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PorousFlowCapillaryPressure Class Referenceabstract

Base class for capillary pressure for multiphase flow in porous media. More...

#include <PorousFlowCapillaryPressure.h>

Inheritance diagram for PorousFlowCapillaryPressure:
[legend]

Public Member Functions

 PorousFlowCapillaryPressure (const InputParameters &parameters)
 
virtual void initialize () final
 
virtual void execute () final
 
virtual void finalize () final
 
virtual void initialSetup () override
 
virtual Real capillaryPressure (Real saturation) const
 Capillary pressure is calculated as a function of true saturation. More...
 
virtual Real dCapillaryPressure (Real saturation) const
 Derivative of capillary pressure wrt true saturation. More...
 
virtual Real d2CapillaryPressure (Real saturation) const
 Second derivative of capillary pressure wrt true saturation. More...
 
virtual Real effectiveSaturation (Real pc) const =0
 Effective saturation as a function of capillary pressure. More...
 
virtual Real dEffectiveSaturation (Real pc) const =0
 Derivative of effective saturation wrt capillary pressure. More...
 
virtual Real d2EffectiveSaturation (Real pc) const =0
 Second derivative of effective saturation wrt capillary pressure. 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. More...
 
Real dCapillaryPressureLogExt (Real s) const
 The derivative of capillary pressure in the logarithmic extension. More...
 
Real d2CapillaryPressureLogExt (Real s) const
 The second derivative of capillary pressure in the logarithmic extension. More...
 
virtual Real capillaryPressureCurve (Real saturation) const =0
 Raw capillary pressure curve (does not include logarithmic extension) More...
 
virtual Real dCapillaryPressureCurve (Real saturation) const =0
 Derivative of raw capillary pressure wrt true saturation. More...
 
virtual Real d2CapillaryPressureCurve (Real saturation) const =0
 Second derivative of raw capillary pressure wrt true saturation. More...
 

Protected Attributes

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. More...
 
Real _pc_ext
 Capillary pressure where the extension meets the raw curve. More...
 
Real _slope_ext
 Gradient of the logarithmic extension. More...
 
const Real _log10
 log(10) More...
 

Detailed Description

Base class for capillary pressure for multiphase flow in porous media.

To implement an effective saturation formulation, override effectiveSaturation() and derivatives. To implement a capillary pressure curve that will include the logarithmic extension, override capillaryPressureCurve() and derivatives.

Note: Capillary pressure is calculated as a function of true saturation, not effective saturation (saturation minus residual). Derivatives are returned wrt true saturation, so no scaling of them is required in objects using these methods.

Includes an optional logarithmic extension in the low saturation region where capillary pressure can go to infinity as saturation tends to 0. Calculation of logarithmic extension from Webb, A simple extension of two-phase characteristic curves to include the dry region, Water Resources Research 36, 1425-1430 (2000)

Definition at line 33 of file PorousFlowCapillaryPressure.h.

Constructor & Destructor Documentation

PorousFlowCapillaryPressure::PorousFlowCapillaryPressure ( const InputParameters &  parameters)

Definition at line 32 of file PorousFlowCapillaryPressure.C.

33  : GeneralUserObject(parameters),
34  _sat_lr(getParam<Real>("sat_lr")),
35  _dseff_ds(1.0 / (1.0 - _sat_lr)),
36  _log_ext(getParam<bool>("log_extension")),
37  _pc_max(getParam<Real>("pc_max")),
38  _sat_ext(0.0),
39  _pc_ext(0.0),
40  _slope_ext(0.0),
41  _log10(std::log(10.0))
42 {
43 }
Real _slope_ext
Gradient of the logarithmic extension.
const Real _pc_max
Maximum capillary pressure (Pa). Note: must be <= 0.
Real _pc_ext
Capillary pressure where the extension meets the raw curve.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
const Real _sat_lr
Liquid residual saturation.
bool _log_ext
Flag to use a logarithmic extension for low saturation.
const Real _dseff_ds
Derivative of effective saturation with respect to saturation.

Member Function Documentation

Real PorousFlowCapillaryPressure::capillaryPressure ( Real  saturation) const
virtual

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
saturationtrue saturation
Returns
capillary pressure (Pa)

Definition at line 59 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlow2PhasePS::capillaryPressure(), finalize(), initialSetup(), PorousFlowFluidStateWaterNCG::thermophysicalProperties(), and PorousFlowFluidStateBrineCO2::thermophysicalProperties().

60 {
61  if (_log_ext && saturation < _sat_ext)
63  else
65 }
Real capillaryPressureLogExt(Real s) const
The capillary pressure in the logarithmic extension.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
bool _log_ext
Flag to use a logarithmic extension for low saturation.
virtual Real capillaryPressureCurve(Real saturation) const =0
Raw capillary pressure curve (does not include logarithmic extension)
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
virtual Real PorousFlowCapillaryPressure::capillaryPressureCurve ( Real  saturation) const
protectedpure virtual

Raw capillary pressure curve (does not include logarithmic extension)

Parameters
saturationtrue saturation
Returns
capillary pressure (Pa)

Implemented in PorousFlowCapillaryPressureBC, PorousFlowCapillaryPressureVG, PorousFlowCapillaryPressureBW, PorousFlowCapillaryPressureConst, and PorousFlowCapillaryPressureRSC.

Referenced by capillaryPressure(), finalize(), interceptFunction(), and interceptFunctionDeriv().

Real PorousFlowCapillaryPressure::capillaryPressureLogExt ( Real  s) const
protected

The capillary pressure in the logarithmic extension.

Parameters
sliquid saturation
Returns
capillary pressure in logarithmic extension

Definition at line 92 of file PorousFlowCapillaryPressure.C.

Referenced by capillaryPressure(), and finalize().

93 {
94  return _pc_ext * std::pow(10.0, _slope_ext * (saturation - _sat_ext));
95 }
Real _slope_ext
Gradient of the logarithmic extension.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real _pc_ext
Capillary pressure where the extension meets the raw curve.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real PorousFlowCapillaryPressure::d2CapillaryPressure ( Real  saturation) const
virtual

Second derivative of capillary pressure wrt true saturation.

Parameters
saturationtrue saturation
Returns
second derivative of capillary pressure with respect to true saturation

Definition at line 77 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowFluidStateFlashBase::computeQpProperties(), PorousFlow2PhasePS::d2CapillaryPressure_dS2(), and finalize().

78 {
79  if (_log_ext && saturation < _sat_ext)
81  else
83 }
Real d2CapillaryPressureLogExt(Real s) const
The second derivative of capillary pressure in the logarithmic extension.
virtual Real d2CapillaryPressureCurve(Real saturation) const =0
Second derivative of raw capillary pressure wrt true saturation.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
bool _log_ext
Flag to use a logarithmic extension for low saturation.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
virtual Real PorousFlowCapillaryPressure::d2CapillaryPressureCurve ( Real  saturation) const
protectedpure virtual

Second derivative of raw capillary pressure wrt true saturation.

Parameters
saturationtrue saturation
Returns
second derivative of capillary pressure with respect to true saturation

Implemented in PorousFlowCapillaryPressureBC, PorousFlowCapillaryPressureVG, PorousFlowCapillaryPressureBW, PorousFlowCapillaryPressureConst, and PorousFlowCapillaryPressureRSC.

Referenced by d2CapillaryPressure(), finalize(), and interceptFunctionDeriv().

Real PorousFlowCapillaryPressure::d2CapillaryPressureLogExt ( Real  s) const
protected

The second derivative of capillary pressure in the logarithmic extension.

Parameters
sliquid saturation
Returns
second derivative of capillary pressure in logarithmic extension

Definition at line 104 of file PorousFlowCapillaryPressure.C.

Referenced by d2CapillaryPressure(), and finalize().

105 {
106  return _pc_ext * _slope_ext * _slope_ext * _log10 * _log10 *
107  std::pow(10.0, _slope_ext * (saturation - _sat_ext));
108 }
Real _slope_ext
Gradient of the logarithmic extension.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real _pc_ext
Capillary pressure where the extension meets the raw curve.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
virtual Real PorousFlowCapillaryPressure::d2EffectiveSaturation ( Real  pc) const
pure virtual

Second derivative of effective saturation wrt capillary pressure.

Parameters
pccapillary pressure
Returns
second derivative of effective saturation wrt capillary pressure

Implemented in PorousFlowCapillaryPressureBC, PorousFlowCapillaryPressureVG, PorousFlowCapillaryPressureBW, PorousFlowCapillaryPressureConst, and PorousFlowCapillaryPressureRSC.

Referenced by PorousFlow2PhasePP::d2EffectiveSaturation_dP2(), PorousFlow1PhaseP::d2EffectiveSaturation_dP2(), and finalize().

Real PorousFlowCapillaryPressure::dCapillaryPressure ( Real  saturation) const
virtual

Derivative of capillary pressure wrt true saturation.

Parameters
saturationtrue saturation
Returns
derivative of capillary pressure with respect to true saturation

Definition at line 68 of file PorousFlowCapillaryPressure.C.

Referenced by PorousFlowFluidStateFlashBase::computeQpProperties(), PorousFlow2PhasePS::dCapillaryPressure_dS(), and finalize().

69 {
70  if (_log_ext && saturation < _sat_ext)
72  else
74 }
virtual Real dCapillaryPressureCurve(Real saturation) const =0
Derivative of raw capillary pressure wrt true saturation.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
bool _log_ext
Flag to use a logarithmic extension for low saturation.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real dCapillaryPressureLogExt(Real s) const
The derivative of capillary pressure in the logarithmic extension.
virtual Real PorousFlowCapillaryPressure::dCapillaryPressureCurve ( Real  saturation) const
protectedpure virtual

Derivative of raw capillary pressure wrt true saturation.

Parameters
saturationtrue saturation
Returns
derivative of capillary pressure with respect to true saturation

Implemented in PorousFlowCapillaryPressureBC, PorousFlowCapillaryPressureVG, PorousFlowCapillaryPressureBW, PorousFlowCapillaryPressureConst, and PorousFlowCapillaryPressureRSC.

Referenced by dCapillaryPressure(), finalize(), interceptFunction(), and interceptFunctionDeriv().

Real PorousFlowCapillaryPressure::dCapillaryPressureLogExt ( Real  s) const
protected

The derivative of capillary pressure in the logarithmic extension.

Parameters
sliquid saturation
Returns
derivative of capillary pressure in logarithmic extension

Definition at line 98 of file PorousFlowCapillaryPressure.C.

Referenced by dCapillaryPressure(), and finalize().

99 {
100  return _pc_ext * _slope_ext * _log10 * std::pow(10.0, _slope_ext * (saturation - _sat_ext));
101 }
Real _slope_ext
Gradient of the logarithmic extension.
ExpressionBuilder::EBTerm pow(const ExpressionBuilder::EBTerm &left, T exponent)
Real _pc_ext
Capillary pressure where the extension meets the raw curve.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
virtual Real PorousFlowCapillaryPressure::dEffectiveSaturation ( Real  pc) const
pure virtual

Derivative of effective saturation wrt capillary pressure.

Parameters
pccapillary pressure (Pa)
Returns
derivative of effective saturation wrt capillary pressure

Implemented in PorousFlowCapillaryPressureBC, PorousFlowCapillaryPressureVG, PorousFlowCapillaryPressureBW, PorousFlowCapillaryPressureConst, and PorousFlowCapillaryPressureRSC.

Referenced by PorousFlow2PhasePP::dEffectiveSaturation_dP(), PorousFlow1PhaseP::dEffectiveSaturation_dP(), and finalize().

virtual Real PorousFlowCapillaryPressure::effectiveSaturation ( Real  pc) const
pure virtual

Effective saturation as a function of capillary pressure.

Parameters
pccapillary pressure (Pa)
Returns
effective saturation

Implemented in PorousFlowCapillaryPressureBC, PorousFlowCapillaryPressureVG, PorousFlowCapillaryPressureBW, PorousFlowCapillaryPressureConst, and PorousFlowCapillaryPressureRSC.

Referenced by PorousFlow2PhasePP::effectiveSaturation(), PorousFlow1PhaseP::effectiveSaturation(), and finalize().

Real PorousFlowCapillaryPressure::effectiveSaturationFromSaturation ( Real  saturation) const
protected

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
saturationtrue saturation
Returns
effective saturation

Definition at line 86 of file PorousFlowCapillaryPressure.C.

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

87 {
88  return (saturation - _sat_lr) / (1.0 - _sat_lr);
89 }
const Real _sat_lr
Liquid residual saturation.
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
virtual void PorousFlowCapillaryPressure::execute ( )
inlinefinalvirtual

Definition at line 39 of file PorousFlowCapillaryPressure.h.

39 {};
Real PorousFlowCapillaryPressure::extensionSaturation ( ) const
protected

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

Returns
saturation where logarithmic extension begins

Definition at line 111 of file PorousFlowCapillaryPressure.C.

Referenced by finalize(), and initialSetup().

112 {
113  // Initial guess for saturation where extension matches curve
114  Real sat = _sat_lr + 0.01;
115 
116  // Calculate the saturation where the extension matches the derivative of the
117  // raw capillary pressure curve
118  const unsigned int max_its = 20;
119  const Real nr_tol = 1.0e-8;
120  unsigned int iter = 0;
121 
122  while (std::abs(interceptFunction(sat)) > nr_tol)
123  {
124  sat = sat - interceptFunction(sat) / interceptFunctionDeriv(sat);
125 
126  iter++;
127  if (iter > max_its)
128  break;
129  }
130 
131  return sat;
132 }
Real interceptFunction(Real s) const
Calculates the saturation where the logarithmic extension to capillary pressure at low saturation...
const Real _sat_lr
Liquid residual saturation.
Real interceptFunctionDeriv(Real s) const
Calculates the saturation where the logarithmic extension to capillary pressure at low saturation...
virtual void PorousFlowCapillaryPressure::finalize ( )
inlinefinalvirtual

Definition at line 40 of file PorousFlowCapillaryPressure.h.

40 {};
virtual void PorousFlowCapillaryPressure::initialize ( )
inlinefinalvirtual

Definition at line 38 of file PorousFlowCapillaryPressure.h.

38 {};
void PorousFlowCapillaryPressure::initialSetup ( )
overridevirtual

Definition at line 46 of file PorousFlowCapillaryPressure.C.

Referenced by finalize().

47 {
48  // If _log_ext = true, calculate the saturation where the the logarithmic
49  // extension meets the raw capillary pressure curve.
50  if (_log_ext)
51  {
54  _slope_ext = (std::log10(_pc_ext) - std::log10(_pc_max)) / _sat_ext;
55  }
56 }
Real _slope_ext
Gradient of the logarithmic extension.
Real extensionSaturation() const
Calculates the saturation where the logarithmic extension to capillary pressure meets the raw curve u...
const Real _pc_max
Maximum capillary pressure (Pa). Note: must be <= 0.
virtual Real capillaryPressure(Real saturation) const
Capillary pressure is calculated as a function of true saturation.
Real _pc_ext
Capillary pressure where the extension meets the raw curve.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve.
bool _log_ext
Flag to use a logarithmic extension for low saturation.
Real PorousFlowCapillaryPressure::interceptFunction ( Real  s) const
protected

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

Parameters
seffective saturation
Returns
capillary pressure function in the logarithmic extension

Definition at line 135 of file PorousFlowCapillaryPressure.C.

Referenced by extensionSaturation(), and finalize().

136 {
139 
140  return std::log10(pc) - saturation * dpc / (_log10 * pc) - std::log10(_pc_max);
141 }
virtual Real dCapillaryPressureCurve(Real saturation) const =0
Derivative of raw capillary pressure wrt true saturation.
const Real _pc_max
Maximum capillary pressure (Pa). Note: must be <= 0.
virtual Real capillaryPressureCurve(Real saturation) const =0
Raw capillary pressure curve (does not include logarithmic extension)
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)
Real PorousFlowCapillaryPressure::interceptFunctionDeriv ( Real  s) const
protected

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

Parameters
seffective saturation
Returns
derivative of logarithmic extension function

Definition at line 144 of file PorousFlowCapillaryPressure.C.

Referenced by extensionSaturation(), and finalize().

145 {
149 
150  return saturation * (dpc * dpc / pc - d2pc) / (_log10 * pc);
151 }
virtual Real dCapillaryPressureCurve(Real saturation) const =0
Derivative of raw capillary pressure wrt true saturation.
virtual Real d2CapillaryPressureCurve(Real saturation) const =0
Second derivative of raw capillary pressure wrt true saturation.
virtual Real capillaryPressureCurve(Real saturation) const =0
Raw capillary pressure curve (does not include logarithmic extension)
void FORTRAN_CALL() saturation(double &P, double &T, int &N, int &nerr)

Member Data Documentation

const Real PorousFlowCapillaryPressure::_dseff_ds
protected
const Real PorousFlowCapillaryPressure::_log10
protected
bool PorousFlowCapillaryPressure::_log_ext
protected
Real PorousFlowCapillaryPressure::_pc_ext
protected

Capillary pressure where the extension meets the raw curve.

Definition at line 179 of file PorousFlowCapillaryPressure.h.

Referenced by capillaryPressureLogExt(), d2CapillaryPressureLogExt(), dCapillaryPressureLogExt(), and initialSetup().

const Real PorousFlowCapillaryPressure::_pc_max
protected
Real PorousFlowCapillaryPressure::_sat_ext
protected

Saturation where the logarithmic extension meets the raw curve.

Definition at line 177 of file PorousFlowCapillaryPressure.h.

Referenced by capillaryPressure(), capillaryPressureLogExt(), d2CapillaryPressure(), d2CapillaryPressureLogExt(), dCapillaryPressure(), dCapillaryPressureLogExt(), and initialSetup().

const Real PorousFlowCapillaryPressure::_sat_lr
protected

Liquid residual saturation.

Definition at line 169 of file PorousFlowCapillaryPressure.h.

Referenced by effectiveSaturationFromSaturation(), and extensionSaturation().

Real PorousFlowCapillaryPressure::_slope_ext
protected

Gradient of the logarithmic extension.

Definition at line 181 of file PorousFlowCapillaryPressure.h.

Referenced by capillaryPressureLogExt(), d2CapillaryPressureLogExt(), dCapillaryPressureLogExt(), and initialSetup().


The documentation for this class was generated from the following files: