Effect of medium heterogeneities on reactive dissolution of carbonates

The influence of medium heterogeneities on wormhole formation in carbonates is studied using a two-scale continuum model. The model describes the coupling between the transport and reaction processes occurring at the pore and Darcy scales. The medium heterogeneity is represented through initial porosity (or permeability) field by introducing a randomly generated normal distribution of local porosity values. Heterogeneity in the rock is characterized by the magnitude of maximum variation in local porosity value from the average porosity and by the length scale over which this variation occurs. It is found that heterogeneity in a rock affects not only the structure of the patterns formed during reactive dissolution but also the amount of acid required to achieve a given increase in permeability. The volume of acid required decreases as the heterogeneity magnitude or length scale are increased and this is particularly noticeable at high injection rates of acid. At intermediate injection rates, the required acid volume decreases gradually and an optimum value in heterogeneity magnitude may exist. This has been attributed to excessive branching in a pattern when the medium becomes extremely heterogeneous. In addition, the amount of acid required to breakthrough is found to depend on the initial rock porosity and dimensions of the rock being acidized. Finally, a novel way to characterize heterogeneity is defined, where heterogeneity at the core-scale is expressed using a heterogeneity parameter, ϖϖ as a product of the heterogeneity magnitude and length scale, and is validated for a given rock type at different injection conditions.