Numerical Modeling and Simulation of Coupled Processes of Mineral Dissolution and Fluid Flow in Fractured Carbonate Formations

Abstract

Carbonate formations usually contain multi-scale fractures, cavities, and even caves within the carbonate rocks. Carbonate rocks undergo various chemical reactions with the injecting fluids during waterflooding, which may lead to the evolution of a fracture system induced by dissolution processes. This development of a natural fracture system may eventually lead to the formation of large-scale well-connected void space features, resulting in early breakthrough, unwanted production, and small increases in bottom-hole pressure. Consequently, a numerical model that accurately describes the dynamic behavior of natural fracture evolution is essential for better forecasting and optimization of production during waterflooding processes. In this paper, we have developed a mathematical model that combines the Stokes–Brinkman and reactive-transport equations to describe the coupled processes of fluid flow, solute transport, and chemical reaction. Application of the Stokes–Brinkman equation as the momentum balance model in the coupled process allows accurate modeling of the evolution process of a natural fracture system. The proposed mathematical model involves a coupled system of highly nonlinear partial differential equations. We have developed and implemented a numerical procedure that solves the Stokes–Brinkman equation by the mixed finite element method and solves the reactive-transport equation using the control volume finite difference method in a sequential fashion. Numerical validation and sensitivity studies have been performed using the proposed numerical solution procedure. The preliminary numerical results demonstrate that the fracture connectivity, flow velocity, and reaction rate are the dominant factors in fracture evolution.