key: cord-286230-0si3pv3e
authors: Wang, Wenlu; Yoneda, Minoru
title: Determination of the optimal penetration factor for evaluating the invasion process of aerosols from a confined source space to an uncontaminated area
date: 2020-06-10
journal: Sci Total Environ
DOI: 10.1016/j.scitotenv.2020.140113
sha: 
doc_id: 286230
cord_uid: 0si3pv3e

Abstract Due to the outbreak and spread of COVID-19, SARS-CoV-2 has been proven to survive in aerosols for hours. Virus-containing aerosols may intrude into an uncontaminated area from a confined source space under certain ventilated conditions. The penetration factor, which is the most direct parameter for evaluating the invasion process, can effectively reflect the penetration fraction of aerosols and the shielding efficiency of buildings. Based on the observed concentrations of aerosols combined with a widely used concentration model, four numerical calculations of the penetration factor are proposed in this study. A theoretical time-correction P est was applied to a size-dependent P avg by proposing a correction coefficient r, and the error analysis of the real-time P(t) and the derived P d were also performed. The results indicated that P avg supplied the most stable values for laboratory penetration simulations. However, the time-correction is of little significance under current experimental conditions. P(t) and P d are suitable for rough evaluation under certain conditions due to the inevitability of particles detaching and re-entering after capture. The proposed optimal penetration factor and the error analysis of each method in this study can provide insight into the penetration mechanism, and also provide a rapid and accurate assessment method for preventing and controlling the spread of the epidemic.

The global outbreak of coronavirus disease has seriously endangered the health and safety of all human beings. Scientists have conducted extensive research on the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), referring to transmission dynamics [1] [2] [3] , removal technology [4] , and climate factor [5] . Correia et al. (2020) pointed out that improper use of the ventilation system could aggravate the spread of the virus [6] .

Doremalen et al. (2020) experimentally generated SARS-CoV-2-containing aerosols with a diameter of less than 5 m, and illustrated that SARS-CoV-2 can survive and be infectious in aerosols for hours, in some cases even days on surfaces [7] . Moreover, it is well known that coronavirus is more likely to exist in confined and poorly ventilated spaces. In this case, aerosols can carry or combine with viruses into an uncontaminated area under certain ventilated conditions. However, the most effective evaluation method for aerosols penetrating from the polluted area or the source area to the unpolluted space is still not clear.

In recent decades, the fate of aerosols penetrating from outdoor has received widespread attention from scientists due to the direct relationship with human health [8] [9] [10] [11] [12] . Related penetration research is usually carried out in two ways: field measurement and laboratory simulation. Field experiments are always conducted in real buildings such as school classrooms, dormitories, and offices [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] , while a test chamber or a building brick is usually used as the object to simulate the indoor or outdoor environment in laboratory simulations [22] [23] [24] [25] [26] [27] . The difference between laboratory simulation and field testing is a greater control of the conditions in a laboratory setting. Additionally, the change in concentration of aerosols is one of the basic characteristics in the penetration process. Based Journal Pre-proof J o u r n a l P r e -p r o o f on the law of mass balance, Thatcher et al (2003) had represented the indoor concentration over time "t" as [28] ,

where, C in and C out are the indoor and outdoor particle concentrations (cm -3 ), a is air exchange rate (AER) (h -1 ) associated with ventilation system, k is the rate of particles deposition loss onto interior surfaces (h -1 ), while P is the penetration factor. G, S, F, K and H represent the particle generation from the indoor source, particles for dissociation/vaporization, the formation of new particles due to chemical reactions, the particles for coagulation and for hygroscopic growth (cm -3 h -1 ), respectively.

For the source, concentrations, size of particles and the experimental conditions used in most simulations, it is assumed that the effects of dissociation/vaporization (S), new chemical formation (F), coagulation (K) and hygroscopic growth (H) are avoided in the analysis. If the study only focuses on the single penetration process, the indoor source (G) also has no significance. In this case, Eq. (1) is simplified to the expression with parameter a, k and P, as

Similarly, assuming that the particle flow passing from the outdoor compartment is the only path under ideal conditions, the outdoor particle concentration in a confined space could be affected by the air exchange rate "a" of the indoor compartment and the deposition rate "k" of outdoor particles. Therefore, the outdoor particle concentration over time can be expressed as,

It is assumed that a certain number of particles tend to penetrate from the outdoor compartment at time "t" under the action of a ventilator, but only a portion enters the indoor Journal Pre-proof J o u r n a l P r e -p r o o f compartment while the rest is trapped by the sash gap. In this case, "P 0 " represents the total proportion of the particles participating in the penetration at a certain AER "a". If those trapped particles do not detach and re-enter the outdoor compartment, P 0 can be estimated as 1.

A review of the literature shows that the portion of "P" entering the indoor compartment can be defined as follows: the parameter P, associated with infiltration airflow, denotes the fraction of outdoor particles passing through building cracks, leakage paths and window openings [29] [30] [31] . In Eq. (2), "a" and "k" are the only influencing factors, and the equilibrium

In the experiments of penetration simulations in recent decades, Eq. (4) is widely used for quantification of the particle penetration through building cracks. Thornburg et al (2001) reported penetration factor using this equation, and C in and C out were described as the time average of the indoor and outdoor concentrations [29] ; Rim et al (2013) mentioned in the derivation that the equation was for the particle size category [31] ; while other literatures defaulted the P value to the size-resolved one [14, 32, 33] . However, there is little reference to the optimal method for determining the P value.

J o u r n a l P r e -p r o o f and continuous particle source could not be provided. This is also the limiting factor for laboratory simulations. Therefore, two questions require further discussions: (1) "is the parameter P of Eq. (4) without a time attribute suitable for the case where the concentration changes in a confined source space?" and (2) "what is the optimal P value?".

Based on the aforementioned properties of SARS-CoV-2 regarding its ability to survive in aerosols for hours, FPs/ UFPs may carry or combine with SARS-CoV-2 and then penetrate into uncontaminated areas together. To evaluate the invasion process of aerosols from a confined source space to an uncontaminated area, based on our previous work and the widely used concentration model Eq.

(2)-Eq. (4), we will thus be (1) proposing four numerical calculations of penetration factor, the size-dependent P avg , the time-corrected P est , the realtime P(t), and the direct-derived P d ; (2) comparing and evaluating the observed indoor concentrations and the estimated ones; and (3) selecting the optimal P value for penetration process. The proposed optimal P value and the error analysis could help provide insight into the penetration mechanism, and can also provide a rapid and accurate assessment method for preventing and controlling the spread of the epidemic.

Based on our previous work on penetration simulation for emergency evacuation, Fig. 1 gives the schematic of the whole experimental system, including a simulation system and a In this study, the outdoor compartment simulates a closed source space filled with viruscontaining aerosols, where a certain amount of particles (around 1.010 4 cm -3 ) are introduced at the initial moment; while the indoor compartment with an initial concentration close to zero simulates an uncontaminated room. Due to the particle flow gradually passing through the crack and entering the indoor compartment while the ventilation system is in operation, the series of the indoor and the outdoor concentrations recorded at every time "t" reported in our previous research exhibits a tendency for continuous attenuation [27] . The AER of the ventilation system was controlled from 0. 

J o u r n a l P r e -p r o o f

Assuming C in (t) and C out (t) as the real-time indoor and outdoor concentrations for instantaneous calculation, respectively, and P(t) as the real-time value of penetration factor at time t, or P avg representing the average penetration factor for a short-term evaluation, Eq. (4) can be expressed as,

and

where, C in,avg and C out,avg are the time-averaged concentrations for each particle size. P(t) is "time-dependent/ size-averaged" penetration factor of the indoor compartment, that is, the penetration factor corresponds to the total concentration per minute at the average diameter.

P avg is "size-dependent/ time-averaged" penetration factor of the indoor compartment,

representing the penetration factor corresponding to the average concentration of 36 minutes at each particle size. However, P avg is a size-dependent parameter without a time property.

Therefore, the theoretical value P est is introduced for time correction in this study.

In case of C in 0, C in (0) and C out (0) represent for the initial conditions. Therefore, by integrating Eq. (2) and Eq. (3), the real-time concentrations at t time can be obtained as follows,

Considering the continuous change in concentration from 0 to T time, then

Combined Eq. (6), Eq. (10) and Eq. (12),

Here, we defined the item "

" involving in the parameters "a" "k" and "t" as "correction coefficient r", then

so,

In case of C in =0,

To search for an approximation close to the expected value, a simple equation is visually derived from the ratio of Eq. (7) and Eq. (8) (assumed P 0 = 1) to directly estimate the penetration factor, J o u r n a l P r e -p r o o f

Here, P d represents a time series of approximate values over 36 minutes.

In case of C in (0) =0, Eq. (18) changes to

P d can be also used to estimate the penetration factor at a certain time t. Compared to P(t)

in Eq. (5), P d calculated by Eq. (19) ignores the effect of k but adds the time attribute.

If taking the indoor compartment as the research object, and also fully considering the situation where C out gradually decreases in the laboratory simulation experiment, Eq. (3) is

where, t represents time interval, and the indoor concentration at "t+t" time is estimated as,

In this study, the deposition rate k was approximated using the model of Okuyama according to our published work, the value of which is less than 0.25 h -1 with a particle size of less than 500 nm [27, 34] . The penetration factor P, denoted as P(t), P avg , P est and P d , respectively, is substituted into Eq. (21) , and the optimal P value is discussed and determined by comparing with the observed indoor concentration over time.

J o u r n a l P r e -p r o o f

In the experiment, four size segments, 69-100 nm, 100-200 nm, 200-300 nm and 300-500 nm, were divided according to their similar P avg in each segment. Fig. 3 gives the relationship between correction coefficient r and the elapsed time (taking 69-100 nm as an example).

These curves are extended indefinitely, and they all finally equal to 1. The larger the AER, the shorter the time. As displayed in Table 1 , each time average value of P(t), P avg and P d shows a growth trend with the increase of AER, which is consistent with the literature that a high AER corresponds to a high P value when C out is higher than C in [27] , but for P est . In addition, the average values of P avg in the four size segments are gradually approaching that of P est as AER is increasing.

Moreover, P(t) at an AER of 3.70 h -1 , P d at AERs of more than 1. 

In Fig. 4 , the dotted curves present the observed indoor concentration and the estimated concentrations from P(t), P avg , P est and P d at 0.31 h -1 , 1.20 h -1 and 3.70 h -1 , respectively. The curve using the P est value clearly deviates from the observed concentration. It means the time-corrected P est has a large error, while the real-time P(t), the size-dependent P avg and the direct-derived P d are much closer to the expected value. Additionally, the change trend of the curves, growth, maintenance and decline, is summarized in Table 2 , referring to C out > C in , C out = C in and C out < C in , respectively, which are consistent with the previous reported results J o u r n a l P r e -p r o o f

In the case of C in 0, Eq. (16) gives the theory relationship between P est and P avg .

Numerically, the two values gradually approach each other as AER increases (see Table 1 ).

In Eq. (16) there are two terms, " 1 " and " + • (0) (0) ". In the laboratory simulation, the initial concentration can be seen as a constant, and the value of "a" ranges from 0.31 h -1 to 3.70 h -1 with k being negligible compared to the increased AER. Therefore, " + " tends to 1 with the increases of AER and the term "

" has little effect on the value P est . In the term " 1 ", r plays an important role. As shown in Table 3 , the correction coefficient r for different size segment at different AER values will have similar maximum and minimum. Generally, correction coefficient r values are all less than 1, ranging from 0.006 to 0.737. Therefore, the estimated-P est is around 1.37-167 times larger than the size-dependent P avg . Therefore, the time correction under the effect of the correction coefficient r is of little significance due to the simulated ideal experimental conditions in the laboratory, including the good airtightness of the experimental chamber, the mild testing environment, and the controllable particle concentration and ventilation power. In this case, the controllable concentration ratio of the indoor and the outdoor results in the averaged concentrations being similar to the real-time ones. In contrast, it can be speculated that P est could become necessary for the system if the outdoor concentration is much higher than the indoor one, or if there is a large AER (i.e. a »3.70 h -1 ), but further demonstration it still needed. found for smaller UFP (d p <30 nm) the loss due to deposition is substantially higher than that due to AER, and deposition rate k usually decreases to less than 0.1 h -1 at a particle size of more than 100 nm [33] . Additionally, both P(t) and P avg originate from Eq. (4) and this equation has set "C in (0) = 0" as a prerequisite while P est in Eq. (16) and P d in Eq. (18) include the condition of "C in (0)  0". It can be considered that P est in Eq. (16) and P d in Eq.

(18) are the corrections of the default item of the initial indoor concentration. In terms of P values, Table 1 shows the average and standard deviation of P(t), P avg , P est and P d in four size segments, respectively. A large standard deviation indicates that the variation of P value in the size segment fluctuates greatly over 36 minutes, with the largest errors appearing on P(t) at the AER of 3.70 h -1 . P(t) in Eq. (5) contains two terms, " + " and " ( ) ( ) ". For the first term " + ", it has reported that deposition rate k usually < 0.1 h -1 as d p > 100 nm and k < 0.25 h -1 as d p < 100nm [33] [34] , so the term is around 1 to 2 (AER ranges from 0.30 h -1 to 3.70 h -1 ). As we can see in Table 1 , the values of P(t) is greater than 1 at a large AER of 3.70 h -1 with the term " Based on the experimental basis [27] , the curve of indoor concentration shows three trends during 36 minutes at the three different settings of AERs (Table 2) . Before the decline, the curve of growth and maintenance last 0.233 h (first 14 minutes) at the AER of 3.70 h -1 , that is, P(t) can only be ensured ranging from 0 to 1 before the occurrence of "C out < C in ".

Additionally, the real-time value is greater than 1, indicating that the indoor concentration is already higher than outdoor and P(t) is no longer applicable for evaluation. Different with P(t), the AER "a" and the time attribute "t", contained in the term " 1 ", gives the main contribution to the P d value. As shown in Table 1 , P d indicates a higher value than other three P values at a small AER of less than 1.20 h -1 , but the relative errors between the estimated results at P d and the observed concentrations are similar to P(t) and P avg in Table 5 ; while in the later period (last 22 minutes) and at a large AER of more than 1.20 h -1 , "a" and "t" " tends to zero). The concentrations estimated from P(t) and P d therefore have more significant errors than the actual observed concentration in the early period prior to 0.233 hours, especially when the AER is more than or equal to 1.20 h -1 (Table 5) . Similarly, P d in Eq. (18) including the term of " " has insignificant correction because the initial indoor concentration tends to zero in this study.

Additionally, as described in Eq. (8), we assumed "P 0 = 1" under the ideal condition,

indicating that those trapped particles do not detach and re-enter the outdoor compartment.

However, the errors indicate that the assumed P 0 exists and the value of P 0 is less than 1, J o u r n a l P r e -p r o o f implying that detaching and re-entering are inevitable in the actual situation. Therefore, in a 36-minute penetration evaluation, both P(t) and P d are applicable to conditions where the AER is less than 1.20 h -1 , but they cannot be equal due to the different derivations. In addition, P(t) can be also used for the late stage at the AER as 1.20 h -1 , and unlike " 1 " in P d , " + " in P(t) has a certain correction effect on the P value under the condition of AER less than 1.20 h -1 .

It is worth noting that the estimated result at P avg has small errors among all the P values at each size segment and at each AER in Table 5 . Like P(t) in Eq. (5), the " + " term eliminates the effect from AER to some extent, and C in, avg and C out, avg in Eq. (6) Therefore, the estimation at P avg is more stable than other values.

In contrast, the increase of the AER value tends to decrease the error from P est , i.e. from Similarly, a large AER reduces the action time of the r value. In addition, the overall P est value far exceeding 1 indicates its inapplicability in the 36-minute evaluation. Similar to P d in Eq. (18) , P est in Eq. (16) includes the condition of "C in (0)  0" and is insignificant for the correction of P avg due to a low ratio of "

" in this study, and may even cause large errors.

Additionally, for systems with large indoor and outdoor concentration changes or an existing large AER (i.e. a > 3.70 h -1 ), whether or not the error caused by P est would decrease still needs further demonstration. 

This work proposes four numerical calculations of penetration factor to select the optimal value. In addition, a widely used concentration model is employed to evaluate the penetration process of aerosols from a confined source space to an uncontaminated area within 36 min, and the following conclusions can be applied to the invasion evaluation of virus-containing aerosols.

During the 36-minute penetration process in this study, the proposed correction coefficient r has its own time limit if time-correction is necessary under some non-ideal condition.

J o u r n a l P r e -p r o o f Additionally, size-dependent P avg is time-corrected to be P est by the correction coefficient r.

However, the time correction is of little significance due to the simulated ideal experimental conditions in the laboratory within the current experimental 36 min. P est was assumed to be necessary for the system if the confined source space has a much higher initial concentration than the indoor one or there is a large AER (i.e. a »3.70 h -1 ), but it still needs further demonstration.

The error analysis of the real-time P(t) and the direct-derived P d proves that the assumed P 0 exists and the value of P 0 is less than 1 in the actual situation, indicating that detaching and re-entering are inevitable. Both of them are only suitable for rough evaluation in the case of AER less than 1.20 h -1 and P(t) is also applicable to the later stage when the AER is equal to 1.20 h -1 . Additionally, the size-dependent P avg is the optimal value among the four under current experimental conditions, due to minimal effect from the AER value and fluctuations in concentration.

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This work was financially supported by the Nuclear Regulation Authority (NRA) Japan and Japan Atomic Energy Agency (JAEA).