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 liquidHeatCapacity(const Evaluation& temperature,
const Evaluation& /*pressure*/)
{
/* according Reid et al. : Missenard group contrib. method (s. example 5-8) */
/* Mesitylen: C9H12 : 3* CH3 ; 1* C6H5 (phenyl-ring) ; -2* H (this was to much!) */
/* linear interpolation between table values [J/(mol K)]*/
Evaluation H, CH3, C6H5;
if(temperature<298.) {
// extrapolation for temperature < 273K
H = 13.4 + 1.2*(temperature-273.0)/25.; // 13.4 + 1.2 = 14.6 = H(T=298K) i.e. interpolation of table values 273<T<298
CH3 = 40.0 + 1.6*(temperature-273.0)/25.; // 40 + 1.6 = 41.6 = CH3(T=298K)
C6H5 = 113.0 + 4.2*(temperature-273.0)/25.; // 113 + 4.2 =117.2 = C6H5(T=298K)
}
else if((temperature>=298.0)&&(temperature<323.)){ // i.e. interpolation of table values 298<T<323
H = 14.6 + 0.9*(temperature-298.0)/25.;
CH3 = 41.6 + 1.9*(temperature-298.0)/25.;
C6H5 = 117.2 + 6.2*(temperature-298.0)/25.;
}
else if((temperature>=323.0)&&(temperature<348.)){// i.e. interpolation of table values 323<T<348
H = 15.5 + 1.2*(temperature-323.0)/25.;
CH3 = 43.5 + 2.3*(temperature-323.0)/25.;
C6H5 = 123.4 + 6.3*(temperature-323.0)/25.;
}
else {
assert(temperature>=348.0);
// extrapolation for temperature > 373K
H = 16.7+2.1*(temperature-348.0)/25.; // probably leads to underestimates
CH3 = 45.8+2.5*(temperature-348.0)/25.;
C6H5 = 129.7+6.3*(temperature-348.0)/25.;
}
return (C6H5 + 3*CH3 - 2*H)/molarMass(); // J/(mol K) -> J/(kg K)
}
static Evaluation gasEnthalpy(const Evaluation& temperature,
const Evaluation& /*pressure*/)
{
// method of Joback
const Scalar cpVapA = 31.15;
const Scalar cpVapB = -0.01357;
const Scalar cpVapC = 2.680e-5;
const Scalar cpVapD = -1.168e-8;
// calculate: \int_0^T c_p dT
return
1/molarMass()* // conversion from [J/(mol K)] to [J/(kg K)]
temperature*(cpVapA + temperature*
(cpVapB/2 + temperature*
(cpVapC/3 + temperature*
(cpVapD/4))));
//#warning NIST DATA STUPID INTERPOLATION
// Scalar T2 = 300.;
// Scalar T1 = 285.;
// Scalar h2 = 311200.;
// Scalar h1 = 295580.;
// Scalar h = h1+ (h2-h1) / (T2-T1) * (T-T1);
// return h ;
}
static Evaluation gasInternalEnergy(const Evaluation& temperature,
const Evaluation& pressure)
{
return
gasEnthalpy(temperature, pressure) -
1/molarMass()* // conversion from [J/(mol K)] to [J/(kg K)]
IdealGas::R*temperature; // = pressure * spec. volume for an ideal gas
}
Real
BrineFluidProperties::massFractionToMoleFraction(Real xnacl) const
{
// The average molar mass of brine from the mass fraction
Real Mbrine = molarMass(xnacl);
// The mole fraction is then
return xnacl * Mbrine / _Mnacl;
}
void initComchanMolars(Comchan &comchan) {
comchan.carbonM = 12.0107;
comchan.hydrogenM = 1.008;
comchan.oxygenM = 15.9994;
comchan.carbondioxideM = molarMass(0,1,2, comchan);
comchan.ethanolM = molarMass(6,2,1, comchan);
comchan.waterM = molarMass(2,0,1, comchan);
comchan.monosaccharideM = molarMass(12,6,6, comchan);
comchan.disaccharideM = molarMass(22,12,11, comchan);
comchan.ethanolEoC = 1058000;
comchan.sucroseEoC = 5648000;
comchan.enthalpyC = comchan.sucroseEoC - comchan.ethanolEoC*4;
comchan.watergL = 1000;
comchan.ethanolgL = 789;
comchan.carbondioxidegL = 1.98;
comchan.disaccharidegL = 1590;
comchan.monosaccharidegL = 1540;
comchan.lastLoaded = -1;
comchan.currentElement = 0;
}
static Evaluation gasHeatCapacity(const Evaluation& temperature,
const Evaluation& /*pressure*/)
{
// method of Joback
const Scalar cpVapA = 31.15;
const Scalar cpVapB = -0.01357;
const Scalar cpVapC = 2.680e-5;
const Scalar cpVapD = -1.168e-8;
return
1/molarMass()* // conversion from [J/(mol K)] to [J/(kg K)]
cpVapA + temperature*
(cpVapB + temperature*
(cpVapC + temperature*
(cpVapD)));
}
Real
BrineFluidProperties::rho(Real pressure, Real temperature, Real xnacl) const
{
Real n1, n2, n11, n12, n1x1, n20, n21, n22, n23, n2x1, Tv;
Real water_density;
// The correlation requires the pressure in bar, not Pa.
Real pbar = pressure * 1.0e-5;
Real pbar2 = pbar * pbar;
Real pbar3 = pbar2 * pbar;
// The correlation requires mole fraction
Real Xnacl = massFractionToMoleFraction(xnacl);
n11 = -54.2958 - 45.7623 * std::exp(-9.44785e-4 * pbar);
n21 = -2.6142 - 2.39092e-4 * pbar;
n22 = 0.0356828 + 4.37235e-6 * pbar + 2.0566e-9 * pbar2;
n1x1 = 330.47 + 0.942876 * std::sqrt(pbar) + 0.0817193 * pbar - 2.47556e-8 * pbar2 +
3.45052e-10 * pbar3;
n2x1 = -0.0370751 + 0.00237723 * std::sqrt(pbar) + 5.42049e-5 * pbar + 5.84709e-9 * pbar2 -
5.99373e-13 * pbar3;
n12 = -n1x1 - n11;
n20 = 1.0 - n21 * std::sqrt(n22);
n23 = n2x1 - n20 - n21 * std::sqrt(1.0 + n22);
// The temperature Tv where the brine has the same molar volume as pure water
// Note: correlation uses temperature in Celcius
n1 = n1x1 + n11 * (1.0 - Xnacl) + n12 * (1.0 - Xnacl) * (1.0 - Xnacl);
n2 = n20 + n21 * std::sqrt(Xnacl + n22) + n23 * Xnacl;
Tv = n1 + n2 * (temperature - _T_c2k);
// The density of water at temperature Tv
// Note: convert Tv to Kelvin to calculate water density
water_density = _water_fp->rho(pressure, Tv + _T_c2k);
// The brine density is given by the water density scaled by the ratio of
// brine molar mass to pure water molar mass
return water_density * molarMass(xnacl) / _Mh2o;
}
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 liquidDensity(const Evaluation& temperature, const Evaluation& /*pressure*/)
{ return molarLiquidDensity_(temperature)*molarMass(); }
static Evaluation gasDensity(const Evaluation& temperature, const Evaluation& pressure)
{ return IdealGas<Scalar>::density(Evaluation(molarMass()), temperature, pressure); }
static Evaluation liquidEnthalpy(const Evaluation& temperature, const Evaluation& /*pressure*/)
{
return 120.0/molarMass() * temperature; // [J/kg]
}
static Evaluation gasPressure(const Evaluation& temperature, const Evaluation& density)
{
// Assume an ideal gas
return IdealGas::pressure(temperature, density/molarMass());
}
static Evaluation gasDensity(const Evaluation& temperature, const Evaluation& pressure)
{
// Assume an ideal gas
return IdealGas::density(Evaluation(molarMass()), temperature, pressure);
}
static Evaluation gasDensity(const Evaluation& temperature, const Evaluation& pressure)
{
// Assume an ideal gas
return molarMass()*IdealGas::molarDensity(temperature, pressure);
}