276 lines
8.6 KiB
C++
276 lines
8.6 KiB
C++
// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
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// vi: set et ts=4 sw=4 sts=4:
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/*
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This file is part of the Open Porous Media project (OPM).
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OPM is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 2 of the License, or
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(at your option) any later version.
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OPM is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with OPM. If not, see <http://www.gnu.org/licenses/>.
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Consult the COPYING file in the top-level source directory of this
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module for the precise wording of the license and the list of
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copyright holders.
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*/
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/*!
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* \file
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*
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* \copydoc Opm::CO2
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*/
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#ifndef OPM_CO2_HPP
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#define OPM_CO2_HPP
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#include <opm/material/Constants.hpp>
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#include <opm/material/IdealGas.hpp>
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#include <opm/material/components/Component.hpp>
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#include <opm/material/common/MathToolbox.hpp>
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#include <opm/material/common/UniformTabulated2DFunction.hpp>
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#include <cmath>
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namespace Opm {
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/*!
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* \brief A class for the CO2 fluid properties
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*
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* Under reservoir conditions, CO2 is typically in supercritical
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* state. These properties can be provided in tabulated form, which is
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* necessary for this component. The template is used by the
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* fluidsystem \c BrineCO2FluidSystem. If thermodynamic precision
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* is not a top priority, the much simpler component \c Opm::SimpleCO2 can be
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* used instead
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*/
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template <class Scalar>
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class CO2 : public Component<Scalar, CO2<Scalar>>
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{
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static constexpr Scalar R = Constants<Scalar>::R;
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static const UniformTabulated2DFunction<double>& tabulatedEnthalpy;
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static const UniformTabulated2DFunction<double>& tabulatedDensity;
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public:
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static const Scalar brineSalinity;
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/*!
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* \brief A human readable name for the CO2.
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*/
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static const char* name()
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{ return "CO2"; }
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/*!
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* \brief The mass in [kg] of one mole of CO2.
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*/
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static Scalar molarMass()
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{ return 44e-3; }
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/*!
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* \brief Returns the critical temperature [K] of CO2
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*/
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static Scalar criticalTemperature()
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{ return 273.15 + 30.95; /* [K] */ }
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/*!
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* \brief Returns the critical pressure [Pa] of CO2
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*/
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static Scalar criticalPressure()
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{ return 73.8e5; /* [N/m^2] */ }
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/*!
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* \brief Returns the temperature [K]at CO2's triple point.
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*/
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static Scalar tripleTemperature()
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{ return 273.15 - 56.35; /* [K] */ }
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/*!
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* \brief Returns the pressure [Pa] at CO2's triple point.
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*/
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static Scalar triplePressure()
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{ return 5.11e5; /* [N/m^2] */ }
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/*!
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* \brief Returns the pressure [Pa] at CO2's triple point.
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*/
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// static Scalar minTabulatedPressure()
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// { return tabulatedEnthalpy.minPress(); /* [N/m^2] */ }
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/*!
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* \brief Returns the pressure [Pa] at CO2's triple point.
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*/
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// static Scalar maxTabulatedPressure()
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// { return tabulatedEnthalpy.maxPress(); /* [N/m^2] */ }
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/*!
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* \brief Returns the pressure [Pa] at CO2's triple point.
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*/
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// static Scalar minTabulatedTemperature()
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// { return tabulatedEnthalpy.minTemp(); /* [N/m^2] */ }
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/*!
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* \brief Returns the pressure [Pa] at CO2's triple point.
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*/
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// static Scalar maxTabulatedTemperature()
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// { return tabulatedEnthalpy.maxTemp(); /* [N/m^2] */ }
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/*!
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* \brief The vapor pressure in [N/m^2] of pure CO2
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* at a given temperature.
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*
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* See:
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*
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* R. Span and W. Wagner: A New Equation of State for Carbon
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* Dioxide Covering the Fluid Region from the Triple‐Point
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* Temperature to 1100 K at Pressures up to 800 MPa. Journal of
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* Physical and Chemical Reference Data, 25 (6), pp. 1509-1596,
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* 1996
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*/
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template <class Evaluation>
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static Evaluation vaporPressure(const Evaluation& T)
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{
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static constexpr Scalar a[4] =
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{ -7.0602087, 1.9391218, -1.6463597, -3.2995634 };
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static constexpr Scalar t[4] =
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{ 1.0, 1.5, 2.0, 4.0 };
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// this is on page 1524 of the reference
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Evaluation exponent = 0;
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Evaluation Tred = T/criticalTemperature();
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for (int i = 0; i < 4; ++i)
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exponent += a[i]*pow(1 - Tred, t[i]);
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exponent *= 1.0/Tred;
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return exp(exponent)*criticalPressure();
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}
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/*!
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* \brief Returns true iff the gas phase is assumed to be compressible
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*/
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static bool gasIsCompressible()
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{ return true; }
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/*!
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* \brief Returns true iff the gas phase is assumed to be ideal
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*/
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static bool gasIsIdeal()
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{ return false; }
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/*!
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* \brief Specific enthalpy of gaseous CO2 [J/kg].
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*/
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template <class Evaluation>
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static Evaluation gasEnthalpy(const Evaluation& temperature,
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const Evaluation& pressure,
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bool extrapolate = false)
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{
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return tabulatedEnthalpy.eval(temperature, pressure, extrapolate);
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}
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/*!
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* \brief Specific internal energy of CO2 [J/kg].
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*/
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template <class Evaluation>
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static Evaluation gasInternalEnergy(const Evaluation& temperature,
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const Evaluation& pressure,
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bool extrapolate = false)
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{
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const Evaluation h = gasEnthalpy(temperature, pressure, extrapolate);
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const Evaluation rho = gasDensity(temperature, pressure, extrapolate);
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return h - (pressure / rho);
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}
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/*!
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* \brief The density of CO2 at a given pressure and temperature [kg/m^3].
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*/
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template <class Evaluation>
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static Evaluation gasDensity(const Evaluation& temperature,
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const Evaluation& pressure,
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bool extrapolate = false)
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{
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return tabulatedDensity.eval(temperature, pressure, extrapolate);
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}
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/*!
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* \brief The dynamic viscosity [Pa s] of CO2.
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*
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* Equations given in: - Vesovic et al., 1990
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* - Fenhour etl al., 1998
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*/
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template <class Evaluation>
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static Evaluation gasViscosity(Evaluation temperature,
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const Evaluation& pressure,
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bool extrapolate = false)
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{
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constexpr Scalar a0 = 0.235156;
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constexpr Scalar a1 = -0.491266;
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constexpr Scalar a2 = 5.211155e-2;
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constexpr Scalar a3 = 5.347906e-2;
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constexpr Scalar a4 = -1.537102e-2;
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constexpr Scalar d11 = 0.4071119e-2;
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constexpr Scalar d21 = 0.7198037e-4;
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constexpr Scalar d64 = 0.2411697e-16;
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constexpr Scalar d81 = 0.2971072e-22;
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constexpr Scalar d82 = -0.1627888e-22;
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constexpr Scalar ESP = 251.196;
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if(temperature < 275.) // regularization
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temperature = 275.0;
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Evaluation TStar = temperature/ESP;
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// mu0: viscosity in zero-density limit
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const Evaluation logTStar = log(TStar);
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Evaluation SigmaStar = exp(a0 + logTStar*(a1 + logTStar*(a2 + logTStar*(a3 + logTStar*a4))));
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Evaluation mu0 = 1.00697*sqrt(temperature) / SigmaStar;
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const Evaluation rho = gasDensity(temperature, pressure, extrapolate); // CO2 mass density [kg/m^3]
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// dmu : excess viscosity at elevated density
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Evaluation dmu =
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d11*rho
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+ d21*rho*rho
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+ d64*pow(rho, 6.0)/(TStar*TStar*TStar)
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+ d81*pow(rho, 8.0)
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+ d82*pow(rho, 8.0)/TStar;
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return (mu0 + dmu)/1.0e6; // conversion to [Pa s]
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}
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/*!
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* \brief Specific isobaric heat capacity of the component [J/kg]
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* as a liquid.
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*
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* This function uses the fact that heat capacity is the partial
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* derivative of enthalpy function with respect to temperature.
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*
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* \param temperature Temperature of component \f$\mathrm{[K]}\f$
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* \param pressure Pressure of component \f$\mathrm{[Pa]}\f$
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*/
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template <class Evaluation>
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static Evaluation gasHeatCapacity(const Evaluation& temperature, const Evaluation& pressure)
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{
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constexpr Scalar eps = 1e-6;
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// use central differences here because one-sided methods do
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// not come with a performance improvement. (central ones are
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// more accurate, though...)
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const Evaluation h1 = gasEnthalpy(temperature - eps, pressure);
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const Evaluation h2 = gasEnthalpy(temperature + eps, pressure);
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return (h2 - h1) / (2*eps) ;
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}
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};
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} // namespace Opm
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#endif
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