Numerical Investigation of Wormhole Formation During Matrix Acidizing of Carbonate Rocks by Coupling Stokes-Brinkman Equation with Reactive Transport Model Under Radial Flow Conditions

Abstract

Abstract Matrix acidizing of carbonate formations has been widely used as a practical stimulation technique to improve well performance near the wellbore. The principle of a matrix acidizing treatment is to create wormholes by the dissolution of carbonate rocks. The dissolution pattern can affect the efficiency of the acidizing based on the flow conditions. The actual acidizing treatments are performed by injecting acidic fluid into the formation through a wellbore resulting in a radial flow in the porous media. Consequently, a mathematical model under radial flow conditions can accurately characterize mineral dissolution patterns, which provide valuable guidelines for designing of acidizing treatments. In this paper, we have developed a 3D mathematical model that couples the Stokes-Brinkman equation and reactive-transport equations under radial flow conditions, which has been utilized for modeling the mineral dissolution processes during the acidizing treatment. We have developed and implemented a numerical procedure that solves the Stokes-Brinkman equation and the reactive transport equations by the staggered grid finite difference method and the control volume finite difference method in cylindrical coordinates, respectively, in a sequential fashion. Numerical validation and experiments have been performed using the proposed numerical solution procedure. Two dimensionless numbers, Damköhler number (Da) and Peclet number (Pe), are used in the simulation study to characterize the competitive coupling effects among the advection, diffusion, and chemical reactions. We have performed the numerical experiments to investigate the type of dissolution correlated to the variations of Da and Pe numbers based on the synthetic radial core-flooding scenarios. The numerical results demonstrate that the proposed model is capable of describing the matrix acidizing treatments under radial flow conditions due to the advantage of the Stokes-Brinkman equation for flow in fractured porous media. The Da and Pe numbers are two crucial factors that can affect flow conditions, transport behavior of solute, and chemical reactions. Mineral dissolution patterns take different forms according to various Da and Pe numbers and various alterations of rock properties are obtained accordingly. In addition, the emergence of the wormhole structure during the injection of acid is discussed in this paper. This work presents a 3D mathematical model allowing us to simulate a matrix acidizing process at exact downhole environments. We present the numerical experiments and sensitivity studies of mineral dissolution in carbonate rocks to investigate the coupling effect of fluid flow and reactive transport process on the wormhole formation for a better matrix acidizing design in field operations.