void
CO2FluidPropertiesTest::partialDensity()
{
REL_TEST("partial density", _fp->partialDensity(373.15), 1182.8, 5.0e-2);
REL_TEST("partial density", _fp->partialDensity(473.35), 880.0, 5.0e-2);
REL_TEST("partial density", _fp->partialDensity(573.15), 593.8, 5.0e-2);
}
/*
* Verify calculation of Henry constant with brine correction. Note: the values
* calculated compare well by eye to the values presented in Figure 4 of
* Battistelli et al, "A fluid property module for the TOUGH2 simulator for saline
* brines with non-condensible gas"
*/
TEST_F(PorousFlowBrineCO2Test, henryConstant)
{
Real T = 373.15;
Real Xnacl = 0.1;
Real Kh, dKh_dT, dKh_dX;
_fp->henryConstant(T, Xnacl, Kh, dKh_dT, dKh_dX);
REL_TEST(Kh, 7.46559e+08, 1.0e-3);
T = 473.15;
Xnacl = 0.2;
_fp->henryConstant(T, Xnacl, Kh, dKh_dT, dKh_dX);
REL_TEST(Kh, 1.66069e+09, 1.0e-3);
// Test the derivative wrt temperature
const Real dT = 1.0e-4;
Real Kh2, dKh2_dT, dKh2_dX;
_fp->henryConstant(T + dT, Xnacl, Kh, dKh_dT, dKh_dX);
_fp->henryConstant(T - dT, Xnacl, Kh2, dKh2_dT, dKh2_dX);
REL_TEST(dKh_dT, (Kh - Kh2) / (2.0 * dT), 1.0e-5);
// Test the derivative wrt Xnacl
const Real dx = 1.0e-8;
_fp->henryConstant(T, Xnacl + dx, Kh, dKh_dT, dKh_dX);
_fp->henryConstant(T, Xnacl - dx, Kh2, dKh2_dT, dKh2_dX);
REL_TEST(dKh_dX, (Kh - Kh2) / (2.0 * dx), 1.0e-5);
}
/*
* Verify calculation of enthalpy of dissolution. Note: the values calculated compare
* well by eye to the values presented in Figure 4 of Battistelli et al, "A fluid property
* module for the TOUGH2 simulator for saline brines with non-condensible gas"
*/
TEST_F(PorousFlowBrineCO2Test, enthalpyOfDissolutionGas)
{
// T = 50C
Real T = 323.15;
Real Xnacl = 0.1;
// Enthalpy of dissolution of CO2 in brine
Real hdis, dhdis_dT, dhdis_dX;
_fp->enthalpyOfDissolutionGas(T, Xnacl, hdis, dhdis_dT, dhdis_dX);
REL_TEST(hdis, -3.20130e5, 1.0e-3);
// T = 350C
T = 623.15;
// Enthalpy of dissolution of CO2 in brine
_fp->enthalpyOfDissolutionGas(T, Xnacl, hdis, dhdis_dT, dhdis_dX);
REL_TEST(hdis, 9.83813e+05, 1.0e-3);
// Test the derivative wrt temperature
const Real dT = 1.0e-4;
Real hdis1, dhdis1_dT, dhdis1_dX, hdis2, dhdis2_dT, dhdis2_dX;
_fp->enthalpyOfDissolutionGas(T + dT, Xnacl, hdis1, dhdis1_dT, dhdis1_dX);
_fp->enthalpyOfDissolutionGas(T - dT, Xnacl, hdis2, dhdis2_dT, dhdis2_dX);
REL_TEST(dhdis_dT, (hdis1 - hdis2) / (2.0 * dT), 1.0e-5);
// Test the derivative wrt salt mass fraction
const Real dx = 1.0e-8;
_fp->enthalpyOfDissolutionGas(T, Xnacl + dx, hdis1, dhdis1_dT, dhdis1_dX);
_fp->enthalpyOfDissolutionGas(T, Xnacl - dx, hdis2, dhdis2_dT, dhdis2_dX);
REL_TEST(dhdis_dX, (hdis1 - hdis2) / (2.0 * dx), 1.0e-5);
}
/**
* Verify calculation of Henry's constant using data from
* Guidelines on the Henry's constant and vapour liquid distribution constant
* for gases in H20 and D20 at high temperatures, IAPWS (2004).
*/
TEST_F(MethaneFluidPropertiesTest, henry)
{
REL_TEST(_fp->henryConstant(300.0), 4069.0e6, REL_TOL_EXTERNAL_VALUE);
REL_TEST(_fp->henryConstant(400.0), 6017.1e6, REL_TOL_EXTERNAL_VALUE);
REL_TEST(_fp->henryConstant(500.0), 2812.9e6, REL_TOL_EXTERNAL_VALUE);
REL_TEST(_fp->henryConstant(600.0), 801.8e6, REL_TOL_EXTERNAL_VALUE);
}
/*
* Verify calculation of enthalpy of dissolution. Note: the values calculated compare
* well by eye to the values presented in Figure 4 of Battistelli et al, "A fluid property
* module for the TOUGH2 simulator for saline brines with non-condensible gas"
*/
TEST_F(PorousFlowWaterNCGTest, enthalpyOfDissolution)
{
// T = 50C
Real T = 323.15;
// Enthalpy of dissolution of NCG in water
Real hdis, dhdis_dT;
_fp->enthalpyOfDissolution(T, hdis, dhdis_dT);
REL_TEST(hdis, -3.45731e5, 1.0e-3);
// T = 350C
T = 623.15;
// Enthalpy of dissolution of NCG in water
_fp->enthalpyOfDissolution(T, hdis, dhdis_dT);
REL_TEST(hdis, 1.23423e+06, 1.0e-3);
// Test the derivative wrt temperature
const Real dT = 1.0e-4;
Real hdis2, dhdis2_dT;
_fp->enthalpyOfDissolution(T + dT, hdis, dhdis_dT);
_fp->enthalpyOfDissolution(T - dT, hdis2, dhdis2_dT);
REL_TEST(dhdis_dT, (hdis - hdis2) / (2.0 * dT), 1.0e-5);
}
void
CO2FluidPropertiesTest::melting()
{
REL_TEST("melting", _fp->meltingPressure(217.03), 2.57e6, 1.0e-2);
REL_TEST("melting", _fp->meltingPressure(235.29), 95.86e6, 1.0e-2);
REL_TEST("melting", _fp->meltingPressure(266.04), 286.77e6, 1.0e-2);
}
/**
* Verify calculation of the derivatives of all properties by comparing with finite
* differences
*/
TEST_F(MethaneFluidPropertiesTest, derivatives)
{
const Real tol = REL_TOL_DERIVATIVE;
const Real p = 10.0e6;
Real T = 350.0;
DERIV_TEST(_fp->rho, _fp->rho_from_p_T, p, T, tol);
DERIV_TEST(_fp->mu, _fp->mu_dpT, p, T, tol);
DERIV_TEST(_fp->e, _fp->e_dpT, p, T, tol);
DERIV_TEST(_fp->h, _fp->h_dpT, p, T, tol);
DERIV_TEST(_fp->k, _fp->k_dpT, p, T, tol);
// Test derivative of enthalpy for T > 755 as well as it has a different formulation
T = 800.0;
DERIV_TEST(_fp->h, _fp->h_dpT, p, T, tol);
// Henry's constant
T = 350.0;
const Real dT = 1.0e-4;
Real dKh_dT_fd = (_fp->henryConstant(T + dT) - _fp->henryConstant(T - dT)) / (2.0 * dT);
Real Kh = 0.0, dKh_dT = 0.0;
_fp->henryConstant_dT(T, Kh, dKh_dT);
REL_TEST(Kh, _fp->henryConstant(T), REL_TOL_SAVED_VALUE);
REL_TEST(dKh_dT_fd, dKh_dT, REL_TOL_DERIVATIVE);
}
/**
* Verify calculation of Henry's constant using data from
* Guidelines on the Henry's constant and vapour liquid distribution constant
* for gases in H20 and D20 at high temperatures, IAPWS (2004).
*/
TEST_F(CO2FluidPropertiesTest, henry)
{
REL_TEST("henry", _fp->henryConstant(300.0), 173.63e6, 1.0e-3);
REL_TEST("henry", _fp->henryConstant(400.0), 579.84e6, 1.0e-3);
REL_TEST("henry", _fp->henryConstant(500.0), 520.79e6, 1.0e-3);
REL_TEST("henry", _fp->henryConstant(600.0), 259.53e6, 1.0e-3);
}
void
CO2FluidPropertiesTest::viscosity()
{
REL_TEST("viscosity", _fp->mu(20.199, 280.0), 14.15e-6, 1.0e-3);
REL_TEST("viscosity", _fp->mu(15.105, 360.0), 17.94e-6, 1.0e-3);
REL_TEST("viscosity", _fp->mu(10.664, 500.0), 24.06e-6, 1.0e-3);
}
void
CO2FluidPropertiesTest::thermalConductivity()
{
REL_TEST("thermal conductivity", _fp->k(23.435, 250.0), 13.45e-3, 1.0e-3);
REL_TEST("thermal conductivity", _fp->k(18.579, 300.0), 17.248e-3, 1.0e-3);
REL_TEST("thermal conductivity", _fp->k(11.899, 450.0), 29.377e-3, 1.0e-3);
}
/*
* Verify calculation of equilibrium mass fraction and derivatives
*/
TEST_F(PorousFlowWaterNCGTest, equilibriumMassFraction)
{
const Real p = 1.0e6;
const Real T = 350.0;
const Real dp = 1.0e-2;
const Real dT = 1.0e-6;
Real Xncg, dXncg_dp, dXncg_dT, Yh2o, dYh2o_dp, dYh2o_dT;
Real Xncg1, dXncg1_dp, dXncg1_dT, Yh2o1, dYh2o1_dp, dYh2o1_dT;
Real Xncg2, dXncg2_dp, dXncg2_dT, Yh2o2, dYh2o2_dp, dYh2o2_dT;
_fp->equilibriumMassFractions(p, T, Xncg, dXncg_dp, dXncg_dT, Yh2o, dYh2o_dp, dYh2o_dT);
_fp->equilibriumMassFractions(
p - dp, T, Xncg1, dXncg1_dp, dXncg1_dT, Yh2o1, dYh2o1_dp, dYh2o1_dT);
_fp->equilibriumMassFractions(
p + dp, T, Xncg2, dXncg2_dp, dXncg2_dT, Yh2o2, dYh2o2_dp, dYh2o2_dT);
Real dXncg_dp_fd = (Xncg2 - Xncg1) / (2.0 * dp);
Real dYh2o_dp_fd = (Yh2o2 - Yh2o1) / (2.0 * dp);
REL_TEST(dXncg_dp, dXncg_dp_fd, 1.0e-6);
REL_TEST(dYh2o_dp, dYh2o_dp_fd, 1.0e-6);
_fp->equilibriumMassFractions(
p, T - dT, Xncg1, dXncg1_dp, dXncg1_dT, Yh2o1, dYh2o1_dp, dYh2o1_dT);
_fp->equilibriumMassFractions(
p, T + dT, Xncg2, dXncg2_dp, dXncg2_dT, Yh2o2, dYh2o2_dp, dYh2o2_dT);
Real dXncg_dT_fd = (Xncg2 - Xncg1) / (2.0 * dT);
Real dYh2o_dT_fd = (Yh2o2 - Yh2o1) / (2.0 * dT);
REL_TEST(dXncg_dT, dXncg_dT_fd, 1.0e-6);
REL_TEST(dYh2o_dT, dYh2o_dT_fd, 1.0e-6);
}
/*
* Verify calculation of enthalpy of dissolution of CO2. Note: the values calculated compare
* well by eye to the values presented in Figure 6 of Duan and Sun, An improved model
* calculating CO2 solubility in pure water and aqueous NaCl solutions from 273 to 533 K
* and from 0 to 2000 bar, Chemical geology, 193, 257--271 (2003)
*/
TEST_F(PorousFlowBrineCO2Test, enthalpyOfDissolution)
{
// T = 50C
Real T = 323.15;
// Enthalpy of dissolution of CO2 in water
Real hdis, dhdis_dT;
_fp->enthalpyOfDissolution(T, hdis, dhdis_dT);
REL_TEST(hdis, -3.38185e5, 1.0e-3);
// T = 350C
T = 623.15;
// Enthalpy of dissolution of CO2 in water
_fp->enthalpyOfDissolution(T, hdis, dhdis_dT);
REL_TEST(hdis, 5.78787e5, 1.0e-3);
// Test the derivative wrt temperature
const Real dT = 1.0e-4;
Real hdis1, dhdis1_dT, hdis2, dhdis2_dT;
_fp->enthalpyOfDissolution(T + dT, hdis1, dhdis1_dT);
_fp->enthalpyOfDissolution(T - dT, hdis2, dhdis2_dT);
REL_TEST(dhdis_dT, (hdis1 - hdis2) / (2.0 * dT), 1.0e-5);
}
/**
* Verify calculation of the derivatives in all regions by comparing with finite
* differences
*/
TEST_F(Water97FluidPropertiesTest, derivatives)
{
// Region 1
Real p = 3.0e6;
Real T = 300.0;
regionDerivatives(p, T, 1.0e-6);
// Region 2
p = 3.5e3;
T = 300.0;
regionDerivatives(p, T, 1.0e-6);
// Region 3
p = 26.0e6;
T = 650.0;
regionDerivatives(p, T, 1.0e-2);
// Region 4 (saturation curve)
T = 300.0;
Real dT = 1.0e-4;
Real dpSat_dT_fd = (_fp->vaporPressure(T + dT) - _fp->vaporPressure(T - dT)) / (2.0 * dT);
Real pSat = 0.0, dpSat_dT = 0.0;
_fp->vaporPressure_dT(T, pSat, dpSat_dT);
REL_TEST("dvaporPressure_dT", dpSat_dT, dpSat_dT_fd, 1.0e-6);
// Region 5
p = 30.0e6;
T = 1500.0;
regionDerivatives(p, T, 1.0e-6);
// Viscosity
Real rho = 998.0, drho_dp = 0.0, drho_dT = 0.0;
T = 298.15;
Real drho = 1.0e-4;
Real dmu_drho_fd =
(_fp->mu_from_rho_T(rho + drho, T) - _fp->mu_from_rho_T(rho - drho, T)) / (2.0 * drho);
Real mu = 0.0, dmu_drho = 0.0, dmu_dT = 0.0;
_fp->mu_drhoT_from_rho_T(rho, T, drho_dT, mu, dmu_drho, dmu_dT);
ABS_TEST("mu", mu, _fp->mu_from_rho_T(rho, T), 1.0e-15);
REL_TEST("dmu_dp", dmu_drho, dmu_drho_fd, 1.0e-6);
// To properly test derivative wrt temperature, use p and T and calculate density,
// so that the change in density wrt temperature is included
p = 1.0e6;
dT = 1.0e-4;
_fp->rho_dpT(p, T, rho, drho_dp, drho_dT);
_fp->mu_drhoT_from_rho_T(rho, T, drho_dT, mu, dmu_drho, dmu_dT);
Real dmu_dT_fd = (_fp->mu_from_rho_T(_fp->rho(p, T + dT), T + dT) -
_fp->mu_from_rho_T(_fp->rho(p, T - dT), T - dT)) /
(2.0 * dT);
REL_TEST("dmu_dT", dmu_dT, dmu_dT_fd, 1.0e-6);
}
/*
* Verify calculation of the Duan and Sun activity coefficient and its derivatives wrt
* pressure, temperature and salt mass fraction
*/
TEST_F(PorousFlowBrineCO2Test, activityCoefficientCO2Brine)
{
const Real p = 10.0e6;
Real T = 350.0;
Real Xnacl = 0.1;
const Real dp = 1.0e-1;
const Real dT = 1.0e-6;
const Real dx = 1.0e-8;
// Low temperature regime
Real gamma, dgamma_dp, dgamma_dT, dgamma_dX;
_fp->activityCoefficient(p, T, Xnacl, gamma, dgamma_dp, dgamma_dT, dgamma_dX);
ABS_TEST(gamma, 1.43276649338, 1.0e-8);
Real gamma_2, dgamma_2_dp, dgamma_2_dT, dgamma_2_dX;
_fp->activityCoefficient(p + dp, T, Xnacl, gamma_2, dgamma_2_dp, dgamma_2_dT, dgamma_2_dX);
Real dgamma_dp_fd = (gamma_2 - gamma) / dp;
REL_TEST(dgamma_dp, dgamma_dp_fd, 1.0e-6);
_fp->activityCoefficient(p, T + dT, Xnacl, gamma_2, dgamma_2_dp, dgamma_2_dT, dgamma_2_dX);
Real dgamma_dT_fd = (gamma_2 - gamma) / dT;
REL_TEST(dgamma_dT, dgamma_dT_fd, 1.0e-6);
_fp->activityCoefficient(p, T, Xnacl + dx, gamma_2, dgamma_2_dp, dgamma_2_dT, dgamma_2_dX);
Real dgamma_dX_fd = (gamma_2 - gamma) / dx;
REL_TEST(dgamma_dX, dgamma_dX_fd, 1.0e-6);
// High temperature regime
T = 523.15;
_fp->activityCoefficientHighTemp(T, Xnacl, gamma, dgamma_dT, dgamma_dX);
ABS_TEST(gamma, 1.50047006243, 1.0e-8);
_fp->activityCoefficientHighTemp(T + dT, Xnacl, gamma_2, dgamma_2_dT, dgamma_2_dX);
dgamma_dT_fd = (gamma_2 - gamma) / dT;
REL_TEST(dgamma_dT, dgamma_dT_fd, 1.0e-6);
_fp->activityCoefficientHighTemp(T, Xnacl + dx, gamma_2, dgamma_2_dT, dgamma_2_dX);
dgamma_dX_fd = (gamma_2 - gamma) / dx;
REL_TEST(dgamma_dX, dgamma_dX_fd, 1.0e-6);
// Check that both formulations return gamma = 1 for Xnacl = 0
Xnacl = 0.0;
T = 350.0;
_fp->activityCoefficient(p, T, Xnacl, gamma, dgamma_dp, dgamma_dT, dgamma_dX);
ABS_TEST(gamma, 1.0, 1.0e-12);
T = 523.15;
_fp->activityCoefficientHighTemp(T, Xnacl, gamma, dgamma_dT, dgamma_dX);
ABS_TEST(gamma, 1.0, 1.0e-12);
}
void
CO2FluidPropertiesTest::derivatives()
{
Real p = 1.0e6;
Real T = 350.0;
// Finite differencing parameters
Real dp = 1.0e1;
Real dT = 1.0e-4;
// density
Real drho_dp_fd = (_fp->rho(p + dp, T) - _fp->rho(p - dp, T)) / (2.0 * dp);
Real drho_dT_fd = (_fp->rho(p, T + dT) - _fp->rho(p, T - dT)) / (2.0 * dT);
Real rho = 0.0, drho_dp = 0.0, drho_dT = 0.0;
_fp->rho_dpT(p, T, rho, drho_dp, drho_dT);
ABS_TEST("rho", rho, _fp->rho(p, T), 1.0e-15);
REL_TEST("drho_dp", drho_dp, drho_dp_fd, 1.0e-6);
REL_TEST("drho_dT", drho_dT, drho_dT_fd, 1.0e-6);
// enthalpy
Real dh_dp_fd = (_fp->h(p + dp, T) - _fp->h(p - dp, T)) / (2.0 * dp);
Real dh_dT_fd = (_fp->h(p, T + dT) - _fp->h(p, T - dT)) / (2.0 * dT);
Real h = 0.0, dh_dp = 0.0, dh_dT = 0.0;
_fp->h_dpT(p, T, h, dh_dp, dh_dT);
ABS_TEST("h", h, _fp->h(p, T), 1.0e-15);
REL_TEST("dh_dp", dh_dp, dh_dp_fd, 1.0e-6);
REL_TEST("dh_dT", dh_dT, dh_dT_fd, 1.0e-6);
// internal energy
Real de_dp_fd = (_fp->e(p + dp, T) - _fp->e(p - dp, T)) / (2.0 * dp);
Real de_dT_fd = (_fp->e(p, T + dT) - _fp->e(p, T - dT)) / (2.0 * dT);
Real e = 0.0, de_dp = 0.0, de_dT = 0.0;
_fp->e_dpT(p, T, e, de_dp, de_dT);
ABS_TEST("e", e, _fp->e(p, T), 1.0e-15);
REL_TEST("de_dp", de_dp, de_dp_fd, 1.0e-6);
REL_TEST("de_dT", de_dT, de_dT_fd, 1.0e-6);
// Viscosity
rho = 15.105;
T = 360.0;
Real drho = 1.0e-4;
Real dmu_drho_fd = (_fp->mu(rho + drho, T) - _fp->mu(rho - drho, T)) / (2.0 * drho);
Real dmu_dT_fd = (_fp->mu(rho, T + dT) - _fp->mu(rho, T - dT)) / (2.0 * dT);
Real mu = 0.0, dmu_drho = 0.0, dmu_dT = 0.0;
_fp->mu_drhoT(rho, T, mu, dmu_drho, dmu_dT);
ABS_TEST("mu", mu, _fp->mu(rho, T), 1.0e-15);
REL_TEST("dmu_dp", dmu_drho, dmu_drho_fd, 1.0e-6);
REL_TEST("dmu_dT", dmu_dT, dmu_dT_fd, 1.0e-6);
}
/**
* Verify calculation of vapor pressure, vapor density and saturated liquid
* density using experimental data from
* Duschek et al., Measurement and correlation of the (pressure, density, temperature)
* relation of cabon dioxide II. Saturated-liquid and saturated-vapor densities and
* the vapor pressure along the entire coexstance curve, J. Chem. Thermo. 22 (1990).
* As we are comparing with experimental data, calculated values within 1% are
* considered satisfactory.
*/
TEST_F(CO2FluidPropertiesTest, vapor)
{
// Vapor pressure
REL_TEST("vapor", _fp->vaporPressure(217.0), 0.52747e6, 1.0e-2);
REL_TEST("vapor", _fp->vaporPressure(245.0), 1.51887e6, 1.0e-2);
REL_TEST("vapor", _fp->vaporPressure(303.8), 7.32029e6, 1.0e-2);
// Saturated vapor density
REL_TEST("saturated vapor density", _fp->saturatedVaporDensity(217.0), 14.0017, 1.0e-2);
REL_TEST("saturated vapor density", _fp->saturatedVaporDensity(245.0), 39.5048, 1.0e-2);
REL_TEST("saturated vapor density", _fp->saturatedVaporDensity(303.8), 382.30, 1.0e-2);
// Saturated liquid density
REL_TEST("saturated liquid density", _fp->saturatedLiquidDensity(217.0), 1177.03, 1.0e-2);
REL_TEST("saturated liquid density", _fp->saturatedLiquidDensity(245.0), 1067.89, 1.0e-2);
REL_TEST("saturated liquid density", _fp->saturatedLiquidDensity(303.8), 554.14, 1.0e-2);
}
/**
* Verify calculation of Sodium Properties from ANL/RE-95/2 report
* "Thermodynamic and Transport Properties of Sodium Liquid and Vapor"
* from ANL Reactor Engineering Division.
*/
TEST_F(SodiumPropertiesTest, testSodium)
{
double T = 500; // K
REL_TEST("thermal_conductivity", _fp->k(T), 80.09125, 1.0E-5);
REL_TEST("enthalpy", _fp->h(T), 381886.450000, 1.0E-5);
REL_TEST("heat_capacity", _fp->heatCapacity(T), 1345.578559, 1.0E-2);
REL_TEST("temperature", _fp->temperature(_fp->h(T)), T, 1.0E-5);
REL_TEST("density", _fp->rho(T), 896.9929544, 1E-05);
REL_TEST("drhodT", _fp->drho_dT(T), -0.224167872, 1E-05);
REL_TEST("drhodh", _fp->drho_dh(_fp->h(T)), -0.00016659590, 1E-2);
}
/**
* Verify calculation of Sodium Properties from ANL/RE-95/2 report
* "Thermodynamic and Transport Properties of Sodium Liquid and Vapor"
* from ANL Reactor Engineering Division.
*/
TEST_F(SodiumPropertiesTest, testSodium)
{
Real T = 500; // K
REL_TEST(_fp->k(T), 80.09125, 1.0E-5);
REL_TEST(_fp->h(T), 381886.450000, 1.0E-5);
REL_TEST(_fp->heatCapacity(T), 1345.578559, 1.0E-2);
REL_TEST(_fp->temperature(_fp->h(T)), T, 1.0E-5);
REL_TEST(_fp->rho(T), 896.9929544, 1E-05);
REL_TEST(_fp->drho_dT(T), -0.224167872, 1E-05);
REL_TEST(_fp->drho_dh(_fp->h(T)), -0.00016659590, 1E-2);
}
/*
* Verify calculation of the equilibrium constants and their derivatives wrt temperature
*/
TEST_F(PorousFlowBrineCO2Test, equilibriumConstants)
{
Real T = 350.0;
const Real dT = 1.0e-6;
Real K0H2O, dK0H2O_dT, K0CO2, dK0CO2_dT;
_fp->equilibriumConstantH2O(T, K0H2O, dK0H2O_dT);
_fp->equilibriumConstantCO2(T, K0CO2, dK0CO2_dT);
ABS_TEST(K0H2O, 0.412597711705, 1.0e-10);
ABS_TEST(K0CO2, 74.0435888596, 1.0e-10);
Real K0H2O_2, dK0H2O_2_dT, K0CO2_2, dK0CO2_2_dT;
_fp->equilibriumConstantH2O(T + dT, K0H2O_2, dK0H2O_2_dT);
_fp->equilibriumConstantCO2(T + dT, K0CO2_2, dK0CO2_2_dT);
Real dK0H2O_dT_fd = (K0H2O_2 - K0H2O) / dT;
Real dK0CO2_dT_fd = (K0CO2_2 - K0CO2) / dT;
REL_TEST(dK0H2O_dT, dK0H2O_dT_fd, 1.0e-6);
REL_TEST(dK0CO2_dT, dK0CO2_dT_fd, 1.0e-6);
// Test the high temperature formulation
T = 450.0;
_fp->equilibriumConstantH2O(T, K0H2O, dK0H2O_dT);
_fp->equilibriumConstantCO2(T, K0CO2, dK0CO2_dT);
ABS_TEST(K0H2O, 8.75944517916, 1.0e-10);
ABS_TEST(K0CO2, 105.013867434, 1.0e-10);
_fp->equilibriumConstantH2O(T + dT, K0H2O_2, dK0H2O_2_dT);
_fp->equilibriumConstantCO2(T + dT, K0CO2_2, dK0CO2_2_dT);
dK0H2O_dT_fd = (K0H2O_2 - K0H2O) / dT;
dK0CO2_dT_fd = (K0CO2_2 - K0CO2) / dT;
REL_TEST(dK0H2O_dT, dK0H2O_dT_fd, 1.0e-6);
REL_TEST(dK0CO2_dT, dK0CO2_dT_fd, 1.0e-5);
}
/*
* Verify calculation of the partial density of CO2 and its derivative wrt temperature
*/
TEST_F(PorousFlowBrineCO2Test, partialDensity)
{
const Real T = 473.15;
const Real dT = 1.0e-6;
Real partial_density, dpartial_density_dT;
_fp->partialDensityCO2(T, partial_density, dpartial_density_dT);
ABS_TEST(partial_density, 893.332, 1.0e-3);
Real partial_density_2, dpartial_density_2_dT;
_fp->partialDensityCO2(T + dT, partial_density_2, dpartial_density_2_dT);
Real dpartial_density_dT_fd = (partial_density_2 - partial_density) / dT;
REL_TEST(dpartial_density_dT, dpartial_density_dT_fd, 1.0e-6);
}
/**
* Verify calculation of thermophysical properties of methane using
* verification data provided in
* Irvine Jr, T. F. and Liley, P. E. (1984) Steam and Gas Tables with
* Computer Equations
*/
TEST_F(MethaneFluidPropertiesTest, properties)
{
// Pressure = 10 MPa, temperature = 350 K
Real p = 10.0e6;
Real T = 350.0;
const Real tol = REL_TOL_EXTERNAL_VALUE;
REL_TEST(_fp->rho_from_p_T(p, T), 55.13, tol);
REL_TEST(_fp->h(p, T), 708.5e3, tol);
REL_TEST(_fp->e(p, T), 527.131e3, tol);
REL_TEST(_fp->s(p, T), 11.30e3, tol);
REL_TEST(_fp->cp_from_p_T(p, T), 2.375e3, tol);
REL_TEST(_fp->cv_from_p_T(p, T), 1.857e3, tol);
REL_TEST(_fp->c(p, T), 481.7, tol);
REL_TEST(_fp->mu(p, T), 0.01276e-3, tol);
REL_TEST(_fp->k(p, T), 0.04113, tol);
// Test s, h and cp for temperatures > 755K as well as these methods have a
// different formulation in this regime
T = 800.0;
REL_TEST(_fp->h(p, T), 2132.0e3, tol);
REL_TEST(_fp->s(p, T), 13.83e3, tol);
REL_TEST(_fp->cp_from_p_T(p, T), 3.934e3, tol);
}
/**
* Verify calculation of the NACL properties the solid halite phase.
* Density data from Brown, "The NaCl pressure standard", J. Appl. Phys., 86 (1999).
*
* Values for cp and enthalpy are difficult to compare against. Instead, the
* values provided by the BrineFluidProperties UserObject were compared against
* simple correlations, eg. from NIST sodium chloride data.
*
* Values for thermal conductivity from Urqhart and Bauer,
* Experimental determination of single-crystal halite thermal conductivity,
* diffusivity and specific heat from -75 C to 300 C, Int. J. Rock Mech.
* and Mining Sci., 78 (2015)
*/
TEST_F(NaClFluidPropertiesTest, halite)
{
// Density and cp
Real p0, p1, p2, T0, T1, T2;
const Real tol = REL_TOL_EXTERNAL_VALUE;
p0 = 30.0e6;
p1 = 60.0e6;
p2 = 80.0e6;
T0 = 300.0;
T1 = 500.0;
T2 = 700.0;
REL_TEST(_fp->rho_from_p_T(p0, T0), 2167.88, tol);
REL_TEST(_fp->rho_from_p_T(p1, T1), 2116.0, tol);
REL_TEST(_fp->rho_from_p_T(p2, T2), 2056.8, tol);
REL_TEST(_fp->cp_from_p_T(p0, T0), 0.865e3, 40.0 * tol);
REL_TEST(_fp->cp_from_p_T(p1, T1), 0.922e3, 40.0 * tol);
REL_TEST(_fp->cp_from_p_T(p2, T2), 0.979e3, 40.0 * tol);
// Test enthalpy at the triple point pressure of water
Real pt = 611.657;
ABS_TEST(_fp->h_from_p_T(pt, 273.16), 0.0, tol);
REL_TEST(_fp->h_from_p_T(pt, 573.15), 271.13e3, tol);
REL_TEST(_fp->h_from_p_T(pt, 673.15), 366.55e3, tol);
// Thermal conductivity (function of T only)
REL_TEST(_fp->k_from_p_T(p0, 323.15), 5.488, 10.0 * tol);
REL_TEST(_fp->k_from_p_T(p0, 423.15), 3.911, 10.0 * tol);
REL_TEST(_fp->k_from_p_T(p0, 523.15), 3.024, 20.0 * tol);
}
TEST_F(IdealGasFluidPropertiesTest, testAll)
{
const Real T = 120. + 273.15; // K
const Real p = 101325; // Pa
const Real rho = _fp->rho_from_p_T(p, T);
const Real v = 1 / rho;
const Real e = _fp->e_from_p_rho(p, rho);
const Real s = _fp->s_from_v_e(v, e);
const Real h = _fp->h_from_p_T(p, T);
Real e_inv = _fp->e_from_T_v(T, v);
REL_TEST(e_inv, e, 10.0 * REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->e_from_T_v, T, v, 10.0 * REL_TOL_DERIVATIVE);
Real p_inv = _fp->p_from_T_v(T, v);
REL_TEST(p_inv, p, 10.0 * REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->p_from_T_v, T, v, 10.0 * REL_TOL_DERIVATIVE);
REL_TEST(_fp->h_from_T_v(T, v), h, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->h_from_T_v, T, v, 10.0 * REL_TOL_DERIVATIVE);
REL_TEST(_fp->s_from_T_v(T, v), s, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->s_from_T_v, T, v, 10.0 * REL_TOL_DERIVATIVE);
REL_TEST(_fp->cv_from_T_v(T, v), _fp->cv(), REL_TOL_CONSISTENCY);
REL_TEST(_fp->p_from_h_s(h, s), p, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->p_from_h_s, h, s, REL_TOL_DERIVATIVE);
REL_TEST(_fp->rho_from_p_s(p, s), rho, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->rho_from_p_s, p, s, REL_TOL_DERIVATIVE);
REL_TEST(_fp->p_from_v_e(v, e), p, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->p_from_v_e, v, e, REL_TOL_DERIVATIVE);
REL_TEST(_fp->T_from_v_e(v, e), T, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->T_from_v_e, v, e, REL_TOL_DERIVATIVE);
REL_TEST(_fp->c_from_v_e(v, e), 398.896207251962, REL_TOL_SAVED_VALUE);
REL_TEST(_fp->cp_from_v_e(v, e), 987.13756097561, REL_TOL_SAVED_VALUE);
REL_TEST(_fp->cv_from_v_e(v, e), 700.09756097561, REL_TOL_SAVED_VALUE);
REL_TEST(_fp->mu_from_v_e(v, e), 0.0, 1e-15);
REL_TEST(_fp->k_from_v_e(v, e), 0.0, 1e-15);
REL_TEST(_fp->beta_from_p_T(p, T), 2.54355843825512e-3, REL_TOL_SAVED_VALUE);
REL_TEST(_fp->s_from_v_e(v, e), 2.58890011905277e3, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->s_from_v_e, v, e, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->rho_from_p_T(p, T), 0.897875065343506, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->rho_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->v_from_p_T(p, T), 1.0 / 0.897875065343506, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->v_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->e_from_p_rho(p, rho), 2.75243356097561e5, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->e_from_p_rho, p, rho, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->h_from_p_T(p, T), 3.88093132097561e5, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->h_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->s_from_p_T(p, T), 2.588900119052767e3, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->s_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->s_from_h_p(h, p), 2.588900119052767e3, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->s_from_h_p, h, p, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->e_from_p_T(p, T), 2.75243356097561e5, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->e_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->molarMass(), 34.522988492890422, REL_TOL_SAVED_VALUE);
ABS_TEST(_fp->T_from_p_h(p, h), T, REL_TOL_CONSISTENCY);
}
TEST_F(IdealGasFluidPropertiesTest, testAll)
{
// Test when R and gamma are provided
Real T = 120. + 273.15; // K
Real p = 101325; // Pa
const Real rho = _fp->rho_from_p_T(p, T);
const Real v = 1.0 / rho;
const Real e = _fp->e_from_p_rho(p, rho);
const Real s = _fp->s_from_v_e(v, e);
const Real h = _fp->h_from_p_T(p, T);
Real e_inv = _fp->e_from_T_v(T, v);
REL_TEST(e_inv, e, 10.0 * REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->e_from_T_v, T, v, 10.0 * REL_TOL_DERIVATIVE);
Real p_inv = _fp->p_from_T_v(T, v);
REL_TEST(p_inv, p, 10.0 * REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->p_from_T_v, T, v, 10.0 * REL_TOL_DERIVATIVE);
REL_TEST(_fp->h_from_T_v(T, v), h, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->h_from_T_v, T, v, 10.0 * REL_TOL_DERIVATIVE);
REL_TEST(_fp->s_from_T_v(T, v), s, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->s_from_T_v, T, v, 10.0 * REL_TOL_DERIVATIVE);
REL_TEST(_fp->cv_from_T_v(T, v), _fp->cv_from_v_e(v, e), REL_TOL_CONSISTENCY);
REL_TEST(_fp->p_from_h_s(h, s), p, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->p_from_h_s, h, s, REL_TOL_DERIVATIVE);
REL_TEST(_fp->rho_from_p_s(p, s), rho, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->rho_from_p_s, p, s, REL_TOL_DERIVATIVE);
REL_TEST(_fp->p_from_v_e(v, e), p, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->p_from_v_e, v, e, REL_TOL_DERIVATIVE);
REL_TEST(_fp->T_from_v_e(v, e), T, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->T_from_v_e, v, e, REL_TOL_DERIVATIVE);
REL_TEST(_fp->c_from_v_e(v, e), 398.896207251962, REL_TOL_SAVED_VALUE);
REL_TEST(_fp->cp_from_v_e(v, e), 987.13756097561, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->cp_from_v_e, v, e, REL_TOL_DERIVATIVE);
REL_TEST(_fp->cv_from_v_e(v, e), 700.09756097561, REL_TOL_SAVED_VALUE);
REL_TEST(_fp->mu_from_v_e(v, e), 18.23e-6, 1e-15);
REL_TEST(_fp->k_from_v_e(v, e), 25.68e-3, 1e-15);
REL_TEST(_fp->beta_from_p_T(p, T), 2.54355843825512e-3, REL_TOL_SAVED_VALUE);
REL_TEST(_fp->s_from_v_e(v, e), 2.58890011905277e3, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->s_from_v_e, v, e, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->rho_from_p_T(p, T), 0.897875065343506, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->rho_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->v_from_p_T(p, T), 1.0 / 0.897875065343506, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->v_from_p_T, p, T, REL_TOL_DERIVATIVE);
REL_TEST(_fp->e_from_p_rho(p, rho), 2.75243356098e5, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->e_from_p_rho, p, rho, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->h_from_p_T(p, T), 3.88093132097561e5, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->h_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->s_from_p_T(p, T), 2.588900119052767e3, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->s_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->s_from_h_p(h, p), 2.588900119052767e3, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->s_from_h_p, h, p, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->e_from_p_T(p, T), 2.75243356097561e5, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->e_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->molarMass(), 0.0289662061037, REL_TOL_SAVED_VALUE);
ABS_TEST(_fp->T_from_p_h(p, h), T, REL_TOL_CONSISTENCY);
REL_TEST(_fp->mu_from_p_T(p, T), 18.23e-6, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->mu_from_p_T, p, T, REL_TOL_DERIVATIVE);
REL_TEST(_fp->k_from_p_T(p, T), 25.68e-3, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->k_from_p_T, p, T, REL_TOL_DERIVATIVE);
REL_TEST(_fp->cv_from_p_T(p, T), 700.09756097561, REL_TOL_SAVED_VALUE);
REL_TEST(_fp->cp_from_p_T(p, T), 987.13756097561, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->cp_from_p_T, p, T, REL_TOL_DERIVATIVE);
// Test when R and gamma are not provided
const Real molar_mass = 0.029;
const Real cv = 718.0;
const Real cp = 1005.0;
const Real thermal_conductivity = 0.02568;
const Real entropy = 1767.24985689;
const Real viscosity = 18.23e-6;
Real henry = 0.0;
const Real R = 8.3144598;
const Real tol = REL_TOL_CONSISTENCY;
p = 1.0e6;
T = 300.0;
REL_TEST(_fp_pT->beta_from_p_T(p, T), 1.0 / T, tol);
REL_TEST(_fp_pT->cp_from_p_T(p, T), cp, tol);
REL_TEST(_fp_pT->cv_from_p_T(p, T), cv, tol);
REL_TEST(_fp_pT->c_from_p_T(p, T), std::sqrt(cp * R * T / (cv * molar_mass)), tol);
REL_TEST(_fp_pT->k_from_p_T(p, T), thermal_conductivity, tol);
REL_TEST(_fp_pT->k_from_p_T(p, T), thermal_conductivity, tol);
REL_TEST(_fp_pT->s_from_p_T(p, T), entropy, tol);
REL_TEST(_fp_pT->rho_from_p_T(p, T), p * molar_mass / (R * T), tol);
REL_TEST(_fp_pT->e_from_p_T(p, T), cv * T, tol);
REL_TEST(_fp_pT->mu_from_p_T(p, T), viscosity, tol);
REL_TEST(_fp_pT->mu_from_p_T(p, T), viscosity, tol);
REL_TEST(_fp_pT->h_from_p_T(p, T), cp * T, tol);
ABS_TEST(_fp_pT->henryConstant(T), henry, tol);
DERIV_TEST(_fp_pT->rho_from_p_T, p, T, REL_TOL_DERIVATIVE);
DERIV_TEST(_fp_pT->mu_from_p_T, p, T, REL_TOL_DERIVATIVE);
DERIV_TEST(_fp_pT->e_from_p_T, p, T, REL_TOL_DERIVATIVE);
DERIV_TEST(_fp_pT->h_from_p_T, p, T, REL_TOL_DERIVATIVE);
DERIV_TEST(_fp_pT->k_from_p_T, p, T, REL_TOL_DERIVATIVE);
Real dhenry_dT;
_fp_pT->henryConstant(T, henry, dhenry_dT);
ABS_TEST(dhenry_dT, 0.0, tol);
}
TEST_F(IdealRealGasMixtureFluidPropertiesTest, test)
{
Real T = 400.;
Real p = 100000.;
std::vector<Real> x = {0.9};
// pure fluids
Real rho_nitrogen = _fp_nitrogen->rho_from_p_T(p, T);
Real rho_steam = _fp_steam->rho_from_p_T(p, T);
REL_TEST(rho_nitrogen, 0.84228968026683726, REL_TOL_CONSISTENCY);
REL_TEST(rho_steam, 0.61493738819320221, REL_TOL_CONSISTENCY);
// mixture properties
Real rho_mix = _fp_mix->rho_from_p_T(p, T, x);
Real v_mix = _fp_mix->v_from_p_T(p, T, x);
Real e_mix = _fp_mix->e_from_p_T(p, T, x);
Real c_mix = _fp_mix->c_from_p_T(p, T, x);
Real cp_mix = _fp_mix->cp_from_p_T(p, T, x);
Real cv_mix = _fp_mix->cv_from_p_T(p, T, x);
Real mu_mix = _fp_mix->mu_from_p_T(p, T, x);
Real k_mix = _fp_mix->k_from_p_T(p, T, x);
REL_TEST(rho_mix, 0.88183704292782583, REL_TOL_CONSISTENCY);
REL_TEST(v_mix, 1.1339963636363655, REL_TOL_CONSISTENCY);
REL_TEST(e_mix, 523068.96363636368, REL_TOL_CONSISTENCY);
REL_TEST(c_mix, 418.49693534182865, REL_TOL_CONSISTENCY);
REL_TEST(cp_mix, 1083.6715000000002, REL_TOL_CONSISTENCY);
REL_TEST(cv_mix, 771.82250000000022, REL_TOL_CONSISTENCY);
REL_TEST(mu_mix, 0.000013317970680742846, REL_TOL_CONSISTENCY);
REL_TEST(k_mix, 0.026852020459600251, REL_TOL_CONSISTENCY);
// check inverse functions of (v,e)
Real p_mix = _fp_mix->p_from_v_e(v_mix, e_mix, x);
Real T_mix = _fp_mix->T_from_v_e(v_mix, e_mix, x);
REL_TEST(p_mix, p, REL_TOL_CONSISTENCY);
REL_TEST(T_mix, T, REL_TOL_CONSISTENCY);
//////////////////////////////////////////////////////////////////////////////
// note that the VAPOR_MIX_DERIV_TEST works for binary mixtures only (for now)
//////////////////////////////////////////////////////////////////////////////
// check analytical derivatives from (p,T)
VAPOR_MIX_DERIV_TEST(_fp_mix->rho_from_p_T, p, T, x, REL_TOL_DERIVATIVE);
VAPOR_MIX_DERIV_TEST(_fp_mix->v_from_p_T, p, T, x, REL_TOL_DERIVATIVE);
// the following test fails since the pertubation in VAPOR_MIX_DERIV_TEST
// is too small if v(p,T) is iterated within e_from_p_T
// VAPOR_MIX_DERIV_TEST(_fp_mix->e_from_p_T, p, T, x, REL_TOL_DERIVATIVE);
Real e, de_dp, de_dT;
std::vector<Real> de_dx;
de_dx.resize(_fp_mix->getNumberOfSecondaryVapors());
_fp_mix->e_from_p_T(p, T, x, e, de_dp, de_dT, de_dx);
Real dp = p * 1.e-5;
Real p1 = _fp_mix->e_from_p_T(p - dp, T, x);
Real p2 = _fp_mix->e_from_p_T(p + dp, T, x);
Real de_dp_num = (p2 - p1) / (2.0 * dp);
REL_TEST(de_dp, de_dp_num, REL_TOL_DERIVATIVE);
// check analytical derivatives from (v,e)
VAPOR_MIX_DERIV_TEST(_fp_mix->p_from_v_e, v_mix, e_mix, x, REL_TOL_DERIVATIVE);
VAPOR_MIX_DERIV_TEST(_fp_mix->T_from_v_e, v_mix, e_mix, x, REL_TOL_DERIVATIVE);
// check analytical derivatives from (T,v)
VAPOR_MIX_DERIV_TEST(_fp_mix->p_from_T_v, T, v_mix, x, REL_TOL_DERIVATIVE);
VAPOR_MIX_DERIV_TEST(_fp_mix->e_from_T_v, T, v_mix, x, REL_TOL_DERIVATIVE);
// state-of-the-art mixture model comparison
T = 360.;
p = 100000.;
x[0] = 0.5;
rho_mix = _fp_mix->rho_from_p_T(p, T, x); // 0.7362935
v_mix = _fp_mix->v_from_p_T(p, T, x); // 1.3581540
e_mix = _fp_mix->e_from_p_T(p, T, x); // 1380586.9
c_mix = _fp_mix->c_from_p_T(p, T, x); // 428.1928
cp_mix = _fp_mix->cp_from_p_T(p, T, x); // 1479.7114
cv_mix = _fp_mix->cv_from_p_T(p, T, x); // 1090.5912
// these quantities cannot be calculated with the state-of-the-art mixture model
// mu_mix = _fp_mix->mu_from_p_T(p, T, x);
// k_mix = _fp_mix->k_from_p_T(p, T, x);
REL_TEST(rho_mix, 0.7362935, 0.115554);
REL_TEST(v_mix, 1.3581540, 0.103585);
REL_TEST(e_mix, 1380586.9, 0.023648);
REL_TEST(c_mix, 428.1928, 0.017535);
REL_TEST(cp_mix, 1479.7114, 0.146444);
REL_TEST(cv_mix, 1090.5912, 0.183001);
}
/*
* Verify calculation of liquid density, viscosity, enthalpy, and derivatives
*/
TEST_F(PorousFlowBrineCO2Test, liquidProperties)
{
const Real p = 1.0e6;
const Real T = 350.0;
const Real Xnacl = 0.1;
FluidStatePhaseEnum phase_state;
const unsigned int np = _fp->numPhases();
const unsigned int nc = _fp->numComponents();
std::vector<FluidStateProperties> fsp(np, FluidStateProperties(nc));
// Liquid region
Real Z = 0.0001;
_fp->massFractions(p, T, Xnacl, Z, phase_state, fsp);
EXPECT_EQ(phase_state, FluidStatePhaseEnum::LIQUID);
// Verify fluid density and viscosity
_fp->liquidProperties(p, T, Xnacl, fsp);
Real liquid_density = fsp[0].density;
Real liquid_viscosity = fsp[0].viscosity;
Real liquid_enthalpy = fsp[0].enthalpy;
Real co2_partial_density, dco2_partial_density_dT;
_fp->partialDensityCO2(T, co2_partial_density, dco2_partial_density_dT);
Real brine_density = _brine_fp->rho(p, T, Xnacl);
Real density = 1.0 / (Z / co2_partial_density + (1.0 - Z) / brine_density);
Real viscosity = _brine_fp->mu(p, T, Xnacl);
Real brine_enthalpy = _brine_fp->h(p, T, Xnacl);
Real hdis, dhdis_dT;
_fp->enthalpyOfDissolution(T, hdis, dhdis_dT);
Real co2_enthalpy = _co2_fp->h(p, T);
Real enthalpy = (1.0 - Z) * brine_enthalpy + Z * (co2_enthalpy + hdis);
ABS_TEST(liquid_density, density, 1.0e-12);
ABS_TEST(liquid_viscosity, viscosity, 1.0e-12);
ABS_TEST(liquid_enthalpy, enthalpy, 1.0e-12);
// Verify fluid density and viscosity derivatives
Real ddensity_dp = fsp[0].ddensity_dp;
Real ddensity_dT = fsp[0].ddensity_dT;
Real ddensity_dZ = fsp[0].ddensity_dZ;
Real ddensity_dX = fsp[0].ddensity_dX;
Real dviscosity_dp = fsp[0].dviscosity_dp;
Real dviscosity_dT = fsp[0].dviscosity_dT;
Real dviscosity_dZ = fsp[0].dviscosity_dZ;
Real dviscosity_dX = fsp[0].dviscosity_dX;
Real denthalpy_dp = fsp[0].denthalpy_dp;
Real denthalpy_dT = fsp[0].denthalpy_dT;
Real denthalpy_dZ = fsp[0].denthalpy_dZ;
Real denthalpy_dX = fsp[0].denthalpy_dX;
// Derivatives wrt pressure
const Real dp = 1.0;
_fp->liquidProperties(p + dp, T, Xnacl, fsp);
Real rho1 = fsp[0].density;
Real mu1 = fsp[0].viscosity;
Real h1 = fsp[0].enthalpy;
_fp->liquidProperties(p - dp, T, Xnacl, fsp);
Real rho2 = fsp[0].density;
Real mu2 = fsp[0].viscosity;
Real h2 = fsp[0].enthalpy;
REL_TEST(ddensity_dp, (rho1 - rho2) / (2.0 * dp), 1.0e-4);
REL_TEST(dviscosity_dp, (mu1 - mu2) / (2.0 * dp), 1.0e-5);
REL_TEST(denthalpy_dp, (h1 - h2) / (2.0 * dp), 1.0e-4);
// Derivatives wrt temperature
const Real dT = 1.0e-4;
_fp->liquidProperties(p, T + dT, Xnacl, fsp);
rho1 = fsp[0].density;
mu1 = fsp[0].viscosity;
h1 = fsp[0].enthalpy;
_fp->liquidProperties(p, T - dT, Xnacl, fsp);
rho2 = fsp[0].density;
mu2 = fsp[0].viscosity;
h2 = fsp[0].enthalpy;
REL_TEST(ddensity_dT, (rho1 - rho2) / (2.0 * dT), 1.0e-6);
REL_TEST(dviscosity_dT, (mu1 - mu2) / (2.0 * dT), 1.0e-6);
REL_TEST(denthalpy_dT, (h1 - h2) / (2.0 * dT), 1.0e-6);
// Derivatives wrt Xnacl
const Real dx = 1.0e-8;
_fp->liquidProperties(p, T, Xnacl + dx, fsp);
rho1 = fsp[0].density;
mu1 = fsp[0].viscosity;
h1 = fsp[0].enthalpy;
_fp->liquidProperties(p, T, Xnacl - dx, fsp);
rho2 = fsp[0].density;
mu2 = fsp[0].viscosity;
h2 = fsp[0].enthalpy;
REL_TEST(ddensity_dX, (rho1 - rho2) / (2.0 * dx), 1.0e-6);
REL_TEST(dviscosity_dX, (mu1 - mu2) / (2.0 * dx), 1.0e-6);
REL_TEST(denthalpy_dX, (h1 - h2) / (2.0 * dx), 1.0e-6);
// Derivatives wrt Z
const Real dZ = 1.0e-8;
_fp->massFractions(p, T, Xnacl, Z + dZ, phase_state, fsp);
_fp->liquidProperties(p, T, Xnacl, fsp);
rho1 = fsp[0].density;
mu1 = fsp[0].viscosity;
h1 = fsp[0].enthalpy;
_fp->massFractions(p, T, Xnacl, Z - dZ, phase_state, fsp);
_fp->liquidProperties(p, T, Xnacl, fsp);
rho2 = fsp[0].density;
mu2 = fsp[0].viscosity;
h2 = fsp[0].enthalpy;
REL_TEST(ddensity_dZ, (rho1 - rho2) / (2.0 * dZ), 1.0e-6);
ABS_TEST(dviscosity_dZ, (mu1 - mu2) / (2.0 * dZ), 1.0e-6);
REL_TEST(denthalpy_dZ, (h1 - h2) / (2.0 * dZ), 1.0e-6);
// Two-phase region
Z = 0.045;
_fp->massFractions(p, T, Xnacl, Z, phase_state, fsp);
EXPECT_EQ(phase_state, FluidStatePhaseEnum::TWOPHASE);
// Verify fluid density and viscosity derivatives
_fp->liquidProperties(p, T, Xnacl, fsp);
ddensity_dp = fsp[0].ddensity_dp;
ddensity_dT = fsp[0].ddensity_dT;
ddensity_dX = fsp[0].ddensity_dX;
ddensity_dZ = fsp[0].ddensity_dZ;
dviscosity_dp = fsp[0].dviscosity_dp;
dviscosity_dT = fsp[0].dviscosity_dT;
dviscosity_dX = fsp[0].dviscosity_dX;
dviscosity_dZ = fsp[0].dviscosity_dZ;
denthalpy_dp = fsp[0].denthalpy_dp;
denthalpy_dT = fsp[0].denthalpy_dT;
denthalpy_dZ = fsp[0].denthalpy_dZ;
denthalpy_dX = fsp[0].denthalpy_dX;
// Derivatives wrt pressure
_fp->massFractions(p + dp, T, Xnacl, Z, phase_state, fsp);
_fp->liquidProperties(p + dp, T, Xnacl, fsp);
rho1 = fsp[0].density;
mu1 = fsp[0].viscosity;
h1 = fsp[0].enthalpy;
_fp->massFractions(p - dp, T, Xnacl, Z, phase_state, fsp);
_fp->liquidProperties(p - dp, T, Xnacl, fsp);
rho2 = fsp[0].density;
mu2 = fsp[0].viscosity;
h2 = fsp[0].enthalpy;
REL_TEST(ddensity_dp, (rho1 - rho2) / (2.0 * dp), 1.0e-4);
REL_TEST(dviscosity_dp, (mu1 - mu2) / (2.0 * dp), 1.0e-5);
REL_TEST(denthalpy_dp, (h1 - h2) / (2.0 * dp), 1.0e-4);
// Derivatives wrt temperature
_fp->massFractions(p, T + dT, Xnacl, Z, phase_state, fsp);
_fp->liquidProperties(p, T + dT, Xnacl, fsp);
rho1 = fsp[0].density;
mu1 = fsp[0].viscosity;
h1 = fsp[0].enthalpy;
_fp->massFractions(p, T - dT, Xnacl, Z, phase_state, fsp);
_fp->liquidProperties(p, T - dT, Xnacl, fsp);
rho2 = fsp[0].density;
mu2 = fsp[0].viscosity;
h2 = fsp[0].enthalpy;
REL_TEST(ddensity_dT, (rho1 - rho2) / (2.0 * dT), 1.0e-6);
REL_TEST(dviscosity_dT, (mu1 - mu2) / (2.0 * dT), 1.0e-6);
REL_TEST(denthalpy_dT, (h1 - h2) / (2.0 * dT), 1.0e-6);
// Derivatives wrt Xnacl
_fp->massFractions(p, T, Xnacl + dx, Z, phase_state, fsp);
_fp->liquidProperties(p, T, Xnacl + dx, fsp);
rho1 = fsp[0].density;
mu1 = fsp[0].viscosity;
h1 = fsp[0].enthalpy;
_fp->massFractions(p, T, Xnacl - dx, Z, phase_state, fsp);
_fp->liquidProperties(p, T, Xnacl - dx, fsp);
rho2 = fsp[0].density;
mu2 = fsp[0].viscosity;
h2 = fsp[0].enthalpy;
REL_TEST(ddensity_dX, (rho1 - rho2) / (2.0 * dx), 1.0e-6);
REL_TEST(dviscosity_dX, (mu1 - mu2) / (2.0 * dx), 1.0e-6);
REL_TEST(denthalpy_dX, (h1 - h2) / (2.0 * dx), 1.0e-6);
// Derivatives wrt Z
_fp->massFractions(p, T, Xnacl, Z + dZ, phase_state, fsp);
_fp->liquidProperties(p, T, Xnacl, fsp);
rho1 = fsp[0].density;
mu1 = fsp[0].viscosity;
h1 = fsp[0].enthalpy;
_fp->massFractions(p, T, Xnacl, Z - dZ, phase_state, fsp);
_fp->liquidProperties(p, T, Xnacl, fsp);
rho2 = fsp[0].density;
mu2 = fsp[0].viscosity;
h2 = fsp[0].enthalpy;
ABS_TEST(ddensity_dZ, (rho1 - rho2) / (2.0 * dZ), 1.0e-6);
ABS_TEST(dviscosity_dZ, (mu1 - mu2) / (2.0 * dZ), 1.0e-6);
ABS_TEST(denthalpy_dZ, (h1 - h2) / (2.0 * dZ), 1.0e-6);
}
/*
* Verify calculation of gas saturation and derivatives in the two-phase region
*/
TEST_F(PorousFlowWaterNCGTest, twoPhase)
{
const Real p = 1.0e6;
const Real T = 350.0;
FluidStatePhaseEnum phase_state;
std::vector<FluidStateProperties> fsp(2, FluidStateProperties(2));
// In the two-phase region, the mass fractions are the equilibrium values, so
// a temporary value of Z can be used (as long as it corresponds to the two-phase
// region)
Real Z = 0.45;
_fp->massFractions(p, T, Z, phase_state, fsp);
EXPECT_EQ(phase_state, FluidStatePhaseEnum::TWOPHASE);
// Calculate Z that gives a saturation of 0.25
Real gas_saturation = 0.25;
Real liquid_pressure = p + _pc->capillaryPressure(1.0 - gas_saturation);
// Calculate gas density and liquid density
_fp->gasProperties(p, T, fsp);
_fp->liquidProperties(liquid_pressure, T, fsp);
// The mass fraction that corresponds to a gas_saturation = 0.25
Z = (gas_saturation * fsp[1].density * fsp[1].mass_fraction[1] +
(1.0 - gas_saturation) * fsp[0].density * fsp[0].mass_fraction[1]) /
(gas_saturation * fsp[1].density + (1.0 - gas_saturation) * fsp[0].density);
// Calculate the gas saturation and derivatives
_fp->saturationTwoPhase(p, T, Z, fsp);
ABS_TEST(fsp[1].saturation, gas_saturation, 1.0e-8);
// Test the derivatives
const Real dp = 1.0e-1;
gas_saturation = fsp[1].saturation;
Real dgas_saturation_dp = fsp[1].dsaturation_dp;
Real dgas_saturation_dT = fsp[1].dsaturation_dT;
Real dgas_saturation_dZ = fsp[1].dsaturation_dZ;
_fp->massFractions(p + dp, T, Z, phase_state, fsp);
_fp->gasProperties(p + dp, T, fsp);
_fp->saturationTwoPhase(p + dp, T, Z, fsp);
Real gsat1 = fsp[1].saturation;
_fp->massFractions(p - dp, T, Z, phase_state, fsp);
_fp->gasProperties(p - dp, T, fsp);
_fp->saturationTwoPhase(p - dp, T, Z, fsp);
Real gsat2 = fsp[1].saturation;
REL_TEST(dgas_saturation_dp, (gsat1 - gsat2) / (2.0 * dp), 1.0e-6);
// Derivative wrt T
const Real dT = 1.0e-4;
_fp->massFractions(p, T + dT, Z, phase_state, fsp);
_fp->gasProperties(p, T + dT, fsp);
_fp->saturationTwoPhase(p, T + dT, Z, fsp);
gsat1 = fsp[1].saturation;
_fp->massFractions(p, T - dT, Z, phase_state, fsp);
_fp->gasProperties(p, T - dT, fsp);
_fp->saturationTwoPhase(p, T - dT, Z, fsp);
gsat2 = fsp[1].saturation;
REL_TEST(dgas_saturation_dT, (gsat1 - gsat2) / (2.0 * dT), 1.0e-6);
// Derivative wrt Z
const Real dZ = 1.0e-8;
_fp->massFractions(p, T, Z, phase_state, fsp);
_fp->gasProperties(p, T, fsp);
_fp->saturationTwoPhase(p, T, Z + dZ, fsp);
gsat1 = fsp[1].saturation;
_fp->saturationTwoPhase(p, T, Z - dZ, fsp);
gsat2 = fsp[1].saturation;
REL_TEST(dgas_saturation_dZ, (gsat1 - gsat2) / (2.0 * dZ), 1.0e-6);
}
/*
* Verify calculation of liquid density, viscosity, enthalpy and derivatives. Note that as
* density and viscosity don't depend on mass fraction, only the liquid region needs to be
* tested (the calculations are identical in the two phase region). The enthalpy does depend
* on mass fraction, so should be tested in the two phase region as well as the liquid region
*/
TEST_F(PorousFlowWaterNCGTest, liquidProperties)
{
const Real p = 1.0e6;
const Real T = 350.0;
std::vector<FluidStateProperties> fsp(2, FluidStateProperties(2));
// Verify fluid density and viscosity
_fp->liquidProperties(p, T, fsp);
Real liquid_density = fsp[0].density;
Real liquid_viscosity = fsp[0].viscosity;
Real density = _water_fp->rho_from_p_T(p, T);
Real viscosity = _water_fp->mu(p, T);
ABS_TEST(liquid_density, density, 1.0e-12);
ABS_TEST(liquid_viscosity, viscosity, 1.0e-12);
// Verify derivatives
Real ddensity_dp = fsp[0].ddensity_dp;
Real ddensity_dT = fsp[0].ddensity_dT;
Real ddensity_dZ = fsp[0].ddensity_dZ;
Real dviscosity_dp = fsp[0].dviscosity_dp;
Real dviscosity_dT = fsp[0].dviscosity_dT;
Real dviscosity_dZ = fsp[0].dviscosity_dZ;
Real denthalpy_dp = fsp[0].denthalpy_dp;
Real denthalpy_dT = fsp[0].denthalpy_dT;
Real denthalpy_dZ = fsp[0].denthalpy_dZ;
const Real dp = 1.0;
_fp->liquidProperties(p + dp, T, fsp);
Real rho1 = fsp[0].density;
Real mu1 = fsp[0].viscosity;
Real h1 = fsp[0].enthalpy;
_fp->liquidProperties(p - dp, T, fsp);
Real rho2 = fsp[0].density;
Real mu2 = fsp[0].viscosity;
Real h2 = fsp[0].enthalpy;
REL_TEST(ddensity_dp, (rho1 - rho2) / (2.0 * dp), 1.0e-6);
REL_TEST(dviscosity_dp, (mu1 - mu2) / (2.0 * dp), 1.0e-5);
REL_TEST(denthalpy_dp, (h1 - h2) / (2.0 * dp), 1.0e-5);
const Real dT = 1.0e-4;
_fp->liquidProperties(p, T + dT, fsp);
rho1 = fsp[0].density;
mu1 = fsp[0].viscosity;
h1 = fsp[0].enthalpy;
_fp->liquidProperties(p, T - dT, fsp);
rho2 = fsp[0].density;
mu2 = fsp[0].viscosity;
h2 = fsp[0].enthalpy;
REL_TEST(ddensity_dT, (rho1 - rho2) / (2.0 * dT), 1.0e-6);
REL_TEST(dviscosity_dT, (mu1 - mu2) / (2.0 * dT), 1.0e-6);
REL_TEST(denthalpy_dT, (h1 - h2) / (2.0 * dT), 1.0e-5);
Real Z = 0.0001;
const Real dZ = 1.0e-8;
FluidStatePhaseEnum phase_state;
_fp->massFractions(p, T, Z, phase_state, fsp);
_fp->liquidProperties(p, T, fsp);
denthalpy_dp = fsp[0].denthalpy_dp;
denthalpy_dT = fsp[0].denthalpy_dT;
denthalpy_dZ = fsp[0].denthalpy_dZ;
_fp->massFractions(p, T, Z + dZ, phase_state, fsp);
_fp->liquidProperties(p, T, fsp);
h1 = fsp[0].enthalpy;
_fp->massFractions(p, T, Z - dZ, phase_state, fsp);
_fp->liquidProperties(p, T, fsp);
h2 = fsp[0].enthalpy;
REL_TEST(denthalpy_dZ, (h1 - h2) / (2.0 * dZ), 1.0e-6);
// Density and viscosity don't depend on Z, so derivatives should be 0
ABS_TEST(ddensity_dZ, 0.0, 1.0e-12);
ABS_TEST(dviscosity_dZ, 0.0, 1.0e-12);
// Check enthalpy calculations in the two phase region as well. Note that the mass fractions
// vary with pressure and temperature in this region
Z = 0.45;
_fp->massFractions(p, T, Z, phase_state, fsp);
_fp->liquidProperties(p, T, fsp);
denthalpy_dp = fsp[0].denthalpy_dp;
denthalpy_dT = fsp[0].denthalpy_dT;
denthalpy_dZ = fsp[0].denthalpy_dZ;
_fp->massFractions(p + dp, T, Z, phase_state, fsp);
_fp->liquidProperties(p + dp, T, fsp);
h1 = fsp[0].enthalpy;
_fp->massFractions(p - dp, T, Z, phase_state, fsp);
_fp->liquidProperties(p - dp, T, fsp);
h2 = fsp[0].enthalpy;
REL_TEST(denthalpy_dp, (h1 - h2) / (2.0 * dp), 1.0e-5);
_fp->massFractions(p, T + dT, Z, phase_state, fsp);
_fp->liquidProperties(p, T + dT, fsp);
h1 = fsp[0].enthalpy;
_fp->massFractions(p, T - dT, Z, phase_state, fsp);
_fp->liquidProperties(p, T - dT, fsp);
h2 = fsp[0].enthalpy;
REL_TEST(denthalpy_dT, (h1 - h2) / (2.0 * dT), 1.0e-5);
_fp->massFractions(p, T, Z + dZ, phase_state, fsp);
_fp->liquidProperties(p, T, fsp);
h1 = fsp[0].enthalpy;
_fp->massFractions(p, T, Z - dZ, phase_state, fsp);
_fp->liquidProperties(p, T, fsp);
h2 = fsp[0].enthalpy;
ABS_TEST(denthalpy_dZ, (h1 - h2) / (2.0 * dZ), 1.0e-5);
}
TEST_F(StiffenedGasFluidPropertiesTest, testAll)
{
const Real T = 20. + 273.15; // K
const Real p = 101325; // Pa
const Real rho = _fp->rho_from_p_T(p, T);
const Real v = 1 / rho;
const Real e = _fp->e_from_p_rho(p, rho);
const Real s = _fp->s_from_v_e(v, e);
const Real h = _fp->h_from_p_T(p, T);
Real e_inv = _fp->e_from_T_v(T, v);
REL_TEST(e_inv, e, 10.0 * REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->e_from_T_v, T, v, 10.0 * REL_TOL_DERIVATIVE);
Real p_inv = _fp->p_from_T_v(T, v);
REL_TEST(p_inv, p, 10.0 * REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->p_from_T_v, T, v, 10.0 * REL_TOL_DERIVATIVE);
REL_TEST(_fp->h_from_T_v(T, v), h, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->h_from_T_v, T, v, 10.0 * REL_TOL_DERIVATIVE);
REL_TEST(_fp->s_from_T_v(T, v), s, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->s_from_T_v, T, v, 10.0 * REL_TOL_DERIVATIVE);
REL_TEST(_fp->cv_from_T_v(T, v), _fp->cv_from_v_e(v, e), REL_TOL_CONSISTENCY);
REL_TEST(_fp->p_from_h_s(h, s), p, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->p_from_h_s, h, s, REL_TOL_DERIVATIVE);
REL_TEST(_fp->rho_from_p_s(p, s), rho, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->rho_from_p_s, p, s, 1e-5);
REL_TEST(_fp->p_from_v_e(v, e), p, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->p_from_v_e, v, e, REL_TOL_DERIVATIVE);
REL_TEST(_fp->T_from_v_e(v, e), T, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->T_from_v_e, v, e, REL_TOL_DERIVATIVE);
REL_TEST(_fp->c_from_v_e(v, e), 1.299581997797754e3, REL_TOL_SAVED_VALUE);
REL_TEST(_fp->cp_from_v_e(v, e), 4267.6, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->cp_from_v_e, v, e, REL_TOL_DERIVATIVE);
REL_TEST(_fp->cv_from_v_e(v, e), 1816, REL_TOL_SAVED_VALUE);
REL_TEST(_fp->mu_from_v_e(v, e), 0.001, 1e-15);
REL_TEST(_fp->k_from_v_e(v, e), 0.6, 1e-15);
REL_TEST(_fp->beta_from_p_T(p, T), 3.411222923418045e-3, REL_TOL_SAVED_VALUE);
REL_TEST(_fp->s_from_v_e(v, e), -2.656251807629821e4, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->s_from_v_e, v, e, 1e-5);
ABS_TEST(_fp->rho_from_p_T(p, T), 1.391568186319449e3, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->rho_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->v_from_p_T(p, T), 1.0 / 1.391568186319449e3, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->v_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->e_from_p_rho(p, rho), 8.397412646416598e4, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->e_from_p_rho, p, rho, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->h_from_p_T(p, T), 8.404693999999994e4, 1e-10);
DERIV_TEST(_fp->h_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->s_from_p_T(p, T), -2.6562518076298216e4, 4 * REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->s_from_p_T, p, T, REL_TOL_DERIVATIVE);
ABS_TEST(_fp->s_from_h_p(h, p), -2.6562518076298216e4, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->s_from_h_p, h, p, 1e-5);
ABS_TEST(_fp->e_from_p_T(p, T), 8.397412646416575e4, 1e-10);
DERIV_TEST(_fp->e_from_p_T, p, T, REL_TOL_DERIVATIVE);
REL_TEST(_fp->T_from_p_h(p, h), T, REL_TOL_CONSISTENCY);
REL_TEST(_fp->mu_from_p_T(p, T), 0.001, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->mu_from_p_T, p, T, REL_TOL_DERIVATIVE);
REL_TEST(_fp->k_from_p_T(p, T), 0.6, REL_TOL_CONSISTENCY);
DERIV_TEST(_fp->k_from_p_T, p, T, REL_TOL_DERIVATIVE);
REL_TEST(_fp->cv_from_p_T(p, T), 1816, REL_TOL_SAVED_VALUE);
REL_TEST(_fp->cp_from_p_T(p, T), 4267.6, REL_TOL_SAVED_VALUE);
DERIV_TEST(_fp->cp_from_p_T, p, T, REL_TOL_DERIVATIVE);
}
/*
* Verify calculation of gas density, viscosity, enthalpy and derivatives
*/
TEST_F(PorousFlowWaterNCGTest, gasProperties)
{
const Real p = 1.0e6;
const Real T = 350.0;
FluidStatePhaseEnum phase_state;
std::vector<FluidStateProperties> fsp(2, FluidStateProperties(2));
// Gas region
Real Z = 0.995;
_fp->massFractions(p, T, Z, phase_state, fsp);
EXPECT_EQ(phase_state, FluidStatePhaseEnum::GAS);
// Verify fluid density, viscosity and enthalpy
_fp->gasProperties(p, T, fsp);
Real gas_density = fsp[1].density;
Real gas_viscosity = fsp[1].viscosity;
Real gas_enthalpy = fsp[1].enthalpy;
Real density =
_ncg_fp->rho_from_p_T(Z * p, T) + _water_fp->rho_from_p_T(_water_fp->vaporPressure(T), T);
Real viscosity =
Z * _ncg_fp->mu(Z * p, T) + (1.0 - Z) * _water_fp->mu(_water_fp->vaporPressure(T), T);
Real enthalpy =
Z * _ncg_fp->h(Z * p, T) + (1.0 - Z) * _water_fp->h(_water_fp->vaporPressure(T), T);
ABS_TEST(gas_density, density, 1.0e-8);
ABS_TEST(gas_viscosity, viscosity, 1.0e-8);
ABS_TEST(gas_enthalpy, enthalpy, 1.0e-8);
// Verify derivatives
Real ddensity_dp = fsp[1].ddensity_dp;
Real ddensity_dT = fsp[1].ddensity_dT;
Real ddensity_dZ = fsp[1].ddensity_dZ;
Real dviscosity_dp = fsp[1].dviscosity_dp;
Real dviscosity_dT = fsp[1].dviscosity_dT;
Real dviscosity_dZ = fsp[1].dviscosity_dZ;
Real denthalpy_dp = fsp[1].denthalpy_dp;
Real denthalpy_dT = fsp[1].denthalpy_dT;
Real denthalpy_dZ = fsp[1].denthalpy_dZ;
const Real dp = 1.0e-1;
_fp->gasProperties(p + dp, T, fsp);
Real rho1 = fsp[1].density;
Real mu1 = fsp[1].viscosity;
Real h1 = fsp[1].enthalpy;
_fp->gasProperties(p - dp, T, fsp);
Real rho2 = fsp[1].density;
Real mu2 = fsp[1].viscosity;
Real h2 = fsp[1].enthalpy;
REL_TEST(ddensity_dp, (rho1 - rho2) / (2.0 * dp), 1.0e-6);
REL_TEST(dviscosity_dp, (mu1 - mu2) / (2.0 * dp), 1.0e-6);
REL_TEST(denthalpy_dp, (h1 - h2) / (2.0 * dp), 1.0e-6);
const Real dT = 1.0e-3;
_fp->gasProperties(p, T + dT, fsp);
rho1 = fsp[1].density;
mu1 = fsp[1].viscosity;
h1 = fsp[1].enthalpy;
_fp->gasProperties(p, T - dT, fsp);
rho2 = fsp[1].density;
mu2 = fsp[1].viscosity;
h2 = fsp[1].enthalpy;
REL_TEST(ddensity_dT, (rho1 - rho2) / (2.0 * dT), 1.0e-6);
REL_TEST(dviscosity_dT, (mu1 - mu2) / (2.0 * dT), 1.0e-6);
REL_TEST(denthalpy_dT, (h1 - h2) / (2.0 * dT), 1.0e-6);
// Note: mass fraction changes with Z
const Real dZ = 1.0e-8;
_fp->massFractions(p, T, Z + dZ, phase_state, fsp);
_fp->gasProperties(p, T, fsp);
rho1 = fsp[1].density;
mu1 = fsp[1].viscosity;
h1 = fsp[1].enthalpy;
_fp->massFractions(p, T, Z - dZ, phase_state, fsp);
_fp->gasProperties(p, T, fsp);
rho2 = fsp[1].density;
mu2 = fsp[1].viscosity;
h2 = fsp[1].enthalpy;
REL_TEST(ddensity_dZ, (rho1 - rho2) / (2.0 * dZ), 1.0e-6);
REL_TEST(dviscosity_dZ, (mu1 - mu2) / (2.0 * dZ), 1.0e-6);
REL_TEST(denthalpy_dZ, (h1 - h2) / (2.0 * dZ), 1.0e-6);
// Check derivatives in the two phase region as well. Note that the mass fractions
// vary with pressure and temperature in this region
Z = 0.45;
_fp->massFractions(p, T, Z, phase_state, fsp);
EXPECT_EQ(phase_state, FluidStatePhaseEnum::TWOPHASE);
_fp->gasProperties(p, T, fsp);
ddensity_dp = fsp[1].ddensity_dp;
ddensity_dT = fsp[1].ddensity_dT;
ddensity_dZ = fsp[1].ddensity_dZ;
dviscosity_dp = fsp[1].dviscosity_dp;
dviscosity_dT = fsp[1].dviscosity_dT;
dviscosity_dZ = fsp[1].dviscosity_dZ;
denthalpy_dp = fsp[1].denthalpy_dp;
denthalpy_dT = fsp[1].denthalpy_dT;
denthalpy_dZ = fsp[1].denthalpy_dZ;
_fp->massFractions(p + dp, T, Z, phase_state, fsp);
_fp->gasProperties(p + dp, T, fsp);
rho1 = fsp[1].density;
mu1 = fsp[1].viscosity;
h1 = fsp[1].enthalpy;
_fp->massFractions(p - dp, T, Z, phase_state, fsp);
_fp->gasProperties(p - dp, T, fsp);
rho2 = fsp[1].density;
mu2 = fsp[1].viscosity;
h2 = fsp[1].enthalpy;
REL_TEST(ddensity_dp, (rho1 - rho2) / (2.0 * dp), 1.0e-6);
REL_TEST(dviscosity_dp, (mu1 - mu2) / (2.0 * dp), 1.0e-6);
REL_TEST(denthalpy_dp, (h1 - h2) / (2.0 * dp), 1.0e-6);
_fp->massFractions(p, T + dT, Z, phase_state, fsp);
_fp->gasProperties(p, T + dT, fsp);
rho1 = fsp[1].density;
mu1 = fsp[1].viscosity;
h1 = fsp[1].enthalpy;
_fp->massFractions(p, T - dT, Z, phase_state, fsp);
_fp->gasProperties(p, T - dT, fsp);
rho2 = fsp[1].density;
mu2 = fsp[1].viscosity;
h2 = fsp[1].enthalpy;
REL_TEST(ddensity_dT, (rho1 - rho2) / (2.0 * dT), 1.0e-6);
REL_TEST(dviscosity_dT, (mu1 - mu2) / (2.0 * dT), 1.0e-6);
REL_TEST(denthalpy_dT, (h1 - h2) / (2.0 * dT), 1.0e-6);
_fp->massFractions(p, T, Z + dZ, phase_state, fsp);
_fp->gasProperties(p, T, fsp);
rho1 = fsp[1].density;
mu1 = fsp[1].viscosity;
h1 = fsp[1].enthalpy;
_fp->massFractions(p, T, Z - dZ, phase_state, fsp);
_fp->gasProperties(p, T, fsp);
rho2 = fsp[1].density;
mu2 = fsp[1].viscosity;
h2 = fsp[1].enthalpy;
ABS_TEST(ddensity_dZ, (rho1 - rho2) / (2.0 * dZ), 1.0e-6);
ABS_TEST(dviscosity_dT, (mu1 - mu2) / (2.0 * dZ), 1.0e-6);
ABS_TEST(denthalpy_dZ, (h1 - h2) / (2.0 * dZ), 1.0e-6);
}
