Pore-scale modelling of the combined effect of physical and chemical heterogeneity on reactive flows

We perform direct numerical simulations to study the combined impact of physical and chemical heterogeneity in subsurface rock to provide insights into the source of the discrepancy observed between mineral dissolution rates observed in laboratory experiments and in field-scale natural systems. The ultimate goal of this work is to use pore-scale simulation to compute upscaled properties - such as effective reaction rate - for use in larger-scale models.We present a methodology to simulate multispecies reactive flow through pore-space images obtained from micro-tomography. Using the sequential non-iterative approach, we couple the simulation of the transport equations with an advanced geochemical solver designed specifically for applications that require sequential equilibrium calculations. This geochemical solver uses novel numerical methods for the solution of multiphase chemical equilibrium and kinetics problems in a well-stirred batch model. Our model assumes that reactions can be classified into fast reactions, which are considered to be in equilibrium, and slow reactions, considered to be controlled by kinetics. This assumption of partial equilibrium simplifies the problem by replacing differential equations with algebraic ones. We allow for chemical heterogeneity of the solid phase by associating each voxel to a different mineral and reaction rate. A steady-state flow problem is solved in the pore space using a finite volume method to calculate the velocity field. Then we solve an advection-diffusion equation for the concentration and, modelling each liquid voxel as a well-mixed batch with a solid wall where applicable, we calculate reaction using the aforementioned geochemical solver. Both fluid-fluid and fluid-solid reactions are considered, geometry changes due to dissolution and precipitation are taken into account, and the velocity field is updated. We present the validation tests for acidic brine injected into rock for a range of transport (Péclet number) and reactive (Damköhler number) conditions. This serves as a basis for the study of the impact of physical and chemical heterogeneities on effective reaction rates, and pore-by-pore comparison with laboratory experiments on micro-CT images of natural rock samples.