/*
* Verify calculation of total mass fraction given a gas saturation
*/
TEST_F(PorousFlowWaterNCGTest, totalMassFraction)
{
const Real p = 1.0e6;
const Real T = 350.0;
const Real s = 0.2;
Real Z = _fp->totalMassFraction(p, T, s);
// Test that the saturation calculated in this fluid state using Z is equal to s
FluidStatePhaseEnum phase_state;
std::vector<FluidStateProperties> fsp(2, FluidStateProperties(2));
_fp->massFractions(p, T, Z, phase_state, fsp);
EXPECT_EQ(phase_state, FluidStatePhaseEnum::TWOPHASE);
_fp->gasProperties(p, T, fsp);
Real liquid_pressure = p + _pc->capillaryPressure(1.0 - s);
_fp->liquidProperties(liquid_pressure, T, fsp);
_fp->saturationTwoPhase(p, T, Z, fsp);
ABS_TEST(fsp[1].saturation, s, 1.0e-8);
}
Real
PorousFlowWaterNCG::totalMassFraction(
Real pressure, Real temperature, Real /* Xnacl */, Real saturation, unsigned int qp) const
{
// Check whether the input temperature is within the region of validity
checkVariables(temperature);
// FluidStateProperties data structure
std::vector<FluidStateProperties> fsp(_num_phases, FluidStateProperties(_num_components));
FluidStateProperties & liquid = fsp[_aqueous_phase_number];
FluidStateProperties & gas = fsp[_gas_phase_number];
// Calculate equilibrium mass fractions in the two-phase state
Real Xncg, dXncg_dp, dXncg_dT, Yh2o, dYh2o_dp, dYh2o_dT;
equilibriumMassFractions(
pressure, temperature, Xncg, dXncg_dp, dXncg_dT, Yh2o, dYh2o_dp, dYh2o_dT);
// Save the mass fractions in the FluidStateMassFractions object
const Real Yncg = 1.0 - Yh2o;
liquid.mass_fraction[_aqueous_fluid_component] = 1.0 - Xncg;
liquid.mass_fraction[_gas_fluid_component] = Xncg;
gas.mass_fraction[_aqueous_fluid_component] = Yh2o;
gas.mass_fraction[_gas_fluid_component] = Yncg;
// Gas properties
gasProperties(pressure, temperature, fsp);
// Liquid properties
const Real liquid_saturation = 1.0 - saturation;
const Real liquid_pressure = pressure - _pc.capillaryPressure(liquid_saturation, qp);
liquidProperties(liquid_pressure, temperature, fsp);
// The total mass fraction of ncg (Z) can now be calculated
const Real Z = (saturation * gas.density * Yncg + liquid_saturation * liquid.density * Xncg) /
(saturation * gas.density + liquid_saturation * liquid.density);
return Z;
}
/*
* Verify calculation of total mass fraction given a gas saturation
*/
TEST_F(PorousFlowBrineCO2Test, totalMassFraction)
{
const Real p = 1.0e6;
const Real T = 350.0;
const Real Xnacl = 0.1;
const Real s = 0.2;
Real Z = _fp->totalMassFraction(p, T, Xnacl, s);
// Test that the saturation calculated in this fluid state using Z is equal to s
FluidStatePhaseEnum phase_state;
const unsigned int np = _fp->numPhases();
const unsigned int nc = _fp->numComponents();
std::vector<FluidStateProperties> fsp(np, FluidStateProperties(nc));
_fp->massFractions(p, T, Xnacl, Z, phase_state, fsp);
EXPECT_EQ(phase_state, FluidStatePhaseEnum::TWOPHASE);
_fp->gasProperties(p, T, fsp);
Real liquid_pressure = p + _pc->capillaryPressure(1.0 - s);
_fp->liquidProperties(liquid_pressure, T, Xnacl, fsp);
_fp->saturationTwoPhase(p, T, Xnacl, Z, fsp);
ABS_TEST(fsp[1].saturation, s, 1.0e-8);
}
/*
* Verify calculation of actual mass fraction and derivatives depending on value of
* total mass fraction
*/
TEST_F(PorousFlowWaterNCGTest, MassFraction)
{
const Real p = 1.0e6;
const Real T = 350.0;
FluidStatePhaseEnum phase_state;
std::vector<FluidStateProperties> fsp(2, FluidStateProperties(2));
// Liquid region
Real Z = 0.0001;
_fp->massFractions(p, T, Z, phase_state, fsp);
EXPECT_EQ(phase_state, FluidStatePhaseEnum::LIQUID);
// Verfify mass fraction values
Real Xncg = fsp[0].mass_fraction[1];
Real Yncg = fsp[1].mass_fraction[1];
Real Xh2o = fsp[0].mass_fraction[0];
Real Yh2o = fsp[1].mass_fraction[0];
ABS_TEST(Xncg, Z, 1.0e-8);
ABS_TEST(Yncg, 0.0, 1.0e-8);
ABS_TEST(Xh2o, 1.0 - Z, 1.0e-8);
ABS_TEST(Yh2o, 0.0, 1.0e-8);
// Verify derivatives
Real dXncg_dp = fsp[0].dmass_fraction_dp[1];
Real dXncg_dT = fsp[0].dmass_fraction_dT[1];
Real dXncg_dZ = fsp[0].dmass_fraction_dZ[1];
Real dYncg_dp = fsp[1].dmass_fraction_dp[1];
Real dYncg_dT = fsp[1].dmass_fraction_dT[1];
Real dYncg_dZ = fsp[1].dmass_fraction_dZ[1];
ABS_TEST(dXncg_dp, 0.0, 1.0e-8);
ABS_TEST(dXncg_dT, 0.0, 1.0e-8);
ABS_TEST(dXncg_dZ, 1.0, 1.0e-8);
ABS_TEST(dYncg_dp, 0.0, 1.0e-8);
ABS_TEST(dYncg_dT, 0.0, 1.0e-8);
ABS_TEST(dYncg_dZ, 0.0, 1.0e-8);
// Gas region
Z = 0.995;
_fp->massFractions(p, T, Z, phase_state, fsp);
EXPECT_EQ(phase_state, FluidStatePhaseEnum::GAS);
// Verfify mass fraction values
Xncg = fsp[0].mass_fraction[1];
Yncg = fsp[1].mass_fraction[1];
Xh2o = fsp[0].mass_fraction[0];
Yh2o = fsp[1].mass_fraction[0];
ABS_TEST(Xncg, 0.0, 1.0e-8);
ABS_TEST(Yncg, Z, 1.0e-8);
ABS_TEST(Xh2o, 0.0, 1.0e-8);
ABS_TEST(Yh2o, 1.0 - Z, 1.0e-8);
// Verify derivatives
dXncg_dp = fsp[0].dmass_fraction_dp[1];
dXncg_dT = fsp[0].dmass_fraction_dT[1];
dXncg_dZ = fsp[0].dmass_fraction_dZ[1];
dYncg_dp = fsp[1].dmass_fraction_dp[1];
dYncg_dT = fsp[1].dmass_fraction_dT[1];
dYncg_dZ = fsp[1].dmass_fraction_dZ[1];
ABS_TEST(dXncg_dp, 0.0, 1.0e-8);
ABS_TEST(dXncg_dT, 0.0, 1.0e-8);
ABS_TEST(dXncg_dZ, 0.0, 1.0e-8);
ABS_TEST(dYncg_dp, 0.0, 1.0e-8);
ABS_TEST(dYncg_dT, 0.0, 1.0e-8);
ABS_TEST(dYncg_dZ, 1.0, 1.0e-8);
// Two phase region. In this region, the mass fractions and derivatives can
// be verified using the equilibrium mass fraction derivatives that have
// been verified above
Z = 0.45;
_fp->massFractions(p, T, Z, phase_state, fsp);
EXPECT_EQ(phase_state, FluidStatePhaseEnum::TWOPHASE);
// Equilibrium mass fractions and derivatives
Real Xncg_eq, dXncg_dp_eq, dXncg_dT_eq, Yh2o_eq, dYh2o_dp_eq, dYh2o_dT_eq;
_fp->equilibriumMassFractions(
p, T, Xncg_eq, dXncg_dp_eq, dXncg_dT_eq, Yh2o_eq, dYh2o_dp_eq, dYh2o_dT_eq);
// Verfify mass fraction values
Xncg = fsp[0].mass_fraction[1];
Yncg = fsp[1].mass_fraction[1];
Xh2o = fsp[0].mass_fraction[0];
Yh2o = fsp[1].mass_fraction[0];
ABS_TEST(Xncg, Xncg_eq, 1.0e-8);
ABS_TEST(Yncg, 1.0 - Yh2o_eq, 1.0e-8);
ABS_TEST(Xh2o, 1.0 - Xncg_eq, 1.0e-8);
ABS_TEST(Yh2o, Yh2o_eq, 1.0e-8);
// Verify derivatives wrt p and T
dXncg_dp = fsp[0].dmass_fraction_dp[1];
dXncg_dT = fsp[0].dmass_fraction_dT[1];
dXncg_dZ = fsp[0].dmass_fraction_dZ[1];
dYncg_dp = fsp[1].dmass_fraction_dp[1];
dYncg_dT = fsp[1].dmass_fraction_dT[1];
dYncg_dZ = fsp[1].dmass_fraction_dZ[1];
ABS_TEST(dXncg_dp, dXncg_dp_eq, 1.0e-8);
ABS_TEST(dXncg_dT, dXncg_dT_eq, 1.0e-8);
ABS_TEST(dXncg_dZ, 0.0, 1.0e-8);
ABS_TEST(dYncg_dp, -dYh2o_dp_eq, 1.0e-8);
ABS_TEST(dYncg_dT, -dYh2o_dT_eq, 1.0e-8);
ABS_TEST(dYncg_dZ, 0.0, 1.0e-8);
// Use finite differences to verify derivative wrt Z is unaffected by Z
const Real dZ = 1.0e-8;
_fp->massFractions(p, T, Z + dZ, phase_state, fsp);
Real Xncg1 = fsp[0].mass_fraction[1];
Real Yncg1 = fsp[1].mass_fraction[1];
_fp->massFractions(p, T, Z - dZ, phase_state, fsp);
Real Xncg2 = fsp[0].mass_fraction[1];
Real Yncg2 = fsp[1].mass_fraction[1];
ABS_TEST(dXncg_dZ, (Xncg1 - Xncg2) / (2.0 * dZ), 1.0e-8);
ABS_TEST(dYncg_dZ, (Yncg1 - Yncg2) / (2.0 * dZ), 1.0e-8);
}
/*
* 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);
}
/*
* 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);
}
/*
* 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 density, viscosity enthalpy, and derivatives. Note that as
* these properties don't depend on mass fraction, only the gas region needs to be
* tested (the calculations are identical in the two phase region)
*/
TEST_F(PorousFlowBrineCO2Test, gasProperties)
{
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));
// Gas region
Real Z = 0.995;
_fp->massFractions(p, T, Xnacl, 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 = _co2_fp->rho(p, T);
Real viscosity = _co2_fp->mu(p, T);
Real enthalpy = _co2_fp->h(p, 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, Xnacl, 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, Xnacl, 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-8);
ABS_TEST(dviscosity_dZ, (mu1 - mu2) / (2.0 * dZ), 1.0e-8);
ABS_TEST(denthalpy_dZ, (h1 - h2) / (2.0 * dZ), 1.0e-6);
}
/*
* Verify calculation of actual mass fraction and derivatives depending on value of
* total mass fraction
*/
TEST_F(PorousFlowBrineCO2Test, MassFraction)
{
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);
// Verfify mass fraction values
Real Xco2 = fsp[0].mass_fraction[1];
Real Yco2 = fsp[1].mass_fraction[1];
Real Xh2o = fsp[0].mass_fraction[0];
Real Yh2o = fsp[1].mass_fraction[0];
Real Xnacl2 = fsp[0].mass_fraction[2];
ABS_TEST(Xco2, Z, 1.0e-8);
ABS_TEST(Yco2, 0.0, 1.0e-8);
ABS_TEST(Xh2o, 1.0 - Z, 1.0e-8);
ABS_TEST(Yh2o, 0.0, 1.0e-8);
ABS_TEST(Xnacl2, Xnacl, 1.0e-8);
// Verify derivatives
Real dXco2_dp = fsp[0].dmass_fraction_dp[1];
Real dXco2_dT = fsp[0].dmass_fraction_dT[1];
Real dXco2_dX = fsp[0].dmass_fraction_dX[1];
Real dXco2_dZ = fsp[0].dmass_fraction_dZ[1];
Real dYco2_dp = fsp[1].dmass_fraction_dp[1];
Real dYco2_dT = fsp[1].dmass_fraction_dT[1];
Real dYco2_dX = fsp[1].dmass_fraction_dX[1];
Real dYco2_dZ = fsp[1].dmass_fraction_dZ[1];
Real dXnacl_dX = fsp[0].dmass_fraction_dX[2];
ABS_TEST(dXco2_dp, 0.0, 1.0e-8);
ABS_TEST(dXco2_dT, 0.0, 1.0e-8);
ABS_TEST(dXco2_dX, 0.0, 1.0e-8);
ABS_TEST(dXco2_dZ, 1.0, 1.0e-8);
ABS_TEST(dYco2_dp, 0.0, 1.0e-8);
ABS_TEST(dYco2_dT, 0.0, 1.0e-8);
ABS_TEST(dYco2_dX, 0.0, 1.0e-8);
ABS_TEST(dYco2_dZ, 0.0, 1.0e-8);
ABS_TEST(dXnacl_dX, 1.0, 1.0e-8);
// Gas region
Z = 0.995;
_fp->massFractions(p, T, Xnacl, Z, phase_state, fsp);
EXPECT_EQ(phase_state, FluidStatePhaseEnum::GAS);
// Verfify mass fraction values
Xco2 = fsp[0].mass_fraction[1];
Yco2 = fsp[1].mass_fraction[1];
Xh2o = fsp[0].mass_fraction[0];
Yh2o = fsp[1].mass_fraction[0];
Real Ynacl = fsp[1].mass_fraction[2];
ABS_TEST(Xco2, 0.0, 1.0e-8);
ABS_TEST(Yco2, Z, 1.0e-8);
ABS_TEST(Xh2o, 0.0, 1.0e-8);
ABS_TEST(Yh2o, 1.0 - Z, 1.0e-8);
ABS_TEST(Ynacl, 0.0, 1.0e-8);
// Verify derivatives
dXco2_dp = fsp[0].dmass_fraction_dp[1];
dXco2_dT = fsp[0].dmass_fraction_dT[1];
dXco2_dX = fsp[0].dmass_fraction_dX[1];
dXco2_dZ = fsp[0].dmass_fraction_dZ[1];
dYco2_dp = fsp[1].dmass_fraction_dp[1];
dYco2_dT = fsp[1].dmass_fraction_dT[1];
dYco2_dX = fsp[1].dmass_fraction_dX[1];
dYco2_dZ = fsp[1].dmass_fraction_dZ[1];
Real dYnacl_dX = fsp[1].dmass_fraction_dX[2];
ABS_TEST(dXco2_dp, 0.0, 1.0e-8);
ABS_TEST(dXco2_dT, 0.0, 1.0e-8);
ABS_TEST(dXco2_dX, 0.0, 1.0e-8);
ABS_TEST(dXco2_dZ, 0.0, 1.0e-8);
ABS_TEST(dYco2_dp, 0.0, 1.0e-8);
ABS_TEST(dYco2_dT, 0.0, 1.0e-8);
ABS_TEST(dYco2_dX, 0.0, 1.0e-8);
ABS_TEST(dYnacl_dX, 0.0, 1.0e-8);
ABS_TEST(dYco2_dX, 0.0, 1.0e-8);
// Two phase region. In this region, the mass fractions and derivatives can
// be verified using the equilibrium mass fraction derivatives that have
// been verified above
Z = 0.45;
_fp->massFractions(p, T, Xnacl, Z, phase_state, fsp);
EXPECT_EQ(phase_state, FluidStatePhaseEnum::TWOPHASE);
// Equilibrium mass fractions and derivatives
Real Xco2_eq, dXco2_dp_eq, dXco2_dT_eq, dXco2_dX_eq, Yh2o_eq, dYh2o_dp_eq, dYh2o_dT_eq,
dYh2o_dX_eq;
_fp->equilibriumMassFractions(p,
T,
Xnacl,
Xco2_eq,
dXco2_dp_eq,
dXco2_dT_eq,
dXco2_dX_eq,
Yh2o_eq,
dYh2o_dp_eq,
dYh2o_dT_eq,
dYh2o_dX_eq);
// Verfify mass fraction values
Xco2 = fsp[0].mass_fraction[1];
Yco2 = fsp[1].mass_fraction[1];
Xh2o = fsp[0].mass_fraction[0];
Yh2o = fsp[1].mass_fraction[0];
ABS_TEST(Xco2, Xco2_eq, 1.0e-8);
ABS_TEST(Yco2, 1.0 - Yh2o_eq, 1.0e-8);
ABS_TEST(Xh2o, 1.0 - Xco2_eq, 1.0e-8);
ABS_TEST(Yh2o, Yh2o_eq, 1.0e-8);
// Verify derivatives wrt p, T
dXco2_dp = fsp[0].dmass_fraction_dp[1];
dXco2_dT = fsp[0].dmass_fraction_dT[1];
dXco2_dX = fsp[0].dmass_fraction_dX[1];
dXco2_dZ = fsp[0].dmass_fraction_dZ[1];
dYco2_dp = fsp[1].dmass_fraction_dp[1];
dYco2_dT = fsp[1].dmass_fraction_dT[1];
dYco2_dX = fsp[1].dmass_fraction_dX[1];
dYco2_dZ = fsp[1].dmass_fraction_dZ[1];
ABS_TEST(dXco2_dp, dXco2_dp_eq, 1.0e-8);
ABS_TEST(dXco2_dT, dXco2_dT_eq, 1.0e-8);
ABS_TEST(dXco2_dX, dXco2_dX_eq, 1.0e-8);
ABS_TEST(dXco2_dZ, 0.0, 1.0e-8);
ABS_TEST(dYco2_dp, -dYh2o_dp_eq, 1.0e-8);
ABS_TEST(dYco2_dT, -dYh2o_dT_eq, 1.0e-8);
ABS_TEST(dYco2_dX, -dYh2o_dX_eq, 1.0e-8);
ABS_TEST(dYco2_dZ, 0.0, 1.0e-8);
// Use finite differences to verify derivative wrt Z is unaffected by Z
const Real dZ = 1.0e-8;
_fp->massFractions(p, T, Xnacl, Z + dZ, phase_state, fsp);
Real Xco21 = fsp[0].mass_fraction[1];
Real Yco21 = fsp[1].mass_fraction[1];
_fp->massFractions(p, T, Xnacl, Z - dZ, phase_state, fsp);
Real Xco22 = fsp[0].mass_fraction[1];
Real Yco22 = fsp[1].mass_fraction[1];
ABS_TEST(dXco2_dZ, (Xco21 - Xco22) / (2.0 * dZ), 1.0e-8);
ABS_TEST(dYco2_dZ, (Yco21 - Yco22) / (2.0 * dZ), 1.0e-8);
}