Solving seepage equation based on deep learning

Journal Information

J. Hefei Univ. Tech. (Nat. Sci.), Aug.2025, Vol.48 No.8: 1117-1124

DOI: 10.3969/j.issn.1003-5060.2025.08.017

Authors

GUO Bumin $ ^{1,2} $, XU Yantao $ ^{1,2} $, WU Guang'ai $ ^{3} $, ZHANG Wen $ ^{1,2} $,

(1. China Oilfield Services Limited, Tianjin 300459, China; 2. Tianjin Enterprise Key Laboratory of Offshore Oil Difficult-to-Produce Reserves Exploitation, Tianjin 300459, China; 3. CNOOC Research Institute Co., Ltd., Beijing 100029, China; 4. School of Mathematics, Hefei University of Technology, Hefei 230601, China)

Abstract and Keywords

Abstract: Deep learning-based forward and inverse modeling is currently a research hotspot. The seepage equation is a mathematical model describing the motions of fluids in porous media, and it has nonlinearities and source-sink terms, which brings great challenges to deep learning solution. In this paper, a physical constraint-based deep learning method for solving the seepage equation is proposed and applied to the reservoir parameter inversion. Aiming at the problem of strong nonlinearity and source-sink terms, a multilevel residual framework is proposed for learning the pressure change characteristics around the wells so as to better conform to the physical laws. By nonlinear transformation of the input temporal and spatial coordinates and introducing adaptive parameters to increase the flexibility of the network and the expressive ability of the model, the seepage equation can be intelligently solved. This solution method only relies on the bottomhole pressure data, without the need for traditional numerical calculations, and can achieve the forward modeling and parameter inversion with high efficiency. Results of numerical experiments show that the method can accurately solve the bottomhole pressure under variable well flow rates and effectively invert multiple reservoir parameters, whether in homogeneous or heterogeneous reservoirs.

Keywords: deep learning; automatic inversion; physical constraints; heterogeneous reservoir; multiparameter inversion

作者信息

郭布民 $ ^{1,2} $，徐延涛 $ ^{1,2} $，武广瑷 $ ^{3} $，张雯 $ ^{1,2} $，杨浩 $ ^{1,2} $，

（1. 中海油田服务股份有限公司，天津 300459；2. 天津市海洋石油难动用储量开采企业重点实验室，天津 300459；3. 中海油研究总院有限责任公司，北京 100029；4. 合肥工业大学数学学院，安徽合肥 230601）

摘要和关键词

摘要: 基于深度学习的正演与反演是当前研究热点,而渗流方程是描述流体在多孔介质中运动的数学模型,该方程存在非线性和源汇项,给深度学习求解带来了很大挑战。文章提出基于物理约束的深度学习的渗流方程求解方法,并将其应用在油藏参数反演中。针对非线性强和源汇项的问题,提出多级残差框架用于学习井周围压力变化特征,从而更好地符合物理规律;对输入的时间与空间坐标进行非线性变换,引入自适应参数,增加网络的灵活性和模型的表达能力,实现渗流方程的智能求解。该求解方法仅依赖于井底的压力数据,无需传统的数值计算即可实现正演与参数高效反演。数值实验结果表明,无论在均质储层还是在非均质油藏中,该方法都能够精确求解变井流量条件下的井底压力,并有效反演出储层中的多个参数。

关键词: 深度学习；自动反演；物理约束；非均质油藏；多参数反演

Funding

国家自然科学基金资助项目（12172115；12372244）

合肥工业大学学报(自然科学版)

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