Evacuation route optimization under real-time toxic gas dispersion through CFD simulation and Dijkstra algorithm

Highlights

• An approach for route optimization under toxic gas dispersion is proposed.

• The modified algorithm combining CFD results and Dijkstra algorithm is presented.

• The real-time toxic gas dispersion is performed by CFD simulation.

• Effect of pre-evacuation time on the route optimization is investigated.

• Effect of safety protection on the route optimization is quantified.

Abstract

Evacuation route optimization plays an important role in safe evacuation for toxic leakage accidents. We propose an approach for route optimization under real-time toxic gas dispersion by combining computational fluid dynamics (CFD) code and the Dijkstra algorithm. CFD code is used to simulate the toxic gas dispersion to predict the spatial-temporal distribution of concentrations, which is related to the calculation of the inhaled dose. Taking the dose as the weights of arcs, the concentrations predicted by CFD are embedded into the modified Dijkstra algorithm to calculate the optimal route with minimal total inhaled dose. The results show that the time before evacuation affects the evacuation route optimization, and the death probability exhibits an “S”-shaped growth as time increases. The optimal route may vary with wind direction dominating the direction of toxic gas dispersion because of the change of weights of arcs. Workers wearing protective equipment are allowed to pass through areas with high-concentration toxic gas, and the length of the optimal evacuation route decreases with the level of safety protection. The proposed methodology with appropriate modification is suitable for evacuation route optimization in fires.

Introduction

The chemical industry involves a large number of toxic substances, including hydrogen fluoride, chlorine, etc. Due to personnel operation faults, equipment failure, and poor safety management, toxic gas leakage accidents may occur in chemical plants (Gai et al., 2018). Toxic gases are released and follow the air to diffuse in chemical plants, posing a serious hazard to the exposed workers. For example, on April 16, 2004, a leakage accident of chlorine occurred in Chongqing city of China, causing nine people to be killed and about 150,000 people to be evacuated (Yu et al., 2009). When such an accident occurs, there are two feasible protective actions: one is to shelter in place, and the other is to evacuate to safe areas. Shelter cannot provide an adequate level of protection; therefore, people are commonly protected through evacuation (Xu et al., 2021). There are many routes for people to travel from the affected area to the safe area. If there is one route with the minimal inhaled dose during the emergency evacuation, the evacuee is hardly harmed when traveling along this route. Therefore, under real-time toxic gas dispersion, it is of great significance for reducing the consequences of accidents to find an optimal route with the minimal inhaled dose.

The shortest path (SP) algorithms have been employed to solve various problems of route optimization, including the Dijkstra algorithm, the Bellman–Ford algorithm, and the Floyd–Warshall algorithm (Goodrich and Tamassia, 2014). This method converts the disaster parameters (such as path length, travel time, toxic gas concentration, and thermal radiation) into weight values and assigns the weights to arcs. The SP algorithm can find a route with the smallest sum of weights, which is also called the optimal route. As a common SP algorithm, the Dijkstra algorithm has been widely invoked for route optimization (Fabiano et al., 2005; Dou et al., 2019). Yuan et al. (2009) modified the Dijkstra algorithm, taking into account the influence of the travel speed on route optimization. The speed was expressed as a continuous decrease function with respect to time, and the travel time was taken as the optimized goal to calculate the optimal evacuation route under the real-time effect of disaster extension. Chen et al. (2018) solved the two-way route planning model by using Dijkstra algorithm. Sun et al. (2020) converted failure probability into risk entropy to represent the weight of arc. The Dijkstra algorithm was employed to find the shortest path of accident escalation. Feng et al. (2020) used the Dijkstra algorithm to solve the model, whose objective was to minimize the cost and transport length when the location of emergency supplies repositories was selected.

Recently, evacuation route optimization related to toxic leakage accidents is attracting more attention of researchers. Xu et al. (2021)presented a modification of the Dijkstra algorithm to solve the multi-objective problem for emergency route planning of the ammonia leakage accidents. The ammonia concentration of each arc was estimated by the Gaussian plume model to calculate the toxicant dose, so that health consequences of the evacuee could be calculated. They took one or more factors in health consequences or evacuation time as the optimized goal to prove the feasibility of the modified algorithm. Shen et al. (2015) used the Gaussian plume model to calculate the concentration distribution of chlorine in the chemical park. The concentration was integrated as the toxic dose inhaled by personnel, which was as weight assigned to each arc. They used the Dijkstra algorithm to calculate the optimal route to the emergency shelter with minimal total weight. Gai et al. (2017) used the Areal Locations of Hazardous Atmospheres (ALOHA) model to predict the toxic gas concentration and modified the Dijkstra algorithm. Based on the Pareto-optimal theory, they established heuristic algorithms to minimize evacuation time and individual evacuation risk along a route, verifying the multi-objective optimization model.

It is worth noting that previous studies, related to the route optimization for toxic gas leakage accidents, used the gas concentration generated by integral models (such as ALOHA model, Gaussian plume model, etc.) to calculate the weights. However, compared with numerical models, the concentration predicted by computational fluid dynamics (CFD) software (such as ANSYS-Fluent, CFX, etc.) is more accurate. CFD software can simulate the indoor and outdoor dense gas dispersion, and the predicted concentrations of dense gas showed good agreement with the experimental results (Dong et al., 2017; Tan et al., 2018a, 2018b; Tauseef et al., 2011; Xing et al., 2013). Most importantly, CFD software can simulate the gas flow over complicated geometries and predict the concentration fields with multiple large obstacles, while numerical models fail to make it (Dong et al., 2017; Pontiggia et al., 2010; Tan et al., 2018b; Xing et al., 2013). These obstacles cause wakes, stagnating zones, recirculation, and preferential paths to arise in wind fields, thereby changing wind velocity and wind direction, which greatly affects the toxic gas dispersion and the distribution of concentrations (Pontiggia et al., 2010). There are many large obstacles, such as equipment and buildings, in the chemical plants, indicating that CFD simulation is more suitable for the prediction of toxic gas concentrations. When one employs the SP algorithm to calculate the optimal evacuation route, the accuracy of toxic gas concentrations directly affects the optimization result.

In our study, CFD software ANSYS-Fluent (version 19.0) is utilized to simulate real-time toxic gas dispersion, so as to obtain more accurate concentrations of toxic gas. Next, the concentrations are embedded into the Dijkstra algorithm to calculate the optimal evacuation route under real-time toxic gas dispersion. The modified algorithm can provide decision support for emergency response for toxic gas leakage accidents occurring in chemical industries.