Adaption of the fully implicit scheme to the three-phase flow model. More...
#include <dumux/common/properties.hh>
#include <dumux/material/fluidstates/immiscible.hh>
#include <dumux/material/fluidmatrixinteractions/3p/thermalconductivitysomerton3p.hh>
#include <dumux/porousmediumflow/properties.hh>
#include <dumux/porousmediumflow/immiscible/localresidual.hh>
#include <dumux/porousmediumflow/nonisothermal/model.hh>
#include <dumux/porousmediumflow/nonisothermal/indices.hh>
#include <dumux/porousmediumflow/nonisothermal/iofields.hh>
#include "indices.hh"
#include "volumevariables.hh"
#include "iofields.hh"
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Adaption of the fully implicit scheme to the three-phase flow model.
This model implements three-phase flow of three fluid phases \(\alpha \in \{ water, gas, NAPL \}\). The standard multiphase Darcy approach is used as the equation for the conservation of momentum, i.e.
\[ v_\alpha = - \frac{k_{r\alpha}}{\mu_\alpha} \textbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_{\alpha} {\textbf g} \right) \]
By inserting this into the equations for the conservation of the phase mass, one gets
\[ \phi \frac{\partial \varrho_\alpha S_\alpha}{\partial t} - \text{div} \left\{ \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_{\alpha} \mathbf{g} \right) \right\} - q_\alpha = 0 \;. \]
The model uses commonly applied auxiliary conditions like \(S_w + S_n + S_g = 1\) for the saturations. Furthermore, the phase pressures are related to each other via capillary pressures between the fluid phases, which are functions of the saturation, e.g. according to the approach of Parker et al.
The used primary variables are gas phase pressure \(p_g\), water saturation \(S_w\) and NAPL saturation \(S_n\).
Namespaces | |
namespace | Dumux |
namespace | Dumux::Properties |
namespace | Dumux::Properties::TTag |
Type tag for numeric models. | |