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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 | // SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
6 | // | ||
7 | /*! | ||
8 | * \file | ||
9 | * \ingroup Components | ||
10 | * \brief A much simpler (and thus potentially less buggy) version of | ||
11 | * pure CO2. | ||
12 | */ | ||
13 | #ifndef DUMUX_SIMPLE_CO2_HH | ||
14 | #define DUMUX_SIMPLE_CO2_HH | ||
15 | |||
16 | #include <dune/common/stdstreams.hh> | ||
17 | |||
18 | #include <dumux/common/parameters.hh> | ||
19 | #include <dumux/material/idealgas.hh> | ||
20 | |||
21 | #include <cmath> | ||
22 | |||
23 | #include <dumux/material/components/base.hh> | ||
24 | #include <dumux/material/components/gas.hh> | ||
25 | |||
26 | namespace Dumux::Components { | ||
27 | |||
28 | /*! | ||
29 | * \ingroup Components | ||
30 | * \brief A simple version of pure CO2 | ||
31 | * | ||
32 | * \tparam Scalar The type used for scalar values | ||
33 | */ | ||
34 | template <class Scalar> | ||
35 | class SimpleCO2 | ||
36 | : public Components::Base<Scalar, SimpleCO2<Scalar> > | ||
37 | , public Components::Gas<Scalar, SimpleCO2<Scalar> > | ||
38 | { | ||
39 | using IdealGas = Dumux::IdealGas<Scalar>; | ||
40 | |||
41 | public: | ||
42 | /*! | ||
43 | * \brief A human readable name for the CO2. | ||
44 | */ | ||
45 | static std::string name() | ||
46 |
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|
10 | { return "SimpleCO2"; } |
47 | |||
48 | /*! | ||
49 | * \brief The mass in \f$\mathrm{[kg/mol]}\f$ of one mole of CO2. | ||
50 | */ | ||
51 | static constexpr Scalar molarMass() | ||
52 | { return 44.0e-3; /* [kg/mol] */ } | ||
53 | |||
54 | /*! | ||
55 | * \brief Returns the critical temperature \f$\mathrm{[K]}\f$ of CO2 | ||
56 | */ | ||
57 | static Scalar criticalTemperature() | ||
58 | { return 273.15 + 30.95; /* [K] */ } | ||
59 | |||
60 | /*! | ||
61 | * \brief Returns the critical pressure \f$\mathrm{[Pa]}\f$ of CO2 | ||
62 | */ | ||
63 | static Scalar criticalPressure() | ||
64 | { return 73.8e5; /* [Pa] */ } | ||
65 | |||
66 | /*! | ||
67 | * \brief Returns the temperature \f$\mathrm{[K]}\f$ at CO2's triple point. | ||
68 | */ | ||
69 | static Scalar tripleTemperature() | ||
70 | { return 273.15 - 56.35; /* [K] */ } | ||
71 | |||
72 | /*! | ||
73 | * \brief Returns the pressure \f$\mathrm{[Pa]}\f$ at CO2's triple point. | ||
74 | */ | ||
75 | static Scalar triplePressure() | ||
76 | { return 5.11e5; /* [N/m^2] */ } | ||
77 | |||
78 | |||
79 | /*! | ||
80 | * \brief Specific enthalpy of CO2 \f$\mathrm{[J/kg]}\f$. | ||
81 | * source: Shomate Equation for a temperature range of 298. to 1200K. | ||
82 | * with components published by NIST \cite NIST | ||
83 | * https://webbook.nist.gov/cgi/cbook.cgi?ID=C124389&Mask=1&Type=JANAFG&Table=on | ||
84 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
85 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
86 | */ | ||
87 | ✗ | static const Scalar gasEnthalpy(Scalar temperature, | |
88 | Scalar pressure) | ||
89 | { | ||
90 | ✗ | const Scalar t = temperature/1000; | |
91 | ✗ | constexpr double a = 24.99735; | |
92 | ✗ | constexpr double b = 55.18696; | |
93 | ✗ | constexpr double c = -33.69137; | |
94 | ✗ | constexpr double d = 7.948387; | |
95 | ✗ | constexpr double e = -0.136638; | |
96 | ✗ | constexpr double f = -403.6075; | |
97 | ✗ | constexpr double h = -393.5224; | |
98 | ✗ | return (a*t + b*t*t/2 + c*t*t*t/3 + d*t*t*t*t/4 - e/t +f -h)*1000/molarMass(); //conversion from kJ/mol to J/kg | |
99 | } | ||
100 | |||
101 | /*! | ||
102 | * \brief Specific internal energy of CO2 \f$\mathrm{[J/kg]}\f$. | ||
103 | * | ||
104 | * Definition of enthalpy: \f$h= u + pv = u + p / \rho\f$. | ||
105 | * Rearranging for internal energy yields: \f$u = h - pv\f$. | ||
106 | * Exploiting the Ideal Gas assumption (\f$pv = R_{\textnormal{specific}} T\f$)gives: \f$u = h - R / M T \f$. | ||
107 | * | ||
108 | * The universal gas constant can only be used in the case of molar formulations. | ||
109 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
110 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
111 | */ | ||
112 | static const Scalar gasInternalEnergy(Scalar temperature, | ||
113 | Scalar pressure) | ||
114 | { | ||
115 | // 1/molarMass: conversion from [J/(mol K)] to [J/(kg K)] | ||
116 | // R*T/molarMass: pressure *spec. volume for an ideal gas | ||
117 | return gasEnthalpy(temperature, pressure) | ||
118 | - 1.0/molarMass()*IdealGas::R*temperature; | ||
119 | } | ||
120 | |||
121 | /*! | ||
122 | * \brief Returns true if the gas phase is assumed to be compressible | ||
123 | */ | ||
124 | static constexpr bool gasIsCompressible() | ||
125 | { return true; } | ||
126 | |||
127 | /*! | ||
128 | * \brief Returns true if the gas phase viscostiy is constant | ||
129 | */ | ||
130 | static constexpr bool gasViscosityIsConstant() | ||
131 | { return false; } | ||
132 | |||
133 | /*! | ||
134 | * \brief The density \f$\mathrm{[kg/m^3]}\f$ of CO2 at a given pressure and temperature. | ||
135 | * | ||
136 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
137 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
138 | */ | ||
139 | static Scalar gasDensity(Scalar temperature, Scalar pressure) | ||
140 | 5191746 | { return IdealGas::density(molarMass(), temperature, pressure); } | |
141 | |||
142 | /*! | ||
143 | * \brief The molar density of CO2 in \f$\mathrm{[mol/m^3]}\f$ at a given pressure and temperature. | ||
144 | * | ||
145 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
146 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
147 | * | ||
148 | */ | ||
149 | static Scalar gasMolarDensity(Scalar temperature, Scalar pressure) | ||
150 | 5191544 | { return IdealGas::molarDensity(temperature, pressure); } | |
151 | |||
152 | /*! | ||
153 | * \brief Returns true if the gas phase is assumed to be ideal | ||
154 | */ | ||
155 | static constexpr bool gasIsIdeal() | ||
156 | { return true; } | ||
157 | |||
158 | /*! | ||
159 | * \brief The pressure of CO2 in \f$\mathrm{[Pa]}\f$ at a given density and temperature. | ||
160 | * | ||
161 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
162 | * \param density density of component in \f$\mathrm{[kg/m^3]}\f$ | ||
163 | */ | ||
164 | static Scalar gasPressure(Scalar temperature, Scalar density) | ||
165 | { return IdealGas::pressure(temperature, density/molarMass()); } | ||
166 | |||
167 | /*! | ||
168 | * \brief The dynamic viscosity \f$\mathrm{[Pa*s]}\f$ of CO2. | ||
169 | * Equations given in: - Vesovic et al., 1990 | ||
170 | * - Fenhour et al., 1998 | ||
171 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
172 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
173 | * TODO: this does not look like a really "simple" parameterization. Can this be simplified further? | ||
174 | */ | ||
175 | 5191645 | static Scalar gasViscosity(Scalar temperature, Scalar pressure) | |
176 | { | ||
177 | 5191645 | constexpr double a0 = 0.235156; | |
178 | 5191645 | constexpr double a1 = -0.491266; | |
179 | 5191645 | constexpr double a2 = 5.211155E-2; | |
180 | 5191645 | constexpr double a3 = 5.347906E-2; | |
181 | 5191645 | constexpr double a4 = -1.537102E-2; | |
182 | |||
183 | 5191645 | constexpr double d11 = 0.4071119E-2; | |
184 | 5191645 | constexpr double d21 = 0.7198037E-4; | |
185 | 5191645 | constexpr double d64 = 0.2411697E-16; | |
186 | 5191645 | constexpr double d81 = 0.2971072E-22; | |
187 | 5191645 | constexpr double d82 = -0.1627888E-22; | |
188 | |||
189 | 5191645 | constexpr double ESP = 251.196; | |
190 | |||
191 |
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5191645 | if(temperature < 275.0) // regularisation |
192 | { | ||
193 | 4 | temperature = 275.0; | |
194 | 4 | Dune::dgrave << "Temperature below 275K in viscosity function:" | |
195 | 4 | << "Regularizing temperature to 275K. " << std::endl; | |
196 | } | ||
197 | |||
198 | |||
199 | 5191645 | const double TStar = temperature/ESP; | |
200 | |||
201 | /* mu0: viscosity in zero-density limit */ | ||
202 | using std::exp; | ||
203 | using std::log; | ||
204 | using std::sqrt; | ||
205 | 5191645 | const double logTStar = log(TStar); | |
206 | 10383290 | const double SigmaStar = exp(a0 + a1*logTStar | |
207 | 5191645 | + a2*logTStar*logTStar | |
208 | 5191645 | + a3*logTStar*logTStar*logTStar | |
209 | 5191645 | + a4*logTStar*logTStar*logTStar*logTStar ); | |
210 | 5191645 | const double mu0 = 1.00697*sqrt(temperature) / SigmaStar; | |
211 | |||
212 | /* dmu : excess viscosity at elevated density */ | ||
213 | 5191645 | const double rho = gasDensity(temperature, pressure); /* CO2 mass density [kg/m^3] */ | |
214 | |||
215 | using Dune::power; | ||
216 | 5191645 | const double dmu = d11*rho + d21*rho*rho + d64*power(rho, 6)/(TStar*TStar*TStar) | |
217 | 10383290 | + d81*power(rho, 8) + d82*power(rho, 8)/TStar; | |
218 | |||
219 | 5191645 | return (mu0 + dmu)/1.0E6; /* conversion to [Pa s] */ | |
220 | } | ||
221 | |||
222 | |||
223 | /*! | ||
224 | * \brief Thermal conductivity \f$\mathrm{[[W/(m*K)]}\f$ of CO2. | ||
225 | * | ||
226 | * Thermal conductivity of CO2 at T=20°C, see: | ||
227 | * http://www.engineeringtoolbox.com/carbon-dioxide-d_1000.html | ||
228 | * | ||
229 | * \param temperature absolute temperature in \f$\mathrm{[K]}\f$ | ||
230 | * \param pressure of the phase in \f$\mathrm{[Pa]}\f$ | ||
231 | */ | ||
232 | ✗ | static Scalar gasThermalConductivity(Scalar temperature, Scalar pressure) | |
233 | { | ||
234 | ✗ | return 0.087; | |
235 | } | ||
236 | |||
237 | /*! | ||
238 | * \brief Specific isobaric heat capacity of CO2 \f$\mathrm{[J/(kg*K)]}\f$. | ||
239 | * source: Shomate Equation for a temperature range of 298. to 1200K. | ||
240 | * with components published by NIST \cite NIST | ||
241 | * https://webbook.nist.gov/cgi/cbook.cgi?ID=C124389&Mask=1&Type=JANAFG&Table=on | ||
242 | * \param temperature temperature of component in \f$\mathrm{[K]}\f$ | ||
243 | * \param pressure pressure of component in \f$\mathrm{[Pa]}\f$ | ||
244 | */ | ||
245 | ✗ | static Scalar gasHeatCapacity(Scalar temperature, Scalar pressure) | |
246 | { | ||
247 | 101 | const Scalar t = temperature/1000; | |
248 | 101 | constexpr double a = 24.99735; | |
249 | 101 | constexpr double b = 55.18696; | |
250 | 101 | constexpr double c = -33.69137; | |
251 | 101 | constexpr double d = 7.948387; | |
252 | 101 | constexpr double e = -0.136638; | |
253 | 101 | return (a + b*t + c*t*t + d*t*t*t + e/(t*t))/molarMass(); | |
254 | } | ||
255 | |||
256 | }; | ||
257 | |||
258 | } // end namespace Dumux::Components | ||
259 | |||
260 | #endif | ||
261 |