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Numerical simulation of wormhole propagation with the mixed hybridized discontinuous Galerkin finite element method.

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Title: Numerical simulation of wormhole propagation with the mixed hybridized discontinuous Galerkin finite element method.
Authors: Zhang, Jiansong1 (AUTHOR) jzhang@upc.edu.cn, Zhu, Jiang2 (AUTHOR) jiang@lncc.br, Guo, Hui1 (AUTHOR) sdugh@163.com, Wang, Yiming1 (AUTHOR) 1164324059@qq.com, Liu, Yanyu1 (AUTHOR) 1872371250@qq.com
Source: Computers & Mathematics with Applications. Aug2026, Vol. 216, p129-146. 18p.
Subjects: Finite element method, Reactive flow, Acidity, Porosity, Carbonate reservoirs, Computer simulation, Petroleum reservoirs
Abstract: The acid treatment of carbonate reservoirs is a widely adopted technique for enhancing the productivity of oil and gas reservoirs. In this paper, we propose a novel hybridized mixed discontinuous Galerkin (HMDG) finite element method to simulate the dissolution process near the wellbore, commonly referred to as the wormhole phenomenon. The key contributions of this work include the application of hybridization techniques to both pressure and concentration equations, the use of an upwind scheme for convection-dominant case, and the introduction of a "cut-off" operator to ensure porosity boundedness. Compared with traditional discontinuous Galerkin methods, the proposed approach yields a global system with fewer unknowns, significantly reducing computational costs. We rigorously analyze the existence and uniqueness of the solution for the new method and derive optimal error estimates using the developed framework. Numerical examples are provided to validate the theoretical findings. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:The acid treatment of carbonate reservoirs is a widely adopted technique for enhancing the productivity of oil and gas reservoirs. In this paper, we propose a novel hybridized mixed discontinuous Galerkin (HMDG) finite element method to simulate the dissolution process near the wellbore, commonly referred to as the wormhole phenomenon. The key contributions of this work include the application of hybridization techniques to both pressure and concentration equations, the use of an upwind scheme for convection-dominant case, and the introduction of a "cut-off" operator to ensure porosity boundedness. Compared with traditional discontinuous Galerkin methods, the proposed approach yields a global system with fewer unknowns, significantly reducing computational costs. We rigorously analyze the existence and uniqueness of the solution for the new method and derive optimal error estimates using the developed framework. Numerical examples are provided to validate the theoretical findings. [ABSTRACT FROM AUTHOR]
ISSN:08981221
DOI:10.1016/j.camwa.2026.05.013