Research on Reservoir History Matching Method Based on Real⁃Coded Genetic Algorithm and Connectivity Model

doi:10.12422/j.issn.1672-6952.2025.03.008

Abstract

Abstract:

The optimization process in reservoir history matching belongs to the high?dimensional system's optimal control problem, and the selection of a suitable optimization algorithm is crucial for achieving a good fitting effect. As gradient?based methods face challenges in computing the gradient of the objective function, intelligent optimization algorithms with stochastic properties are widely applied in reservoir optimization processes. A method for reservoir history matching based on real?number coding genetic algorithm RGA and connectivity model was proposed. This method eliminates the need for encoding and decoding operations by directly using feasible solutions obtained from traditional solving methods as initial parameters for the improved genetic algorithm, thereby reducing the complexity of the search space. In RGA, real?number coding is employed to represent parameters, enabling the algorithm to handle continuous variables directly, thus enhancing search accuracy and convergence speed. A adaptive selection strategies, crossover, and mutation operations are introduced in this paper to further enhance the algorithm's performance. Application of RGA to the history matching problem in a mechanistic model demonstrates that RGA can effectively improve fitting results and find relatively optimal solutions in a short time. Therefore, this method has significant potential for widespread application in reservoir history matching problems.

Key words: Reservoir history matching, Optimization algorithm, Real?coded, Genetic algorithm, Numerical simulation of oil reservoirs

摘要：

油藏历史拟合优化问题属于高维系统最优控制问题，选择合适的优化算法对实现良好的拟合效果至关重要。由于梯度类方法在计算目标函数梯度时存在困难，随机性智能优化算法被广泛应用于油藏优化过程。提出了一种基于实数编码遗传算法（RGA）与连通性模型的油藏历史拟合问题的方法。该方法无须编码解码操作，直接将传统方法求解得到的可行解作为改进遗传算法的初始参数，可有效降低搜索空间的复杂性；在RGA中，采用实数编码直接表示参数，算法能够处理连续变量，可提升搜索的精度和收敛速度；引入自适应选择策略、交叉与变异操作，可进一步优化算法性能。结果表明，RGA能够有效提高拟合效果，并在较短时间内获得较优解，该方法在油藏历史拟合领域具有广阔的应用前景。

关键词: 油藏历史拟合, 优化算法, 实数编码, 遗传算法, 油藏数值模拟

CLC Number:

TE331

Ainiwaer AILIYAER, Chunli ZHAO, Feng LIU. Research on Reservoir History Matching Method Based on Real⁃Coded Genetic Algorithm and Connectivity Model[J]. Journal of Liaoning Petrochemical University, 2025, 45(3): 57-63.

艾力牙尔·艾尼瓦尔, 赵春立, 刘峰. 基于实数编码遗传算法与连通性模型的油藏历史拟合方法研究[J]. 辽宁石油化工大学学报, 2025, 45(3): 57-63.

Figures/Tables 10

Table 1 The correspondence of biological genetic concepts in GA

生物遗传概念	GA中的对应关系
个体	问题的可行解
种群	一组可行解
染色体	对应可行解的编码
基因	染色体上的编码单元
适应度	自适应值
选择	自适应值与最优值越接近，越可能作为一个可行解被保留
交配	通过交配原则产生一组新解的过程
变异	编码的某一分量发生变化的过程
进化结束	算法达到终止条件，输出全局最优解

Fig.1 The process of real?number encoding genetic algorithm

Fig.2 The chart of fitness value ranking selection mechanism and roulette selection mechanism diagram

Table 2 The specific process of RGA algorithm for reservoir connectivity model parameter optimization

输入：目标函数D，种群数量N_p，交叉概率P_c，变异概率P_m，最大迭代次数K，优化下界u^low，优化上界u^up，模型计算初始值m⁰(传导率和控制体积构成向量)
输出：最优解 M，最优解对应的目标函数值
1	令k=0,初始化种群
2	$m i, j 0 = m i 0 + r a n d (0,1) × (u u p - u l o w), i = 1,2, ⋯, H; j = 1,2, ⋯, N p$
3	While不满足终止条件
4	计算适应度值 $D (m j k)$
5	按照适应度值排列，选择适应度值最高的3个个体 $m f 1 k$ 、 $m f 2 k$ 、 $m f 3 k$ 进行变异操作： $v j k = m f 1 k + P m (m f 2 k - m f 3 k), j ≠ f 1 ≠ f 2 ≠ f 3$
6	生成随机数，进行交叉操作
7	If $r a n d (0,1) ≤ P c$
8	$g i, j k = v i, j k$
9	Else
10	$g i, j k = m i, j k$
11	End
12	计算两个适应度值 $D (g j k)$ 和 $D (m j k)$ ，进行选择操作
13	If $D (g j k) ≤ D (m j k)$
14	$m j k + 1 = g j k$
15	Else
16	$m j k + 1 = m j k$
17	End
18	边界吸收，令k=k+1
19	End

Table 2 The specific process of RGA algorithm for reservoir connectivity model parameter optimization

输入：目标函数D，种群数量N_p，交叉概率P_c，变异概率P_m，最大迭代次数K，优化下界u^low，优化上界u^up，模型计算初始值m⁰(传导率和控制体积构成向量)
输出：最优解 M，最优解对应的目标函数值
1	令k=0,初始化种群
2	$m i, j 0 = m i 0 + r a n d (0,1) × (u u p - u l o w), i = 1,2, ⋯, H; j = 1,2, ⋯, N p$
3	While不满足终止条件
4	计算适应度值 $D (m j k)$
5	按照适应度值排列，选择适应度值最高的3个个体 $m f 1 k$ 、 $m f 2 k$ 、 $m f 3 k$ 进行变异操作： $v j k = m f 1 k + P m (m f 2 k - m f 3 k), j ≠ f 1 ≠ f 2 ≠ f 3$
6	生成随机数，进行交叉操作
7	If $r a n d (0,1) ≤ P c$
8	$g i, j k = v i, j k$
9	Else
10	$g i, j k = m i, j k$
11	End
12	计算两个适应度值 $D (g j k)$ 和 $D (m j k)$ ，进行选择操作
13	If $D (g j k) ≤ D (m j k)$
14	$m j k + 1 = g j k$
15	Else
16	$m j k + 1 = m j k$
17	End
18	边界吸收，令k=k+1
19	End

Table 3 Distribution diagram of other petrophysical parameters of reservoir

参数	数值
水相压缩系数/MPa^-1	5.00×10^-3
油相压缩系数/MPa^-1	5.02×10^-3
岩石压缩系数/MPa^-1	6.50×10^-3
油相黏度/(mPa·s)	21.8
水相黏度/(mPa·s)	1.0
原始地层压力/MPa	22

Fig.3 Well Location Distribution Map

Fig.4 Iterative Optimization Results of Objective Function

Fig.5 The results of historical matching of water cut in production wells based on GA and RGA

Fig.6 Prediction results of production wells daily oil production based on GA and RGA

Fig.7 Quantitative characterization diagram of conductivity and dimensionless control volume based on RGA inversion

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