key: cord-0974280-ckn9peej
authors: Zhang, Sheng; Ai, Zhengtao; Lin, Zhang
title: Occupancy-aided ventilation for both airborne infection risk control and work productivity
date: 2020-12-05
journal: Build Environ
DOI: 10.1016/j.buildenv.2020.107506
sha: 5d4f528f382abd23573feaece660ee58003fa0c5
doc_id: 974280
cord_uid: ckn9peej

Reducing airborne infectious risk is crucial for controlling infectious respiratory diseases (e.g., COVID-19). The airborne transmissibility of COVID-19 is high so that the common ventilation rate may be insufficient to dilute the airborne pathogens, particularly in public buildings with a relatively large occupancy density. Reducing occupancy can reduce the pathogen load thereby reducing airborne infection risk. However, reduced occupancy deteriorates work productivity due to the lost hours of work. This study proposes an occupancy-aided ventilation strategy for constraining the airborne infection risk and minimizing the loss of work productivity. Firstly, two mechanisms of occupancy schedule (alternative changeovers between normal occupancy and reduced occupancy) for reducing the airborne infection risk and loss of work productivity are revealed based on analyzing features of the indoor concentration profile of exhaled aerosols. Secondly, optimization of the occupancy schedule is developed to maximize the total time length of normal occupancy for the minimum loss in work productivity while satisfying the constraint on airborne infection risk (e.g., with the reproduction number less than one). The airborne infection risk is evaluated with the rebreathed fraction model. Case studies on COVID-19 in a classroom demonstrate that the proposed occupancy-aided ventilation is effective with an earning ratio of 1.67 (the ratio of the improvement in health outcome to the loss in work productivity) and is robust to the variable occupancy loads and occupancy flexibilities.

work productivity due to the lost work hours from the workers who would otherwise 1 have fully occupied the room and worked for the entire period of each shift. Thus, it 2 requires a new strategy to effectively combine reducing occupancy with ventilation, 3 which reasonably balances the reduction in airborne infection risk and the loss in 4 work productivity, particularly for public buildings. 5

This study proposes an occupancy-aided ventilation strategy for the desired airborne 6 infection risk control with minimum work productivity loss. Two mechanisms of 7 occupancy schedule of the occupancy-aided ventilation are revealed and the 8 optimization of the occupancy schedule is developed (Section 2). Case studies for 9 airborne infection control of COVID-19 in a classroom are conducted to demonstrate 10 the effectiveness of the proposed occupancy-aided ventilation, and application issues 11 and robustness of the proposed occupancy-aided ventilation are further discussed 12 (Sections 3 and 4). 13

The general process of the occupancy-aided ventilation proposed is introduced first, 15 from which it can be seen that the occupancy schedule is the core of the 16 occupancy-aided ventilation (Section 2.1). Then, mechanisms of scheduling the 17 occupancy are revealed for good overall performance regarding controlling the 18 airborne infection risk and reducing the loss in work productivity (Section 2.2). 19

Furthermore, an optimization of the occupancy schedule is developed based on the 20 genetic algorithm (an optimization algorithm) to maximize the work productivity 21 while satisfying the constraint on the airborne infection risk control (Section 2.3). 22

The occupancy-aided ventilation operates the ventilation system at the maximal 24 ventilation rate with reduced occupancy. Given that the maximal ventilation rate is 25 insufficient to dilute and remove indoor exhaled aerosols for airborne infection risk 26 control [15] , the occupancy is reduced, as a supplementary measure, to reduce the 27 indoor exhaled aerosols. The proposed occupancy-aided ventilation serves normal and 28 reduced occupancies. The indoor concentration of exhaled aerosols increases and 1 decreases during the normal occupancy and reduced occupancy respectively (Figures 2 1(a) and 1(b)). The entire ventilation process (e.g., determined by office hours or 3 school hours) includes several changeovers between the normal and reduced 4 occupancies. Thus, with the occupancy-aided ventilation, the ventilation system 5 operates at its maximal capacity, and the occupancy alternatively shifts between 6 reduced and normal occupancies. The ventilation system can be natural ventilation or 7 mechanical ventilation. For public buildings, mechanical ventilation may be more 8 common. The changeover is controlled by the upper and lower limits of indoor 9 exhaled aerosol concentration. When the indoor exhaled aerosol concentration reaches 10 the upper limit, the normal occupancy is changed to the reduced occupancy. The 11 corresponding period is defined as the unit period of normal occupancy (UPNO) 12 ( Figure 1(c) ). When the indoor exhaled aerosol concentration reduces to the lower 13 limit, the reduced occupancy is changed to the normal occupancy. The corresponding 14 period is defined as the unit period of reduced occupancy (UPRO) (Figure 1(c) ). 15

However, using the upper and lower limits of indoor concentration of exhaled 16 aerosols to schedule the occupancy has two disadvantages. First, it could be costly to 17 monitor the indoor concentration of exhaled aerosols accurately. Second, the period of 18 normal occupancy or reduced occupancy could be variable, which might cause 19 inconvenience to the work arrangement. For example, the starting-up stage of the 20 entire ventilation process has normal occupancy, and its period could be longer than 21 that of normal occupancy in the occupancy cycle, because the initial indoor exhaled 22 aerosol concentration of the starting-up stage could be lower than the lower limit of 23 indoor exhaled aerosol concentration (Figure 1(c) ). To address these disadvantages, 24 this study firstly calculates the unit periods of normal occupancy and reduced 25 occupancy in the occupancy cycle from the upper and lower limits of indoor exhaled 26 aerosol concentration, and then determines the occupancy schedule by the two unit 27 periods. That is that the occupancy schedule consists of the unit period of normal 28 occupancy and the unit period of reduced occupancy alternatively until the end of the 29 entire ventilation process. that the unit period of normal occupancy should not be too long (i.e., the upper limit 2 of indoor exhaled aerosol concentration should not be too high). Otherwise, the 3 occupants would stay in an environment with a high concentration of exhaled aerosols 4 for a long time. However, the accumulative period of normal occupancy should be 5 sufficiently long for work productivity. The accumulative period of normal occupancy 6 refers to the time length of normal occupancy in the entire occupancy schedule, which 7 is determined by the unit period and number of normal occupancy. Thus, the 8 accumulative period of normal occupancy should be divided into as many units of 9 normal occupancy as possible. This indicates that a smaller unit period of normal 10 occupancy is preferred for airborne infection risk control. 11

On the other hand, Figure 1 Moreover, the ending stage should be effectively utilized for work productivity. As 27 shown in Figure 1 (c), the entire ventilation process can end at t e1 when the indoor 28 exhaled aerosol concentration is low due to the reduced occupancy. The low indoor 29 exhaled aerosol concentration at the ending point is a waste because all occupants are 30 supposed to leave the shared space when the entire ventilation process ends (i.e., the working period is over). This indicates that the ending stage has not been effectively 1 utilized for work productivity. The entire ventilation process also may end at t e2 when 2 the indoor exhaled aerosol concentration is high (close to the upper limit of indoor 3 concentration of exhaled aerosols) due to the normal occupancy. The high indoor 4 exhaled aerosol concentration at the ending point indicates that the ending stage has 5 been effectively utilized for work productivity. Thus, the unit periods of normal and 6 reduced occupancies should be co-determined to make the entire ventilation process 7 end close to the upper limit of indoor exhaled aerosol concentration. 8

From the above explanations, two mechanisms of scheduling normal occupancy and 9 reduced occupancy can be summarized. First, a smaller unit period of normal 10 occupancy and a smaller unit period of reduced occupancy are preferred for airborne 11 infection risk control. Second, the unit periods of normal and reduced occupancies 12 should be co-determined to ensure that the entire ventilation process ends close to the 13 upper limit of indoor exhaled aerosol concentration for work productivity. It should be 14 noted that a shorter unit period of normal occupancy also indicates more disturbance 15 to work. Thus, the unit period of normal occupancy should be limited by the work 16 nature, which can be predefined by users (e.g., employers or managers). The unit 17 period of reduced occupancy should not be too short because it takes time for 18 occupants to leave and come back to the shared space. 19

The airborne infection risk in this study is evaluated by the rebreathed fraction. The 21 rebreathed fraction is defined as the proportion of the air exhaled by others in the 22 inhaled air, which equals the ratio of the volume of exhaled air by all occupants in the 23 room to the room volume (Equation 1) [18] . The smaller the rebreathed fraction, the 24 lower the airborne infection risk [19] . According to the mass conservation law, the 25 CO 2 exhaled into the room equals the CO 2 increase in the room (Equation 2) [18] . 26

Based on Equations 1 and 2, the rebreathed fraction is calculated as the ratio of the 27 CO 2 concentration difference in indoor air and outdoor air to the CO 2 concentration in 28 the exhaled air (Equation 3) [18] . The CO 2 concentrations in the outdoor air and 29 exhaled air are relatively stable [20, 21] . Thus, the indoor CO 2 concentration is the core of the calculation of the rebreathed fraction. The indoor CO 2 concentration is 1 calculated by Equation 4 according to the mass conservation law for well-mixed 2 conditions, which is mainly determined by the CO 2 generation rate and the ventilation 3 rate [19] . The ventilation rate is determined such that the maximal indoor CO 2 4 concentration for the designed occupancy capacity should not exceed the value 5 stipulated by indoor air quality standards, e.g., 800 ppm above the outdoor CO 2 6 concentration for air quality of Category II according to ISO 17772 [22] . The CO 2 7 generation rate of a typical person is calculated by Equation 5 [23] . Thus, the 8 occupancy schedule determines the CO 2 generation rate, thereby determining the 9 rebreathed fraction. 10

Where f is the rebreathed fraction; V is the room volume (m 3 ); V b is the volume of 11 exhaled air into the room (m 3 ), which is the net exhaled air into the room while part of 12 the exhaled air is removed to outdoors by ventilation; C in , C o , and C a are the CO 2 13 concentrations in indoor air, outdoor air, and exhaled air respectively (ppm); is the 14 indoor CO 2 generation rate by all occupants (ml/s); Q is the ventilation rate (m 3 /s); ∆t 15 is the time interval (s) and i is the i th time interval;

is the CO 2 generation rate of 16 a typical person (ml/s); e is the correction factor, which is 0.85 and 0.75 for Chinese 17 males and females respectively; RQ is the molar ratio of the exhaled CO 2 to the 18 inhaled O 2 , which is 0.83 for a typical adult at light/sedentary activities; H is the 19 height (m); M is the metabolic rate (W/m 2 ); W is the mass (kg). 20

In the proposed optimization, an optimization algorithm is used to search the trials of 21 upper and lower limits of indoor exhaled aerosol concentration. The genetic algorithm 22 is adopted in this study, which is a search heuristic mimicking Charles Darwin's 23 theory of natural selection (i.e., selection, crossover, and mutation) [24], and has been 1 widely used to search the optimal trials [25]. Since the airborne infection risk is 2 evaluated by the rebreathed fraction which is calculated from the CO 2 concentration 3 (Equation 3), CO 2 is used as the biomarker of the exhaled aerosols. The search range 4 of the upper limit of indoor CO 2 concentration is between the lower and upper steady 5 values of indoor CO 2 concentration (Equations 6 and 7). The upper limit of indoor 6 CO 2 concentration can be lower than the stipulated one by indoor air standards 7 because the occupancy load can be smaller than the designed occupancy capacity 8 period is four hours (a morning/afternoon session). The outdoor CO 2 concentration is 20 400 ppm [21], and the CO 2 concentration in the exhaled air is 37,500 ppm [18] . The 21 unit period of normal occupancy is limited to be within 30 min -90 min, and the unit 22 period of reduced occupancy is limited to be larger than 5 min. When the occupancy 23 load ratio and occupancy flexibility are both 100% and the normalized mean 24 rebreathed fraction is limited to less than 0.8, Figure 3 shows the indoor CO 2 25 concentration profiles of the conventional ventilation strategy and the proposed normal occupancy merely), the indoor CO 2 concentration increases from 400 ppm and 1 tends to converge to 1200 ppm (i.e., 800 ppm above the outdoor CO 2 concentration 2

[22]). The developed optimization (Figure 2 ) determines the upper and lower limits of 3 indoor CO 2 concentration as 1178 ppm and 918 ppm respectively, and the 4 corresponding unit periods of normal occupancy and reduced occupancy are 55 min 5 and 9 min respectively. The entire ventilation process is interrupted by two units of 6 reduced occupancy, and the indoor CO 2 concentration is effectively reduced. The 7 entire ventilation process ends at a concentration of indoor CO 2 concentration close to 8 the upper limit of indoor CO 2 concentration. Thus, the occupancy schedule from the 9 developed optimization follows the mechanisms of the occupancy schedule (Section 10 2.2). 

The three constraints in the developed optimization require to be predefined by users 16 (Figure 2 ). The two constraints on the unit periods of normal occupancy and reduced 17 occupancy are determined mainly according to the work requirements and the 18 environment (Section 2.1), and the effects of the constraint on airborne infection risk 19 (i.e., the normalized mean rebreathed fraction) are further investigated to provide 20 guidelines for users. Figure 5 shows that when the requirement on airborne infection 21 risk improves (with a reduced normalized mean rebreathed fraction), the entire 22 ventilation process is broken by more units of reduced occupancy, which is explained 23 as follows. The reduced normalized mean rebreathed fraction indicates the 24 accumulative period of reduced occupancy needs to be prolonged. According to the 25 mechanism of the occupancy schedule (Section 2.2), a short unit period of reduced 26 occupancy is preferred for airborne infection risk control. Thus, with the prolonged 27 accumulative period of reduced occupancy, it is broken into more units to achieve a 28 short unit period of reduced occupancy (not greater than 19 min in Figure 5 ).

Moreover, it can be observed from Figure 5 that for the different constraints on the 1 normalized mean rebreathed fraction, the entire ventilation process always ends at a 2 high indoor CO 2 concentration close to the upper limit of indoor CO 2 concentration, 3 which again is consistent with the mechanism of occupancy schedule for work 4 productivity (Section 2.2). When the airborne transmissibility (i.e., the quantum generation rate) of the concerned 10 infectious respiratory disease is known, the airborne infection risk can be calculated 11 by Equation 10 from the rebreathed fraction [18] . One inhaled quantum indicates an 12 infection risk of 63% and might involve a large number of organisms [27] , which 13 implicitly considers the infectious source strength, infectivity, biological decay of 14 pathogens, etc. NMRF < 0.9 NMRF < 0.8 NMRF < 0.7 NMRF < 0.6 NMRF < 0.5 evaluation can account for the pathogen removal effects of filters, masks, air cleaner, 1 etc. via the removal efficiency of pathogens (i.e., φ in Equation 10). Dai and Zhao [15] 2 suggested that the airborne infection risk should be constrained to be less 1% or even 3 be less than 0.1%, and the corresponding constrain on the mean rebreathed fraction 4 can be inversely calculated from Equation 10. Rudnick and Milton [18] suggested that 5 the mean rebreathed fraction should be controlled to make the reproduction number 6 less than one (Equations 11 and 12) . With the airborne infection risk, the production 7 number is calculated by Equation 11 , which is the number of the susceptible will be 8 infected due to airborne transmission. The method suggested by Rudnick and Milton 9

[18] is more reasonable because a reproduction number less than one indicates that Where P is the airborne infection risk; f is the mean rebreathed fraction; I is the 19 number of infectors; q is the quantum generation rate (h -1 ); t is the exposure time (h); 20 n is the number of occupants; R is the reproduction number; K is the removal 21 efficiency of pathogens by filters, masks, air cleaners, etc. 

The ventilation system is designed for 25 occupants, but the classroom might have 5 less than 25 occupants during the normal occupancy with the occupancy load ratio 6 less than 100%. With a decreasing occupancy load ratio, the ventilation rate per 7 occupant in the shared space increases and the indoor CO 2 concentration decreases 8 [16] . Figure 8 shows that the maximal indoor CO 2 concentration decreases from 9 around 1140 ppm to 550 ppm when the occupancy load ratio reduces from 100% to 10 20%. Again, the entire ventilation process ends at an indoor CO 2 concentration close 11 to the respective upper limit of indoor CO 2 concentration with the varying occupancy 12 load ratios, which further validates the mechanisms of occupancy schedule revealed in 13 

As discussed in Section 2.3, it might be impractical for all occupants to leave the 7 shared space for reduced occupancy limited by the work nature, and the effects of the 8 occupancy flexibility on the effectiveness of the proposed occupancy-aided 9 ventilation are investigated. Lower occupancy flexibility indicates fewer occupants 10 would leave the shared space for reduced occupancy. As a result, the reduction effects 11 of the reduced occupancy on indoor CO 2 concentration and rebreathed fraction 12 deteriorate (Figures 9 and 10) . The rebreathed fraction is weighted by the occupancy 13 flexibility (Equation 13). The occupancy flexibility is nil for the normal occupancy, 14

indicating that all occupants are in the shared space. When the occupancy flexibility is 15 less than 100% for reduced occupancy, the rebreathed fraction sharply reduces first 16 due to the reduced number of occupants and then reduces gradually due to the reduced 17 indoor CO 2 concentration ( Figure 10) J o u r n a l P r e -p r o o f 80%, and 100%, the entire ventilation process always ends at an indoor CO 2 1 concentration close to the upper limit of indoor CO 2 concentration for work 2 productivity (Section 2.2). However, when the occupancy flexibility is 20%, the 3 reduced occupancy has to last for 150 min until the end of the entire ventilation 4 process to satisfy that the normalized mean rebreathed fraction should be less than 0.8. 5

The contribution of the reduced occupancy to the work productivity is also taken into 6 account, because some occupants are working during the reduced occupancy when the 7 occupancy flexibility is less than 100% (Equation 14 ). For all the five occupancy 8 flexibilities, the normalized mean rebreathed fraction is less than 0.8 (around 0. for, e.g., the potential congestion of corridors caused by the changeover between the 8 normal and reduced occupancies and the exit/entry ways of leaving/entering the 9 shared indoor environments. Furthermore, the evaluations of the airborne infection risk 10 and work productivity in this study are simplified to some extent. It is challenging to 11 evaluate work productivity accurately because it is affected by multiple factors in 12 complicated manners (e.g., the mental and physiological conditions and the quality of 13 indoor thermal environments [31] ). This study evaluates the work productivity from the 14 accumulative period of normal occupancy in a simplified manner, which follows the 15 logic that a longer accumulative period of normal occupancy indicates a prolonged 16 working time length, thereby increasing the work productivity. the assumption that the pathogen distribution in the indoor air is uniform (Equations 2 1 and 4). However, the pathogen distribution is inevitably non-uniform [9] . This 2 assumption has been widely used and is regarded as acceptable for mixing ventilation 3 [18] . When the ventilation system employs advanced air distribution which delivers 4 fresh and clean air effectively to the breathing zone, e.g., displacement ventilation and 5 stratum ventilation [9, 21] , the assumption of uniform distribution of airborne 6 pathogens might cause large errors, and new evaluation methods are required to 7 account for the effects of the non-uniformly distributed airborne pathogens on the 8 airborne infection risk [32] . Moreover, the airborne infection risk evaluation requires 9 the number of infectors, while it is challenging to deterministically obtain the number 10 of infectors unless the epidemical data are available. During the design of proper 11 interventions fighting severe infectious diseases, the number of infectors is generally 12 assumed to a small number (e.g., 1 or 2) [15, 18, 19, 29 ]. This assumption is relatively 13 reasonable for severe infectious diseases in public buildings, because symptomatic 14 infectors of severe infectious diseases are generally quarantined and not allowed to 15 attend public buildings. In the future study, probability analysis will be developed to 16 include the effects of the number of infectors. 17

Given that ventilation rates commonly encountered may be insufficient for airborne 19 infection risk control of COVID-19 (particularly for public buildings), the 20 occupancy-aided ventilation proposed in this study schedules the occupancy with 21 normal and reduced occupancy, and uses the reduced occupancy as a supplement to (2) The unit periods of normal and reduced occupancies should be co-determined to

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