Modeling and Simulation of Reactive Dissolution and Wormhole Formation in Carbonate Rocks
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Reactive dissolution of carbonate rocks is a common technique used to stimulate the oil and gas wells. In this process, an acidic solution is injected into the porous rock. The acid dissolves some of the rock and creates highly conducting channels. These channels facilitate the flow of hydrocarbons during the production phase and lead to enhanced production. The shape and structure of these conducting channels depends upon the combined effect of acid transport, reaction, and rock properties. For instance, at a very low injection rate (such that the characteristic time scale for reaction is very low compared to acid transport), acid continues dissolving the entire face of the rock, causing facial dissolution. Conversely, at a very high injection rate (such that the characteristic time scale for acid transport is very low compared to reaction), acid reaches every part of the domain and increases the porosity and permeability uniformly, causing uniform dissolution. At intermediate flow rates, where both convection and transverse dispersion are comparable in magnitude, long channels called wormholes are formed. These are recognized as the most efficient means to stimulate wells. In this work, we present 3-D numerical simulations and analysis of reactive dissolution and wormhole formation in carbonates with Newtonian and non-Newtonian acids using a two-scale continuum model. More specifically, we present a sensitivity analysis of the dissolution process with respect to acid injection rate, molecular diffusivity, rheological models, dissolution rate constant and rock properties such as initial average permeability, heterogeneity and permeability-porosity relationships. Additionally, we develop a new two-parameter (pore connectivity and pore broadening) structure-property relation to account for change in permeability, pore radius and interfacial area per unit volume with porosity, unlike to previous studies where only one parameter was used. We also present scaling criteria to estimate the wormhole tip diameter and optimum acid injection rate, for vuggy and non-vuggy carbonates with Newtonian and non-Newtonian acids. Finally, we present the flow dynamics of acid during wormhole formation and compare the simulation results with the available experimental data.