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

d2EffectiveSaturation()

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 31 of file PorousFlowRogersStallybrassClements.C.

Referenced by PorousFlowCapillaryPressureRSC::d2EffectiveSaturation(), and TEST().

{
  Real x = (pc - shift) / scale;
  Real ex = std::exp(x);
  return (0.75 * ex * ex * std::pow(1.0 + ex, -2.5) - 0.5 * ex * std::pow(1.0 + ex, -1.5)) / scale /
         scale;
}

dEffectiveSaturation()

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 23 of file PorousFlowRogersStallybrassClements.C.

Referenced by PorousFlowCapillaryPressureRSC::dEffectiveSaturation(), and TEST().

{
  Real x = (pc - shift) / scale;
  Real ex = std::exp(x);
  return -0.5 * ex * std::pow(1.0 + ex, -1.5) / scale;
}

effectiveSaturation()

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 15 of file PorousFlowRogersStallybrassClements.C.

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

{
  Real x = (pc - shift) / scale;
  Real ex = std::exp(x);
  return std::pow(1.0 + ex, -0.5);
}