Numerical investigation of a fully coupled micro-macro model for mineral dissolution and precipitation

Mineral dissolution and precipitation alter a porous medium's structure and its bulk properties. Due to the medium's heterogeneity and lack in dynamic pore-scale measurements, there has been an increasing interest in comprehensive models accessing such phenomena on the macroscale without disregarding available pore-scale information. Such micro-macro models may be derived from detailed pore-scale models applying upscaling techniques and comprise several levels of couplings. Our model consists of transport equations at the scale of the porous medium (macroscale) while taking the processes of convection and diffusion into account. They include averaged time- and space-dependent coefficient functions which are in turn explicitly computed by means of auxiliary cell problems (microscale). Structural changes due to dissolution and precipitation reactions result in a time- and space-dependent domain on which cell problems are defined. The interface between the mineral and the fluid, and consequently the explicit geometric structure, is characterized by means of a level set. Here, information from the transport equations' solutions is taken into account (micro-macroscale). A numerical scheme is introduced which enables evaluating such complex settings. For the level-set equation, an upwind scheme by Rouy and Tourin is applied. An extended finite element method is used for the evaluation of the cell problems while the transport equations are solved applying mixed finite elements. Ultimately, we investigate the potentially degenerating bulk properties of the medium such as porosity and effective diffusion. Moreover, we apply our approach to the dissolution of an array of calcite grains in the micro-macro context and validate our numerical scheme.