From 5e6261a60ea053750db81c42db80527f02bc1f58 Mon Sep 17 00:00:00 2001
From: Dmitry Pavlov <dmitry.pavlov@outlook.com>
Date: Tue, 31 Aug 2021 01:36:55 +0300
Subject: [PATCH] [material] Add option to PengRobinson::computeMolarVolume
- Ignoring the first two roots of the equation for Z in the
smallest one is zero or negative. There was a comment
documenting that behavior, but it was not implemented.
- Throwing NumericalProblem if no positive Z has been found
or the number of roots is 2 or more than 3
(no check was in place)
- Throwing NumericalProblem if the found molar volume turned
out to be zero, negative, or NaN. (Replacing assert)
- Added handleUnphysicalPhase flag (true by default). If false, the
single-root case is not checked for critical state of
the fluid (otherwise, Michelsen test for a mix of
hydrocarbons does not work).
---
dumux/material/eos/pengrobinson.hh | 113 +++++++++++++++++++----------
1 file changed, 75 insertions(+), 38 deletions(-)
diff --git a/dumux/material/eos/pengrobinson.hh b/dumux/material/eos/pengrobinson.hh
index 5fa32ac250..aa81c029af 100644
--- a/dumux/material/eos/pengrobinson.hh
+++ b/dumux/material/eos/pengrobinson.hh
@@ -141,18 +141,29 @@ public:
* \param params Parameters
* \param phaseIdx The phase index
* \param isGasPhase Specifies the phase state
+ * \param handleUnphysicalPhase Special handling of the case when the EOS has only one
+ intersection with the pressure, and the intersection does not correspond to
+ the given phase (the phase is thus considered unphysical). If it happens in
+ the case of critical fluid, the critical molar volume is returned for the
+ unphysical phase. If the fluid is not critical, a proper extremum of the
+ EOS is returned for the unphysical phase. If the parameter is false and the
+ EOS has only one intersection with the pressure, the molar volume is computed
+ from that single intersection, not depending of the given phase (gas or
+ fluid). If the EOS has three intersections with the pressure, this parameter
+ is ignored.
*/
template <class FluidState, class Params>
static Scalar computeMolarVolume(const FluidState &fs,
Params ¶ms,
int phaseIdx,
- bool isGasPhase)
+ bool isGasPhase,
+ bool handleUnphysicalPhase = true)
{
Scalar Vm = 0;
Scalar T = fs.temperature(phaseIdx);
Scalar p = fs.pressure(phaseIdx);
-
+
Scalar a = params.a(phaseIdx); // "attractive factor"
Scalar b = params.b(phaseIdx); // "co-volume"
@@ -165,12 +176,22 @@ public:
Scalar a3 = Astar - Bstar*(3*Bstar + 2);
Scalar a4 = Bstar*(- Astar + Bstar*(1 + Bstar));
+ Scalar Z[3] = {}; // zero-initializer
+ int numSol = invertCubicPolynomial(Z, a1, a2, a3, a4);
+
// ignore the first two results if the smallest
// compressibility factor is <= 0.0. (this means that if we
// would get negative molar volumes for the liquid phase, we
// consider the liquid phase non-existant.)
- Scalar Z[3] = {0.0,0.0,0.0};
- int numSol = invertCubicPolynomial(Z, a1, a2, a3, a4);
+ // Note that invertCubicPolynomial sorts the roots in ascending order
+ if (numSol > 1 && Z[0] <= 0.0) {
+ Z[0] = Z[numSol - 1];
+ numSol = 1;
+ }
+
+ if (numSol > 0 && Z[0] <= 0)
+ DUNE_THROW(NumericalProblem, "No positive compressibility factors found");
+
if (numSol == 3) {
// the EOS has three intersections with the pressure,
// i.e. the molar volume of gas is the largest one and the
@@ -181,38 +202,22 @@ public:
Vm = Z[0]*RT/p;
}
else if (numSol == 1) {
- // the EOS only has one intersection with the pressure,
- // for the other phase, we take the extremum of the EOS
- // with the largest distance from the intersection.
- Scalar VmCubic = Z[0]*RT/p;
-
- if (T > criticalTemperature_(a, b)) {
- // if the EOS does not exhibit any extrema, the fluid
- // is critical...
- Vm = VmCubic;
- handleCriticalFluid_(Vm, fs, params, phaseIdx, isGasPhase);
- }
- else {
- // find the extrema (if they are present)
- Scalar Vmin, Vmax, pmin, pmax;
- using std::min;
- using std::max;
- if (findExtrema_(Vmin, Vmax,
- pmin, pmax,
- a, b, T))
- {
- if (isGasPhase)
- Vm = max(Vmax, VmCubic);
- else
- Vm = min(Vmin, VmCubic);
- }
- else
- Vm = VmCubic;
- }
+ // the EOS has only one intersection with the pressure
+
+ Vm = Z[0]*RT/p;
+
+ // Handle single root case specially unless told otherwise
+ if (handleUnphysicalPhase)
+ Vm = handleSingleRoot_(Vm, fs, params, phaseIdx, isGasPhase);
}
+ else
+ DUNE_THROW(NumericalProblem, "Unexpected number of roots in the equation for compressibility factor: " << numSol);
using std::isfinite;
- assert(isfinite(Vm) && Vm > 0);
+
+ if (!isfinite(Vm) || Vm <= 0)
+ DUNE_THROW(NumericalProblem, "Bad molar volume");
+
return Vm;
}
@@ -279,8 +284,43 @@ public:
{ return params.pressure()*computeFugacityCoeff(params); }
protected:
+
+ /*
+ * Handle single-root case in the equation of state. The problem here is
+ * that only one phase exists in this case, while we should also figure out
+ * something to return for the other phase. For reference, see Andreas
+ * Lauser's thesis: http://dx.doi.org/10.18419/opus-516 (page 32).
+ */
+ template <class FluidState, class Params>
+ static Scalar handleSingleRoot_(Scalar Vm,
+ const FluidState &fs,
+ const Params ¶ms,
+ int phaseIdx,
+ bool isGasPhase)
+ {
+ Scalar T = fs.temperature(phaseIdx);
+
+ // for the other phase, we take the extremum of the EOS
+ // with the largest distance from the intersection.
+ if (T > criticalTemperature_(params.a(phaseIdx), params.b(phaseIdx))) {
+ // if the EOS does not exhibit any extrema, the fluid
+ // is critical...
+ return handleCriticalFluid_(Vm, fs, params, phaseIdx, isGasPhase);
+ }
+ else {
+ // find the extrema (if they are present)
+ Scalar Vmin, Vmax, pmin, pmax;
+ using std::min;
+ using std::max;
+ if (findExtrema_(Vmin, Vmax, pmin, pmax,
+ params.a(phaseIdx), params.b(phaseIdx), T))
+ return isGasPhase ? max(Vmax, Vm) : min(Vmin, Vm);
+ }
+ return Vm;
+ }
+
template <class FluidState, class Params>
- static void handleCriticalFluid_(Scalar &Vm,
+ static Scalar handleCriticalFluid_(Scalar Vm,
const FluidState &fs,
const Params ¶ms,
int phaseIdx,
@@ -290,10 +330,7 @@ protected:
using std::max;
using std::min;
- if (isGasPhase)
- Vm = max(Vm, Vcrit);
- else
- Vm = min(Vm, Vcrit);
+ return isGasPhase ? max(Vm, Vcrit) : min(Vm, Vcrit);
}
static void findCriticalPoint_(Scalar &Tcrit,
--
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