Novel Brinkman-Triple-Porosity-Permeability Model for Fluid Flow

Researchers from Shaanxi Normal University have proposed a novel Brinkman-triple-porosity-permeability model to describe fluid flow between filled conduits, matrix, micro-caves, and micro-fractures. The model removes the assumptions of sequential flow and allows direct communication of fluid between different porosity types. The study was financially supported by the National Natural Science Foundation of China and has been peer-reviewed.

Key Takeaways:

• The Brinkman-triple-porosity-permeability model is a novel approach to describe fluid flow in complex porous media, removing the assumptions of sequential flow and allowing direct communication between different porosity types.
• The model is proposed and solved using the discontinuous Galerkin method for spatial discretization and the backward Euler method for temporal discretization.
• Optimal error estimates are derived for both semi-discrete and fully discrete schemes, and the stability of these schemes is established.
• The validity of the model is confirmed through three numerical experiments, exploring characteristics such as optimal convergence rates for different mesh types and numerical formats.
• The model has been demonstrated in a multi-stage hydraulically fractured horizontal wellbore, connecting a vertical production casing to a cased-hole completion.
• The research has been conducted by Rui Li, Ying Zhang, and Zhangxin Chen from Shaanxi Normal University.

Statistics:

• The research was supported by the National Natural Science Foundation of China, the Natural Science Foundation of Shaanxi Province, and the Fundamental Research Funds for the Central Universities.
• The model is proposed to capture the viscous flow effects that may occur when the free-flow region is occupied by proppants or rock particles.
• The spatial discretization is performed using a discontinuous Galerkin method, while temporal discretization is performed using the backward Euler method.
• Optimal accuracy is achieved for both semi-discrete and fully discrete schemes, with derived error estimates.

Sources:

• A Brinkman-triple-porosity-permeability Model and Its Discontinuous Galerkin Methods. Communications In Nonlinear Science and Numerical Simulation, 2025;150.
• Elsevier: www.elsevier.com
• Communications In Nonlinear Science and Numerical Simulation: www.journals.elsevier.com/communications-in-nonlinear-science-and-numerical-simulation/
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