Research on the Evolution Models and Risk of Disaster-Induced Storage Tank Explosions in a Smart City

Abstract

An important goal of smart cities is to ensure city safety and reduce city risks. However, because the chemical industry park is often located interior and surroundings of a city, it is easy to induce explosions in case of natural disasters, causing serious losses. To investigate the possibility of explosion damage to other storage tanks in chemical industrial parks caused by tank explosions, the evolution process of tank explosion damage was studied, and an analysis method to determine the most unfavorable process was provided. This method is based on regional grid division and shock wave overpressure calculation to obtain the probability of damage at the grid location. Based on the system fault evolution process, the space fault network model was used to calculate the explosion damage evolution process of each storage tank, and the most unfavorable situation was finally determined. The paper assumes a positive linear relationship between the damage probability of the affected storage tank and the likelihood of explosion. The paper provides a calculation method for regional grid division, tank explosion overpressure, and damage probability. A mathematical model for the evolution process of tank explosion damage was constructed, and it is believed that the damage effects of tanks are a logical superposition. The results can provide a reference for controlling the explosion process in chemical industrial parks under the most unfavorable conditions and realize intelligent analysis and prediction of regional risks.

1. Introduction

Research on city safety based on a smart city is one of the main tasks of smart cities. The rapid development of cities has led to unreasonable city planning. In particular, the chemical industrial parks exist around and even inside the city, its danger is huge. When a storage tank explosion occurs in chemical industrial parks for some reason, it will have a serious impact on the surrounding city. Therefore, smart city not only needs real-time monitoring of chemical industrial parks but also needs appropriate mathematical models to predict the possibility, scope, and extent of these risks. Especially when the city encounters natural disasters, leakage, fire, and explosion in the chemical industrial parks will be the inevitable result. The serious impact on the city is a problem that smart city needs to focus on.

At present, the research on fire and explosion in chemical industrial parks caused by various disasters is increasing gradually. A case study of human and infrastructure vulnerability from floating tank explosions in chemical plants [1]; Simulation of LPG storage tank explosion accident scenario [2]; Acrylate storage tank explosion accident [3]; Effect of roof explosion on roof performance under multi-field coupling [4], etc. These results study multiple explosion cases, from which we understand the interaction between the explosion process and tank protection. The initial explosion of the storage tank in the chemical industrial parks will lead to the subsequent explosion process of the other storage tanks may also be different. This is of course related to the volume and substance of the storage tank itself, but also related to the relative position between the storage tanks, but also to consider the superposition of multiple storage tank explosions. So in the case of limited human, financial, and material resources, how to prevent the first explosion of key storage tanks and avoid the most adverse consequences has become the core issue of research. In a smart city, these safety issues require responsive theories and algorithms to predict, prevent, and handle. The latest researches on smart city safety include information fusion methods in smart city and city environments [5]; Intelligent city safety Human intelligent system [6]; Sustainable service intelligent fire safety management [7]; Artificial Intelligence changes city environment in a smart city [8]; Safety and smart city [9]; Fire safety management Policy for smart cities [10]; smart city public safety data resource management [11]; Artificial intelligence video surveillance to solve public security problems [12]. These studies study smart city safety from multiple perspectives, but they can not provide an effective mathematical model for the role. Because the mathematical model of the tank explosion process is missing. The existing research makes it difficult to achieve the goal of smart city safety from this perspective.

To realize the safety of a smart city, natural disasters that may cause storage tank explosions in chemical industrial parks are studied. To understand the mechanism of storage tank explosion induced by natural disasters, the impact of chemical industrial park explosions on the city, and its intelligent prediction and warning. Finally, the mathematical description of the evolution process of explosion damage of storage tanks is established. The evolution process of the most unfavorable explosion damage of the storage tank was determined, and the basis for preventing explosion accidents was provided. It also provides the basic theory for realizing the safety of a smart city.

This paper unfolds as follows: Section 2 covers related work; Section 3 details our methodology and proposed method; Section 4 presents the implementation details, experimental results, and analysis. Finally, Section 5 draws conclusions.

2. Related Work

2.1. Smart City and City Safety

Smart city refers to the realization of city planning, construction, management, and service of comprehensive intelligence and information through advanced technologies such as the Internet of Things, big data, cloud computing, and artificial intelligence. Smart cities are highly interconnected, data-driven, automated, and intelligent, as well as convenient and efficient.

These characteristics make smart city play an important role in improving city management efficiency, optimizing city services, and improving citizens’ quality of life. City safety means that the city maintains stable, orderly, and coordinated development in various fields such as politics, economy, society, culture, and ecological environment, and does not pose a threat to the safety of citizens’ lives and property. City safety is an important guarantee for the sustainable development of the city and is the cornerstone of maintaining social stability and improving the quality of life of residents. However, city safety is faced with many challenges, such as natural disasters and social security problems.

In a smart city, city safety is an important factor. Smart cities can improve the city safety level more effectively by using advanced technologies. For example, the intelligent transportation system can monitor the traffic situation in real-time, optimize the traffic flow, and reduce the occurrence of traffic accidents. Through the intelligent security system, it can monitor the city’s public security situation in real-time, and predict and prevent the occurrence of security incidents; Through the emergency incident response platform, you can quickly locate the incident, analyze the response strategy, and provide accurate and rapid response and rescue.

Relevant studies include deep learning for IoT-based smart city security [13], assessing and forecasting collective urban heat exposure of smart cities [14], offloaded task execution for fog-enabled smart cities [15], edge AI-based smart intersection for traffic signal [16], et al. Smart cities can also improve the capability of a city to respond to natural disasters. Through big data analysis and cloud computing technology, the occurrence probability and impact scope of natural disasters can be predicted, providing a scientific basis for city disaster prevention and reduction. Smart devices and systems in smart cities can also provide strong support for disaster relief and improve rescue efficiency.

Therefore, smart city and city safety complement each other. The construction of a smart city helps to improve the level of city safety, and the demand for city safety also promotes the development of smart cities. With the continuous progress of technology and the continuous expansion of application scenarios, smart cities will play a greater role in the field of city safety.

2.2. Natural Disasters Causing Tank Explosion

The natural disasters that induce tank explosions mainly include earthquakes, typhoons, and floods. Relevant studies include chemical industry disaster risk assessment [17], dynamic risk assessment of spherical storage tanks [18], hydrogen explosion characteristics and disaster effects [19], typhoon-induced domino accidents in storage tank areas [20], quantitative explosion process hazard analysis [21], etc.

The ground shaking during the earthquake is mainly divided into horizontal and vertical directions. Strong ground vibration in the horizontal direction will seriously affect the stability of the storage tank. The effects of the earthquake will extend to the walls of the tank, resulting in irregular bumps and wrinkles. These deformations develop further and may form holes and even lead to local fractures. In addition, the seismic horizontal force will also cause the tank and the medium to shake, making the connection between the tank top and the tank wall failure. For the external floating roof tank, the primary and secondary sealing structure between the floating plate and the tank wall may fail, resulting in the leakage of the medium in the tank. The welds and anchorage joints of storage tanks that have been used for a long time can also be damaged by the vertical forces of an earthquake.

The process of tank explosion induced by the earthquake may be strong ground vibration in the horizontal direction → shaking of tank body and medium → irregular concave-convex and wrinkle of tank wall → hole formation → local instability → medium leakage in cracked tank → tank explosion.

The principle of storage tank explosion induced by typhoon involves many aspects. First of all, the typhoon generates wind load on the storage tank, and when the wind force exceeds the design wind load of the storage tank, the storage tank structure may be damaged. Secondly, the typhoon will cause a decrease in atmospheric pressure, which may cause the internal pressure of the storage tank (gauge pressure) to exceed the design value, resulting in tank overpressure. In addition, the heavy rainfall brought by the typhoon may also increase the humidity around the storage tank, which will have a corrosive effect on the material and structure of the storage tank, further reducing its safety.

The process of tank explosion induced by typhoon may be: Typhoon produces wind load on the tank → tank overpressure → tank structure damage → tank leakage → tank explosion.

The flood may directly impact the storage tank, especially when the flood side impacts the horizontal storage tank at a certain Angle, the impact force can cause damage to the storage tank structure. Tank size and load level play a key role in this scenario. In general, the larger the size of the storage tank, the closer the flood impact force may be to the situation under the positive Angle impact, and the more likely it is to fail. On the contrary, for the same type of storage tank, the larger the loading level, the smaller the impact force on the storage tank, and the storage tank is relatively safer. Flooding may cause the tank foundation to loosen or shift, which will affect the stability of the tank. Foundation failure can cause tanks to tilt or deform, which can lead to tank breakage or leakage. If flammable and explosive substances are stored in the tank, flood immersion may cause these substances to come into contact with moisture, which in turn triggers a chemical reaction or accelerates the decomposition of the substance. These chemical reactions can produce heat, gas, or other flammable substances, increasing the risk of explosion. On top of that, if there is a leak in the tank, the leaking flammable material may mix with the air to form an explosive mixture. In flood areas, there may be other ignition sources, such as short circuits in electrical equipment, frictional sparks, or lightning, which may ignite explosive mixtures and cause explosions.

The process of tank explosion induced by flood may be a direct impact of flood on tank →loosening or displacement of tank foundation → tank inclination or deformation → tank structure damage → tank rupture or leakage → tank explosion.

Therefore, to prevent the explosion of storage tanks caused by natural disasters, a series of measures need to be taken, including strengthening the structural design of storage tanks, improving the seismic, wind resistance, and flood control capacity of storage tanks, regular safety inspection and maintenance, and establishing sound emergency plans. Take timely countermeasures to reduce the impact of natural disasters on storage tank safety. These natural disasters may lead to the explosion of storage tanks, so considering the impact of these natural disasters is the basis for smart cities to ensure the safety of chemical industrial parks.

2.3. Impact of Chemical Industrial Parks and Intelligent Prediction-Warning

The explosion of chemical industrial parks has many effects on the city and usually has serious consequences. The explosion may lead to a large number of casualties and pose a direct threat to the life and safety of city residents. The explosion may cause a fire, further aggravate the harm degree of the accident, and may produce toxic and harmful smoke, posing a threat to the health of city residents. Explosions may also cause damage to city infrastructure, such as buildings, roads, Bridges, etc., affecting the normal operation of the city. Relevant studies include evaluating the spatial layout of fire stations in chemical industrial parks [22], chemical industrial park safety in China [23], emergency evacuation behavior rules of pedestrians under fire and explosion [24], considering the domino effect and the identification of major hazard [25,26], et al.

To reduce the impact of chemical industrial park explosions on the city, the intelligent prediction and early warning system of smart cities plays a vital role. These systems utilize advanced technologies, such as the Internet of Things, big data, cloud computing, and artificial intelligence, to conduct real-time monitoring and early warning of the safety status of chemical industrial parks.

Specifically, the intelligent prediction and early warning system can monitor the key parameters such as temperature, pressure, and gas concentration in the chemical industrial parks in real-time, and immediately start the alarm mechanism once it is abnormal. For example, the temperature sensor can accurately sense the temperature change of the equipment and the environment during the casting process, find abnormally high temperatures, immediately start the alarm mechanism, stop production in time, or take cooling measures to prevent fire and explosion caused by overheating. Pressure sensors detect internal pressure fluctuations during production. When the pressure exceeds the threshold, a warning signal is sent immediately to prevent device rupture caused by high pressure. The gas sensor can detect the concentration of combustible gases and toxic and harmful gases in the air in real time, and effectively prevent the accumulation of gas leaks resulting in explosions or poisoning accidents.

In addition to real-time monitoring, the intelligent prediction and early warning system of smart cities can also identify possible safety risks and risk points in advance through data analysis and model prediction. Based on historical data and real-time monitoring data, the system can establish a risk assessment model to accurately predict the safety situation of chemical industrial parks. When a safety accident is predicted, the system automatically triggers the early warning mechanism to remind personnel to take countermeasures to avoid the accident or reduce the impact of the accident.

In addition, the intelligent prediction and early warning system can also be integrated with other security management systems to form an integrated safety management platform. Through information sharing and collaborative work, all systems can jointly improve the safety management level of chemical industrial parks and reduce the probability of safety accidents.

In general, the intelligent prediction and early warning system of smart cities plays a crucial role in the safety management of chemical industrial parks. Through real-time monitoring, data analysis, and early warning mechanisms, they can effectively reduce the impact of chemical industrial park explosions and other safety accidents on the city, and protect the life and property safety of city residents and the normal operation of the city. Of course, it requires an effective storage tank explosion process mechanism in chemical industrial parks, to realize the smart city to predict, prevent, and control the risks caused by storage tank explosions in chemical industrial parks to the city in the case of natural disasters, to ensure the safety of the city.

3. Proposed Method

3.1. Overpressure Calculation of Storage Tank Explosion

The main accidents in chemical industrial parks are pool fires, flash fires, fireballs, and jet fires. The explosions involved are divided into the following types: confined vapor cloud explosion (CVCE), boiling liquid expanding vapor cloud explosion (BLEVE), vapor cloud explosion (UVCE), and dust explosion (DE). The destructive energy of pool fire and fireballs is much greater than that of jet fire. The conditions of flash fire are almost the same as those of a vapor cloud explosion, but the explosion energy is much smaller than that of a vapor cloud. Fireballs and BLEVE also occur under almost the same conditions. Pool fire is thermal radiation and UVCE is shock wave. The former must be heated at a relatively close distance and continuously if the interaction between tanks is to increase the damage probability; the latter can still cause other tank damage at a longer distance through an overpressure shock wave. On the other hand, if thermal radiation and shock waves are considered, the shock wave will cause damage to the storage tank before the thermal radiation and make it explode. Therefore, the shock wave generated by the explosion overpressure of the storage tank is used as the interaction to study the explosion damage evolution of the remaining storage tanks after setting the initial explosion tank.

The idea of grid division is to divide the parking area to form a griding matrix. The region is divided into small parts in the form of a matrix, and the segmented region is used as the unit of calculation [27,28]. The variation of various parameters in a small region is relatively stable, and the gradient changes in adjacent regions. The damage probability distribution caused by the explosion is also represented by a griding matrix. At the same time, MATHLAB has high efficiency for matrix superposition calculation, which is suitable for calculating the evolution process of explosion damage to storage tanks. When the storage tank is damaged and a spherical vapor cloud is formed, an explosion occurs.

The instantaneous explosion shock wave is estimated with TNT equivalent, as shown in Equation (1).

$$W_{TNT}=\frac{1.8\alpha W_f{Q}_f}{Q_{TNT}}$$

(1)

In the equation, $\alpha$ is the vapor cloud equivalent coefficient, 0.02–14.9%, and its value is set to be 44%; $W_f$ is the total mass of fuel in the vapor cloud, Kg; $Q_f$ is the combustion heat of fuel, KJ/kg; $Q_{TNT}$ is the explosive heat of fuel, and its value is set to be 4120–4690 KJ/kg.

Various parameters of the shock wave are generally expressed by the proportional distance $z_e=r/{W_{TNT}}^{1/3}$, where r is the distance between the measuring point and the explosion source, /m. The relationship between the lateral peak overpressure of TNT explosion on flat ground and z_e is shown in Equation (2). The overpressure function relationship can be obtained by synthesizing the above-shown process $\Delta p$.

$$\frac{\Delta p}{p_0}=\frac{1616[1+{(\frac{z_e}{4.5})}^2]}{\sqrt{1+{(\frac{z_e}{0.048})}^2}\sqrt{1+{(\frac{z_e}{0.32})}^2}\sqrt{1+{(\frac{z_e}{1.35})}^2}}$$

(2)

In the equation: $\Delta p$ is the peak explosion overpressure at r, Pa; b is the surrounding environment pressure, Pa.

For the studied chemical industrial parks with multiple storage tanks, $X$ is set to represent the region-wide boundary, /m; $x\in \left\{0,1,\dots ,X\right\}$ is the coordinate of the grid-wide edge; $Y$ represents the region-high boundary /m; $y\in \left\{0,1,\dots ,Y\right\}$ is the coordinate of the grid-high edge. $O$ is the set of tanks, $O=\left\{o_1,\dots ,o_N\right\}$, $N$ is the number of tanks, $n\in \left[1,N\right]$ and $o_n$ is the nth tank. The coordinate of $o_n$ is $(x_n,y_n)$. For all positions $x,y,x\in \left\{0,1,\dots ,X\right\},y\in \left\{0,1,\dots ,Y\right\}$ in $Z$, the distance from position $x_n,y_n$ in $o_n$ is $r_{x,y}=\sqrt{{\left(x_n-x\right)}^2+{\left(y_n-y\right)}^2}$. Replace $r$ in $z_e=r/{W_{TNT}}^{1/3}$ with $r_{x,y}$, then the overpressure of tank $o_n$ explosion in the area $Z_{X\times Y}$ (hereinafter referred to as $Z$) of chemical industrial parks is $\Delta P_{o_n/Z}$ (abbreviated as $\Delta P_{o_n}=\Delta P_{o_n/Z}=F_{\Delta p}(x_n,y_n,P_o,\alpha ,W_f,Q_f,Q_{TNT})$). $\Delta P_{o_n}$ is a functional expression to calculate the overpressure of all grid positions in region $Z$ when tank $o_n$ explodes.

The flow chart of the above-related algorithms is shown in Figure 1. The part of the theory is based on reference [29].

3.2. Probability of Tank Damage in the Explosion Area

Set the damage probability expression of $o_n$ explosion in region $Z$ be q $q_{o_n}=F_q\left(x,y,L,\Delta P_{o_n}\right)$, $x,y$ represents the coordinates of the meshed position in the region. According to the damage probability model caused by overpressure of commonly used equipment [30,31], it can be seen that when the impacted storage tank is a normal pressure vessel and the pressure is greater than 22 KPa, the damaging effect will occur, as shown in Equation (3). When the impacted storage tank is a high-pressure vessel and the pressure is greater than 17 KPa, the damaging effect will occur, as shown in Equation (4).

$$q_{o_n}=\{\begin{array}{l}\left(-18.96+2.44\ln \left(\Delta P_{o_n}\left(x,y\right)\right)\right)/100,\Delta P_{o_n}\left(x,y\right)\ge 22 \mathrm{KPa}\\ 0,\Delta P_{o_n}\left(x,y\right)<22 \mathrm{KPa}\end{array}$$

(3)

$$q_{o_n}=\{\begin{array}{l}\left(-42.44+4.33l\ln \left(\Delta P_{o_n}\left(x,y\right)\right)\right)/100,\Delta P_{o_n}\left(x,y\right)\ge 17 \mathrm{KPa}\\ 0,\Delta P_{o_n}\left(x,y\right)<17 \mathrm{KPa}\end{array}$$

(4)

where $L$ represents the type of pressure vessel, $L=1$ is normal pressure, and $L=2$ is high pressure.

By combining Equations (3) and (4), the probability $q_{o_n}$ of damage to the storage tank at any position $\left(x,y\right)$ in region $Z$ caused by the explosion of the storage tank $o_n$ can be obtained, as shown in Equation (5) [29].

$$q_{o_n}=F_q\left(x,y,L,\Delta P_{o_n}\right)=\{\begin{array}{l}\{\begin{array}{l}\left(-18.96+2.44\ln \left(\Delta P_{o_n}\left(x,y\right)\right)\right)/100,\Delta P_{o_n}\left(x,y\right)\ge 22 \mathrm{KPa}\\ 0,\Delta P_{o_n}\left(x,y\right)<22 \mathrm{KPa}\end{array},L=1\\ \{\begin{array}{l}\left(-42.44+4.33l\ln \left(\Delta P_{o_n}\left(x,y\right)\right)\right)/100,\Delta P_{o_n}\left(x,y\right)>17 \mathrm{KPa}\\ 0,\Delta P_{o_n}\left(x,y\right)<17 \mathrm{KPa}\end{array},L=2\end{array}$$

(5)

Two concepts of grid position damage probability and damage probability distribution are introduced here. Grid position damage probability can be referred to as damage probability, which refers to the damage probability of a storage tank explosion to a storage tank at a grid position. The damage probability is meaningful only when both the exploded tank and the affected tank exist at the same time, which can be expressed as $q_{o_n\to o_i}$. The damage probability distribution is a matrix representation of the damage probability of the exploded storage tank at all locations in the park after the shock wave is generated. Only damage probability was used in this study.

3.3. Mathematical Description of the Evolution Process of Tank Damage

If the process of tank explosion and subsequent tank damage is taken as a system, then these damages are the failure of the system. The system fault evolution process proposed by [32] can be described and the mathematical model of the supporting spatial fault network theory can be used for calculation. For details, please refer to reference [33]. In this paper, the basic idea of system fault evolution was used to analyze the evolution of storage tank explosion damage. The entire damage process needs to start with the explosion of a storage tank, so assume that the tank explodes, i.e., the probability is 100%. When the storage tank explodes, the shock wave overpressure will inevitably affect all other storage tanks in the park, causing their damage probability to change. The tanks with the highest probability of subsequent damage are considered the most likely to have a subsequent explosion. After the explosion of the two tanks, the other tanks were successively subjected to the explosion overpressure of the two tanks, resulting in the superposition of damage degree. According to the system fault evolution process and the expression of the spatial fault network, these effects should be the logical superposition of various damage effects [32]. Finally, the superposition is completed to judge and set the damage probability of all other storage tanks after the explosion of the storage tank. The analysis process of explosion damage evolution of storage tanks in chemical industrial parks composed of N storage tanks is given below.

When $o_n$ is used as the starting point for the explosion of the storage tank, $o_n\in O$, has an impact on other storage tanks $o_i\in O$($i\ne n$). Determine what the maximum probability of damage to all remaining tanks is $Max\left\{{q_{o_n}}_{\to o_i}\right\}$, then $o_i$ is the tank most likely to explode next time. Set $O=O/o_n$ and indicate that $o_n$ is removed from the set of $O$, and $\overline{O}=\overline{O}\cup o_n$ indicate that object $o_n$ is added in order in the set of $\overline{O}$, that is, $\overline{O}$ is the set of all tank explosion orders obtained after determining the first explosion tank. The explosion of the first tank $o_n$ is used to determine the most likely explosion of the second tank, so there are $n-2$ judgment and comparison processes, because the first is set, and the remaining tanks after the last comparison are no longer compared.

Set $q_{o_n\to o_i}=F_q\left(x_i,y_i,L,\Delta P_{o_n}\right)$ represent the probability of damage caused by tank $o_n$ explosion to tank i at $(x_i,y_i)$ position.

The first judgment and comparison process is set as the initial explosion tank, $Q_1=Max\left\{q_{o_n\to o_i}\right\},\overline{O}=o_n\cup o_i,O=O/o_i,n=i$.

During the second judgment and comparison process, the damage probability of other tanks is traversed under the influence, and the maximum damage probability is determined under the influence of the previous tank explosion, $Q_2=Max\left\{Q_1+\left(1-Q_1\right)q_{o_n\to o_i}\right\},\overline{O}=\overline{O}\cup o_i,O=O/o_i,n=i$.

The intermediate comparison process is omitted.

During the $n-2$ judgment and comparison process, the damage probability of the last two tanks is determined under the $o_n$ influence, and the maximum damage probability is determined under the influence of the previous tank explosion $Q_{n-2}=Max\left\{Q_{n-3}+\left(1-Q_{n-3}\right)q_{o_n\to o_i}\right\}$, $\overline{O}=\overline{O}\cup o_i,O=O/o_i,n=i$.

The second judgment and comparison process is determined by the impact of the previous tank explosion, $o_{n-1}=\left\{Q_{n-2}+\left(1-Q_{n-2}\right)q_{o_n\to o_i}\right\}$, $\overline{O}=\overline{O}\cup o_i,O=\varphi$.

Finally, $\overline{O}$ is the set of the maximum damage probability of the tank explosion sequence with $o_n$ as the initial explosion condition. However, $Q=\left[100\%,Q_1,Q_2,\dots ,Q_{n-1}\right]$ is the corresponding damage probability. When all tanks are set separately as initial explosion tanks, a different set of tank explosion sequences ${\overline{O}}_{1~N}$ with maximum damage probability can be obtained. Further, these N detonation sequences can be compared to determine the most unfavorable detonation sequence.

4. Experiments Analysis

4.1. Experimental Subjects

The surrounding environment pressure of chemical industrial parks in a city is $P_0=$ 103,000 Pa, the equivalent coefficient of steam cloud is $\alpha =0.04$, and the explosive heat of combustible material is $Q_{TNT}=4686$ KJ/Kg. The relative position diagram of storage tanks in chemical industrial parks is shown in

Table 1. Material parameters stored in storage tanks.

Storage Tank	Matter	$\mathit{x}$/m	$\mathit{y}$/m	Volume/m2	Density kg/m3	Combustion Heat ${\mathit{Q}}_{\mathit{f}}$/KJ/kg	Type
$o_1$	gasoline	300	700	2000	730	41,868	High pressure
$o_2$	gasoline	800	100	2500	730	41,868	High pressure
$o_3$	Ethyl alcohol	700	700	1200	800	22,890	High pressure
$o_4$	Ethyl alcohol	300	500	1900	800	22,890	High pressure

. Parameters of substances stored in the tank are shown in Table 1. The chemical industrial park is 1000 m × 1000 m area,$x\in \left\{0,1,\dots ,1000\right\}\mathrm{m},y\in \left\{0,1,\dots ,1000\right\}\mathrm{m}$.

Four storage tanks in the area $O=\left\{o_1,o_2,o_3,o_4\right\}$.

4.2. Experimental Process

In the first comparison, $o_n=o_1,o_i\in \left\{o_2,o_3,o_4\right\},\overline{O}=\left\{o_1\right\},O=\left\{o_2,o_3,o_4\right\}$, $o_1$ the explosion traverses the impact on all tanks in the area.

The effect on the $o_2$ tank, $\Delta P_{o_n}=F_{\Delta P}\left(300,700,103000,0.04,1.46\times {10}^6,41868,4686\right)$.

The influence degree of $\Delta P_{o_n}$ in region $Z$ is obtained. Since $o_2$ is high pressure and $q_{o_n}$ is selected, the damage probability in $Z$ is obtained. $q_{o_n\to o_2}$ is the damage probability caused by $o_n$ to $o_2$, that is, the damage probability of $o_n$ to $o_2$, and the calculation result is $q_{o_n\to o_2}=10.04\%$. Similarly, $q_{o_n\to o_3}$ and $o_3$ belong to high-pressure storage tanks, then $q_{o_n\to o_3}=4.93\%$; $q_{o_n\to o_4}$ where $o_4$ belongs to the high-pressure storage tank, then $q_{o_n\to o_4}=4.09\%$. So $Q_1=Max\left\{10.04\%,4.93\%,4.09\%\right\}=q_{o_n\to o_2}$, then $\overline{O}=o_1\cup o_2=\left\{o_1,o_2\right\},O=\left\{o_3,o_4\right\},Q_1=10.04\%$.

The second comparison, this time $\overline{O}=\left\{o_1,o_2\right\},O=\left\{o_3,o_4\right\},o_n=o_2,o_i\in \left\{o_3,o_4\right\}$, $Q_2=Max\left\{Q_1+\left(1-Q_1\right)q_{o_2\to o_3},Q_1+\left(1-Q_1\right)q_{o_2\to o_4}\right\}$, Where $o_3$ of $q_{o_2\to o_3}$ is high pressure, then $q_{o_2\to o_3}=4.07\%$; The $o_4$ of $q_{o_2\to o_4}$ is high pressure, $q_{o_2\to o_3}=8.42\%$. $Q_2=Max\left\{13.70\%,17.61\%\right\}=q_{o_2\to o_4}$, then $\overline{O}=\overline{O}\cup o_4=\left\{o_1,o_2,o_4\right\}. O=\left\{o_3\right\},o_n=o_4,o_i\in \left\{o_3\right\}$. $Q_3=Max\left\{Q_2+\left(1-Q_2\right)q_{o_4\to o_3}\right\}$, $o_3$ of $q_{o_4\to o_3}$ is the high-pressure storage tank, $q_{o_4\to o_3}=7.44\%$, $Q_3=17.61\%+\left(1-17.61\%\right)\times 7.44\%=23.74\%$.

Through the above-shown process, we can see that when $o_1$ explodes first, the order of maximum damage probability is $\overline{O}=\left\{o_1,o_2,o_4,o_3\right\}$. The corresponding damage probability is $Q=\left\{100\%,10.04\%,17.61\%,23.47\%\right\}$.

When hypothesis $o_2$ explodes first, $Q_1=Max\left\{q_{o_2\to o_1},q_{o_2\to o_3},q_{o_2\to o_4}\right\}=\left\{13.07\%,4.07\%,8.42\%\right\}=13.07\%$, $q_{o_1\to o_3}=4.93\%$, $q_{o_1\to o_4}=4.09\%$, so $Q_2=Max\left\{13.07\%+\left(1-13.07\%\right)\times q_{o_1\to o_3},13.07\%+\left(1-13.07\%\right)q_{o_1\to o_4}\right\}$, $=Max\left\{17.36\%,16.62\%\right\}=17.36\%$. $q_{o_3\to o_4}=6.81\%$, so $Q_3=Max\left\{17.36\%+\left(1-17.36\%\right)q_{o_3\to o_4}\right\}=22.99\%$. At this moment,$\overline{O}=\left\{o_2,o_1,o_4,o_3\right\}$, $Q=\left\{100\%,13.07\%,17.36\%,22.99\%\right\}$.

When hypothesis $o_3$ explodes first, $Q_1=Max\left\{q_{o_3\to o_1},q_{o_3\to o_2},q_{o_3\to o_4}\right\}=Max\left\{4.1\%,1.3\%,3.3\%\right\}=4.1\%$. $q_{o_1\to o_2}=10.04\%,q_{o_1\to o_4}=4.09\%$, so $Q_2=Max\left\{4.1\%+\left(1-4.1\%\right)q_{o_1\to o_2},4.1\%+\left(1-4.1\%\right)q_{o_1\to o_4}\right\}$$=Max\left\{21.80\%,16.62\right\}=21.80\%$. $q_{o_2\to o_4}=5.12\%$, so $Q_3=Max\left\{21.80\%+\left(1-21.80\%\right)q_{o_2\to o_4}\right\}=25.38\%$. Finally $\overline{O}=\left\{o_3,o_1,o_2,o_4\right\}$, $Q=\left\{100\%,4.1\%,21.80\%,25.38\%\right\}$.

When hypothesis $o_4$ explodes first, $Q_1=Max\left\{q_{o_4\to o_1},q_{o_4\to o_2},q_{o_4\to o_3}\right\}=Max\left\{4.41\%,6.12\%,4.41\%\right\}=6.12\%$. $q_{o_2\to o_1}=13.07\%$, $q_{o_2\to o_3}=4.07\%$, so $Q_2=Max\left\{6.12\%+\left(1-6.12\%\right)q_{o_2\to o_1},6.12\%+\left(1-6.12\%\right)q_{o_2\to o_3}\right\}$$=Max\left\{18.39\%,9.93\%\right\}=18.39\%$.

$q_{o_1\to o_3}=7.74\%$, so $Q_3=Max\left\{18.39\%+\left(1-18.39\%\right)q_{o_1\to o_3}\right\}=23.75\%$. Finally, $\overline{O}=\left\{o_4,o_2,o_1,o_3\right\}$, $Q=\left\{100\%,6.12\%,18.39\%,23.75\%\right\}$.

4.3. Experimental Analysis and Summary

The intelligent analysis process of different tank explosions using the above-shown method is shown in Figure 2.

It can be seen that the damage process of storage tank explosion caused by different storage tank explosions is different. On the surface, it is caused by the different volume, location, and storage material of the tank, but in fact, it is due to the different evolutionary order of the damage of the remaining tanks caused by the initial explosion of different tanks. This evolutionary sequence depends locally on tank volume, location, and storage material, and macroscopically on causality of interactions. The change process of the causal relationship can be compared to the system fault evolution process proposed by the author and can be calculated mathematically using the spatial fault network theory. This is embodied in the mathematical description of the process of tank explosion in Section 2.3. It has been explained above that the damage probability can be analogous to the explosion possibility of the affected storage tank. The greater the damage probability, the more likely the storage tank is to explode, which is a positive relationship.

The worst case can therefore be determined based on different $\overline{O}$ and $Q$ corresponding scenarios. For example, the maximum damage probabilities obtained from the above four storage tanks as initial explosion storage tanks are respectively $Q=\left\{100\%,10.04\%,17.61\%,23.47\%\right\}$, $Q=\left\{100\%,13.07\%,17.36\%,22.99\%\right\}$, $Q=\left\{100\%,4.1\%,21.80\%,25.38\%\right\}$ and $Q=\left\{100\%,6.12\%,18.39\%,23.75\%\right\}$. If it is determined from the Angle of ensuring the minimum damage probability of all subsequent tanks, it can be obtained that the average damage probability of subsequent tanks after $o_1$ explodes is 17.04%, $o_2$ is 17.80%, $o_3$ is 17.09%, and $o_4$ is 16.07%. Therefore, it can be seen that the worst case in all cases is the case of the tank $o_2$ as the initial explosion tank. Therefore, in the case of limited manpower, and financial and material resources, priority should be given to preventing the explosion of storage tanks.

The theory in this paper is the theory of the system fault evolution process proposed by the authors, which uses the mathematical model of the space fault network. The tank explosion process was improved with the theory. The characteristic of the algorithm is to study the tank explosion process caused by different disasters. Once the probability of disaster-induced tank explosion is determined, this method can be used to calculate the process, possibility, and scope of all tank explosions in the chemical industry park. This study is the basis for the subsequent study of the scope, degree, and preventive measures of risks caused by various disasters in the chemical industry park. Of course, considering the uncertainty of the environment is also one of the main directions to be studied in the future. It is also possible to consider the distributed solution for multiple regions to improve the solution speed, and fault identification and diagnosis can also be further studied [34,35].

5. Conclusions

The research of this paper is based on the calculation method of overpressure in the explosion area of the storage tank and the damage probability of the storage tank proposed earlier by the author. The evolution process of storage tank damage caused by storage tank explosion is described as the evolution process of a system fault, which can be described mathematically by using the spatial fault network theory. The main conclusions are as follows:

• Based on previous studies, a method suitable for the calculation of overpressure and damage probability of storage tank explosion area is established. The method is based on regional grid division and shock wave overpressure calculation. Firstly, the overpressure in the explosion zone of the tank is calculated. Then the damage probability of the grid position is calculated according to the relative position of the explosion tank and the affected tank. There is a positive linear relationship between the damage probability and the explosion possibility of the affected tank, so the difference in the explosion possibility can be determined by the difference in the damage probability;
• The system fault evolution process is used to describe the damage evolution process caused by tank explosion, and the mathematical method of spatial fault network is used to describe the damage evolution process. It is concluded that the damage to other tanks caused by tank explosion shock waves is or logical superposition. The corresponding method in the mathematical model of spatial fault network theory can be used to describe the damage evolution process. The analysis process of explosion damage evolution of storage tanks in chemical industrial parks composed of N storage tanks is presented. According to this process, the evolution process of explosion damage of storage tanks in chemical industrial parks composed of four different tanks is studied, and the damage probability of each tank in the most adverse process is obtained.