The Effect of Acid Injection Rate on Carbonate Acidizing Performance in a Two-Dimensional Heterogeneous Model

Carbonate acidizing modeling presents an effective tool to determine dynamic behavior trends during matrix acidizing treatment. A successful matrix acidizing process requires a minimum volume of injected acid while creating highly conductive wormholes. In this work, the two-scale continuum model was used to simulate carbonate acidizing using finite difference approach.  This model describes the reactive transport of acid at the Darcy scale and determines the local permeability, porosity, pore radius, and solid-fluid interfacial area changes at the pore-scale through structure-property relationships. In this study, a two-dimensional model was employed with constant flow rate inlet boundary condition, constant pressure outlet boundary condition, and no flow boundary condition on the lateral sides. To perform a grid independent verification, the normalized acid concentration was plotted versus mesh elements which, then, results in determining the optimum number of grid blocks. To solve governing equations, finite difference approach was used by employing initial and boundary conditions. The results of the two-dimensional homogeneous model revealed that there is a uniform acid concentration profile with a reduction trend during the model length. A sensitivity study on acid injection velocity in a heterogeneous model showed that there is an optimum injection velocity of 0.33 to 1.5 cm/s in which deep wormholes with a minimal amount of acid are created. Moreover, as time passes, the reactive dissolution process takes place and results in a dynamic change in the model porosity. This model indicated a good capability to qualitatively capture the experimentally observed wormhole propagation and growth.