static Evaluation vaporPressure(const Evaluation& temperature)
{
typedef MathToolbox<Evaluation> Toolbox;
if (temperature > criticalTemperature())
return criticalPressure();
if (temperature < tripleTemperature())
return 0; // N2 is solid: We don't take sublimation into
// account
// note: this is the ancillary equation given on page 1368
const Evaluation& sigma = 1.0 - temperature/criticalTemperature();
const Evaluation& sqrtSigma = Toolbox::sqrt(sigma);
const Scalar N1 = -6.12445284;
const Scalar N2 = 1.26327220;
const Scalar N3 = -0.765910082;
const Scalar N4 = -1.77570564;
return
criticalPressure() *
Toolbox::exp(criticalTemperature()/temperature*
(sigma*(N1 +
sqrtSigma*N2 +
sigma*(sqrtSigma*N3 +
sigma*sigma*sigma*N4))));
}
static Evaluation molarLiquidDensity_(Evaluation temperature)
{
typedef MathToolbox<Evaluation> Toolbox;
temperature = Toolbox::min(temperature, 500.0); // regularization
temperature = Toolbox::max(temperature, 250.0);
const Scalar Z_RA = 0.2556; // from equation
const Evaluation& expo = 1.0 + Toolbox::pow(1.0 - temperature/criticalTemperature(), 2.0/7.0);
const Evaluation& V = Consts::R*criticalTemperature()/criticalPressure()*Toolbox::pow(Z_RA, expo); // liquid molar volume [cm^3/mol]
return 1.0/V; // molar density [mol/m^3]
}
static Evaluation gasViscosity(const Evaluation& temperature, const Evaluation& /*pressure*/)
{
typedef MathToolbox<Evaluation> Toolbox;
const Scalar Tc = criticalTemperature();
const Scalar Vc = 90.1; // critical specific volume [cm^3/mol]
const Scalar omega = 0.037; // accentric factor
const Scalar M = molarMass() * 1e3; // molar mas [g/mol]
const Scalar dipole = 0.0; // dipole moment [debye]
Scalar mu_r4 = 131.3 * dipole / std::sqrt(Vc * Tc);
mu_r4 *= mu_r4;
mu_r4 *= mu_r4;
Scalar Fc = 1 - 0.2756*omega + 0.059035*mu_r4;
const Evaluation& Tstar = 1.2593 * temperature/Tc;
const Evaluation& Omega_v =
1.16145*Toolbox::pow(Tstar, -0.14874) +
0.52487*Toolbox::exp(- 0.77320*Tstar) +
2.16178*Toolbox::exp(- 2.43787*Tstar);
const Evaluation& mu = 40.785*Fc*Toolbox::sqrt(M*temperature)/(std::pow(Vc, 2./3)*Omega_v);
// convertion from micro poise to Pa s
return mu/1e6 / 10;
}
static Evaluation vaporPressure(const Evaluation& T)
{
typedef Opm::MathToolbox<Evaluation> Toolbox;
if (T > criticalTemperature())
return criticalPressure();
if (T < tripleTemperature())
return 0; // water is solid: We don't take sublimation into account
static const Scalar n[10] = {
0.11670521452767e4, -0.72421316703206e6, -0.17073846940092e2,
0.12020824702470e5, -0.32325550322333e7, 0.14915108613530e2,
-0.48232657361591e4, 0.40511340542057e6, -0.23855557567849,
0.65017534844798e3
};
Evaluation sigma = T + n[8]/(T - n[9]);
Evaluation A = (sigma + n[0])*sigma + n[1];
Evaluation B = (n[2]*sigma + n[3])*sigma + n[4];
Evaluation C = (n[5]*sigma + n[6])*sigma + n[7];
Evaluation tmp = 2.0*C/(Toolbox::sqrt(B*B - 4.0*A*C) - B);
tmp *= tmp;
tmp *= tmp;
return 1e6*tmp;
}
static Evaluation heatVap(const Evaluation& temperature, const Evaluation& /*pressure*/)
{
typedef MathToolbox<Evaluation> Toolbox;
Evaluation T = Toolbox::min(temperature, criticalTemperature()); // regularization
T = Toolbox::max(T, 0.0); // regularization
const Scalar T_crit = criticalTemperature();
const Scalar Tr1 = boilingTemperature()/criticalTemperature();
const Scalar p_crit = criticalPressure();
// Chen method, eq. 7-11.4 (at boiling)
const Scalar DH_v_boil =
Consts::R * T_crit * Tr1
* (3.978 * Tr1 - 3.958 + 1.555*std::log(p_crit * 1e-5 /*Pa->bar*/ ) )
/ (1.07 - Tr1); /* [J/mol] */
/* Variation with temp according to Watson relation eq 7-12.1*/
const Evaluation& Tr2 = T/criticalTemperature();
const Scalar n = 0.375;
const Evaluation& DH_vap = DH_v_boil * Toolbox::pow(((1.0 - Tr2)/(1.0 - Tr1)), n);
return (DH_vap/molarMass()); // we need [J/kg]
}
static Evaluation gasViscosity(Evaluation temperature, const Evaluation& /*pressure*/, bool /*regularize*/=true)
{
typedef MathToolbox<Evaluation> Toolbox;
temperature = Toolbox::min(temperature, 500.0); // regularization
temperature = Toolbox::max(temperature, 250.0);
// reduced temperature
const Evaluation& Tr = temperature/criticalTemperature();
Scalar Fp0 = 1.0;
Scalar xi = 0.00474;
const Evaluation& eta_xi =
Fp0*(0.807*Toolbox::pow(Tr,0.618)
- 0.357*Toolbox::exp(-0.449*Tr)
+ 0.34*Toolbox::exp(-4.058*Tr)
+ 0.018);
return eta_xi/xi/1e7; // [Pa s]
}
/*!
* \brief Molar volume of a component at the critical point [m^3/mol].
*/
static Scalar criticalMolarVolume(unsigned compIdx)
{
return
(compIdx == H2OIdx)
? H2O::criticalMolarVolume()
: (compIdx == C1Idx)
? 0.290*R*criticalTemperature(C1Idx)/criticalPressure(C1Idx)
: (compIdx == C3Idx)
? 0.277*R*criticalTemperature(C3Idx)/criticalPressure(C3Idx)
: (compIdx == C6Idx)
? 0.264*R*criticalTemperature(C6Idx)/criticalPressure(C6Idx)
: (compIdx == C10Idx)
? 0.257*R*criticalTemperature(C10Idx)/criticalPressure(C10Idx)
: (compIdx == C15Idx)
? 0.245*R*criticalTemperature(C15Idx)/criticalPressure(C15Idx)
: (compIdx == C20Idx)
? 0.235*R*criticalTemperature(C20Idx)/criticalPressure(C20Idx)
: 1e100;
}
