BlackOilFluidSystem: some improvements
the biggest one was that the Rs factor was used incorrectly: instead of "surface volume of gas per volume of saturated reservoir oil" it is defined as "surface volume of gas which a volume unit of surface oil dissolves at reservoir pressure". Besides this, there are a few smallish improvements like the oil density being a function which can be called without having the boilerplate objects (i.e., the fluid state and parameter cache objects) instantiated.
This commit is contained in:
Andreas Lauser
@@ -303,40 +303,18 @@ public:
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// depending of the mass fraction in gas
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int n = gasDissolutionFactorSpline_.numSamples()*5;
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int delta =
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(gasDissolutionFactorSpline_.xMax() - gasDissolutionFactorSpline_.xMin())
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/(n + 1);
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(gasDissolutionFactorSpline_.xMax() - gasDissolutionFactorSpline_.xMin())/(n + 1);
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SplineSamplingPoints pSatSamplePoints;
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Scalar X_oG = 0;
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for (int i=0; i <= n && X_oG < 0.7; ++ i) {
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Scalar pSat = i*delta + gasDissolutionFactorSpline_.xMin();
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for (int i=0; i <= n; ++ i) {
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Scalar pSat = gasDissolutionFactorSpline_.xMin() + i*delta;
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X_oG = saturatedOilGasMassFraction(pSat);
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std::pair<Scalar, Scalar> val(X_oG, pSat);
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pSatSamplePoints.push_back(val);;
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};
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saturationPressureSpline_.setContainerOfTuples(pSatSamplePoints, /*type=*/Spline::Monotonic);
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if (0) {
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// some output only helpful for debugging
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int n = 1000;
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Scalar pMin = 10e6;
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Scalar pMax = 35e6;
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std::cerr.precision(16);
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for (int i = 0; i < n; ++i) {
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Scalar p = Scalar(i)/n*(pMax - pMin) + pMin;
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Scalar X_ogf = saturatedOilGasMassFraction(p);
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Scalar pPrime = oilSaturationPressure(X_ogf);
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std::cerr << p << " "
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<< X_ogf << " "
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<< pPrime << " "
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<< p - pPrime << " "
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<< "\n";
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};
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exit(1);
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pSatSamplePoints.push_back(val);
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}
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saturationPressureSpline_.setContainerOfTuples(pSatSamplePoints, /*type=*/Spline::Monotonic);
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}
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//! \copydoc BaseFluidSystem::phaseName
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@@ -414,52 +392,7 @@ public:
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switch (phaseIdx) {
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case waterPhaseIdx: return waterDensity_(p);
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case gasPhaseIdx: return gasDensity_(p);
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case oilPhaseIdx: {
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Scalar pSat = oilSaturationPressure(fluidState.massFraction(oilPhaseIdx, gasCompIdx));
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// retrieve the gas formation factor and the oil formation volume factor
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Scalar Rs = gasDissolutionFactorSpline_.eval(pSat, /*extrapolate=*/true);
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Scalar Bo = oilFormationVolumeFactor(pSat);
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// retrieve the derivatives of the oil formation volume
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// factor and the gas formation factor regarding pressure
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Scalar dBo_dp = oilFormationVolumeFactorSpline_.evalDerivative(pSat, /*extrapolate=*/true);
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Scalar dRs_dp = gasDissolutionFactorSpline_.evalDerivative(pSat, /*extrapolate=*/true);
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// define the derivatives of oil regarding oil component
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// mass fraction and pressure
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Scalar drhoo_dXoO =
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surfaceDensity_[oilPhaseIdx]*
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(1 + oilCompressibility()*(p - 1.0135e5));
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Scalar drhoo_dp =
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oilCompressibility();
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// Calculate the derivative of the density of saturated
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// oil regarding pressure
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Scalar drhoosat_dp = - surfaceDensity_[oilPhaseIdx]*dBo_dp / (Bo * Bo);
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// calculate the derivative of the gas component mass
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// fraction regarding pressure in saturated oil
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Scalar dXoOsat_dp =
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- surfaceDensity_[gasPhaseIdx]/surfaceDensity_[oilPhaseIdx]
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*(Bo * dRs_dp + Rs * dBo_dp);
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// Using the previous derivatives, define a derivative
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// for the oil density in regard to the gas mass fraction.
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Scalar drhoo_dXoG =
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drhoo_dXoO + (drhoo_dp - drhoosat_dp) / dXoOsat_dp;
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// calculate the composition of saturated oil.
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Scalar XoGsat = surfaceDensity_[gasPhaseIdx]/surfaceDensity_[oilPhaseIdx] * Rs * Bo;
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Scalar XoOsat = 1.0 - XoGsat;
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Scalar rhoo =
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surfaceDensity_[oilPhaseIdx]/Bo*(1 + drhoo_dp*(p - pSat))
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+ (XoOsat - fluidState.massFraction(oilPhaseIdx, oilCompIdx))*drhoo_dXoO
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+ (XoGsat - fluidState.massFraction(oilPhaseIdx, gasCompIdx))*drhoo_dXoG;
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return rhoo;
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}
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case oilPhaseIdx: return oilDensity(p, fluidState.massFraction(oilPhaseIdx, gasCompIdx));
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}
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OPM_THROW(std::logic_error, "Unhandled phase index " << phaseIdx);
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@@ -624,8 +557,7 @@ public:
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*/
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static Scalar oilCompressibility()
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{
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return
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(1.1200 - 1.1189)/((5000 - 4000)*6894.76); // [kg/m^3 / Pa)]
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return (1.1200 - 1.1189)/((5000 - 4000)*6894.76); // [kg/m^3 / Pa)]
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}
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/*!
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@@ -658,36 +590,27 @@ public:
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OPM_THROW(NumericalProblem, "Could find the oil saturation pressure for X_o^g = " << X_oG);
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}
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// the mass fraction of the gas component in the oil phase in a
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// flash experiment
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static Scalar saturatedOilGasMassFraction(Scalar pressure)
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{
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// first, we calculate the total reservoir oil phase density
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// [kg/m^3]
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Scalar rho_gRef = surfaceDensity_[gasPhaseIdx];
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Scalar B_o = oilFormationVolumeFactor(pressure);
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Scalar rho_o = surfaceDensity(oilPhaseIdx)/B_o;
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// then, we calculate the mass of the gas component [kg/m^3]
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// in the oil phase. This is equivalent to the gas formation
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// factor [m^3/m^3] at current pressure times the gas density
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// [kg/m^3] at standard pressure
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// calculate the mass of the gas component [kg/m^3] in the oil phase. This is
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// equivalent to the gas formation factor [m^3/m^3] at current pressure times the
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// gas density [kg/m^3] at standard pressure
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Scalar rho_oG = gasDissolutionFactor(pressure) * rho_gRef;
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// with these quantities it is pretty easy to calculate to the
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// composition of the oil phase in terms of mass fractions
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return rho_oG/rho_o;
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// we now have the total density of saturated oil and the partial density of the
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// gas component within it. The gas mass fraction is the ratio of these two.
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return rho_oG/(surfaceDensity(oilPhaseIdx) + rho_oG);
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}
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// the mole fraction of the gas component in the oil phase in a
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// flash experiment
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// the mole fraction of the gas component of a gas-saturated oil phase
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static Scalar saturatedOilGasMoleFraction(Scalar pressure)
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{
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// calculate the mass fractions of gas and oil
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Scalar XoG = saturatedOilGasMassFraction(pressure);
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//Scalar XoO = 1.0 - XoG;
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// which can be converted to mole fractions, given the
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// components' molar masses
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@@ -700,7 +623,7 @@ public:
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return xoG;
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}
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// density of oil in a flash experiment
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// density of gas-saturated oil
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static Scalar saturatedOilDensity(Scalar pressure)
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{
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// oil formation volume factor at reservoir pressure
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@@ -717,13 +640,61 @@ public:
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return rhoRef * BoRef/Bo;
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}
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// density of gas (potentially) under-saturated oil
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static Scalar oilDensity(Scalar oilPressure, Scalar massFractionGasInOil)
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{
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Scalar poSat = oilSaturationPressure(massFractionGasInOil);
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// retrieve the gas formation factor and the oil formation volume factor
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Scalar Rs = gasDissolutionFactorSpline_.eval(poSat, /*extrapolate=*/true);
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Scalar Bo = oilFormationVolumeFactor(poSat);
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// retrieve the derivatives of the oil formation volume
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// factor and the gas formation factor regarding pressure
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Scalar dBo_dp = oilFormationVolumeFactorSpline_.evalDerivative(poSat, /*extrapolate=*/true);
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Scalar dRs_dp = gasDissolutionFactorSpline_.evalDerivative(poSat, /*extrapolate=*/true);
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// define the derivatives of oil regarding oil component
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// mass fraction and pressure
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Scalar drhoo_dXoO =
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surfaceDensity_[oilPhaseIdx]
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* (1 + oilCompressibility()*(oilPressure - 1.0135e5));
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Scalar drhoo_dp = oilCompressibility();
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// Calculate the derivative of the density of saturated
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// oil regarding pressure
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Scalar drhoosat_dp = - surfaceDensity_[oilPhaseIdx]*dBo_dp / (Bo * Bo);
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// calculate the derivative of the gas component mass
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// fraction regarding pressure in saturated oil
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Scalar dXoOsat_dp =
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- surfaceDensity_[gasPhaseIdx]/surfaceDensity_[oilPhaseIdx]
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*(Bo * dRs_dp + Rs * dBo_dp);
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// Using the previous derivatives, define a derivative
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// for the oil density in regard to the gas mass fraction.
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Scalar drhoo_dXoG =
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drhoo_dXoO + (drhoo_dp - drhoosat_dp) / dXoOsat_dp;
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// calculate the composition of saturated oil.
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Scalar XoGsat = surfaceDensity_[gasPhaseIdx]/surfaceDensity_[oilPhaseIdx] * Rs * Bo;
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Scalar XoOsat = 1.0 - XoGsat;
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Scalar rhoo =
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surfaceDensity_[oilPhaseIdx]/Bo*(1 + drhoo_dp*(oilPressure - poSat))
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+ (XoOsat - (1 - massFractionGasInOil))*drhoo_dXoO
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+ (XoGsat - massFractionGasInOil)*drhoo_dXoG;
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return rhoo;
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}
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private:
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static Scalar gasDensity_(Scalar pressure)
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{
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// gas formation volume factor at reservoir pressure
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Scalar Bg = gasFormationVolumeFactor(pressure);
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// gas formation volume factor at standard pressure
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Scalar BgRef = refFormationVolumeFactor_[gasPhaseIdx];
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