diff --git a/dumux/porousmediumflow/2p2c/model.hh b/dumux/porousmediumflow/2p2c/model.hh index e745b67d750dcb7f2c384aa7e2a632ca52bb55dd..1c02de629461151ea024e0029a5aef352fea47e3 100644 --- a/dumux/porousmediumflow/2p2c/model.hh +++ b/dumux/porousmediumflow/2p2c/model.hh @@ -19,55 +19,53 @@ /*! * \file * \ingroup TwoPTwoCModel - * \brief Adaption of the fully implicit scheme to the - * two-phase two-component fully implicit model. + * \brief Properties for a two-phase, two-component model for flow in porous media. * * This model implements two-phase two-component flow of two compressible and * partially miscible fluids \f$\alpha \in \{ w, n \}\f$ composed of the two components - * \f$\kappa \in \{ w, a \}\f$. The standard multiphase Darcy - * approach is used as the equation for the conservation of momentum: + * \f$\kappa \in \{ \kappa_w, \kappa_n \}\f$, where \f$\kappa_w\f$ and \f$\kappa_n\f$ are + * the main components of the wetting and nonwetting phases, respectively. + * The governing equations are the mass or the mole conservation equations of the two components, + * depending on the property UseMoles. The mass balance equations are given as: * \f[ - v_\alpha = - \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} - \left(\textbf{grad}\, p_\alpha - \varrho_{\alpha} \mathbf{g} \right) - * \f] + \phi \frac{\partial (\sum_\alpha \rho_\alpha X_\alpha^\kappa S_\alpha)}{\partial t} + - \sum_\alpha \text{div} \left\{ \rho_\alpha X_\alpha^\kappa v_\alpha \right\} + - \sum_\alpha \text{div} \mathbf{F}_{\mathrm{diff, mass}, \alpha}^\kappa + - \sum_\alpha q_\alpha^\kappa = 0 \qquad \kappa \in \{\kappa_w, \kappa_n\} \, , \alpha \in \{w, n\}, + \f] + * using the mass fractions \f$X_\alpha^\kappa\f$ and the mass densities \f$\rho_\alpha\f$, while + * the mole balance equations use the mole fractions \f$x_\alpha^\kappa\f$ and molar + * densities \f$\varrho_{m, \alpha}\f$: + * \f[ + \phi \frac{\partial (\sum_\alpha \varrho_{m, \alpha} x_\alpha^\kappa S_\alpha)}{\partial t} + + \sum_\alpha \text{div} \left\{ \varrho_{m, \alpha} x_\alpha^\kappa v_\alpha \right\} + + \sum_\alpha \text{div} \mathbf{F}_{\mathrm{diff, mole}, \alpha}^\kappa + - \sum_\alpha q_\alpha^\kappa = 0 \qquad \kappa \in \{\kappa_w, \kappa_n\} \, , \alpha \in \{w, n\}. + \f] + * Boundary conditions and sources have to be defined by the user in the corresponding + * units. The default setting for the property UseMoles can be found in the 2pnc model. + * + * Per default, the Darcy's and Fick's law are used for the fluid phase velocities and the + * diffusive fluxes, respectively. See dumux/flux/darcyslaw.hh and dumux/flux/fickslaw.hh + * for more details. * - * By inserting this into the equations for the conservation of the - * components, one gets one transport equation for each component - * \f{eqnarray*} - && \phi \frac{\partial (\sum_\alpha \varrho_\alpha \frac{M^\kappa}{M_\alpha} x_\alpha^\kappa S_\alpha )} - {\partial t} - - \sum_\alpha \text{div} \left\{ \varrho_\alpha \frac{M^\kappa}{M_\alpha} x_\alpha^\kappa - \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} - (\textbf{grad}\, p_\alpha - \varrho_{\alpha} \mathbf{g}) \right\} - \nonumber \\ \nonumber \\ - &-& \sum_\alpha \text{div} \left\{ D_{\alpha,\text{pm}}^\kappa \varrho_{\alpha} - \textbf{grad} X^\kappa_{\alpha} \right\} - - \sum_\alpha q_\alpha^\kappa = 0 \qquad \kappa \in \{w, a\} \, , - \alpha \in \{w, g\} - \f} + * By using constitutive relations for the capillary pressure \f$p_c = p_n - p_w\f$ and + * relative permeability \f$k_{r\alpha}\f$ and taking advantage of the fact that \f$S_w + S_n = 1\f$ + * and \f$x^{\kappa_w}_\alpha + x^{\kappa_n}_\alpha = 1\f$, the number of unknowns can be reduced to two. + * In single-phase regimes, the used primary variables are either \f$p_w\f$ and \f$S_n\f$ (default) + * or \f$p_n\f$ and \f$S_w\f$. The formulation which ought to be used can be specified by setting + * the Formulation property to either + * TwoPTwoCFormulation::pwsn or TwoPTwoCFormulation::pnsw. * - * By using constitutive relations for the capillary pressure \f$p_c = - * p_n - p_w\f$ and relative permeability \f$k_{r\alpha}\f$ and taking - * advantage of the fact that \f$S_w + S_n = 1\f$ and \f$x^\kappa_w + x^\kappa_n = 1\f$, the number of - * unknowns can be reduced to two. - * The used primary variables are, like in the two-phase model, either \f$p_w\f$ and \f$S_n\f$ - * or \f$p_n\f$ and \f$S_w\f$. The formulation which ought to be used can be - * specified by setting the Formulation property to either - * TwoPTwoCFormulation::pwsn or TwoPTwoCFormulation::pnsw. By - * default, the model uses \f$p_w\f$ and \f$S_n\f$. - * Moreover, the second primary variable depends on the phase state, since a - * primary variable switch is included. The phase state is stored for all nodes - * of the system. - * The model is able to use either mole or mass fractions. The property useMoles can be set to either true or false in the - * problem file. Make sure that the according units are used in the problem setup. useMoles is set to true by default. - * Following cases can be distinguished: + * In two-phase flow regimes the second primary variable depends on the phase state and is the mole or mass + * fraction (depending on the property UseMoles). The following cases can be distinguished: *
*
• Both phases are present: The saturation is used (either \f$S_n\f$ or \f$S_w\f$, dependent on the chosen Formulation), * as long as \f$0 < S_\alpha < 1\f$
• . - *
• Only wetting phase is present: The mole fraction of, e.g., air in the wetting phase \f$x^a_w\f$ is used, - * as long as the maximum mole fraction is not exceeded \f$(x^a_w - * • Only nonwetting phase is present: The mole fraction of, e.g., water in the nonwetting phase, \f$x^w_n\f$, is used, - * as long as the maximum mole fraction is not exceeded \f$(x^w_n + *
• Only wetting phase is present: The mole fraction of the nonwetting phase main component in the wetting phase \f$x^{\kappa_n}_w\f$ is used, + * as long as the maximum mole fraction is not exceeded \f$(x^{\kappa_n}_w + * • Only nonwetting phase is present: The mole fraction of the wetting phase main component in the nonwetting phase, \f$x^{\kappa_w}_n\f$, is used, + * as long as the maximum mole fraction is not exceeded \f$(x^{\kappa_w}_n *
*/