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RegularizedVanGenuchten.hpp
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27 #ifndef OPM_REGULARIZED_VAN_GENUCHTEN_HPP
28 #define OPM_REGULARIZED_VAN_GENUCHTEN_HPP
29 
30 #include "VanGenuchten.hpp"
32 
34 
35 #include <algorithm>
36 
37 namespace Opm {
38 
70 template <class TraitsT, class ParamsT = RegularizedVanGenuchtenParams<TraitsT> >
71 class RegularizedVanGenuchten : public TraitsT
72 {
73  typedef ::Opm::VanGenuchten<TraitsT, ParamsT> VanGenuchten;
74 
75 public:
76  typedef TraitsT Traits;
77  typedef ParamsT Params;
78 
79  typedef typename Traits::Scalar Scalar;
80 
82  static const int numPhases = Traits::numPhases;
83  static_assert(numPhases == 2,
84  "The regularized van Genuchten capillary pressure law only "
85  "applies to the case of two fluid phases");
86 
89  static const bool implementsTwoPhaseApi = true;
90 
93  static const bool implementsTwoPhaseSatApi = true;
94 
97  static const bool isSaturationDependent = true;
98 
101  static const bool isPressureDependent = false;
102 
105  static const bool isTemperatureDependent = false;
106 
109  static const bool isCompositionDependent = false;
110 
115  template <class Container, class FluidState>
116  static void capillaryPressures(Container& values, const Params& params, const FluidState& fs)
117  {
118  typedef typename std::remove_reference<decltype(values[0])>::type Evaluation;
119 
120  values[Traits::wettingPhaseIdx] = 0.0; // reference phase
121  values[Traits::nonWettingPhaseIdx] = pcnw<FluidState, Evaluation>(params, fs);
122  }
123 
128  template <class Container, class FluidState>
129  static void saturations(Container& values, const Params& params, const FluidState& fs)
130  {
131  typedef typename std::remove_reference<decltype(values[0])>::type Evaluation;
132 
133  values[Traits::wettingPhaseIdx] = Sw<FluidState, Evaluation>(params, fs);
134  values[Traits::nonWettingPhaseIdx] = 1 - values[Traits::wettingPhaseIdx];
135  }
136 
141  template <class Container, class FluidState>
142  static void relativePermeabilities(Container& values, const Params& params, const FluidState& fs)
143  {
144  typedef typename std::remove_reference<decltype(values[0])>::type Evaluation;
145 
146  values[Traits::wettingPhaseIdx] = krw<FluidState, Evaluation>(params, fs);
147  values[Traits::nonWettingPhaseIdx] = krn<FluidState, Evaluation>(params, fs);
148  }
149 
162  template <class FluidState, class Evaluation = typename FluidState::Scalar>
163  static Evaluation pcnw(const Params& params, const FluidState& fs)
164  {
165  const auto& Sw = decay<Evaluation>(fs.saturation(Traits::wettingPhaseIdx));
166  return twoPhaseSatPcnw(params, Sw);
167  }
168 
169  template <class Evaluation>
170  static Evaluation twoPhaseSatPcnw(const Params& params, const Evaluation& Sw)
171  {
172  // retrieve the low and the high threshold saturations for the
173  // unregularized capillary pressure curve from the parameters
174  const Scalar SwThLow = params.pcnwLowSw();
175  const Scalar SwThHigh = params.pcnwHighSw();
176 
177  // make sure that the capillary pressure observes a derivative
178  // != 0 for 'illegal' saturations. This is favourable for the
179  // newton solver (if the derivative is calculated numerically)
180  // in order to get the saturation moving to the right
181  // direction if it temporarily is in an 'illegal' range.
182  if (Sw < SwThLow) {
183  return params.pcnwLow() + params.pcnwSlopeLow()*(Sw - SwThLow);
184  }
185  else if (Sw > SwThHigh)
186  {
187  Scalar yTh = params.pcnwHigh();
188  Scalar m1 = (0.0 - yTh)/(1.0 - SwThHigh)*2;
189 
190  if (Sw < 1.0) {
191  // use spline between threshold Sw and 1.0
192  const Spline<Scalar>& sp = params.pcnwHighSpline();
193 
194  return sp.eval(Sw);
195  }
196  else {
197  // straight line for Sw > 1.0
198  return m1*(Sw - 1.0) + 0.0;
199  }
200  }
201 
202  // if the effective saturation is in an 'reasonable'
203  // range, we use the real van genuchten law...
204  return VanGenuchten::twoPhaseSatPcnw(params, Sw);
205  }
206 
221  template <class FluidState, class Evaluation = typename FluidState::Scalar>
222  static Evaluation Sw(const Params& params, const FluidState& fs)
223  {
224  const Evaluation& pC =
225  decay<Evaluation>(fs.pressure(Traits::nonWettingPhaseIdx))
226  - decay<Evaluation>(fs.pressure(Traits::wettingPhaseIdx));
227  return twoPhaseSatSw(params, pC);
228  }
229 
230  template <class Evaluation>
231  static Evaluation twoPhaseSatSw(const Params& params, const Evaluation& pC)
232  {
233  // retrieve the low and the high threshold saturations for the
234  // unregularized capillary pressure curve from the parameters
235  const Scalar SwThLow = params.pcnwLowSw();
236  const Scalar SwThHigh = params.pcnwHighSw();
237 
238  // calculate the saturation which corrosponds to the
239  // saturation in the non-regularized verision of van
240  // Genuchten's law
241  if (pC <= 0) {
242  // invert straight line for Sw > 1.0
243  Scalar m1 = params.pcnwSlopeHigh();
244  return pC/m1 + 1.0;
245  }
246 
247  Evaluation Sw = VanGenuchten::twoPhaseSatSw(params, pC);
248 
249  // invert the regularization if necessary
250  if (Sw <= SwThLow) {
251  // invert the low saturation regularization of pC()
252  Scalar pC_SwLow = VanGenuchten::twoPhaseSatPcnw(params, SwThLow);
253  return (pC - pC_SwLow)/params.pcnwSlopeLow() + SwThLow;
254  }
255  else if (SwThHigh < Sw /* && Sw < 1.0*/)
256  {
257  // invert spline between threshold saturation and 1.0
258  const Spline<Scalar>& spline = params.pcnwHighSpline();
259 
260  return spline.template intersectInterval<Evaluation>(/*x0=*/SwThHigh, /*x1=*/1.0,
261  /*a=*/0, /*b=*/0, /*c=*/0, /*d=*/pC);
262  }
263 
264  return Sw;
265  }
266 
271  template <class FluidState, class Evaluation = typename FluidState::Scalar>
272  static Evaluation Sn(const Params& params, const FluidState& fs)
273  { return 1 - Sw<FluidState, Evaluation>(params, fs); }
274 
275  template <class Evaluation>
276  static Evaluation twoPhaseSatSn(const Params& params, const Evaluation& pc)
277  { return 1 - twoPhaseSatSw(params, pc); }
278 
293  template <class FluidState, class Evaluation = typename FluidState::Scalar>
294  static Evaluation krw(const Params& params, const FluidState& fs)
295  {
296  const auto& Sw = decay<Evaluation>(fs.saturation(Traits::wettingPhaseIdx));
297  return twoPhaseSatKrw(params, Sw);
298  }
299 
300  template <class Evaluation>
301  static Evaluation twoPhaseSatKrw(const Params& params, const Evaluation& Sw)
302  {
303  // regularize
304  if (Sw <= 0)
305  return 0.0;
306  else if (Sw >= 1)
307  return 1.0;
308 
309  return VanGenuchten::twoPhaseSatKrw(params, Sw);
310  }
311 
326  template <class FluidState, class Evaluation = typename FluidState::Scalar>
327  static Evaluation krn(const Params& params, const FluidState& fs)
328  {
329  const Evaluation& Sw =
330  1.0 - decay<Evaluation>(fs.saturation(Traits::nonWettingPhaseIdx));
331  return twoPhaseSatKrn(params, Sw);
332  }
333 
334  template <class Evaluation>
335  static Evaluation twoPhaseSatKrn(const Params& params, const Evaluation& Sw)
336  {
337  // regularize
338  if (Sw <= 0)
339  return 1.0;
340  else if (Sw >= 1)
341  return 0.0;
342 
343  return VanGenuchten::twoPhaseSatKrn(params, Sw);
344  }
345 };
346 
347 } // namespace Opm
348 
349 #endif
Parameters that are necessary for the regularization of VanGenuchten "material law".
Class implementing cubic splines.
Implementation of the van Genuchten capillary pressure - saturation relation.
Implementation of the regularized van Genuchten's capillary pressure / relative permeability <-> satu...
Definition: RegularizedVanGenuchten.hpp:72
static const int numPhases
The number of fluid phases.
Definition: RegularizedVanGenuchten.hpp:82
static const bool isCompositionDependent
Specify whether the quantities defined by this material law are dependent on the phase composition.
Definition: RegularizedVanGenuchten.hpp:109
static Evaluation krn(const Params &params, const FluidState &fs)
Regularized version of the relative permeability for the non-wetting phase of the medium implied by t...
Definition: RegularizedVanGenuchten.hpp:327
static const bool implementsTwoPhaseApi
Specify whether this material law implements the two-phase convenience API.
Definition: RegularizedVanGenuchten.hpp:89
static void saturations(Container &values, const Params &params, const FluidState &fs)
Calculate the saturations of the phases starting from their pressure differences.
Definition: RegularizedVanGenuchten.hpp:129
static const bool isSaturationDependent
Specify whether the quantities defined by this material law are saturation dependent.
Definition: RegularizedVanGenuchten.hpp:97
static Evaluation Sn(const Params &params, const FluidState &fs)
Calculate the non-wetting phase saturations depending on the phase pressures.
Definition: RegularizedVanGenuchten.hpp:272
static const bool isPressureDependent
Specify whether the quantities defined by this material law are dependent on the absolute pressure.
Definition: RegularizedVanGenuchten.hpp:101
static Evaluation pcnw(const Params &params, const FluidState &fs)
A regularized van Genuchten capillary pressure-saturation curve.
Definition: RegularizedVanGenuchten.hpp:163
static const bool isTemperatureDependent
Specify whether the quantities defined by this material law are temperature dependent.
Definition: RegularizedVanGenuchten.hpp:105
static Evaluation Sw(const Params &params, const FluidState &fs)
A regularized van Genuchten saturation-capillary pressure curve.
Definition: RegularizedVanGenuchten.hpp:222
static void relativePermeabilities(Container &values, const Params &params, const FluidState &fs)
Returns the relative permeabilities of the phases dependening on the phase saturations.
Definition: RegularizedVanGenuchten.hpp:142
static const bool implementsTwoPhaseSatApi
Specify whether this material law implements the two-phase convenience API which only depends on the ...
Definition: RegularizedVanGenuchten.hpp:93
static Evaluation krw(const Params &params, const FluidState &fs)
Regularized version of the relative permeability for the wetting phase of the medium implied by the v...
Definition: RegularizedVanGenuchten.hpp:294
static void capillaryPressures(Container &values, const Params &params, const FluidState &fs)
Calculate the pressure difference of the phases in the most generic way.
Definition: RegularizedVanGenuchten.hpp:116
Implementation of the van Genuchten capillary pressure - saturation relation.
Definition: VanGenuchten.hpp:56
static Evaluation twoPhaseSatPcnw(const Params &params, const Evaluation &Sw)
The saturation-capillary pressure curve according to van Genuchten using a material law specific API.
Definition: VanGenuchten.hpp:194