Convergence analysis of mixed numerical schemes for reactive in a porous medium

This paper deals with the numerical analysis of an upscaled model describing the reactive flow in a porous medium. The solutes are transported by advection and diffusion and undergo precipitation and dissolution. The reaction term and, in particular, the dissolution term has a particular, multi-valued character, which leads to stiff dissolution fronts. We consider the Euler implicit method for the temporal discretization and the mixed finite element for the discretization in time. More precisely, we use the lowest order Raviart-Thomas elements. As an intermediate step we consider also a semi-discrete mixed variational formulation (continuous in space). We analyse the numerical schemes and prove the convergence to the continuous formulation. Apart from the proof for the convergence, this also yields an existence proof for the solution of the model in mixed variational formulation. Numerical experiments are performed to study the convergence behavior

Upscaling of non-isothermal reactive porous media flow under dominant Péclet number : the effect of changing porosity

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 onedimensional 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

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

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, and we take into account the possible change in aperture that 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 thin strip become infinitely thin, deriving one-dimensional effective equations

Upscaling of non-isothermal reactive porous media flow under dominant Péclet number : the effect of changing porosity

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 onedimensional 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

A mixed finite element discretization scheme for a concrete carbonation model with concentration-dependent porosity

We discuss a prototypical reaction-diffusion-flow problem in saturated/unsaturated porous media. The special features of our problem are: the reaction produces water and therefore the flow and transport are coupled in both directions and moreover, the reaction may alter the microstructure. This means we have a variable porosity in our model. For the spatial discretization we propose a mass conservative scheme based on the mixed finite element method (MFEM). The scheme is semi-implicit in time. Error estimates are obtained for some particular cases. We apply our finite element methodology for the case of concrete carbonation – one of the most important physico-chemical processes affecting the durability of concrete

Gauge-fixing, semiclassical approximation and potentials for graded Chern-Simons theories

We perform the Batalin-Vilkovisky analysis of gauge-fixing for graded Chern-Simons theories. Upon constructing an appropriate gauge-fixing fermion, we implement a Landau-type constraint, finding a simple form of the gauge-fixed action. This allows us to extract the associated Feynman rules taking into account the role of ghosts and antighosts. Our gauge-fixing procedure allows for zero-modes, hence is not limited to the acyclic case. We also discuss the semiclassical approximation and the effective potential for massless modes, thereby justifying some of our previous constructions in the Batalin-Vilkovisky approach.Comment: 46 pages, 4 figure