A Study on a Quantitative Analysis Method for Fire and Explosion Risk Assessment of Offshore Platforms

Proper design of the explosion loads is of vital importance in the risk assessment of explosions for offshore oil and gas installations. A quantitative assessment method for gas explosion loads in process modules of offshore platform is proposed in this paper. The proposed approach achieves the following three objectives: (a) defining a suitable number of leak scenarios quantitatively based on the Latin Hypercube Sampling (LHS) technique and statistical analysis; (b) defining the explosion scenarios according to the computational fluid dynamics (CFD) dispersion analysis results in the sampled leak scenarios; (c) designing the explosion loads on interested areas according to the CFD analysis results in different explosion scenarios and exceedance probability methods. The proposed method was applied to a process module of an example offshore platform. The pressure loads on interested areas of the example platform are very close to that suggested in Det Norske Veritas (DNV) codes. The method developed in this paper can benefit the engineers on better assessment of gas explosion risk in process modules for offshore installations.


Introduction
Explosion accident caused by the hydrocarbon leak is one of the most significant accidents, which should be considered thoroughly in the offshore oil and gas industry. e structural response analysis under explosion loads is a very important task in the risk assessment of explosion accidents. In 1988, huge loss of Piper Alpha platform in the UK North Sea prompted the UK government to actively promote the application of risk assessment methods in the offshore oil and gas platforms [1]. Since 1990, there were 27 international research projects related to fire and explosion of offshore oil and gas equipment [2]. e BFETS JIP project [3,4] and EFEF JIP project [5][6][7][8][9] were turned out to be the two most important topics. To fulfill this work well, the explosion loads must be designed suitably according to different possible explosion scenarios. Figure 1 illustrates its role in the explosion risk assessment.
For hydrocarbon leak caused explosion, when the leak happens and is not ignited immediately, a certain size gas cloud will be formulated as the dispersion continued. If this cloud is ignited at a certain time, gas explosion may happen. erefore, the main procedure gaining explosion loads in a certain explosion scenario includes the following steps: (1) defining a suitable leak scenario first; (2) carrying out the dispersion analysis; (3) determining the explosion scenario; (4) conducting explosion analysis at last. However, there are lots of possible leak scenarios and explosion scenarios in an arbitrary installation. erefore, a suitable number of scenarios should be determined, which has been documented by several international codes [10][11][12][13][14][15][16]. e happening probability of explosion scenarios should also be analyzed so that the design loads can be determined according to the exceedance probability.
Nevertheless, when defining specific parameters of possible leak scenarios, limited tools can be utilized; the leak scenario parameters are generally determined by expert judgment [13], which is a kind of qualitative way and could not be widely used. Paik [2,8] proposed a concept of defining leak scenarios based on the Latin Hypercube Sampling (LHS) technique. However, the method on obtaining probability functions for most parameters is not presented. e LHS technique is a widely used sampling method, which is suitable for small size sample. e LHS technique has been applied on offshore installations in many aspects [17,18].
Key issue of determining the explosion scenarios falls on how to extract useful information from the gas dispersion analysis results. Many CFD-based tools such as ANSYS Fluent [19], FDS [20], and FLACS [21] are capable to conduct the dispersion analysis. However, the analysis results commonly cannot be directly used for the explosion analysis. Among all the useful tools, FLACS can give more useful information and is recognized as a suitable tool to do the dispersion analysis. For the explosion analysis, different predicting tools have been developed, which are typically represented by TNT Equivalency method, TNO Multienergy method, and CFD-based method [22]. e TNT method could only be used at some distance when applied to gas explosions, since gas explosions are strong enough as TNT explosions. Similarly, the Multienergy method does not give the maximum overpressure in the gas cloud. It predicts the decay of overpressure with distance instead, starting at some distance from the cloud [23]. Among CFD models, FLACS has been used in the modeling of explosion after accidental release in onshore or offshore facilities [24] and has been improved and validated by many studies to demonstrate the validity of its predictions [25]. e happening probability of explosion scenarios is affected by many factors (for example, leak frequency, wind direction probability, leak direction probability, and ignition probability), which have been studied by many researchers [26][27][28]. Spouge [29] provided a comprehensive elaboration on the frequency and probability analysis method for the risk assessment of marine equipment. Paik [26] defined the fire explosion frequency as the product of leakage frequency and fire frequency. However, he did not point out the different calculation methods of the fire frequency between immediate fire and delay fire. Taking this factor into consideration, Dan [30] assessed the fire and explosion risk of LNG-FPSO based on several assumptions. Nevertheless, considering the complexity of the issue, especially the ignition probability, many established tools are still not practicable, and some simple assumptions are usually adopted.
In addition, the method in the codes (e.g., DNV codes) is based on qualitative analysis; in addition to the structural analysis in high risk, there is no clear or procedure for calculating the probability and consequence of scenarios, such as how to determine fire explosion scenarios that need to be analyzed and how to calculate the probability and consequences of scenes.
is type of risk analysis relies heavily on the engineer's experience and lack of quantitative analysis methods.
FLACS is used to simulate the gas explosion scenario and compare with the recommendations in the specification to verify the analysis method. e method developed in this paper can benefit the engineers on better assessment of gas explosion risk in process modules for offshore installations.
According to the problems mentioned above, in this paper, an effective approach was put forward to choose fire explosion scenes integrating application of scene frequency and probability analysis method, CFD analysis technology, etc. Furthermore, a set of risk assessment methods for fire and explosion caused by gas leakage based on quantitative analysis was come up with. e proposed method is explained in detail by conducting quantitative analysis of gas explosion load for an example offshore platform. It should be pointed out that the proposed approach in this paper is mainly aimed at the fire and explosion scenarios caused by gas leakage, but not applicable to other fire and explosion scenarios. However, this method still provides a valuable direction to make the selection of fire and explosion scenarios not only depend on experience when parameters and data are selected reasonably.

Procedure for Quantitative Analysis of Gas
Explosion Loads in Offshore Platforms e main procedure for quantitative analysis of gas explosion loads in this paper is illustrated in Figure 2.
Except the hydrocarbon type, other parameters mentioned above are random variables considering the uncertain property of leak scenario. Once the leak location is known, the hydrocarbon type can usually be determined. erefore, according to the statistical theory, if the probability functions of different variables are acquired, multiple groups of variable values can be obtained through a suitable sampling method.
en, the leak scenarios can be determined. Six variables are chosen to represent the leak scenario: (i) Leak amount (ii) Leak rate (iii) Leak direction (iv) Leak location (X, Y, Z) (v) Wind direction (vi) Wind speed e cumulative distribution functions (CDF) of different variables are mainly gained by statistical analysis of the data from some history database or literatures, and the detailed procedure will be introduced in Section 3. After obtaining the probability functions of different variables, the Latin Hypercube Sampling (LHS) method was chosen to sample a suitable number of variable groups. e main concept of the LHS method will be introduced in Section 4. e second step is to determine the explosion scenarios based on the sampled leak scenarios. Dispersion analysis in different leak scenarios should be conducted first, and CFD theory-based FLACS code was employed to conduct this work.
en, explosion scenario parameters (such as explosion cloud size and location) used for explosion load analysis can be acquired based on the dispersion results. Detailed procedure of this step is introduced in Section 5. e last step is to determine the explosion loads on interested regions. FLACS code was chosen to conduct the explosion load analysis of each scenario. e happening probability of each explosion scenario is also calculated in this step. Based on the load and probability of each scenario, 2 Advances in Civil Engineering the design accidental load method can be employed and exceedance probability curve for interested regions can also be established. en, the load corresponding to a certain probability level can be obtained. Detailed procedure of this step is introduced in Section 6.

Leak Scenarios' Selection for Example Platform
is section describes the detailed procedure of obtaining the cumulative distribution functions of different leak variables for an example platform, as well as the way of realization of the LHS method in MATLAB program.

Basic Information for Example Platform.
e example oil and gas platform used in this paper is based on empirical assumption with the basic layout information from AP-PENDIX B.3 in API RP 14J [31,32]. Basic layout information of different equipment for the employed example platform is depicted in Figure 3. Its 3D geometrical model and corresponding inner equipment layout can be illustrated in Figure 4. In this paper, the compressor station area was not considered in the explosion loads assessment process and was expressed by a block on the left side of the geometrical model. It is assumed that the main processed medium is oil. erefore, petroleum gas is the considered leak gas. Possible leak equipment is shown in Figure 5.

Source Data Collection.
e relationship between the leak amount and leak rate is very complex, which involves the leak time, pressure, outlet area, etc. Due to the lack of reliable data to infer the relationship between the leak amount and leak rate, it was assumed that there is no relevance between the leak amount and leak rate in this paper. For the investigation on the hydrocarbon explosion and fire risks in offshore installations, some researchers, such as Professor Paik [26] from Busan University in Korea, also take the samples with a high leak rate and a small leak amount to conduct the analyses. e collected source data of different variables will be used to obtain the probability function of these variables for statistical analysis and have a decisive effect on the variable probability functions' type and leak scenario sampling results.
erefore, the source data should be treated thoroughly.
Generally, source data should be obtained from different failure databases. For some data that are not easy to obtain, empirical assumption can be used. Typical failure data related to hydrocarbon release and explosion accidents [29] contain WOAD, OREDA, Offshore Incident Database, Hydrocarbon Release Data, Offshore Blowout Database and Technical Blowout Database, etc. Leak data, which include leak amount and leak rate, should be obtained from installations that has similar functions. For instance, if oil producing jacket platform is considered to conduct explosion assessment, data from drilling platforms will not be suitable. However, data from installations (FPSO, TLP, Spar, jacket platform, and semisubmersible) that are used for    producing oil are suitable, though the platform types are different. Wind data should be acquired from the waters where the considered installation is located in.
For the example platform considered in this paper, leak amount data is collected from 135 FPSOs in the waters of the UK with time from 1994 to 2008 [33] and is shown in Figure 6. Leak rate data is obtained from installations in North Sea [34] and is shown in Figure 7. e example platform is assumed to be located in West Africa Sea, and the Wind data of a West Africa Sea [27] area are used, which are shown in Figures 8 and 9.

Variable Probability Functions
3.3.1. Leak Direction Selecting Method. In this paper, leak direction is thought to be greatly dependent on the leak location. us, it will not have a unique probability function. Methods for selecting leak direction are given below: (i) For valves, connections, and riser end, each leak location has 6 possible leak directions: +X/−X/+Y/ −Y/+Z/−Z. Each direction can be given a unique number. A number can be selected out by random extraction, and then the direction is selected.
(ii) For pipes, 4 possible leak directions are shown in Figure 10, and the selection method is similar to valves. (iii) For vessels and gas station, each leak point will only have a unique leak direction, which is shown in Figure 10.

Leak Location CDF and Sampling
Procedure. e CDF of leak location is the most difficult function to obtain in all variables. As illustrated in Figure 5, 6 kinds of equipment types are possible to leak, and some equipment is more than one, for example, there are 19 valves, 16 connections, and 9 vessels. All equipment is dispersedly distributed in threedimensional space of the considered zone, which will make it hard to get the CDF of leak location.
To solve the problem, the main procedure developed in this paper is shown in Figure 11. First, classify the possible leak equipment into several groups; then, calculate the total frequency of each group based on the unit leak frequency of each kind of equipment; then, statistically analyze the total frequency of different equipment groups and establish the cumulative probability function. e method of calculating total leak frequency of different equipment types are as follows: Pipes : Total leak frequency � unit leak frequency × pipe length, Valves : Total leak frequency � unit leak frequency × total valve numbers, Connections : Total leak frequency � unit leak frequency × total connection numbers, Vessels and gas station : Total leak frequency � unit leak frequency × total face areas,  where unit leak frequency is leak frequency per meter of pipe (for pipe); leak frequency per valve (for valve); leak frequency per connection (for connection); leak frequency per m 2 face area (for vessel and gas station).
For the example considered in this paper, the classified equipment groups have been shown in Figure 5 and the frequency calculation results are shown in Table 1. e unit frequencies of different equipment are based on OREADA database and empirical assumption. Each equipment group corresponds to a unique range of the variable, and the range length is 1 (nondimensional). For the example considered in this paper, the corresponding relationship between the equipment group and the variable range is shown in Table 1.
Transferred variable range refers to the character l in equation (2). In Table 1, each equipment corresponds to a specific range of the variable l. When a value of F(l) is randomly sampled, the value of the variable l can be obtained through equation (2), and the leaking equipment then can be found according to the interval in which the value l falls. For example, F(l) ranges from 0 to 1, and its value can be obtained by generating a random number from 0 to 1, such as 0.2. Later, the value of the variable l can be obtained by taking the inverse function of F(l), and its value are within the range of 0∼1. is transferred variable range l falls in the interval corresponding to the pipeline equipment; finally, the leakage point will be determined in the pipe. Figure 12(a) is the histogram for total frequencies of different equipment groups. On the strength of statistical analysis, the CDF of equipment transferred variable can be expressed as equation (2), and the graphical expression of the equation is shown in Figure 12(b): rough the proposed procedure, the established CDF of different equipment groups can suitably reflect the leak probability of different groups and therefore can suitably reflect the leak probability of different leak locations (equipment group level) in the considered zone. Based on the established CDF, LHS sampling can distribute some leak  Advances in Civil Engineering location points to each group. However, the main information that LHS sampling can give is the specific number of leak points for different equipment groups. e distributed leak location points still have no specific coordinate information.
Before explaining how to get the specific coordinate of different leak points, some basic assumptions are given: (i) For valves, connections, and riser end, each equipment only has one leak location, which is located at the equipment center (ii) For pipes, each meter length pipe will correspond to one leak location, which is located at the center of the pipe segment (iii) For vessels and gas station, only 6 leak points are specified, which are located at the center of different faces, as shown in Figure 10 Actually, if a leakage happens, the leak point may not be the points given by the assumption. e assumed leak points are actually representative points of some leak areas. e leak point assumptions are thought reasonable in this paper. e reason is that the representative leak points are not far away from the real leak points and will not affect the dispersion results too much.
According to the leak point assumption, the procedure to acquire the specific coordinate of different leak points is shown in Figure 13. Actually, the main problem that the procedure in Figure 13 will solve is how to suitably select some representative leak points of the considered equipment group according to the LHS sampled variable values. As illustrated in this figure, through LHS sampling, three sampled variable values fall in the variable range of an equipment group. If the equipment group has N sim representative leak points (each leak point can be given to a unique number), the variable range of this equipment group can be divided into N sim parts, and the three sampled variable values will fall in three unique parts, which are the m st , n st , and o st parts. By randomly arranging the array [1, 2, . . . , N sim ], the m st , n st , and o st locations will also have a unique number N a , N b , and N c . en, representative leak points corresponding to number N a , N b , and N c can be selected as the leak points, and the coordinate of the leak location are known. It should be mentioned that the LHS      Advances in Civil Engineering sampled variable number in a group range are not constant, may be more than 3, or less than 3. Nevertheless, the procedure is similar.

Leak Amount CDF.
Leak amount is represented by variable a here. According to data from Figure 6, leak amount is ranked in 3 levels. Based on the statistical method, the probability of each amount level can be calculated by summing the leak numbers of each amount level and then dividing the summed value by the total leak numbers. Assuming the probability in each leak amount level is a constant, the CDF of leak amount can be expressed as equation (3), and the graphical expression of the equation is shown in Figure 14: 0.001452 · (a − 1) + 0.535373, 1 < a ≤ 300, 0.000044(a − 300) + 0.969407, 300 < a ≤ 1000. Table 2 provides the relevant information on gas leakage rates of FPSO in the PSA (2011b) report in the waters off Norway and the UK. Leak rate is represented by variable r and is classified into two levels. Similar statistical method to leak amount is used here. To acquire the CDF of the leak rate, the upper limit of the leak rate is assumed to be 3.4 kg/s. e CDF of the leak rate is as equation (4), and the graphical expression of the equation is shown in Figure 15:

Wind Direction CDF.
Wind direction and wind speed are represented by variables d and s, respectively. Similar method to leak amount is also used here. e CDF of d and s can be expressed as equations (5) and (6)

Latin Hypercube Sampling (LHS)
4.1. LHS Method. LHS method is based on the idea of Latin square-an n × n table filled with n different symbols in such a way that each symbol occurs exactly once in each row and exactly once in each column. Latin Hypercube is the generalization of this concept to an arbitrary number of dimensions, whereby each symbol is the only one in each axisaligned hyperplane containing it [26]. Compared to the Monte Carlo Sampling method, the LHS method needs much less samples to properly represent the whole probability distribution of the variable. So far, several LHS  Advances in Civil Engineering methods can be chosen, and one of them used in this paper can be expressed as where x i,j is the jth sample value of the ith variable; F −1 i is the CDF inverse function of the ith variable; N sim is the sampling number of each variable; and π i (1), . . . , π i (N sim ) is the random permutation of 1, . . . , N sim .
According to the content of the study, the uncertainty variables that constitute the leakage scenario are represented as random variables (a total of 8 groups) in this paper. Combining the relevant historical data using statistical methods to determine the probability of each random variable function, a certain number of random number groups can be generated by random sampling, which corresponds to the same number of leakage scenarios.
In the present example, 50 scenarios were randomly selected using the Latin hypercube sampling (LHS) technique. e method was employed as follows. e probability density distribution of each of the eight random variables is divided into 50 ranges, with the interval of each range determined to ensure that the area below the curve between the probability density versus random variable is equal. e representative value of the random variable for each segment is defined as the average value of that segment. e center of the area is taken as the representative value of the segment at the tail of the probability density distribution. e advantage of Latin hypercube sampling (LHS) is that it can achieve a more reasonable distribution law of representative parameters in the case of a small sample number. erefore, based on Latin hypercube sampling (LHS) method M random number groups can be extracted in this Step:1 Step:2 Randperm sampling for specific equipment Step  Advances in Civil Engineering paper, and each array has a unique set of random variables for different parameters. erefore, a leakage scenario can be determined. Finally, a total of M leakage scenarios are selected to represent a large number of potential leakage scenarios. By this way, the M scenarios generated can reasonably represent the possible leakage scenarios. Figure 18 shows the concept of LHS sampling with one variable, and Figure 19 illustrates the example of two-variable LHS with N sim � 8.

Sampling Process and Results.
e LHS sampling process is conducted in MATLAB program. By using command "randperm," the array [1, 2, . . . , N sim ] is randomly arranged. According to equation (7), the randomly arranged array is substituted into the inverse function of the CDF with different variables, and variable value arrays can be obtained. Variable values for leak amount, leak rate, wind speed, and wind direction can be used directly. For leak location and leak direction, procedure mentioned above should be conducted to get the final information. 50 leak scenarios for the considered platform sampled by the proposed approach are shown in Table 3.

Analysis Setting Up.
To get the explosion scenarios, dispersion analysis should be conducted first according to the 50 leak scenarios. CFD theory-based FLACS code was chosen to conduct the task, and 50 dispersion models were established. As the main considered platform volume is 20 m × 20 m × 5 m, the simulation volume of each dispersion model is set as 100 m × 100 m × 15 m. Figure 20 shows typical grid solution for dispersion models. e grid near the leak location is refined in the direction perpendicular to the leak direction.
e refined grid size is 0.2 m and is stretched smoothly to the main control grid size (1 m). e 1 m grid size is the main size in the platform zone and is stretched smoothly from the platform boundary to the simulation zone boundary.
Besides the parameters listed in Table 3, some key parameter sets can be seen in Table 4, and other parameter are set according to FLACS user's manual [35].
In this paper, the FLACS CFD model was employed to compute the release amount by mainly setting the specified leak rate and leak duration. Once the values of the leak rate and leak duration are determined, the leak amount in the FLACS CFD model can be gained, which   10 Advances in Civil Engineering will be consistent with the values obtained by LHS from statistical data.

Analysis Results. As one of the most important results
in the dispersion analysis, the "equivalent stoichiometric gas volume" in different scenarios is employed to get the explosion scenarios. As known, each kind of flammable gas has its flammable limit, which means that the volume ratio between the fuel and air must be in a suitable range and then the fuel can be ignited. ere is also a most suitable ratio that the combustion will produce the greatest amount of heat.
e "equivalent stoichiometric gas volume" actually transforms the flammable gas volume into a volume with most suitable fuel/air ratio. e transformation method is shown in where E actual is the expansion factor for the actual fuel/air ratio and E stoich is the expansion factor for the stoichiometric fuel/air ratio. "Equivalent stoichiometric gas volume" in FLACS code output is represented by parameter "Q8." In addition, the comparison between the volumes of flammable gas and equivalent stoichiometric gas for a leak scenario is illustrated in Figure 21. It can be found that the volume of flammable gas is larger than that of equivalent stoichiometric gas, and other 49 scenarios show similar phenomenon. Figure 22 depicts the "equivalent stoichiometric gas volume" results for 50 leak scenarios. Leak durations for 29 scenarios are less than 10 s and can only produce small size equivalent gas cloud. About 21 scenarios have longer leak duration, the maximum volumes of formulated equivalent gas clouds range from tens of m 3 to hundreds of m 3 . Most of these scenarios will come to a steady state after a certain period of dispersion, which is reflected by the changeless equivalent gas volume. e other valuable result is the gas concentration distribution in the platform zone, which will be used to define the location of gas explosion cloud. Figure 23 shows the concentration distribution of a scenario with XY view at a certain time. It can be clearly observed that most of the volume is located at the bottom and the left of the platform zone. e location of gas explosion cloud can be relatively and reasonably determined by distinguishing the concentration distribution figures.

Explosion Scenarios.
As FLACS code is also adopted to conduct the gas explosion simulation in this paper, some key parameters in different scenarios should be determined according to the dispersion simulation results.
ese key parameters contain gas cloud volume, gas cloud location (X, Y, Z), and gas cloud size (L X , L Y , L Z ).

Gas Cloud Volume.
e maximum equivalent stoichiometric gas volume (V disper ) that formulated during the dispersion process of each scenario will be used as the base value to calculate the gas explosion cloud volume (V exp lo ).
e relationship between V exp lo and V disper can be expressed as follows: where f 1 : porosity factor, which is defined by "1/porosity of the platform zone" and is set as 1.5 in the considered example platform; f 2 : pressure revision factor, which is used to consider the under predicted overpressure of FLACS code (studies show that the overpressure predicted by FLACS Advances in Civil Engineering code were under predicted for about 20∼30%), and its value is set as 1.3; f 3 : safety factor, which is used to think of the great uncertainty of explosion, and its value is set as 2.
As illustrated in Figure 24, the reason to set the porosity factor f 1 can be explained: when a gas cloud is put in the platform, the cloud actually contains some blocks, and the cloud volume is not the volume of its size; in the view of the gas cloud size is usually calculated directly from V exp lo , this issue is resolved effectively by introducing the porosity factor f 1 .

Gas Cloud Size and Location.
By observing the concentration distribution figures, these two parameters can be determined. Actually, this process cannot be summarized as a standard procedure. And to some extent, the analysis e main constraint of this process is V exp lo and concentration distribution figures. As a reference, the process of determining the two parameters for the example platform will be described below.
According to the concentration distribution figures of the 50 scenarios, the law of determining gas cloud size is as follows: where Z H is the height between two decks; X 1 , X 2 , Y 1 , and Y 2 are shown in Figure 25.

Analysis Results.
Pressure is the main considered loads for explosion. Four kinds of pressure loads can be output from FLACS, which are point overpressure (P), point overpressure impulse (PIMP), panel pressure (PP), and panel pressure impulse (PPIMP). Typical output form is value-time curve of these parameters, as shown in Figure 27. e max P/PP or PP/PPIMP of the considered location can be extracted and used for load design.

Probability Analysis.
e explosion probability should also be determined before finally plotting the explosion probability exceedance curve. e event tree depicted in Figure 28 can be used to calculate the probability of each scenario. Branch 1 in Figure 28 represents the process of an explosion scenario, and the probability can be calculated by  According to Table 1, the total leak frequency of this platform is calculated as 405.95/10 6 hrs, which means that the platform will leak 4 times a year. erefore, if the considered time is 1 year, P leak � 1. As the whole possible happening leak scenarios are represented by 50 scenarios, therefore, P dispersion for each scenario is 1/50 � 0.02. For ignition probability, the method in literature [26] is thought suitable, and the calculation information for example platform is shown in Table 7. However, the results given in Table 7 are the ignition probability of the whole platform, and P ignition of each scenario should be corrected according to its volume size. e correction method can be expressed as follows: Once the values of P leak , P dispersion , and P ignition are determined, P explosion for each explosion scenario can be   29  28  27  26  25  24  23  22  21  20  19  18  17  16  15  14  13  12  11  10  9  0  5  10 15 20 Advances in Civil Engineering calculated by equation (11), and the corresponding results are summarized in Table 5.

Design Accidental Loads.
When the pressure loads on the considered area and happening probability for each explosion scenarios are known, the probability exceedance curve can be established. en, according to the probability exceedance curve, the design loads at a certain probability exceedance value can be obtained, which are known as design accidental loads. e pressure and impulse curves of the panel that separates the compressor station and the process area are extracted out for different scenarios. Figure 29 plots the pressure and impulse probability exceedance curves of the  Figure 26: Typical grid solution for explosion models. Boundary conditions "Plane_Wave" Ignition "1 m 3 , in the bottom center of the control volume" Medium volume fractions "Ethylene: 15%;" "Propylene: 5%;" "Propane: 50%;" "Butane: 20%;" "Hydrogen: 10%" Advances in Civil Engineering assumption, it can be found that the predicted load values are very close to that suggested in the guides. e suggested design loads in Table D1 of DNV OS-101 [36] are shown in Table 8.

Conclusions
Integrating application of the LHS method, FLACS code, and exceedance probability technique, this paper proposed a quantitative assessment method for gas explosion loads in process modules of offshore platforms. And some key problems involved in establishing the whole procedure were well solved. e key problems are as follows: (i) Establishing reasonable probability functions and suitably sampling process of different leak variables, among which leak location variable is the most difficult to be solved so that the sampled leak scenarios can suitably represent the possible scenarios (ii) Easy and exercisable ways of defining explosion scenarios based on CFD dispersion analysis results (iii) Easy and exercisable ways of calculating explosion scenario happening probability e proposed method was applied to a process module of an offshore platform. According to the sampled 50 leak scenarios of this example platform, it can be found that the sampled results for each variable have suitably represent the probability distribution of these variables based on their statistical information, which means that the sampled leak scenarios can suitably represent the possible leak scenarios. e designed maximum pressure load on interested areas of the example platform is 1.2 bar, which is very close to 1.5 bar that    18 Advances in Civil Engineering suggested in DNV codes. It can demonstrate the effectiveness and feasibility of the proposed method. e main advantage of the proposed method is that the process of sampling leak scenarios can be very easy to control. As the LHS technique is executed in program, for any number of scenarios that needed to be sampled, if the CDF function of each variable is established, the only needed task is to set the sample number. And as long as the sampled number is not too small, the sampled results will always well represent the probability distribution of each variable. It should be noted that large sample number will lead to too much CFD analyses, which is not recommended here.

Abbreviations
N sim : Sampling number of each variable V equivalent : Equivalent stoichiometric gas volume V flammable : Volume of flammable gas E actual : Expansion factor for actual fuel/air ratio E stoich : Expansion factor for stoichiometric fuel/air ratio V disper : Maximum equivalent stoichiometric gas volume formulated during the dispersion process V explo : Gas explosion cloud volume f 1 : Porosity factor f 2 : Pressure revision factor f 3 : Safety factor P leak : Leak probability for the whole platform P dispersion : Happening probability for each leak scenario P ignition : Ignition probability for each explosion scenario P total ignition : Ignition probability for the whole platform.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest
e authors declare no conflicts of interest.

Authors' Contributions
Z.S., H.Y., and W.R. contributed to methodology; Z.S., H.Y., and W.R. helped with the software; W.R., Z.S., and H.Y. validated the study; Z.S., H.Y., and W.R. carried out formal analysis; Z.S. and H.Y. carried out investigation; Z.S., H.Y., and W.R. helped with the resources; Z.S., H.Y., and W.R. carried out data curation; Z.S. and H.Y. wrote the original draft; W.R. and Z.S. reviewed and edited the study; Y.B. supervised the study; Y. B. looked after project administration.