3.1-git
DUNE for Multi-{Phase, Component, Scale, Physics, ...} flow and transport in porous media
components/brine.hh
Go to the documentation of this file.
1// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
2// vi: set et ts=4 sw=4 sts=4:
3/*****************************************************************************
4 * See the file COPYING for full copying permissions. *
5 * *
6 * This program is free software: you can redistribute it and/or modify *
7 * it under the terms of the GNU General Public License as published by *
8 * the Free Software Foundation, either version 3 of the License, or *
9 * (at your option) any later version. *
10 * *
11 * This program is distributed in the hope that it will be useful, *
12 * but WITHOUT ANY WARRANTY; without even the implied warranty of *
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
14 * GNU General Public License for more details. *
15 * *
16 * You should have received a copy of the GNU General Public License *
17 * along with this program. If not, see <http://www.gnu.org/licenses/>. *
18 *****************************************************************************/
24#ifndef DUMUX_BRINE_HH
25#define DUMUX_BRINE_HH
26
27#include <cmath>
28
30
34
38
39namespace Dumux {
40namespace Components {
41
51template <class Scalar,
52 class H2O_Tabulated = Components::TabulatedComponent<Components::H2O<Scalar>>>
53class Brine
54: public Components::Base<Scalar, Brine<Scalar, H2O_Tabulated> >
55, public Components::Liquid<Scalar, Brine<Scalar, H2O_Tabulated> >
56, public Components::Gas<Scalar, Brine<Scalar, H2O_Tabulated> >
57{
59public:
61
63 static constexpr Scalar R = Constants<Scalar>::R;
64
68 static std::string name()
69 { return "Brine"; }
70
74 static Scalar salinity()
75 {
76 static const Scalar salinity = getParam<Scalar>("Brine.Salinity");
77 return salinity;
78 }
79
84 static Scalar molarMass()
85 {
86 const Scalar M1 = H2O::molarMass();
87 const Scalar M2 = Components::NaCl<Scalar>::molarMass(); // molar mass of NaCl [kg/mol]
88 return M1*M2/(M2 + ThisType::salinity()*(M1 - M2));
89 };
90
94 static Scalar criticalTemperature()
95 { return H2O::criticalTemperature(); }
96
100 static Scalar criticalPressure()
101 { return H2O::criticalPressure(); }
102
106 static Scalar tripleTemperature()
107 { return H2O::tripleTemperature(); }
108
112 static Scalar triplePressure()
113 { return H2O::triplePressure(); }
114
121 static Scalar vaporPressure(Scalar temperature)
122 {
123 Scalar ps = H2O::vaporPressure(temperature); //Saturation vapor pressure for pure water
124 Scalar pi = 0;
125 using std::log;
126 if (ThisType::salinity() < 0.26) // here we have hard coded the solubility limit for NaCl
127 pi = (R * temperature * log(1- ThisType::salinity())); // simplified version of Eq 2.29 in Vishal Jambhekar's Promo
128 else
129 pi = (R * temperature * log(0.74));
130 using std::exp;
131 ps *= exp((pi)/(R*temperature));// Kelvin's law for reduction in saturation vapor pressure due to osmotic potential
132 return ps;
133 }
134
141 static const Scalar gasEnthalpy(Scalar temperature, Scalar pressure)
143
156 static const Scalar liquidEnthalpy(Scalar T, Scalar p)
157 {
158 /*Numerical coefficients from PALLISER*/
159 static const Scalar f[] = {
160 2.63500E-1, 7.48368E-6, 1.44611E-6, -3.80860E-10
161 };
162
163 /*Numerical coefficients from MICHAELIDES for the enthalpy of brine*/
164 static const Scalar a[4][3] = {
165 { +9633.6, -4080.0, +286.49 },
166 { +166.58, +68.577, -4.6856 },
167 { -0.90963, -0.36524, +0.249667E-1 },
168 { +0.17965E-2, +0.71924E-3, -0.4900E-4 }
169 };
170
171 const Scalar theta = T - 273.15;
172 const Scalar salSat = f[0] + f[1]*theta + f[2]*theta*theta + f[3]*theta*theta*theta;
173
174 /*Regularization*/
175 using std::min;
176 using std::max;
177 const Scalar salinity = min(max(ThisType::salinity(),0.0), salSat);
178
179 const Scalar hw = H2O::liquidEnthalpy(T, p)/1E3; /* kJ/kg */
180
181 /*DAUBERT and DANNER*/
182 /*U=*/const Scalar h_NaCl = (3.6710E4*T + 0.5*(6.2770E1)*T*T - ((6.6670E-2)/3)*T*T*T
183 +((2.8000E-5)/4)*(T*T*T*T))/(58.44E3)- 2.045698e+02; /* kJ/kg */
184
185 const Scalar m = (1E3/58.44)*(salinity/(1-salinity));
186
187 using std::pow;
188 Scalar d_h = 0;
189 for (int i = 0; i<=3; i++) {
190 for (int j=0; j<=2; j++) {
191 d_h = d_h + a[i][j] * pow(theta, i) * pow(m, j);
192 }
193 }
194
195 /* heat of dissolution for halite according to Michaelides 1971 */
196 const Scalar delta_h = (4.184/(1E3 + (58.44 * m)))*d_h;
197
198 /* Enthalpy of brine without any dissolved gas */
199 const Scalar h_ls1 =(1-salinity)*hw + salinity*h_NaCl + salinity*delta_h; /* kJ/kg */
200 return h_ls1*1E3; /*J/kg*/
201 }
202
215 static const Scalar liquidHeatCapacity(Scalar temperature, Scalar pressure)
216 {
217 const Scalar eps = temperature*1e-8;
219 }
220
233 static const Scalar gasHeatCapacity(Scalar temperature,
234 Scalar pressure)
235 {
237 }
238
245 static const Scalar gasInternalEnergy(Scalar temperature,
246 Scalar pressure)
247 {
249 }
250
257 static const Scalar liquidInternalEnergy(Scalar temperature,
258 Scalar pressure)
259 {
261 }
262
269 static Scalar gasDensity(Scalar temperature, Scalar pressure)
271
280 static Scalar gasMolarDensity(Scalar temperature, Scalar pressure)
282
286 static constexpr bool gasIsIdeal()
287 { return H2O::gasIsIdeal(); }
288
292 static constexpr bool gasIsCompressible()
293 { return H2O::gasIsCompressible(); }
294
298 static constexpr bool liquidIsCompressible()
299 { return H2O::liquidIsCompressible(); }
300
311 static Scalar liquidDensity(Scalar temperature, Scalar pressure)
312 {
313 using std::max;
314 const Scalar TempC = temperature - 273.15;
315 const Scalar pMPa = pressure/1.0E6;
316 const Scalar salinity = max(0.0, ThisType::salinity());
317
318 const Scalar rhow = H2O::liquidDensity(temperature, pressure);
319
320 const Scalar density = rhow +
321 1000*salinity*(
322 0.668 +
323 0.44*salinity +
324 1.0E-6*(
325 300*pMPa -
326 2400*pMPa*salinity +
327 TempC*(
328 80.0 +
329 3*TempC -
330 3300*salinity -
331 13*pMPa +
332 47*pMPa*salinity)));
333 assert(density > 0.0);
334 return density;
335 }
336
344 static Scalar liquidMolarDensity(Scalar temperature, Scalar pressure)
346
353 static Scalar gasPressure(Scalar temperature, Scalar density)
355
363 static Scalar liquidPressure(Scalar temperature, Scalar density)
364 {
365 // We use the Newton method for this. For the initial value we
366 // assume the pressure to be 10% higher than the vapor
367 // pressure
368 Scalar pressure = 1.1*vaporPressure(temperature);
369 const Scalar eps = pressure*1e-7;
370
371 Scalar deltaP = pressure*2;
372
373 using std::abs;
374 for (int i = 0; i < 5 && abs(pressure*1e-9) < abs(deltaP); ++i) {
376
377 Scalar df_dp;
380 df_dp /= 2*eps;
381
382 deltaP = - f/df_dp;
383
384 pressure += deltaP;
385 }
386 assert(pressure > 0.0);
387 return pressure;
388 }
389
396 static Scalar gasViscosity(Scalar temperature, Scalar pressure)
398
410 static Scalar liquidViscosity(Scalar temperature, Scalar pressure)
411 {
412 // regularisation
413 using std::max;
414 temperature = max(temperature, 275.0);
415 const Scalar salinity = max(0.0, ThisType::salinity());
416
417 using std::pow;
418 using std::exp;
419 const Scalar T_C = temperature - 273.15;
420 const Scalar A = (0.42*pow((pow(salinity, 0.8)-0.17), 2) + 0.045)*pow(T_C, 0.8);
421 const Scalar mu_brine = 0.1 + 0.333*salinity + (1.65+91.9*salinity*salinity*salinity)*exp(-A);
422 assert(mu_brine > 0.0);
423 return mu_brine/1000.0;
424 }
425
435 static Scalar liquidThermalConductivity(Scalar temperature, Scalar pressure)
437};
438
439template <class Scalar, class H2O>
440struct IsAqueous<Brine<Scalar, H2O>> : public std::true_type {};
441
442} // end namespace Components
443
444} // end namespace Dumux
445
446#endif
The infrastructure to retrieve run-time parameters from Dune::ParameterTrees.
Interface for components that have a gas state.
Material properties of pure water .
Interface for components that have a liquid state.
Material properties of pure salt .
Tabulates all thermodynamic properties of a given untabulated chemical species.
make the local view function available whenever we use the grid geometry
Definition: adapt.hh:29
std::string temperature() noexcept
I/O name of temperature for equilibrium models.
Definition: name.hh:51
std::string pressure(int phaseIdx) noexcept
I/O name of pressure for multiphase systems.
Definition: name.hh:34
std::string density(int phaseIdx) noexcept
I/O name of density for multiphase systems.
Definition: name.hh:65
constexpr double eps
epsilon for checking direction of scvf normals
Definition: test_tpfafvgeometry_nonconforming.cc:44
Definition: components/base.hh:43
Definition: components/base.hh:47
A class for the brine fluid properties.
Definition: components/brine.hh:57
static Scalar liquidViscosity(Scalar temperature, Scalar pressure)
The dynamic viscosity of pure brine.
Definition: components/brine.hh:410
static const Scalar liquidEnthalpy(Scalar T, Scalar p)
Specific enthalpy of liquid brine .
Definition: components/brine.hh:156
static Scalar molarMass()
The molar mass in of brine. This assumes that the salt is pure NaCl.
Definition: components/brine.hh:84
static Scalar gasMolarDensity(Scalar temperature, Scalar pressure)
The molar density of steam in at a given pressure and temperature. We take the value of the H2O gas ...
Definition: components/brine.hh:280
static Scalar tripleTemperature()
Returns the temperature at brine's triple point. Here, it is assumed to be equal to that of pure wat...
Definition: components/brine.hh:106
static Scalar gasPressure(Scalar temperature, Scalar density)
The pressure of steam in at a given density and temperature.
Definition: components/brine.hh:353
static const Scalar liquidInternalEnergy(Scalar temperature, Scalar pressure)
Specific internal energy of liquid brine .
Definition: components/brine.hh:257
static Scalar salinity()
Return the constant salinity.
Definition: components/brine.hh:74
static const Scalar gasHeatCapacity(Scalar temperature, Scalar pressure)
Specific isobaric heat capacity of water steam .
Definition: components/brine.hh:233
static Scalar criticalPressure()
Returns the critical pressure of brine. Here, it is assumed to be equal to that of pure water.
Definition: components/brine.hh:100
static const Scalar gasEnthalpy(Scalar temperature, Scalar pressure)
Specific enthalpy of gaseous brine . Only water volatile and salt is suppose to stay in the liquid ph...
Definition: components/brine.hh:141
static constexpr Scalar R
The ideal gas constant .
Definition: components/brine.hh:63
static Scalar gasDensity(Scalar temperature, Scalar pressure)
The density of steam at a given pressure and temperature .
Definition: components/brine.hh:269
static Scalar liquidPressure(Scalar temperature, Scalar density)
The pressure of brine in at a given density and temperature.
Definition: components/brine.hh:363
static Scalar liquidMolarDensity(Scalar temperature, Scalar pressure)
The molar density of brine in at a given pressure and temperature.
Definition: components/brine.hh:344
static Scalar vaporPressure(Scalar temperature)
The vapor pressure in of pure brine at a given temperature. Here, it is assumed to be equal to that ...
Definition: components/brine.hh:121
static Scalar triplePressure()
Returns the pressure at brine's triple point. Here, it is assumed to be equal to that of pure water.
Definition: components/brine.hh:112
static Scalar liquidThermalConductivity(Scalar temperature, Scalar pressure)
Thermal conductivity of a brine .
Definition: components/brine.hh:435
static const Scalar liquidHeatCapacity(Scalar temperature, Scalar pressure)
Specific isobaric heat capacity of brine .
Definition: components/brine.hh:215
static Scalar gasViscosity(Scalar temperature, Scalar pressure)
The dynamic viscosity of steam.
Definition: components/brine.hh:396
static constexpr bool liquidIsCompressible()
Returns true if the liquid phase is assumed to be compressible.
Definition: components/brine.hh:298
static std::string name()
A human readable name for the brine.
Definition: components/brine.hh:68
static Scalar criticalTemperature()
Returns the critical temperature of brine. Here, it is assumed to be equal to that of pure water.
Definition: components/brine.hh:94
static const Scalar gasInternalEnergy(Scalar temperature, Scalar pressure)
Specific internal energy of steam .
Definition: components/brine.hh:245
static constexpr bool gasIsCompressible()
Returns true if the gas phase is assumed to be compressible.
Definition: components/brine.hh:292
static constexpr bool gasIsIdeal()
Returns true if the gas phase is assumed to be ideal.
Definition: components/brine.hh:286
static Scalar liquidDensity(Scalar temperature, Scalar pressure)
The density of pure brine at a given pressure and temperature .
Definition: components/brine.hh:311
Interface for components that have a gas state.
Definition: gas.hh:41
Material properties of pure water .
Definition: h2o.hh:61
Interface for components that have a liquid state.
Definition: liquid.hh:41
static constexpr Scalar molarMass()
The molar mass of NaCl in .
Definition: nacl.hh:60
Tabulates all thermodynamic properties of a given untabulated chemical species.
Definition: tabulatedcomponent.hh:82
static const Scalar gasEnthalpy(Scalar temperature, Scalar pressure)
Specific enthalpy of the gas .
Definition: tabulatedcomponent.hh:238
static Scalar gasPressure(Scalar temperature, Scalar density)
The pressure of gas in at a given density and temperature.
Definition: tabulatedcomponent.hh:368
static Scalar criticalTemperature()
Returns the critical temperature in of the component.
Definition: tabulatedcomponent.hh:184
static const Scalar gasHeatCapacity(Scalar temperature, Scalar pressure)
Specific isobaric heat capacity of the gas .
Definition: tabulatedcomponent.hh:292
static Scalar liquidThermalConductivity(Scalar temperature, Scalar pressure)
The thermal conductivity of liquid water .
Definition: tabulatedcomponent.hh:619
static Scalar gasDensity(Scalar temperature, Scalar pressure)
The density of gas at a given pressure and temperature .
Definition: tabulatedcomponent.hh:456
static const Scalar liquidEnthalpy(Scalar temperature, Scalar pressure)
Specific enthalpy of the liquid .
Definition: tabulatedcomponent.hh:265
static Scalar triplePressure()
Returns the pressure in at the component's triple point.
Definition: tabulatedcomponent.hh:202
static Scalar criticalPressure()
Returns the critical pressure in of the component.
Definition: tabulatedcomponent.hh:190
static const Scalar gasInternalEnergy(Scalar temperature, Scalar pressure)
Specific internal energy of the gas .
Definition: tabulatedcomponent.hh:346
static constexpr Scalar molarMass()
The molar mass in of the component.
Definition: tabulatedcomponent.hh:178
static Scalar gasViscosity(Scalar temperature, Scalar pressure)
The dynamic viscosity of gas.
Definition: tabulatedcomponent.hh:538
static Scalar tripleTemperature()
Returns the temperature in at the component's triple point.
Definition: tabulatedcomponent.hh:196
static constexpr bool liquidIsCompressible()
Returns true if the liquid phase is assumed to be compressible.
Definition: tabulatedcomponent.hh:439
static Scalar liquidDensity(Scalar temperature, Scalar pressure)
The density of liquid at a given pressure and temperature .
Definition: tabulatedcomponent.hh:495
static Scalar gasMolarDensity(Scalar temperature, Scalar pressure)
The molar density of gas in at a given pressure and temperature.
Definition: tabulatedcomponent.hh:485
static Scalar vaporPressure(Scalar T)
The vapor pressure in of the component at a given temperature.
Definition: tabulatedcomponent.hh:211
static constexpr bool gasIsCompressible()
Returns true if the gas phase is assumed to be compressible.
Definition: tabulatedcomponent.hh:433
static constexpr bool gasIsIdeal()
Returns true if the gas phase is assumed to be ideal.
Definition: tabulatedcomponent.hh:445
A central place for various physical constants occuring in some equations.
Definition: constants.hh:39
Base class for all components Components provide the thermodynamic relations for the liquid,...