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Add interface for wet gas

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The pvt interface is extened to handle wet gas
1. A function for rvSat is added to the interface
2. An interface that takes rv and the fluid condition as an input for
the gas properties is added. The old interface without rv and the fluid
condition is kept in the file.
3. The new interface is implemented in BlackoilPropsAd and
BlackoilPropsAdFromDeck.

A simulator that tests wet gas is not yet implemented.
This commit is contained in:
Tor Harald Sandve 2013-12-13 17:01:43 +01:00
parent 69b74fb580
commit 3c5b0b9e73
5 changed files with 420 additions and 16 deletions
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170
opm/autodiff/BlackoilPropsAd.cpp
View File

@ -166,6 +166,35 @@ namespace Opm
return mu.col(pu_.phase_pos[Gas]);
}
/// Gas viscosity.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
V BlackoilPropsAd::muGas(const V& pg,
const V& rv,
const std::vector<PhasePresence>& /*cond*/,
const Cells& cells) const
{
if (!pu_.phase_used[Gas]) {
OPM_THROW(std::runtime_error, "Cannot call muGas(): gas phase not present.");
}
const int n = cells.size();
assert(pg.size() == n);
const int np = props_.numPhases();
Block z = Block::Zero(n, np);
if (pu_.phase_used[Oil]) {
// Faking a z with the right ratio:
// rv = zo/zg
z.col(pu_.phase_pos[Oil]) = rv;
z.col(pu_.phase_pos[Gas]) = V::Ones(n, 1);
}
Block mu(n, np);
props_.viscosity(n, pg.data(), z.data(), cells.data(), mu.data(), 0);
return mu.col(pu_.phase_pos[Gas]);
}
/// Water viscosity.
/// \param[in] pw Array of n water pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
@ -268,6 +297,45 @@ namespace Opm
return ADB::function(mu.col(pu_.phase_pos[Gas]), jacs);
#endif
}
/// Gas viscosity.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n viscosity values.
ADB BlackoilPropsAd::muGas(const ADB& pg,
const ADB& rv,
const std::vector<PhasePresence>& cond,
const Cells& cells) const
{
#if 1
return ADB::constant(muGas(pg.value(), rv.value(),cond,cells), pg.blockPattern());
#else
if (!pu_.phase_used[Gas]) {
OPM_THROW(std::runtime_error, "Cannot call muGas(): gas phase not present.");
}
const int n = cells.size();
assert(pg.value().size() == n);
const int np = props_.numPhases();
Block z = Block::Zero(n, np);
if (pu_.phase_used[Oil]) {
// Faking a z with the right ratio:
// rv = zo/zg
z.col(pu_.phase_pos[Oil]) = rv;
z.col(pu_.phase_pos[Gas]) = V::Ones(n, 1);
}
Block mu(n, np);
Block dmu(n, np);
props_.viscosity(n, pg.value().data(), z.data(), cells.data(), mu.data(), dmu.data());
ADB::M dmu_diag = spdiag(dmu.col(pu_.phase_pos[Gas]));
const int num_blocks = pg.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dmu_diag * pg.derivative()[block];
}
return ADB::function(mu.col(pu_.phase_pos[Gas]), jacs);
#endif
}
// ------ Formation volume factor (b) ------
@ -357,6 +425,36 @@ namespace Opm
return matrix.col(gi*np + gi);
}
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
V BlackoilPropsAd::bGas(const V& pg,
const V& rv,
const std::vector<PhasePresence>& /*cond*/,
const Cells& cells) const
{
if (!pu_.phase_used[Gas]) {
OPM_THROW(std::runtime_error, "Cannot call bGas(): gas phase not present.");
}
const int n = cells.size();
assert(pg.size() == n);
const int np = props_.numPhases();
Block z = Block::Zero(n, np);
if (pu_.phase_used[Oil]) {
// Faking a z with the right ratio:
// rv = zo/zg
z.col(pu_.phase_pos[Oil]) = rv;
z.col(pu_.phase_pos[Gas]) = V::Ones(n, 1);
}
Block matrix(n, np*np);
props_.matrix(n, pg.data(), z.data(), cells.data(), matrix.data(), 0);
const int gi = pu_.phase_pos[Gas];
return matrix.col(gi*np + gi);
}
/// Water formation volume factor.
/// \param[in] pw Array of n water pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
@ -454,6 +552,44 @@ namespace Opm
return ADB::function(matrix.col(column), jacs);
}
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
ADB BlackoilPropsAd::bGas(const ADB& pg,
const ADB& rv,
const std::vector<PhasePresence>& /*cond*/,
const Cells& cells) const
{
if (!pu_.phase_used[Gas]) {
OPM_THROW(std::runtime_error, "Cannot call muGas(): gas phase not present.");
}
const int n = cells.size();
assert(pg.value().size() == n);
const int np = props_.numPhases();
Block z = Block::Zero(n, np);
if (pu_.phase_used[Oil]) {
// Faking a z with the right ratio:
// rv = zo/zg
z.col(pu_.phase_pos[Oil]) = rv.value();
z.col(pu_.phase_pos[Gas]) = V::Ones(n, 1);
}
Block matrix(n, np*np);
Block dmatrix(n, np*np);
props_.matrix(n, pg.value().data(), z.data(), cells.data(), matrix.data(), dmatrix.data());
const int phase_ind = pu_.phase_pos[Gas];
const int column = phase_ind*np + phase_ind; // Index of our sought diagonal column.
ADB::M db_diag = spdiag(dmatrix.col(column));
const int num_blocks = pg.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = db_diag * pg.derivative()[block];
}
return ADB::function(matrix.col(column), jacs);
}
// ------ Rs bubble point curve ------
@ -461,7 +597,7 @@ namespace Opm
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
V BlackoilPropsAd::rsMax(const V& po,
V BlackoilPropsAd::rsSat(const V& po,
const Cells& cells) const
{
// Suppress warning about "unused parameters".
@ -475,7 +611,37 @@ namespace Opm
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
ADB BlackoilPropsAd::rsMax(const ADB& po,
ADB BlackoilPropsAd::rsSat(const ADB& po,
const Cells& cells) const
{
// Suppress warning about "unused parameters".
static_cast<void>(po);
static_cast<void>(cells);
OPM_THROW(std::runtime_error, "Method rsMax() not implemented.");
}
// ------ Rs bubble point curve ------
/// Bubble point curve for Rs as function of oil pressure.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
V BlackoilPropsAd::rvSat(const V& po,
const Cells& cells) const
{
// Suppress warning about "unused parameters".
static_cast<void>(po);
static_cast<void>(cells);
OPM_THROW(std::runtime_error, "Method rsMax() not implemented.");
}
/// Bubble point curve for Rs as function of oil pressure.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
ADB BlackoilPropsAd::rvSat(const ADB& po,
const Cells& cells) const
{
// Suppress warning about "unused parameters".

65
opm/autodiff/BlackoilPropsAd.hpp
View File

@ -124,6 +124,17 @@ namespace Opm
V muGas(const V& pg,
const Cells& cells) const;
/// Gas viscosity.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n gas solution factor values.
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n viscosity values.
V muGas(const V& pg,
const V& rv,
const std::vector<PhasePresence>& cond,
const Cells& cells) const;
/// Water viscosity.
/// \param[in] pw Array of n water pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
@ -149,6 +160,16 @@ namespace Opm
ADB muGas(const ADB& pg,
const Cells& cells) const;
/// Gas viscosity.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n gas solution factor values.
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n viscosity values.
ADB muGas(const ADB& pg,
const ADB& rv,
const std::vector<PhasePresence>& cond,
const Cells& cells) const;
// ------ Formation volume factor (b) ------
@ -177,6 +198,17 @@ namespace Opm
V bGas(const V& pg,
const Cells& cells) const;
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
V bGas(const V& pg,
const V& rv,
const std::vector<PhasePresence>& cond,
const Cells& cells) const;
/// Water formation volume factor.
/// \param[in] pw Array of n water pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
@ -203,22 +235,47 @@ namespace Opm
const Cells& cells) const;
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
ADB bGas(const ADB& pg,
const ADB& rv,
const std::vector<PhasePresence>& cond,
const Cells& cells) const;
// ------ Rs bubble point curve ------
/// Bubble point curve for Rs as function of oil pressure.
/// Solution gas/oil ratio and its derivatives at saturated condition as a function of p.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
V rsMax(const V& po,
V rsSat(const V& po,
const Cells& cells) const;
/// Bubble point curve for Rs as function of oil pressure.
/// Solution gas/oil ratio and its derivatives at saturated condition as a function of p.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
ADB rsMax(const ADB& po,
ADB rsSat(const ADB& po,
const Cells& cells) const;
// ------ Rv condensation curve ------
/// Vapor oil/gas ratio and its derivatives at saturated conditions as a function of p.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
V rvSat(const V& po,
const Cells& cells) const;
/// Vapor oil/gas ratio and its derivatives at saturated conditions as a function of p.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
ADB rvSat(const ADB& po,
const Cells& cells) const;
// ------ Relative permeability ------

116
opm/autodiff/BlackoilPropsAdFromDeck.cpp
View File

@ -439,6 +439,33 @@ namespace Opm
return b;
}
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
V BlackoilPropsAdFromDeck::bGas(const V& pg,
const V& rv,
const std::vector<PhasePresence>& cond,
const Cells& cells) const
{
if (!phase_usage_.phase_used[Gas]) {
OPM_THROW(std::runtime_error, "Cannot call muGas(): gas phase not present.");
}
const int n = cells.size();
assert(pg.size() == n);
V b(n);
V dbdp(n);
V dbdr(n);
props_[phase_usage_.phase_pos[Gas]]->b(n, pg.data(), rv.data(), &cond[0],
b.data(), dbdp.data(), dbdr.data());
return b;
}
/// Water formation volume factor.
/// \param[in] pw Array of n water pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
@ -519,9 +546,42 @@ namespace Opm
V b(n);
V dbdp(n);
V dbdr(n);
const double* rs = 0;
const double* rv = 0;
props_[phase_usage_.phase_pos[Gas]]->b(n, pg.value().data(), rs,
props_[phase_usage_.phase_pos[Gas]]->b(n, pg.value().data(), rv,
b.data(), dbdp.data(), dbdr.data());
ADB::M dbdp_diag = spdiag(dbdp);
const int num_blocks = pg.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = dbdp_diag * pg.derivative()[block];
}
return ADB::function(b, jacs);
}
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
ADB BlackoilPropsAdFromDeck::bGas(const ADB& pg,
const ADB& rv,
const std::vector<PhasePresence>& cond,
const Cells& cells) const
{
if (!phase_usage_.phase_used[Gas]) {
OPM_THROW(std::runtime_error, "Cannot call muGas(): gas phase not present.");
}
const int n = cells.size();
assert(pg.size() == n);
V b(n);
V dbdp(n);
V dbdr(n);
props_[phase_usage_.phase_pos[Gas]]->b(n, pg.value().data(), rv.value().data(), &cond[0],
b.data(), dbdp.data(), dbdr.data());
ADB::M dbdp_diag = spdiag(dbdp);
@ -541,7 +601,7 @@ namespace Opm
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
V BlackoilPropsAdFromDeck::rsMax(const V& po,
V BlackoilPropsAdFromDeck::rsSat(const V& po,
const Cells& cells) const
{
if (!phase_usage_.phase_used[Oil]) {
@ -551,7 +611,7 @@ namespace Opm
assert(po.size() == n);
V rbub(n);
V drbubdp(n);
props_[Oil]->rbub(n, po.data(), rbub.data(), drbubdp.data());
props_[Oil]->rsSat(n, po.data(), rbub.data(), drbubdp.data());
return rbub;
}
@ -559,7 +619,7 @@ namespace Opm
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
ADB BlackoilPropsAdFromDeck::rsMax(const ADB& po,
ADB BlackoilPropsAdFromDeck::rsSat(const ADB& po,
const Cells& cells) const
{
if (!phase_usage_.phase_used[Oil]) {
@ -569,7 +629,7 @@ namespace Opm
assert(po.size() == n);
V rbub(n);
V drbubdp(n);
props_[Oil]->rbub(n, po.value().data(), rbub.data(), drbubdp.data());
props_[Oil]->rsSat(n, po.value().data(), rbub.data(), drbubdp.data());
ADB::M drbubdp_diag = spdiag(drbubdp);
const int num_blocks = po.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
@ -579,6 +639,50 @@ namespace Opm
return ADB::function(rbub, jacs);
}
// ------ Condensation curve ------
/// Condensation curve for Rv as function of oil pressure.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
V BlackoilPropsAdFromDeck::rvSat(const V& po,
const Cells& cells) const
{
if (!phase_usage_.phase_used[Gas]) {
OPM_THROW(std::runtime_error, "Cannot call rvMax(): gas phase not present.");
}
const int n = cells.size();
assert(po.size() == n);
V rv(n);
V drvdp(n);
props_[Oil]->rvSat(n, po.data(), rv.data(), drvdp.data());
return rv;
}
/// Condensation curve for Rv as function of oil pressure.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
ADB BlackoilPropsAdFromDeck::rvSat(const ADB& po,
const Cells& cells) const
{
if (!phase_usage_.phase_used[Gas]) {
OPM_THROW(std::runtime_error, "Cannot call rvMax(): gas phase not present.");
}
const int n = cells.size();
assert(po.size() == n);
V rv(n);
V drvdp(n);
props_[Oil]->rvSat(n, po.value().data(), rv.data(), drvdp.data());
ADB::M drvdp_diag = spdiag(drvdp);
const int num_blocks = po.numBlocks();
std::vector<ADB::M> jacs(num_blocks);
for (int block = 0; block < num_blocks; ++block) {
jacs[block] = drvdp_diag * po.derivative()[block];
}
return ADB::function(rv, jacs);
}
// ------ Relative permeability ------
/// Relative permeabilities for all phases.

40
opm/autodiff/BlackoilPropsAdFromDeck.hpp
View File

@ -178,6 +178,17 @@ namespace Opm
V bGas(const V& pg,
const Cells& cells) const;
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
V bGas(const V& pg,
const V& rv,
const std::vector<PhasePresence>& cond,
const Cells& cells) const;
/// Water formation volume factor.
/// \param[in] pw Array of n water pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
@ -203,6 +214,16 @@ namespace Opm
ADB bGas(const ADB& pg,
const Cells& cells) const;
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
ADB bGas(const ADB& pg,
const ADB& rv,
const std::vector<PhasePresence>& cond,
const Cells& cells) const;
// ------ Rs bubble point curve ------
@ -210,16 +231,31 @@ namespace Opm
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
V rsMax(const V& po,
V rsSat(const V& po,
const Cells& cells) const;
/// Bubble point curve for Rs as function of oil pressure.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
ADB rsMax(const ADB& po,
ADB rsSat(const ADB& po,
const Cells& cells) const;
// ------ Rv condensation curve ------
/// Condensation curve for Rv as function of oil pressure.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
V rvSat(const V& po,
const Cells& cells) const;
/// Condensation curve for Rv as function of oil pressure.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
ADB rvSat(const ADB& po,
const Cells& cells) const;
// ------ Relative permeability ------

45
opm/autodiff/BlackoilPropsAdInterface.hpp
View File

@ -176,6 +176,18 @@ namespace Opm
V bGas(const V& pg,
const Cells& cells) const = 0;
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
virtual
V bGas(const V& pg,
const V& rv,
const std::vector<PhasePresence>& cond,
const Cells& cells) const = 0;
/// Water formation volume factor.
/// \param[in] pw Array of n water pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
@ -204,6 +216,17 @@ namespace Opm
ADB bGas(const ADB& pg,
const Cells& cells) const = 0;
/// Gas formation volume factor.
/// \param[in] pg Array of n gas pressure values.
/// \param[in] rv Array of n vapor oil/gas ratio
/// \param[in] cond Array of n objects, each specifying which phases are present with non-zero saturation in a cell.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n formation volume factor values.
virtual
ADB bGas(const ADB& pg,
const ADB& rv,
const std::vector<PhasePresence>& cond,
const Cells& cells) const = 0;
// ------ Rs bubble point curve ------
@ -212,7 +235,7 @@ namespace Opm
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
virtual
V rsMax(const V& po,
V rsSat(const V& po,
const Cells& cells) const = 0;
/// Bubble point curve for Rs as function of oil pressure.
@ -220,7 +243,25 @@ namespace Opm
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
virtual
ADB rsMax(const ADB& po,
ADB rsSat(const ADB& po,
const Cells& cells) const = 0;
// ------ Rs bubble point curve ------
/// Bubble point curve for Rs as function of oil pressure.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
virtual
V rvSat(const V& po,
const Cells& cells) const = 0;
/// Bubble point curve for Rs as function of oil pressure.
/// \param[in] po Array of n oil pressure values.
/// \param[in] cells Array of n cell indices to be associated with the pressure values.
/// \return Array of n bubble point values for Rs.
virtual
ADB rvSat(const ADB& po,
const Cells& cells) const = 0;
// ------ Relative permeability ------