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

Authors: Zhaohui Shang; Huibin Yan; Weidong Ruan; Yong Bai
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

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.


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## Body

## 1. 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. The 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]. The BFETS JIP project [3, 4] and EFEF JIP project [5–9] 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.Figure 1
Role of defining explosion loads in risk assessment process.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. Therefore, 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. Therefore, a suitable number of scenarios should be determined, which has been documented by several international codes [10–16]. The 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. The LHS technique is a widely used sampling method, which is suitable for small size sample. The 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]. The 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].The 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 [26–28]. 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. This 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. The 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. The 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.


## 2. Procedure for Quantitative Analysis of Gas Explosion Loads in Offshore Platforms

The main procedure for quantitative analysis of gas explosion loads in this paper is illustrated in Figure2.Figure 2
Procedure for quantitative analysis of gas explosion loads.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. Therefore, 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. Then, 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 speedThe 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 Section3. After obtaining the probability functions of different variables, the Latin Hypercube Sampling (LHS) method was chosen to sample a suitable number of variable groups. The main concept of the LHS method will be introduced in Section 4.The 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. Then, 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 Section5.The last step is to determine the explosion loads on interested regions. FLACS code was chosen to conduct the explosion load analysis of each scenario. The happening probability of each explosion scenario is also calculated in this step. Based on the load and probability of each scenario, the design accidental load method can be employed and exceedance probability curve for interested regions can also be established. Then, the load corresponding to a certain probability level can be obtained. Detailed procedure of this step is introduced in Section6.


## 3. Leak Scenarios’ Selection for Example Platform

This 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.


### 3.1. Basic Information for Example Platform

The example oil and gas platform used in this paper is based on empirical assumption with the basic layout information from APPENDIX 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. Therefore, petroleum gas is the considered leak gas. Possible leak equipment is shown in Figure 5.Figure 3
Basic layout information of example platform.Figure 4
3D geometrical model of considered example platform. (a) General view. (b) Inner equipment.
(a)(b)Figure 5
Possible equipment groups.


### 3.2. Source Data Collection

The 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.The 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. Therefore, 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. The 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.Figure 6
Leak amount data from 135 FPSOs in the UK.Figure 7
Leak rate data from installations in the North Sea.Figure 8
Wind direction data in West Africa Sea.Figure 9
Wind speed data in West Africa Sea.


### 3.3. 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. Thus, 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 Figure10, 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 Figure10.Figure 10
Possible leak location and direction of different equipment.
(a)(b)(c)


#### 3.3.2. Leak Location CDF and Sampling Procedure

The CDF of leak location is the most difficult function to obtain in all variables. As illustrated in Figure5, 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 three-dimensional 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 Figure11. 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. The method of calculating total leak frequency of different equipment types are as follows:(1)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 m2 face area (for vessel and gas station).Figure 11
Main procedure to obtain the CDF of equipment groups.For the example considered in this paper, the classified equipment groups have been shown in Figure5 and the frequency calculation results are shown in Table 1. The 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.Table 1
Equipment group frequency calculation and corresponding transferred variable range.
EquipmentUnit frequencyLength/area/countsTotal frequencyProbabilityTransferred variable rangePipe0.518592.50.2370-1Valves2.551948.450.1241-2Connections216320.0822-3Volume-10.757556.250.1443-4Volume-20.752720.250.0524-5Volume-30.752720.250.0525-6Volume-40.751712.750.0336-7Volume-50.751712.750.0337-8Volume-60.752518.750.0488-9Volume-70.75860.0159-10Volume-80.751712.750.03310-11Volume-90.751712.750.03311-12Riser201200.05112-13Gas station0.755440.50.10413-14Transferred variable range refers to the characterl in equation (2). In Table 1, each equipment corresponds to a specific range of the variable l. When a value of Fl 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, Fl 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 Fl, and its value are within the range of 0∼1. This transferred variable range l falls in the interval corresponding to the pipeline equipment; finally, the leakage point will be determined in the pipe.Figure12(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):(2)Fl=0.2372l,0≤l≤1,0.7243+0.0327l−7,7<l≤8,0.2372+0.1242l−1,1<l≤2,0.7570+0.0481l−8,8<l≤9,0.3615+0.0821l−2,2<l≤3,0.8051+0.0154l−9,9<l≤10,0.4435+0.1442l−3,3<l≤4,0.8205+0.0327l−10,10<l≤11,0.5878+0.0519l−4,4<l≤5,0.8532+0.0327l−11,11<l≤12,0.6379+0.0519l−5,5<l≤6,0.8859+0.0513l−12,12<l≤13,0.6916+0.0327l−6,6<l≤7,0.9372+0.1039l−13,13<l≤14.Figure 12
(a) Leak frequency of leak location variable; (b) CDF of leak location variable.
(a)(b)Through 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 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. The 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 Figure10Actually, if a leakage happens, the leak point may not be the points given by the assumption. The assumed leak points are actually representative points of some leak areas. The leak point assumptions are thought reasonable in this paper. The 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 Figure13. 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 Nsim representative leak points (each leak point can be given to a unique number), the variable range of this equipment group can be divided into Nsim parts, and the three sampled variable values will fall in three unique parts, which are the mst, nst, and ost parts. By randomly arranging the array 1,2,…,Nsim, the mst, nst, and ost locations will also have a unique number Na,Nb,andNc. Then, representative leak points corresponding to number Na,Nb,andNc can be selected as the leak points, and the coordinate of the leak location are known. It should be mentioned that the LHS sampled variable number in a group range are not constant, may be more than 3, or less than 3. Nevertheless, the procedure is similar.Figure 13
Procedure to get the specific coordinate of leak location.


#### 3.3.3. Leak Amount CDF

Leak amount is represented by variablea 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:(3)Fa=0.535373⋅a,0≤a≤1,0.001452⋅a−1+0.535373,1<a≤300,0.000044a−300+0.969407,300<a≤1000.Figure 14
Leak amount cumulative distribution function from 135 FPSOs in UK.


#### 3.3.4. Leak Rate CDF

Table2 provides the relevant information on gas leakage rates of FPSO in the PSA (2011b) report in the waters off Norway and the UK.Table 2
Information of gas leak rate for FPSOs in North Sea (PSA, 2011b).
Leak rateCountryNumber of gas leaksInterval probabilityEquipment number>1 kg/sNorway (59°N Lat.)350.2010382UK173550.1–1 kg/sNorway (59°N Lat.)1180.7990382UK49355Leak rate is represented by variabler 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. The CDF of the leak rate is as equation (4), and the graphical expression of the equation is shown in Figure 15:(4)Fr=0.887826⋅r−0.1,0.1≤r≤1,0.083732⋅r−1+0.799,1<r≤3.4.Figure 15
Leak rate cumulative distribution function from installations in the North Sea.


#### 3.3.5. Wind Direction CDF

Wind direction and wind speed are represented by variablesd and s, respectively. Similar method to leak amount is also used here. The CDF of d and s can be expressed as equations (5) and (6), and the corresponding graphical expressions are shown in Figures 16 and 17:(5)Fd=0.007473⋅d,0≤d≤45,0.002349⋅d−45+0.33628,45<d≤90,0.00076⋅d−90+0.442,90<d≤135,0.000416⋅d−135+0.4762,135<d≤180,0.000475⋅d−180+0.49491,180<d≤225,0.000334⋅d−225+0.51628,225<d≤270,0.0018⋅d−270+0.53129,270<d≤315,0.008617⋅d−315+0.6123,315<d≤360,(6)Fs=0.047538⋅s,0≤s≤2,0.169147⋅s−2+0.095075,2<s≤4,0.20134⋅s−4+0.433368,4<s≤6,0.074346⋅s−6+0.836068,6<s≤8,0.00723⋅s−8+0.984768,8<s≤10,0.000325⋅s−10+0.999228,10<s≤12,0.00005⋅s−12+0.999878,12<s≤14,0.000025⋅s−14+0.999978,14<s≤16.Figure 16
Wind direction cumulative distribution function in West Africa Sea.Figure 17
Wind speed cumulative distribution function in West Africa Sea.


## 3.1. Basic Information for Example Platform

The example oil and gas platform used in this paper is based on empirical assumption with the basic layout information from APPENDIX 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. Therefore, petroleum gas is the considered leak gas. Possible leak equipment is shown in Figure 5.Figure 3
Basic layout information of example platform.Figure 4
3D geometrical model of considered example platform. (a) General view. (b) Inner equipment.
(a)(b)Figure 5
Possible equipment groups.


## 3.2. Source Data Collection

The 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.The 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. Therefore, 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. The 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.Figure 6
Leak amount data from 135 FPSOs in the UK.Figure 7
Leak rate data from installations in the North Sea.Figure 8
Wind direction data in West Africa Sea.Figure 9
Wind speed data in West Africa Sea.


## 3.3. 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. Thus, 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 Figure10, 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 Figure10.Figure 10
Possible leak location and direction of different equipment.
(a)(b)(c)


### 3.3.2. Leak Location CDF and Sampling Procedure

The CDF of leak location is the most difficult function to obtain in all variables. As illustrated in Figure5, 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 three-dimensional 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 Figure11. 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. The method of calculating total leak frequency of different equipment types are as follows:(1)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 m2 face area (for vessel and gas station).Figure 11
Main procedure to obtain the CDF of equipment groups.For the example considered in this paper, the classified equipment groups have been shown in Figure5 and the frequency calculation results are shown in Table 1. The 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.Table 1
Equipment group frequency calculation and corresponding transferred variable range.
EquipmentUnit frequencyLength/area/countsTotal frequencyProbabilityTransferred variable rangePipe0.518592.50.2370-1Valves2.551948.450.1241-2Connections216320.0822-3Volume-10.757556.250.1443-4Volume-20.752720.250.0524-5Volume-30.752720.250.0525-6Volume-40.751712.750.0336-7Volume-50.751712.750.0337-8Volume-60.752518.750.0488-9Volume-70.75860.0159-10Volume-80.751712.750.03310-11Volume-90.751712.750.03311-12Riser201200.05112-13Gas station0.755440.50.10413-14Transferred variable range refers to the characterl in equation (2). In Table 1, each equipment corresponds to a specific range of the variable l. When a value of Fl 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, Fl 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 Fl, and its value are within the range of 0∼1. This transferred variable range l falls in the interval corresponding to the pipeline equipment; finally, the leakage point will be determined in the pipe.Figure12(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):(2)Fl=0.2372l,0≤l≤1,0.7243+0.0327l−7,7<l≤8,0.2372+0.1242l−1,1<l≤2,0.7570+0.0481l−8,8<l≤9,0.3615+0.0821l−2,2<l≤3,0.8051+0.0154l−9,9<l≤10,0.4435+0.1442l−3,3<l≤4,0.8205+0.0327l−10,10<l≤11,0.5878+0.0519l−4,4<l≤5,0.8532+0.0327l−11,11<l≤12,0.6379+0.0519l−5,5<l≤6,0.8859+0.0513l−12,12<l≤13,0.6916+0.0327l−6,6<l≤7,0.9372+0.1039l−13,13<l≤14.Figure 12
(a) Leak frequency of leak location variable; (b) CDF of leak location variable.
(a)(b)Through 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 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. The 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 Figure10Actually, if a leakage happens, the leak point may not be the points given by the assumption. The assumed leak points are actually representative points of some leak areas. The leak point assumptions are thought reasonable in this paper. The 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 Figure13. 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 Nsim representative leak points (each leak point can be given to a unique number), the variable range of this equipment group can be divided into Nsim parts, and the three sampled variable values will fall in three unique parts, which are the mst, nst, and ost parts. By randomly arranging the array 1,2,…,Nsim, the mst, nst, and ost locations will also have a unique number Na,Nb,andNc. Then, representative leak points corresponding to number Na,Nb,andNc can be selected as the leak points, and the coordinate of the leak location are known. It should be mentioned that the LHS sampled variable number in a group range are not constant, may be more than 3, or less than 3. Nevertheless, the procedure is similar.Figure 13
Procedure to get the specific coordinate of leak location.


### 3.3.3. Leak Amount CDF

Leak amount is represented by variablea 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:(3)Fa=0.535373⋅a,0≤a≤1,0.001452⋅a−1+0.535373,1<a≤300,0.000044a−300+0.969407,300<a≤1000.Figure 14
Leak amount cumulative distribution function from 135 FPSOs in UK.


### 3.3.4. Leak Rate CDF

Table2 provides the relevant information on gas leakage rates of FPSO in the PSA (2011b) report in the waters off Norway and the UK.Table 2
Information of gas leak rate for FPSOs in North Sea (PSA, 2011b).
Leak rateCountryNumber of gas leaksInterval probabilityEquipment number>1 kg/sNorway (59°N Lat.)350.2010382UK173550.1–1 kg/sNorway (59°N Lat.)1180.7990382UK49355Leak rate is represented by variabler 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. The CDF of the leak rate is as equation (4), and the graphical expression of the equation is shown in Figure 15:(4)Fr=0.887826⋅r−0.1,0.1≤r≤1,0.083732⋅r−1+0.799,1<r≤3.4.Figure 15
Leak rate cumulative distribution function from installations in the North Sea.


### 3.3.5. Wind Direction CDF

Wind direction and wind speed are represented by variablesd and s, respectively. Similar method to leak amount is also used here. The CDF of d and s can be expressed as equations (5) and (6), and the corresponding graphical expressions are shown in Figures 16 and 17:(5)Fd=0.007473⋅d,0≤d≤45,0.002349⋅d−45+0.33628,45<d≤90,0.00076⋅d−90+0.442,90<d≤135,0.000416⋅d−135+0.4762,135<d≤180,0.000475⋅d−180+0.49491,180<d≤225,0.000334⋅d−225+0.51628,225<d≤270,0.0018⋅d−270+0.53129,270<d≤315,0.008617⋅d−315+0.6123,315<d≤360,(6)Fs=0.047538⋅s,0≤s≤2,0.169147⋅s−2+0.095075,2<s≤4,0.20134⋅s−4+0.433368,4<s≤6,0.074346⋅s−6+0.836068,6<s≤8,0.00723⋅s−8+0.984768,8<s≤10,0.000325⋅s−10+0.999228,10<s≤12,0.00005⋅s−12+0.999878,12<s≤14,0.000025⋅s−14+0.999978,14<s≤16.Figure 16
Wind direction cumulative distribution function in West Africa Sea.Figure 17
Wind speed cumulative distribution function in West Africa Sea.


## 3.3.1. Leak Direction Selecting Method

In this paper, leak direction is thought to be greatly dependent on the leak location. Thus, 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 Figure10, 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 Figure10.Figure 10
Possible leak location and direction of different equipment.
(a)(b)(c)


## 3.3.2. Leak Location CDF and Sampling Procedure

The CDF of leak location is the most difficult function to obtain in all variables. As illustrated in Figure5, 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 three-dimensional 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 Figure11. 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. The method of calculating total leak frequency of different equipment types are as follows:(1)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 m2 face area (for vessel and gas station).Figure 11
Main procedure to obtain the CDF of equipment groups.For the example considered in this paper, the classified equipment groups have been shown in Figure5 and the frequency calculation results are shown in Table 1. The 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.Table 1
Equipment group frequency calculation and corresponding transferred variable range.
EquipmentUnit frequencyLength/area/countsTotal frequencyProbabilityTransferred variable rangePipe0.518592.50.2370-1Valves2.551948.450.1241-2Connections216320.0822-3Volume-10.757556.250.1443-4Volume-20.752720.250.0524-5Volume-30.752720.250.0525-6Volume-40.751712.750.0336-7Volume-50.751712.750.0337-8Volume-60.752518.750.0488-9Volume-70.75860.0159-10Volume-80.751712.750.03310-11Volume-90.751712.750.03311-12Riser201200.05112-13Gas station0.755440.50.10413-14Transferred variable range refers to the characterl in equation (2). In Table 1, each equipment corresponds to a specific range of the variable l. When a value of Fl 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, Fl 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 Fl, and its value are within the range of 0∼1. This transferred variable range l falls in the interval corresponding to the pipeline equipment; finally, the leakage point will be determined in the pipe.Figure12(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):(2)Fl=0.2372l,0≤l≤1,0.7243+0.0327l−7,7<l≤8,0.2372+0.1242l−1,1<l≤2,0.7570+0.0481l−8,8<l≤9,0.3615+0.0821l−2,2<l≤3,0.8051+0.0154l−9,9<l≤10,0.4435+0.1442l−3,3<l≤4,0.8205+0.0327l−10,10<l≤11,0.5878+0.0519l−4,4<l≤5,0.8532+0.0327l−11,11<l≤12,0.6379+0.0519l−5,5<l≤6,0.8859+0.0513l−12,12<l≤13,0.6916+0.0327l−6,6<l≤7,0.9372+0.1039l−13,13<l≤14.Figure 12
(a) Leak frequency of leak location variable; (b) CDF of leak location variable.
(a)(b)Through 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 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. The 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 Figure10Actually, if a leakage happens, the leak point may not be the points given by the assumption. The assumed leak points are actually representative points of some leak areas. The leak point assumptions are thought reasonable in this paper. The 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 Figure13. 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 Nsim representative leak points (each leak point can be given to a unique number), the variable range of this equipment group can be divided into Nsim parts, and the three sampled variable values will fall in three unique parts, which are the mst, nst, and ost parts. By randomly arranging the array 1,2,…,Nsim, the mst, nst, and ost locations will also have a unique number Na,Nb,andNc. Then, representative leak points corresponding to number Na,Nb,andNc can be selected as the leak points, and the coordinate of the leak location are known. It should be mentioned that the LHS sampled variable number in a group range are not constant, may be more than 3, or less than 3. Nevertheless, the procedure is similar.Figure 13
Procedure to get the specific coordinate of leak location.


## 3.3.3. Leak Amount CDF

Leak amount is represented by variablea 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:(3)Fa=0.535373⋅a,0≤a≤1,0.001452⋅a−1+0.535373,1<a≤300,0.000044a−300+0.969407,300<a≤1000.Figure 14
Leak amount cumulative distribution function from 135 FPSOs in UK.


## 3.3.4. Leak Rate CDF

Table2 provides the relevant information on gas leakage rates of FPSO in the PSA (2011b) report in the waters off Norway and the UK.Table 2
Information of gas leak rate for FPSOs in North Sea (PSA, 2011b).
Leak rateCountryNumber of gas leaksInterval probabilityEquipment number>1 kg/sNorway (59°N Lat.)350.2010382UK173550.1–1 kg/sNorway (59°N Lat.)1180.7990382UK49355Leak rate is represented by variabler 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. The CDF of the leak rate is as equation (4), and the graphical expression of the equation is shown in Figure 15:(4)Fr=0.887826⋅r−0.1,0.1≤r≤1,0.083732⋅r−1+0.799,1<r≤3.4.Figure 15
Leak rate cumulative distribution function from installations in the North Sea.


## 3.3.5. Wind Direction CDF

Wind direction and wind speed are represented by variablesd and s, respectively. Similar method to leak amount is also used here. The CDF of d and s can be expressed as equations (5) and (6), and the corresponding graphical expressions are shown in Figures 16 and 17:(5)Fd=0.007473⋅d,0≤d≤45,0.002349⋅d−45+0.33628,45<d≤90,0.00076⋅d−90+0.442,90<d≤135,0.000416⋅d−135+0.4762,135<d≤180,0.000475⋅d−180+0.49491,180<d≤225,0.000334⋅d−225+0.51628,225<d≤270,0.0018⋅d−270+0.53129,270<d≤315,0.008617⋅d−315+0.6123,315<d≤360,(6)Fs=0.047538⋅s,0≤s≤2,0.169147⋅s−2+0.095075,2<s≤4,0.20134⋅s−4+0.433368,4<s≤6,0.074346⋅s−6+0.836068,6<s≤8,0.00723⋅s−8+0.984768,8<s≤10,0.000325⋅s−10+0.999228,10<s≤12,0.00005⋅s−12+0.999878,12<s≤14,0.000025⋅s−14+0.999978,14<s≤16.Figure 16
Wind direction cumulative distribution function in West Africa Sea.Figure 17
Wind speed cumulative distribution function in West Africa Sea.


## 4. Latin Hypercube Sampling (LHS)

### 4.1. LHS Method

LHS method is based on the idea of Latin square–ann×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 axis-aligned 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 methods can be chosen, and one of them used in this paper can be expressed as(7)xi,j=Fi−1πij−0.5Nsim,where xi,j is the jth sample value of the ith variable; Fi−1 is the CDF inverse function of the ith variable; Nsim is the sampling number of each variable; and πi1,…,πiNsim is the random permutation of 1,…,Nsim.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. The method was employed as follows. The 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. The representative value of the random variable for each segment is defined as the average value of that segment. The center of the area is taken as the representative value of the segment at the tail of the probability density distribution.The 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. Therefore, based on Latin hypercube sampling (LHS) methodM random number groups can be extracted in this paper, and each array has a unique set of random variables for different parameters. Therefore, 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.Figure18 shows the concept of LHS sampling with one variable, and Figure 19 illustrates the example of two-variable LHS with Nsim = 8.Figure 18
Schematic of one-variable LHS.Figure 19
Schematic of two-variable LHS with 8 samples.


### 4.2. Sampling Process and Results

The LHS sampling process is conducted in MATLAB program. By using command “randperm,” the array1,2,…,Nsim 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 Table3.Table 3
50 Leak scenarios sampled by LHS method.
Leak scenario no.Leak amount (kg)Leak rate (kg/s)Wind speed (m/s)Wind directionLocationX (m)LocationY (m)LocationZ (m)Leak direction10.210.296.46344.914.2521.50.25Z−2771.350.885.87313.727211.5Y−3203.951.614.5828.107.7514.50.6Z+4217.722.335.3738.81221.51X+5231.500.653.5176.374.25192.75Y−6313.730.904.1859.3419.523.34.6Y−793.723.043.27349.555.722.54.4Z−811.062.802.68337.945.85180.75Y−9272.843.285.28302.614.517.80.35Y−100.360.993.399.374.25191Y−11107.500.453.62340.261122.51Z+120.730.613.0341.481.25241Y+130.322.097.80280.394.527.34.8Z+14176.390.414.6844.161.2521.52.25Z−150.840.954.9822.7516271.25Z+160.242.565.9720.07312.52Y−170.690.475.47358.831.2517.80.85Z−180.500.382.80321.706201X−190.061.133.8612.0411.422.50.5X+200.580.135.57347.237.513.70.85Z+21121.280.521.8997.631122.10.5Y−220.280.860.63319.38215.54.6X+230.430.814.78356.51424.54.6X+240.920.205.676.6913243.5Z+250.170.594.084.01316.52Y+26286.610.343.74335.626.9515.50.35X+27259.061.854.48326.34114.52X−2852.390.688.73328.661.25242.75Y+29190.171.372.9214.723.521.51X−3079.950.707.2684.881323.51.5Y−310.880.635.7717.40514.52X+32245.280.181.4750.831325.51.5Y+330.090.722.32291.50514.52X+340.130.567.53354.1918.5270.75X+350.020.792.56168.203.2512.31.35Z+36135.060.434.8867.861628.50.75Y−370.650.225.08317.057.5150.75X+380.990.972.44123.957.717.54.4Z−390.540.540.2136.134.7521.52.75X+40162.610.115.18333.30314.54Z+410.770.926.99330.9818.521.34.8Z+420.620.316.1930.783.411.54.6X−430.390.251.05342.5912.927.70.25Y−44148.840.743.15266.07314.54Z+450.950.502.21205.486231.5X−4624.840.834.28324.025.85120.75X−4766.170.163.9833.466.312.51.35X−480.470.776.731.346.7511.50.35X490.800.272.09351.877.518.50.55Z+5038.610.364.3825.431527.750.6Y+


## 4.1. LHS Method

LHS method is based on the idea of Latin square–ann×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 axis-aligned 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 methods can be chosen, and one of them used in this paper can be expressed as(7)xi,j=Fi−1πij−0.5Nsim,where xi,j is the jth sample value of the ith variable; Fi−1 is the CDF inverse function of the ith variable; Nsim is the sampling number of each variable; and πi1,…,πiNsim is the random permutation of 1,…,Nsim.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. The method was employed as follows. The 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. The representative value of the random variable for each segment is defined as the average value of that segment. The center of the area is taken as the representative value of the segment at the tail of the probability density distribution.The 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. Therefore, based on Latin hypercube sampling (LHS) methodM random number groups can be extracted in this paper, and each array has a unique set of random variables for different parameters. Therefore, 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.Figure18 shows the concept of LHS sampling with one variable, and Figure 19 illustrates the example of two-variable LHS with Nsim = 8.Figure 18
Schematic of one-variable LHS.Figure 19
Schematic of two-variable LHS with 8 samples.


## 4.2. Sampling Process and Results

The LHS sampling process is conducted in MATLAB program. By using command “randperm,” the array1,2,…,Nsim 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 Table3.Table 3
50 Leak scenarios sampled by LHS method.
Leak scenario no.Leak amount (kg)Leak rate (kg/s)Wind speed (m/s)Wind directionLocationX (m)LocationY (m)LocationZ (m)Leak direction10.210.296.46344.914.2521.50.25Z−2771.350.885.87313.727211.5Y−3203.951.614.5828.107.7514.50.6Z+4217.722.335.3738.81221.51X+5231.500.653.5176.374.25192.75Y−6313.730.904.1859.3419.523.34.6Y−793.723.043.27349.555.722.54.4Z−811.062.802.68337.945.85180.75Y−9272.843.285.28302.614.517.80.35Y−100.360.993.399.374.25191Y−11107.500.453.62340.261122.51Z+120.730.613.0341.481.25241Y+130.322.097.80280.394.527.34.8Z+14176.390.414.6844.161.2521.52.25Z−150.840.954.9822.7516271.25Z+160.242.565.9720.07312.52Y−170.690.475.47358.831.2517.80.85Z−180.500.382.80321.706201X−190.061.133.8612.0411.422.50.5X+200.580.135.57347.237.513.70.85Z+21121.280.521.8997.631122.10.5Y−220.280.860.63319.38215.54.6X+230.430.814.78356.51424.54.6X+240.920.205.676.6913243.5Z+250.170.594.084.01316.52Y+26286.610.343.74335.626.9515.50.35X+27259.061.854.48326.34114.52X−2852.390.688.73328.661.25242.75Y+29190.171.372.9214.723.521.51X−3079.950.707.2684.881323.51.5Y−310.880.635.7717.40514.52X+32245.280.181.4750.831325.51.5Y+330.090.722.32291.50514.52X+340.130.567.53354.1918.5270.75X+350.020.792.56168.203.2512.31.35Z+36135.060.434.8867.861628.50.75Y−370.650.225.08317.057.5150.75X+380.990.972.44123.957.717.54.4Z−390.540.540.2136.134.7521.52.75X+40162.610.115.18333.30314.54Z+410.770.926.99330.9818.521.34.8Z+420.620.316.1930.783.411.54.6X−430.390.251.05342.5912.927.70.25Y−44148.840.743.15266.07314.54Z+450.950.502.21205.486231.5X−4624.840.834.28324.025.85120.75X−4766.170.163.9833.466.312.51.35X−480.470.776.731.346.7511.50.35X490.800.272.09351.877.518.50.55Z+5038.610.364.3825.431527.750.6Y+


## 5. Explosion Scenarios’ Selection for Example Platform

### 5.1. CFD-Based Dispersion Analysis

#### 5.1.1. 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. Figure20 shows typical grid solution for dispersion models. The grid near the leak location is refined in the direction perpendicular to the leak direction. The refined grid size is 0.2 m and is stretched smoothly to the main control grid size (1 m). The 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.Figure 20
Typical grid solution for dispersion models.Besides the parameters listed in Table3, some key parameter sets can be seen in Table 4, and other parameter are set according to FLACS user’s manual [35].Table 4
Main dispersion parameter sets.
Boundary conditions“Wind: +X, +Y;” “Nozzle: −X, −Y, +Z, −Z”Leak type“JET”Outlet area“0.04 m2”Time set“Start leak time:5 s;” “total analysis time: 5+ leak duration +5 (s)”Medium volume fractions“Ethylene: 15%;” “Propylene: 5%;” “Propane: 50%;” “Butane: 20%;” “Hydrogen: 10%”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 will be consistent with the values obtained by LHS from statistical data.


#### 5.1.2. 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. There is also a most suitable ratio that the combustion will produce the greatest amount of heat. The “equivalent stoichiometric gas volume” actually transforms the flammable gas volume into a volume with most suitable fuel/air ratio. The transformation method is shown in(8)∑Vequivalent=∑Vflammable×EactualEstoich,where Eactual is the expansion factor for the actual fuel/air ratio and Estoich 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 Figure21. 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 21
Comparison between volumes of flammable gas and equivalent stoichiometric gas for a leak scenario.Figure22 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 m3 to hundreds of m3. 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.Figure 22
Equivalent stoichiometric gas volumes for 50 leak scenarios.The other valuable result is the gas concentration distribution in the platform zone, which will be used to define the location of gas explosion cloud. Figure23 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. The location of gas explosion cloud can be relatively and reasonably determined by distinguishing the concentration distribution figures.Figure 23
Concentration distribution of a scenario at a certain time. (a) 0.5 m, (b) 2.3 m, (c) 3.7 m, and (d) 4.5 m.
(a)(b)(c)(d)


### 5.2. 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. These key parameters contain gas cloud volume, gas cloud locationX,Y,Z, and gas cloud size LX,LY,LZ.


#### 5.2.1. Gas Cloud Volume

The maximum equivalent stoichiometric gas volumeVdisper that formulated during the dispersion process of each scenario will be used as the base value to calculate the gas explosion cloud volume Vexplo. The relationship between Vexplo and Vdisper can be expressed as follows:(9)Vexplo=f1⋅f2⋅f3⋅Vdisper,where f1: porosity factor, which is defined by “1/porosity of the platform zone” and is set as 1.5 in the considered example platform; f2: pressure revision factor, which is used to consider the under predicted overpressure of FLACS code (studies show that the overpressure predicted by FLACS code were under predicted for about 20∼30%), and its value is set as 1.3; f3: safety factor, which is used to think of the great uncertainty of explosion, and its value is set as 2.As illustrated in Figure24, the reason to set the porosity factor f1 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 Vexplo, this issue is resolved effectively by introducing the porosity factor f1.Figure 24
Gas explosion cloud example.


#### 5.2.2. 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 results would be affected by different analysts. The main constraint of this process isVexplo 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:(10)IfVexplo≤ZH3,thenLX=LY=LZ=Vexplo1/3,IfZH3<Vexplo≤ZH⋅X12,thenLz=ZH,LX=LY=VexploZH1/2,IfZH⋅X12<Vexplo≤ZH⋅X1⋅Y1,thenLz=ZH,LX=X1,LY=VexploZH⋅X1,IfZH⋅X1⋅Y1<Vexplo≤ZH⋅X2⋅Y1,thenLz=ZH,LX=VexploZH⋅Y1,LY=Y1,IfZH⋅X2⋅Y1<Vexplo≤ZH⋅X2⋅Y2,thenLz=ZH,LX=X2,LY=VexploZH⋅X2,where ZH is the height between two decks; X1,X2,Y1,andY2 are shown in Figure 25.Figure 25
Schematic ofX1, X2, Y1, and Y2.As the main law of determining the location of explosion gas cloud, this cloud is relatively put at the center of dispersion gas cloud. 50 determined explosion scenarios of the example platform are listed in Table5.Table 5
50 explosion scenarios.
Explosion scenario noVolume of gas cloud (m3)Location of gas cloudSize of gas cloudIgnition probabilityX (m)Y (m)Z (m)LX (m)LY (m)LZ (m)16.7864.518.501.91.91.91.61E − 072530.41.51408.18.151.26E − 0531501.5010017.417.453.56E − 054290.161.714.207.67.656.89E − 0651014010014.314.352.41E − 05614430100171753.42E − 0571489.8010017.317.353.54E − 058324.871.51408.18.157.71E − 069869.7010013.213.252.06E − 051020.0073.517.502.72.72.74.75E − 0711417.30.913.409.29.259.90E − 061219.188023.802.72.72.74.55E − 071315.912027.52.52.52.52.53.78E − 0714460.20.713.209.69.651.09E − 051530.10816.921.51.93.13.13.17.14E − 07168.03401002221.91E − 071711.19301802.32.32.32.66E − 07185.382617.501.81.81.81.28E − 07196.59118.120.501.91.91.91.56E − 07206.708912.501.91.91.91.59E − 0721228.152.114.606.86.855.41E − 062226.09101123336.19E − 072325.54552223336.06E − 072425.5451220.513336.06E − 072520.202217.502.72.72.74.79E − 0726158.732.6515.1505.75.753.77E − 0627368.941.213.708.68.658.76E − 0628620.1012.4011.211.251.47E − 0529413.40.9513.4509.19.159.81E − 0630546012.75010.510.551.30E − 053119.2278.312.502.72.72.74.56E − 0732557.7012.7010.610.651.32E − 053324.188.11302.92.92.95.74E − 07341.9518.526.501.31.31.34.63E − 083514.3522122.52.52.52.53.41E − 0736280.81.7514.2507.57.556.66E − 063720.5148.31502.72.72.74.87E − 073834.63251603.33.33.38.22E − 073918.60362102.72.72.74.41E − 0740111.15315.505552.64E − 06411.9517193.71.31.31.34.63E − 084216.61411002.62.62.63.94E − 074311.232122702.32.32.32.67E − 07441329.9010016.316.353.16E − 054523.432102.92.92.95.55E − 07462342.0514.5506.96.955.55E − 0647312.781.5514.0507.97.957.42E − 064826.94901103336.40E − 074931.12271703.23.23.27.39E − 075066.372004.14.14.11.57E − 06


## 5.1. CFD-Based Dispersion Analysis

### 5.1.1. 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. Figure20 shows typical grid solution for dispersion models. The grid near the leak location is refined in the direction perpendicular to the leak direction. The refined grid size is 0.2 m and is stretched smoothly to the main control grid size (1 m). The 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.Figure 20
Typical grid solution for dispersion models.Besides the parameters listed in Table3, some key parameter sets can be seen in Table 4, and other parameter are set according to FLACS user’s manual [35].Table 4
Main dispersion parameter sets.
Boundary conditions“Wind: +X, +Y;” “Nozzle: −X, −Y, +Z, −Z”Leak type“JET”Outlet area“0.04 m2”Time set“Start leak time:5 s;” “total analysis time: 5+ leak duration +5 (s)”Medium volume fractions“Ethylene: 15%;” “Propylene: 5%;” “Propane: 50%;” “Butane: 20%;” “Hydrogen: 10%”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 will be consistent with the values obtained by LHS from statistical data.


### 5.1.2. 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. There is also a most suitable ratio that the combustion will produce the greatest amount of heat. The “equivalent stoichiometric gas volume” actually transforms the flammable gas volume into a volume with most suitable fuel/air ratio. The transformation method is shown in(8)∑Vequivalent=∑Vflammable×EactualEstoich,where Eactual is the expansion factor for the actual fuel/air ratio and Estoich 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 Figure21. 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 21
Comparison between volumes of flammable gas and equivalent stoichiometric gas for a leak scenario.Figure22 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 m3 to hundreds of m3. 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.Figure 22
Equivalent stoichiometric gas volumes for 50 leak scenarios.The other valuable result is the gas concentration distribution in the platform zone, which will be used to define the location of gas explosion cloud. Figure23 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. The location of gas explosion cloud can be relatively and reasonably determined by distinguishing the concentration distribution figures.Figure 23
Concentration distribution of a scenario at a certain time. (a) 0.5 m, (b) 2.3 m, (c) 3.7 m, and (d) 4.5 m.
(a)(b)(c)(d)


## 5.1.1. 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. Figure20 shows typical grid solution for dispersion models. The grid near the leak location is refined in the direction perpendicular to the leak direction. The refined grid size is 0.2 m and is stretched smoothly to the main control grid size (1 m). The 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.Figure 20
Typical grid solution for dispersion models.Besides the parameters listed in Table3, some key parameter sets can be seen in Table 4, and other parameter are set according to FLACS user’s manual [35].Table 4
Main dispersion parameter sets.
Boundary conditions“Wind: +X, +Y;” “Nozzle: −X, −Y, +Z, −Z”Leak type“JET”Outlet area“0.04 m2”Time set“Start leak time:5 s;” “total analysis time: 5+ leak duration +5 (s)”Medium volume fractions“Ethylene: 15%;” “Propylene: 5%;” “Propane: 50%;” “Butane: 20%;” “Hydrogen: 10%”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 will be consistent with the values obtained by LHS from statistical data.


## 5.1.2. 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. There is also a most suitable ratio that the combustion will produce the greatest amount of heat. The “equivalent stoichiometric gas volume” actually transforms the flammable gas volume into a volume with most suitable fuel/air ratio. The transformation method is shown in(8)∑Vequivalent=∑Vflammable×EactualEstoich,where Eactual is the expansion factor for the actual fuel/air ratio and Estoich 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 Figure21. 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 21
Comparison between volumes of flammable gas and equivalent stoichiometric gas for a leak scenario.Figure22 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 m3 to hundreds of m3. 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.Figure 22
Equivalent stoichiometric gas volumes for 50 leak scenarios.The other valuable result is the gas concentration distribution in the platform zone, which will be used to define the location of gas explosion cloud. Figure23 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. The location of gas explosion cloud can be relatively and reasonably determined by distinguishing the concentration distribution figures.Figure 23
Concentration distribution of a scenario at a certain time. (a) 0.5 m, (b) 2.3 m, (c) 3.7 m, and (d) 4.5 m.
(a)(b)(c)(d)


## 5.2. 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. These key parameters contain gas cloud volume, gas cloud locationX,Y,Z, and gas cloud size LX,LY,LZ.


### 5.2.1. Gas Cloud Volume

The maximum equivalent stoichiometric gas volumeVdisper that formulated during the dispersion process of each scenario will be used as the base value to calculate the gas explosion cloud volume Vexplo. The relationship between Vexplo and Vdisper can be expressed as follows:(9)Vexplo=f1⋅f2⋅f3⋅Vdisper,where f1: porosity factor, which is defined by “1/porosity of the platform zone” and is set as 1.5 in the considered example platform; f2: pressure revision factor, which is used to consider the under predicted overpressure of FLACS code (studies show that the overpressure predicted by FLACS code were under predicted for about 20∼30%), and its value is set as 1.3; f3: safety factor, which is used to think of the great uncertainty of explosion, and its value is set as 2.As illustrated in Figure24, the reason to set the porosity factor f1 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 Vexplo, this issue is resolved effectively by introducing the porosity factor f1.Figure 24
Gas explosion cloud example.


### 5.2.2. 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 results would be affected by different analysts. The main constraint of this process isVexplo 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:(10)IfVexplo≤ZH3,thenLX=LY=LZ=Vexplo1/3,IfZH3<Vexplo≤ZH⋅X12,thenLz=ZH,LX=LY=VexploZH1/2,IfZH⋅X12<Vexplo≤ZH⋅X1⋅Y1,thenLz=ZH,LX=X1,LY=VexploZH⋅X1,IfZH⋅X1⋅Y1<Vexplo≤ZH⋅X2⋅Y1,thenLz=ZH,LX=VexploZH⋅Y1,LY=Y1,IfZH⋅X2⋅Y1<Vexplo≤ZH⋅X2⋅Y2,thenLz=ZH,LX=X2,LY=VexploZH⋅X2,where ZH is the height between two decks; X1,X2,Y1,andY2 are shown in Figure 25.Figure 25
Schematic ofX1, X2, Y1, and Y2.As the main law of determining the location of explosion gas cloud, this cloud is relatively put at the center of dispersion gas cloud. 50 determined explosion scenarios of the example platform are listed in Table5.Table 5
50 explosion scenarios.
Explosion scenario noVolume of gas cloud (m3)Location of gas cloudSize of gas cloudIgnition probabilityX (m)Y (m)Z (m)LX (m)LY (m)LZ (m)16.7864.518.501.91.91.91.61E − 072530.41.51408.18.151.26E − 0531501.5010017.417.453.56E − 054290.161.714.207.67.656.89E − 0651014010014.314.352.41E − 05614430100171753.42E − 0571489.8010017.317.353.54E − 058324.871.51408.18.157.71E − 069869.7010013.213.252.06E − 051020.0073.517.502.72.72.74.75E − 0711417.30.913.409.29.259.90E − 061219.188023.802.72.72.74.55E − 071315.912027.52.52.52.52.53.78E − 0714460.20.713.209.69.651.09E − 051530.10816.921.51.93.13.13.17.14E − 07168.03401002221.91E − 071711.19301802.32.32.32.66E − 07185.382617.501.81.81.81.28E − 07196.59118.120.501.91.91.91.56E − 07206.708912.501.91.91.91.59E − 0721228.152.114.606.86.855.41E − 062226.09101123336.19E − 072325.54552223336.06E − 072425.5451220.513336.06E − 072520.202217.502.72.72.74.79E − 0726158.732.6515.1505.75.753.77E − 0627368.941.213.708.68.658.76E − 0628620.1012.4011.211.251.47E − 0529413.40.9513.4509.19.159.81E − 0630546012.75010.510.551.30E − 053119.2278.312.502.72.72.74.56E − 0732557.7012.7010.610.651.32E − 053324.188.11302.92.92.95.74E − 07341.9518.526.501.31.31.34.63E − 083514.3522122.52.52.52.53.41E − 0736280.81.7514.2507.57.556.66E − 063720.5148.31502.72.72.74.87E − 073834.63251603.33.33.38.22E − 073918.60362102.72.72.74.41E − 0740111.15315.505552.64E − 06411.9517193.71.31.31.34.63E − 084216.61411002.62.62.63.94E − 074311.232122702.32.32.32.67E − 07441329.9010016.316.353.16E − 054523.432102.92.92.95.55E − 07462342.0514.5506.96.955.55E − 0647312.781.5514.0507.97.957.42E − 064826.94901103336.40E − 074931.12271703.23.23.27.39E − 075066.372004.14.14.11.57E − 06


## 5.2.1. Gas Cloud Volume

The maximum equivalent stoichiometric gas volumeVdisper that formulated during the dispersion process of each scenario will be used as the base value to calculate the gas explosion cloud volume Vexplo. The relationship between Vexplo and Vdisper can be expressed as follows:(9)Vexplo=f1⋅f2⋅f3⋅Vdisper,where f1: porosity factor, which is defined by “1/porosity of the platform zone” and is set as 1.5 in the considered example platform; f2: pressure revision factor, which is used to consider the under predicted overpressure of FLACS code (studies show that the overpressure predicted by FLACS code were under predicted for about 20∼30%), and its value is set as 1.3; f3: safety factor, which is used to think of the great uncertainty of explosion, and its value is set as 2.As illustrated in Figure24, the reason to set the porosity factor f1 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 Vexplo, this issue is resolved effectively by introducing the porosity factor f1.Figure 24
Gas explosion cloud example.


## 5.2.2. 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 results would be affected by different analysts. The main constraint of this process isVexplo 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:(10)IfVexplo≤ZH3,thenLX=LY=LZ=Vexplo1/3,IfZH3<Vexplo≤ZH⋅X12,thenLz=ZH,LX=LY=VexploZH1/2,IfZH⋅X12<Vexplo≤ZH⋅X1⋅Y1,thenLz=ZH,LX=X1,LY=VexploZH⋅X1,IfZH⋅X1⋅Y1<Vexplo≤ZH⋅X2⋅Y1,thenLz=ZH,LX=VexploZH⋅Y1,LY=Y1,IfZH⋅X2⋅Y1<Vexplo≤ZH⋅X2⋅Y2,thenLz=ZH,LX=X2,LY=VexploZH⋅X2,where ZH is the height between two decks; X1,X2,Y1,andY2 are shown in Figure 25.Figure 25
Schematic ofX1, X2, Y1, and Y2.As the main law of determining the location of explosion gas cloud, this cloud is relatively put at the center of dispersion gas cloud. 50 determined explosion scenarios of the example platform are listed in Table5.Table 5
50 explosion scenarios.
Explosion scenario noVolume of gas cloud (m3)Location of gas cloudSize of gas cloudIgnition probabilityX (m)Y (m)Z (m)LX (m)LY (m)LZ (m)16.7864.518.501.91.91.91.61E − 072530.41.51408.18.151.26E − 0531501.5010017.417.453.56E − 054290.161.714.207.67.656.89E − 0651014010014.314.352.41E − 05614430100171753.42E − 0571489.8010017.317.353.54E − 058324.871.51408.18.157.71E − 069869.7010013.213.252.06E − 051020.0073.517.502.72.72.74.75E − 0711417.30.913.409.29.259.90E − 061219.188023.802.72.72.74.55E − 071315.912027.52.52.52.52.53.78E − 0714460.20.713.209.69.651.09E − 051530.10816.921.51.93.13.13.17.14E − 07168.03401002221.91E − 071711.19301802.32.32.32.66E − 07185.382617.501.81.81.81.28E − 07196.59118.120.501.91.91.91.56E − 07206.708912.501.91.91.91.59E − 0721228.152.114.606.86.855.41E − 062226.09101123336.19E − 072325.54552223336.06E − 072425.5451220.513336.06E − 072520.202217.502.72.72.74.79E − 0726158.732.6515.1505.75.753.77E − 0627368.941.213.708.68.658.76E − 0628620.1012.4011.211.251.47E − 0529413.40.9513.4509.19.159.81E − 0630546012.75010.510.551.30E − 053119.2278.312.502.72.72.74.56E − 0732557.7012.7010.610.651.32E − 053324.188.11302.92.92.95.74E − 07341.9518.526.501.31.31.34.63E − 083514.3522122.52.52.52.53.41E − 0736280.81.7514.2507.57.556.66E − 063720.5148.31502.72.72.74.87E − 073834.63251603.33.33.38.22E − 073918.60362102.72.72.74.41E − 0740111.15315.505552.64E − 06411.9517193.71.31.31.34.63E − 084216.61411002.62.62.63.94E − 074311.232122702.32.32.32.67E − 07441329.9010016.316.353.16E − 054523.432102.92.92.95.55E − 07462342.0514.5506.96.955.55E − 0647312.781.5514.0507.97.957.42E − 064826.94901103336.40E − 074931.12271703.23.23.27.39E − 075066.372004.14.14.11.57E − 06


## 6. Design Explosion Loads for Example Platform

### 6.1. CFD-Based Explosion Analysis

#### 6.1.1. Analysis Setting Up

According to the 50 explosion scenarios, 50 explosion models were established within the framework of the FLACS code. The control grid size in the platform zone is 1 m and is stretched smoothly from the platform boundary to the simulation zone boundary. Figure26 shows a typical grid solution for explosion models.Figure 26
Typical grid solution for explosion models.Besides the parameters listed in Table5, some key parameter sets are listed in Table 6, and other parameters are set according to FLACS user’s manual [35].Table 6
Main explosion parameter sets.
Boundary conditions“Plane_Wave”Ignition“1 m3, in the bottom center of the control volume”Medium volume fractions“Ethylene: 15%;” “Propylene: 5%;” “Propane: 50%;” “Butane: 20%;” “Hydrogen: 10%”


#### 6.1.2. 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 Figure27. The max P/PP or PP/PPIMP of the considered location can be extracted and used for load design.Figure 27
Typical pressure output: (a) P/PP curve; (b) PIMP/PPIMP curve.
(a)(b)


### 6.2. Probability Analysis

The explosion probability should also be determined before finally plotting the explosion probability exceedance curve. The event tree depicted in Figure28 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(11)Pexplosion=Pleak×Pdispersion×Pignition.Figure 28
Event tree of the gas explosion.According to Table1, the total leak frequency of this platform is calculated as 405.95/106 hrs, which means that the platform will leak 4 times a year. Therefore, if the considered time is 1 year, Pleak = 1. As the whole possible happening leak scenarios are represented by 50 scenarios, therefore, Pdispersion 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 Pignition of each scenario should be corrected according to its volume size. The correction method can be expressed as follows:(12)Pignition=Vdisper⋅f1Vplatform⋅Pignitiontotal.Table 7
Ignition probability calculation.
ItemUnit prob (E)AgeMaintenanceManningTechSubtotalNumberTotalHot work1.14–4—————00Rotating machineryPump9.60–50.901.001.000.800.7211.33E − 4Compressor2.30–3—————00Generator3.50–3—————00Electrical equipment2.60–60.901.001.000.800.72400 m21.44E − 3Other equipment (1)2.60–60.901.001.000.800.72400 m21.44E − 3Other equipment (2)1.30–61.001.001.001.001.00400 m21.16E − 3Human factor3.00–61.001.000.601.000.60400 m22.00E − 3Sum6.17E − 3Once the values ofPleak, Pdispersion, and Pignition are determined, Pexplosion for each explosion scenario can be calculated by equation (11), and the corresponding results are summarized in Table 5.


### 6.3. 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. Then, 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.The pressure and impulse curves of the panel that separates the compressor station and the process area are extracted out for different scenarios. Figure29 plots the pressure and impulse probability exceedance curves of the considered panel. As recommended in many international guides [11, 36], loads corresponding to 10−4 probability level are usually used as the design loads. Therefore, design pressure and impulse for this panel are set as 0.12 MPa (1.2 bar) and 0.01 MPa·s (0.1 bar·s). As the data selected in this paper are all based on history database and reasonable assumption, it can be found that the predicted load values are very close to that suggested in the guides. The suggested design loads in Table D1 of DNV OS-101 [36] are shown in Table 8.Figure 29
Pressure (a) and impulse (b) exceedance probability curves of a panel of example platform.
(a)(b)Table 8
Suggested explosion load design values in DNV.
Offshore installationAreaDesign blast overpressure (bar)Pulse duration (s)Production platform, fixedProcess area, medium sized, solid upper, and lower decks, 3 storeys, 1 or 2 side open1.50.2


## 6.1. CFD-Based Explosion Analysis

### 6.1.1. Analysis Setting Up

According to the 50 explosion scenarios, 50 explosion models were established within the framework of the FLACS code. The control grid size in the platform zone is 1 m and is stretched smoothly from the platform boundary to the simulation zone boundary. Figure26 shows a typical grid solution for explosion models.Figure 26
Typical grid solution for explosion models.Besides the parameters listed in Table5, some key parameter sets are listed in Table 6, and other parameters are set according to FLACS user’s manual [35].Table 6
Main explosion parameter sets.
Boundary conditions“Plane_Wave”Ignition“1 m3, in the bottom center of the control volume”Medium volume fractions“Ethylene: 15%;” “Propylene: 5%;” “Propane: 50%;” “Butane: 20%;” “Hydrogen: 10%”


### 6.1.2. 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 Figure27. The max P/PP or PP/PPIMP of the considered location can be extracted and used for load design.Figure 27
Typical pressure output: (a) P/PP curve; (b) PIMP/PPIMP curve.
(a)(b)


## 6.1.1. Analysis Setting Up

According to the 50 explosion scenarios, 50 explosion models were established within the framework of the FLACS code. The control grid size in the platform zone is 1 m and is stretched smoothly from the platform boundary to the simulation zone boundary. Figure26 shows a typical grid solution for explosion models.Figure 26
Typical grid solution for explosion models.Besides the parameters listed in Table5, some key parameter sets are listed in Table 6, and other parameters are set according to FLACS user’s manual [35].Table 6
Main explosion parameter sets.
Boundary conditions“Plane_Wave”Ignition“1 m3, in the bottom center of the control volume”Medium volume fractions“Ethylene: 15%;” “Propylene: 5%;” “Propane: 50%;” “Butane: 20%;” “Hydrogen: 10%”


## 6.1.2. 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 Figure27. The max P/PP or PP/PPIMP of the considered location can be extracted and used for load design.Figure 27
Typical pressure output: (a) P/PP curve; (b) PIMP/PPIMP curve.
(a)(b)


## 6.2. Probability Analysis

The explosion probability should also be determined before finally plotting the explosion probability exceedance curve. The event tree depicted in Figure28 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(11)Pexplosion=Pleak×Pdispersion×Pignition.Figure 28
Event tree of the gas explosion.According to Table1, the total leak frequency of this platform is calculated as 405.95/106 hrs, which means that the platform will leak 4 times a year. Therefore, if the considered time is 1 year, Pleak = 1. As the whole possible happening leak scenarios are represented by 50 scenarios, therefore, Pdispersion 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 Pignition of each scenario should be corrected according to its volume size. The correction method can be expressed as follows:(12)Pignition=Vdisper⋅f1Vplatform⋅Pignitiontotal.Table 7
Ignition probability calculation.
ItemUnit prob (E)AgeMaintenanceManningTechSubtotalNumberTotalHot work1.14–4—————00Rotating machineryPump9.60–50.901.001.000.800.7211.33E − 4Compressor2.30–3—————00Generator3.50–3—————00Electrical equipment2.60–60.901.001.000.800.72400 m21.44E − 3Other equipment (1)2.60–60.901.001.000.800.72400 m21.44E − 3Other equipment (2)1.30–61.001.001.001.001.00400 m21.16E − 3Human factor3.00–61.001.000.601.000.60400 m22.00E − 3Sum6.17E − 3Once the values ofPleak, Pdispersion, and Pignition are determined, Pexplosion for each explosion scenario can be calculated by equation (11), and the corresponding results are summarized in Table 5.


## 6.3. 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. Then, 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.The pressure and impulse curves of the panel that separates the compressor station and the process area are extracted out for different scenarios. Figure29 plots the pressure and impulse probability exceedance curves of the considered panel. As recommended in many international guides [11, 36], loads corresponding to 10−4 probability level are usually used as the design loads. Therefore, design pressure and impulse for this panel are set as 0.12 MPa (1.2 bar) and 0.01 MPa·s (0.1 bar·s). As the data selected in this paper are all based on history database and reasonable assumption, it can be found that the predicted load values are very close to that suggested in the guides. The suggested design loads in Table D1 of DNV OS-101 [36] are shown in Table 8.Figure 29
Pressure (a) and impulse (b) exceedance probability curves of a panel of example platform.
(a)(b)Table 8
Suggested explosion load design values in DNV.
Offshore installationAreaDesign blast overpressure (bar)Pulse duration (s)Production platform, fixedProcess area, medium sized, solid upper, and lower decks, 3 storeys, 1 or 2 side open1.50.2


## 7. 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. The 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 probabilityThe 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. The designed maximum pressure load on interested areas of the example platform is 1.2 bar, which is very close to 1.5 bar that suggested in DNV codes. It can demonstrate the effectiveness and feasibility of the proposed method.The 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.



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*Source: 3098719-2020-10-09.xml*