Large-Scale Model for the Dissolution of Heterogeneous Porous Formations: Theory and Numerical Validation

In this paper, we study the dissolution of a porous formation made of soluble and insoluble materials with various types of Darcy-scale heterogeneities. Based on the assumption of scale separations, i.e., the convective and diffusive Damkohler numbers are smaller than certain limits which are documented in the paper, we apply large-scale upscaling to the Darcy-scale model to develop large-scale equations, which are used to describe the dissolution of porous formations with Darcy-scale heterogeneities. History-dependent closure problems are provided to get the effective parameters in the large-scale model. The large-scale model validity is tested by comparing numerical results for a 1D flow problem in a stratified system and a 2D flow problem in a nodular system to the Darcy-scale ones. The good agreement between results at Darcy and large scales shows the robustness of the large-scale model in representing the Darcy-scale results for the stratified system, even when the dissolution front is very sharp. Large-scale results for the nodular system represent satisfactorily the averaged Darcy-scale behaviors when the dissolution front is relatively thick, i.e., when model assumptions are satisfied, while there may be as expected some discrepancy generated between direct numerical simulations and large-scale results in the case of thin dissolution front. Overall, this study demonstrates the possibility of building a fully homogenized large-scale model incorporating dissolution history effects, and that the resulting large-scale model is capable to catch the main features of the Darcy-scale results within its applicability domain.

Automated summary

This paper investigates the dissolution of porous formations with various Darcy-scale heterogeneities, demonstrating the ability of a large-scale model to accurately capture the main features of Darcy-scale results within its applicability domain. The large-scale model shows good agreement with Darcy-scale results for stratified systems, especially when the dissolution front is sharp, while some discrepancies may arise in the case of thin dissolution fronts. Overall, the study highlights the potential of a fully homogenized large-scale model incorporating dissolution history effects.