The acid treatment of carbonate reservoirs is a widely employed technique for enhancing the productivity of oil and gas reservoirs. In this paper, we present a novel combined hybridized mixed discontinuous Galerkin (HMDG) finite element method to simulate the dissolution process near the wellbore, commonly referred to as the wormhole phenomenon. The primary contribution of this work lies in the application of hybridization techniques to both the pressure and concentration equations. Additionally, an upwind scheme is utilized to address convection-dominant scenarios, and a ``cut-off" operator is introduced to maintain the boundedness of porosity. Compared to traditional discontinuous Galerkin methods, the proposed approach results in a global system with fewer unknowns and sparser stencils, thereby significantly reducing computational costs. We analyze the existence and uniqueness of the new combined method and derive optimal error estimates using the developed technique. Numerical examples are provided to validate the theoretical analysis.

翻译：碳酸盐岩储层酸化处理是提高油气藏产能的常用技术。本文提出了一种新型组合式杂交混合间断伽辽金有限元方法，用于模拟井筒附近的溶解过程，即通常所称的蚓孔现象。本工作的主要贡献在于将杂交技术同时应用于压力方程和浓度方程。此外，采用迎风格式处理对流主导工况，并引入“截断”算子以保持孔隙度的有界性。与传统间断伽辽金方法相比，所提方法形成的全局系统具有更少的未知量和更稀疏的模板，从而显著降低了计算成本。我们分析了新组合方法解的存在唯一性，并利用所发展的技术推导了最优误差估计。数值算例验证了理论分析结果。