A CFD-Based Decision Matrix for Evacuation Planning: Minimizing Exposure to Hazardous Chemicals

Abstract

The extent of casualty and property loss due to chemical accidents depends on how well the emergency action plan was established in advance and how fast the warning notice and evacuation orders are given to the public. Assistant methods for the establishment of protective action plans have been developed for several decades. However, the currently developed decision trees are complicated, so they may require a detailed analysis, and previous decision matrices do not consider the indoor and outdoor concentration directly and hence do not allow a change in evacuation order. In this study, five key parameters, report time, toxic cloud arrival/removal time and indoor/outdoor concentration, are selected for the evacuation decision, and the effectiveness of leakage and wind speed on five parameters is investigated. CFD simulations are performed for the various values of mass flow rate and wind speed. Near the release point of toxic gas, the maximum concentration is unaffected by wind speed, but the mass flow rate significantly influences it at low wind speeds. In the far field, the maximum concentration decreases with increasing wind speed. The termination time for shelter-in-place, suggesting a shift to evacuation, decreases with both higher mass flow rate and wind speed. For smaller mass flow rates ($\dot{m}=0.1\mathrm{kg}/\mathrm{s}$), indoor concentration exceeds outdoor levels after 25.9 min, while for larger mass flow rates ($\dot{m}=2.0\mathrm{kg}/\mathrm{s}$), this time shortens to 15.2 min. Increasing wind speed from 0.5 $\mathrm{m}/\mathrm{s}$ to 5.0 $\mathrm{m}/\mathrm{s}$ decreases the equilibrium concentration from 13.9 $\mathrm{ppm}$ to 3.4 $\mathrm{ppm}$ and reduces the escape time from 48.9 min to 16.0 min. Overall, higher mass flow rates and wind speeds shorten the equilibrium and escape times, improving toxic cloud removal efficiency. Based on the simulation results, a new evacuation decision matrix is developed which minimizes the total exposure concentration. This study provides the proper evacuation time along distance which eventually prevents traffic congestion because of the simultaneous escape rush.

1. Introduction

Chemical accidents are mainly classified into four types: gas release, fire, explosion, and gas cloud [1]. Serious hazardous chemical accidents have occurred continually even though safety management systems has improved remarkably. On 7 May 2020, styrene vapor was released at LG polymers India in the city of Visakhapatnam, and it caused 12 deaths and 585 injuries [2]. On 4 August 2020, approximately 2750 tonnes of ammonium nitrate stored at the port of Beirut exploded and resulted in at least 210 deaths, 6500 injuries, and USD 15 billion in property damage [3]. The resulting vapor cloud spread over around 3 $\mathrm{km}$.

When a chemical accident takes place in a region, the first step is to determine the corresponding action between evacuation and shelter in place (hereafter denoted as SIP). Once the evacuation method is chosen, the process is executed sequentially by ordering an evacuation message, propagating alerts, checking people’s response to an order, and preparing for evacuation, which depends on age, gender, degree of education, and previous similar experiences [4]. However, all the above processes become meaningful if the decision maker brings out a proper order by collecting correct information. For the investigation of the accident cause or obtaining precise information to decide the evacuation method, a dispersion simulation is applied to the chemical accident field.

As the evaluation technology using simulation of toxic cloud dispersion has improved, it has become able to predict how far toxic materials will spread. Two kinds of simulation models are commonly utilized. One is the hazard modeling program based on the Gaussian model found in the Korea Off-site Risk Assessment support tool (KORA), Areal Locations Of Hazardous Atmosphere (ALOHA), and Phast. These tools also support the dense gas model, which is found in SLAB in KORA, DEGADIS (Dense Gas Dispersion) in ALOHA, and UDM (Unified Dispersion Model) in Phast. These programs are widely utilized in the field of emergency response planning due to their low computational cost, particularly for modeling potential chemical release scenarios and estimating affected areas. However, they exhibit limited accuracy at low wind speeds and do not account for terrain effects. For better prediction, modifications to the Gaussian model are developed for low wind speeds [5]. The other is the Computational Fluid Dynamics (CFD) model, found in programs such as FLACS, Fluent, COMSOL, and Star-ccm+, which provide more accurate results and also can be applied to find the best evacuation pathway [6] and in emergency planning [7]. Furthermore, CFD helps make predictions in fire modeling and informs initial emergency evacuation distance for emergency response strategies [8], thereby mitigating potential risks and reducing societal losses. With the development of simulation models, machine learning has been recently used to predict an emergency evacuation [9] and find optimized evacuation routes [10,11]. Dynamic risk analysis is employed to propose evacuation path planning [12]. Although huge advances in computer technology have been achieved over the past decade, the research on decision methods for evacuation has been stagnant for more than a decade.

Several methods to help protective action decisions have been developed. Checklists illustrate the attributions of parameters used in to evacuation methods, decision trees provide the choice between evacuation and SIP through yes/no questions, and decision matrices derive the appropriate consequences by using key parameters [13]. The above-mentioned methods mostly depend on the manager’s decisions, which vary due to individuals’ different experiences and knowledge. Because of these reasons, more quantitative and objective data are requested to judge the exact evacuation time and method.

In particular, Glickman and Ujihara [14] developed a decision matrix based on two parameters, critical dose and the arrival time of the toxic cloud. Even though it helps to decide on either an evacuation order or SIP, it does not allow a change in decision due to time and distance transition. It is more harmful to stay for a long time even after the cloud passes or the indoor toxic concentration becomes higher than outside. Sorensen et al. [13] indicated the importance of changing a protective action because remaining in a shelter for a long time after the toxic cloud has passed results in the worst situation. Therefore, it is necessary to recognize the right time to evacuate during SIP by considering the accident report time and toxic cloud retention time, which are related to the average toxic concentration in the building during the in-place protection. For the prevention of mass chaos, a sequential emergency plan is essential, and it is necessary to make the evacuation time different according to the distance from the toxic source. Knowing one’s own evacuation time along with distance will help the public to evacuate efficiently and sequentially by preventing the congestion caused by many people in the range of toxic effects evacuating at the same time.

At the moment of chemical accidents, evacuations occur more frequently than SIP. SIP is not very common, but it can be an effective protective action in several cases, such as mass toxic cloud stagnation or the lack of preparation time for evacuation. Melnikova et al. [15] investigated the ratio of the evacuation and SIP order. Among 57,975 incidents reported by the Hazardous Substances Emergency Events Surveillance (HSEES) system during 1999–2008 in nine states in the United States, the total number of ordered evacuations and SIP were 4281 (7.4%) and 509 (0.9%), respectively. When an inadequate order is given, it will cause a disaster. Sorensen [16] collected chemical accident data in the years 1980–1984 and analyzed 295 cases in which an evacuation method was applied. Injury occurred in 25 percent of the evacuations because of chemical exposure while evacuating. For this reason, the evacuation and the SIP should be ordered at the same time depending on the distance from the chemical release source.

For the proper evacuation decision, two key parameters, wind speed and mass flow rate, need to be considered. The wind speed is related to the arrival time of the toxic cloud which informs when the toxic cloud arrives. Thus, the public can prepare for the evacuation if they have enough time to evacuate before the toxic cloud arrives. The mass flow rate of the release point affects the indoor and outdoor concentration and tells how much toxic materials are emitted.

In this study, the effect of those two factors on the decision between evacuation and SIP is investigated. Furthermore, a novel decision matrix is suggested by considering not only the toxic cloud arrival time but also the removal time and report time. Therefore, it is possible to calculate the total exposure concentration in a house during SIP. This study provides a new methodology of evacuation decision based on evacuation time and the quantitative action plan to the public by predicting the arrival time and concentration in the house, which makes the public evacuate sequentially and prevents the traffic jam originally.

2. Basic Flow Description

Many numerical studies on dispersion have been conducted [17,18,19]. In this section, numerical modeling of dispersion is investigated using FLACS software, version v10.7 r1, released in November 2017. The flow concerned in this study is a turbulent dispersion in the atmosphere with the imposed shear force of the wind. The fluid is a hydrogen chloride gas and is assumed to behave as an ideal gas with a compressible flow.

2.1. Cfd Modelling

The flow of fluid is governed by three equations: conservation of mass, momentum, and transport. The governing equation for gas transport is as follows [20]:

$${\displaystyle \frac{\partial }{\partial t}}\left({\beta }_v\rho Y_{fuel}\right)+{\displaystyle \frac{\partial }{{\partial x}_j}}\left({\beta }_j\rho u_j{Y}_{fuel}\right)={\displaystyle \frac{\partial }{{\partial x}_j}}\left({\beta }_j{\displaystyle \frac{{\mu }_{eff}}{{\sigma }_{fuel}}}{\displaystyle \frac{\partial Y_{fuel}}{\partial x_j}}\right)+R_{fuel}$$

(1)

where $R_{fuel}$ is the fuel reaction rate (zero since there is no reaction), ${\sigma }_{fuel}$ is the turbulent Prandtl–Schmidt number, ${\beta }_v$ is the volume porosity of mesh, ${\beta }_j$ is the area porosity of mesh, $\rho$ is the gas density, $Y_{fuel}$ is the gas concentration, $u_j$ is the velocity of the wind, and ${\mu }_{eff}$ is the effective viscosity.

The FLACS solves RANS (Reynolds-Averaged Navier–Stokes) equations based on the standard k–$\epsilon$ model [21]. For better solution accuracy, the FLACS uses the SIMPLE pressure correction method for convergence and the second-order scheme for the diffusive and convective fluxes [22]. The CFD simulation was performed using a workstation equipped with dual intel Xeon E5-2630 v4 2.2 GHz processor and the computation time was approximately 80 h per simulation of each case.

The simulation parameters are listed in

Table 1. Simulation parameters.

Parameters	Symbols	Values
Domain size	X	−10∼3000 m
	Y	0∼300 m
	Z	0∼100 m
Simulation control	$\Delta t$	0.01 s
Leak condition	D	0.1016 m
	$t_l$	10 min
	$\dot{m}$	0.1, 0.5, 1.0, 2.0 kg/s
Meteorological condition	$V_{wind}$	0.5, 1.5, 3.0, 5.0 m/s
	T	25 °C

. X, Y, and Z correspond to streamwise, spanwise, and vertical directions in a Cartesian coordinate system. The domain size of X, Y, and Z directions is, respectively, 3010 $\mathrm{m}$, 300 $\mathrm{m}$, and 100 $\mathrm{m}$, which covers dispersion distance during simulation time. The number of 1,080,000 (144 × 150 × 50) grids displayed in Figure 1a is used in the simulation. A grid sensitivity analysis has been performed using three different grid resolutions listed in

Table 2. Three types of grids used for the sensitivity study.

Grid	Cells	Number of Cells (X, Y, Z)
Coarse	417,600	(87, 120, 40)
Medium	707,200	(136, 130, 40)
Fine	1,080,000	(144, 150, 50)

. The concentrations calculated at monitoring points with a coarse grid fluctuate on average by 21% and 26%, respectively, compared to medium and fine grids. The average deviation between the medium and fine grids is less than 5%, and the deviation converges as the number of cells increases. Therefore, the fine grid with 1,080,000 cells was chosen in the simulation to obtain high computational precision.

The domain is uniformly divided by 2 $\mathrm{m}$ in the Y and Z directions and it is stretched by a factor of 1.05 in the X direction from 100 $\mathrm{m}$. In Figure 1b, 30 monitoring points are located up to 3000 $\mathrm{m}$ at 100 $\mathrm{m}$ intervals to investigate the indoor and outdoor concentrations at each location. The simulation time step, $\Delta t$, is 0.01 s. Iterations in FLACS are repeated until a mass residual of less than ${10}^{-4}$ is obtained [20]. As presented in

Table 3. Boundary conditions.

Direction	Boundary	Direction	Boundary
XLO	Wind	XHI	Nozzle
YLO	Wind	YHI	Wind
ZLO	Nozzle	ZHI	Wind

, the wind boundary condition is applied to all inflows and parallel directions, while the nozzle boundary condition is implemented at the outflow. The lower boundaries in the X, Y, and Z directions are designated as XLO, YLO, and ZLO, respectively, with the upper boundaries correspondingly labeled as XHI, YHI, and ZHI. The wind direction is oriented from X- to X+, corresponding to the horizontal axis. The leak source is located at (0 $\mathrm{m}$, 150 $\mathrm{m}$, 5 $\mathrm{m}$) within the domain and the diameter of the leak source is 10.16 ${\mathrm{cm}}^2$ (4 inches) with an area of 0.0081 ${\mathrm{m}}^2$. $t_l$ represents the duration of the leak and the toxic material is assumed to be continuously emitted for 10 min under four different mass flow rate (denoted by $\dot{m}$) conditions, as suggested by the EPA (Environmental Protection Agency) [23], which recommends a 10 min release for worst-case scenarios involving toxic gases. T denotes the ambient temperature, which is 25 °C.

In FLACS, the Monin–Obukhov length [24] is a measure of the stability of the atmospheric boundary layer and is estimated from Pasquill classes [25]. The stable atmosphere, Pasquill class F, is selected, as it represents the worst meteorological condition for dispersion [23]. $V_{wind}$ is the reference wind speed defined at a reference height of 5.0 $\mathrm{m}$, where the wind velocity equals the reference wind speed. The value of $V_{wind}$ varies from 0.5 $\mathrm{m}/\mathrm{s}$ to 5.0 $\mathrm{m}/\mathrm{s}$ in the simulation. The wind velocity profile, defined in FLACS using the wind wizard, follows a logarithmic distribution, as shown below [20]:

$$\begin{array}{ccc}\hfill U\left(z\right)& =& {\displaystyle \frac{u^{*}}{\kappa }}\left[ln\left({\displaystyle \frac{(z-z_d)+z_0}{z_0}}\right)-{\psi }_u\left(z\right)\right]\hfill \end{array}$$

(2)

where $u^{*}$ is the friction velocity, $z_d$ is the canopy height, $z_0$ is the atmospheric roughness length, $\kappa$ is the von Kármán constant, and ${\psi }_u\left(z\right)$ is $-17(1-exp(-0.29{\displaystyle \frac{z}{L}}))$, the function related to Monin–Obukhov length (L).

Table 4. Simulation cases.

Case	$\dot{\mathit{m}}$ (kg/s)	${\mathit{V}}_{\mathit{wind}}$ (m/s)	Case	$\dot{\mathit{m}}$ (kg/s)	${\mathit{V}}_{\mathit{wind}}$ (m/s)
Case1	0.1	0.5	Case9	1.0	5.0
Case2	0.1	1.5	Case10	1.0	1.5
Case3	0.1	3.0	Case11	1.0	3.0
Case4	0.1	5.0	Case12	1.0	5.0
Case5	0.5	0.5	Case13	2.0	0.5
Case6	0.5	1.5	Case14	2.0	1.5
Case7	0.5	3.0	Case15	2.0	3.0
Case8	0.5	1.5	Case16	2.0	5.0

illustrates the 16 simulation cases, with changes in two key parameters: $\dot{m}$ and $V_{wind}$. Changes in the mass flow rate affect the outlet velocity and leakage, which are related to the maximum exposure concentration and retention time. Wind speed contributes to the change of indoor concentration and termination time of SIP. The effect of these key parameters on exposure concentration will be discussed in Section 3.3.

2.2. Toxic Materials

The working fluid is hydrogen chloride (hereafter denoted as HCl) gas. The molar mass and density of HCl are 36.46 $\mathrm{g}/\mathrm{mol}$ and 1.49 $\mathrm{kg}/{\mathrm{m}}^3$, respectively, which is slightly denser than air (molar mass: 28.96 $\mathrm{g}/\mathrm{mol}$). HCl is an acid that can form aerosol clouds and inhalation of HCl can cause serious respiratory problems. It is classified as an extremely hazardous substance by the U.S. Environmental Protection Agency. Regarding toxicity, the National Research Council (NRC) recommends a 24-h Short-term Public Emergency Guidance Level (SPEGL) value of 1 $\mathrm{ppm}$ to protect sensitive populations such as children and the elderly [26]. The American Conference of Governmental and Industrial Hygienists (ACGIH) established a Threshold Limit Value (TLV) ceiling of 2 $\mathrm{ppm}$ and the Occupational Safety and Health Administration (OSHA) set an 8-h Time-Weighted Average (TWA) as a ceiling value of 2 $\mathrm{ppm}$ in 2019. Among the above values, the lowest value of 1 $\mathrm{ppm}$ is applied to evaluate the simulation results because the consideration of both the worst accident scenario (10 min release) and the most strict emergency guidance level is more appropriate for the evaluation to prepare for the protective action plan and minimize the total exposure concentration.

2.3. Air Exchange Rate

Changes in indoor concentration are highly related to the air exchange rate (hereafter denoted as ACH). ACH is defined as the air exchange rate per hour, which measures the amount of indoor air replaced with outside air and given by

$$\begin{array}{c}\hfill \mathrm{ACH}(1/h)={\displaystyle \frac{Q(m^3/h)}{V\left(m^3\right)}}\end{array}$$

(3)

where Q is the volumetric flow rate of air in cubic meters per hour and V is the volume of the building.

South Korea established regulations for building facility standards in 2006. The minimum ventilation value was set at 0.7 ACH in 2006 but was reduced to 0.5 ACH in 2013 to promote energy savings [27]. In comparison, the average air exchange rate for housing in the United States ranges from 0.7 to 0.8 ACH [28] and increases with wind speed [29]. Sorensen et al. [13] indicated that a well-constructed energy-efficient house has an ACH of 0.1, which can increase up to 0.8 ACH due to strong winds and high temperature. For an average house, the ACH can range from 0.3 to 2.4. In reality, 1 ACH does not represent a 100% replacement of indoor air with outside air in an hour, as some of the toxic gas entering the building may also leave the building. Fletcher and Saunders [29] indicated that only 63% of the air is replaced at 1.0 ACH. In the simulation, the air is assumed to be uniform and perfectly mixed, meaning that toxic gas entering the shelter does not leave. Therefore, 1 ACH represents 100% of air replacement in the simulation. A value of 0.7 ACH is selected for the simulation, considering South Korea’s ventilation regulations and the average ACH value observed in U.S. housing.

3. Numerical Results of Dispersion

Now, the ideas and relations of the leakage of toxic material and meteorological conditions to indoor and outdoor concentration are examined using CFD simulations. Key results that demonstrate the evacuation decision analysis are presented here. The retention time of a toxic cloud, denoted as $t_r$, refers to the duration for which the toxic cloud remains in the region. The total exposure concentration is calculated by integrating the instantaneous concentration over the retention time and given by the following equation:

$$\begin{array}{ccc}\hfill C_t& =& {\int }_{t_i}^{t_e}C\left(t\right)dt=\sum _{t=t_i}^{t_e}\left(C\left(t\right)\Delta t\right)\hfill \end{array}$$

(4)

where $C_t$ is the total exposure concentration, $t_i$ is the start time at the moment that the toxic cloud enters the given region, $t_e$ is the end time at the moment that the toxic cloud leaves the given region, $C\left(t\right)$ is the instantaneous concentration, which is calculated in Equation (1), and $\Delta t$ is the simulation time step.

The average concentration is calculated by dividing the total exposure concentration by the retention time and given by

$$\begin{array}{ccc}\hfill \overline{C}& =& {\displaystyle \frac{{\int }_{t_i}^{t_e}C\left(t\right)dt}{t_r}}={\displaystyle \frac{{\displaystyle \sum _{t=t_i}^{t_e}}\left(C\left(t\right)\Delta t\right)}{t_r}}\hfill \end{array}$$

(5)

where $\overline{C}$ is the average concentration and $t_r$ is the retention time of a toxic cloud, which is equal to $t_e-t_i$.

The concentration rate is obtained by dividing the average concentration by the retention time and is defined as follows:

$$\begin{array}{ccc}\hfill \dot{C}(ppm/min)& =& {\displaystyle \frac{\overline{C}}{t_r}}\hfill \end{array}$$

(6)

where $\dot{C}$ is the concentration rate.

The concentration rate indicates how quickly the concentration of a toxic cloud changes and provides critical information for determining whether SIP is an appropriate protective action.

The outdoor concentration, defined as $C_{outdoor}$, is equal to the instantaneous concentration, which is evaluated in FLACS using the transport Equation (1). The indoor concentration is obtained by integrating the outdoor concentration and air exchange rate over the retention time and is defined as follows:

$$\begin{array}{ccc}\hfill C_{indoor}& =& {\int }_{t_i}^{t_e}\Delta t\left({\displaystyle \frac{ACH}{3600}}\right)C_{outdoor}\left(t\right)dt\hfill \end{array}$$

(7)

where $\Delta t$ is the simulation time step, which is 0.01 s, and $ACH$ is the air exchange rate, which is 0.7 (1/h).

3.1. Results for Total Exposure Concentration Along Distance

Health can be affected by both acute toxicity and cumulative toxic exposure. The criterion for evaluating the danger of acute toxicity is assessed in terms of the concentration rate. Figure 2 shows the change in outdoor concentration along the distance at $\dot{m}=2.0\mathrm{kg}/\mathrm{s}$ and $V_{wind}=1.5\mathrm{m}/\mathrm{s}$. The retention time increases as the monitoring point moves farther from the release site, while the average concentration and concentration rate decrease due to the molecular diffusion. Although the retention time at 0.5 $\mathrm{km}$ (13.8 $\min$) is shorter than that at 3.0 $\mathrm{km}$ (23.3 $\min$), as shown in Figure 2a, the total exposure concentration at 0.5 $\mathrm{km}$, which accumulates during the retention time, is 2.5 times higher than that at 3.0 $\mathrm{km}$, as illustrated in Figure 2b. The outdoor concentration rate at 0.5 $\mathrm{km}$ is 7.29 ppm/min, while at 3.0 $\mathrm{km}$, it is 0.96 ppm/min. Therefore, the evacuation method should be determined immediately after a chemical accident is reported. People in close proximity to the release site should evacuate immediately if sufficient preparation time is available. For the prevention of traffic jams during an evacuation, different evacuation methods and times need to be ordered, respectively, for each region, since the arrival time of a toxic cloud varies along distance, as shown in Figure 2a. If the toxic substance has not yet reached a residential area and sufficient evacuation time is secured, human casualties can be reduced by evacuating sequentially from those living near the source of the leak. For example, if evacuation is appropriate for residents at both 2.0 $\mathrm{km}$ and 3.0 $\mathrm{km}$, the evacuation order should first be issued to the residents living in the 2.0 $\mathrm{km}$ area, followed by those within the 3.0 $\mathrm{km}$ zone. As shown in Figure 2b, the exposure concentration is higher closer to the source of the leak. Therefore, residents near the release site should prioritize SIP as the first protective action.

On the other hand, if there is not enough time to evacuate the site or if the toxic cloud has already overwhelmed the site, the SIP method may be a better decision than an evacuation since the total exposure concentration outside exceeds the total exposure concentration inside all monitoring points from 0.5 $\mathrm{km}$ to 3.0 $\mathrm{km}$, as shown in Figure 3. However, this does not imply that staying inside is always the safest option, as the indoor concentration may eventually exceed the outdoor concentration at some point after the center of the toxic cloud has passed. In the following section, the exact evacuation timing is examined, focusing on the moment when the two concentration curves, indoor and outdoor concentration profiles, intersect.

3.2. Indoor and Outdoor Concentration Change

In order to gain further insight, the outdoor concentration is compared to the indoor concentration at various mass flow rates and wind speeds. If SIP is chosen as the protective action, the next step is to determine when SIP can be safely terminated, allowing people to exit the shelter. Prolonged SIP may be more harmful than evacuation because the indoor concentration will eventually exceed the outdoor concentration as the toxic cloud passes out of the region.

Figure 4 shows the indoor and outdoor concentration profiles at $V_{wind}=0.5\mathrm{m}/\mathrm{s}$ and 500 $\mathrm{m}$ from the chemical release point for four different mass flow rates, $\dot{m}$ = 0.1, 0.5, 1.0, 2.0 kg/s. For a small mass flow rate ($\dot{m}=0.1\mathrm{kg}/\mathrm{s}$, Figure 4a), the indoor concentration begins to increase at 8 min and exceeds the outdoor concentration at 25.9 min after the release of hydrogen chloride gas. For a large mass flow rate ($\dot{m}=2.0\mathrm{kg}/\mathrm{s}$, Figure 4d), the indoor concentration starts to increase at 1 min and exceeds the outdoor concentration at 15.2 min after the toxic material release. Due to the increased outlet velocity and leakage, the toxic cloud reaches the monitoring point of 500 $\mathrm{m}$ 8 times faster and the removal time of the toxic cloud decreases by 41%. Even though the escape time from inside to outside decreases from 25.9 min to 15.2 min, the concentration of equilibrium point at which the indoor concentration becomes equal to the outdoor concentration remains similar, as shown in Figure 4. This occurs because the retention time of the toxic cloud shows little variation. In summary, the termination time of SIP at a fixed location becomes shorter with a large leak at constant wind speed.

Figure 5 shows the indoor and outdoor concentration profile at $\dot{m}=2.0\mathrm{kg}/\mathrm{s}$ and 3000 $\mathrm{m}$ from the chemical release point for four different wind speeds, $V_{wind}=0.5,1.5,3.0,5.0\mathrm{m}/\mathrm{s}$. Compared to Figure 4, it shows that the concentration of equilibrium point (hereafter denoted as $C_{eq}$) decreases from 13.9 $\mathrm{ppm}$ to 3.4 $\mathrm{ppm}$ as the wind speed increases from 0.5 $\mathrm{m}/\mathrm{s}$ to 5.0 $\mathrm{m}/\mathrm{s}$. Moreover, the escape time when the indoor concentration exceeds the outdoor concentration becomes shorter by a third from 48.9 min to 16.0 min since the retention time of the toxic cloud and the maximum concentration decrease. The area underneath the concentration curve in Figure 4 and Figure 5 represents the total exposure concentration, which is the numerator in Equation (5). Note that higher wind velocity results in a greater mitigation effect on the hazard posed by the toxic gas.

The toxic cloud is transported by two mechanisms: advection and diffusion. The propagation of the toxic cloud is described by two models, a “top-hat” (or rectangular) form in which maximum outdoor concentration remains constant, and a “mountain” (or parabolic) form in which outdoor concentration decreases exponentially over time [14]. The “top-hat” concentration profile occurs due to strong advection when the mass flow rate of toxic gas increases or the wind speed is high. On the other hand, this profile gradually smooths out and transitions to a “mountain” form when the mass flow rate is lower or the wind speed is reduced.

The relative significance of advection to diffusion effects is characterized by the Peclet number (denoted by $Pe$) and given by [30]

$$\begin{array}{ccc}\hfill \mathit{Pe}& =& {\displaystyle \frac{UL}{D}}\hfill \end{array}$$

(8)

where U is the characteristic velocity, L is the domain length and D is the diffusive coefficient.

The Peclet number increases as the velocity of the toxic cloud rises, driven by a large mass flow rate or high wind speed. For small Pe (≪1), advection is significantly smaller than diffusion, making advection negligible. Conversely, for large Pe (≫1), advection dominates and diffusion becomes negligible.

In Figure 4, it is observed that the slope of the rising curve in the concentration profile becomes steeper and the maximum concentration becomes flatter as the mass flow rate increases near the release point. The slope of the falling curve in the concentration profile decreases exponentially due to the slow wind speed. A smaller mass flow rate results in a mountain form (Figure 4a) and a larger mass flow rate results in a top-hat form (Figure 4d) at the constant low wind speed near the toxic gas release point. At the same $\dot{m}$ and $V_{wind}$, the concentration profile near the source at $d=500m$ behaves as a top-hat form, as shown in Figure 4d, and spreads out in the far field at $d=3000m$, as shown in Figure 5a.

Figure 5a–d illustrate the transformation of the outdoor concentration profile from a top-hat shape to a mountain shape as wind velocity increases, driven by strong advection. When advection dominates during dispersion, the indoor concentration exceeds the outdoor concentration more quickly even though $C_{eq}$ decreases. The equilibrium time (hereafter denoted as $t_{eq}$) is defined as the time at which the indoor concentration equals the outdoor concentration, i.e., $C_{indoor}=C_{outdoor}$. Figure 4 shows that $t_{eq}$ reduces by 41% from 25.9 min to 15.2 min as $\dot{m}$ increases from 0.1 kg/s to 2.0 kg/s. Similarly, Figure 5 shows that $t_{eq}$ reduces by 67% from 48.9 min to 16.2 min as $V_{wind}$ increases from 0.5 $\mathrm{m}/\mathrm{s}$ to 5.0 $\mathrm{m}/\mathrm{s}$. In the event of a large toxic gas leak or windy meteorological conditions, the toxic cloud passes over residential areas quickly, causing the outdoor concentration to drop below the indoor concentration in a shorter period. Therefore, if a SIP order is issued, it may be necessary to reconsider the evacuation strategy, as remaining indoors for an extended period could result in higher toxic exposure than evacuation.

3.3. Results for Various Wind Speeds and Mass Flow Rates

Figure 6 shows the concentration contours and the affected regions for various wind speeds and mass flow rates. For a fixed mass flow rate, $\dot{m}=2.0\mathrm{kg}/\mathrm{s}$, the size of the toxic cloud region contracts in all directions as wind speed increases from $0.5\mathrm{m}/\mathrm{s}$ to $5.0\mathrm{m}/\mathrm{s}$, as shown in Figure 6a,b. In contrast, for a fixed wind speed, $V_{wind}=0.5\mathrm{m}/\mathrm{s}$, the toxic cloud region expands in all directions as the amount of leak increases from $0.1\mathrm{kg}/\mathrm{s}$ to $2.0\mathrm{kg}/\mathrm{s}$, as shown in Figure 6c,d.

Figure 7 shows the retention time, maximum concentration, and average concentration at various wind speeds and constant mass flow rate, $\dot{m}=2.0\mathrm{kg}/\mathrm{s}$. This figure highlights how retention time changes with wind speed. As the wind speed increases, the retention time decreases due to the stronger influence of advection. However, the maximum concentration remains nearly constant regardless of wind speed, as it is primarily determined by the mass flow rate. While the concentration at the core of the toxic gas cloud remains unchanged, the concentration in the outer regions of the cloud decreases as the cloud disperses. For a large leak, $C_{max}$ remains constant across different wind speeds. As a result, it may be hazardous to go outside, even briefly, since exposure to a high concentration is likely. In this case, the SIP method is preferred because high wind speeds facilitate the rapid removal of toxic clouds. At low wind speeds, the difference between $C_{max}$ and $\overline{C}$ becomes larger because convection and diffusion occur more slowly, leading to a more prolonged exposure to toxic gases.

Figure 8 illustrates the retention time, maximum concentration, and average concentration at various mass flow rates for a constant wind speed, $V_{wind}=5.0\mathrm{m}/\mathrm{s}$. Unlike wind speed, changes in the mass flow rate affect both the maximum and average concentrations. As the mass flow rate increases, both $C_{max}$ and $\overline{C}$ increase, as a larger amount of leakage introduces more toxic material into the environment. However, the retention time remains constant despite the increased mass flow rate. This is because, at a fixed wind speed, the advection rate, which plays a critical role in toxic cloud dispersion, does not change. In Figure 7 and Figure 8, it is notable that when the ratio of $C_{max}$ to $C_{avg}$ approaches 1, the concentration profile resembles a “top-hat” shape, as previously shown in Figure 4d and Figure 5d.

The maximum outdoor concentration is a crucial parameter for assessing the toxic effects on human health. With the same amount of total exposure concentration over time, exposure to a higher peak concentration causes more fatal hazards to health. This concept is captured by the toxic load and given by [31]

$$\begin{array}{ccc}\hfill \mathrm{Toxic}\mathrm{Load}& =& {\int }_0^{\infty }C{\left(t\right)}^{n}dt\hfill \end{array}$$

(9)

where n is the dimensionless toxic load exponent, which indicates how much more dangerous to health the exposure to a high toxic concentration is compared to low-concentration exposure [32].

Near the source ($d=500m,1000m$ in Figure 7), $C_{max}$ remains constant across various wind speeds, whereas at far field ($d=3000m$ in Figure 5), $C_{max}$ decreases from 55 $\mathrm{ppm}$ to 30 $\mathrm{ppm}$ as the wind speed increases from 0.5 $\mathrm{m}/\mathrm{s}$ to 5.0 $\mathrm{m}/\mathrm{s}$ for a large mass flow rate ($\dot{m}=2.0\mathrm{kg}/\mathrm{s}$). This behavior can be attributed to the initial outlet velocity of the leak, which is much greater than the ambient wind velocity. As a result, the inertia of the toxic cloud dominates the advection process near the release point. Consequently, people close to the release site are exposed to critical toxicity levels regardless of the wind speed, making it imperative to initiate protective actions immediately to avoid exposure to peak toxic concentrations. However, as the toxic cloud moves further from the source, the inertia of the toxic cloud decays and the cloud begins to disperse more gradually, driven primarily by the wind. At this stage, the effect of the initial outlet velocity becomes negligible, and the wind velocity plays a more significant role in the cloud’s dispersion.

At a high wind speed, $C_{max}$ increases with mass flow rate, even near the source, as shown in Figure 8. Here, wind velocity becomes a key determinant of the $C_{max}$ value. However, at a low wind speed ($V_{wind}=0.5\mathrm{m}/\mathrm{s}$), $C_{max}$ remains constant near the source, regardless of variations in mass flow rate. This occurs because the influence of mass flow rate becomes relatively more dominant than the low wind speed. Note that $C_{max}$ for all four cases presented in Figure 4 remains approximately 140 $\mathrm{ppm}$, reinforcing the observation that, near the source, high concentrations persist even with small leaks and low wind speeds. Overall, from Figure 4, Figure 7 and Figure 8, the effectiveness of wind speed and mass flow rate on $C_{max}$ is summarized in the table. Near the source, as presented in

Table 5. Maximum concentration near source.

${\mathit{V}}_{\mathit{wind}}$	Small $\dot{\mathit{m}}$ (0.1 kg/s)	Large $\dot{\mathit{m}}$ (2.0 kg/s)
Low (0.5 $\mathrm{m}/\mathrm{s}$)	143 $\mathrm{ppm}$	132 $\mathrm{ppm}$
High (5.0 $\mathrm{m}/\mathrm{s}$)	15 $\mathrm{ppm}$	139 $\mathrm{ppm}$

, the maximum concentration remains high, even with small leaks and low wind speeds. It only decreases significantly under conditions of high wind speed and small leak rates.

4. Evacuation Decision Matrix

There are two primary strategies, for reducing casualties during wildfires [33] or chemical accidents: evacuation and SIP. SIP is a protective action to provide public safety by going indoors and following the recommended instructions [34]. Evacuation, on the other hand, involves the controlled relocation of a population from an area of known danger or unacceptable risk to a safer location [35]. Several kinds of research have been performed to investigate the health effects when applying the above two strategies. Chan et al. [36,37] quantified the effectiveness of SIP by calculating the population that would be exposed to toxic load limits indoors and outdoors. The comparison to the reference concentration, such as Emergency Response Planning Guideline (ERPG), Immediately Dangerous to Life or Health (IDLH), Time-Weighted Average (TWA), etc., may be useful to investigate the harm to health during the evacuation or SIP. These critical exposure thresholds help define protective action decisions [14] and develop shelter trees [35]. However, the critical concentration alone does not directly determine whether evacuation or SIP is the better strategy, as it does not control indoor or outdoor concentrations. Instead, the decision must be based on key factors, including report time, toxic cloud arrival/removal time, and indoor/outdoor concentration profiles relative to the distance from the release point. Fundamentally, the choice of the lower exposure concentration between evacuation and SIP is made by comparing indoor and outdoor concentrations. A new decision matrix is developed considering report time, arrival time, and indoor/outdoor concentration.

4.1. A New Decision Matrix

The decision matrix in Figure 9a suggests five protective action plans, which include two cases where people should stay inside (SIP) and three cases where evacuation is required. The first SIP scenario, labeled ➁, occurs when there is insufficient time to prepare for evacuation, even if the toxic cloud has not yet reached the inhabited area. For example, if evacuation preparations are not completed by the time the toxic cloud arrives (e.g., $t_i$ 9:10 a.m.), SIP should be implemented immediately. The remaining time should be used to issue SIP instructions, such as closing windows, turning off HVAC systems, sealing doors, and selecting appropriate shelter rooms [38]. The second SIP scenario, labeled ➂, occurs when the indoor concentration is lower than the outdoor concentration. If the chemical accident is reported after the toxic cloud has already arrived (e.g., 9:15 a.m.), those already indoors should continue to shelter in place, while people outside should seek shelter in the nearest available building. On the other hand, if the indoor concentration becomes higher than the outdoor concentration, a change of evacuation decision needs to be considered and the evacuation should be ordered, like case ➃. In addition to that, two evacuation scenarios are identified. Case ➀ occurs if there is sufficient time to prepare for evacuation before the toxic cloud arrives (i.e., report time + preparation time < arrival time). In this case, the public should be instructed to evacuate. Case ➄ occurs once the toxic cloud has dissipated, allowing for safe evacuation.

The decision tree in Figure 9b provides a detailed explanation of the logic behind the decision matrix in Figure 9a. The top tier in the evacuation decision tree is the report time, which plays a crucial role in minimizing the loss due to chemical accidents. Once the chemical accident is reported, a corresponding response procedure will be prepared. The speed of this initial report is critical, as a prompt report allows for the consideration of all five possible cases (Cases ➀ to ➄) before the toxic cloud arrives. However, if the accident is reported after the toxic cloud has already arrived, only three protective action options remain (Cases ➂, ➃, and ➄). Furthermore, if the first report contains valuable data on wind speed and the amount of leakage as discussed earlier, a more accurate decision on the evacuation method along the distance from the chemical accident location may be performed. Recognizing the importance of timely reporting, the Korean Chemical Control Act enacted in 2015 mandates that chemical accidents must be reported within 15 min of their occurrence, ensuring a rapid response and minimizing potential harm.

For the establishment of a risk management plan, local governments and chemical companies should prepare the protective plans in advance by simulating a virtual scenario and collecting information on how to respond to each imaginary accident scenario. This will enable the public to know when to terminate SIP and prepare for evacuation during a chemical accident. The chemical companies may apply the decision matrix developed in this study to their own risk management plans by possessing equipment to measure the local weather condition and choosing the appropriate scenario based on the collected information. This will finally lead to minimizing the exposure concentration of hazardous chemicals and casualties.

4.2. Algorithm for an Evacuation Decision

Several studies have been conducted on algorithmic models for evacuation in the event of a chemical accident. Xu et al. [39] proposed the model and algorithm for dynamic emergency route planning by considering the evacuation speed of different population types and various risk components. Gai et al. [40] optimized the multi-objective evacuation routing to minimize travel time and individual evacuation risk. The algorithm for the new evacuation decision matrix has been developed, as shown in Figure 10. The algorithm consists of six inputs, including four time variables ($t_c$, $t_{pre}$, $t_i$, $t_e$) and two concentration variables ($C_{indoor}$, $C_{outdoor}$). The current time, $t_c$, is defined as the time when the chemical accident is reported and announced to the public. The preparation time for evacuation, $t_{pre}$, is defined as the required time to escape from the current location, which depends on age, gender, previous experiences, etc., and it can be estimated through regular training.

In the evacuation decision algorithm, the first step in determining evacuation strategies involves comparing $t_c$ and $t_i$, as the appropriate evacuation method depends on whether the current location is enveloped by toxic gas. If $t_i>t_c$, indicating that the toxic gas has not yet reached the current location, the next step is to compare $t_{pre}$ with $(t_i-t_c)$ to evaluate whether sufficient time is secured for evacuation preparation. Finally, if sufficient preparation time for evacuation is available before the toxic cloud arrives, i.e., $(t_i-t_c)-t_{pre}>0$, the public can decide to leave the residential area. On the other hand, if $(t_i-t_c)<t_{pre}$, indicating that the public cannot evacuate the site before the toxic gas arrives, the SIP method takes priority. The comparison process is then iteratively repeated using a loop algorithm until either the toxic gas disperses from the site or the indoor concentration exceeds the outdoor concentration, prompting a shift in the evacuation strategy from SIP to evacuation. Now, when the current time is between the toxic cloud’s arrival and removal time, i.e., $t_i<t_c<t_e$, the comparison of $C_{indoor}$ and $C_{outdoor}$ is necessary to determine the appropriate time to evacuate. In this scenario, the SIP method is maintained until either $t_c>t_e$ or $C_{indoor}>C_{outdoor}$, indicating that remaining indoors has become more hazardous than evacuating to the outside.

In practical application, the evacuation time of $t_e$, which equals $(t_i+t_r)$ in Equation (5), can be estimated. The retention time, $t_r$, can be obtained from the simulation in advance, like Figure 2, and $t_i$ can be recognized once the toxic cloud arrives in the region. Therefore, during the SIP, the public can calculate the remaining time ($t_e-t_c$) to evacuate. The best-case evacuation scenario is for $(t_i-t_c-t_{pre}>0)$ where there is no damage from hazardous materials. The worst-case evacuation scenario is for $(t_c>t_e)$ where the toxic clouds already overwhelm the inhabited area and the toxic loads accumulate completely over the entire time.

Many studies have been performed to determine the more effective method between evacuation and SIP during chemical accidents. However, existing approaches typically recommend selecting one of these two methods without considering the possibility of switching between the two. They also fail to specify the optimal timing for changing from SIP to evacuation or vice versa, even though such transitions may be necessary in some scenarios. Most previous studies focus on parameters like the critical dose of hazardous chemicals and the arrival time of toxic clouds. However, in practice, more critical factors are the indoor concentration of toxic substances and the report time of the accident. This is because comparing the indoor concentration to the outdoor concentration provides a clear indication of the optimal time for evacuation. In contrast, comparing the critical dose to the indoor concentration does not offer sufficient information to determine whether to stay indoors or evacuate. To address these limitations, a new decision matrix has been developed, which considers both the arrival time of the toxic gas and the comparison of indoor and outdoor concentrations. In this matrix, the report time is positioned at the top of the decision tree, serving as the first step in determining the appropriate protective action. By comparing the report time with the arrival time of the toxic cloud and the evacuation preparation time, this approach enables the formulation of a more accurate and timely protective action plan.

5. Conclusions

A new evacuation decision matrix has been developed using five key parameters: report time, toxic cloud arrival/removal time, and indoor/outdoor concentrations. CFD simulations were conducted to assess the impact of mass flow rate and wind speed on these decision parameters. The results show that higher wind speeds mitigate the toxic effect by dispersing the cloud more rapidly, but they also cause indoor concentrations to exceed outdoor levels more quickly due to strong advection. For a small mass flow rate ($\dot{m}=0.1\mathrm{kg}/\mathrm{s}$), the indoor concentration begins to rise at 8 min and surpasses the outdoor concentration at 25.9 min. In contrast, for a large mass flow rate ($\dot{m}=2.0\mathrm{kg}/\mathrm{s}$), these times are significantly reduced to 1 min and 15.2 min, respectively, due to faster outlet velocity and increased leakage. As the wind speed increases from 0.5 $\mathrm{m}/\mathrm{s}$ to 5.0 $\mathrm{m}/\mathrm{s}$, the equilibrium concentration decreases from 13.9 $\mathrm{ppm}$ to 3.4 $\mathrm{ppm}$, while the time for indoor concentrations to exceed outdoor levels is reduced by one-third, from 48.9 min to 16.0 min, due to reduced toxic cloud retention time and maximum concentration. Moreover, the equilibrium time decreases by 41% from 25.9 min to 15.2 min as $\dot{m}$ increases from 0.1 kg/s to 2.0 kg/s, and by 67% from 48.9 min to 16.2 min as $V_{wind}$ increases from 0.5 $\mathrm{m}/\mathrm{s}$ to 5.0 $\mathrm{m}/\mathrm{s}$.

The change of evacuation order from shelter in place to evacuation must be considered immediately in conditions of high wind speed, as the termination time for SIP becomes much shorter. This occurs because the outdoor concentration profile transitions from a “mountain” shape to a “top-hat” shape, leading to a significant reduction in the toxic cloud retention time as wind speed increases. The retention time of toxic clouds increases with distance due to the accumulation of dispersive toxic clouds. Even though the retention time at 0.5 $\mathrm{km}$ (13.8 $\min$) is shorter than that at 3.0 $\mathrm{km}$ (23.3 $\min$), the total exposure concentration at 0.5 $\mathrm{km}$ during the retention time is approximately 2.5 times higher than that at 3.0 $\mathrm{km}$. As a result, the termination time of shelter in place takes longer as the distance from the leak source increases. In the case of a large leak, the preparation time for evacuation is not sufficient for the public near the release point; hence, immediate SIP should be planned in advance.

The dispersion of toxic clouds varies with the distance from the release point. the maximum concentration remains high even in cases of small leaks and low wind speeds, except in the case of a small leak combined with high wind speed. Therefore, in scenarios involving low wind speed or a large mass flow rate, it is essential to pre-plan the SIP strategy, as exposure to higher peak concentrations poses a more severe health risk according to the concept of toxic load. At greater distances from the source, the mass flow rate becomes a more significant factor affecting the maximum concentration, regardless of wind speed. Changes in the mass flow rate at both low and high wind speeds have a noticeable impact on maximum concentration levels at far-field locations. The simulations in this study were conducted under the assumption of an air exchange rate of 0.7. However, for practical applications, it is crucial to account for the porous media effects of windows, doors, and other openings that may influence the air exchange rate and, consequently, the indoor concentration of toxic gases.