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Functions
PorousFlowRogersStallybrassClements Namespace Reference

Rogers-Stallybrass-Clements version of effective saturation as a function of capillary pressure. More...

Functions

Real effectiveSaturation (Real pc, Real shift, Real scale)
 Effective saturation as a function of capillary pressure. More...
 
Real dEffectiveSaturation (Real pc, Real shift, Real scale)
 Derivative of effective saturation wrt capillary pressure. More...
 
Real d2EffectiveSaturation (Real pc, Real shift, Real scale)
 Second derivative of effective saturation wrt capillary pressure. More...
 

Detailed Description

Rogers-Stallybrass-Clements version of effective saturation as a function of capillary pressure.

valid for residual saturations = 0, and viscosityOil = 2*viscosityWater. (the "2" is important here!). C Rogers, MP Stallybrass and DL Clements "On two phase filtration under gravity and with boundary infiltration: application of a Backlund transformation" Nonlinear Analysis Theory Methods and Applications 7 (1983) 785–799.

Function Documentation

Real PorousFlowRogersStallybrassClements::d2EffectiveSaturation ( Real  pc,
Real  shift,
Real  scale 
)

Second derivative of effective saturation wrt capillary pressure.

Parameters
pccapillary pressure
shiftRSC's shift parameter
scaleRSC's scale parameter
Returns
second derivative of effective saturation wrt capillary pressure

Definition at line 29 of file PorousFlowRogersStallybrassClements.C.

Referenced by PorousFlowCapillaryPressureRSC::d2EffectiveSaturation(), and PorousFlow2PhasePP_RSC::d2EffectiveSaturation_dP2().

30 {
31  Real x = (pc - shift) / scale;
32  Real ex = std::exp(x);
33  return (0.75 * ex * ex * std::pow(1.0 + ex, -2.5) - 0.5 * ex * std::pow(1.0 + ex, -1.5)) / scale /
34  scale;
35 }
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real PorousFlowRogersStallybrassClements::dEffectiveSaturation ( Real  pc,
Real  shift,
Real  scale 
)

Derivative of effective saturation wrt capillary pressure.

Parameters
pccapillary pressure
shiftRSC's shift parameter
scaleRSC's scale parameter
Returns
derivative of effective saturation wrt capillary pressure

Definition at line 21 of file PorousFlowRogersStallybrassClements.C.

Referenced by PorousFlowCapillaryPressureRSC::dEffectiveSaturation(), and PorousFlow2PhasePP_RSC::dEffectiveSaturation_dP().

22 {
23  Real x = (pc - shift) / scale;
24  Real ex = std::exp(x);
25  return -0.5 * ex * std::pow(1.0 + ex, -1.5) / scale;
26 }
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real PorousFlowRogersStallybrassClements::effectiveSaturation ( Real  pc,
Real  shift,
Real  scale 
)

Effective saturation as a function of capillary pressure.

Parameters
pccapillary pressure
shiftRSC's shift parameter
scaleRSC's scale parameter
Returns
effective saturation

Definition at line 13 of file PorousFlowRogersStallybrassClements.C.

Referenced by PorousFlowCapillaryPressureRSC::effectiveSaturation(), and PorousFlow2PhasePP_RSC::effectiveSaturation().

14 {
15  Real x = (pc - shift) / scale;
16  Real ex = std::exp(x);
17  return std::pow(1.0 + ex, -0.5);
18 }
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)