Modeling and analysis of wormhole formation in reactive dissolution of carbonate rocks

A two-scale continuum model is used to simulate reactive dissolution of carbonate rocks in radial flow. The three main types of patterns observed in linear and radial flow experiments, namely, compact, wormhole and uniform patterns are numerically simulated. The fractal nature of wormholes observed in laboratory experiments is established and confirmed through simulations and the fractal dimension is quantitatively matched. The dependence of wormhole fractal dimension, optimum injection rate and minimum pore volumes required to breakthrough the medium on heterogeneity magnitude and aspect ratio is investigated. A new criterion to predict the optimum injection rate for wormhole formation in radial flow is derived and validated. It is observed that the wormhole penetration depth increases with injection time as t^b, where the exponent b is found to be approximately 0.66, as observed in the experiments. A critical level of heterogeneity magnitude seems to exist below which the minimum pore volumes required to breakthrough are much higher.