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3.1-git
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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3.1-git
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
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Single-phase, multi-component Darcy flow with mineralization. More...
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.
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| file | porousmediumflow/1pncmin/model.hh |
| A single-phase, multi-component model considering mineralization processes. | |
1.9.3