Occupancy and Air Quality Model for Outdoor Events: A Strategy for Preventing Disease Transmission at Mass Events

Abstract

This paper proposes a novel model to determine occupancy density for outdoor events to prevent infectious disease transmission caused by the impossibility of proper dilution of human effluents in the atmosphere. It uses standardization processes to calculate natural ventilation air renewal and establishes theoretical occupancy based on activity and exhaled air percentage, aiming for indoor air quality comparable to the IDA2 standards. The study focuses on mass events in Mostoles (Spain), analyzing street activities and bullring events. It found that above a certain height in the open air, infection risk is low, eliminating capacity limitations. The resulting mathematical expressions can be adapted to different pathogens, ensuring the quality of indoor air conditions through capacity control. The process determines the ventilation required based on physical activity, considering both unrestricted and restricted situations. The relationship between required and available ventilation prevents disease transmission. The method’s effectiveness is demonstrated through comparisons between estimates and environmental measurements during Mostoles events. The maximum outdoor occupancy at ground level to achieve air quality comparable to the IDA2 standards is determined to be 2.36 persons/m², while to prevent the transmission of SARS-CoV-2 it is determined to be 1.98 persons/m². In addition, transmission will not occur during mass gatherings in locations over five meters above ground level. In conclusion, this model provides an adaptable tool to prevent the spread of infectious diseases at outdoor events by ensuring adequate air quality through occupancy control.

1. Introduction

Pollution of the environment is one of the most significant factors influencing the quality of life of individuals. It is responsible for the development of numerous respiratory diseases and the premature death of thousands of people annually [1,2,3].

In recent decades, humanity has made significant strides in the fields of science and technology. However, these advances have not been without consequence, with negative impacts on the environment becoming increasingly evident [4,5,6]. In order to mitigate the effects of pollution, the United Nations (UN) has agreed on an action plan, called Agenda 2030, with Sustainable Development Goals. Among other actions, this plan promotes the reduction of industrial gas emissions, which are responsible for the majority of respiratory infections and cardiovascular diseases [7,8,9,10].

Furthermore, the European Union has implemented initiatives with the objective of achieving a clean atmosphere and quality outdoor air. One of the initial actions has been to establish limitations on the concentration of pollutants in the air, with the objective of preventing their impact on people’s quality of life and creating an adequate, healthy environment that prevents diseases and favors a healthy and healthful life, in accordance with the quality standards of the World Health Organization [11]. In addition, the Eighth European Environment Action Program aspires to attain an environment devoid of toxic substances and characterized by clean and healthy air [12].

In accordance with the European Union regulations, Spain has devised a series of strategies with the objective of safeguarding the atmosphere, regulating the quality of breathable air, and effectively addressing the most pressing environmental concerns of the present era [13,14,15,16].

This commitment to healthy environments also encompasses the habitability conditions of buildings. It is therefore imperative to ensure that indoor air quality standards are met in buildings in order to achieve adequate levels of health and comfort, which are prerequisites for a healthy life [17,18,19,20,21].

The Scientific Committee on Health and Environmental Risks (SCHER), which provides counsel to the European Commission, and the United States Environmental Protection Agency (EPA) have identified indoor air quality in buildings as a critical issue. This is because people spend the majority of their time indoors [22,23], both at home and at work. These organizations advocate the elimination of pollutants commonly found within buildings. This is achieved through the use of methodologies based on CO₂ concentration, which allow for the identification and subsequent avoidance of pollutants through the implementation of minimum ventilation flow rates [24,25,26,27,28].

In Spain, the regulations governing indoor air quality in buildings are particularly rigorous, with quality levels varying according to the type of building and its intended use [29]. It is recommended that companies specializing in the installation and assembly of ventilation equipment comply with specific measures to prevent the transmission of disease, especially in residential and educational buildings, in order to prevent the incidence of SARS-CoV-2 [30,31,32].

The majority of computational models employed in the study of ventilation flow rates in buildings adhere to the steady-state CO₂ methodology developed at Harvard University [33]. This study methodology has also been employed to ascertain, in a secure manner, the occupancy rates of buildings under natural ventilation conditions, as stipulated by European regulations [11,12,34].

A common and significant issue in the context of public health is the necessity to assess the ventilation requirements of semi-enclosed spaces where large gatherings occur (Figure 1). In the context of such venues, the risks associated with poor air quality are often overlooked, primarily due to their outdoor location. However, there is evidence of the transmission of infectious diseases during mass events [35,36]. Although in indoor environments these risks are associated with insufficient ventilation [37,38], this same relationship has not been established outdoors, despite the availability of outdoor models of the behavior of both air flow [39,40,41,42,43] and environmental pollutants, including particulate matter [44,45,46,47], which is similar to the aerosols responsible for the transmission of this type of disease [2,36].

These spaces must be designed to ensure the health and safety of the occupants, and to prevent the transmission of infectious diseases through the air [48,49,50]. It is of paramount importance to ascertain the requisite environmental quality standard to ensure the safe execution of the activities in question. This entails the implementation of effective monitoring procedures to assess air quality and the establishment of limits on the maximum occupancy of the aforementioned enclosures [51,52,53].

In accordance with the aforementioned premises, a theoretical calculation method was designed for this research. The objective of the present research is not to evaluate environmental contamination; rather, it is to examine ventilation conditions that prevent airborne transmission of pathogens. Consequently, the reference values will be consistent with those observed in outdoor environments. This method considers the deterioration of air quality in crowded open spaces similar to that indoors and takes CO₂ concentration as an indicator and a reference factor to determine the occupancy of semi-enclosures that host a multitude of activities. It is based on the quality standards of the applicable European regulations [11]. The methodology enables the theoretical occupancy of a semi-enclosure to be determined based on the natural air renewal flows and the type of activity carried out, taking into account an estimation of the percentage of air coming from exhalations. To this end, an experimental field study was conducted to monitor recreational–festive activities in which a large group of people coincided simultaneously. In order to assess local thermal comfort, it is necessary to consider a number of factors, including air currents, the vertical difference in air temperature, the presence of hot and cold floors, and the asymmetry of radiant temperature. Finally, an open-air height is established at which infection is unlikely to occur, thus establishing a capacity limit [54]. The proposed mathematical expressions can be adapted to accommodate any type of pathogen. Additionally, control of the gauges enables the attainment of the same air quality conditions as those established by regulations for indoor environments [34].

The proposed method of analysis is validated by applying it to mass events held in open spaces during the Patron Saint Festivities of the city of Mostoles (Madrid, Spain), held in September 2022. This entails a prospective field study, during which critical factors such as CO₂ concentration and ventilation are monitored in different mass events. These events are observed at street level and in the city’s bullring (Figure 1), as it is an open space where the public is located at high altitude and has a known capacity for each of the activities carried out inside.

1.1. Background

Firstly, the occupancy density that allows natural ventilation is determined in comparison to the clean air flow required by each attendee in order to ensure that the air quality is in accordance with the Category IDA2 indoor air quality standards [29], as air renewal in crowded environments is not ensured by the fact that we are outdoors. Furthermore, in the event of a risk situation, four additional levels of safety are proposed. One of these is based on the ventilation required by the steady-state CO₂ methodology of Harvard University [33] to avoid the transmission of SARS-CoV-2.

In order to facilitate comprehension of the results, ten activities have been delineated, ranging from a sedentary state to active participation in sports activities. Consequently, ten values of ventilation flow rate are established for each of the five safety levels, with the objective of determining the maximum occupancy for each of the situations analyzed.

Carbon dioxide (CO₂) is employed as a marker element, which, in addition to being naturally present in clean air, is generated by the occupants of the spaces under analysis through breathing. Its value is linked to the activity being carried out at a specific time [55,56]. Each of the five levels of activity is associated with an increase in CO₂ concentration as a consequence of the exhalation of the occupants through breathing. This process ensures that a requisite quantity of clean air is delivered to each of the scenarios under examination. As these are open spaces, the clean air is provided by natural outdoor movement, which depends on the atmospheric conditions at any given time. This process allows for the determination of standardized air velocities, which in turn enables the theoretical volume of air to be calculated for ventilation around occupants, depending on their height [57,58]. The occupancy density for each of the ten activities is determined by comparing the available ventilation flow rate with its reference value. This allows the situation that best suits the behavior of CO₂ in each situation to be identified.

1.1.1. CO₂ Concentration

The analysis factors developed permit the establishment of interactions between individuals attending events in a facility under analysis, taking into account the volume of carbon dioxide (CO₂) exhaled by each individual, a factor related to their metabolic activity [59]. Conversely, it is acknowledged that CO₂ is an appropriate marker for study purposes, as it is a bioeffluent with behavior analogous to that of the novel coronavirus [52].

Concurrently, the natural ventilation of the spaces in which the activities are conducted is considered, as it is a factor that ensures a reduction in the persistence time of the gaseous atmosphere and, consequently, the concentration of potential pathogens present therein. Consequently, the determination of this parameter can be regarded as a reliable indicator of the degree of occupancy [60,61].

The general values of metabolic consumption associated with an average person [62] have been defined according to the following expression, as shown in Table 1:

$${\mathrm{C}\mathrm{O}}_2=6.36·{10}^{-5}·\mathrm{M}$$

(1)

where

qCO₂ = CO₂ generation rate in L/s per person

M = Metabolism rate in W/m²

Table 1. The metabolic rate is subject to adaptation in accordance with the nature of the activity in question [62].

Type of Activity	Metabolism (W/m2)	Type of Associated Activity
Sedentary work	70	Rest/Low activity
Light standing work	100	Low activity
Walking (1.6 Km/h)	100	Low activity
Light work	130	Low/Moderate activity
Dancing	165	Moderate activity
Moderate work	165	Moderate activity
Walking (5 Km/h)	200	Moderate/High activity
Heavy work	230	High activity
Gym/swimming recreation	260	High/Very high activity
Gym/team sport	300	Very high activity

Table 1. The metabolic rate is subject to adaptation in accordance with the nature of the activity in question [62].

Type of Activity	Metabolism (W/m2)	Type of Associated Activity
Sedentary work	70	Rest/Low activity
Light standing work	100	Low activity
Walking (1.6 Km/h)	100	Low activity
Light work	130	Low/Moderate activity
Dancing	165	Moderate activity
Moderate work	165	Moderate activity
Walking (5 Km/h)	200	Moderate/High activity
Heavy work	230	High activity
Gym/swimming recreation	260	High/Very high activity
Gym/team sport	300	Very high activity

It is evident that ventilation facilitates the dilution of CO₂ present in the environment. If human respiration is considered the sole source of CO₂ generation, in spaces where there are sufficient occupants who have remained for an extended period to reach an equilibrium, ventilation is evaluated through a balance of matter [63].

1.1.2. Reference Values

The fundamental prerequisite for the research in question is that the ventilation conditions in outdoor environments are analogous to those required by Category IDA2 in indoor semi-enclosures. In such an environment, the CO₂ concentration between the ventilated area and the clean area must not deviate from a value of 500 ppm [29] for the air quality to be considered good air quality. In the event that a control based on the environmental conditions of diseases with a transmission capacity similar to SARS-CoV-2 is required, the environmental limits applied by the steady-state CO₂ method shall be used for the calculation [33].

Furthermore, conventional levels of action in industrial hygiene are proposed at 75%, 50%, and 25% of the limit value, with the aforementioned values being considered in relation to the air quality of Category IDA2 [29].

1.1.3. Climatology

Finally, it was determined that climatology should be included as a factor that can influence the conditions of occupation of outdoor spaces. To obtain the most reliable results possible for occupation, climatological data were also collected, as shown in

Table 2. The climatological data were collected on the days when samples were taken during the festivities honoring the patron saint of Mostoles [64].

Values	10 September 2022	13 September 2022	14 September 2022	15 September 2022
Maximum temperature (°C)	32	25	23	24
Minimum temperature (°C)	20	17	15	17
Max. air velocity (Km/h)	34	34	30	15
Min. air velocity (Km/h)	15	7	9	5
Average air velocity (Km/h)	25	16	15	10
Relative humidity (%)	45	60	85	90
Sky condition	Clear	Very cloudy	Very cloudy	Very cloudy
Precipitations	-	-	Rain	Rain

.

Given the availability of different standardized air velocities outdoors, some of which are linked to the behavior of carbon dioxide, it is necessary to select the one that best suits each situation analyzed. For the calculations, it has been estimated that the CO₂ concentration in an unoccupied environment is 400 ppm, both for sedentary and light activities. Similarly, it is assumed that the sites are always obstructed, necessitating the application of a ventilation efficiency factor of 5 [65].

2. Materials and Methods

The maximum occupancy density in outdoor environments is determined by comparing the ventilation flow rate required for each of the scenarios considered and the natural ventilation available in each case.

2.1. Required Ventilation Flow Rate

In order to ascertain the rate of CO₂ generation per capita in instances where a concentration of individuals is present in a public space, the following expression is employed [53]:

$$\mathrm{q}{\mathrm{C}\mathrm{O}}_2=6.36·{10}^{-5}·\mathrm{M}\Rightarrow \mathrm{q}{\mathrm{C}\mathrm{O}}_2=6.36·{10}^{-5}·100\Rightarrow \mathrm{q}{\mathrm{C}\mathrm{O}}_2=6.36·{10}^{-3} {\displaystyle \raisebox{1ex}{$\mathrm{L}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.}$$

(2)

Similarly, in order to determine the ventilation flow rate required in an indoor enclosure per person in order to comply with the same criteria established in the RITE (its acronym in Spanish), the following expression is applied [29]:

$$\begin{array}{c}{\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{R}\mathrm{I}\mathrm{T}\mathrm{E}}={\displaystyle \frac{{\mathrm{q}}_{{\mathrm{C}\mathrm{O}}_2}}{500}}·{10}^6\Rightarrow {\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{d} 75\mathrm{\%}}={\displaystyle \frac{6.36·{10}^{-3}}{500}}·{10}^6\\ \Rightarrow {\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{d} \mathrm{R}\mathrm{I}\mathrm{T}\mathrm{E}}=12.72 {\displaystyle \raisebox{1ex}{$\mathrm{L}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}·\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{o}\mathrm{n}$}\right.}\end{array}$$

(3)

The ventilation flow rates required for the control of airborne infectious diseases during a standing activity are obtained in the same way, but with consideration of the differing limit values proposed. As a point of reference, the limits established by the steady-state CO₂ method are employed in the following expression [33]:

$$\begin{array}{c}{\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{d}}={\displaystyle \frac{{\mathrm{q}}_{{\mathrm{C}\mathrm{O}}_2}}{420}}·{10}^6\Rightarrow {\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{d}}={\displaystyle \frac{6.36·{10}^{-3}}{420}}·{10}^6\\ \Rightarrow {\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{d}}=15.14 {\displaystyle \raisebox{1ex}{$\mathrm{L}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}·\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{o}\mathrm{n}$}\right.}\end{array}$$

(4)

The occupancy is determined by comparing the reference value (Q_required) which is specific to each activity and safety level with the available ventilation.

2.2. Natural Outdoor Ventilation

Outdoor ventilation is a highly variable phenomenon. In order to design a tool to determine occupancy prior to the events, it is necessary to have standardized air velocities. In this context, the calculation standards for explosive atmospheres are the most restrictive and involve a safety aspect [65,66,67].

The calculation method for classified areas underwent a significant transformation from numerical to graphical resolution when the version EN 60079-10-1:2016 [66] replaced that of 2010. This methodology is maintained with the current version EN 60079-10-1:2022 [65]. However, the application guide based on the previous methodology, EN 202007:2006 IN [67], was not revoked until 2021 due to the fact that the calculation bases for ventilation, although not required, are still valid, in addition to being the only standard in the family that allows the outdoor ventilation flow rate to be determined from ambient conditions.

Open spaces are defined by their unlimited volume and their capacity to absorb substances introduced into the atmosphere. This means that the risk of infection is localized to the immediate environment of the emitter, rather than extending to remote areas [67]. In outdoor settings, low wind speeds result in a high number of air changes. In order to circumvent the utilization of statistical atmospheric values, which are only valid for specific locations, standardized air velocities are employed for the calculation of fire and explosion hazardous areas. These areas are restrictive and carry a high safety requirement for any location. The number of air changes outdoors is considered to be 0.03 s⁻¹, a reference value associated with a wind speed of 0.5 m/s, the reference speed in outdoor environments that adapts to the behavior of CO₂ in the atmosphere [65,66,67]. A hazardous reference volume is established to ensure that emissions produced by an infected person experience high dilution in the air. The following expressions shall be applicable [67]:

$$\begin{array}{c}{\mathrm{V}}_0={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{0.03}}={\displaystyle \frac{\mathrm{w}·{\mathrm{A}}_{\mathrm{w}}}{0.03}}\\ \mathrm{L}={\displaystyle \frac{\mathrm{w}}{0.03}}={\displaystyle \frac{0.5}{0.03}}=15 \mathrm{m}\end{array}$$

(5)

where

V₀ = Reference cube volume or total volume to be ventilated (m³)

Q_min = Minimum volume flow rate of fresh air (m³/s)

w = Air velocity (m/s)

A_w = Area of the plane traversed by the air inside the cube, i.e., the cross section (m²)

L = Side of the cube under consideration, or the length of the air path inside the volume to be ventilated V₀ (m)

2.3. Application of Outdoor Ventilation Parameters and Obtaining Theoretical Occupancy

Individuals situated within the designated ventilation zone are regarded as impediments that diminish the efficacy of the emissions dilution capacity of an infected individual. This situation necessitates the introduction of an efficiency factor into the ventilation system to guarantee dilution and minimize the risk of contagion to the remaining residents. Its empirical value varies between 1 and 5 and in open environments with the presence of a very high number of impediments to the free circulation of air, which can greatly reduce the effective dilution capacity, the value considered is 5 [65]. A square surface with a side of 15 m is considered, and the number of people emitting CO₂ in the outdoor volume under analysis is determined. This number is then compared with the limit values to be proposed.

$$\begin{array}{c}{15}^3=5·{\displaystyle \frac{{\mathrm{Q}}_{\mathrm{a} \mathrm{m}\mathrm{i}\mathrm{n}}}{0.03}}\to {\mathrm{Q}}_{\mathrm{a} \mathrm{m}\mathrm{i}\mathrm{n}}=20.25 {\mathrm{m}}^3/\mathrm{s}\\ {\displaystyle \frac{{\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{d}}}{{10}^3}}·\mathrm{n}\mathrm{o}. \mathrm{o}\mathrm{f} \mathrm{p}\mathrm{e}\mathrm{o}\mathrm{p}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{i}\mathrm{n}\mathrm{g}={\mathrm{Q}}_{\mathrm{a} \mathrm{m}\mathrm{i}\mathrm{n}}\\ \mathrm{n}\mathrm{o}. \mathrm{o}\mathrm{f} \mathrm{p}\mathrm{e}\mathrm{o}\mathrm{p}\mathrm{l}\mathrm{e} \mathrm{e}\mathrm{m}\mathrm{i}\mathrm{t}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e} \mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}={\displaystyle \frac{\mathrm{n}\mathrm{o}. \mathrm{o}\mathrm{f} \mathrm{p}\mathrm{e}\mathrm{o}\mathrm{p}\mathrm{l}\mathrm{e} \mathrm{i}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{i}\mathrm{n}\mathrm{g}}{{15}^2}}\end{array}$$

(6)

The theoretical occupancy of the exterior space under analysis is obtained by means of the following expression:

$$\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{o}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{p}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e} \mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}={\displaystyle \frac{90}{{\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{d}}}}$$

(7)

The degree of occupancy according to the different heights is determined by the standard outdoor air velocities and the volume of the space to be ventilated.

$$\begin{array}{c}{\mathrm{L}}_0={\displaystyle \frac{\mathrm{w}}{{\mathrm{C}}_0}}\to {\mathrm{C}}_0={\displaystyle \frac{\mathrm{w}}{15}}\\ {15}^3=5·{\displaystyle \frac{{\mathrm{Q}}_{\mathrm{a} \mathrm{m}\mathrm{i}\mathrm{n}}}{{\mathrm{C}}_0}}\to {\mathrm{Q}}_{\mathrm{a} \mathrm{m}\mathrm{i}\mathrm{n}}=45·\mathrm{w} {\mathrm{m}}^3/\mathrm{s}\\ \mathrm{T}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{o}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{p}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e} \mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}=200·{\displaystyle \frac{\mathrm{w}}{{\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{d}}}}\end{array}$$

(8)

Finally, the occupancy density per activity performed is established by comparing it with its reference value (Q_required).

Applying the same reasoning, we determine the maximum theoretical occupancy in activities where the public must stand, ensuring a minimum air quality of Category IDA2, with an air speed at ground level of 0.5 m/s [29].

$$\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{o}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{p}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e} \mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}=200·{\displaystyle \frac{0.5}{12.72}}=7.86$$

(9)

3. Results

The calculation procedures outlined in Section 2.1 of the document were employed to determine the ventilation flow rates required per person in an indoor semi-enclosure, in accordance with the criteria established by the RITE [29], as illustrated in

Table 3. The ventilation flow rate required for outdoor activities.

Type of Activity	Sedentary Work	Light Standing Work	Walking (1.6 Km/h)	Light Work	Dancing	Moderte Work	Walking (5 Km/h)	Heavy Work	Gym/Swimming Recreation	Gym/Team Sport
Qrequired (L/s·person)	9	12.72	12.80	16.60	21.00	21.00	25.40	29.20	33.00	38.20

.

Conversely, the results obtained for the five safety levels during a standing outdoor activity are shown in

Table 4. Ventilation flow rate for a standing public activity with sanitary restrictions.

qCO2 (L/s·Person)	Qrequired RITE (L/s·Person)	Qrequired 75% (L/s·Person)	Qrequired 50% (L/s·Person)	Qrequired 25% (L/s·Person)	Qrequired [33] (L/s·Person)
0.0064	12.72	27.83	23.70	20.00	15.14

, which provides a reference value for all the activities considered in the research. These results were calculated using the data presented in Section 2.1 of the document.

The theoretical occupancy obtained for the various outdoor activities that must be carried out in compliance with the aforementioned Category IDA2 [29], as a function of the estimated air velocity, is presented in

Table 5. Theoretical outdoor occupancy as a function of available air velocity (air quality Category IDA2).

Activity		Estimated Air Velocity (m/s)
		0.15	0.30	0.50	0.6	1.00	2.00
Number of persons/m2	Sedentary work	3.33	6.67	11.11	13.33	22.22	44.44
	Light standing work	2.34	4.69	7.86	9.38	15.63	31.25
	Walking (1.6 Km/h)	2.34	4.69	7.86	9.38	15.63	31.25
	Light work	1.81	3.61	6.02	7.23	12.05	24.10
	Dancing	1.43	2.86	4.76	5.71	9.52	19.05
	Moderate work	1.43	2.86	4.76	5.71	9.52	19.05
	Walking (5 Km/h)	1.18	2.36	3.94	4.72	7.87	15.75
	Heavy work	1.03	2.05	3.42	4.11	6.85	13.70
	Gym/swimming recreation	0.91	1.82	3.03	3.64	6.06	12.12
	Gym/team sport	0.79	1.57	2.62	3.14	5.24	10.47

, based on the expressions in Section 2.3 of the document.

It is necessary to indicate at this point that, although the air speed of 0.5 m/s established by both EN 202007:2006 IN [67] and EN IEC 60079-10-1:2022 [65], can be taken as a reference at ground level, in order to determine the rest of the values it is necessary to take into account the relative density of CO₂ in the air. This does not correspond to any of the established assumptions, so it has been decided to use the model of EN IEC 60079-10-1:2022 [65], which allows for generating two values for each height considered (elevated terraces, balconies, bleachers, etc.). As illustrated in Figure 2 and Figure 3, the behavior at heights below 5 m above ground level (Figure 2) and above 5 m above ground level (Figure 3) can be observed.

Figure 2 depicts the behavior of gas as a function of height. The gray line represents the behavior of gas as a light gas at a height of less than 5 m. The yellow line represents the behavior of a heavy gas between a height of 2 and 5 m. Finally, the orange-colored line represents heavy gas behavior at a height of less than 2 m.

If the behavior of CO₂ is considered analogous to that of a heavy gas, the occupancy values obtained are lower due to the diminished efficiency of ventilation. Conversely, if the gas is considered to be a light gas, its dilution remains stable up to a height of five meters.

As shown in Figure 3, the blue line on the graph represents the general behavior of a light gas at a height above 5 m in the absence of obstacles. In contrast, the brown line on the graph represents the behavior of a heavy gas at heights above 5 m without the presence of obstacles.

It is also possible to control a health crisis through air quality by controlling occupancy in open spaces using the values required by applying the environmental limits (Figure 4), the one established through the steady-state CO₂ method, and the classic levels of action in industrial hygiene, at 75%, 50%, and 25% of the limit values. These values are considered in relation to the air quality of Category IDA2 [29].

Nevertheless, a gathering of individuals in an area exceeding five meters in diameter, as a consequence of air velocity, can also be regarded as an obstacle-free zone. The results obtained for this case are presented in Figure 4.

The Technical Building Code in Spain (CTE as its acronym in Spanish) [68] stipulates that an occupancy density of 0.25 m²/person applies to enclosures with standing spectators and 0.5 m²/person to semi-enclosed areas. Consequently, in the case of a large-scale event, the maximum occupancy density will be four persons/m². This situation allows us to conclude that, for locations situated at a height of five meters in outdoor enclosures, the transmission of SARS-CoV-2 would not occur at leisure events.

4. Discussion

The most prevalent chemical element in the characterization of indoor air quality with prolonged human presence is carbon dioxide (CO₂), which is associated with human physical activity [59] and has been widely employed to mitigate the risk of aerosol-borne respiratory diseases, such as COVID-19, and serves as a reliable indicator for predicting occupancy rates [40], even in isolation centers [40,69].

The results of the established calculation methods indicate that CO₂ concentration, obtained by direct measurement, exhibits considerable variability. Therefore, the criterion of grouping them according to the estimated density of occupation is adopted, considering the difficulty of walking (

Table 6. CO₂ measurements at ground level at mass events.

Estimation of Walking Difficulty	CO2 Concentration (ppm)
	Min. Value	Max. Value
Clear public roads	460	500
Walking without difficulty	600	650
It is easy to walk, but you have to avoid other pedestrians	700	750
It is easy to walk, but walking is hindered	800	900
Walking with difficulty	900	1000
Walking is not possible, but mobility is maintained	1000	1200
Mobility is hindered	1200	1300
Mobility is practically impaired	1300	1400
Mobility is impaired	1400	1500
Total impossibility of mobility	1500	1680

).

Equally, the application of established calculation models as presented in

Table 7. Occupancy density at ground level at mass events. In order to achieve this objective, the values set forth in the EN IEC 60079-10-1:2022 standard [65] and those established in the EN 202007:2006 IN standard [67] are utilized as reference points.

CO2 Concentration (ppm)	Estimated Occupancy Density (Persons/m2)
	Sedentary Activity		Light Activity
	EN IEC 60079-10-1	UNE EN 202007 IN	EN IEC 60079-10-1	UNE EN 202007 IN
480	0.5	1.8	0.4	1.3
650	1.7	5.6	1.2	3.9
750	2.3	7.8	1.6	5.5
850	3.0	10.0	2.1	7.0
950	3.7	12.2	2.6	8.6
1100	4.7	15.6	3.3	10.9
1250	5.7	18.9	4.0	13.3
1350	6.3	21.1	4.5	14.8
1450	7.0	23.3	4.9	16.4
1550	7.7	25.6	5.4	18.0

demonstrates the theoretical occupancy values within the public thoroughfare.

As illustrated, provided that the walking process is not impeded by obstacles or crowding of people in the occupied spaces, the model that best fits the results obtained is the light activity model. Nevertheless, when normal movement of people is impeded, the sedentary activity model yields superior results [65,67].

The results indicate that carbon dioxide behaves at ground level as a heavy gas, in accordance with the dilution patterns established in the EN IEC 60079-10-1:2022 standard [65].

The maximum density at a mass event is considered to be four people per square meter (4 p/m²), and in large crowds where walking is not possible there may be between seven and eight people per square meter (7–8 p/m²).

The data obtained from the bullring in Mostoles allow for the analysis of crowded events in an open area at different heights. In this case, the air velocity values of the EN IEC 60079-10-1:2022 standard [65] are applied. Despite the fact that carbon dioxide is 1.5 times heavier than air, the two behavior models (light gases and heavy gases) are utilized to ascertain which model best aligns with the outcomes observed.

The activity in question is considered to be of a sedentary nature, with an occupancy density of 0.5 m²/person. This is due to the fact that the public is seated and the bleachers do not have defined seats [68].

The seating area of the Mostoles bullring has a capacity of 5000 individuals and a height range of 2 m to 12 m (no occupancy is permitted above a height of 9 m). The seating area is arranged in a staggered configuration, with a height differential of 50 cm between adjacent rows. The measurements were taken in circular perimeters, with a difference of one meter in height every two steps. The results of the study, as presented in

Table 8. The concentration of CO₂ at varying heights at large-scale events is a topic of interest.

Height (m)	CO2 Concentration (ppm) Estimated Occupancy Density of Two Persons/m2
	10 September 2022 (21:00 h)	13 September 2022 (11:00 h)	14 September 2022 (11:00 h)	15 September 2022 (20:00 h)
2	750	700	700	750
3	750	600	600	600
4	600	500	600	600
5	600	500	500	550
6	550	450	450	500
7	450	450	450	500
8	450	-	450	450

, are as follows:

The data presented here correspond to the average obtained along the circular route of the bullring, with values only taken from areas where the capacity was full. The outcomes of the study (

Table 9. A comparison between the actual and estimated height for an occupancy of two persons per square meter.

Height (m)	Estimated Height (m) Occupancy Density: 2 Persons/m2
	10 September 2022 (21:00 h)		13 September 2022 (11:00 h)		14 September 2022 (11:00 h)		15 September 2022 (20:00 h)
	Light Gas Model	Heavy Gas Model	Light Gas Model	Heavy Gas Model	Light Gas Model	Heavy Gas Model	Light Gas Model	Heavy Gas Model
2	1.2	0.1	1.5	0.1	1.5	0.1	1.2	0.1
3	1.2	0.1	2.5	0.6	2.5	0.6	2.5	0.1
4	2.5	0.6	4.1	2.8	2.5	0.6	2.5	0.6
5	2.5	0.6	4.1	2.8	4.1	2.8	3.2	0.6
6	3.2	1.3	5.3	5.8	5.3	5.8	4.1	1.3
7	5.3	5.8	5.3	5.8	5.3	5.8	4.1	5.8
8	5.3	5.8	-	-	5.3	5.8	5.3	5.8

) are contrasted with the projections derived from the models developed in accordance with the EN IEC 60079-10-1:2022 standard [65].

It is observed that both models exhibit greater restrictions than the actual values, with the light gas behavior offering the most accurate approximation. It is important to note that on the days on which the measurements were taken, the air velocity was consistently higher than the standardized values.

5. Conclusions

The proposed methodology allows for the prediction of optimal capacity for large outdoor events, thereby ensuring the health and safety of attendees.

The tool which has been designed allows the Civil Protection Services to manage the gauging according to the desired air quality, even in situations of sanitary restriction such as those experienced during the COVID-19 pandemic. This management proposal enables the determination of the ventilation values required, contingent upon the nature of the activities being conducted. This includes consideration of events occurring within semi-enclosures with individuals situated at varying heights.

One limitation of the method is the variability in outdoor ambient conditions, with temperature, relative humidity and the mechanisms of atmospheric particulate removal and formation affecting air pollutant concentrations. Nevertheless, it is possible to standardize the ventilation conditions by applying the regulations pertaining to explosive atmospheres whose restrictive parameters imply the assumption of a high level of certainty in results.

It is possible to adapt the results to specific locations, assuming a higher level of occupation, both in the design phase and during the implementation stage. In the design phase, characteristic values of wind speed are used, to which mathematical expressions are applied that predict its behavior. These expressions are dependent on the proximity of the terrain [70,71,72]. Furthermore, the system can be adapted during development by implementing a gauging control system based on CO₂ concentration. This system is especially recommended for the development of mass events in risk situations that require greater control of air quality, as occurred recently during the health crisis caused by SARS-CoV-2.

The results of the conducted analyses indicate that CO₂ exhibits behavior at ground level that is consistent with the dilution patterns of a heavy gas, whereas, at altitude, its behavior is more akin to that of a light gas.

In light of the aforementioned considerations, the analysis leads to the conclusion that the equation for determining the maximum occupancy density during mass activities at ground level is as follows:

$$\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l} \mathrm{o}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{p}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{y} \mathrm{p}\mathrm{e}\mathrm{r} \mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e} \mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}={\displaystyle \frac{30}{{\mathrm{Q}}_{\mathrm{r}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{d}}}}$$

(10)

From this expression, it has been determined that the maximum occupancy in outdoor semi-enclosures at ground level, to have air quality that meets Category IDA2 for interiors, is 2.36 persons per square meter (2.36 p/m²). Conversely, to prevent the transmission of SARS-CoV-2 through natural ventilation, the maximum occupancy is 1.98 persons per square meter (1.98 p/m²).

It can be reasonably assumed that the maximum density at a mass event is four people per square meter (4 p/m²) [68], given that the location is above five meters in height outdoors. Therefore, it can be concluded that SARS-CoV-2 transmission would not occur at leisure events.

It is also worth noting the potential for occupancy values to be calculated based on individual characteristics, such as height, weight, and heart rate, as these parameters are linked to the volume of carbon dioxide exhaled and, consequently, related to the presence of products of human metabolism called bioeffluents [2,36].