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Density.cpp
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/**
* \copyright
* Copyright (c) 2020, OpenGeoSys Community (http://www.opengeosys.org)
* Distributed under a Modified BSD License.
* See accompanying file LICENSE.txt or
* http://www.opengeosys.org/project/license
*
*/
#include <iostream>
#include <math.h>
#include <vector>
#include <cstdlib>
#include <cmath>
#include "IAPWS-IF97.h"
#include "Density.h"
using namespace std;
double density::Ds, density::Vs;
density::density(void) {}
density::~density(void) {}
void density::MaoModel(double T, double P, double m, int f)
{
double R = 83.14472, N0 = 6.0221367E+23, pai = 3.14159265,
qe = 1.60217733E-19, kB = 1.380658E-23, D0 = 8.85418781762E-12;
double dP = 1.0e-2, dH2O, dH2Oa, dH2Ob, Av, D1000, C, B, DD;
dH2O = IF97::density(T, P / 10.0);
dH2Oa = IF97::density(T, (P - dP) / 10.0);
dH2Ob = IF97::density(T, (P + dP) / 10.0);
const double U[10] = {0.0, 3.4279e+2, -5.0866e-3, 9.4690e-7, -2.0525,
3.1159e+3, -1.8289e+2, -8.0325e+3, 4.2142e+6, 2.1417};
D1000 = U[1] * exp(U[2] * T + U[3] * T * T);
C = U[4] + U[5] / (U[6] + T);
B = U[7] + U[8] / T + U[9] * T;
DD = D1000 + C * log((B + P) / (B + 1000));
// Aphia = 1.0/3.0*pow(2.0*pai*N0*dH2Oa,0.5) *
// pow(qe*qe/(4.0*pai*D0*Da*kB*T),1.5); Aphib
// = 1.0/3.0*pow(2.0*pai*N0*dH2Ob,0.5) *
// pow(qe*qe/(4.0*pai*D0*Db*kB*T),1.5); Av = -2.0*R*T*(Aphib-Aphia)/dP/10.0;
Av = -4.0 * R * T / 3.0 * pow(2.0 * pai * N0, 0.5) *
pow(qe * qe / (4.0 * pai * D0 * kB * T), 1.5) *
(pow(dH2O, 0.5) * (-1.5 * pow(DD, -2.5) * C / (B + P)) +
pow(DD, -1.5) * 0.5 * pow(dH2O, -0.5) * (dH2Ob - dH2Oa) / (2.0 * dP));
// cout << " Av---- " << Av << endl;
const double c[7][24] = {
{0.0,
1.17271480E+03,
1.40527916E-01,
-5.53962649E-04,
1.72402126E-06,
-1.57184556E-01,
8.89959461E-04,
-1.52090064E-06,
0.0,
7.33553879E-04,
4.06701494E-05,
-2.38873863E-07,
3.94900863E-10,
-3.56131664E-03,
-6.18472877E-07,
3.00484214E-08,
-1.02229075E-10,
0.0,
2.35592818E-06,
-2.68117086E-05,
-2.17228726E-06,
1.19732313E-08,
-1.51104808E-11,
3.83403994E-05},
{0.0,
1.06607098E+03,
-8.39622456E-03,
5.35429127E-04,
7.55373789E-07,
-4.19512335E-02,
1.45082899E-04,
-3.47807732E-07,
0.0,
1.10913788E-03,
1.14498252E-04,
-5.51181270E-07,
7.05483955E-10,
-5.05734723E-03,
-1.32747828E-06,
4.77261581E-08,
-1.76888377E-10,
0.0,
6.40541237E-06,
3.07698827E-05,
-1.64042763E-05,
7.06784935E-08,
-6.50338372E-11,
-4.50906014E-05},
{0.0,
2.90812061E+02,
6.54111195E+00,
-1.61831978E-02,
1.46280384E-05,
1.41397987E+00,
-1.07266230E-02,
2.64506021E-05,
-2.19789708E-08,
3.02182158E-03,
-2.15621394E-04,
9.24163206E-07,
-1.10089434E-09,
2.87018859E-03,
-6.73119697E-06,
1.68332473E-06,
-7.99645640E-09,
1.11881560E-11,
-6.59292385E-05,
-2.02369103E-04,
-1.70609099E-05,
1.00510108E-07,
-1.86624642E-10,
1.91919166E-03},
{0.0,
1.18880927E+03,
-1.43194546E+00,
3.87973220E-03,
-2.20330377E-06,
6.38745038E-01,
-5.51728055E-03,
1.50231562E-05,
-1.35757912E-08,
8.43627549E-04,
5.25365072E-04,
-1.87204100E-06,
4.20263897E-09,
-1.18062548E-01,
6.07424747E-06,
-1.20268210E-06,
5.23784551E-09,
-8.23940319E-12,
9.75167613E-05,
-4.92959181E-05,
-2.73642775E-05,
5.42602386E-08,
-1.95602825E-10,
1.00921935E-02},
{0.0,
1.12080057E+03,
-2.61669538E-01,
1.52042960E-03,
-6.89131095E-07,
-5.11802652E-02,
2.22234857E-04,
-5.66464544E-07,
2.92950266E-10,
2.43934633E-03,
-1.42746873E-04,
7.35840529E-07,
-9.43615480E-10,
-5.18606814E-03,
-6.16536928E-07,
-1.04523561E-07,
4.52637296E-10,
-1.05076158E-12,
2.31544709E-05,
-1.09663211E-04,
1.90836111E-05,
-9.25997994E-08,
1.54388261E-10,
-1.29354832E-03},
{0.0,
1.11894213E+03,
-7.37321458E-01,
1.77908655E-03,
0.0,
0.0,
0.0,
0.0,
0.0,
2.21225680E-03,
6.62517291E-05,
-2.37296050E-07,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
-4.21300430E-04,
0.0,
9.46738388E-09,
0.0,
0.0},
{0.0,
1.10229139E+03,
-7.53497776E-01,
1.92829036E-03,
0.0,
0.0,
-1.15406910E-04,
0.0,
0.0,
2.57437715E-03,
1.64541676E-05,
-9.30035886E-08,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0,
0.0},
};
const double mr[7] = {10.0, 6.0, 6.0, 2.0, 5.0, 2.0, 1.5};
const double Ms[7] = {42.394, 58.443, 74.551, 95.236,
110.986, 158.536, 206.286};
double Imx, Imrx, hIx, hIrx, CA, CB, CC;
if (f == 0 || f == 1 || f == 2)
{
Imx = m;
Imrx = mr[f];
CA = 2.0;
CB = 2.0;
CC = 2.0;
}
else
{
Imx = 3.0 * m;
Imrx = 3.0 * mr[f];
CA = 6.0;
CB = 4.0;
CC = 8.0;
}
hIx = log(1.0 + 1.2 * pow(Imx, 0.5)) / (2.0 * 1.2);
hIrx = log(1.0 + 1.2 * pow(Imrx, 0.5)) / (2.0 * 1.2);
if (m == 0)
density::Ds = dH2O / 1000.0;
else
density::Ds =
(1000 + m * Ms[f]) / m /
((1 / m - 1 / mr[f]) * 1.0e6 / dH2O + CA * Av * (hIx - hIrx) +
1.0 / mr[f] *
(c[f][1] + c[f][2] * T + c[f][3] * pow(T, 2.0) +
c[f][4] * pow(T, 3.0) +
P * (c[f][5] + c[f][6] * T + c[f][7] * pow(T, 2.0) +
c[f][8] * pow(T, 3.0))) +
CB * R * T * (m - mr[f]) *
(c[f][9] / (T - 227.0) + c[f][10] + c[f][11] * T +
c[f][12] * pow(T, 2.0) + c[f][13] / (647.0 - T) +
P * (c[f][14] / (T - 227.0) + c[f][15] + c[f][16] * T +
c[f][17] * pow(T, 2.0) + c[f][18] / (647 - T))) +
CC * R * T * (m * m - pow(mr[f], 2.0)) *
(c[f][19] / (T - 227.0) + c[f][20] + c[f][21] * T +
c[f][22] * pow(T, 2.0) + c[f][23] / (647.0 - T)));
density::Vs = 1.0 / mr[f] *
(c[f][1] + c[f][2] * T + c[f][3] * pow(T, 2.0) +
c[f][4] * pow(T, 3.0) +
P * (c[f][5] + c[f][6] * T + c[f][7] * pow(T, 2.0) +
c[f][8] * pow(T, 3.0))) -
1.0e6 / mr[f] / dH2O - CA * Av * hIrx -
CB * R * T * mr[f] *
(c[f][9] / (T - 227.0) + c[f][10] + c[f][11] * T +
c[f][12] * pow(T, 2.0) + c[f][13] / (647.0 - T) +
P * (c[f][14] / (T - 227.0) + c[f][15] + c[f][16] * T +
c[f][17] * pow(T, 2.0) + c[f][18] / (647.0 - T))) -
CC * R * T * pow(mr[f], 2.0) *
(c[f][19] / (T - 227.0) + c[f][20] + c[f][21] * T +
c[f][22] * pow(T, 2.0) + c[f][23] / (647.0 - T));
}
double density::MultiDensity(
double T, double P, vector<double> mv, vector<int> fv)
{
const double Ms[7] = {42.394, 58.443, 74.551, 95.236,
110.986, 158.536, 206.286};
double mz = 0, mc = 0, mc0 = 0, Mt = 1000.0, Vt = 0, Vex, Vw;
int i, fr = 1, n = (int)fv.size();
density::MaoModel(T, P, 0.0, 0);
Vw = 1000.0 / density::Ds;
Vt = Vw;
for (i = 0; i < n; i++)
{
if (fv[i] == 0 || fv[i] == 1 || fv[i] == 2)
mc = mv[i];
else
mc = 3.0 * mv[i];
if (mc > mc0)
fr = fv[i];
mc0 = mc;
mz += mc;
Mt += mv[i] * Ms[fv[i]];
density::MaoModel(T, P, mv[i], fv[i]);
// cout << " Ds " << tdensity::Ds << endl;
Vt += mv[i] * density::Vs;
}
if (fr != 0 && fr != 1 && fr != 2)
mz /= 3.0;
density::MaoModel(T, P, mz, fr);
Vex = (1000.0 + mz * Ms[fr]) / density::Ds - Vw - mz * density::Vs;
Vt += Vex;
return Mt / Vt;
}
double density::ExcessM(double mv[])
{
double mex = 0.0;
mex += mv[0];
mex += mv[1];
mex += mv[2];
mex += 3.0 * mv[3];
mex += 3.0 * mv[4];
mex += mv[5];
mex += 3.0 * mv[6];
mex += 3.0 * mv[7];
return 0.5 * mex;
}
double density::Multi_density(double T, double P, double mv[])
{
double Vs[8];
const double Ms[8] = {6.941, 22.990, 39.098, 24.305,
40.080, 35.453, 96.058, 60.009}; // moleculer weight
double Mt = 1000.0, Vt = 0, Vex, Vw, mex;
int i;
// 0-Li, 1-Na, 2-K, 3-Mg, 4-Ca, 5-Cl, 6-SO4, 7-CO3
// calc Partial Moler Volume
// ref solute KCl, set Vs_K = Vs_Cl
density::MaoModel(T, P, 0.0, 2);
Vs[2] = 0.5 * density::Vs;
Vs[5] = 0.5 * density::Vs;
// Vs_Li = Vs_LiCl - Vs_Cl
density::MaoModel(T, P, 0.0, 0);
Vs[0] = density::Vs - Vs[5];
// Vs_Na
density::MaoModel(T, P, 0.0, 1);
Vs[1] = density::Vs - Vs[5];
// Vs_Mg = Vs_Na
Vs[3] = Vs[1];
// Vs_Ca = Vs_K
Vs[4] = Vs[2];
Vs[6] = 1.5 * Vs[5];
Vs[7] = 1.5 * Vs[5];
//=========
density::MaoModel(T, P, 0.0, 0);
Vw = 1000.0 / density::Ds;
Vt = Vw;
for (i = 0; i <= 7; i++)
{
Mt += mv[i] * Ms[i];
Vt += mv[i] * Vs[i];
}
mex = density::ExcessM(mv);
density::MaoModel(T, P, mex, 1);
Vex =
(1000.0 + mex * (Ms[1] + Ms[5])) / density::Ds - Vw - mex * density::Vs;
// cout << endl << mex<< " " << (1000.0+mex*(Ms[1]+Ms[5]))/density::Ds << "
// " << Vw<< " " << Vex << endl;
Vt += Vex;
// cout << " " << Mt << " " << Vt << endl;
return Mt / Vt;
}
double density::CO2brine(double T, double P, double mNaCl, double mCO2)
{
double Ps /*,mTot*/, V2, Dens;
if (mNaCl < 0.0 || mNaCl > 6.0 || mCO2 < 0.0)
{
Dens = -1.0;
goto T01;
}
if (T < 273.15 || T > 573.15 || P < 0.001 || P > 1000.0)
{
Dens = -1.0;
goto T01;
}
Ps = IF97::Psat(T) * 10.0;
if (Ps > P)
{
Dens = IF97::density(T, P / 10.0) / 1000.0;
cout << " Ps " << endl;
goto T01;
}
// mTot = 55.5084 +mNaCl +mCO2;
density::MaoModel(T, P, mNaCl, 1);
V2 = 18.0153 / IF97::density(T, P / 10.0) * 1000.0 *
(1.0 + 0.38384020e-3 * T * T - 0.55953850 * T + 0.30429268e3 -
0.72044305e5 / T + 0.63003388e7 / T / T +
(-0.57709332e-5 * T * T + 0.82764653e-2 * T - 0.43813556e1 +
0.10144907e4 / T - 0.86777045e5 / T / T) *
P / 10.0);
Dens = (1000.0 + 58.4428 * mNaCl + 44.0098 * mCO2) /
((1000.0 + 58.4428 * mNaCl) / density::Ds + V2 * mCO2);
T01:
return Dens;
}
// 0-Li, 1-Na, 2-K, 3-Mg, 4-Ca, 5-Cl, 6-SO4, 7-CO3
double density::CO2_MultiBrine_density(double T,
double P,
double mv[],
double mCO2)
{
double Ps, V2, Dens, Dens_B, Mt = 1000.0;
const double Ms[8] = {6.941, 22.990, 39.098, 24.305,
40.080, 35.453, 96.058, 60.009}; // moleculer weight
int i;
Ps = IF97::Psat(T) * 10.0;
if (Ps > P)
{
Dens = IF97::density(T, P / 10.0) / 1000.0;
goto T01;
}
Dens_B = density::Multi_density(T, P, mv);
for (i = 0; i <= 7; i++)
Mt += mv[i] * Ms[i];
V2 = 18.0153 / IF97::density(T, P / 10.0) * 1000.0 *
(1.0 + 0.38384020e-3 * T * T - 0.55953850 * T + 0.30429268e3 -
0.72044305e5 / T + 0.63003388e7 / T / T +
(-0.57709332e-5 * T * T + 0.82764653e-2 * T - 0.43813556e1 +
0.10144907e4 / T - 0.86777045e5 / T / T) *
P / 10.0);
Dens = (Mt + 44.0098 * mCO2) / (Mt / Dens_B + V2 * mCO2);
T01:
return Dens;
}
// 0-Li, 1-Na, 2-K, 3-Mg, 4-Ca, 5-Cl, 6-SO4, 7-CO3
double density::concentration_water(double T,
double P,
double cv[],
double cv_CO2) // unit mol/m3
{
const double Ms[8] = {6.941, 22.990, 39.098, 24.305,
40.080, 35.453, 96.058, 60.009}; // moleculer weight
double mv[8], mCO2, dens, d0, d1, mass, densx, err = 1.0e-4;
int i, ix;
d0 = 0.8;
d1 = 1.5;
for (ix = 0; ix < 8; ix++)
{
dens = 0.5 * (d0 + d1); // unit g/cm3
mass = dens * 1.0e6; // unit (g)
for (i = 0; i < 8; i++)
mass -= cv[i] * Ms[i];
mass -= cv_CO2 * 44.01;
for (i = 0; i < 8; i++)
{
mv[i] = 1000.0 * cv[i] / mass;
// cout << mv[i] << " " ;
}
mCO2 = 1000.0 * cv_CO2 / mass;
// cout << mCO2 << endl;
densx = density::CO2_MultiBrine_density(T, P, mv, mCO2);
// cout << " dens " << dens << " densx " << densx << endl;
if (abs(dens - densx) < err)
break;
else if (dens > densx)
d1 = dens;
else
d0 = dens;
}
return mass / 18.015;
}