Treatment of reactive interfaces in pore-scale reactive transport with the phase-field method

Friday, 19 December 2014
Christian Huber, Georgia Institute of Technology Main Campus, Earth and Atmospheric Sciences, Atlanta, GA, United States and Paolo Roberto Di Palma, Istituto di Ricerca Sulle Aqua, Roma, Italy
The two major challenges for continuum reactive transport models are the treatment of interfaces between different phases (multi-fluids like DNAPL-water, or solid-fluid) and the ability to model transient chemical gradients at the pore-scale. Pore-scale models allow us to deal naturally with chemical gradients at the discrete scale and they generally consider interfaces as boundary conditions that satisfy a local, but modified, mass balance equation. In other word grains do not take part in the mass balance of chemical species besides providing a boundary condition for the fluid. For instance, heterogeneous reactions at solid-fluid boundaries are framed as a balance between incoming chemical flux and reactions. Due to complex topology of interfaces in natural porous media, the treatment of heterogeneous reactions depends on the orientation of the interface and therefore requires a special care. It can become complicated and tedious especially when interfaces are allowed to evolve with time.

Approaches such as the enthalpy method, which was developed for solving moving interfaces during melting processes, offer the advantage of a treatment that is independent of the shape of the moving interface. Similar methods have been used for modeling multiphase flows with diffuse interface successfully. Here, we expand on these approaches and introduce a phase-field approach to introduce heterogeneous reactions in single and multiphase reactive flows at the pore-scale. Mass conservation is solved in each phase and we introduce interface conditions as a source/sink term in the conservation equation rather than a boundary condition. The advantages are that the method becomes independent of the (time-dependent) topology of the interface and automatically enforces local mass conservation between the different constituents of the domain. We show validations of the model and applications to multispecies reactive transport, isotope fractionation during calcite growth and finally chemical reactions between immiscible fluids.