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
 pc capillary pressure shift RSC's shift parameter scale RSC's scale parameter
Returns
second derivative of effective saturation wrt capillary pressure

Definition at line 29 of file PorousFlowRogersStallybrassClements.C.

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
 pc capillary pressure shift RSC's shift parameter scale RSC's scale parameter
Returns
derivative of effective saturation wrt capillary pressure

Definition at line 21 of file PorousFlowRogersStallybrassClements.C.

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
 pc capillary pressure shift RSC's shift parameter scale RSC's scale parameter
Returns
effective saturation

Definition at line 13 of file PorousFlowRogersStallybrassClements.C.

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)