A space–time second-order algorithm based on finite volume method for Brinkman flow and reactive transport model in porous media with variable fractures

Abstract

In this paper, Brinkman flow is introduced to simulate fluid flow within fractures affected by the resistance from porous media and viscous shear on fractures walls. Due to the existence of chemical reactions, reactive transport is considered in fractured porous media. The reactions alter the porous media and fractures locally, thus the equations for evolution of porosity, fracture aperture and precipitation concentration are extended to the highly coupled model of Brinkman flow and advection-diffusion-reaction transport in fractured porous media. Generally, fractures and their intersections are treated as low-dimensional immersed objects to obtain hybrid-dimensional coupled models. A space–time algorithm based on finite volume method is constructed to solve the hybrid-dimensional coupled system, by decoupling the ODEs and PDEs at each time level sequentially. The simulation of each physical process including discontinuous pressure, concentration and reaction terms can be realized effectively. Besides, the proposed algorithm can be developed to high-dimensional porous media with multiple intersecting fractures easily. Error estimates illustrate that the proposed algorithm can achieve space–time second-order accuracy. Numerical experiments are provided to confirm the accuracy and effectiveness of the proposed algorithm with variable temporal steps in porous media embedded with variable fractures.