Modeling and analysis of reactive dissolution of carbonate rocks

Stimulation of carbonate reservoirs using an acid is often employed to increase hydrocarbon production rate. The reaction between the acid and the carbonate rock is influenced by the competition between flow and dispersion occurring at the Darcy scale and inter-phase mass transfer and reaction at the pore scale. As the acid is injected into the rock, it dissolves the soluble material and increases the local porosity. When heterogeneities in permeability or porosity are encountered by the advancing reaction front, preferential flow occurs, bringing more acid to higher permeability regions and triggering instability in the reaction front. As a result, different types of dissolution patterns are formed depending on the injection rate. For instance, at low injection velocities, reaction front is thin and face dissolution occurs, while higher rates lead to uniform dissolution of the medium. 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 increase medium permeability.;In this work, a two-scale continuum model that incorporates the phenomena occurring at both the pore and Darcy scale is used to study wormholing in both linear and radial flow conditions. The structure of resulting patterns is characterized in terms of the wormhole diameter and fractal dimension. It is found that the amount of acid required to increase permeability by a given factor is lower and the optimum injection rate corresponding to wormhole formation is higher for radial flow as compared to linear flow. The effect of various parameters like injection rate, domain-size, initial porosity and reaction rate on wormhole formation is investigated. The wormhole propagation rate and pressure decline with time as a result of dissolution are computed for radial flow and compared with experimental data. A criterion for predicting the optimum injection rate is developed and verified using experimental data. An expression relating the wormhole diameter to the transport and reaction parameters is also developed. Finally, the effect of medium heterogeneity at both the Darcy and core scale on reactive dissolution is studied and a novel way of characterizing heterogeneity is developed.