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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
34#include <string_view>
35
36namespace Opm {
37
46template <class Scalar, class H2O>
47class BrineDynamic : public Component<Scalar, BrineDynamic<Scalar, H2O> >
48{
49public:
50
54 static std::string_view name()
55 { return "Brine"; }
56
60 static bool gasIsIdeal()
61 { return H2O::gasIsIdeal(); }
62
66 static bool gasIsCompressible()
67 { return H2O::gasIsCompressible(); }
68
73 { return H2O::liquidIsCompressible(); }
74
80 template <class Evaluation>
81 static Evaluation molarMass(const Evaluation& salinity)
82 {
83 const Scalar M1 = H2O::molarMass();
84 const Evaluation X2 = salinity; // mass fraction of salt in brine
85 return M1*mM_salt/(mM_salt + X2*(M1 - mM_salt));
86 }
87
91 static Scalar criticalTemperature()
92 { return H2O::criticalTemperature(); /* [K] */ }
93
97 static Scalar criticalPressure()
98 { return H2O::criticalPressure(); /* [N/m^2] */ }
99
103 static Scalar criticalVolume()
104 { return H2O::criticalVolume(); /* [m3/kmol] */ }
105
109 static Scalar acentricFactor()
110 { return H2O::acentricFactor(); }
111
115 static Scalar tripleTemperature()
116 { return H2O::tripleTemperature(); /* [K] */ }
117
121 static Scalar triplePressure()
122 { return H2O::triplePressure(); /* [N/m^2] */ }
123
127 template <class Evaluation>
128 static Evaluation vaporPressure(const Evaluation& T)
129 { return H2O::vaporPressure(T); /* [N/m^2] */ }
130
134 template <class Evaluation>
135 static Evaluation gasEnthalpy(const Evaluation& temperature,
136 const Evaluation& pressure)
137 { return H2O::gasEnthalpy(temperature, pressure); /* [J/kg] */ }
138
147 template <class Evaluation>
148 static Evaluation liquidEnthalpy(const Evaluation& temperature,
149 const Evaluation& pressure,
150 const Evaluation& salinity)
151 {
152 // Numerical coefficents from Palliser and McKibbin
153 static constexpr Scalar f[] = {
154 2.63500e-1, 7.48368e-6, 1.44611e-6, -3.80860e-10
155 };
156
157 // Numerical coefficents from Michaelides for the enthalpy of brine
158 static constexpr Scalar a[4][3] = {
159 { -9633.6, -4080.0, +286.49 },
160 { +166.58, +68.577, -4.6856 },
161 { -0.90963, -0.36524, +0.249667e-1 },
162 { +0.17965e-2, +0.71924e-3, -0.4900e-4 }
163 };
164
165 const Evaluation theta = temperature - 273.15;
166
167 Evaluation S = salinity;
168 const Evaluation S_lSAT =
169 f[0]
170 + f[1]*theta
171 + f[2]*pow(theta, 2)
172 + f[3]*pow(theta, 3);
173
174 // Regularization
175 if (S > S_lSAT)
176 S = S_lSAT;
177
178 const Evaluation hw = H2O::liquidEnthalpy(temperature, pressure)/1e3; // [kJ/kg]
179
180 // From Daubert and Danner
181 const Evaluation h_NaCl =
182 (3.6710e4*temperature
183 + (6.2770e1/2)*temperature*temperature
184 - (6.6670e-2/3)*temperature*temperature*temperature
185 + (2.8000e-5/4)*pow(temperature, 4.0))/58.44e3
186 - 2.045698e+02; // [kJ/kg]
187
188 const Evaluation m = S/(1-S)/58.44e-3;
189
190 Evaluation d_h = 0;
191 for (int i = 0; i<=3; ++i) {
192 for (int j = 0; j <= 2; ++j) {
193 d_h += a[i][j] * pow(theta, i) * pow(m, j);
194 }
195 }
196
197 const Evaluation delta_h = 4.184/(1e3 + (58.44 * m))*d_h;
198
199 // Enthalpy of brine
200 const Evaluation h_ls = (1-S)*hw + S*h_NaCl + S*delta_h; // [kJ/kg]
201 return h_ls*1e3; // convert to [J/kg]
202 }
203
204
208 template <class Evaluation>
209 static Evaluation liquidHeatCapacity(const Evaluation& temperature,
210 const Evaluation& pressure)
211 {
212 Scalar eps = scalarValue(temperature)*1e-8;
213 return (liquidEnthalpy(temperature + eps, pressure) - liquidEnthalpy(temperature, pressure))/eps;
214 }
215
219 template <class Evaluation>
220 static Evaluation gasHeatCapacity(const Evaluation& temperature,
221 const Evaluation& pressure)
222 { return H2O::gasHeatCapacity(temperature, pressure); }
223
227 template <class Evaluation>
228 static Evaluation gasInternalEnergy(const Evaluation& temperature,
229 const Evaluation& pressure)
230 {
231 return
232 gasEnthalpy(temperature, pressure) -
233 pressure/gasDensity(temperature, pressure);
234 }
235
239 template <class Evaluation>
240 static Evaluation liquidInternalEnergy(const Evaluation& temperature,
241 const Evaluation& pressure)
242 {
243 return
244 liquidEnthalpy(temperature, pressure) -
245 pressure/liquidDensity(temperature, pressure);
246 }
247
251 template <class Evaluation>
252 static Evaluation gasDensity(const Evaluation& temperature, const Evaluation& pressure)
253 { return H2O::gasDensity(temperature, pressure); }
254
262 template <class Evaluation>
263 static Evaluation liquidDensity(const Evaluation& temperature, const Evaluation& pressure, const Evaluation& salinity, bool extrapolate = false)
264 {
265 Evaluation tempC = temperature - 273.15;
266 Evaluation pMPa = pressure/1.0E6;
267
268 const Evaluation rhow = H2O::liquidDensity(temperature, pressure, extrapolate);
269 return
270 rhow +
271 1000*salinity*(
272 0.668 +
273 0.44*salinity +
274 1.0E-6*(
275 300*pMPa -
276 2400*pMPa*salinity +
277 tempC*(
278 80.0 +
279 3*tempC -
280 3300*salinity -
281 13*pMPa +
282 47*pMPa*salinity)));
283 }
284
288 template <class Evaluation>
289 static Evaluation gasPressure(const Evaluation& temperature, const Evaluation& density)
290 { return H2O::gasPressure(temperature, density); }
291
295 template <class Evaluation>
296 static Evaluation liquidPressure(const Evaluation& temperature, const Evaluation& density)
297 {
298 // We use the newton method for this. For the initial value we
299 // assume the pressure to be 10% higher than the vapor
300 // pressure
301 Evaluation pressure = 1.1*vaporPressure(temperature);
302 Scalar eps = scalarValue(pressure)*1e-7;
303
304 Evaluation deltaP = pressure*2;
305 for (int i = 0;
306 i < 5
307 && std::abs(scalarValue(pressure)*1e-9) < std::abs(scalarValue(deltaP));
308 ++i)
309 {
310 const Evaluation f = liquidDensity(temperature, pressure) - density;
311
312 Evaluation df_dp = liquidDensity(temperature, pressure + eps);
313 df_dp -= liquidDensity(temperature, pressure - eps);
314 df_dp /= 2*eps;
315
316 deltaP = - f/df_dp;
317
318 pressure += deltaP;
319 }
320
321 return pressure;
322 }
323
327 template <class Evaluation>
328 static Evaluation gasViscosity(const Evaluation& temperature, const Evaluation& pressure)
329 { return H2O::gasViscosity(temperature, pressure); }
330
339 template <class Evaluation>
340 static Evaluation liquidViscosity(const Evaluation& temperature, const Evaluation& /*pressure*/, const Evaluation& salinity)
341 {
342 Evaluation T_C = temperature - 273.15;
343 if(temperature <= 275.) // regularization
344 T_C = 275.0;
345
346 Evaluation A = (0.42*Opm::pow((Opm::pow(salinity, 0.8)-0.17), 2) + 0.045)*pow(T_C, 0.8);
347 Evaluation mu_brine = 0.1 + 0.333*salinity + (1.65+91.9*salinity*salinity*salinity)*exp(-A);
348
349 return mu_brine/1000.0; // convert to [Pa s] (todo: check if correct cP->Pa s is times 10...)
350 }
351
352 //Molar mass salt (assumes pure NaCl) [kg/mol]
353 static constexpr Scalar mM_salt = 58.44e-3;
354
355};
356
357} // namespace Opm
358
359#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:48
static Evaluation molarMass(const Evaluation &salinity)
The molar mass in of the component.
Definition BrineDynamic.hpp:81
static Scalar tripleTemperature()
Returns the temperature at water's triple point.
Definition BrineDynamic.hpp:115
static Evaluation gasDensity(const Evaluation &temperature, const Evaluation &pressure)
The density of steam in at a given pressure and temperature.
Definition BrineDynamic.hpp:252
static std::string_view name()
A human readable name for the component.
Definition BrineDynamic.hpp:54
static Evaluation gasViscosity(const Evaluation &temperature, const Evaluation &pressure)
The dynamic viscosity of steam.
Definition BrineDynamic.hpp:328
static Evaluation liquidEnthalpy(const Evaluation &temperature, const Evaluation &pressure, const Evaluation &salinity)
Specific enthalpy of the pure component in liquid.
Definition BrineDynamic.hpp:148
static Scalar criticalPressure()
Returns the critical pressure of water.
Definition BrineDynamic.hpp:97
static Scalar criticalVolume()
Returns the critical volume of water.
Definition BrineDynamic.hpp:103
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:263
static Evaluation liquidPressure(const Evaluation &temperature, const Evaluation &density)
The pressure of liquid water in at a given density and temperature.
Definition BrineDynamic.hpp:296
static Evaluation liquidViscosity(const Evaluation &temperature, const Evaluation &, const Evaluation &salinity)
The dynamic viscosity of pure water.
Definition BrineDynamic.hpp:340
static bool gasIsCompressible()
Returns true iff the gas phase is assumed to be compressible.
Definition BrineDynamic.hpp:66
static Evaluation gasHeatCapacity(const Evaluation &temperature, const Evaluation &pressure)
Specific isobaric heat capacity of water steam .
Definition BrineDynamic.hpp:220
static Evaluation gasEnthalpy(const Evaluation &temperature, const Evaluation &pressure)
Specific enthalpy of the pure component in gas.
Definition BrineDynamic.hpp:135
static Scalar acentricFactor()
Definition BrineDynamic.hpp:109
static Evaluation liquidHeatCapacity(const Evaluation &temperature, const Evaluation &pressure)
Specific isobaric heat capacity of liquid water .
Definition BrineDynamic.hpp:209
static bool liquidIsCompressible()
Returns true iff the liquid phase is assumed to be compressible.
Definition BrineDynamic.hpp:72
static Scalar triplePressure()
Returns the pressure at water's triple point.
Definition BrineDynamic.hpp:121
static bool gasIsIdeal()
Returns true iff the gas phase is assumed to be ideal.
Definition BrineDynamic.hpp:60
static Scalar criticalTemperature()
Returns the critical temperature of water.
Definition BrineDynamic.hpp:91
static Evaluation liquidInternalEnergy(const Evaluation &temperature, const Evaluation &pressure)
Specific internal energy of liquid water .
Definition BrineDynamic.hpp:240
static Evaluation gasPressure(const Evaluation &temperature, const Evaluation &density)
The pressure of steam in at a given density and temperature.
Definition BrineDynamic.hpp:289
static Evaluation vaporPressure(const Evaluation &T)
The vapor pressure in of pure water at a given temperature.
Definition BrineDynamic.hpp:128
static Evaluation gasInternalEnergy(const Evaluation &temperature, const Evaluation &pressure)
Specific internal energy of steam and water vapor .
Definition BrineDynamic.hpp:228
Abstract base class of a pure chemical species.
Definition Component.hpp:44
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