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 中国石油大学学报(自然科学版)  2019, Vol. 43 Issue (4): 143-150  DOI:10.3969/j.issn.1673-5005.2019.04.017 0

### 引用本文 [复制中英文]

[复制中文]
QI Xinge, WANG Haiqing, TIAN Yingshuai, et al. Safety coefficient of control room load based on gas cloud explosion[J]. Journal of China University of Petroleum (Edition of Natural Science), 2019, 43(4): 143-150. DOI: 10.3969/j.issn.1673-5005.2019.04.017.
[复制英文]

### 文章历史

1. 中国石油大学(华东)机电工程学院, 山东青岛 266580;
2. 深圳燃气集团安全管理部, 广东深圳 518040

Safety coefficient of control room load based on gas cloud explosion
QI Xinge1 , WANG Haiqing1 , TIAN Yingshuai2 , CHEN Guoming1
1. ollege of Mechanical and Electronic Engineering in China University of Petroleum (East China), Qingdao 266580, China;
2. Department of Safety Management, Shenzhen Gas Group Company Limited, Shenzhen 518040, China
Abstract: The research on the explosion load of the control room mainly includes two aspects, which are the architectural design load and the probabilistic explosion load. But the effect of uncertainty of the input parameters and calculation model on the output results has not been fully considered. It is difficult to ensure the conservativeness of the design index when detecting the gas cloud by using the GDS system. So the calculation and analysis method of safety coefficient was proposed, aiming at the explosion load of control room and other equipment under control(EUC) based on the uncertainty theory, by analyzing the process of gas leakage dispersion and gas cloud explosion. The input parameters with significant impacts on the explosion consequence have been selected, and the Latin hypercube sampling was used to determine the input samples. The calculation model of equivalent cloud size was proposed based on the Gaussian diffusion theory.The shock wave overpressure was used as the output in the light of the application of the multi-energy method. The Monte Carlo method and Sobol index method were used to calculate the uncertainty and parameter sensitivity respectively, and then the safety coefficient was obtained. The results show that applying the methodology to a LNG tank area, the uncertainty parameter can be selected and their interval can be determined according to the actual working conditions. Comparing by scatter plot of explosion overpressure and input parameters, the safety coefficient can be quantitatively obtained in different leakage scenarios. Data analysis shows that the safety coefficient can enhance the conservation of EUC's explosive load. In addition, it can improve the ability to prevent and control accidents, and provide the basis for GDS system detection.
Keywords: safety coefficient    uncertainty    parameter sensitivity    gas leak    explosion

1 不确定度理论

2 爆炸结果模型及参数分析

2.1 气体泄漏

 ${Q_{\rm{L}}} = {C_{\rm{d}}}A\rho \sqrt {\frac{{2\left( {p - {p_0}} \right)}}{\rho } + \frac{{u_1^2}}{2}} .$ (1)

2.2 气体扩散的等价气云

 $\begin{array}{*{20}{l}} {C(x,y,z) = \frac{{{Q_L}}}{{2{\rm{ \mathsf{ π} }}{\sigma _y}{\sigma _z}u}}\exp \left[ { - \frac{1}{2}{{\left( {\frac{y}{{{\sigma _y}}}} \right)}^2}} \right] \times }\\ {\left\{ {\exp \left[ { - \frac{1}{2}{{\left( {\frac{{z - {H_r}}}{{{\sigma _z}}}} \right)}^2}} \right] + \exp \left[ { - \frac{1}{2}{{\left( {\frac{{z + {H_r}}}{{{\sigma _z}}}} \right)}^2}} \right]} \right\}.} \end{array}$ (2)

 $y = \pm \sqrt { - 2\ln \frac{{2{\rm{ \mathsf{ π} }}C{\sigma _y}{\sigma _z}u}}{{{Q_{\rm{L}}}}} + 2\ln \left\{ {\exp \left[ { - \frac{1}{2}{{\left( {\frac{{z - {H_{\rm{r}}}}}{{{\sigma _z}}}} \right)}^2}} \right] + \exp \left[ { - \frac{1}{2}{{\left( {\frac{{z + {H_{\rm{r}}}}}{{{\sigma _z}}}} \right)}^2}} \right]} \right\}} \cdot \left| {{\sigma _y}} \right|.$ (3)

 ${S_{{\rm{ESC}}}} = {\rm{ \mathsf{ π} }}ab,$ (4)

 $a = x_{\rm{d}}^{\max }/2,$
 $b = y_{\rm{d}}^{\max }/2.$

 ${V_{{\rm{ESC}}}} = \frac{1}{3}{S_{{\rm{ESC}}}}z_{\rm{d}}^{\max }.$ (5)
2.3 多能法计算爆炸后果

 图 1 多能法计算爆炸后果流程 Fig.1 Flow chart of explosion consequence calculation by multi-energy method
 $E = 3.5 \times {10^3}{V_{{\rm{ESC}}}}.$ (6)

 ${R^\prime } = \frac{z}{{{{\left( {E/{p_0}} \right)}^{1/3}}}}.$ (7)

 ${P_{\rm{s}}} = {p_0}{p^\prime }.$ (8)

3 基于MC模型的参数不确定度

(1) 确定不确定度来源。不确定度分析的主要目的是依据模型的不确定性与输入的不确定性修正预测结果。对计算模型中涉及的参数进行分析, 确定不确定性参数。

(2) 确定不确定性参数的概率特征并生成随机输入样本。依据以往的扩散场景、历史数据等拟合得到输入参数的概率密度函数, 基于概率密度函数用抽样法得到离散分布的样本[17-18]。样本的大小以及抽样方法的选择决定了MC模型模拟的精度。

 $1 - {\left( {\frac{a}{{100}}} \right)^M} \ge \frac{b}{{100}}.$ (9)

(3) 以生成的样本为输入计算对应的输出, 并利用期望与标准差的值对不确定性分析结果进行表征, 得到输出结果的不确定度, 表示为

 $\bar y = \frac{1}{M}\sum\limits_{i = 1}^M {{y_i}} .$ (10)
 ${u^2}(\bar y) = \frac{1}{{M - 1}}\sum\limits_{i = 1}^M {{{\left( {{y_i} - \bar y} \right)}^2}} .$ (11)

4 安全系数 4.1 不确定性参数的全局参数敏感性

(1) 假定某一函数Y, 可表示为自变量为X的一系列函数之和, 即

 $\begin{array}{*{20}{l}} {Y = {f_0} + \sum\limits_{i = 1}^d {{f_i}} \left( {{X_i}} \right) + \sum\limits_{i < j}^d {{f_{ij}}} \left( {{X_i},{X_j}} \right) + \cdots + {f_{1,2, \cdots ,d}}\left( {{X_1},} \right.}\\ {\left. {{X_2}, \cdots ,{X_d}} \right).} \end{array}$ (12)

 $\begin{array}{l} {f_0} = E\left( Y \right),\\ {f_i}\left( {{X_i}} \right) = E\left( {Y\left| {{X_i}} \right.} \right) - {f_0},\\ {f_{ij}}\left( {{X_i},{X_j}} \right) = E\left( {Y|{X_i},{X_j}} \right) - {f_0} - {f_i} - {f_j}. \end{array}$ (13)

(2) 参数xi的方差可表示为

 $\begin{array}{l} {V_i} = va{r_{{X_i}}}\left( {{E_{{X_{ \sim i}}}}\left( {Y|{X_i}} \right)} \right),\\ {V_{ij}} = va{r_{{X_{ij}}}}\left( {{E_{{X_{ \sim ij}}}}\left( {Y|{X_i},{X_j}} \right)} \right) - {V_i} - {V_j}. \end{array}$ (14)

 ${\rm var}(Y) = \sum\limits_{i = 1}^d {{V_i}} + \sum\limits_{i < j}^d {{f_{ij}}} + {V_{1,2, \cdots ,d}}.$ (15)

(3) 输入参数xi对输出y的影响可通过一阶敏感性指数确定, 表示为

 ${S_i} = \frac{{{V_i}}}{{var(Y)}}.$ (16)
4.2 安全系数计算

 ${u_{\rm{c}}} = \sum\limits_{k = 1}^p {{u_k}} (\bar y){S_k}.$ (17)

 ${s_{\rm{c}}} = 1 - {u_{\rm{c}}}.$ (18)

 图 2 控制室载荷安全系数计算流程 Fig.2 Calculation flow of safety coefficient
5 案例分析

5.1 输入样本选择

(1) 输入样本大小确定。

(2) 不确定性参数取值区间确定。

5.2 不确定度与参数敏感性

 图 3 样本区间内超压值散点图 Fig.3 Overpressure scatter plot in sample interval
 图 4 参数敏感度过程矩阵超压柱形图 Fig.4 Overpressure histogram of process matrix to calculate parameter sensitivity

6 结论

(1) 以等价气云爆炸事故为基础, 综合考虑了气体泄漏扩散过程与气云爆炸过程中的不确定性因素, 实现了以控制室为代表的建筑物爆炸载荷安全系数的确定。

(2) 应用于某LNG罐区, 得到不同场景下的安全系数, 增加了控制室等建筑物冲击波超压爆炸载荷的保守性, 为GDS系统探测设计输入提供理论支持。

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