Upscaling of Nonisothermal Reactive Porous Media Flow under Dominant Péclet Number: The Effect of Changing Porosity

Abstract

Motivated by rock-fluid interactions occurring in a geothermal reservoir, we present a two-dimensional pore scale model of a thin strip consisting of void space and grains, with fluid flow through the void space. Ions in the fluid are allowed to precipitate onto the grains, while minerals in the grains are allowed to dissolve into the fluid, taking into account the possible change in the aperture of the strip that these two processes cause. Temperature variations and possible effects of the temperature in both fluid density and viscosity and in the mineral precipitation and dissolution reactions are included. For the pore scale model equations, we investigate the limit as the width of the strip approaches zero, deriving one-dimensional effective equations. We assume that the convection is dominating over diffusion in the system, resulting in Taylor dispersion in the upscaled equations and a Forchheimer-type term in Darcy's law. Some numerical results where we compare the upscaled model with three simpler versions are presented: two still honoring the changing aperture of the strip but not including Taylor dispersion, and one where the aperture of the strip is fixed but contains dispersive terms.