Optimizing Ventilation Systems in Barcelona Schools: An AHP-Based Assessment for Improved Indoor Air Quality and Comfort

Abstract

The success of educational institutions is fundamentally intertwined with the well-being and academic progress of their students. In this context, indoor air quality (IAQ) and thermal comfort play a critical role in creating conducive learning environments that support both health and academic performance. This work evaluates six ventilation systems and strategies for enhancing IAQ and thermal comfort, which prevail in educational buildings in the Spanish region of Catalonia. To do so, a multi-criteria analysis is performed based on the Analytic Hierarchy Process (AHP) method, considering economic, social, and environmental aspects. Ventilation systems are pairwise compared in terms of six criteria: initial and maintenance cost, classroom air quality, students’ thermal comfort in summer and winter, and energy consumption. Subsequently, weighted combinations of these criteria are established to rank the ventilation systems under five case scenarios. The results indicate that natural ventilation systems, particularly those with atriums and courtyards (N-AAC), offer a balanced solution, achieving satisfactory IAQ and thermal comfort while being more cost-effective and environmentally sustainable in certain contexts. The variation in the best solution across different scenarios demonstrates that the optimal choice is highly context-dependent, influenced by factors such as budget, climate, and infrastructure. This research provides a valuable foundation and methodology for decision-makers in educational institutions, supporting the selection of ventilation systems that maximize sustainability while enhancing students’ comfort and fostering learning environments.

1. Introduction

In the realm of education, the pursuit of optimal learning environments stands as an essential objective. The success of educational institutions is fundamentally intertwined with the well-being and academic progress of their students [1]. Among the multifaceted factors that contribute to fostering an environment conducive to learning [2], two foundational elements emerge as pivotal: indoor air quality (IAQ) [3] and thermal comfort [4].

Research indicates that CO₂ concentration functions as a practical gauge of indoor air quality (IAQ) acceptability, as well as the adequacy of air exchange and the infusion of fresh air into indoor spaces [5]. Standards provide thresholds of CO₂ concentration emitted by users breathing in an indoor space as an indicator of IAQ. CO₂ levels over 1000 ppm indicate an indoor air potential problem [6]. When this limit is overcome, air becomes stagnant [7]. Prolonged exposure to elevated concentrations may eventually engender a host of deleterious effects [8], including headaches, tachycardia and nausea [9], memory disturbances and lack of concentration [10], blurred vision, sweating, restlessness, vomiting or flushed skin [11], and obviously increases the risk of cross-infection of airborne viruses [12,13] and heightened absenteeism [10]. Moreover, empirical evidence attests to a clear and well-documented correlation between superior indoor air quality and enhanced learning outcomes, as elucidated in the study by [14] or [15].

In an average-size classroom of 25 students, concentrations above this limit of CO₂ are commonly reached during a class. Just in Spain, more than 8 million school-aged children spend approximately 1300 h a year—adding up to 21,000 h over the course of a normal compulsory 16-year school career—inside an average-size classroom like the aforementioned. The Reglamento de Instalaciones Térmicas en los Edificios (RITE) [16], published in 2007, mandates that newly constructed non-residential buildings include mechanical ventilation systems. However, most of the 28,816 Spanish schools are located in older buildings constructed before 2007. These buildings often lack mechanical ventilation or have systems in poor condition. Consequently, their most viable option to ensure adequate indoor air quality (IAQ) is to open doors and windows. This approach must be carefully managed to avoid generating strong airflows and compromising students’ comfort [17]. However, reality proves that, especially during cold seasons, occupants may not follow the recommendations of opening windows due to thermal discomfort, and, therefore, indoor air quality can be compromised [18,19,20,21].

On the other hand, if recommendations are followed, energy consumption rises to neutralize thermal discomfort. Such a dilemma complicates the task for teachers, who have the responsibility to manage when, how, and for how long to ventilate their classrooms based on nothing other than rather vague guidelines or personal perceptions of the occupants.

As an example of the problem, refs. [22,23] carried out an IAQ and thermal comfort experimental campaign in 32 classrooms of primary and secondary schools in Catalonia, Spain. Part of this campaign was focused in the same region of the present study, which corresponds to the Barcelona Metropolitan Area (coordinates 41°22′57″ N 2°10′37″ E). This coastal area has a population of 3.3 million people, a surface area of 636 km², and a Coastal Mediterranean climate with warm summers, moderately cold winters, and little rain. As a conclusion of this work, it was found that, on average, only 71% of the measured schools met the minimum requirement for indoor air quality (IAQ), as defined by the Indoor Air (IDA) 2 standard (<920 ppm) across all seasons—particularly, during spring, 82% of the time, during summer, 94%, and during winter, 51%. Additionally, all measured schools met the requirement for IAQ, as defined by the Indoor Air (IDA) 3 standard (<990 ppm) only 52% of the time. Regarding thermal comfort, the study revealed that, on average, only 74% of the measured schools met the minimum requirement (17–27 °C, 30–70%) throughout the year. In detail, during spring, 89% of the time, during summer, 27%, and during winter, 95%. Furthermore, all measured schools achieved the optimal thermal comfort requirement only 19% of the time. Finally, the results indicate that good conditions of thermal comfort and air quality were observed only during 7.5% of the overall study period.

Optimizing air quality and indoor environmental comfort within educational institutions stands as a critical determinant for the physical and cognitive well-being of both students and educators [23,24]. Thus, the imperative to enhance indoor air quality and comfort levels constitutes an overarching educational prerogative and emerges as an indispensable investment in the scholastic odyssey of students and the professional milieu of educators. Consequently, achieving proper IAQ and thermal comfort in classrooms through effective heating, ventilation, and air conditioning (HVAC) systems is paramount to creating an environment where students can focus on their studies and thrive academically [25,26,27]. While numerous studies in the literature address the impact of indoor air quality (IAQ) and thermal comfort on students’ performance, as well as data-driven and numerical models predicting CO₂ evolution or influencing factors, there is a notable gap in research offering practical tools to guide infrastructure managers in making informed ventilation system investments. The choice of a ventilation system is highly context-dependent, requiring a nuanced approach that considers the specific characteristics and constraints of each educational environment.

In this manuscript, we address this gap by proposing a robust and flexible methodology designed to navigate this complex decision-making process. Our approach equips educators, school administrators, and infrastructure managers with a valuable framework to assess and select ventilation systems tailored to their unique circumstances. By exploring critical facets of IAQ and thermal comfort and analyzing various ventilation strategies and systems, we provide actionable insights that ensure a conducive educational environment. This methodology not only prioritizes student well-being and academic achievement but also adapts to the specific operational and contextual needs of different educational institutions, facilitating informed and effective decision-making.

2. Methods

2.1. Ventilation Strategies

Research has demonstrated that well-ventilated classrooms enhance cognitive performance, information retention, and overall comfort among students. Adequate ventilation not only reduces the risk of respiratory infections but also contributes to a more alert and focused student body. Furthermore, by maintaining a thermally comfortable environment, ventilation strategies can help optimize the learning conditions, ensuring that students can engage more effectively in their studies. The careful design and implementation of ventilation strategies can mitigate indoor air pollutants, regulate temperature and humidity, and consequently enhance cognitive function, ultimately fostering a healthier and more productive educational experience.

Ventilation strategies in classrooms can be broadly categorized as natural, mechanical, or hybrid systems. Natural ventilation harnesses external air through windows, doors, or other openings, promoting air exchange and dilution of indoor contaminants. Mechanical ventilation relies on active systems to control airflow, offering precise regulation of environmental parameters. Hybrid approaches combine both natural and mechanical elements, capitalizing on the strengths of each to optimize IAQ. These strategies are essential for managing indoor pollutant levels, including carbon dioxide, particulate matter, and volatile organic compounds, thus preventing the buildup of contaminants that can impair cognitive function and compromise student well-being.

In the context of this investigation, six distinct ventilation configurations were examined within Barcelona educational institutes, representing prevalent systems in these environments. The depicted configurations are as follows: Figure 1a–d illustrates variations of natural ventilation, Figure 1e demonstrates a hybrid ventilation system, and Figure 1f portrays a centralized mechanical ventilation system.

Particularly, Figure 1a showcases single-sided natural ventilation (N-SSV), where only one side of the classrooms’ windows is opened, resulting in limited airflow circulation within the room. Figure 1b presents natural cross-ventilation (N-CRV) in the same classrooms, achieved by opening windows or doors on opposite sides of the room. This configuration promotes faster air recirculation compared to N-SSV. However, it is worth noting that, in this case, it is assumed that a portion of the incoming air originates from within the building, potentially containing contaminants and offering lower air quality compared to external air sources. Figure 1c,d illustrates natural ventilation configurations incorporating atria and courtyards (N-AAC), respectively. In both cases, airflow is established, traversing the classrooms from the external environment in multiple directions. For the purposes of this study, it is posited that the incoming air in N-AAC systems is cleaner and possesses a higher flow rate compared to that in N-CRV.

Figure 1e represents the hybrid ventilation system, which combines natural ventilation with mechanical recirculation (H-NMR). This hybrid approach augments natural ventilation by incorporating mechanical components, such as fans, to simulate the airflow patterns generated by an N-AAC system.

Lastly, Figure 1f depicts a centralized mechanical ventilation system (M-CVS). These systems typically offer precise control over air temperature, applicable for both summer and winter conditions, and often include air quality control measures like filtration. In this study, it is assumed that mechanical ventilation systems installed in educational institutions possess these features, including both supply and exhaust ventilation, and operate with all windows closed.

It is important to note that the assumptions made in this analysis are based on ventilation systems commonly used in educational buildings in Barcelona, where the study is focused. The characteristics of these buildings, such as local building codes, climatic conditions, and typical architectural designs, were considered in selecting the systems and methods used in the assessment. As such, the findings and conclusions are most directly applicable to this context, although the general principles may be adapted for use in other locations with similar conditions. Specific details may vary among individual installations, but the core assumptions are grounded in the common systems observed in the Barcelona context.

Although the diagrams presented in Figure 1 might be applicable to other public utility buildings, this study’s insights are specifically tailored to address the operational and functional priorities of educational institutions. Classrooms have unique ventilation requirements, stemming from their high occupancy density and prolonged exposure times, as well as the sensitivity of the primary occupants—students—to air quality. Consequently, any extrapolation of the presented findings to other building types, such as offices or other public spaces, would require adjustments to account for their distinct characteristics, usage patterns, and occupant demographics.

2.2. Analytic Hierarchy Process (AHP) Method

Among the different alternative methodologies [28] this examination of various ventilation systems has been conducted through the Analytic Hierarchy Process (AHP) method. The AHP, originally devised by Saaty [29], is a linear additive model that converts subjective assessments of relative importance into a set of overall scores that are, respectively, based on pairwise comparisons between criteria and between options. This method and derived ones have been successfully applied in evaluating technical ventilation systems in buildings and other infrastructure, such as office spaces [30], pharmaceutical cleanrooms [31], electronic cleanrooms [32], coal mines [33,34], LNG construction platforms [35], and tunnels [36]. The AHP process comprises five steps.

• Decomposition of the problem into evaluation criteria: To conduct an AHP analysis, the initial step involves breaking down the problem being analyzed into distinct study variables, which are commonly known as evaluation criteria. This decomposition can be achieved by organizing them into various categories or groups.
• Construction of the pairwise comparison matrix: To build the pairwise comparison matrix, the decision maker is asked to rate the importance of one particular criterion in relation to another in the context of the decision that is addressed. This involves conducting pairwise comparisons between each of the alternatives, assigning a score of relative importance to them. The scores used for each pairwise comparison are selected from a numerical or linguistic rating scale called the Saaty scale [29], ranging from 1 to 9. A rating of 1 signifies identical preference, while a rating of 9 indicates extremely preferred, with 5 being synonymous with strongly preferred. Further details are provided in Section 3.1.
• Checking the consistency of the pairwise comparison matrix: Typically, some inconsistencies may arise during the assessment of the comparison of each alternative (which may cause errors and uncertainty over logical results). The AHP incorporates an effective technique for checking the consistency of the evaluations made by the decision maker when building each of the pairwise comparison matrices involved in the process. In this sense, Saaty introduced the Consistency Ratio (CR) for the pairwise consistency matrix. If the CR exceeds 10%, it is recommended that the decision-maker revise the elicited preferences. The CR may be calculated using the Consistency Index (CI) and the Random Index (RI), according to Equation (1).

  $$CR={\displaystyle \frac{ConsistencyIndex}{RandomIndex}}={\displaystyle \frac{CI}{RI}}$$

  (1)
  Saaty proposed to compute the Consistency Index (CI) by means of the largest eigenvalue (λ_max) and the size (m) of the pairwise comparison matrix, according to Equation (2).

  $$IC={\displaystyle \frac{{\lambda }_{max}-n}{n-1}}$$

  (2)
  The Random Index, i.e., the Consistency Index when the entries of A are completely random. The values of RI for small problems (n ≤ 10) are shown in

  Table 1. Random Consistency Index (RI).

  Matrix Size n	1	2	3	4	5	6	7	8	9	10
  RI	0.00	0.00	0.58	0.9	1.12	1.24	1.32	1.41	1.45	1.51

  .
• Calculate the score of the variables: A number of methods can be used to estimate the set of scores that are most consistent with the relativities expressed in the pairwise comparison matrix. Saaty’s basic method of identifying the value of the weights depends on relatively advanced ideas in matrix algebra and calculates the weights as the elements in the eigenvector associated with the maximum eigenvalue of the matrix. A more straightforward alternative, which also has some theoretical grounding, is to (1) calculate the geometric mean of each row in the matrix, (2) total the geometric means, and (3) normalize each of the geometric means by dividing each one by the total calculated in the preceding step. The weights estimated by the two different methods (taken to a number of significant figures for greater accuracy) are not identical, but it is common for them to be very close.
• Assignation of a relative weight to each evaluation criterion and prioritization definition: The final step involves applying the relative weight of each criterion (chosen by decision-makers) to its corresponding vector and then establishing the priority order of the different alternatives. These steps help in making informed decisions by quantifying the importance of criteria and determining the preferred options within a given set of alternatives. Different approaches may be used to conceal the interests of different stakeholders (the director and the teachers of the school, the family representatives, infrastructure managers, or even public administration) willing to participate in the decision and, thus, assign weights [37,38].

2.3. Evaluation Criteria

The comparative evaluation of ventilation systems expounded in this manuscript is rooted in the holistic theme of sustainable development, intertwining its vital aspects with IAQ and its consequences on student performance. In accordance with this paradigm, the AHP methodology has been harnessed, and sustainability has been conceptualized through the prism of its three fundamental pillars: economic viability, social well-being, and environmental harmony. To operationalize this approach, a comprehensive set of six indicators has been meticulously selected to meet the essential attribute criteria outlined by Keeney and Raifa [39] for a decision-making system: they must be complete, operational, decomposable, non-redundant, minimal, discriminatory, and comprehensive.

Specifically, within the economic dimension, two pivotal indicators demand consideration: the (i) initial cost and the (ii) maintenance cost. The initial cost embodies the financial outlay necessitated for the inception and implementation of a ventilation system and assumes a paramount role in the selection process of ventilation technologies. Conversely, the maintenance cost encapsulates the resources indispensable for the continual upkeep of ventilation systems, ensuring their sustained operational integrity throughout their lifecycle.

Within the social domain, a triad of indicators assumes significance. First and foremost, (iii) indoor air quality within educational spaces emerges as a pivotal criterion for delineating the choice among competing ventilation methodologies. Different systems may exhibit divergent filtration capabilities, thereby directly impacting the air quality within classrooms. Concurrently, thermal comfort assumes a salient role, being a critical determinant influenced by the ventilation modality. The latter has a direct bearing on factors such as temperature, humidity, and air velocity within classrooms. Given the substantial disparities in thermal comfort requirements between summer and winter, a bifurcated evaluation approach has been adopted, leading to the creation of distinct indicators for (iv) summer and (v) winter thermal comfort.

Lastly, the environmental aspects are taken into account through the inherent (vi) energy consumption of each ventilation system, which is closely tied to carbon emissions. Indeed, we view energy consumption as a robust proxy for evaluating carbon emissions, as these two indicators are intrinsically linked.

Furthermore, energy efficiency is also directly related to the operational costs of the system, so these are indirectly taken into account when assessing the environmental impact. This multifaceted framework provides a comprehensive and robust foundation for the thoughtful selection of ventilation systems in educational buildings, aligning with the principles of sustainable development and environmental stewardship.

2.4. Weighted Analysis

Based on the results obtained from the multi-criteria study presented in the previous section, a weighted analysis of results is conducted in five different ways (five case studies) for the indicators used in pairwise comparisons.

Table 2. Case Scenarios studied.

	Economic	Social	Environmental
Scenario 1	33%	33%	33%
Scenario 2	20%	60%	20%
Scenario 3	15%	50%	35%
Scenario 4	20%	40%	40%
Scenario 5	40%	40%	20%

presents the five combinations of weights determined for the requirements used in this study (economic, social, and environmental). Within the economic aspects, 80% representativeness has been assigned to the initial cost in all cases, with the remaining 20% allocated to maintenance costs. For the social requirement, 50% representativeness has been assigned to air quality, while the remaining 50% has been distributed evenly between thermal comfort in summer and winter. This distribution implies that each of these indicators has a 25% representativeness of the social requirement. The sole criterion for environmental aspects is energy consumption, and therefore, it represents 100% of this category.

3. Results and Discussion

3.1. Results of the AHP

This section presents the pairwise comparative evaluation of the five ventilation operating systems. To do so, the AHP matrices developed using Saaty’s method for each of the considered indicators are displayed, i.e., initial cost, maintenance cost, air quality, summer thermal comfort, winter thermal comfort, and energy consumption.

In order to obtain these scoring AHP matrices, the authors conducted a literature review to qualitatively assess each ventilation system against the six evaluation criteria. The findings of this information search and qualitative assessment are summarized in

Table 3. Qualitative assessment of the ventilation systems.

Ventilation System	Investment Cost	Maintenance Cost	Indoor Air Quality (IAQ)	Thermal Comfort (Summer)	Thermal Comfort (Winter)	Energy Consumption
Single-Sided Natural Ventilation (N-SSV)	Negligible—No extra installation is required (*)	Negligible—No mechanical parts need to be maintained [40].	Poor—Dependent on outdoor air quality [41]; very limited air renovation due to low wind velocities [42].	Poor—Not effective cooling due to low wind velocities [21,43].	Moderate—Reduce indoor overheating due to excessive heating from the radiators [43] and low wind velocities [42] allow to control the air exchange rate.	Negligible—No electricity is consumed [40].
Natural Cross-Ventilation (N-CRV)	Negligible—No extra installation is required (*)	Negligible—No mechanical parts need to be maintained [40].	Good—Dependent on outdoor air quality [41]; Larger openings generally lead to higher airflow rates [44].	Moderate—Better than N-SSV but may not meet thermal comfort standards during heatwaves [45].	Poor—High airflow rates [44] can significantly hinder effective control of indoor overheating from the radiators.	Negligible—No electricity is consumed [40].
Natural Ventilation with Atria and Courtyards (N-AAC)	Negligible—No extra installation is required (*)	Negligible—No mechanical parts need to be maintained [40].	Very good—Dependent on outdoor air quality [41]; a higher ratio between courtyard/atria width and building height improves ventilation efficiency [46].	Very good—Courtyard and atria enhance airflow, but depends on the geometrical design [47].	Poor—High airflow rates [46] can significantly hinder effective control of indoor overheating from the radiators.	Negligible—No electricity is consumed [40].
Hybrid Ventilation with Mechanical Recirculation (H-NMR)	Moderate—Investing in ceiling fans requires minimal upfront costs [48].	Very Small—New high-efficiency ceiling fans use maintenance-free motors [49].	Very Good—Dependent on outdoor air quality [41]; air exchange can be optimized with adequate fans [50].	Very good—Provides reasonable comfort levels under optimal fan rotation speed [50].	Poor—High airflow rates [50] can significantly hinder effective control of indoor overheating from the radiators.	Very low- Ceiling fans are energy-efficient devices [51].
Centralized Mechanical Ventilation System (M-CVS)	High—Significantly higher initial costs compared to hybrid systems [52].	High—HVAC system maintenance accounts for over 65% of facility management costs [53].	Excellent—Well-maintained HVAC systems help reduce microbiological contamination and improve indoor air quality [54].	Excellent—HVAC technologies provide very efficient solutions for thermal comfort [55,56].	Excellent—HVAC technologies provide very efficient solutions for thermal comfort [55,56].	High—HVAC systems consume a high amount of energy compared to ceiling fans [51].

(*) The authors assumed that investment cost is 0 since no extra installation is required.

. This qualitative assessment formed the basis for the pairwise comparison analysis, where Saaty’s fundamental scale was applied to assign numerical values reflecting the relative importance of each system according to the criteria [29]. These values range from 1 to 9 as follows:

• Equal importance: Two systems contribute equally to the objective;
• Weak;
• Moderate importance: Experience and judgment slightly favor one system over another;
• Moderate plus;
• Strong importance: Experience and judgment strongly favor one system over another;
• Strong plus;
• Very strong or demonstrated importance: A system is favored very strongly over another; its dominance is demonstrated in practice;
• Very, very strong;
• Extreme importance: The evidence favoring one system over another is of the highest possible order of affirmation.

It should be noted that the pairwise comparison and, consequently, the evaluation have been carried out with the assumption that each ventilation operating system operates continuously throughout the school year and cannot be combined at any point with any other systems. This is a needed simplification for executing the evaluation, as a classroom may have different operating systems that can be used depending on what is most beneficial for those inside. For example, a single classroom could operate with a single-side ventilation system (N-VUL) or cross-ventilation (N-CRV), depending on which elements are open and closed, even though this was not explicitly considered. This simplification of reality allows for an initial approximation, which, logically, necessitates a cautious and critically discerning consideration of the results obtained.

3.1.1. Initial Investment Cost

In the framework of sustainability assessment, the first factor to evaluate within the economic pillar is the initial cost (

Table 4. AHP Matrix for Initial Investment Cost.

Initial Investment Cost
	N-SSV	N-CRV	N-AAC	H-NMR	M-CVS	Results
N-SSV	1	1	1	3	9	0.290
N-CRV	1	1	1	3	9	0.290
N-AAC	1	1	1	3	9	0.290
H-NMR	1/3	1/3	1/3	1	3	0.097
M-CVS	1/9	1/9	1/9	1/3	1	0.032

). It has been assumed that the cost is the same for all three natural ventilation operating systems, resulting in identical scores of 1 when comparing them. This assumption makes sense when considering that all educational classrooms have doors and windows, and therefore, the cost of single-side ventilation (N-VUL) or cross-ventilation (N-CRV) is the same. Furthermore, the existence of atriums and courtyards (N-AAC) could not be identified as a parameter systematically increasing or decreasing construction costs in the studied buildings, as it depends on each particular case. Consequently, it is reasonable to assume that, in overall terms, the initial cost of this alternative is similar to that of N-VUL and N-CRV.

Moreover, centralized ventilation systems (M-CVS) and natural ventilation with mechanical recirculation (H-NMR) are more expensive to install than natural ventilation systems. In both cases, additional investment is required to add devices to the building that complement its original architectural elements, which, in principle, would allow for the application of natural ventilation through the opening and closing of doors, windows, and other openings. The mechanical ventilation system M-CVS requires the highest initial investment, resulting in a relative score of 9 for natural systems in all cases. As for the hybrid system H-NMR, its cost exclusively includes mechanical elements installed punctually in classrooms and does not require a larger infrastructure. Therefore, its relative score in comparison to the latter is 3 and, in relation to natural ventilation systems, is 1/3.

3.1.2. Maintenance Cost

The second factor to consider within the framework of sustainability assessment for the economic pillar is maintenance costs (

Table 5. AHP Matrix for the Maintenance Cost.

Maintenance Cost of Ventilation Systems
	N-SSV	N-CRV	N-AAC	H-NMR	M-CVS	Results
N-SSV	1	1	1	2	9	0.278
N-CRV	1	1	1	2	9	0.278
N-AAC	1	1	1	2	9	0.278
H-NMR	1/2	1/2	1/2	1	4	0.136
M-CVS	1/9	1/9	1/9	1/4	1	0.032

). For natural ventilation operating systems, the economic investment required is almost negligible. This is because, unless major renovations are undertaken, the doors and windows of educational buildings typically withstand their entire useful life without significant interventions beyond hinge lubrication or knob and lock adjustments. Additionally, for the same reasons as in the case of initial costs, the score obtained when comparing these systems among themselves is also 1 in all cases.

The expenditure associated with the maintenance of the hybrid system can be expressed as the sum of the allocations directed towards the upkeep of doors and windows, augmented by the resources allocated to mechanical devices. Consequently, this maintenance cost exceeds that required for natural components. Nonetheless, it is imperative to note that maintenance for devices such as fans remains exceedingly minimal. Consequently, when examined collectively, the overall maintenance cost of the hybrid system is also relatively low. Therefore, the comparative evaluation of natural systems in relation to this hybrid solution merits a rating of only 2 points.

Conversely, the centralized mechanical system once again occupies the opposing end of the spectrum due to its considerably more substantial maintenance requirements. Consequently, when juxtaposed with natural and hybrid systems, its relative ratings are 1/9 and 1/4, respectively.

3.1.3. Indoor Air Quality

Turning to the social component of the sustainability framework, the first factor to evaluate is indoor air quality within classrooms (

Table 6. AHP Matrix for Indoor Air Quality.

Classroom Air Quality
	N-SSV	N-CRV	N-AAC	H-NMR	M-CVS	Results
N-SSV	1	1/3	1/3	1/3	1/9	0.053
N-CRV	3	1	1	1	1/3	0.158
N-AAC	3	1	1	1	1/3	0.158
H-NMR	3	1	1	1	1/3	0.158
M-CVS	9	3	3	3	1	0.474

). The findings reveal that, on a global scale, systems with higher initial and maintenance costs tend to provide superior indoor air quality. This outcome is logically consistent, as allocating financial resources to install ventilation mechanisms that replace classroom air with more contaminated air would be unjustifiable.

The centralized mechanical ventilation system, equipped with filters, offers the highest air quality. Conversely, the natural ventilation system operating from a single side allows for external air exchange, assuming the external air is cleaner than that within the classroom but with lower airflow. Consequently, the mechanical system scores 9 in comparison to the latter.

Cross-ventilation via natural means obtains a score of 3 when compared to single-side ventilation, as the airflow resulting from openings in more than one classroom wall is notably higher than that generated by a single-side approach. Furthermore, when atriums or courtyards exist, the same score is obtained since, in winter conditions, the classroom doors and windows are closed, so IAQ is not improved due to higher airflow. Finally, the hybrid system aims to mimic external air exchange patterns akin to the aforementioned natural system, thereby earning it a score of 6 when compared to single-side natural ventilation.

3.1.4. Thermal Comfort

The second factor to consider within the social component of the sustainability framework is thermal comfort in classrooms. In this case, two scenarios have been distinguished. The first scenario pertains to a summer situation (

Table 7. AHP Matrix for Thermal Comfort in Classrooms in Summer.

Thermal Comfort in Classrooms in Summer
	N-SSV	N-CRV	N-AAC	H-NMR	M-CVS	Results
N-SSV	1	1/3	1/6	1/6	1/9	0.039
N-CRV	3	1	1	1/2	1/3	0.116
N-AAC	6	1	1	1/2	1/3	0.179
H-NMR	6	2	2	1	1/2	0.248
M-CVS	9	3	3	2	1	0.418

), in which the objective is to maximize air circulation using natural and hybrid systems to mitigate the sensation of heat within the classroom. The second scenario involves a winter situation (

Table 8. AHP Matrix for Thermal Comfort in Classrooms in Winter.

Thermal Comfort in Classrooms in Winter
	N-SSV	N-CRV	N-AAC	H-NMR	M-CVS	Results
N-SSV	1	3	3	3	1/3	0.200
N-CRV	1/3	1	1	1	1/9	0.067
N-AAC	1/3	1	1	1	1/9	0.067
H-NMR	1/3	1	1	1	1/9	0.067
M-CVS	3	9	9	9	1	0.600

), where the opposite objective is pursued, aiming to minimize the exchange of air with the external environment.

In the summer scenario, centralized mechanical ventilation once again scores the highest, as it allows for precise control of air temperature, while natural ventilation is rated the lowest since it minimizes outdoor air circulation. Consequently, the score for the former is 1, and the latter is rated 9 in comparison.

In the intermediate range, we find the other two natural ventilation systems and the hybrid system. As previously mentioned in the context of air quality, cross-ventilation generates a higher airflow than single-sided natural ventilation. Likewise, natural ventilation with atriums or courtyards and the hybrid system yield an even higher airflow, which is comparable among them. Therefore, when compared to single-sided natural ventilation, the relative scores are 3 for cross-ventilation and 6 for atriums/courtyards and the hybrid system.

In the winter season, the centralized mechanical ventilation system receives the highest rating due to its notable capacity for air temperature control and its capacity to function as a heating system. Conversely, the lowest ratings are assigned to natural cross-ventilation systems, atrium and courtyard-based systems, and the hybrid system in this particular scenario. This discrepancy arises from the fact that, in these three cases, the classroom would almost instantaneously exchange its entire volume of air with the exterior environment. Consequently, the relative rating for the mechanical system in comparison to these three systems is 9.

Natural ventilation, on the other hand, falls into an intermediate scenario, albeit closer to other natural and hybrid systems than to the mechanical system. In this context, it is important to note that the temperature of the exchanged air cannot be regulated, although its flow rate would be lower than that of cross-ventilation and the airflow generated when atriums, courtyards, or mechanical recirculation with fans are in use. Thus, its rating relative to these systems is 3, but when compared to centralized mechanical ventilation, it is rated at 1/3.

3.1.5. Energy Consumption

Finally, the last factor considered serves as a proxy for the environmental impacts within the sustainability framework: energy consumption. In the context of energy efficiency criteria (

Table 9. AHP Matrix for Energy Consumption.

Energy Consumption of Ventilation Systems
	N-SSV	N-CRV	N-AAC	H-NMR	M-CVS	Results
N-SSV	1	1	1	2	9	0.279
N-CRV	1	1	1	2	9	0.279
N-AAC	1	1	1	2	9	0.279
H-NMR	1/2	1/2	1/2	1	3	0.130
M-CVS	1/9	1/9	1/9	1/3	1	0.034

), the mechanical ventilation system with centralized ventilation exhibits the highest energy consumption. This is attributed to the need for regulating air properties such as temperature and humidity, in addition to the requirement for air circulation throughout all exit points within the building. Furthermore, these systems commonly incorporate automatic control systems that contribute to energy consumption.

Conversely, natural ventilation systems are situated at the opposite end of the spectrum, characterized by negligible energy consumption, except in cases where electrical components or similar devices are employed for the operation of doors and windows, which is not prevalent in the majority of the analyzed facilities. As for hybrid systems, their energy consumption is moderately higher, as it necessitates the operation of fans or equivalent mechanisms.

Taking the aforementioned factors into consideration, the relative energy efficiency scores among all-natural systems are denoted as 1. In comparison, the scores for hybrid and mechanical solutions are 2 and 9, respectively, when juxtaposed with the natural ventilation systems.

3.2. Discussion of the AHP Results

A summary of the estimated set of scores that are most consistent with the relativities expressed in the pairwise comparison matrixes for each evaluation criterion is presented in

Table 10. Summary of the AHP matrixes for the 6 criteria considered.

	Initial Investment Cost	Maintenance Cost	Classroom Air Quality	Thermal Comfort in Summer	Thermal Comfort in Winter	Energy Consumption
N-SSV	0.29	0.28	0.05	0.04	0.20	0.28
N-CRV	0.29	0.28	0.16	0.12	0.07	0.28
N-AAC	0.29	0.28	0.16	0.18	0.07	0.28
H-NMR	0.10	0.14	0.16	0.25	0.07	0.13
M-CVS	0.03	0.03	0.47	0.42	0.60	0.03

. Finally,

Table 11. Consistency Index of AHP Matrices.

	Initial Investment Cost	Maintenance Cost	Classroom Air Quality	Thermal Comfort in Summer	Thermal Comfort in Winter	Energy Consumption
Consistency	0.000	0.000	0.000	0.026	0.000	0.006

presents the pairwise comparison Consistency Index computed for each indicator. As evident from the results, in 5 out of the 6 indicators, it can be deduced that the consistency is high, as the index approaches zero. In the context of summer thermal comfort, the Consistency Index remains favorable, albeit it reaches a value of 0.026. It is noteworthy that for matrices of size 5 × 5 or larger, values up to 0.1 are acceptable in terms of consistency.

3.3. Results and Discussion of the Weighted Analysis

Table 12. Assessment of each ventilation system.

	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5
N-SSV	0.218	0.165	0.184	0.203	0.205
N-CRV	0.230	0.188	0.203	0.219	0.221
N-AAC	0.236	0.198	0.211	0.225	0.227
H-NMR	0.131	0.141	0.140	0.136	0.131
M-CVS	0.186	0.308	0.262	0.217	0.216

displays the scores achieved by the five ventilation operating systems in each of the analyzed scenarios of the weighted analysis. In addition, Figure 2 graphically illustrates the same results in a radar chart format, presenting them collectively and succinctly for optimal visual comprehension.

For Case Scenario 1, wherein economic, social, and environmental aspects carry equal weight, the system yielding the most favorable outcomes is the natural ventilation system with atriums and courtyards (N-AAC). This phenomenon can be elucidated by the fact that, in terms of initial costs, maintenance expenditures, and energy consumption (constituting 66% of the overall score), natural systems exhibit superior performance. Furthermore, with regard to air quality and thermal comfort during the summer (comprising 25% of the overall assessment), this system is only equaled or surpassed by the mechanical and hybrid systems, respectively.

In Case Scenario 2, social criteria clearly exert the most significant influence, constituting 60% of the overall score. Meanwhile, economic and environmental aspects equally share the remaining 40%. Consequently, the mechanically operated central ventilation system (M-CVS) emerges as the highest-rated option, as it attains superior scores in air quality and thermal comfort during both summer and winter. In other words, when the significance of economic expenditure and energy consumption is minimal, the ideal choice is to install a mechanical system that provides filtered and temperature-controlled air to the classrooms.

In Case Scenario 3, social factors also predominate, contributing 50% to the total score, albeit with environmental aspects carrying more weight than economic ones, with 35% and 15%, respectively. Once again, the mechanical system garners the highest rating, excelling in all social criteria, though closely followed by the natural system with atriums and courtyards (N-AAC).

Case Scenario 4 represents a scenario in which social and environmental considerations hold twice the weight of economic ones (40%, 40%, and 20%, respectively). This leads to the natural system with atriums and courtyards being the top-rated choice, while the mechanical system ranks third due to its inability to compensate for its weakest performance in environmental aspects among the five options.

Case Scenario 5 introduces the concept of economic and social aspects being twice as important as environmental considerations (weights of 40%, 40%, and 20%, respectively). This results in outcomes very similar to those of Case 4. In this scenario, the natural system with atriums and courtyards again emerges as the highest-rated option, with the centralized mechanical ventilation system in third place. This can be attributed to the fact that, in this case, M-CVS scores the lowest in both economic aspects of initial cost and maintenance. However, N-AAC stands out among the four alternatives because, on the one hand, along with the other two natural systems, it achieves the highest scores in economic and environmental aspects, and on the other hand, it obtains intermediate scores in thermal comfort during summer, consistently surpassing those of N-VUL and N-CRV.

It is noteworthy to mention the sensitivity of the results to changes in weightings. This indicates that the choice of strategy may vary depending on the criteria and preferences of decision-makers. Thus, it is not possible to universally designate an optimal strategy.

Furthermore, it is important to explain the results obtained by the hybrid system based on natural ventilation with mechanical recirculation (H-NMR), as they are not as favorable as one might expect. This is attributed to the simplification hypothesis presented in the previous section, which penalizes hybrid operations. However, the results do not imply that this operation should be dismissed. On the contrary, in certain circumstances, such as when the goal is to enhance summer thermal comfort with a relatively low investment, H-NMR represents an optimal solution, as indicated by the second indicator of the social requirement. Additionally, in a conceptual framework where ventilation operations can be combined and continuous operation is not necessary, H-NMR could significantly improve the outcomes. For instance, in a winter context, mechanical recirculation could be halted, leading to a more favorable assessment of thermal comfort by solely using N-VUL.

4. Conclusions

This study focuses on evaluating ventilation systems in educational buildings, combining sustainability and student well-being to provide a more comprehensive understanding of how different ventilation strategies are selected. To achieve this, the Analytic Hierarchy Process (AHP) was used, as it offers a clear and structured approach to comparing and assessing various ventilation systems based on multiple criteria. It is important to note that while this analysis is based on general knowledge of ventilation systems in educational settings, the study specifically targets buildings in Barcelona. Although the results are tailored to Barcelona’s context, the principles and methods used can be adapted to other regions with similar conditions.

In this comprehensive evaluation of ventilation systems within educational settings, we have amalgamated the realms of sustainable development and the well-being of students to illuminate a nuanced perspective on the selection of ventilation methodologies. The application of the Analytic Hierarchy Process (AHP) methodology has provided us with a structured framework for assessing and comparing various ventilation systems across multiple criteria.

Our findings underscore the intricate interplay between economic, social, and environmental factors when evaluating ventilation options. The choice of ventilation system is not a one-size-fits-all decision but rather a complex calculus that demands careful consideration of multiple dimensions. In this regard, we have noted that natural ventilation systems, particularly those with atriums and courtyards (N-AAC), offer a compelling balance between economic efficiency, social comfort, and environmental sustainability in certain contexts.

Moreover, the significance of these findings extends beyond the realm of academic discourse. Educational institutions play a pivotal role in shaping the future of societies by nurturing young minds. The selection of an appropriate ventilation system goes beyond mere infrastructure; it affects the physical and cognitive well-being of students. Hence, our study underscores the importance of integrating sustainability principles into educational facilities, fostering a conducive environment for both learning and sustainable living.

It is important to acknowledge the inherent limitations of our study, including simplifications in the assumed operating conditions. Furthermore, the weightings assigned to different criteria are contingent on the specific context and preferences of decision-makers. Therefore, there is no universally optimal ventilation system, and each case should be evaluated with due consideration to its unique circumstances.

In conclusion, this research bridges the gap between sustainability and educational outcomes, providing a valuable foundation for decision-makers in educational institutions as they navigate the challenging task of selecting ventilation systems. As we move forward, it is imperative that our educational facilities prioritize the well-being of students, environmental stewardship, and economic efficiency in tandem, ensuring a holistic and sustainable learning environment for generations to come.