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BrineDynamic.hpp
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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 This file is part of the Open Porous Media project (OPM).
5
6 OPM 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 2 of the License, or
9 (at your option) any later version.
10
11 OPM 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 OPM. If not, see <http://www.gnu.org/licenses/>.
18
19 Consult the COPYING file in the top-level source directory of this
20 module for the precise wording of the license and the list of
21 copyright holders.
22*/
28#ifndef OPM_BRINEDYNAMIC_HPP
29#define OPM_BRINEDYNAMIC_HPP
30
33
34namespace Opm {
35
44template <class Scalar, class H2O>
45class BrineDynamic : public Component<Scalar, BrineDynamic<Scalar, H2O> >
46{
47public:
48
52 static const char* name()
53 { return "Brine"; }
54
58 static bool gasIsIdeal()
59 { return H2O::gasIsIdeal(); }
60
64 static bool gasIsCompressible()
65 { return H2O::gasIsCompressible(); }
66
71 { return H2O::liquidIsCompressible(); }
72
78 template <class Evaluation>
79 static Evaluation molarMass(const Evaluation& salinity)
80 {
81 const Scalar M1 = H2O::molarMass();
82 const Evaluation X2 = salinity; // mass fraction of salt in brine
83 return M1*mM_salt/(mM_salt + X2*(M1 - mM_salt));
84 }
85
89 static Scalar criticalTemperature()
90 { return H2O::criticalTemperature(); /* [K] */ }
91
95 static Scalar criticalPressure()
96 { return H2O::criticalPressure(); /* [N/m^2] */ }
97
101 static Scalar criticalVolume()
102 { return H2O::criticalVolume(); /* [m3/kmol] */ }
103
107 static Scalar acentricFactor()
108 { return H2O::acentricFactor(); }
109
113 static Scalar tripleTemperature()
114 { return H2O::tripleTemperature(); /* [K] */ }
115
119 static Scalar triplePressure()
120 { return H2O::triplePressure(); /* [N/m^2] */ }
121
125 template <class Evaluation>
126 static Evaluation vaporPressure(const Evaluation& T)
127 { return H2O::vaporPressure(T); /* [N/m^2] */ }
128
132 template <class Evaluation>
133 static Evaluation gasEnthalpy(const Evaluation& temperature,
134 const Evaluation& pressure)
135 { return H2O::gasEnthalpy(temperature, pressure); /* [J/kg] */ }
136
145 template <class Evaluation>
146 static Evaluation liquidEnthalpy(const Evaluation& temperature,
147 const Evaluation& pressure,
148 const Evaluation& salinity)
149 {
150 // Numerical coefficents from Palliser and McKibbin
151 static constexpr Scalar f[] = {
152 2.63500e-1, 7.48368e-6, 1.44611e-6, -3.80860e-10
153 };
154
155 // Numerical coefficents from Michaelides for the enthalpy of brine
156 static constexpr Scalar a[4][3] = {
157 { -9633.6, -4080.0, +286.49 },
158 { +166.58, +68.577, -4.6856 },
159 { -0.90963, -0.36524, +0.249667e-1 },
160 { +0.17965e-2, +0.71924e-3, -0.4900e-4 }
161 };
162
163 const Evaluation theta = temperature - 273.15;
164
165 Evaluation S = salinity;
166 const Evaluation S_lSAT =
167 f[0]
168 + f[1]*theta
169 + f[2]*pow(theta, 2)
170 + f[3]*pow(theta, 3);
171
172 // Regularization
173 if (S > S_lSAT)
174 S = S_lSAT;
175
176 const Evaluation hw = H2O::liquidEnthalpy(temperature, pressure)/1e3; // [kJ/kg]
177
178 // From Daubert and Danner
179 const Evaluation h_NaCl =
180 (3.6710e4*temperature
181 + (6.2770e1/2)*temperature*temperature
182 - (6.6670e-2/3)*temperature*temperature*temperature
183 + (2.8000e-5/4)*pow(temperature, 4.0))/58.44e3
184 - 2.045698e+02; // [kJ/kg]
185
186 const Evaluation m = S/(1-S)/58.44e-3;
187
188 Evaluation d_h = 0;
189 for (int i = 0; i<=3; ++i) {
190 for (int j = 0; j <= 2; ++j) {
191 d_h += a[i][j] * pow(theta, i) * pow(m, j);
192 }
193 }
194
195 const Evaluation delta_h = 4.184/(1e3 + (58.44 * m))*d_h;
196
197 // Enthalpy of brine
198 const Evaluation h_ls = (1-S)*hw + S*h_NaCl + S*delta_h; // [kJ/kg]
199 return h_ls*1e3; // convert to [J/kg]
200 }
201
202
206 template <class Evaluation>
207 static Evaluation liquidHeatCapacity(const Evaluation& temperature,
208 const Evaluation& pressure)
209 {
210 Scalar eps = scalarValue(temperature)*1e-8;
211 return (liquidEnthalpy(temperature + eps, pressure) - liquidEnthalpy(temperature, pressure))/eps;
212 }
213
217 template <class Evaluation>
218 static Evaluation gasHeatCapacity(const Evaluation& temperature,
219 const Evaluation& pressure)
220 { return H2O::gasHeatCapacity(temperature, pressure); }
221
225 template <class Evaluation>
226 static Evaluation gasInternalEnergy(const Evaluation& temperature,
227 const Evaluation& pressure)
228 {
229 return
230 gasEnthalpy(temperature, pressure) -
231 pressure/gasDensity(temperature, pressure);
232 }
233
237 template <class Evaluation>
238 static Evaluation liquidInternalEnergy(const Evaluation& temperature,
239 const Evaluation& pressure)
240 {
241 return
242 liquidEnthalpy(temperature, pressure) -
243 pressure/liquidDensity(temperature, pressure);
244 }
245
249 template <class Evaluation>
250 static Evaluation gasDensity(const Evaluation& temperature, const Evaluation& pressure)
251 { return H2O::gasDensity(temperature, pressure); }
252
260 template <class Evaluation>
261 static Evaluation liquidDensity(const Evaluation& temperature, const Evaluation& pressure, const Evaluation& salinity, bool extrapolate = false)
262 {
263 Evaluation tempC = temperature - 273.15;
264 Evaluation pMPa = pressure/1.0E6;
265
266 const Evaluation rhow = H2O::liquidDensity(temperature, pressure, extrapolate);
267 return
268 rhow +
269 1000*salinity*(
270 0.668 +
271 0.44*salinity +
272 1.0E-6*(
273 300*pMPa -
274 2400*pMPa*salinity +
275 tempC*(
276 80.0 +
277 3*tempC -
278 3300*salinity -
279 13*pMPa +
280 47*pMPa*salinity)));
281 }
282
286 template <class Evaluation>
287 static Evaluation gasPressure(const Evaluation& temperature, const Evaluation& density)
288 { return H2O::gasPressure(temperature, density); }
289
293 template <class Evaluation>
294 static Evaluation liquidPressure(const Evaluation& temperature, const Evaluation& density)
295 {
296 // We use the newton method for this. For the initial value we
297 // assume the pressure to be 10% higher than the vapor
298 // pressure
299 Evaluation pressure = 1.1*vaporPressure(temperature);
300 Scalar eps = scalarValue(pressure)*1e-7;
301
302 Evaluation deltaP = pressure*2;
303 for (int i = 0;
304 i < 5
305 && std::abs(scalarValue(pressure)*1e-9) < std::abs(scalarValue(deltaP));
306 ++i)
307 {
308 const Evaluation f = liquidDensity(temperature, pressure) - density;
309
310 Evaluation df_dp = liquidDensity(temperature, pressure + eps);
311 df_dp -= liquidDensity(temperature, pressure - eps);
312 df_dp /= 2*eps;
313
314 deltaP = - f/df_dp;
315
316 pressure += deltaP;
317 }
318
319 return pressure;
320 }
321
325 template <class Evaluation>
326 static Evaluation gasViscosity(const Evaluation& temperature, const Evaluation& pressure)
327 { return H2O::gasViscosity(temperature, pressure); }
328
337 template <class Evaluation>
338 static Evaluation liquidViscosity(const Evaluation& temperature, const Evaluation& /*pressure*/, const Evaluation& salinity)
339 {
340 Evaluation T_C = temperature - 273.15;
341 if(temperature <= 275.) // regularization
342 T_C = 275.0;
343
344 Evaluation A = (0.42*Opm::pow((Opm::pow(salinity, 0.8)-0.17), 2) + 0.045)*pow(T_C, 0.8);
345 Evaluation mu_brine = 0.1 + 0.333*salinity + (1.65+91.9*salinity*salinity*salinity)*exp(-A);
346
347 return mu_brine/1000.0; // convert to [Pa s] (todo: check if correct cP->Pa s is times 10...)
348 }
349
350 //Molar mass salt (assumes pure NaCl) [kg/mol]
351 static constexpr Scalar mM_salt = 58.44e-3;
352
353};
354
355} // namespace Opm
356
357#endif
Abstract base class of a pure chemical species.
A traits class which provides basic mathematical functions for arbitrary scalar floating point values...
A class for the brine fluid properties.
Definition BrineDynamic.hpp:46
static Evaluation molarMass(const Evaluation &salinity)
The molar mass in of the component.
Definition BrineDynamic.hpp:79
static Scalar tripleTemperature()
Returns the temperature at water's triple point.
Definition BrineDynamic.hpp:113
static Evaluation gasDensity(const Evaluation &temperature, const Evaluation &pressure)
The density of steam in at a given pressure and temperature.
Definition BrineDynamic.hpp:250
static Evaluation gasViscosity(const Evaluation &temperature, const Evaluation &pressure)
The dynamic viscosity of steam.
Definition BrineDynamic.hpp:326
static Evaluation liquidEnthalpy(const Evaluation &temperature, const Evaluation &pressure, const Evaluation &salinity)
Specific enthalpy of the pure component in liquid.
Definition BrineDynamic.hpp:146
static Scalar criticalPressure()
Returns the critical pressure of water.
Definition BrineDynamic.hpp:95
static const char * name()
A human readable name for the component.
Definition BrineDynamic.hpp:52
static Scalar criticalVolume()
Returns the critical volume of water.
Definition BrineDynamic.hpp:101
static Evaluation liquidDensity(const Evaluation &temperature, const Evaluation &pressure, const Evaluation &salinity, bool extrapolate=false)
The density of the liquid component at a given pressure in and temperature in .
Definition BrineDynamic.hpp:261
static Evaluation liquidPressure(const Evaluation &temperature, const Evaluation &density)
The pressure of liquid water in at a given density and temperature.
Definition BrineDynamic.hpp:294
static Evaluation liquidViscosity(const Evaluation &temperature, const Evaluation &, const Evaluation &salinity)
The dynamic viscosity of pure water.
Definition BrineDynamic.hpp:338
static bool gasIsCompressible()
Returns true iff the gas phase is assumed to be compressible.
Definition BrineDynamic.hpp:64
static Evaluation gasHeatCapacity(const Evaluation &temperature, const Evaluation &pressure)
Specific isobaric heat capacity of water steam .
Definition BrineDynamic.hpp:218
static Evaluation gasEnthalpy(const Evaluation &temperature, const Evaluation &pressure)
Specific enthalpy of the pure component in gas.
Definition BrineDynamic.hpp:133
static Scalar acentricFactor()
Definition BrineDynamic.hpp:107
static Evaluation liquidHeatCapacity(const Evaluation &temperature, const Evaluation &pressure)
Specific isobaric heat capacity of liquid water .
Definition BrineDynamic.hpp:207
static bool liquidIsCompressible()
Returns true iff the liquid phase is assumed to be compressible.
Definition BrineDynamic.hpp:70
static Scalar triplePressure()
Returns the pressure at water's triple point.
Definition BrineDynamic.hpp:119
static bool gasIsIdeal()
Returns true iff the gas phase is assumed to be ideal.
Definition BrineDynamic.hpp:58
static Scalar criticalTemperature()
Returns the critical temperature of water.
Definition BrineDynamic.hpp:89
static Evaluation liquidInternalEnergy(const Evaluation &temperature, const Evaluation &pressure)
Specific internal energy of liquid water .
Definition BrineDynamic.hpp:238
static Evaluation gasPressure(const Evaluation &temperature, const Evaluation &density)
The pressure of steam in at a given density and temperature.
Definition BrineDynamic.hpp:287
static Evaluation vaporPressure(const Evaluation &T)
The vapor pressure in of pure water at a given temperature.
Definition BrineDynamic.hpp:126
static Evaluation gasInternalEnergy(const Evaluation &temperature, const Evaluation &pressure)
Specific internal energy of steam and water vapor .
Definition BrineDynamic.hpp:226
Abstract base class of a pure chemical species.
Definition Component.hpp:42
static Evaluation liquidDensity(const Evaluation &temperature, const Evaluation &pressure, bool extrapolate=false)
The density of pure water in at a given pressure and temperature.
Definition H2O.hpp:687
static const Scalar criticalTemperature()
Returns the critical temperature of water.
Definition H2O.hpp:95
static Evaluation gasDensity(const Evaluation &temperature, const Evaluation &pressure)
The density of steam in at a given pressure and temperature.
Definition H2O.hpp:562
static bool gasIsCompressible()
Returns true iff the gas phase is assumed to be compressible.
Definition H2O.hpp:540
static Evaluation gasPressure(const Evaluation &temperature, Scalar density)
The pressure of steam in at a given density and temperature.
Definition H2O.hpp:643
static Evaluation vaporPressure(Evaluation temperature)
The vapor pressure in of pure water at a given temperature.
Definition H2O.hpp:141
static Evaluation gasViscosity(const Evaluation &temperature, const Evaluation &pressure)
The dynamic viscosity of steam.
Definition H2O.hpp:790
static Evaluation gasHeatCapacity(const Evaluation &temperature, const Evaluation &pressure)
Specific isobaric heat capacity of water steam .
Definition H2O.hpp:279
static Evaluation liquidEnthalpy(const Evaluation &temperature, const Evaluation &pressure)
Specific enthalpy of liquid water .
Definition H2O.hpp:237
static const Scalar acentricFactor()
The acentric factor of water.
Definition H2O.hpp:89
static bool gasIsIdeal()
Returns true iff the gas phase is assumed to be ideal.
Definition H2O.hpp:627
static const Scalar criticalPressure()
Returns the critical pressure of water.
Definition H2O.hpp:101
static const Scalar molarMass()
The molar mass in of water.
Definition H2O.hpp:83
static bool liquidIsCompressible()
Returns true iff the liquid phase is assumed to be compressible.
Definition H2O.hpp:546
static Evaluation gasEnthalpy(const Evaluation &temperature, const Evaluation &pressure)
Specific enthalpy of water steam .
Definition H2O.hpp:186
static const Scalar tripleTemperature()
Returns the temperature at water's triple point.
Definition H2O.hpp:119
static const Scalar triplePressure()
Returns the pressure at water's triple point.
Definition H2O.hpp:125
static const Scalar criticalVolume()
Returns the critical volume of water.
Definition H2O.hpp:107
This class implements a small container which holds the transmissibility mulitpliers for all the face...
Definition Exceptions.hpp:30