28 #ifndef OPM_BINARY_COEFF_BRINE_CO2_HPP
29 #define OPM_BINARY_COEFF_BRINE_CO2_HPP
34 namespace BinaryCoeff {
40 template<
class Scalar,
class H2O,
class CO2,
bool verbose = true>
42 typedef ::Opm::IdealGas<Scalar>
IdealGas;
43 static const int liquidPhaseIdx = 0;
44 static const int gasPhaseIdx = 1;
54 template <
class Evaluation>
55 static Evaluation
gasDiffCoeff(
const Evaluation& temperature,
const Evaluation& pressure)
58 Scalar k = 1.3806504e-23;
60 Scalar R_h = 1.72e-10;
62 return k / (c * M_PI * R_h) * (temperature / mu);
71 template <
class Evaluation>
95 template <
class Evaluation>
99 const int knownPhaseIdx,
103 Evaluation A = computeA_(temperature, pg);
106 Scalar x_NaCl = salinityToMolFrac_(salinity);
110 if (knownPhaseIdx < 0) {
111 Scalar molalityNaCl = moleFracToMolality_(x_NaCl);
112 Evaluation m0_CO2 = molalityCO2inPureWater_(temperature, pg);
113 Evaluation gammaStar = activityCoefficient_(temperature, pg, molalityNaCl);
114 Evaluation m_CO2 = m0_CO2 / gammaStar;
115 xlCO2 = m_CO2 / (molalityNaCl + 55.508 + m_CO2);
116 ygH2O = A * (1 - xlCO2 - x_NaCl);
122 if (knownPhaseIdx == liquidPhaseIdx)
123 ygH2O = A * (1 - xlCO2 - x_NaCl);
128 if (knownPhaseIdx == gasPhaseIdx)
130 xlCO2 = 1 - x_NaCl - ygH2O / A;
136 template <
class Evaluation>
137 static Evaluation
henry(
const Evaluation& temperature)
148 template <
class Evaluation>
151 Valgrind::CheckDefined(temperature);
152 Valgrind::CheckDefined(pg);
155 Evaluation pg_bar = pg / 1.e5;
156 Evaluation a_CO2 = (7.54e7 - 4.13e4 * temperature);
161 lnPhiCO2 = log(V / (V - b_CO2));
162 lnPhiCO2 += b_CO2 / (V - b_CO2);
163 lnPhiCO2 -= 2 * a_CO2 / (R * pow(temperature, 1.5) * b_CO2) * log((V + b_CO2) / V);
167 * pow(temperature, 1.5)
170 * (log((V + b_CO2) / V)
171 - b_CO2 / (V + b_CO2));
172 lnPhiCO2 -= log(pg_bar * V / (R * temperature));
174 return exp(lnPhiCO2);
185 template <
class Evaluation>
189 const Evaluation& pg_bar = pg / 1.e5;
190 const Evaluation& a_CO2 = (7.54e7 - 4.13e4 * temperature);
191 Scalar a_CO2_H2O = 7.89e7;
193 Scalar b_H2O = 18.18;
199 + b_H2O/(V - b_CO2) - 2*a_CO2_H2O
200 / (R*pow(temperature, 1.5)*b_CO2)*log((V + b_CO2)/V)
201 + a_CO2*b_H2O/(R*pow(temperature, 1.5)*b_CO2*b_CO2)
202 *(log((V + b_CO2)/V) - b_CO2/(V + b_CO2))
203 - log(pg_bar*V/(R*temperature));
204 return exp(lnPhiH2O);
213 static Scalar salinityToMolFrac_(Scalar salinity) {
216 const Scalar Ms = 58.8e-3;
218 const Scalar X_NaCl = salinity;
220 const Scalar x_NaCl = -Mw * X_NaCl / ((Ms - Mw) * X_NaCl - Ms);
229 static Scalar moleFracToMolality_(Scalar x_NaCl)
232 return 55.508 * x_NaCl / (1 - x_NaCl);
242 template <
class Evaluation>
243 static Evaluation molalityCO2inPureWater_(
const Evaluation& temperature,
const Evaluation& pg)
245 const Evaluation& A = computeA_(temperature, pg);
246 const Evaluation& B = computeB_(temperature, pg);
247 const Evaluation& yH2OinGas = (1 - B) / (1. / A - B);
248 const Evaluation& xCO2inWater = B * (1 - yH2OinGas);
249 return (xCO2inWater * 55.508) / (1 - xCO2inWater);
261 template <
class Evaluation>
262 static Evaluation activityCoefficient_(
const Evaluation& temperature,
263 const Evaluation& pg,
266 const Evaluation& lambda = computeLambda_(temperature, pg);
267 const Evaluation& xi = computeXi_(temperature, pg);
268 const Evaluation& lnGammaStar =
269 2*molalityNaCl*lambda + xi*molalityNaCl*molalityNaCl;
270 return exp(lnGammaStar);
281 template <
class Evaluation>
282 static Evaluation computeA_(
const Evaluation& temperature,
const Evaluation& pg)
284 const Evaluation& deltaP = pg / 1e5 - 1;
285 Scalar v_av_H2O = 18.1;
287 const Evaluation& k0_H2O = equilibriumConstantH2O_(temperature);
289 const Evaluation& pg_bar = pg / 1.e5;
290 return k0_H2O/(phi_H2O*pg_bar)*exp(deltaP*v_av_H2O/(R*temperature));
301 template <
class Evaluation>
302 static Evaluation computeB_(
const Evaluation& temperature,
const Evaluation& pg)
304 const Evaluation& deltaP = pg / 1e5 - 1;
305 const Scalar v_av_CO2 = 32.6;
307 const Evaluation& k0_CO2 = equilibriumConstantCO2_(temperature);
309 const Evaluation& pg_bar = pg / 1.e5;
310 return phi_CO2*pg_bar/(55.508*k0_CO2)*exp(-(deltaP*v_av_CO2)/(R*temperature));
320 template <
class Evaluation>
321 static Evaluation computeLambda_(
const Evaluation& temperature,
const Evaluation& pg)
323 static const Scalar c[6] =
324 { -0.411370585, 6.07632013E-4, 97.5347708, -0.0237622469, 0.0170656236, 1.41335834E-5 };
326 Evaluation pg_bar = pg / 1.0E5;
331 + c[3]*pg_bar/temperature
332 + c[4]*pg_bar/(630.0 - temperature)
333 + c[5]*temperature*log(pg_bar);
343 template <
class Evaluation>
344 static Evaluation computeXi_(
const Evaluation& temperature,
const Evaluation& pg)
346 static const Scalar c[4] =
347 { 3.36389723E-4, -1.98298980E-5, 2.12220830E-3, -5.24873303E-3 };
349 Evaluation pg_bar = pg / 1.0E5;
350 return c[0] + c[1]*temperature + c[2]*pg_bar/temperature + c[3]*pg_bar/(630.0 - temperature);
359 template <
class Evaluation>
360 static Evaluation equilibriumConstantCO2_(
const Evaluation& temperature)
362 Evaluation temperatureCelcius = temperature - 273.15;
363 static const Scalar c[3] = { 1.189, 1.304e-2, -5.446e-5 };
364 Evaluation logk0_CO2 = c[0] + temperatureCelcius*(c[1] + temperatureCelcius*c[2]);
365 Evaluation k0_CO2 = pow(10.0, logk0_CO2);
375 template <
class Evaluation>
376 static Evaluation equilibriumConstantH2O_(
const Evaluation& temperature)
378 Evaluation temperatureCelcius = temperature - 273.15;
379 static const Scalar c[4] = { -2.209, 3.097e-2, -1.098e-4, 2.048e-7 };
380 Evaluation logk0_H2O =
381 c[0] + temperatureCelcius*(c[1] + temperatureCelcius*(c[2] + temperatureCelcius*c[3]));
382 return pow(10.0, logk0_H2O);
Relations valid for an ideal gas.
Binary coefficients for brine and CO2.
Definition: Brine_CO2.hpp:41
static Evaluation fugacityCoefficientCO2(const Evaluation &temperature, const Evaluation &pg)
Returns the fugacity coefficient of the CO2 component in a water-CO2 mixture.
Definition: Brine_CO2.hpp:149
static Evaluation henry(const Evaluation &temperature)
Henry coefficent for CO2 in brine.
Definition: Brine_CO2.hpp:137
static void calculateMoleFractions(const Evaluation &temperature, const Evaluation &pg, Scalar salinity, const int knownPhaseIdx, Evaluation &xlCO2, Evaluation &ygH2O)
Returns the mol (!) fraction of CO2 in the liquid phase and the mol_ (!) fraction of H2O in the gas p...
Definition: Brine_CO2.hpp:96
static Evaluation liquidDiffCoeff(const Evaluation &, const Evaluation &)
Binary diffusion coefficent [m^2/s] of CO2 in the brine phase.
Definition: Brine_CO2.hpp:72
static Evaluation fugacityCoefficientH2O(const Evaluation &temperature, const Evaluation &pg)
Returns the fugacity coefficient of the H2O component in a water-CO2 mixture.
Definition: Brine_CO2.hpp:186
static Evaluation gasDiffCoeff(const Evaluation &temperature, const Evaluation &pressure)
Binary diffusion coefficent [m^2/s] of water in the CO2 phase.
Definition: Brine_CO2.hpp:55
static Scalar molarMass()
The mass in [kg] of one mole of CO2.
Definition: CO2.hpp:66
static Evaluation gasViscosity(Evaluation temperature, const Evaluation &pressure, bool extrapolate=false)
The dynamic viscosity [Pa s] of CO2.
Definition: CO2.hpp:203
static Evaluation gasDensity(const Evaluation &temperature, const Evaluation &pressure, bool extrapolate=false)
The density of CO2 at a given pressure and temperature [kg/m^3].
Definition: CO2.hpp:189
static const Scalar molarMass()
The molar mass in of water.
Definition: H2O.hpp:80
Relations valid for an ideal gas.
Definition: IdealGas.hpp:38
static const Scalar R
The ideal gas constant .
Definition: IdealGas.hpp:41