Rheological effects on the acidizing process in carbonate reservoirs

In this work, we present a new formulation to study the flow of a reactive non-Newtonian fluid in porous media. The mathematical model consists of a two-scale continuum model that couples information from the pore scale to Darcy one. In the place of the traditional Darcy Law, we consider a complete linear momentum equation, based on the Continuum Theory of Mixtures. The upscaling is made by an interaction source term that corresponds to the flow resistance caused by the matrix inside the pores, which considers the non-newtonian nature of the fluid. Motivated by the often applied self diverting acids we analyze the rheological dependence on the local level of pH. Simulations are performed using the finite volume method with the OpenFOAM software. We investigate the influence of the Damkohler number and the power-law index over dissolution patterns and Pore Volume to Breakthrough (PVbt) curves. The results are compared with the corresponding Newtonian cases. The effect of both shear rate and pH on viscosity are also studied. We verify a significant dependency of the dissolution patterns and also in the optimum injection rate on the rheology of the fluid. More shear-thinning fluids lead to lower values of PVbt. Although the divergent acids were really able to find different paths for the breakthrough, higher times were needed for this achievement.