Leakage estimation in a chemical tank farm with unsteady adjoint equation and genetic algorithm

doi:10.11949/0438-1157.20240972

Abstract

Abstract:

The genetic algorithm based on fixed detector network is further developed by using the unsteady adjoint equation, and is used to invert the leakage position and leakage rate after leakage in chemical tank area. First, the source-detector relationship is established by unsteady adjoint equations based on computational fluid dynamics (CFD) simulations. Then, the sources are estimated using genetic algorithm. Unsteady adjoint equations can establish the source-detector relationship accurately while saving massive CFD simulation computation, and the high efficiency of genetic algorithm can realize the prompt estimation of leakage. After considering the measurement errors and thresholds of the detectors, estimation is performed for 10 leakage sources. The results show that the estimation accuracy of each source is high. Additionally, the estimation accuracy changing over leakage time is discussed, indicating that the proposed method can promptly and accurately estimate the leakage sources under complex flow conditions.

Key words: leakage estimation, unsteady adjoint equation, genetic algorithm, computational fluid dynamics, diffusion, safety

摘要：

利用非定常伴随方程进一步发展了基于固定探测器网络的遗传算法，并将其用于化工储罐区泄漏后泄漏位置和泄漏率的反演。首先基于计算流体动力学（CFD）模拟，利用非定常伴随方程建立源-探测器关系，然后利用遗传算法对泄漏进行反演。非定常伴随方程在准确建立源-探测器关系的同时，可以节省大量的CFD模拟计算量，且遗传算法的计算高效性可实现对泄漏的快速反演。在考虑了探测器的测量误差和阈值后，对10个泄漏源进行反演，结果表明各泄漏源的反演精度均较高。此外，还讨论了反演精度随泄漏时间的变化情况，表明所提方法可在复杂流动下快速准确地反演泄漏源。

关键词: 泄漏反演, 非定常伴随方程, 遗传算法, 计算流体力学, 扩散, 安全

CLC Number:

X 937

Fuyu WANG, Xuanyi ZHOU. Leakage estimation in a chemical tank farm with unsteady adjoint equation and genetic algorithm[J]. CIESC Journal, 2025, 76(6): 3104-3114.

王富玉, 周晅毅. 结合非定常伴随方程和遗传算法的化工区反演[J]. 化工学报, 2025, 76(6): 3104-3114.

Figures/Tables 13

Fig.1 Process of using the proposed method to estimate the chemical tank farm leakage

Fig.2 Schematic diagram of computational domain

Fig.3 Distributions of unknown sources and detectors

Fig.4 Grid system

Fig.5 Grid sensitivity test

Fig.6 Inflow profiles

Table 1 Solver settings and boundary conditions

项目		设置
仿真模型	计算域	21.75H (x)×12.8H (y)×6H (z)
仿真模型	网格数	1288769个
求解设置	湍流模型	标准k-ε模型^[32]
	速度-压力耦合	压力耦合方程组的半隐式方法（semi-implicit method for pressure-linked equations, SIMPLE）
	对流项离散格式	二阶迎风格式
	扩散项离散格式	二阶迎风格式
	近壁面处理	标准壁面函数
边界条件	入口	速度入口^[33-34]
	出口	自由出流^[32-33]
	顶面和侧面	对称
	地面和储罐	无滑移壁面^[34]
	探测器（求解伴随方程）	源强度为1^{[14, 35]}，时间步长为0.005 s

Fig.7 Time-averaged flow field (z = H/20)

Fig.8 Concentration distribution and detector concentrations over time of S4

Fig.9 Concentration distribution and detector concentrations over time of S7

Fig.10 Estimated results of leakage locations

Table 2 Estimated results （t*=70）

源	$m t r u e, x$ / $m e s t, x$ / $σ e s t, x$ / $N M S E x$	$m t r u e, y$ / $m e s t, y$ / $σ e s t, y$ / $N M S E y$	$m t r u e, z$ / $m e s t, z$ / $σ e s t, z$ / $N M S E z$	$m t r u e, q$ / $m e s t, q$ / $σ e s t, q$ / $N M S E q$
S1	1.12/1.12/0.04/0%	1.54/1.55/0.04/0%	0.04/0.06/0.03/21.25%	3/2.7/0.6/0.9%
S2	1.02/1.06/0.06/0.17%	1.44/1.42/0.02/0.02%	0.01/0.01/0.01/5.08%	3/3.7/0.9/3.9%
S3	1.07/1.08/0.03/0.01%	1.21/1.21/0.01/0%	0.05/0.05/0.01/0.50%	3/4.4/0.5/15.3%
S4	1.02/1.06/0.07/0.12%	1.12/1.14/0.01/0.03%	0.02/0.01/0.01/12.26%	3/4.1/0.8/10.5%
S5	1.14/1.14/0.02/0%	1.07/1.08/0.02/0.01%	0.01/0.02/0.02/26.23%	3/4.2/1.0/11.4%
S6	1.35/1.36/0.07/0%	1.49/1.50/0.04/0%	0.03/0.03/0/1.20%	3/2.2/1.0/9.1%
S7	1.23/1.21/0.08/0.03%	1.44/1.42/0.04/0.02%	0.01/0/0/100+	3/4.0/1.4/9.0%
S8	1.21/1.21/0.01/0%	1.28/1.27/0.01/0%	0.10/0.11/0.03/1.94%	3/3.4/0.8/1.5%
S9	1.28/1.27/0.14/0.02%	1.21/1.21/0.09/0%	0.02/0.02/0.02/3.46%	3/3.3/0.8/1.1%
S10	1.23/1.22/0.09/0.01%	1.12/1.13/0.05/0.01%	0.05/0.05/0/0.06%	3/3.2/0.5/0.3%

Table 2 Estimated results （t*=70）

源	$m t r u e, x$ / $m e s t, x$ / $σ e s t, x$ / $N M S E x$	$m t r u e, y$ / $m e s t, y$ / $σ e s t, y$ / $N M S E y$	$m t r u e, z$ / $m e s t, z$ / $σ e s t, z$ / $N M S E z$	$m t r u e, q$ / $m e s t, q$ / $σ e s t, q$ / $N M S E q$
S1	1.12/1.12/0.04/0%	1.54/1.55/0.04/0%	0.04/0.06/0.03/21.25%	3/2.7/0.6/0.9%
S2	1.02/1.06/0.06/0.17%	1.44/1.42/0.02/0.02%	0.01/0.01/0.01/5.08%	3/3.7/0.9/3.9%
S3	1.07/1.08/0.03/0.01%	1.21/1.21/0.01/0%	0.05/0.05/0.01/0.50%	3/4.4/0.5/15.3%
S4	1.02/1.06/0.07/0.12%	1.12/1.14/0.01/0.03%	0.02/0.01/0.01/12.26%	3/4.1/0.8/10.5%
S5	1.14/1.14/0.02/0%	1.07/1.08/0.02/0.01%	0.01/0.02/0.02/26.23%	3/4.2/1.0/11.4%
S6	1.35/1.36/0.07/0%	1.49/1.50/0.04/0%	0.03/0.03/0/1.20%	3/2.2/1.0/9.1%
S7	1.23/1.21/0.08/0.03%	1.44/1.42/0.04/0.02%	0.01/0/0/100+	3/4.0/1.4/9.0%
S8	1.21/1.21/0.01/0%	1.28/1.27/0.01/0%	0.10/0.11/0.03/1.94%	3/3.4/0.8/1.5%
S9	1.28/1.27/0.14/0.02%	1.21/1.21/0.09/0%	0.02/0.02/0.02/3.46%	3/3.3/0.8/1.1%
S10	1.23/1.22/0.09/0.01%	1.12/1.13/0.05/0.01%	0.05/0.05/0/0.06%	3/3.2/0.5/0.3%

Fig.11 Accuracy skill scores over time

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