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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 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...
 
virtual Real effectiveSaturation (Real pc, unsigned qp=0) const =0
 Effective saturation as a function of capillary pressure. More...
 
virtual Real dEffectiveSaturation (Real pc, unsigned qp=0) const =0
 Derivative of effective saturation wrt capillary pressure. More...
 
virtual Real d2EffectiveSaturation (Real pc, unsigned qp=0) 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 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...
 
virtual Real capillaryPressureCurve (Real saturation, unsigned qp=0) const =0
 Raw capillary pressure curve (does not include logarithmic extension) More...
 
virtual Real dCapillaryPressureCurve (Real saturation, unsigned qp=0) const =0
 Derivative of raw capillary pressure wrt true saturation. More...
 
virtual Real d2CapillaryPressureCurve (Real saturation, unsigned qp=0) 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 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

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) The logarithmic extension is only computed for qp=0. If your overriding class has no qp dependence (capillary pressure is a function only of saturation, for example) then no changes are required. Otherwise, if you use log_extension, you will have to modify this base class to correctly calculate the log-extension parameters at each quadpoint.

Definition at line 40 of file PorousFlowCapillaryPressure.h.

Constructor & Destructor Documentation

◆ PorousFlowCapillaryPressure()

PorousFlowCapillaryPressure::PorousFlowCapillaryPressure ( const InputParameters &  parameters)

Definition at line 37 of file PorousFlowCapillaryPressure.C.

38  : DiscreteElementUserObject(parameters),
39  _sat_lr(getParam<Real>("sat_lr")),
40  _dseff_ds(1.0 / (1.0 - _sat_lr)),
41  _log_ext(getParam<bool>("log_extension")),
42  _pc_max(getParam<Real>("pc_max")),
43  _sat_ext(0.0),
44  _pc_ext(0.0),
45  _slope_ext(0.0),
46  _log10(std::log(10.0))
47 {
48 }
Real _slope_ext
Gradient of the logarithmic extension This is computed only for qp=0.
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 This is computed only for qp=0...
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

◆ capillaryPressure()

Real PorousFlowCapillaryPressure::capillaryPressure ( Real  saturation,
unsigned  qp = 0 
) 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
qpquadpoint 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(), initialSetup(), PorousFlowWaterNCG::thermophysicalProperties(), PorousFlowBrineCO2::thermophysicalProperties(), PorousFlowWaterNCG::totalMassFraction(), and PorousFlowBrineCO2::totalMassFraction().

65 {
66  if (_log_ext && saturation < _sat_ext)
67  return capillaryPressureLogExt(saturation);
68  else
69  return capillaryPressureCurve(saturation, qp);
70 }
virtual Real capillaryPressureCurve(Real saturation, unsigned qp=0) const =0
Raw capillary pressure curve (does not include logarithmic extension)
Real capillaryPressureLogExt(Real s) const
The capillary pressure in the logarithmic extension This implementation assumes capillary-pressure is...
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve This is computed only for qp=0...
bool _log_ext
Flag to use a logarithmic extension for low saturation.

◆ capillaryPressureCurve()

virtual Real PorousFlowCapillaryPressure::capillaryPressureCurve ( Real  saturation,
unsigned  qp = 0 
) 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(), interceptFunction(), and interceptFunctionDeriv().

◆ capillaryPressureLogExt()

Real PorousFlowCapillaryPressure::capillaryPressureLogExt ( Real  s) const
protected

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
sliquid saturation
Returns
capillary pressure in logarithmic extension

Definition at line 97 of file PorousFlowCapillaryPressure.C.

Referenced by capillaryPressure().

98 {
99  return _pc_ext * std::pow(10.0, _slope_ext * (saturation - _sat_ext));
100 }
Real _slope_ext
Gradient of the logarithmic extension This is computed only for qp=0.
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 This is computed only for qp=0...

◆ d2CapillaryPressure()

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

Second derivative of capillary pressure wrt true saturation.

Parameters
saturationtrue saturation
qpquadpoint 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().

83 {
84  if (_log_ext && saturation < _sat_ext)
85  return d2CapillaryPressureLogExt(saturation);
86  else
87  return d2CapillaryPressureCurve(saturation, qp);
88 }
Real d2CapillaryPressureLogExt(Real s) const
The second derivative of capillary pressure in the logarithmic extension This implementation assumes ...
virtual Real d2CapillaryPressureCurve(Real saturation, unsigned qp=0) const =0
Second derivative of raw capillary pressure wrt true saturation.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve This is computed only for qp=0...
bool _log_ext
Flag to use a logarithmic extension for low saturation.

◆ d2CapillaryPressureCurve()

virtual Real PorousFlowCapillaryPressure::d2CapillaryPressureCurve ( Real  saturation,
unsigned  qp = 0 
) 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(), and interceptFunctionDeriv().

◆ d2CapillaryPressureLogExt()

Real PorousFlowCapillaryPressure::d2CapillaryPressureLogExt ( Real  s) const
protected

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
sliquid saturation
Returns
second derivative of capillary pressure in logarithmic extension

Definition at line 109 of file PorousFlowCapillaryPressure.C.

Referenced by d2CapillaryPressure().

110 {
111  return _pc_ext * _slope_ext * _slope_ext * _log10 * _log10 *
112  std::pow(10.0, _slope_ext * (saturation - _sat_ext));
113 }
Real _slope_ext
Gradient of the logarithmic extension This is computed only for qp=0.
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 This is computed only for qp=0...

◆ d2EffectiveSaturation()

virtual Real PorousFlowCapillaryPressure::d2EffectiveSaturation ( Real  pc,
unsigned  qp = 0 
) const
pure virtual

Second derivative of effective saturation wrt capillary pressure.

Parameters
pccapillary pressure
qpquadpoint to use (when effective saturation depends on coupled variables, not just pc)
Returns
second derivative of effective saturation wrt capillary pressure

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

Referenced by PorousFlow2PhasePP::computeQpProperties(), and PorousFlow1PhaseP::computeQpProperties().

◆ dCapillaryPressure()

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

Derivative of capillary pressure wrt true saturation.

Parameters
saturationtrue saturation
qpquadpoint 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().

74 {
75  if (_log_ext && saturation < _sat_ext)
76  return dCapillaryPressureLogExt(saturation);
77  else
78  return dCapillaryPressureCurve(saturation, qp);
79 }
virtual Real dCapillaryPressureCurve(Real saturation, unsigned qp=0) const =0
Derivative of raw capillary pressure wrt true saturation.
Real _sat_ext
Saturation where the logarithmic extension meets the raw curve This is computed only for qp=0...
bool _log_ext
Flag to use a logarithmic extension for low saturation.
Real dCapillaryPressureLogExt(Real s) const
The derivative of capillary pressure in the logarithmic extension This implementation assumes capilla...

◆ dCapillaryPressureCurve()

virtual Real PorousFlowCapillaryPressure::dCapillaryPressureCurve ( Real  saturation,
unsigned  qp = 0 
) 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(), interceptFunction(), and interceptFunctionDeriv().

◆ dCapillaryPressureLogExt()

Real PorousFlowCapillaryPressure::dCapillaryPressureLogExt ( Real  s) const
protected

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
sliquid saturation
Returns
derivative of capillary pressure in logarithmic extension

Definition at line 103 of file PorousFlowCapillaryPressure.C.

Referenced by dCapillaryPressure().

104 {
105  return _pc_ext * _slope_ext * _log10 * std::pow(10.0, _slope_ext * (saturation - _sat_ext));
106 }
Real _slope_ext
Gradient of the logarithmic extension This is computed only for qp=0.
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 This is computed only for qp=0...

◆ dEffectiveSaturation()

virtual Real PorousFlowCapillaryPressure::dEffectiveSaturation ( Real  pc,
unsigned  qp = 0 
) const
pure virtual

Derivative of effective saturation wrt capillary pressure.

Parameters
pccapillary pressure (Pa)
qpquadpoint to use (when effective saturation depends on coupled variables, not just pc)
Returns
derivative of effective saturation wrt capillary pressure

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

Referenced by PorousFlow2PhasePP::computeQpProperties(), and PorousFlow1PhaseP::computeQpProperties().

◆ effectiveSaturation()

virtual Real PorousFlowCapillaryPressure::effectiveSaturation ( Real  pc,
unsigned  qp = 0 
) const
pure virtual

Effective saturation as a function of capillary pressure.

Parameters
pccapillary pressure (Pa)
qpquadpoint to use (when effective saturation depends on coupled variables, not just pc)
Returns
effective saturation

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

Referenced by PorousFlow1PhaseP::buildQpPPSS(), and PorousFlow2PhasePP::buildQpPPSS().

◆ effectiveSaturationFromSaturation()

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 91 of file PorousFlowCapillaryPressure.C.

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

92 {
93  return (saturation - _sat_lr) / (1.0 - _sat_lr);
94 }
const Real _sat_lr
Liquid residual saturation.

◆ extensionSaturation()

Real PorousFlowCapillaryPressure::extensionSaturation ( ) const
protected

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 initialSetup().

117 {
118  // Initial guess for saturation where extension matches curve
119  Real sat = _sat_lr + 0.01;
120 
121  // Calculate the saturation where the extension matches the derivative of the
122  // raw capillary pressure curve
123  const unsigned int max_its = 20;
124  const Real nr_tol = 1.0e-8;
125  unsigned int iter = 0;
126 
127  while (std::abs(interceptFunction(sat)) > nr_tol)
128  {
129  sat = sat - interceptFunction(sat) / interceptFunctionDeriv(sat);
130 
131  iter++;
132  if (iter > max_its)
133  break;
134  }
135 
136  return sat;
137 }
Real interceptFunctionDeriv(Real s) const
Calculates the saturation where the logarithmic extension to capillary pressure at low saturation...
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.

◆ initialize()

virtual void PorousFlowCapillaryPressure::initialize ( )
inlinefinalvirtual

Definition at line 45 of file PorousFlowCapillaryPressure.h.

45 {};

◆ initialSetup()

void PorousFlowCapillaryPressure::initialSetup ( )
overridevirtual

Definition at line 51 of file PorousFlowCapillaryPressure.C.

52 {
53  // If _log_ext = true, calculate the saturation where the the logarithmic
54  // extension meets the raw capillary pressure curve.
55  if (_log_ext)
56  {
59  _slope_ext = (std::log10(_pc_ext) - std::log10(_pc_max)) / _sat_ext;
60  }
61 }
Real _slope_ext
Gradient of the logarithmic extension This is computed only for qp=0.
const Real _pc_max
Maximum capillary pressure (Pa). Note: must be <= 0.
Real extensionSaturation() const
Calculates the saturation where the logarithmic extension to capillary pressure meets the raw curve u...
virtual Real capillaryPressure(Real saturation, unsigned qp=0) 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 This is computed only for qp=0...
bool _log_ext
Flag to use a logarithmic extension for low saturation.

◆ interceptFunction()

Real PorousFlowCapillaryPressure::interceptFunction ( Real  s) const
protected

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
seffective saturation
Returns
capillary pressure function in the logarithmic extension

Definition at line 140 of file PorousFlowCapillaryPressure.C.

Referenced by extensionSaturation().

141 {
142  Real pc = capillaryPressureCurve(saturation);
143  Real dpc = dCapillaryPressureCurve(saturation);
144 
145  return std::log10(pc) - saturation * dpc / (_log10 * pc) - std::log10(_pc_max);
146 }
virtual Real dCapillaryPressureCurve(Real saturation, unsigned qp=0) const =0
Derivative of raw capillary pressure wrt true saturation.
virtual Real capillaryPressureCurve(Real saturation, unsigned qp=0) const =0
Raw capillary pressure curve (does not include logarithmic extension)
const Real _pc_max
Maximum capillary pressure (Pa). Note: must be <= 0.

◆ interceptFunctionDeriv()

Real PorousFlowCapillaryPressure::interceptFunctionDeriv ( Real  s) const
protected

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
seffective saturation
Returns
derivative of logarithmic extension function

Definition at line 149 of file PorousFlowCapillaryPressure.C.

Referenced by extensionSaturation().

150 {
151  Real pc = capillaryPressureCurve(saturation);
152  Real dpc = dCapillaryPressureCurve(saturation);
153  Real d2pc = d2CapillaryPressureCurve(saturation);
154 
155  return saturation * (dpc * dpc / pc - d2pc) / (_log10 * pc);
156 }
virtual Real dCapillaryPressureCurve(Real saturation, unsigned qp=0) const =0
Derivative of raw capillary pressure wrt true saturation.
virtual Real capillaryPressureCurve(Real saturation, unsigned qp=0) const =0
Raw capillary pressure curve (does not include logarithmic extension)
virtual Real d2CapillaryPressureCurve(Real saturation, unsigned qp=0) const =0
Second derivative of raw capillary pressure wrt true saturation.

Member Data Documentation

◆ _dseff_ds

const Real PorousFlowCapillaryPressure::_dseff_ds
protected

◆ _log10

const Real PorousFlowCapillaryPressure::_log10
protected

◆ _log_ext

bool PorousFlowCapillaryPressure::_log_ext
protected

◆ _pc_ext

Real PorousFlowCapillaryPressure::_pc_ext
protected

Capillary pressure where the extension meets the raw curve.

This is computed only for qp=0.

Definition at line 215 of file PorousFlowCapillaryPressure.h.

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

◆ _pc_max

const Real PorousFlowCapillaryPressure::_pc_max
protected

◆ _sat_ext

Real PorousFlowCapillaryPressure::_sat_ext
protected

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

Definition at line 210 of file PorousFlowCapillaryPressure.h.

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

◆ _sat_lr

const Real PorousFlowCapillaryPressure::_sat_lr
protected

Liquid residual saturation.

Definition at line 198 of file PorousFlowCapillaryPressure.h.

Referenced by effectiveSaturationFromSaturation(), and extensionSaturation().

◆ _slope_ext

Real PorousFlowCapillaryPressure::_slope_ext
protected

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

Definition at line 220 of file PorousFlowCapillaryPressure.h.

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


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