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HKF.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
*
*/
/* References
(1).Shock, E. L., Oelkers, E. H., Johnson, J. W., Sverjensky, D. A., and
Helgeson, H. C., 1992. Calculation of the Thermodynamic Properties of Aqueous
Species at High-Pressures and Temperatures- Effective Electrostatic Radii,
Dissociation-Constants and Standard Partial Molal Properties to 1000-Degrees-C
and 5-Kbar. Journal of the Chemical Society-Faraday Transactions 88, 803-826.
(2).Oelkers, E. H. and Helgeson, H. C., 1988. Calculation of the Thermodynamic
and Transport- Properties of Aqueous Species at High-Pressures and Temperatures
- Aqueous Tracer Diffusion- Coefficients of Ions to 1000-Degrees-C and 5-Kb.
Geochimica Et Cosmochimica Acta 52, 63-85.
(3).Duan, Z. H., Moller, N., and Weare, J. H., 1992.
An Equation of State for the Ch4-Co2-H2o System .1. Pure Systems from
0-Degrees-C to 1000-Degrees-C and 0 to 8000 Bar. Geochimica Et Cosmochimica Acta
56, 2605-2617.
(4).Helgeson, H. C., 1992. Effects of complex formation in flowing fluids on the
hydrothermal solubilities of minerals as a function of fluid pressure and
temperature in the critical and supercritical regions of the system H2O.
Geochimica Et Cosmochimica Acta 56, 3191-3207.
*/
#include <limits>
#include <string>
#include <iostream>
#include <fstream>
#include <sstream>
#include <math.h>
#include <cmath>
#include <cstdlib>
#include <iomanip>
#include <vector>
#include <stdio.h>
#include <ctype.h>
#include "VLE.h"
#include "NR.h"
#include "HKF.h"
#include "IO.h"
#include "IAPWS-IF97.h"
//#include "slop98.h"
using namespace std;
HKF::HKF(void) {}
HKF::~HKF(void) {}
int HKF::HKF_OGS_loadparam(std::string species_name0,
int& type,
double& charge,
double param[][4])
{
int i, j;
HKF::SpeciesData spec;
vector<HKF::SpeciesData> species_vector;
vector<int> name_type, phase_type;
spec.name0 = species_name0;
species_vector.clear();
species_vector.push_back(spec);
name_type.clear();
name_type.push_back(-1);
phase_type.clear();
phase_type.push_back(-1);
if (HKF::load_param(species_vector, name_type, phase_type) != 1)
{
// cout << " warning... " << endl;
// type=-1;
// charge=-99;
// for(i=0;i<9;i++)
// for(j=0;j<4;j++)
// param[i][j]=-99;
return 0;
}
else
{
spec = species_vector.back();
type = spec.type;
charge = spec.charge;
for (i = 0; i < 9; i++)
for (j = 0; j < 4; j++)
param[i][j] = spec.param[i][j];
return 1;
}
}
int HKF::HKF_OGS_calc(double T,
double P,
double& G,
double& H,
double& S,
int type,
double charge,
double param[][4])
{
int i, j, res = 1;
HKF::SpeciesData spec;
vector<HKF::SpeciesData> species_vector;
vector<int> name_type, phase_type;
spec.type = type;
spec.charge = charge;
for (i = 0; i < 9; i++)
for (j = 0; j < 4; j++)
spec.param[i][j] = param[i][j];
species_vector.clear();
species_vector.push_back(spec);
if (HelgesonEquation(T, P, species_vector) == 1)
{
spec = species_vector.back();
G = spec.G;
H = spec.H;
S = spec.S;
}
return res;
}
double HKF::HKFcalcw(double T, double P, int ghs)
{
double GG, HH, SS, res;
if (ghs > 2 || ghs < 0)
exit(0);
HH = (IF97::H(T, P / 10.0) / 55.51 - 287.45532) * 1000.0 / 4.18;
SS = (IF97::S(T, P / 10.0) / 55.51 + 0.0632944) * 1000.0 / 4.18;
GG = -125005.0 - HH;
if (ghs == 0)
res = GG;
else if (ghs == 1)
res = HH;
else if (ghs == 2)
res = SS;
return res;
}
double HKF::HKFcalc(
double T, double P, int ghs, std::string name, int sub, int type)
{
if (ghs > 2 || ghs < 0)
exit(0);
SpeciesData ion;
vector<HKF::SpeciesData> Ions;
vector<int> ntv, ptv;
int is_OK;
double res;
ion.name0 = name;
Ions.clear();
ntv.clear();
ptv.clear();
Ions.push_back(ion);
ntv.push_back(sub);
ptv.push_back(type);
is_OK = HKF::load_param(Ions, ntv, ptv);
if (is_OK != 1)
exit(0);
HelgesonEquation(T, P, Ions);
if (ghs == 0)
res = Ions[0].G;
else if (ghs == 1)
res = Ions[0].H;
else if (ghs == 2)
res = Ions[0].S;
return res;
}
int HKF::load_param(
vector<SpeciesData>& spec, vector<int> name_type, vector<int> phase_type)
{
if ((int)spec.size() == (int)name_type.size() &&
(int)spec.size() == (int)phase_type.size())
{
int i, j, js, jx, jz, type = -1, is_spec, is_OK = 0;
vector<string> pies, piesx, piesz, slop98;
vector<int> id_spec; // storage index of name0, which can be found in
// the species list.
int cek, cekz; // check species
string first_char;
id_spec.clear();
is_OK = IO::file2vector("slop98.dat", slop98);
// for(i=0;i<(int)slop98.size();i++){
// cin.get();
// cout << slop98[i] <<endl;
//}
if (is_OK)
{
for (i = 0; i < (int)slop98.size(); i++)
{
first_char = slop98[i].substr(0, 3);
if (first_char == "min" || first_char == "gas" ||
first_char == "aqu")
{
type++;
i++;
}
piesx = IO::string2vector(slop98[i]);
piesz = IO::string2vector(slop98[i + 1]);
for (j = 0; j < (int)spec.size(); j++)
{
// cout << i << " " << slop98[i] << " OK " << endl;
is_spec = 0;
// searching depend on name scform ecform and abbrev
if (name_type[j] == 0 && (int)piesx.size() > 0)
{
if (spec[j].name0 == piesx[0])
is_spec = 1;
}
else if (name_type[j] == 1 && (int)piesx.size() > 1)
{
if (spec[j].name0 == piesx[1])
is_spec = 1;
}
else if (name_type[j] == 2 && (int)piesz.size() > 0)
{
if (spec[j].name0 == piesz[0])
is_spec = 1;
}
else if (name_type[j] == 3 && (int)piesz.size() > 1)
{
if (spec[j].name0 == piesz[1])
is_spec = 1;
}
else
{
// cout << " OK load " << endl;
for (js = 0; js < (int)piesx.size(); js++)
if (spec[j].name0 == piesx[js])
is_spec = 1;
for (js = 0; js < (int)piesz.size(); js++)
if (spec[j].name0 == piesz[js])
is_spec = 1;
}
if (is_spec == 1)
{
// searching depend on phase type
is_spec = 0;
if (phase_type[j] == type || phase_type[j] < 0 ||
phase_type[j] > 5)
is_spec = 1;
}
if (is_spec == 1)
{
id_spec.push_back(j);
spec[j].name = piesx[0];
spec[j].scform = piesx[1];
if ((int)piesz.size() >= 2)
{
spec[j].abbrev = piesz[0];
spec[j].ecform = piesz[1];
}
else
{
spec[j].abbrev = "N/A";
spec[j].ecform = piesz[0];
}
pies = IO::string2vector(slop98[i + 2]);
spec[j].ref[0] = pies[0];
spec[j].ref[1] = pies[1];
spec[j].type = type;
switch (type)
{
case 0:
case 4:
case 5:
for (jx = 0; jx < 3; jx++)
{
pies =
IO::string2vector(slop98[i + jx + 3]);
for (jz = 0; jz < 4; jz++)
if (jz < (int)pies.size())
spec[j].param[jx][jz] =
atof(pies[jz].c_str());
else
spec[j].param[jx][jz] = 0.0;
}
for (jx = 3; jx < 9; jx++)
for (jz = 0; jz < 4; jz++)
spec[j].param[jx][jz] = 0.0;
spec[j].charge = spec[j].param[2][3];
break;
case 1:
pies = IO::string2vector(slop98[i + 3]);
for (jz = 0; jz < 4; jz++)
spec[j].param[0][jz] =
atof(pies[jz].c_str());
pies = IO::string2vector(slop98[i + 4]);
for (jz = 0; jz < 3; jz++)
spec[j].param[1][jz] =
atof(pies[jz].c_str());
spec[j].param[1][3] = 0.0;
for (jz = 0; jz < 4; jz++)
spec[j].param[2][jz] =
atof(pies[jz + 3].c_str());
pies = IO::string2vector(slop98[i + 5]);
for (jz = 0; jz < 3; jz++)
spec[j].param[3][jz] =
atof(pies[jz].c_str());
spec[j].param[3][3] = 0.0;
spec[j].param[4][0] =
atof(slop98[i + 6].c_str());
for (jz = 1; jz < 4; jz++)
spec[j].param[4][jz] = 0.0;
for (jx = 5; jx < 9; jx++)
for (jz = 0; jz < 4; jz++)
spec[j].param[jx][jz] = 0.0;
spec[j].charge = 0.0;
break;
case 2:
pies = IO::string2vector(slop98[i + 3]);
for (jz = 0; jz < 4; jz++)
spec[j].param[0][jz] =
atof(pies[jz].c_str());
pies = IO::string2vector(slop98[i + 4]);
for (jz = 0; jz < 3; jz++)
spec[j].param[1][jz] =
atof(pies[jz].c_str());
spec[j].param[1][3] = 0.0;
for (jz = 0; jz < 4; jz++)
spec[j].param[2][jz] =
atof(pies[jz + 3].c_str());
pies = IO::string2vector(slop98[i + 5]);
for (jz = 0; jz < 3; jz++)
spec[j].param[3][jz] =
atof(pies[jz].c_str());
spec[j].param[3][3] = 0.0;
for (jz = 0; jz < 4; jz++)
spec[j].param[4][jz] =
atof(pies[jz + 3].c_str());
pies = IO::string2vector(slop98[i + 6]);
for (jz = 0; jz < 3; jz++)
spec[j].param[5][jz] =
atof(pies[jz].c_str());
spec[j].param[5][3] = 0.0;
spec[j].param[6][0] =
atof(slop98[i + 7].c_str());
for (jz = 1; jz < 4; jz++)
spec[j].param[6][jz] = 0.0;
for (jx = 7; jx < 9; jx++)
for (jz = 0; jz < 4; jz++)
spec[j].param[jx][jz] = 0.0;
spec[j].charge = 0.0;
break;
case 3:
pies = IO::string2vector(slop98[i + 3]);
for (jz = 0; jz < 4; jz++)
spec[j].param[0][jz] =
atof(pies[jz].c_str());
pies = IO::string2vector(slop98[i + 4]);
for (jz = 0; jz < 3; jz++)
spec[j].param[1][jz] =
atof(pies[jz].c_str());
spec[j].param[1][3] = 0.0;
for (jz = 0; jz < 4; jz++)
spec[j].param[2][jz] =
atof(pies[jz + 3].c_str());
pies = IO::string2vector(slop98[i + 5]);
for (jz = 0; jz < 3; jz++)
spec[j].param[3][jz] =
atof(pies[jz].c_str());
spec[j].param[3][3] = 0.0;
for (jz = 0; jz < 4; jz++)
spec[j].param[4][jz] =
atof(pies[jz + 3].c_str());
pies = IO::string2vector(slop98[i + 6]);
for (jz = 0; jz < 3; jz++)
spec[j].param[5][jz] =
atof(pies[jz].c_str());
spec[j].param[5][3] = 0.0;
for (jz = 0; jz < 4; jz++)
spec[j].param[6][jz] =
atof(pies[jz + 3].c_str());
pies = IO::string2vector(slop98[i + 7]);
for (jz = 0; jz < 3; jz++)
spec[j].param[7][jz] =
atof(pies[jz].c_str());
spec[j].param[7][3] = 0.0;
spec[j].param[8][0] =
atof(slop98[i + 8].c_str());
for (jz = 1; jz < 4; jz++)
spec[j].param[8][jz] = 0.0;
spec[j].charge = 0.0;
break;
default:
break;
} // end switch
} // end if
} // end for
switch (type)
{
case 0:
case 4:
case 5:
i += 5;
break;
case 1:
i += 6;
break;
case 2:
i += 7;
break;
case 3:
i += 8;
break;
default:
break;
}
}
if ((int)id_spec.size() > 0)
{
cekz = 1;
for (i = 0; i < (int)spec.size(); i++)
{
cek = 0;
for (j = 0; j < (int)id_spec.size(); j++)
if (id_spec[j] == i)
cek = 1;
if (cek == 0)
{
cekz = 0;
cout << endl
<< " Warning! " << spec[i].name0 << " ("
<< name_type[i] << ") is NOT in the species list!"
<< endl;
}
}
if (cekz == 1)
return 1; // OK
else
return -1; // species name is incorrect
}
else
return -2; // did nothing
}
else
return 0; // can NOT open species list vector
}
else
exit(0);
}
int HKF::HelgesonEquation(double T, double P, vector<SpeciesData>& spec)
{
double c1, c2, a1, a2, a3, a4, Z, dG, dH, dS,
dV; // aqueous species parameters from database
double Sc1, Sc2, Sa3, Sa4, Sw;
double Hc1, Hc2, Ha1, Ha2, Ha3, Ha4, Hw;
double Gc1, Gc2, Ga1, Ga2, Ga3, Ga4, Gw;
double a0, b0,
c0 /*, Tmax*/; // gases and minerals parameters from database
double theta, psi, eta, Tr, Pr, e, er, Yr, Y, g; // independent on species
double rejr, rej, wr, w, X1; // dependent on species
int i, is_aq = 0;
Tr = 298.15; // p819 Ref.(1)
Pr = 1.0; // p819 Ref.(1)
for (i = 0; i < (int)spec.size(); i++)
if (spec[i].type == 5)
is_aq = 1;
if (is_aq == 1)
{
theta = 228.0; // p819 Ref.(1)
psi = 2600.0; // p819 Ref.(1)
eta = 1.66027E5; // p824 Ref.(1)
e = diel_water(T, P); //(C1) p821 Ref.(1)
er = diel_water(Tr, Pr);
Yr = Yfunc(Tr, Pr); // Yr = -5.8E-5; p824 Ref.(1)
Y = Yfunc(T, P); //(A25) Ref.(1)
g = gfunc(T, P); // Eq(24) p807 Ref.(1)
Sc1 = log(T / Tr);
Sc2 = -(1 / (T - theta) - 1 / (Tr - theta) +
1 / theta * log(Tr * (T - theta) / T / (Tr - theta))) /
theta;
Sa3 = 1 / (T - theta) / (T - theta) * (P - Pr);
Sa4 = 1 / (T - theta) / (T - theta) * log((psi + P) / (psi + Pr));
//(A20) & (B21) Ref.(1)
Hc1 = T - Tr;
Hc2 = -(1.0 / (T - theta) - 1.0 / (Tr - theta));
Ha1 = P - Pr;
Ha2 = log((psi + P) / (psi + Pr));
Ha3 = (2 * T - theta) / pow((T - theta), 2.0) * (P - Pr);
Ha4 = (2 * T - theta) / pow((T - theta), 2.0) *
log((psi + P) / (psi + Pr));
// A(22) & B(23) Ref.(1)
Gc1 = -(T * log(T / Tr) - T + Tr);
Gc2 = -(((1.0 / (T - theta)) - (1.0 / (Tr - theta))) * (theta - T) /
theta -
T / theta / theta * log(Tr * (T - theta) / T / (Tr - theta)));
Ga1 = P - Pr;
Ga2 = log((psi + P) / (psi + Pr));
Ga3 = 1.0 / (T - theta) * (P - Pr);
Ga4 = 1.0 / (T - theta) * log((psi + P) / (psi + Pr));
// A(24) & B(25) Ref.(1)
}
else
{
Yr = g = e = er = Y = 0.0;
Sc1 = Sc2 = Sa3 = Sa4 = 0.0;
Hc1 = Hc2 = Ha1 = Ha2 = Ha3 = Ha4 = 0.0;
Gc1 = Gc2 = Ga1 = Ga2 = Ga3 = Ga4 = 0.0;
}
for (i = 0; i < (int)spec.size(); i++)
{
if (spec[i].type == 5)
{
dG = spec[i].param[0][0];
dH = spec[i].param[0][1];
dS = spec[i].param[0][2];
a1 = spec[i].param[1][0] * 1.0E-1;
a2 = spec[i].param[1][1] * 1.0E+2;
a3 = spec[i].param[1][2];
a4 = spec[i].param[1][3] * 1.0E+4;
c1 = spec[i].param[2][0];
c2 = spec[i].param[2][1] * 1.0E+4;
wr = spec[i].param[2][2] * 1.0E+5;
Z = spec[i].charge;
if (Z == 0)
{
Sw = wr * (Y - Yr); //(A20) Ref.(1)
Gw = wr * (Yr * (T - Tr) + 1.0 / e - 1.0 / er); //(A24) Ref.(1)
Hw = wr *
(T * Y - Tr * Yr + 1.0 / e - 1.0 / er); //(A22) Ref.(1)
}
else
{
rejr = Z * Z * (eta * Yr - 100.0) /
(dS - 71.5 * abs(Z)); //(D1) Ref.(1) & Eq(29) Ref.(4)
rej = rejr + abs(Z) * g; // Eq(6) Ref.(1)
wr = eta * Z * (Z / rejr - 1.0 / 3.082); //(D5) Ref.(1)
w = eta * Z *
(Z / (rejr + abs(Z) * g) -
1.0 / (3.082 + g)); //(D4) Ref.(1)
X1 = -eta * (pow(abs(Z), 3.0) * pow(rej, -2.0) -
Z * pow((3.082 + g), -2.0)); //(B19) Ref.(1)
Sw = w * Y - (1.0 / e - 1.0) * X1 * NR::dfridrX(gfunc, T, P) -
wr * Yr; //(B21) & (B14) Ref.(1)
Hw = w * (1.0 / e - 1.0) + w * T * Y -
T * (1.0 / e - 1.0) * X1 * NR::dfridrX(gfunc, T, P) -
wr * (1.0 / er - 1.0) - wr * Tr * Yr;
Gw = w * (1.0 / e - 1.0) - wr * (1.0 / er - 1.0) +
wr * Yr * (T - Tr);
}
spec[i].S = dS + c1 * Sc1 + c2 * Sc2 + a3 * Sa3 + a4 * Sa4 +
Sw; //(A20) (B21) Ref.(1)
spec[i].G = dG - dS * (T - Tr) + c1 * Gc1 + c2 * Gc2 + a1 * Ga1 +
a2 * Ga2 + a3 * Ga3 + a4 * Ga4 +
Gw; //(A24) (B25) Ref.(1)
spec[i].H = dH + c1 * Hc1 + c2 * Hc2 + a1 * Ha1 + a2 * Ha2 +
a3 * Ha3 + a4 * Ha4 + Hw; //(A22) (B23) Ref.(1)
}
else
{
dG = spec[i].param[0][0];
dH = spec[i].param[0][1];
dS = spec[i].param[0][2];
dV = spec[i].param[0][3];
a0 = spec[i].param[1][0];
b0 = spec[i].param[1][1] * 1.0e-3;
c0 = spec[i].param[1][2] * 1.0e5;
switch (spec[i].type)
{
case 0:
case 4:
// Tmax= spec[i].param[2][0];
spec[i].G = dG - dS * (T - Tr) +
a0 * (T - Tr - T * log(T / Tr)) +
(-1.0 * c0 - b0 * T * Tr * Tr) * (T - Tr) *
(T - Tr) / (2.0 * T * Tr * Tr) +
dV * (P - Pr) * 0.1 /
4.18; // volume, pressure and energy unit
// convert factor
spec[i].H =
dH + a0 * (T - Tr) + b0 / 2.0 * (T * T - Tr * Tr) -
c0 * (1.0 / T - 1.0 / Tr) + dV * (P - Pr) * 0.1 / 4.18;
spec[i].S = dS + a0 * log(T / Tr) + b0 * (T - Tr) -
c0 / 2.0 * (1.0 / T / T - 1.0 / Tr / Tr);
break;
case 1:
case 2:
case 3:
default:
spec[i].G = 0.0;
spec[i].H = 0.0;
spec[i].S = 0.0;
break;
}
}
}
return 1;
}
// calculting the dielectric constant (relative permittivity) of pure water from
// T,P 1000C 5000bar Ref.(1) Appendix C
double HKF::diel_water(double T, double P)
{ // T K, P bar
double k0, k1, k2, k3, k4, Tr, z, dens;
double a1, a2, a3, a4, a5, a6, a7, a8, a9, a10;
Tr = 298.15;
z = T / Tr;
dens = VLE::density_H2O(T, P); // Ref.(3)
a1 = 14.70333593; // Table C1 Ref.(1)
a2 = 212.8462733;
a3 = -115.4445173;
a4 = 19.55210915;
a5 = -83.30347980;
a6 = 32.13240048;
a7 = -6.694098645;
a8 = -37.86202045;
a9 = 68.87359646;
a10 = -27.29401652;
k0 = 1.0; //(C2)
k1 = a1 / z; //(C3)
k2 = a2 / z + a3 + a4 * z; //(C4)
k3 = a5 / z + a6 * z + a7 * z * z; //(C5)
k4 = a8 / z / z + a9 / z + a10; //(C6)
return k0 + k1 * dens + k2 * dens * dens + k3 * pow(dens, 3.0) +
k4 * pow(dens, 4.0); //(C1)
}
double HKF::Ydiff(double T, double P)
{
return 1.0 / diel_water(T, P);
}
double HKF::Yfunc(double T, double P)
{
return -NR::dfridrX(Ydiff, T, P);
}
double HKF::gfunc(double T, double P)
{
double Dw, ag, bg, a1, a2, a3, Tf, Pf;
Dw = VLE::density_H2O(T, P); // Ref.(3)
if (Dw >= 1.0)
return 0.0; // Fig.6 & p811 Ref.(1)
else
{
T = T - 273.15;
ag = -2.037662 + 5.747000E-3 * T -
6.557892E-6 * T * T; // Eq(25) Table 3 p807 Ref.(1)
bg = 6.107361 - 1.074377E-2 * T + 1.268348E-5 * T * T; // Eq(26)
if (T < 155.0 || P > 1000.0)
return ag * pow((1.0 - Dw), bg); // Eq(24) Ref.(1) Fig.6
else
{
a1 = 3.66666E-16; // Table.4 Ref.(1)
a2 = -1.504956E-10;
a3 = 5.01799E-14;
Tf = (T - 155.0) / 300.0;
Pf = 1000.0 - P;
return ag * pow((1.0 - Dw), bg) -
(pow(Tf, 4.8) + a1 * pow(Tf, 16)) *
(a2 * pow(Pf, 3.0) +
a3 * pow(Pf, 4.0)); // Eq(32) & Eq(33) Ref.(1)
}
}
}