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 the complex system of the acid transport along with fracture mechanics and heat transfer 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 FEM. The objective of developing this FEM model is to eliminate the need of using different mapping and coordinate transformation techniques for the fracture propagation model and the acid transport model; hence, diminishing the inaccuracy when meshing the geometry. The developed FEM model has been validated against analytical and numerical models, and it has been verified that the algorithm is stable and robust. The developed model predicts accurate velocity and temperature profiles. In addition, the model can handle acids with non-Newtonian flow behavior at a specific acid viscosity and acid dissolving power. It has been found that acids with shear thinning flow behavior yields shorter acid penetration distance compared to acids that are behaving as a Newtonian fluid. Furthermore, the effect of wormholes on the acid distribution has been studied, and it has been found that high injection rates result in deeper wormholes.
