Modeling, analysis and simulation of wormhole formation in carbonate rocks with in situ cross-linked acids

Abstract

We develop an empirical rheological model to describe the variation of the viscosity of in situ cross-linked acids with temperature, shear rate and pH. We present a two-scale continuum model to describe reactive dissolution of carbonates with in situ cross-linked acids and use it to analyze wormhole formation in single and dual core set-ups. We use scaling analysis of the model to estimate the optimum injection rate for wormhole formation and develop expressions for width and propagation speed of gel and reaction fronts as a function of the rheological parameters. We compare wormhole formation with in situ cross-linked acids to that with Newtonian acids and show that the in situ cross-linked acids lead to lower optimum injection rates and more branched wormholes as compared to Newtonian acids. For the case of constant injection rate through a core, unlike for Newtonian acids, the pressure response for in situ cross-linked acids is non-monotonic with the amount of acid injected and matches with available experimental data. When dissolution is kinetically controlled, the wormhole tip diameter is smaller and pore volume for breakthrough is lower for in situ cross-linked acids as compared to that for Newtonian acids. We identify the mechanism of flow diversion and show that the larger gel resistance in high permeability zones is the key to achieve uniform stimulation. Finally, we provide some guidelines for optimal stimulation of carbonates with in situ cross-linked acids.