From e324b0a929ebd69a84adbfe58bec81b526d67645 Mon Sep 17 00:00:00 2001
From: vishal jambhekar <vishal.jambhekar@iws.uni-stuttgart.de>
Date: Thu, 30 Jul 2015 11:32:43 +0000
Subject: [PATCH] To follow the naming concenvention "brine_varSalinity" is
moved to "brineversalinity". Moreover, a missing binary coefficient file
brine_air is added (Reviewed by Johannes).
git-svn-id: svn://svn.iws.uni-stuttgart.de/DUMUX/dumux/trunk@15197 2fb0f335-1f38-0410-981e-8018bf24f1b0
---
.../material/binarycoefficients/brine_air.hh | 620 ++++++++++++++++++
...ine_varSalinity.hh => brinevarsalinity.hh} | 0
2 files changed, 620 insertions(+)
create mode 100644 dumux/material/binarycoefficients/brine_air.hh
rename dumux/material/components/{brine_varSalinity.hh => brinevarsalinity.hh} (100%)
diff --git a/dumux/material/binarycoefficients/brine_air.hh b/dumux/material/binarycoefficients/brine_air.hh
new file mode 100644
index 0000000000..e7028611d8
--- /dev/null
+++ b/dumux/material/binarycoefficients/brine_air.hh
@@ -0,0 +1,620 @@
+/*****************************************************************************
+ * Copyright (C) 2009 by Andreas Lauser *
+ * Institute for Modelling Hydraulic and Environmental Systems *
+ * University of Stuttgart, Germany *
+ * email: <givenname>.<name>@iws.uni-stuttgart.de *
+ * *
+ * This program is free software: you can redistribute it and/or modify *
+ * it under the terms of the GNU General Public License as published by *
+ * the Free Software Foundation, either version 2 of the License, or *
+ * (at your option) any later version. *
+ * *
+ * This program is distributed in the hope that it will be useful, *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
+ * GNU General Public License for more details. *
+ * *
+ * You should have received a copy of the GNU General Public License *
+ * along with this program. If not, see <http://www.gnu.org/licenses/>. *
+ *****************************************************************************/
+/*!
+ * \file
+ *
+ * \ingroup Binarycoefficients
+ * \brief Binary coefficients for Air and brine.
+ */
+#ifndef DUMUX_BINARY_COEFF_BRINE_Air_HH
+#define DUMUX_BINARY_COEFF_BRINE_Air_HH
+
+#include <dumux/material/components/brine.hh>
+#include <dumux/material/components/h2o.hh>
+#include <dumux/material/components/air.hh>
+#include <dumux/material/idealgas.hh>
+
+namespace Dumux {
+namespace BinaryCoeff {
+/*!
+ * \brief Binary coefficients for brine and Air.
+ */
+template<class Scalar, class Air, bool verbose = true>
+class Brine_Air {
+ typedef Dumux::H2O<Scalar> H2O;
+ // typedef Dumux::Air<Scalar> Air;
+ typedef Dumux::Brine<Scalar,H2O> Brine;
+ typedef Dumux::IdealGas<Scalar> IdealGas;
+ static const int lPhaseIdx = 0; // index of the liquid phase
+ static const int gPhaseIdx = 1; // index of the gas phase
+
+public:
+ /*!
+ * \brief Binary diffusion coefficent [m^2/s] of water in the Air phase.
+ *
+ * According to "Diffusion of Water in Liquid and Supercritical Carbon Dioxide: An NMR Study",Bin Xu et al., 2002
+ * \param temperature the temperature [K]
+ * \param pressure the phase pressure [Pa]
+ */
+ static Scalar gasDiffCoeff(Scalar temperature, Scalar pressure) {
+ //Diffusion coefficient of water in the Air phase
+ const Scalar Theta=1.8;
+ const Scalar Daw=2.13e-5; /* reference value */
+ const Scalar pg0=1.e5; /* reference pressure */
+ const Scalar T0=273.15; /* reference temperature */
+ Scalar Dgaw;
+ Dgaw=Daw*(pg0/pressure)*pow((temperature/T0),Theta);
+ return Dgaw;
+ }
+ ;
+
+ /*!
+ * Lacking better data on water-air diffusion in liquids, we use at the
+ * moment the diffusion coefficient of the air's main component nitrogen!!
+ * \brief Diffusion coefficent \f$\mathrm{[m^2/s]}\f$ for molecular nitrogen in liquid water.
+ *
+ * The empirical equations for estimating the diffusion coefficient in
+ * infinite solution which are presented in Reid, 1987 all show a
+ * linear dependency on temperature. We thus simply scale the
+ * experimentally obtained diffusion coefficient of Ferrell and
+ * Himmelblau by the temperature.
+ *
+ * See:
+ *
+ * R. Reid et al.: "The properties of Gases and Liquids", 4th edition,
+ * pp. 599, McGraw-Hill, 1987
+ *
+ * R. Ferrell, D. Himmelblau: "Diffusion Coeffients of Nitrogen and
+ * Oxygen in Water", Journal of Chemical Engineering and Data,
+ * Vol. 12, No. 1, pp. 111-115, 1967
+ */
+ static Scalar liquidDiffCoeff(Scalar temperature, Scalar pressure) {
+ //Diffusion coefficient of Air in the H2O phase
+ const Scalar Texp = 273.15 + 25; // [K]
+ const Scalar Dexp = 2.01e-9; // [m^2/s]
+ return Dexp * temperature/Texp;
+ };
+
+ /*!
+ * \brief Returns the _mol_ (!) fraction of Air in the liquid
+ * phase and the mol_ (!) fraction of H2O in the gas phase
+ * for a given temperature, pressure, Air density and brine
+ * XlNaCl.
+ *
+ * Implemented according to "Spycher and Pruess 2005"
+ * applying the activity coefficient expression of "Duan and Sun 2003"
+ * and the correlations for pure water given in "Spycher, Pruess and Ennis-King 2003"
+ *
+ * \param temperature the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ * \param XlNaCl the XlNaCl [kg NaCl / kg solution]
+ * \param knownPhaseIdx indicates which phases are present
+ * \param xlAir mole fraction of Air in brine [mol/mol]
+ * \param ygH2O mole fraction of water in the gas phase [mol/mol]
+ */
+ static void calculateMoleFractions(const Scalar temperature,
+ const Scalar pg,
+ const Scalar XlNaCl,
+ const int knownPhaseIdx,
+ Scalar &xlAir,
+ Scalar &ygH2O,
+ Scalar &xlNaCl) {
+ DUNE_THROW(Dune::InvalidStateException, "Function: " << "calculateMoleFractions" << " is invalid.");
+// Scalar A = computeA_(temperature, pg);
+//
+// /* XlNaCl: conversion from mass fraction to mol fraction */
+// xlNaCl = massTomoleFrac_(XlNaCl);
+//
+// // if both phases are present the mole fractions in each phase can be calculate
+// // with the mutual solubility function
+// if (knownPhaseIdx < 0) {
+// Scalar molalityNaCl = molFracToMolality_(xlNaCl); // molality of NaCl //CHANGED
+// Scalar m0_Air = molalityAirinPureWater_(temperature, pg); // molality of Air in pure water
+// Scalar gammaStar = activityCoefficient_(temperature, pg, molalityNaCl);// activity coefficient of Air in brine
+// Scalar m_Air = m0_Air / gammaStar; // molality of Air in brine
+// xlAir = m_Air / (molalityNaCl + 55.508 + m_Air); // mole fraction of Air in brine
+// ygH2O = A * (1 - xlAir - xlNaCl); // mole fraction of water in the gas phase
+// }
+//
+// // if only liquid phase is present the mole fraction of Air in brine is given and
+// // and the virtual equilibrium mole fraction of water in the non-existing gas phase can be estimated
+// // with the mutual solubility function
+// if (knownPhaseIdx == lPhaseIdx) {
+//// ygH2O = A * (1 - xlAir - xlNaCl);
+// DUNE_THROW(Dune::InvalidStateException, "phase index: " << "lPhaseIdx" << " is invalid.");
+//
+// }
+//
+// // if only gas phase is present the mole fraction of water in the gas phase is given and
+// // and the virtual equilibrium mole fraction of Air in the non-existing liquid phase can be estimated
+// // with the mutual solubility function
+// if (knownPhaseIdx == gPhaseIdx) {
+// //y_H2o = fluidstate.
+//// xlAir = 1 - xlNaCl - ygH2O / A;
+// DUNE_THROW(Dune::InvalidStateException, "phase index: " << "gPhaseIdx" << " is invalid.");
+// }
+ }
+
+ /*!
+ * \brief Returns the fugacity coefficient of the Air component in a water-Air mixture
+ * (given in Spycher, Pruess and Ennis-King (2003))
+ *
+ * \param T the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ */
+ static Scalar fugacityCoefficientAir(Scalar T, Scalar pg) {
+
+ Scalar V = 1 / (Air::gasDensity(T, pg) / Air::molarMass()) * 1.e6; // molar volume in cm^3/mol
+ Scalar pg_bar = pg / 1.e5; // gas phase pressure in bar
+ Scalar a_Air = (7.54e7 - 4.13e4 * T); // mixture parameter of Redlich-Kwong equation
+ static const Scalar b_Air = 27.8; // mixture parameter of Redlich-Kwong equation
+ static const Scalar R = IdealGas::R * 10.; // ideal gas constant with unit bar cm^3 /(K mol)
+ Scalar lnPhiAir, phiAir;
+
+ lnPhiAir = log(V / (V - b_Air)) + b_Air / (V - b_Air) - 2 * a_Air / (R
+ * pow(T, 1.5) * b_Air) * log((V + b_Air) / V) + a_Air * b_Air
+ / (R * pow(T, 1.5) * b_Air * b_Air) * (log((V + b_Air) / V)
+ - b_Air / (V + b_Air)) - log(pg_bar * V / (R * T));
+
+ phiAir = exp(lnPhiAir); // fugacity coefficient of Air
+ return phiAir;
+
+ }
+
+ /*!
+ * \brief Returns the fugacity coefficient of the H2O component in a water-Air mixture
+ * (given in Spycher, Pruess and Ennis-King (2003))
+ *
+ * \param T the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ */
+ static Scalar fugacityCoefficientH2O(Scalar T, Scalar pg) {
+
+ Scalar V = 1 / (Air::gasDensity(T, pg) / Air::molarMass()) * 1.e6; // molar volume in cm^3/mol
+ Scalar pg_bar = pg / 1.e5; // gas phase pressure in bar
+ Scalar a_Air = (7.54e7 - 4.13e4 * T);// mixture parameter of Redlich-Kwong equation
+ static const Scalar a_Air_H2O = 7.89e7;// mixture parameter of Redlich-Kwong equation
+ static const Scalar b_Air = 27.8;// mixture parameter of Redlich-Kwong equation
+ static const Scalar b_H2O = 18.18;// mixture parameter of Redlich-Kwong equation
+ static const Scalar R = IdealGas::R * 10.; // ideal gas constant with unit bar cm^3 /(K mol)
+ Scalar lnPhiH2O, phiH2O;
+
+ lnPhiH2O = log(V / (V - b_Air)) + b_H2O / (V - b_Air) - 2 * a_Air_H2O
+ / (R * pow(T, 1.5) * b_Air) * log((V + b_Air) / V) + a_Air
+ * b_H2O / (R * pow(T, 1.5) * b_Air * b_Air) * (log((V + b_Air)
+ / V) - b_Air / (V + b_Air)) - log(pg_bar * V / (R * T));
+ phiH2O = exp(lnPhiH2O); // fugacity coefficient of H2O
+ return phiH2O;
+ }
+
+ /*!
+ * \brief Returns the molality of NaCl (mol NaCl / kg water) for a given mole fraction (mol NaCl / mol solution)
+ *
+ * \param xlNaCl mole fraction of NaCL in brine [mol/mol]
+ */
+ static Scalar molalityNaCl(Scalar XlNaCl) {
+
+ // conversion from mol fraction to molality
+ const Scalar mol_NaCl = XlNaCl / 58.4428e-3;
+
+ return mol_NaCl;
+ }
+
+private:
+ /*!
+ * \brief Returns the molality of NaCl (mol NaCl / kg water) for a given mole fraction
+ *
+ * \param XlNaCl the XlNaCl [kg NaCl / kg solution]
+ */
+ static Scalar massTomoleFrac_(Scalar XlNaCl) {
+
+ DUNE_THROW(Dune::InvalidStateException, "Function: " << "massTomoleFrac_" << " is invalid.");
+
+// const Scalar Mw = H2O::molarMass(); /* molecular weight of water [kg/mol] */
+// const Scalar Ms = 58.8e-3; /* molecular weight of NaCl [kg/mol] */
+//
+// const Scalar X_NaCl = XlNaCl;
+// /* XlNaCl: conversion from mass fraction to mol fraction */
+// const Scalar xlNaCl = -Mw * X_NaCl / ((Ms - Mw) * X_NaCl - Ms);
+// return xlNaCl;
+ }
+
+ /*!
+ * \brief Returns the equilibrium molality of Air (mol Air / kg water) for a
+ * Air-water mixture at a given pressure and temperature
+ *
+ * \param T the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ */
+ static Scalar molalityAirinPureWater_(Scalar temperature, Scalar pg) {
+ Scalar A = computeA_(temperature, pg); // according to Spycher, Pruess and Ennis-King (2003)
+ Scalar B = computeB_(temperature, pg); // according to Spycher, Pruess and Ennis-King (2003)
+ Scalar yH2OinGas = (1 - B) / (1. / A - B); // equilibrium mol fraction of H2O in the gas phase
+ Scalar xAirinWater = B * (1 - yH2OinGas); // equilibrium mol fraction of Air in the water phase
+ Scalar molalityAir = (xAirinWater * 55.508) / (1 - xAirinWater); // Air molality
+ return molalityAir;
+ }
+
+ /*!
+ * \brief Returns the activity coefficient of Air in brine for a
+ * molal description. According to "Duan and Sun 2003"
+ * given in "Spycher and Pruess 2005"
+ *
+ * \param temperature the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ * \param molalityNaCl molality of NaCl (mol NaCl / kg water)
+ */
+ static Scalar activityCoefficient_(Scalar temperature, Scalar pg,
+ Scalar molalityNaCl) {
+ Scalar lambda = computeLambda_(temperature, pg); // lambda_{Air-Na+}
+ Scalar xi = computeXi_(temperature, pg); // Xi_{Air-Na+-Cl-}
+ Scalar lnGammaStar = 2 * lambda * molalityNaCl + xi * molalityNaCl
+ * molalityNaCl;
+ Scalar gammaStar = exp(lnGammaStar);
+ return gammaStar; // molal activity coefficient of Air in brine
+ }
+
+ /*!
+ * \brief Returns the paramater A for the calculation of
+ * them mutual solubility in the water-Air system.
+ * Given in Spycher, Pruess and Ennis-King (2003)
+ *
+ * \param T the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ */
+ static Scalar computeA_(Scalar T, Scalar pg) {
+ Scalar deltaP = pg / 1e5 - 1; // pressure range [bar] from p0 = 1bar to pg[bar]
+ const Scalar v_av_H2O = 18.1; // average partial molar volume of H2O [cm^3/mol]
+ const Scalar R = IdealGas::R * 10;
+ Scalar k0_H2O = equilibriumConstantH2O_(T); // equilibrium constant for H2O at 1 bar
+ Scalar phi_H2O = fugacityCoefficientH2O(T, pg); // fugacity coefficient of H2O for the water-Air system
+ Scalar pg_bar = pg / 1.e5;
+ Scalar A = k0_H2O / (phi_H2O * pg_bar) * exp(deltaP * v_av_H2O / (R * T));
+ return A;
+
+ }
+
+ /*!
+ * \brief Returns the paramater B for the calculation of
+ * the mutual solubility in the water-Air system.
+ * Given in Spycher, Pruess and Ennis-King (2003)
+ *
+ * \param T the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ */
+ static Scalar computeB_(Scalar T, Scalar pg) {
+ Scalar deltaP = pg / 1e5 - 1; // pressure range [bar] from p0 = 1bar to pg[bar]
+ const Scalar v_av_Air = 32.6; // average partial molar volume of Air [cm^3/mol]
+ const Scalar R = IdealGas::R * 10;
+ Scalar k0_Air = equilibriumConstantAir_(T); // equilibrium constant for Air at 1 bar
+ Scalar phi_Air = fugacityCoefficientAir(T, pg); // fugacity coefficient of Air for the water-Air system
+ Scalar pg_bar = pg / 1.e5;
+ Scalar B = phi_Air * pg_bar / (55.508 * k0_Air) * exp(-(deltaP
+ * v_av_Air) / (R * T));
+ return B;
+ }
+
+ /*!
+ * \brief Returns the parameter lambda, which is needed for the
+ * calculation of the Air activity coefficient in the brine-Air system.
+ * Given in Spycher and Pruess (2005)
+ * \param T the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ */
+ static Scalar computeLambda_(Scalar T, Scalar pg) {
+ Scalar lambda;
+ static const Scalar c[6] = { -0.411370585, 6.07632013E-4, 97.5347708,
+ -0.0237622469, 0.0170656236, 1.41335834E-5 };
+
+ Scalar pg_bar = pg / 1.0E5; /* conversion from Pa to bar */
+ lambda = c[0] + c[1] * T + c[2] / T + c[3] * pg_bar / T + c[4] * pg_bar
+ / (630.0 - T) + c[5] * T * std::log(pg_bar);
+
+ return lambda;
+ }
+
+ /*!
+ * \brief Returns the parameter xi, which is needed for the
+ * calculation of the Air activity coefficient in the brine-Air system.
+ * Given in Spycher and Pruess (2005)
+ * \param T the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ */
+ static Scalar computeXi_(Scalar T, Scalar pg) {
+ Scalar xi;
+ static const Scalar c[4] = { 3.36389723E-4, -1.98298980E-5,
+ 2.12220830E-3, -5.24873303E-3 };
+
+ Scalar pg_bar = pg / 1.0E5; /* conversion from Pa to bar */
+ xi = c[0] + c[1] * T + c[2] * pg_bar / T + c[3] * pg_bar / (630.0 - T);
+
+ return xi;
+ }
+
+ /*!
+ * \brief Returns the equilibrium constant for Air, which is needed for the
+ * calculation of the mutual solubility in the water-Air system
+ * Given in Spycher, Pruess and Ennis-King (2003)
+ * \param T the temperature [K]
+ */
+ static Scalar equilibriumConstantAir_(Scalar T) {
+ Scalar TinC = T - 273.15; //temperature in °C
+ static const Scalar c[3] = { 1.189, 1.304e-2, -5.446e-5 };
+ Scalar logk0_Air = c[0] + c[1] * TinC + c[2] * TinC * TinC;
+ Scalar k0_Air = pow(10, logk0_Air);
+ return k0_Air;
+ }
+
+ /*!
+ * \brief Returns the equilibrium constant for H2O, which is needed for the
+ * calculation of the mutual solubility in the water-Air system
+ * Given in Spycher, Pruess and Ennis-King (2003)
+ * \param T the temperature [K]
+ */
+ static Scalar equilibriumConstantH2O_(Scalar T) {
+ Scalar TinC = T - 273.15; //temperature in °C
+ static const Scalar c[4] = { -2.209, 3.097e-2, -1.098e-4, 2.048e-7 };
+ Scalar logk0_H2O = c[0] + c[1] * TinC + c[2] * TinC * TinC + c[3]
+ * TinC * TinC * TinC;
+ Scalar k0_H2O = pow(10, logk0_H2O);
+ return k0_H2O;
+ }
+
+};
+
+/*!
+ * \brief Old version of binary coefficients for Air and brine.
+ * Calculates molfraction of Air in brine according to Duan and Sun 2003
+ * molfraction of H2O has been assumed to be a constant value
+ * For use with the actual brine_co2_system this class still needs to be adapted
+ */
+template<class Scalar, class Air, bool verbose = true>
+class Brine_Air_Old
+{
+ typedef Dumux::H2O<Scalar> H2O;
+ typedef Dumux::Brine<Scalar,H2O> Brine;
+ // typedef Dumux::Air<Scalar> Air;
+ typedef Dumux::IdealGas<Scalar> IdealGas;
+
+public:
+ /*!
+ * \brief Returns the _mole_ (!) fraction of Air in the liquid
+ * phase at a given temperature, pressure and density of
+ * Air.
+ * \param T the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ * \param rhoAir density of Air
+ */
+ static Scalar moleFracAirInBrine(Scalar temperature, Scalar pg, Scalar rhoAir)
+ {
+ // regularisations:
+ if (pg > 2.5e8) {
+ pg = 2.5e8;
+ }
+ if (pg < 2.e5) {
+ pg = 2.e5;
+ }
+ if (temperature < 275.) {
+ temperature = 275;
+ }
+ if (temperature > 600.) {
+ temperature = 600;
+ }
+
+ const Scalar Mw = H2O::molarMass(); /* molecular weight of water [kg/mol] */
+ const Scalar Ms = 58.8e-3; /* molecular weight of NaCl [kg/mol] */
+
+ const Scalar X_NaCl = Brine::XlNaCl;
+ /* XlNaCl: conversion from mass fraction to mole fraction */
+ const Scalar xlNaCl = -Mw * X_NaCl / ((Ms - Mw) * X_NaCl - Ms);
+
+ // XlNaCl: conversion from mole fraction to molality
+ const Scalar mol_NaCl = -55.56 * xlNaCl / (xlNaCl - 1);
+
+ const Scalar A = computeA_(temperature, pg); /* mu_{Air}^{l(0)}/RT */
+ const Scalar B = computeB_(temperature, pg); /* lambda_{Air-Na+} */
+ const Scalar C = computeC_(temperature, pg); /* Xi_{Air-Na+-Cl-} */
+ const Scalar pgAir = partialPressureAir_(temperature, pg);
+ const Scalar phiAir = fugacityCoeffAir_(temperature, pgAir, rhoAir);
+
+ const Scalar exponent = A - log(phiAir) + 2*B*mol_NaCl + C*pow(mol_NaCl,2);
+
+ const Scalar mol_Airw = pgAir / (1e5 * exp(exponent)); /* paper: equation (6) */
+
+ const Scalar x_Airw = mol_Airw / (mol_Airw + 55.56); /* conversion: molality to mole fraction */
+ //Scalar X_Airw = x_Airw*MAir/(x_Airw*MAir + (1-x_Airw)*Mw); /* conversion: mole fraction to mass fraction */
+
+ return x_Airw;
+ }
+
+private:
+ /*!
+ * \brief computation of mu_{Air}^{l(0)}/RT
+ * \param T the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ */
+ static Scalar computeA_(Scalar T, Scalar pg)
+ {
+ static const Scalar c[10] = {
+ 28.9447706,
+ -0.0354581768,
+ -4770.67077,
+ 1.02782768E-5,
+ 33.8126098,
+ 9.04037140E-3,
+ -1.14934031E-3,
+ -0.307405726,
+ -0.0907301486,
+ 9.32713393E-4,
+ };
+
+ const Scalar pg_bar = pg / 1.0E5; /* conversion from Pa to bar */
+ const Scalar Tr = 630.0 - T;
+
+ return
+ c[0] +
+ c[1]*T +
+ c[2]/T +
+ c[3]*T*T +
+ c[4]/Tr +
+ c[5]*pg_bar +
+ c[6]*pg_bar*log(T) +
+ c[7]*pg_bar/T +
+ c[8]*pg_bar/Tr +
+ c[9]*pg_bar*pg_bar/(Tr*Tr);
+ }
+
+ /*!
+ * \brief computation of B
+ *
+ * \param T the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ */
+ static Scalar computeB_(Scalar T, Scalar pg)
+ {
+ const Scalar c1 = -0.411370585;
+ const Scalar c2 = 6.07632013E-4;
+ const Scalar c3 = 97.5347708;
+ const Scalar c8 = -0.0237622469;
+ const Scalar c9 = 0.0170656236;
+ const Scalar c11 = 1.41335834E-5;
+
+ const Scalar pg_bar = pg / 1.0E5; /* conversion from Pa to bar */
+
+ return
+ c1 +
+ c2*T +
+ c3/T +
+ c8*pg_bar/T +
+ c9*pg_bar/(630.0-T) +
+ c11*T*std::log(pg_bar);
+ }
+ /*!
+ * \brief computation of C
+ *
+ * \param T the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ */
+ static Scalar computeC_(Scalar T, Scalar pg)
+ {
+ const Scalar c1 = 3.36389723E-4;
+ const Scalar c2 = -1.98298980E-5;
+ const Scalar c8 = 2.12220830E-3;
+ const Scalar c9 = -5.24873303E-3;
+
+ const Scalar pg_bar = pg / 1.0E5; /* conversion from Pa to bar */
+
+ return
+ c1 +
+ c2*T +
+ c8*pg_bar/T +
+ c9*pg_bar/(630.0-T);
+ }
+ /*!
+ * \brief computation of partial pressure Air
+ *
+ * \param temperature the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ */
+ static Scalar partialPressureAir_(Scalar temperature, Scalar pg)
+ {
+ // We assume that the partial pressure of brine is its vapor
+ // pressure. TODO: Strictly this is assumption is invalid for
+ // Air because the mole fraction of Air in brine can be
+ // considerable
+ return pg - Brine::vaporPressure(temperature);
+ };
+
+ /*!
+ * \brief The fugacity coefficent of Air for a Air-H2O mixture.
+ *
+ * \param temperature the temperature [K]
+ * \param pg the gas phase pressure [Pa]
+ * \param rhoAir the density of Air for the critical volume [kg/m^3]
+ */
+
+ static Scalar fugacityCoeffAir_(Scalar temperature,
+ Scalar pg,
+ Scalar rhoAir)
+ {
+ static const Scalar a[15] = {
+ 8.99288497E-2,
+ -4.94783127E-1,
+ 4.77922245E-2,
+ 1.03808883E-2,
+ -2.82516861E-2,
+ 9.49887563E-2,
+ 5.20600880E-4,
+ -2.93540971E-4,
+ -1.77265112E-3,
+ -2.51101973E-5,
+ 8.93353441E-5,
+ 7.88998563E-5,
+ -1.66727022E-2,
+ 1.3980,
+ 2.96000000E-2
+ };
+
+ // reduced temperature
+ const Scalar Tr = temperature / Air::criticalTemperature();
+ // reduced pressure
+ const Scalar pr = pg / Air::criticalPressure();
+
+ // reduced molar volume. ATTENTION: Vc is _NOT_ the critical
+ // molar volume of Air. See the reference!
+ const Scalar Vc = IdealGas::R*Air::criticalTemperature()/Air::criticalPressure();
+ const Scalar Vr =
+ // molar volume of Air at (temperature, pg)
+ Air::molarMass() / rhoAir
+ *
+ // "pseudo-critical" molar volume
+ 1.0 / Vc;
+
+ // the Z coefficient
+ const Scalar Z = pr * Vr / Tr;
+
+ const Scalar A = a[0] + a[1] / (Tr * Tr) + a[2] / (Tr * Tr * Tr);
+ const Scalar B = a[3] + a[4] / (Tr * Tr) + a[5] / (Tr * Tr * Tr);
+ const Scalar C = a[6] + a[7] / (Tr * Tr) + a[8] / (Tr * Tr * Tr);
+ const Scalar D = a[9] + a[10] / (Tr * Tr) + a[11] / (Tr * Tr * Tr);
+
+ const Scalar lnphiAir =
+ Z - 1 -
+ log(Z) +
+ A/Vr +
+ B/(2*Vr*Vr) +
+ C/(4*Vr*Vr*Vr*Vr) +
+ D/(5*Vr*Vr*Vr*Vr*Vr)
+ +
+ a[12]/(2*Tr*Tr*Tr*a[14])*
+ (
+ a[13] + 1 -
+ ( a[13] + 1 +
+ a[14]/(Vr*Vr)
+ )*std::exp(-a[14]/(Vr*Vr)));
+
+ return std::exp(lnphiAir);
+ }
+
+};
+}
+} // end namespace
+
+#endif
diff --git a/dumux/material/components/brine_varSalinity.hh b/dumux/material/components/brinevarsalinity.hh
similarity index 100%
rename from dumux/material/components/brine_varSalinity.hh
rename to dumux/material/components/brinevarsalinity.hh
--
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