A phase-field modeling study for reaction instability and localized fluid flow in carbonate rocks

As acidic fluids flow and dissolve minerals in carbonate formations, the reaction may localize into a dendritic pattern under certain conditions known as wormhole. Wormhole is considered to be triggered by pore-scale heterogeneity in the rock that promotes preferential flow paths. Therefore, in macroscale (Darcy scale) simulation, numerical models usually need to prescribe a certain degree of macroscopic heterogeneous permeability to promote localized dissolution (wormhole). However, experimental studies have shown that wormholes form in synthetic plasters without apparent heterogeneity, implying that macroscopic heterogeneity is not a necessary prerequisite for wormhole formation and prescribed heterogeneity may impose unnecessary biases. Here, we applied a macroscale wormhole model based on a phase-field approach to demonstrate that wormhole can form in macroscopically homogeneous media as long as the inlet velocity meets the infiltration-reaction instability condition obtained from perturbation analysis. Furthermore, we simulated wormhole growth behaviors in homogeneous and heterogeneous permeability fields with the standard variance values of 0.5, 1.0 and 2.0. The simulation results showed that the normalized injectivity decreases from 3.90 to 3.15 when the standard variance changed from 0.5 to 2.0 indicating that heterogeneity may actually suppress the wormhole growth because an increasing amount of acid infiltrates into the branched wormholes. These findings suggest that permeability heterogeneities should not be treated as a trigger for wormholes in the macroscale numerical simulation. Instead, they should be regarded as parameters that influence the nucleation and growth of wormholes because the permeability field has significant effects on post-acid wormhole geometry and resultant well productivity and injectivity.