1pncmin

Single-phase, multi-component Darcy flow with mineralization. More...

Description

Single-phase, multi-component Darcy flow with mineralization.

This model implements one-phase n-component flow of a compressible fluid composed of the n components $\kappa$ in combination with mineral precipitation and dissolution of the solid phases. The standard multi-phase Darcy approach is used as the equation for the conservation of momentum:

$$v = - \frac{k_{r}}{\mu} \mbox{\bf K} \left(\text{grad}\, p - \varrho_{f} \mbox{\bf g} \right)$$

By inserting this into the equations for the conservation of the components, one gets one transport equation for each component

$$\frac{\partial ( \varrho_f X^\kappa \phi )} {\partial t} - \text{div} \left\{ \varrho_f X^\kappa \frac{k_{r}}{\mu} \mbox{\bf K} (\text{grad}\, p - \varrho_{f} \mbox{\bf g}) \right\} - \text{div} \left\{{\bf D_{pm}^\kappa} \varrho_{f} \text{grad}\, X^\kappa \right\} - q_\kappa = 0 \qquad \kappa \in \{w, a,\cdots \}$$

The solid or mineral phases are assumed to consist of a single component. Their mass balance consist only of a storage and a source term:

$$\frac{\partial \varrho_\lambda \phi_\lambda )} {\partial t} = q_\lambda$$

All equations are discretized using a vertex-centered finite volume (box) or cell-centered finite volume scheme as spatial and the implicit Euler method as time discretization.

The primary variables are the pressure $p$ and the mole fractions of the dissolved components $x^k$. The primary variable of the solid phases is the volume fraction $\phi_\lambda = \frac{V_\lambda}{V_{total}}$.

The source an sink terms link the mass balances of the n-transported component to the solid phases. The porosity $\phi$ is updated according to the reduction of the initial (or solid-phase-free porous medium) porosity $\phi_0$ by the accumulated volume fractions of the solid phases: $\phi = \phi_0 - \sum (\phi_\lambda)$ Additionally, the permeability is updated depending on the current porosity.

Files
file	porousmediumflow/1pncmin/model.hh
	A single-phase, multi-component model considering mineralization processes.