# Determination of the Design Load for Structural Safety Assessment against Gas Explosion in Offshore Topside

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2 and impulse. In this new method, exceedance surface method, the structural response is considered in load determination procedure and acceptance criterion is selected as the load exceedance frequency. For these studies, the explosion scenario data from CFD simulations for the topside structure were used. Dynamic Region Duration change has great influence in this area Quasi-static Region Impulsive Region Figure 1: Dynamic response of a system under explosion load [2] 2. PROBABILISTIC ANALYSIS OF EXPLOSION LOAD As mentioned above, explosion accidents at offshore installation are widely distributed in terms of their consequences and have high uncertainties due to the associated many random variables. Nowadays, the probabilistic approach combined with CFD analysis is practically used to reflect these complex characteristics of explosion loads. Explosion simulation Random variables Regression Analysis PDF of Explosion load Response surface Monte Carlo Simulation scenario (s,x,y,z) Figure 2: Process for determining explosion design load

3 In this paper, existing probabilistic approach is improved in following aspects. For each analysis step, all of the factors which affect the explosion loads are treated as random variables and final results are given as the joint probability distribution of explosion loads which can be applied for the risk based determination of design explosion loads. The modified method for the probabilistic definition of explosion loads is shown schematically in Figure Analysis model The topside structure of a FPSO is selected as the analysis model [3]. Figure 3 shows the analyzed FPSO and the layout of its topside module. The module of separation train is considered for the explosion accidents. All leakage scenarios are selected in this area and the design explosion load is determined. Figure 3: Module arrangement and separation module of analyzed FPSO 2.2 Leakage scenario & dispersion analysis Explosion only occurs when enough amount of flammable gas mixture is cumulated and ignited by some internal or external sources. Therefore, the variables related to gas cloud are the most important factors for the frequency and consequence of the explosion load. To verify the location and size of the flammable gas clouds when leakage is occurred, dispersion analysis can be performed using CFD software, like FLACS [4]. With the leakage of gas, environmental conditions also affect formation of gas cloud and these random variables for the dispersion analysis are given below. Table 1: Random variables for dispersion analysis Random variable Distribution type parameters Wind direction Normal distribution μ=180.9, σ=50.57 Wind speed Weibull distribution α=4.84, β=2.563 Leak rate Weibull distribution (3para.) α=29.39, β=1.454, λ=1.0 Leak duration Weibull distribution (3para.) α=76.76, β=1.712, λ=0.362 Leak direction Uniform distribution C= Leak position X Normal distribution μ=0.437, σ=0.222 Leak position Y Normal distribution μ=0.442, σ=0.198 Leak position Z Uniform distribution C=1 For dispersion analysis, total 50 scenarios are defined via LHS(Latin Hypercube Sampling) method [5]. LHS is a sampling technique to extract the pre-selected number of samples from the individual areas which are defined by dividing probabilistic distribution function of each variable to have the same probability of occurrence. For all leakage scenarios, the result of dispersion analysis can be represented by 8 values as below.

4 Gas cloud volume Gas concentration. Gas cloud position in the X dir. Gas cloud position in the Y dir. Gas cloud position in the Z dir. Gas cloud size in the X dir. Gas cloud size in the Y dir. Gas cloud size in the Z dir 2.3 Explosion analysis Variables for explosion analysis The results of dispersion analysis expressed by 8 random variables are applied as input for explosion analysis. To simplify the analysis process, non-regular shape of flammable gas is converted to cube form which has the highest gas concentration level [4]. Figure 4 shows this concept graphically. (V fuel /V oxygen ) actual ER= (V fuel /V oxygen ) stoichiometric, V f, V e ER = 1.0 Figure 4: Conversion of non-uniform flammable gas to equivalent volume With this assumption, pre-mentioned 8 variables can be reduced to 4 random variables in terms of gas cloud size and location in the X, Y, and Z direction. Figure 5 shows the probabilistic distribution of reduced random variables fitted as normal distribution, gumbel distribution, log-normal distribution, and normal distribution respectively.,v f,v e Figure 5: Probabilistic density function of random variables

5 When a large number of variables act compositely, ignoring the correlation between two or more variables can leads the misunderstanding to the effect of each variable on induced phenomenon. So, in this paper, Pearson product-moment correlation coefficients are calculated to confirm the degree of connection between two variables. Variable Table 2: The correlation coefficient of two variables Cloud size Cloud size 1.0 Cloud position X dir. Y dir. Z dir. Cloud position X dir Y dir Z dir As shown in Table 2, most of the absolute values for correlation coefficients are less than 0.1 and it means no linear relation exists between two variables. Only two results marked as red show weak linear relation but it is small enough to exclude its influence. Additionally, the scatter diagrams of two variables are plotted to check the case of non-linear relation and no strong correlation is found from these graphical results. So, in this paper, each random variable is treated as an independent value The results of explosion analysis Table 3 shows some results of 50 explosion analyses which are conducted for EFEF JIP [3]. For these explosion analyses, 4 random variables defined in previous section are used and FLACS software is selected as the solver. All of the calculations performed using explosion analysis results in following sections are based on these data. Scenario No. Table 3: Analysis results of explosion simulation with FLACS Cloud size [m] Cloud position [m] X dir. Y dir. Z dir. Pressure [MPa] Impulse [MPa*s] E E E E E E E E E E E E Mathematical model of explosion load The inputs of explosion analysis are 4 random variables as referred in Section So, in this scheme, the mathematical model of explosion loads also can be established in terms of 4 variables by a regression analysis and it is defined as a response surface of explosion load. Figure 6 shows the real explosion analysis results and various mathematical models generated. In Figure 6, the estimated explosion load by higher order mathematical model shows good agreement with the CFD analysis results. However, it doesn t mean that the complicated mathematical model has high accuracy because the adequate function of mathematical model for each variable is always different due to its physical characteristics.

6 In this paper, 2 nd order polynomial function which has no combined term is selected for the each explosion response surface. Basic form of selected load response surface is expressed as equation (1). Overpressure or Impulse = a 0 + a i x i + b i x i 2 + ε (1) Figure 6: Mathematical models for the overpressure and impulse 2.5 Probabilistic distribution of explosion load Probabilistic density function of each explosion load For the accurate determination of probabilistic distribution for explosion loads, simulating all probable explosion scenarios with a sophisticated analysis method is the best way, if it is possible. However, this approach is not effective due to the time consumption induced by the large number of scenarios or long simulation time spent by the analysis tool itself. To reduce the calculation cost, in this paper, Monte Carlo simulation using response surface method is introduced to determine the probabilistic density function of overpressure and impulse. Total 1 million leak scenarios are selected considering the distribution of 4 random variables and the consequence of explosion loads are calculated adopting the pre-defined load response surface in Section 2.4. Figure 7 show the determined probabilistic density function of each explosion loads fitted as log-normal distribution function. Figure 7: Approximation of the overpressure & impulse mathematical model Joint probability of overpressure & Impulse Scatter diagram for pre-selected 50 scenarios in Figure 8 is showing a bivariate distribution almost entirely supported on its diagonal line. It means that there is high linear relation between two

8 Pd Id t* Pd Pd Figure 10: Determination of dimensioning explosion load with exceedance curves 3.2 New method (Exceedance frequency surface method) Although dual exceedance curve and P-t curve method are dealing with both component of an explosion load, combination of selected values can be different from the probabilistic expression of an explosion load because the correlation between overpressure and impulse is not considered in detail. So, in this paper, above methods are modified to improve this aspect as mentioned in previous section. From the joint probability density function defined in Section 2.5.2, the exceedance probability surface is generated and it is changed to the leakage frequency term applying the HSE data which includes the information of leak amount and its corresponding frequency [7]. It is assumed the ignition probabilities of all possible scenarios are the same value to simplify the calculation in this paper. To consider the realistic explosion phenomenon, the distribution of ignition probability should be defined in terms of the variable which affects the value of it, like cloud size, location, time, etc. This ignition probability is combined with leak frequency as expressed in equation (2) to calculate the explosion frequency, and exceedance explosion frequency surface is generated with these data. Explosion frequency = Leak frequency x Ignition probability (2) Applying the general risk acceptance criteria as the exceedance frequency, 1.0 x 10-4 /yr, the sets of overpressure and impulse can be determined as a form of a curve that is shown below Figure 12. This Overpressure-Impulse(P-I) design load curve means the relation of two load components at the given risk level. To compare the result of this approach with dual exceedance curve and P-t curve method, the determined design loads by those methods are also plotted. As shown in Figure 12, determined design loads by dual exceedance curve and P-t curve are not located on the P-I curve although these methods are employing the same acceptance criteria. The correlation of overpressure and impulse can be considered as a main reason for these differences. For the determination of a design explosion load with the exceedance surface method, additional criteria should be introduced to select a critical combination of overpressure and impulse among the numerous sets on the curve. As shown in Figure 12, one component of the load converges to a specific value when the other component of the load is getting larger. So, the limit point of each load component should be selected as a reference point to be checked with response criterion because this

9 combination can results in one of the most serious responses among the load sets which is located on an asymptotic curve. To choose the proper limit value of each load component, the generated P-I curve is limited as a restricted region by adopting the design overpressure and impulse determined by dual exceedance curve or P-t curve method. 1.0 x 10-4 /yr Figure 11: Exceedance explosion frequency surface With the 2 load reference points corresponding to maximum value of each load component, final one is defined considering the natural frequency of a target structure, T, and duration of the load, t d, to reflect the inconsistent characteristics of response in dynamic loading region. Finally, design explosion load is selected as the combination of load component which results in the maximum response among the 3 load points. Design load by P-t curve method I d-curve 1 Overpressure asymptotic Design points (P d, I d ) surface Design load by Dual curve method, (P d, I d ) curve (t d = T) 3 Impulse asymptotic 2 Determined P-I design load curve with given criteria, 1.0 x 10-4 /yr P d-curve Figure 12: P-I design load curve from exceedance surface 4. CONCLUSIONS This paper presents the procedure for probabilistic determination of design explosion loads at an offshore facility. All design factors which affect explosion events are expressed as random variables

10 and used to determine the probabilistic density function of explosion loads. When applying load response surface, Monte Carlo simulation is performed for the purpose of reducing calculation time of CFD analysis. Based on the probabilistic density functions, new method to determine the design explosion loads is suggested. In this method, exceedance frequency curves are generated and the design explosion load is selected as the corresponding value to the risk acceptance criteria. Additionally, exceedance frequency surface is generated considering the joint probability of overpressure and impulse to include the correlation effect of two explosion load components. With this exceedance surface, therefore, the sets of design loads which result in great impact on a structure are determined. By the new method above, more exact design loads can be determined than the existing method which uses exceedance curves only. References [1] NORSOK Z-013, Risk and Emergency Preparedness Analysis, Rev. 2, Norwegian Technology Standard Institution, 2001 [2] J. Biggs, Introduction on Structural Dynamics, McGraw-Hill, 1964 [3] JK Paik, J. Czujko, Explosion and Fire Engineering of FPSOs (phase Ⅱ) Definition of Fire and Gas Explosion Design Loads, Research Institute of Ship and Offshore Structural Design Innovation, Pusan National University, 2010 [4] FLACS, GexCon AS ( Norway [5] J. Czujko, Design of Offshore Facilities to Resist Gas Explosion Hazard Engineering Handbook, Corrocean ASA, [6] Oil & Gas UK, Fire and Explosion Guidelines, Issue 1, 2007 [7] HSE, Hydrocarbon Release System,

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