van Genuchten form of capillary pressure. More...

#include <PorousFlowCapillaryPressureVG.h>

Inheritance diagram for PorousFlowCapillaryPressureVG:

Public Member Functions
	PorousFlowCapillaryPressureVG (const InputParameters &parameters)

virtual Real	capillaryPressureCurve (Real saturation, unsigned qp=0) const override
	Raw capillary pressure curve (does not include logarithmic extension) More...

virtual Real	dCapillaryPressureCurve (Real saturation, unsigned qp=0) const override
	Derivative of raw capillary pressure wrt true saturation. More...

virtual Real	d2CapillaryPressureCurve (Real saturation, unsigned qp=0) const override
	Second derivative of raw capillary pressure wrt true saturation. More...

virtual Real	effectiveSaturation (Real pc, unsigned qp=0) const override
	Effective saturation as a function of capillary pressure. More...

virtual Real	dEffectiveSaturation (Real pc, unsigned qp=0) const override
	Derivative of effective saturation wrt capillary pressure. More...

virtual Real	d2EffectiveSaturation (Real pc, unsigned qp=0) const override
	Second derivative of effective saturation wrt capillary pressure. More...

virtual void	initialize () final

virtual void	initialSetup () override

virtual Real	capillaryPressure (Real saturation, unsigned qp=0) const
	Capillary pressure is calculated as a function of true saturation. More...

virtual Real	dCapillaryPressure (Real saturation, unsigned qp=0) const
	Derivative of capillary pressure wrt true saturation. More...

virtual Real	d2CapillaryPressure (Real saturation, unsigned qp=0) const
	Second derivative of capillary pressure wrt true saturation. More...

Protected Member Functions
Real	effectiveSaturationFromSaturation (Real saturation) const
	Effective saturation of liquid phase given liquid saturation and residual liquid saturation. More...

Real	extensionSaturation () const
	Calculates the saturation where the logarithmic extension to capillary pressure meets the raw curve using Newton's method. More...

Real	interceptFunction (Real s) const
	Calculates the saturation where the logarithmic extension to capillary pressure at low saturation. More...

Real	interceptFunctionDeriv (Real s) const
	Calculates the saturation where the logarithmic extension to capillary pressure at low saturation. More...

Real	capillaryPressureLogExt (Real s) const
	The capillary pressure in the logarithmic extension This implementation assumes capillary-pressure is a function of saturation only, and not any other quad-point dependent quantities. More...

Real	dCapillaryPressureLogExt (Real s) const
	The derivative of capillary pressure in the logarithmic extension This implementation assumes capillary-pressure is a function of saturation only, and not any other quad-point dependent quantities. More...

Real	d2CapillaryPressureLogExt (Real s) const
	The second derivative of capillary pressure in the logarithmic extension This implementation assumes capillary-pressure is a function of saturation only, and not any other quad-point dependent quantities. More...

Protected Attributes
const Real	_m
	van Genuchten exponent m More...

const Real	_alpha
	van Genuchten capillary coefficient alpha More...

const Real	_s_scale
	Capillary pressure = f(Seff * s_scale) - pc_sscale, where f is the van Genuchten function. For almost all simulations s_scale=1 will be appropriate. More...

const Real	_pc_sscale
	pc_sscale = f(s_scale), where f is the van Genuchten function More...

const Real	_sat_lr
	Liquid residual saturation. More...

const Real	_dseff_ds
	Derivative of effective saturation with respect to saturation. More...

bool	_log_ext
	Flag to use a logarithmic extension for low saturation. More...

const Real	_pc_max
	Maximum capillary pressure (Pa). Note: must be <= 0. More...

Real	_sat_ext
	Saturation where the logarithmic extension meets the raw curve This is computed only for qp=0. More...

Real	_pc_ext
	Capillary pressure where the extension meets the raw curve. More...

Real	_slope_ext
	Gradient of the logarithmic extension This is computed only for qp=0. More...

const Real	_log10
	log(10) More...

Detailed Description

van Genuchten form of capillary pressure.

From van Genuchten, M. Th., A closed for equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc., 44, 892-898 (1980)

Definition at line 26 of file PorousFlowCapillaryPressureVG.h.

Constructor & Destructor Documentation

◆ PorousFlowCapillaryPressureVG()

PorousFlowCapillaryPressureVG::PorousFlowCapillaryPressureVG ( const InputParameters & parameters )

Definition at line 39 of file PorousFlowCapillaryPressureVG.C.

   : PorousFlowCapillaryPressure(parameters),
     _m(getParam<Real>("m")),
     _alpha(getParam<Real>("alpha")),
     _s_scale(getParam<Real>("s_scale")),
     _pc_sscale(PorousFlowVanGenuchten::capillaryPressure(_s_scale, _alpha, _m, _pc_max))
 {
 }

Member Function Documentation

◆ capillaryPressure()

Real PorousFlowCapillaryPressure::capillaryPressure	(	Real	saturation,
		unsigned	qp = `0`
	)		const

virtualinherited

Capillary pressure is calculated as a function of true saturation.

Note that this method includes the ability to use a logarithmic extension at low saturation.

Parameters

saturation	true saturation
qp	quadpoint to use (when capillary-pressure depends on coupled variables, not just saturation)

Returns: capillary pressure (Pa)

Definition at line 64 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlow2PhasePS::buildQpPPSS(), PorousFlowCapillaryPressure::initialSetup(), PorousFlowWaterNCG::thermophysicalProperties(), PorousFlowBrineCO2::thermophysicalProperties(), PorousFlowWaterNCG::totalMassFraction(), and PorousFlowBrineCO2::totalMassFraction().

 {
   if (_log_ext && saturation < _sat_ext)
     return capillaryPressureLogExt(saturation);
   else
     return capillaryPressureCurve(saturation, qp);
 }

◆ capillaryPressureCurve()

Real PorousFlowCapillaryPressureVG::capillaryPressureCurve	(	Real	saturation,
		unsigned	qp = `0`
	)		const

overridevirtual

Raw capillary pressure curve (does not include logarithmic extension)

Parameters

saturation true saturation

Returns: capillary pressure (Pa)

Implements PorousFlowCapillaryPressure.

Definition at line 49 of file PorousFlowCapillaryPressureVG.C.

 {
   const Real seff = effectiveSaturationFromSaturation(saturation) * _s_scale;
   return PorousFlowVanGenuchten::capillaryPressure(seff, _alpha, _m, _pc_max) - _pc_sscale;
 }

◆ capillaryPressureLogExt()

Real PorousFlowCapillaryPressure::capillaryPressureLogExt ( Real s ) const

protectedinherited

The capillary pressure in the logarithmic extension This implementation assumes capillary-pressure is a function of saturation only, and not any other quad-point dependent quantities.

Parameters

s	liquid saturation

Returns: capillary pressure in logarithmic extension

Definition at line 97 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::capillaryPressure().

 {
   return _pc_ext * std::pow(10.0, _slope_ext * (saturation - _sat_ext));
 }

◆ d2CapillaryPressure()

Real PorousFlowCapillaryPressure::d2CapillaryPressure	(	Real	saturation,
		unsigned	qp = `0`
	)		const

virtualinherited

Second derivative of capillary pressure wrt true saturation.

Parameters

saturation	true saturation
qp	quadpoint to use (when capillary-pressure depends on coupled variables, not just saturation)

Returns: second derivative of capillary pressure with respect to true saturation

Definition at line 82 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlow2PhasePS::computeQpProperties(), and PorousFlowFluidState::computeQpProperties().

 {
   if (_log_ext && saturation < _sat_ext)
     return d2CapillaryPressureLogExt(saturation);
   else
     return d2CapillaryPressureCurve(saturation, qp);
 }

◆ d2CapillaryPressureCurve()

Real PorousFlowCapillaryPressureVG::d2CapillaryPressureCurve	(	Real	saturation,
		unsigned	qp = `0`
	)		const

overridevirtual

Second derivative of raw capillary pressure wrt true saturation.

Parameters

saturation true saturation

Returns: second derivative of capillary pressure with respect to true saturation

Implements PorousFlowCapillaryPressure.

Definition at line 64 of file PorousFlowCapillaryPressureVG.C.

 {
   const Real seff = effectiveSaturationFromSaturation(saturation) * _s_scale;
   return PorousFlowVanGenuchten::d2CapillaryPressure(seff, _alpha, _m, _pc_max) * _dseff_ds *
          _dseff_ds * _s_scale * _s_scale;
 }

◆ d2CapillaryPressureLogExt()

Real PorousFlowCapillaryPressure::d2CapillaryPressureLogExt ( Real s ) const

protectedinherited

The second derivative of capillary pressure in the logarithmic extension This implementation assumes capillary-pressure is a function of saturation only, and not any other quad-point dependent quantities.

Parameters

s	liquid saturation

Returns: second derivative of capillary pressure in logarithmic extension

Definition at line 109 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::d2CapillaryPressure().

 {
   return _pc_ext * _slope_ext * _slope_ext * _log10 * _log10 *
          std::pow(10.0, _slope_ext * (saturation - _sat_ext));
 }

◆ d2EffectiveSaturation()

Real PorousFlowCapillaryPressureVG::d2EffectiveSaturation	(	Real	pc,
		unsigned	qp = `0`
	)		const

overridevirtual

Second derivative of effective saturation wrt capillary pressure.

Parameters

pc	capillary pressure
qp	quadpoint to use (when effective saturation depends on coupled variables, not just pc)

Returns: second derivative of effective saturation wrt capillary pressure

Implements PorousFlowCapillaryPressure.

Definition at line 86 of file PorousFlowCapillaryPressureVG.C.

 {
   return (1.0 / _s_scale) *
          PorousFlowVanGenuchten::d2EffectiveSaturation(pc - _pc_sscale, _alpha, _m);
 }

◆ dCapillaryPressure()

Real PorousFlowCapillaryPressure::dCapillaryPressure	(	Real	saturation,
		unsigned	qp = `0`
	)		const

virtualinherited

Derivative of capillary pressure wrt true saturation.

Parameters

saturation	true saturation
qp	quadpoint to use (when capillary-pressure depends on coupled variables, not just saturation)

Returns: derivative of capillary pressure with respect to true saturation

Definition at line 73 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlow2PhasePS::computeQpProperties(), and PorousFlowFluidState::computeQpProperties().

 {
   if (_log_ext && saturation < _sat_ext)
     return dCapillaryPressureLogExt(saturation);
   else
     return dCapillaryPressureCurve(saturation, qp);
 }

◆ dCapillaryPressureCurve()

Real PorousFlowCapillaryPressureVG::dCapillaryPressureCurve	(	Real	saturation,
		unsigned	qp = `0`
	)		const

overridevirtual

Derivative of raw capillary pressure wrt true saturation.

Parameters

saturation true saturation

Returns: derivative of capillary pressure with respect to true saturation

Implements PorousFlowCapillaryPressure.

Definition at line 56 of file PorousFlowCapillaryPressureVG.C.

 {
   const Real seff = effectiveSaturationFromSaturation(saturation) * _s_scale;
   return PorousFlowVanGenuchten::dCapillaryPressure(seff, _alpha, _m, _pc_max) * _dseff_ds *
          _s_scale;
 }

◆ dCapillaryPressureLogExt()

Real PorousFlowCapillaryPressure::dCapillaryPressureLogExt ( Real s ) const

protectedinherited

The derivative of capillary pressure in the logarithmic extension This implementation assumes capillary-pressure is a function of saturation only, and not any other quad-point dependent quantities.

Parameters

s	liquid saturation

Returns: derivative of capillary pressure in logarithmic extension

Definition at line 103 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::dCapillaryPressure().

 {
   return _pc_ext * _slope_ext * _log10 * std::pow(10.0, _slope_ext * (saturation - _sat_ext));
 }

◆ dEffectiveSaturation()

Real PorousFlowCapillaryPressureVG::dEffectiveSaturation	(	Real	pc,
		unsigned	qp = `0`
	)		const

overridevirtual

Derivative of effective saturation wrt capillary pressure.

Parameters

pc	capillary pressure (Pa)
qp	quadpoint to use (when effective saturation depends on coupled variables, not just pc)

Returns: derivative of effective saturation wrt capillary pressure

Implements PorousFlowCapillaryPressure.

Definition at line 79 of file PorousFlowCapillaryPressureVG.C.

 {
   return (1.0 / _s_scale) *
          PorousFlowVanGenuchten::dEffectiveSaturation(pc - _pc_sscale, _alpha, _m);
 }

◆ effectiveSaturation()

Real PorousFlowCapillaryPressureVG::effectiveSaturation	(	Real	pc,
		unsigned	qp = `0`
	)		const

overridevirtual

Effective saturation as a function of capillary pressure.

Parameters

pc	capillary pressure (Pa)
qp	quadpoint to use (when effective saturation depends on coupled variables, not just pc)

Returns: effective saturation

Implements PorousFlowCapillaryPressure.

Definition at line 72 of file PorousFlowCapillaryPressureVG.C.

 {
   return (1.0 / _s_scale) *
          PorousFlowVanGenuchten::effectiveSaturation(pc - _pc_sscale, _alpha, _m);
 }

◆ effectiveSaturationFromSaturation()

Real PorousFlowCapillaryPressure::effectiveSaturationFromSaturation ( Real saturation ) const

protectedinherited

Effective saturation of liquid phase given liquid saturation and residual liquid saturation.

Note: not to be mistaken with effectiveSaturation(pc) which is a function of capillary pressure.

Parameters

saturation true saturation

Returns: effective saturation

Definition at line 91 of file PorousFlowCapillaryPressure.C.

Referenced by capillaryPressureCurve(), PorousFlowCapillaryPressureBC::capillaryPressureCurve(), d2CapillaryPressureCurve(), PorousFlowCapillaryPressureBC::d2CapillaryPressureCurve(), dCapillaryPressureCurve(), and PorousFlowCapillaryPressureBC::dCapillaryPressureCurve().

 {
   return (saturation - _sat_lr) / (1.0 - _sat_lr);
 }

◆ extensionSaturation()

Real PorousFlowCapillaryPressure::extensionSaturation ( ) const

protectedinherited

Calculates the saturation where the logarithmic extension to capillary pressure meets the raw curve using Newton's method.

This implementation assumes capillary-pressure is a function of saturation only, and not any other quad-point dependent quantities

Returns: saturation where logarithmic extension begins

Definition at line 116 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::initialSetup().

 {
   // Initial guess for saturation where extension matches curve
   Real sat = _sat_lr + 0.01;
 
   // Calculate the saturation where the extension matches the derivative of the
   // raw capillary pressure curve
   const unsigned int max_its = 20;
   const Real nr_tol = 1.0e-8;
   unsigned int iter = 0;
 
   while (std::abs(interceptFunction(sat)) > nr_tol)
   {
     sat = sat - interceptFunction(sat) / interceptFunctionDeriv(sat);
 
     iter++;
     if (iter > max_its)
       break;
   }
 
   return sat;
 }

◆ initialize()

virtual void PorousFlowCapillaryPressure::initialize ( )

inlinefinalvirtualinherited

Definition at line 45 of file PorousFlowCapillaryPressure.h.

45 {};

◆ initialSetup()

void PorousFlowCapillaryPressure::initialSetup ( )

overridevirtualinherited

Definition at line 51 of file PorousFlowCapillaryPressure.C.

 {
   // If _log_ext = true, calculate the saturation where the the logarithmic
   // extension meets the raw capillary pressure curve.
   if (_log_ext)
   {
     _sat_ext = extensionSaturation();
     _pc_ext = capillaryPressure(_sat_ext);
     _slope_ext = (std::log10(_pc_ext) - std::log10(_pc_max)) / _sat_ext;
   }
 }

◆ interceptFunction()

Real PorousFlowCapillaryPressure::interceptFunction ( Real s ) const

protectedinherited

Calculates the saturation where the logarithmic extension to capillary pressure at low saturation.

This is computed for qp=0 only. This implementation assumes capillary-pressure is a function of saturation only, and not any other quad-point dependent quantities

Parameters

s	effective saturation

Returns: capillary pressure function in the logarithmic extension

Definition at line 140 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::extensionSaturation().

 {
   Real pc = capillaryPressureCurve(saturation);
   Real dpc = dCapillaryPressureCurve(saturation);
 
   return std::log10(pc) - saturation * dpc / (_log10 * pc) - std::log10(_pc_max);
 }

◆ interceptFunctionDeriv()

Real PorousFlowCapillaryPressure::interceptFunctionDeriv ( Real s ) const

protectedinherited

Calculates the saturation where the logarithmic extension to capillary pressure at low saturation.

This implementation assumes capillary-pressure is a function of saturation only, and not any other quad-point dependent quantities

Parameters

s	effective saturation

Returns: derivative of logarithmic extension function

Definition at line 149 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowCapillaryPressure::extensionSaturation().

 {
   Real pc = capillaryPressureCurve(saturation);
   Real dpc = dCapillaryPressureCurve(saturation);
   Real d2pc = d2CapillaryPressureCurve(saturation);
 
   return saturation * (dpc * dpc / pc - d2pc) / (_log10 * pc);
 }