PorousFlowBrooksCorey Namespace Reference

Brooks-Corey effective saturation, capillary pressure and relative permeability functions. More...

Functions
Real	effectiveSaturation (Real pc, Real pe, Real lambda)
	Effective saturation as a function of capillary pressure Note: seff = 1 for p >= 0.
Real	dEffectiveSaturation (Real pc, Real pe, Real lambda)
	Derivative of effective saturation wrt porepressure.
Real	d2EffectiveSaturation (Real pc, Real pe, Real lambda)
	Second derivative of effective saturation wrt porepressure.
Real	capillaryPressure (Real seff, Real pe, Real lambda, Real pc_max)
	Capillary pressure as a function of effective saturation.
Real	dCapillaryPressure (Real seff, Real pe, Real lambda, Real pc_max)
	Derivative of capillary pressure wrt effective saturation.
Real	d2CapillaryPressure (Real seff, Real pe, Real lambda, Real pc_max)
	Second derivative of capillary pressure wrt effective saturation.
template<typename T >
T	relativePermeabilityW (const T &seff, Real lambda)
	Relative permeability of the wetting phase as a function of effective saturation.
Real	dRelativePermeabilityW (Real seff, Real lambda)
	Derivative of relative permeability of the wetting phase wrt to effective saturation.
template<typename T >
T	relativePermeabilityNW (const T &seff, Real lambda)
	Relative permeability of the non-wetting phase as a function of effective saturation.
Real	dRelativePermeabilityNW (Real seff, Real lambda)
	Derivative of relative permeability of the non-wetting phase wrt to effective saturation.

Detailed Description

Brooks-Corey effective saturation, capillary pressure and relative permeability functions.

Note: capillary pressure and relative permeability are functions of effective saturation. The derivatives are therefore given wrt effective saturation. These derivatives must be multiplied by the derivative of effective saturation wrt the true saturation in objects using these relations.

From Brooks, R. H. and A. T. Corey (1966), Properties of porous media affecting fluid flow, J. Irrig. Drain. Div., 92, 61-88

Function Documentation

capillaryPressure()

Real PorousFlowBrooksCorey::capillaryPressure	(	Real	seff,
		Real	pe,
		Real	lambda,
		Real	pc_max
	)

Capillary pressure as a function of effective saturation.

Parameters

seff	effective saturation
pe	threshold entry pressure
lambda	Brooks-Corey exponent
pc_max	maximum capillary pressure (Pa)

Returns

capillary pressure (Pa)

Definition at line 42 of file PorousFlowBrooksCorey.C.

{
  if (seff >= 1.0)
    return pe;
  else if (seff <= 0.0)
    return pc_max;
  else
    return std::min(pe * std::pow(seff, -1.0 / lambda), pc_max);
}

Referenced by PorousFlowCapillaryPressureBC::capillaryPressureCurve(), d2CapillaryPressure(), dCapillaryPressure(), TEST(), and TEST().

d2CapillaryPressure()

Real PorousFlowBrooksCorey::d2CapillaryPressure	(	Real	seff,
		Real	pe,
		Real	lambda,
		Real	pc_max
	)

Second derivative of capillary pressure wrt effective saturation.

Parameters

seff	effective saturation
pe	threshold entry pressure
lambda	Brooks-Corey exponent
pc_max	maximum capillary pressure (Pa)

Returns

second derivative of capillary pressure wrt effective saturation

Definition at line 68 of file PorousFlowBrooksCorey.C.

{
  if (seff <= 0.0 || seff > 1.0)
    return 0.0;
  else
  {
    // Return 0 if pc > pc_max
    if (capillaryPressure(seff, pe, lambda, pc_max) >= pc_max)
      return 0.0;
    else
      return (lambda + 1.0) * pe * std::pow(seff, -1.0 / lambda - 2.0) / lambda / lambda;
  }
}

Referenced by PorousFlowCapillaryPressureBC::d2CapillaryPressureCurve(), and TEST().

d2EffectiveSaturation()

Real PorousFlowBrooksCorey::d2EffectiveSaturation	(	Real	pc,
		Real	pe,
		Real	lambda
	)

Second derivative of effective saturation wrt porepressure.

Parameters

pc	capillary pressure
pe	threshold entry pressure
lambda	Brooks-Corey exponent

Returns

second derivative of effective saturation wrt porepressure

Definition at line 33 of file PorousFlowBrooksCorey.C.

{
  if (pc < pe)
    return 0.0;
  else
    return lambda * (lambda + 1.0) * std::pow(pc / pe, -lambda - 2.0) / pe / pe;
}

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

dCapillaryPressure()

Real PorousFlowBrooksCorey::dCapillaryPressure	(	Real	seff,
		Real	pe,
		Real	lambda,
		Real	pc_max
	)

Derivative of capillary pressure wrt effective saturation.

Parameters

seff	effective saturation
pe	threshold entry pressure
lambda	Brooks-Corey exponent
pc_max	maximum capillary pressure (Pa)

Returns

derivative of capillary pressure wrt effective saturation

Definition at line 53 of file PorousFlowBrooksCorey.C.

{
  if (seff <= 0.0 || seff > 1.0)
    return 0.0;
  else
  {
    // Return 0 if pc > pc_max
    if (capillaryPressure(seff, pe, lambda, pc_max) >= pc_max)
      return 0.0;
    else
      return -pe * std::pow(seff, -1.0 / lambda - 1.0) / lambda;
  }
}

Referenced by PorousFlowCapillaryPressureBC::dCapillaryPressureCurve(), TEST(), and TEST().

dEffectiveSaturation()

Real PorousFlowBrooksCorey::dEffectiveSaturation	(	Real	pc,
		Real	pe,
		Real	lambda
	)

Derivative of effective saturation wrt porepressure.

Parameters

pc	capillary pressure
pe	threshold entry pressure
lambda	Brooks-Corey exponent

Returns

derivative of effective saturation wrt porepressure

Definition at line 24 of file PorousFlowBrooksCorey.C.

{
  if (pc < pe)
    return 0.0;
  else
    return -lambda * std::pow(pc / pe, -lambda - 1.0) / pe;
}

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

dRelativePermeabilityNW()

Real PorousFlowBrooksCorey::dRelativePermeabilityNW	(	Real	seff,
		Real	lambda
	)

Derivative of relative permeability of the non-wetting phase wrt to effective saturation.

Parameters

seff	effective saturation
lambda	Brooks-Corey exponent

Returns

derivative of relative permeability wrt effective saturation

Definition at line 93 of file PorousFlowBrooksCorey.C.

{
  // Guard against division by zero
  if (seff <= 0.0 || seff >= 1.0)
    return 0.0;
 
  return seff * (2.0 + (seff * (2.0 + 3.0 * lambda) - 2.0 * lambda) *
                           std::pow(1.0 - seff, 2.0 / lambda) / lambda);
}

Referenced by PorousFlowRelativePermeabilityBCTempl< is_ad >::dRelativePermeability(), TEST(), and TEST().

dRelativePermeabilityW()

Real PorousFlowBrooksCorey::dRelativePermeabilityW	(	Real	seff,
		Real	lambda
	)

Derivative of relative permeability of the wetting phase wrt to effective saturation.

Parameters

seff	effective saturation
lambda	Brooks-Corey exponent

Returns

derivative of relative permeability wrt effective saturation

Definition at line 83 of file PorousFlowBrooksCorey.C.

{
  // Guard against division by zero
  if (seff <= 0.0 || seff >= 1.0)
    return 0.0;
 
  return (2.0 + 3.0 * lambda) * std::pow(seff, (2.0 + 2.0 * lambda) / lambda) / lambda;
}

Referenced by PorousFlowRelativePermeabilityBCTempl< is_ad >::dRelativePermeability(), TEST(), and TEST().

effectiveSaturation()

Real PorousFlowBrooksCorey::effectiveSaturation	(	Real	pc,
		Real	pe,
		Real	lambda
	)

Effective saturation as a function of capillary pressure Note: seff = 1 for p >= 0.

Parameters

pc	capillary pressure
pe	threshold entry pressure
lambda	Brooks-Corey exponent

Returns

effective saturation

Definition at line 15 of file PorousFlowBrooksCorey.C.

{
  if (pc < pe)
    return 1.0;
  else
    return std::pow(pc / pe, -lambda);
}

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

relativePermeabilityNW()

template<typename T >

T PorousFlowBrooksCorey::relativePermeabilityNW	(	const T &	seff,
		Real	lambda
	)

Relative permeability of the non-wetting phase as a function of effective saturation.

Parameters

seff	effective saturation
lambda	Brooks-Corey exponent

Returns

relative permeability

Definition at line 125 of file PorousFlowBrooksCorey.h.

{
  if (MetaPhysicL::raw_value(seff) <= 0.0)
    return 0.0;
  else if (MetaPhysicL::raw_value(seff) >= 1.0)
    return 1.0;
 
  using std::pow;
  return seff * seff * (1.0 - pow(1.0 - seff, (2.0 + lambda) / lambda));
}

Referenced by PorousFlowRelativePermeabilityBCTempl< is_ad >::relativePermeability(), TEST(), TEST(), and TEST().

relativePermeabilityW()

template<typename T >

T PorousFlowBrooksCorey::relativePermeabilityW	(	const T &	seff,
		Real	lambda
	)

Relative permeability of the wetting phase as a function of effective saturation.

Parameters

seff	effective saturation
lambda	Brooks-Corey exponent

Returns

relative permeability

Definition at line 98 of file PorousFlowBrooksCorey.h.

{
  if (MetaPhysicL::raw_value(seff) <= 0.0)
    return 0.0;
  else if (MetaPhysicL::raw_value(seff) >= 1.0)
    return 1.0;
 
  using std::pow;
  return pow(seff, (2.0 + 3.0 * lambda) / lambda);
}

Referenced by PorousFlowRelativePermeabilityBCTempl< is_ad >::relativePermeability(), TEST(), TEST(), and TEST().