Carina Bringedal

Upscaling of Non-isothermal Reactive Porous Media Flow with Changing Porosity

Motivated by rock–fluid interactions occurring in a geothermal reservoir, we present a two-dimensional pore scale model of a periodic porous medium consisting of void space and grains, with fluid flow through the void space. The ions in the fluid are allowed to precipitate onto the grains, while minerals in the grains are allowed to dissolve into the fluid, and we take into account the possible change in pore geometry that these two processes cause, resulting in a problem with a free boundary at the pore scale. We include temperature dependence and possible effects of the temperature both in fluid properties and in the mineral precipitation and dissolution reactions. For the pore scale model equations, we perform a formal homogenization procedure to obtain upscaled equations. A pore scale model consisting of circular grains is presented as a special case of the porous medium.

A model for non-isothermal flow and mineral precipitation and dissolution in a thin strip

Motivated by porosity changes due to chemical reactions caused by injection of cold water in a geothermal reservoir, we propose a two-dimensional pore scale model of a thin strip. The pore scale model includes fluid flow, heat transport and reactive transport where changes in aperture is taken into account. The thin strip consists of void space and grains, where ions are transported in the fluid in the void space. At the interface between void and grain, ions are allowed to precipitate and become part of the grain, or conversely, minerals in the grain can dissolve and become part of the fluid flow, and we honor the possible change in aperture these two processes cause. We include temperature dependence and possible effects of the temperature in both fluid properties and in the mineral precipitation and dissolution reactions. For the pore scale model equations, we investigate the limit as the width of the thin strip approaches zero, deriving upscaled one-dimensional effective equations.

Linear and nonlinear convection in porous media between coaxial cylinders

We uncover novel features of three-dimensional natural convection in porous media by investigating convection in an annular porous cavity contained between two vertical coaxial cylinders. The investigations are made using a linear stability analysis, together with high-order numerical simulations using pseudospectral methods to model the nonlinear regime. The onset of convection cells and their preferred planform are studied, and the stability of the modes with respect to different types of perturbation is investigated. We also examine how variations in the Rayleigh number affect the convection modes and their stability regimes. Compared with previously published data, we show how the problem inherits an increased complexity regarding which modes will be obtained. Some stable secondary modes or mixed modes have been identified and some overlapping stability regions for different convective modes are determined.

Upscaling of Nonisothermal Reactive Porous Media Flow under Dominant Peźclet Number

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 Darcys 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.

Effective Behavior Near Clogging in Upscaled Equations for Non-isothermal Reactive Porous Media Flow

For a non-isothermal reactive flow process, effective properties such as permeability and heat conductivity change as the underlying pore structure evolves. We investigate changes of the effective properties for a two-dimensional periodic porous medium as the grain geometry changes. We consider specific grain shapes and study the evolution by solving the cell problems numerically for an upscaled model derived in Bringedal et al. (Transp Porous Media 114(2):371–393, 2016. doi:10.1007/s11242-015-0530-9). In particular, we focus on the limit behavior near clogging. The effective heat conductivities are compared to common porosity-weighted volume averaging approximations, and we find that geometric averages perform better than arithmetic and harmonic for isotropic media, while the optimal choice for anisotropic media depends on the degree and direction of the anisotropy. An approximate analytical expression is found to perform well for the isotropic effective heat conductivity. The permeability is compared to some commonly used approaches focusing on the limiting behavior near clogging, where a fitted power law is found to behave reasonably well. The resulting macroscale equations are tested on a case where the geochemical reactions cause pore clogging and a corresponding change in the flow and transport behavior at Darcy scale. As pores clog the flow paths shift away, while heat conduction increases in regions with lower porosity.