of q and q

_{b}, before considered: 2.5 l/s person and 0.3 l/(s m

^{2});

**Method**

**TS2.**The air exchange rate is calculated depending on the maximum number of occupants and floor area using the upper values of the parameters q and q

_{b}, in particular, those corresponding to category I of TS EN16798.

_{2}threshold value equal to 1200 ppm). The test cases for which a comparison of the three different strategies were tested are those referred to in Table 2 and identified with labels 5#1 and 4#1. The characteristics of the rooms are provided in Table 1. The following relevant elements can be considered:

- -
- actual number of users: 168 (5#1), 58 (4#1);
- -
- initial CO
_{2}concentration: 1138 ppm (5#1), 678 (4#1); - -
- external CO
_{2}concentration: 500 ppm (value experimentally measured).

_{2}concentrations by using three strategies, the two derived from the European Directive based on the maximum occupancy of the classrooms and the one proposed in the paper based on the real estimation of occupation derived by CO

_{2}measurements. With respect to the two situations analyzed, in the first case (classroom 5#1), when the number of occupants of the room was about 80% of the maximum occupation (168 vs. 208), the air exchange rate obtained with the proposed strategy and based on the idea of maintaining an acceptable level of IAQ was similar to the one proposed with the lower values of the Technical Standard (TS1). However, if the room was only partially occupied (less than 20%, as in the case of classroom 4#1), the required air exchange rate was much lower than both the values obtained with the Technical Standards with important energy savings.

_{2}monitoring is active, allowed for a reduced air exchange rate in both the analyzed situations with respect to the solutions recommended by the current Technical Standards. In particular, in three of the analyzed cases, for strategies TS1 and TS2, the values of the air exchange rate were higher than those based on the proposed strategy, indicating significant energy requirements. Those last values, estimated as a function of typical outdoor temperature, determines energy saving for mechanical ventilation; the values are reported in Table 4 for a reference indoor temperature of 20 °C and the actual value of the external temperature measured during the experimental analysis. The proposed strategy determined, in both cases under analysis, a reduction of value of the air exchange rate with respect to the one required according to the Technical Standards and consequently a reduction of the energy use.

_{2}concentration using the three different values of air exchange rates for the two classrooms analyzed using the same periods (minutes) of the monitoring campaign.

_{2}concentration rise was observed in the basic experimental case, for which no mechanical air exchange rate was applied, and CO

_{2}concentration increased monotonically together with the trend observed with the three different values of air exchange rate. It was observed that a good IAQ could be obtained with each of the three strategies (instead, without mechanical ventilation, high values of indoor CO

_{2}were always measured).

_{2}inside the classrooms but with high energy consumption.

## 5. Definition Optimal Ventilation Rate Based on a Multi-Objective Approach

_{2}concentration are usually overcome, considering that, in these classrooms, the design ventilation rates are provided for the design value for the number of persons in the room. As university classrooms can accommodate a higher number of students than the actual number of occupants present during a standard lecture (as monitored), the choice of the design ventilation rate would lead to exaggerated ventilation rates (and, consequently, energy consumptions). Thus, the choice of modulating the ventilation rate on the basis of the actual number of occupants can reduce ventilation losses and energy consumptions of the fan and of the HVAC system.

_{2}production rate per person specific for the activity performed.

_{2}concentration, then the air exchange rate can be calculated on the basis of the required IAQ and energy efficiency standards, thus obtaining maps similar to those reported in Figure 6 and Figure 7.

_{2}concentration; all the values in the range between 800 and 1500 ppm can be considered valid and, for a given number of occupants, the minimum air exchange rate to be supplied in the room is provided together with the corresponding ventilation load. This last value functions on external and indoor temperatures.

_{2}concentration. Moreover, solutions violating this limit (i.e., 1500 ppm) are not possible. Thus, in this way, an advanced demand controlled ventilation strategy as a result of the application of a multi-objective optimization strategy can be implemented and defined considering a compromise between maintaining high IAQ and controlled energy consumption.

_{i}(x), all expressed in dimensionless terms and representative of each objective (e.g., energy consumption, temperature difference with respect to the imposed value, pollutant concentration, relative humidity). It is also possible to consider different weights, ϕ

_{I}, in order to give varying importance to them:

_{2}concentration and the second one for controlling the energy consumption in connection with the imposed air exchange rate.

_{2}concentration in the form of difference with respect to the available standards, while the second indicator accounts for the energy consumption required to maintain the level of CO

_{2}concentration imposed (e.g., 1500 ppm means upper acceptable value of IAQ), according to the European Standards [14].

_{2}concentration inside the classroom. On the other hand, energy efficiency measures would encourage the reduction of air exchange rate in order to reduce energy consumption for ventilation. An optimal strategy choosing the most suitable air flow rate in the analyzed indoor space can be found by both considering the objectives and aggregating them using appropriate weights. If an equal weight is given to both the objectives, such as in this case, ${\mathsf{\varphi}}_{1}={\mathsf{\varphi}}_{2}=0.5$. In other cases, different values can be given to ${\mathsf{\varphi}}_{\mathrm{i}}$ depending on the importance given to the two concurrent objectives. As example of application of the methodology is the case of the room identified with ID 5 with 122 occupants. The two objectives are, in this case, represented by the following dimensionless indicators:

^{3}/s. Instead, ${\dot{\mathrm{m}}}_{\mathrm{max}}$ represents the air flow rate associated with the maximum IAQ, which is calculated equal to 4 m

^{3}/s in this case; ${\text{}\dot{\mathrm{m}}}_{\mathrm{set}}$ is the air flow rate, found by means of the utility function method. Both objective functions are singularly optimized when they are close to 0. In this case, the utility function is:

^{3}/s and a CO

_{2}concentration equal to 800 ppm. If higher importance is given to energy efficiency, thus maintaining a lower IAQ level inside the room, different weights can be chosen (${\mathsf{\varphi}}_{\mathrm{IAQ}}=0.3\text{}$and ${\mathsf{\varphi}}_{\mathrm{Energy}}=0.7$). In this case, when CO

_{2}concentration is limited at 1000 ppm, an optimal air exchange rate of 0.8 m

^{3}/s is found.

_{2}concentration at steady-state and optimal air flow rate. The results need to be verified and compared with those obtained in other recent papers about post-processing, such as [31,32].

## 6. Conclusions

_{2}concentration rise, the present paper proposes a methodology for correlating the value of air exchange rate required to maintain the maximum permissible CO

_{2}concentration level (1500 ppm) in connection with the real occupation of the same indoor space obtained through the measure of CO

_{2}concentration rise.

_{2}production for each person, in this case estimated as $0.2\text{}\mathrm{L}/\mathrm{min}$. The air flow exchange rates assessed through the proposed method were sensibly lower than those suggested by current Technical Standards and were sensitive to the occupation profile. Considering the two cases, an air exchange rate reduced by a factor 2–3 with respect to the values suggested by European Standards, mainly when the occupation of the room was reduced, was sufficient to maintain acceptable values of IAQ conditions with a relevant reduction of the energy consumption.

_{2}production rate and a specific room tested (two cases were analyzed in particular), integrated maps were provided to find the most suitable air exchange rate, dependent on the number of occupants and on the imposed threshold CO

_{2}concentration value, that needed to be maintained by means of the demand controlled ventilation. In the two cases analyzed in detail, if the occupation was about 70% of the total, the energy consumption for ventilation was similar to the one obtained with the more conservative strategy suggested by Technical Standard (18.4 kWh vs. 16.7 kWh). If the occupation was of the order of 20% with respect to the maximum permitted, the energy consumption could be reduced in a relevant way (4.2 kWh vs. 15.7 kWh); the advantage in terms of energy saving appears to be relevant mainly when the occupation is reduced.

_{2}concentration and energy consumption.

_{2}concentration using commercial sensors, represents a considerable step forward with respect to traditional model-based systems, because it dynamically builds a “just accurate enough” model that could be sufficient to provide optimal decision strategies for operating ventilation rates and HVAC systems in general.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- European Parliament. Directive 2012/27/EU of the European Parliament and of the Council on Energy Efficiency; European Parliament: Brussels, Belgium, 2012. [Google Scholar]
- European Parliament. Directive 2018/844 of the European Parliament and of the Council of 30 May 2018 Amending Directive 2010/31/EU on the Energy Performance of Buildings and DIRECTIVE 2012/27/EU on Energy Efficiency; European Parliament: Brussels, Belgium, 2018; p. 17. [Google Scholar]
- Belmonte, J.F.; Barbosa, R.; Almeida, M.G. CO
_{2}concentrations in a multifamily building in Porto, Portugal: Occupants’ exposure and differential performance of mechanical ventilation control strategies. J. Build. Eng.**2019**, 23, 114–126. [Google Scholar] [CrossRef] - Merema, B.; Delwati, M.; Sourbron, M. Demand controlled ventilation (DCV) in school and office buildings: Lessons learnt from case studies. Energy Build.
**2018**, 172, 349–360. [Google Scholar] [CrossRef] - Mysen, M.; Berntsen, S.; Nafstad, P.; Schild, P. Occupancy density and benefits of demand-controlled ventilation in Norwegian primary schools. Energy Build.
**2005**, 37, 1234–1240. [Google Scholar] [CrossRef] - Wachenfeldt, B.J.; Mysen, M.; Schild, P.G. Air flow rates and energy saving potential in schools with demand-controlled displacement ventilation. Energy Build.
**2007**, 39, 1073–1079. [Google Scholar] [CrossRef] - Simanic, B.; Nordquist, B.; Bagge, H.; Johansson, D. Indoor air temperature, CO
_{2}concentration and ventilation rates: Long-term measurements in newly built low-energy schools in Sweden. J. Build. Eng.**2019**, 25, 100827. [Google Scholar] [CrossRef] - Persily, A.K. Evaluating Building IAQ and Ventilation with Indoor Carbon Dioxide. ASHRAE Trans.
**1997**, 103, 193–204. [Google Scholar] - McLaughlin, J.E.; King, G.A.; Howley, E.T.; Bassett, D.R., Jr.; Ainsworth, B.E. Assessment of the Cosmet K4B2 portable metabolic system. Med. Sci. Sport Exerc.
**2003**, 31, S286. [Google Scholar] [CrossRef] - Satish, U.; Mendell, M.J.; Shekhar, K.; Hotchi, T.; Sullivan, D.; Streufert, S.; Fisk, W.J. Is CO
_{2}an indoor pollutant? Direct effects of Low-to-Moderate CO_{2}Concentrations on Human Decision-Making Performance. Environ. Health Perspect.**2012**, 120, 1671–1678. [Google Scholar] [CrossRef] [Green Version] - Myhrvold, A.N.; Olsen, E.; Lauridsen, O. Indoor environment in schools–pupils health and performance in regard to CO
_{2}concentrations. In Proceedings of the 7th International Conference on Indoor Air Quality and Climate, Nagoya, Japan, 21–26 July 1996; pp. 369–371. [Google Scholar] - Mendell, M.J.; Heath, G.A. Do indoor pollutants and thermal conditions in schools influence student performance? A critical review of the literature. Indoor Air
**2005**, 15, 27–52. [Google Scholar] [CrossRef] - American Society of Heating Refrigerating and Air-Conditioning Engineers (ASHRAE). Ventilation for Acceptable Indoor air Quality; ASHRAE Standard 62.1-2016; ASHRAE: Atlanta, GA, USA, 2016. [Google Scholar]
- European Committee for Standardization (CEN). EN 13779—Ventilation for Non-Residential Buildings—Performance for Ventilation And Room Conditioning Systems; CEN: Brussels, Belgium, 2010. [Google Scholar]
- Johnson, D.L.; Lynch, R.A.; Floyd, E.L.; Wang, J.; Bartels, J.N. Indoor air quality in classrooms: Environmental measures and effective ventilation rate modeling in urban elementary schools. Build. Environ.
**2018**, 136, 185–197. [Google Scholar] [CrossRef] - Chan, W.R.; Li, X.; Singer, B.C.; Pistochini, T.; Vernon, D.; Outcault, S.; Sanguinetti, A.; Modera, M. Ventilation rates in California classrooms: Why many recent HVAC retrofits are not delivering sufficient ventilation. Build. Environ.
**2020**, 167, 106426. [Google Scholar] [CrossRef] - Franco, A.; Leccese, F.; Marchi, L. Occupancy modelling of buildings based on CO
_{2}concentration measurements: An experimental analysis. J. Phys. Conf. Ser.**2019**, 1224, 10. [Google Scholar] [CrossRef] - Chenari, B.; Dias Carrilho, J.; Gameiro Da Silva, M. Towards sustainable, energy-efficient and healthy ventilation strategies in buildings: A review. Renew. Sustain. Energy Rev.
**2016**, 59, 1426–1447. [Google Scholar] [CrossRef] - Szczurek, A.; Maciejewska, M.; Pietrucha, T. Occupancy determination based on time series of CO
_{2}concentration, temperature and relative humidity. Energy Build.**2017**, 147, 142–154. [Google Scholar] [CrossRef] - Chauvin Arnoux Metrix. Chauvin Arnoux C.A 1510. Available online: https://catalog.chauvin-arnoux.it/it_en/c-a-1510.html?___from_store=it_it (accessed on 2 July 2020).
- Hall, J.E.; Guyton, A.C. Diffusion of Oxygen and Carbon Dioxide through the Respiratory Membrane. In Textbook of Medical Physiology; Saunders Elsevier: Philadelphia, PA, UAS, 2011; pp. 485–494. [Google Scholar]
- Leonard, W.R. Measuring human energy expenditure and metabolic function: Basic principles and methods. J. Anthropol. Sci.
**2010**, 88, 221–230. [Google Scholar] - European Committee for Standardization (CEN). EN 16798-1; Energy Performance of Buildings. Ventilation for Buildings. Part 1: Indoor Environmental Input Parameters for Design and Assessment of Energy Performance of Building Addressing Indoor Air Quality, Thermal Environment, Lighting and Acoustics; CEN: Brussels, Belgium, 2019; 82. [Google Scholar]
- Zuraimi, M.S.; Pantazaras, A.; Chaturvedi, K.A.; Yang, H.J.J.; Tham, K.W.; Lee, S.E. Predicting occupancy counts using physical and statistical CO
_{2}-based modeling methodologies. Build. Environ.**2017**, 123, 517–528. [Google Scholar] [CrossRef] - Wolf, S.; Calì, D.; Krogstie, J.; Madsen, H. Carbon dioxide-based occupancy estimation using stochastic differential equations. Appl. Energy
**2019**, 236, 32–41. [Google Scholar] [CrossRef] - O’Neill, Z.D.; Li, Y.; Cheng, H.C.; Zhou, X.; Taylor, S.T. Energy savings and ventilation performance from CO
_{2}-based demand controlled ventilation: Simulation results from ASHRAE RP-1747 (ASHRAE RP-1747). Sci. Technol. Built Environ.**2020**, 26, 257–281. [Google Scholar] [CrossRef] [Green Version] - Nassif, N. A robust CO
_{2}-based demand-controlled ventilation control strategy for multi-zone HVAC systems. Energy Build.**2012**, 45, 72–81. [Google Scholar] [CrossRef] - Batterman, S. Review and extension of CO
_{2}-based methods to determine ventilation rates with application to school classrooms. Int. J. Environ. Res. Public Health**2017**, 14, 145. [Google Scholar] [CrossRef] - Rao, S.S. Engineering Optimization: Theory and Practice, 4th ed.; John Wiley & Sons: Hoboken, NJ, USA, 2009. [Google Scholar]
- Franco, A.; Diaz Vazquez, A.R. A Thermodynamic Based Approach for the Multicriteria Assessment of Energy Conversion Systems. J. Energy Resour. Technol.
**2006**, 128, 346–351. [Google Scholar] [CrossRef] - Park, J.; Loftness, V.; Aziz, A. Post-Occupancy Evaluation and IEQ Measurements from 64 Office Buildings: Critical Factors and Thresholds for User Satisfaction on Thermal Quality. Buildings
**2018**, 8, 156. [Google Scholar] [CrossRef] [Green Version] - Baronti, P.; Barsocchi, P.; Chessa, S.; Mavilia, F.; Palumbo, F. Indoor Bluetooth Low Energy Dataset for Localization, Tracking, Occupancy, and Social Interaction. Sensors
**2018**, 18, 4462. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**Figure 1.**Correlation between derivative of CO

_{2}concentration and air volume per occupants for different values of CO

_{2}production rate per occupant.

**Figure 5.**Correlation between CO

_{2}concentration and air volume per student, obtained in the different experiments provided in [17].

**Figure 7.**Energy consumption at different air exchange rates as well as external and indoor temperatures (classroom 5).

**Figure 8.**Comparison among monitoring results (without mechanical ventilation) and three strategies involving mechanical ventilation for a two hours experience.

Classroom | Building | Level | Max. Occupancy (N) | Floor Surface, S (m^{2}) | Volume V (m^{3}) | Ratio V/S (m^{3}/m^{2}) | Vol. for Student at Full Occupation (m^{3}) |
---|---|---|---|---|---|---|---|

0 | LAB | 1st | 20 | 20 | 58 | 2.90 | 2.90 |

1 | A | 1st | 108 | 88 | 482 | 5.48 | 4.46 |

CL1 | B | 1st | 116 | 216 | 583 | 2.70 | 5.03 |

2 | B | 1st, 2nd | 366 | 336 | 1426 | 4.24 | 3.90 |

3 | C | 4th | 72 | 73 | 212 | 2.90 | 2.94 |

4 | F | 1st | 309 | 286 | 1587 | 5.55 | 5.14 |

5 | F | 1st | 208 | 216 | 1220 | 5.65 | 5.87 |

6 | F | 1st | 109 | 130 | 721 | 5.55 | 6.61 |

7 | F | 1st | 196 | 197 | 1094 | 5.55 | 5.58 |

8 | F | 1st | 104 | 129 | 717 | 5.56 | 6.89 |

9 | F | 1st | 109 | 128 | 711 | 5.55 | 6.52 |

10 | F | 1st | 140 | 131 | 439 | 3.35 | 3.14 |

Experiment Identification (Room/Number) | Number of Students | V/n_{occ} (m^{3}) | CO_{2} Concentration at t = 0 (ppm) | Maximum CO_{2} Concentration Measured | CO_{2} Concentration Increase with t (ppm/s) | Time for Overcoming CO_{2} Threshold (1500 ppm) (min) |
---|---|---|---|---|---|---|

0 | 20 | 2.90 | 704 | 1841 | 0.28 | 20 |

1 | 68 | 7.08 | 782 | 2566 | 0.17 | 72 |

CL1 | 38 | 15.08 | 659 | 1676 | 0.22 | 55 |

3 | 72 | 2.94 | 1264 | 2960 | 0.59 | 6 |

4#1 | 58 | 27.36 | 678 | 1741 | 0.14 | 95 |

4#3 | 93 | 17.06 | 596 | 2685 | 0.18 | 78 |

5#1 | 168 | 7.30 | 1138 | 4913 | 0.52 | 10 |

5#3 | 106 | 11.50 | 1100 | 3409 | 0.26 | 21 |

7#1 | 146 | 7.49 | 791 | 3297 | 0.40 | 24 |

8 | 54 | 13.27 | 1257 | 2383 | 0.37 | 8 |

9#1 | 54 | 13,16 | 1512 | 2334 | 0.43 | 0 |

9#2 | 59 | 12.05 | 1648 | 3369 | 0.26 | 0 |

10#2 | 50 | 8.78 | 695 | 2410 | 0.42 | 27 |

**Table 3.**Comparison among the air flow rate based on technical standards (TS) and with the proposed strategy for two of the classrooms under analysis.

Classroom 5#1 Air Exchange Rate (m^{3}/s) | Classroom 4#1 Air Exchange Rate (m^{3}/s) | |
---|---|---|

Strategy TS 1 | 0.58 | 0.85 |

Strategy TS 2 | 2.42 | 3.15 |

Proposed strategy (based on the actual number of occupants) | 0.64 | 0.22 |

**Table 4.**Energy consumption for air ventilation for the three strategies during a lessons of about 2 h.

Classroom 5#1 | Classroom 4#1 | |
---|---|---|

Monitoring day and starting hour | Jan 12 | Jan 17 |

Average external temperature (°C) | 8.0 | 11.9 |

Ventilation thermal load (Strategy TS 1) (kWh) | 16.7 | 15.7 |

Ventilation thermal load (Strategy TS 2) (kWh) | 69.7 | 60.5 |

Ventilation thermal load (Proposed strategy) (kWh) | 18.4 | 4.2 |

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## Share and Cite

**MDPI and ACS Style**

Franco, A.; Schito, E.
Definition of Optimal Ventilation Rates for Balancing Comfort and Energy Use in Indoor Spaces Using CO_{2} Concentration Data. *Buildings* **2020**, *10*, 135.
https://doi.org/10.3390/buildings10080135

**AMA Style**

Franco A, Schito E.
Definition of Optimal Ventilation Rates for Balancing Comfort and Energy Use in Indoor Spaces Using CO_{2} Concentration Data. *Buildings*. 2020; 10(8):135.
https://doi.org/10.3390/buildings10080135

**Chicago/Turabian Style**

Franco, Alessandro, and Eva Schito.
2020. "Definition of Optimal Ventilation Rates for Balancing Comfort and Energy Use in Indoor Spaces Using CO_{2} Concentration Data" *Buildings* 10, no. 8: 135.
https://doi.org/10.3390/buildings10080135