Acid Transport Modeling Using Finite Element Discretization with Weak Formulation for Simulation of Acid Fracturing

Abstract

The purpose of designing an acid fracturing model is to examine the two factors that measure the effectiveness of the acid fracturing treatment. The two factors are the acid penetration distance and the fracture conductivity after closure stress is reached. The acid fracturing model is designed by coupling a fracture propagation model and an acid transport model. The advanced fracture propagation models are developed numerically by the finite element method (FEM,) or the extended finite element method (XFEM.) However, the acid transport models that are reported in the literature are developed using the finite difference method (FDM.) The finite element method is a more stable and accurate technique to model different types of complex and coupled physics than FDM. Furthermore, FEM is a more powerful and suitable technique for meshing sophisticated geometries such as fractures. Thus, an acid transport model has been developed numerically using the finite element method. The developed model solves the Navier-Stokes equations numerically to get the velocity profile. The acid balance equation is solved considering the convection and diffusion terms in all direction of the fracture and not only across the fracture. This model considers the thermal effect by solving the energy balance equation without neglecting the temperature gradient along the fracture length and height. The developed model predicts accurate acid penetration distance with a relative error of 0.3% compared to the analytical solution, and improves the predicted acid-etched width by more than 8% compared to the reported analytical solutions, which overestimate the acid-etched width because of no taking into account the effect of wormholes when calculating the total leak-off coefficient. Finally, the fracture conductivity, after fracture closure, has been estimated by using correlations.