Modeling of reactive acid transport in fractured porous media with the Extended–FEM based on Darcy-Brinkman-Forchheimer framework

Abstract

In this paper, a fully coupled numerical model is developed based on the X-FEM technique to simulate the reactive acid transport in fractured porous media. The porous medium consists of the solid and fluid phases, in which the fluid phase includes water and acid components, and chemical reactions can be occurred between acid component and solid phase at the solid–fluid interfaces. The governing equations include the mass and momentum conservation laws for fluid phase, and the advective–diffusive transport of acid component that must be solved to obtain the primary unknowns, including the pore fluid pressure, acid concentration, and fluid velocity vector. Applying the Darcy-Brinkman-Forchheimer framework, the velocity field is obtained accurately compared to the Darcy framework. The mass and momentum exchange between the fracture and surrounding porous matrix are incorporated in the weak form of governing equations using the extended finite element method (X-FEM). The X-FEM is applied by employing appropriate enrichment functions to model fractures in porous media. Finally, several numerical examples of acid injection inside both homogenous and heterogeneous fractured porous media are modeled to validate the accuracy and versatility of the proposed model. Moreover, the effects of fracture properties, such as the orientation and aperture, and the matrix properties, such as the diffusion and permeability, together with the injection velocity are investigated on the dissolution patterns. In addition, the wormhole patterns are compared in the DBF and Darcy frameworks.