def test_compressibility(self):
# compressibility of water at [temperature(C), pressure(applied_bar), compressibility (10^6 bar-1)] Millero TABLE V
param = np.array([[5, 0, 49.175], [30, 0, 44.771], [75, 0, 45.622],
[35, 100, 43.305], [55, 300, 40.911]])
# converting param to [temperature(K), pressure(atm), compressibility (atm-1)]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
# 1 atm = 1 applied_atm + 1, according to Millero
param[:, 1] = (param[:, 1] / un.atm_2_bar(1)) + 1
param[:, 2] = (param[:, 2] / 1e6) * un.atm_2_bar(1)
# testing compressibility up to a precision of 10^-9
wfm = fm.WaterPropertiesFineMillero(param[:, 0], param[:, 1])
test_vals = np.allclose(wfm.compressibility(), param[:, 2], 0, 1e-9)
self.assertTrue(test_vals)
def test_a_v(self):
# apparent molal volume [temperature(C), Pressure(bar), molal vol (cc/mol)] Bradley & Pitzer TABLE IV
param = np.array([[10, 100, 1.61], [60, 100, 2.55], [120, 100, 4.91],
[70, 400, 2.59], [25, 600, 1.66]])
# converting param to [temperature(K), pressure(atm), molal vol (cc/mol)]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
param[:, 1] = param[:, 1] / un.atm_2_bar(1)
# testing apparent molal volume up to a precision of 10^-2
wfm = fm.WaterPropertiesFineMillero(param[:, 0], param[:, 1])
test_vals = np.allclose(wfm.a_v(), param[:, 2], 0, 1e-2)
self.assertTrue(test_vals)
def test_molar_vol_infinite_dilution(self):
# parameters in [temperature (C), pressure (bar), partial molal volume of solute cm^3/mol]
param = np.array([[70, 1, 1.781e1], [60, 1, 1.791e1], [90, 1, 1.710e1],
[80, 400, 1.884e1], [60, 800, 2.024e1]])
# converting to [temperature (K), pressure (atm), partial molal volume of solute m^3/mol]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
param[:, 1] = param[:, 1] / un.atm_2_bar(1)
param[:, 2] = param[:, 2] / 1e6
# testing params up to a precision of 10^-8
salt_nacl = nacl.NaClPropertiesRogersPitzer(param[:, 0], param[:, 1])
test_vals = np.allclose(salt_nacl.vp * 1e-6, param[:, 2], 0, 1e-8)
self.assertTrue(test_vals)
def test_a_phi(self):
# osmotic coefficient of water [temperature(C), Pressure(bar), osmotic coefficient] Bradley & Pitzer TABLE II
param = np.array([[10, 100, 3.80e-1], [60, 100, 4.17e-1],
[120, 100, 4.82e-1], [70, 400, 4.19e-1],
[25, 600, 3.81e-1]])
# converting param to [temperature(K), pressure(atm), osmotic coefficient]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
param[:, 1] = param[:, 1] / un.atm_2_bar(1)
# testing osmotic coefficient up to a precision of 10^-3
wfm = fm.WaterPropertiesFineMillero(param[:, 0], param[:, 1])
test_vals = np.allclose(wfm.a_phi(), param[:, 2], 0, 1e-3)
self.assertTrue(test_vals)
def test_a_h(self):
# enthalpy coefficient [temperature(C), Pressure(bar), enthalpy coeff (AH / RT)] Bradley & Pitzer TABLE III
param = np.array([[10, 100, 0.641], [60, 100, 1.180], [120, 100, 2.05],
[70, 400, 1.24], [25, 600, 0.736]])
# converting param to [temperature(K), pressure(atm), enthalpy coeff (AH / RT)]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
param[:, 1] = param[:, 1] / un.atm_2_bar(1)
# testing enthalpy coeff up to a precision of 10^-2
wfm = fm.WaterPropertiesFineMillero(param[:, 0], param[:, 1])
test_vals = np.allclose(
((2 / 3) * wfm.a_h()) / (un.r_gas() * param[:, 0]), param[:, 2], 0,
1e-2)
self.assertTrue(test_vals, (wfm.a_h()) / (un.r_gas() * param[:, 0]))
def test_density(self):
# density of water at [temperature(C), pressure(applied_bar), specific volume] Millero TABLEIV
param = np.array([[5, 0, 1.000036], [30, 0, 1.004369],
[75, 0, 1.025805], [30, 100, 0.999939],
[55, 300, 1.001642]])
# converting param to [temperature(K), pressure(atm), specific volume]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
# 1 atm = 1 applied_atm + 1, according to Millero
param[:, 1] = (param[:, 1] / un.atm_2_bar(1)) + 1
# testing density up to a precision of 10^-6
wfm = fm.WaterPropertiesFineMillero(param[:, 0], param[:, 1])
test_vals = np.allclose(1e3 / wfm.density(), param[:, 2], 0, 1e-6)
self.assertTrue(test_vals)
def test_density_sol(self):
# parameters in [temperature (C), pressure (bar), molality, specific volume of NaCl(aq) cm^3/g]
param = np.array([[60, 1, 1, 0.9797], [60, 1, 0.1, 1.0130],
[60, 1, 0.5, 0.9976], [80, 1, 2, 0.9581],
[80, 1, 3, 0.9293], [80, 1, 0.75, 0.9999],
[70, 200, 1, 0.9772], [90, 200, 3, 0.9280],
[80, 400, 0.1, 1.0074], [90, 600, 0.25, 0.9998]])
# converting to [temperature (K), pressure (atm), molality, specific volume of NaCl(aq) cm^3/g]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
param[:, 1] = param[:, 1] / un.atm_2_bar(1)
# testing params up to a precision of 10^-4
salt_nacl = nacl.NaClPropertiesRogersPitzer(param[:, 0], param[:, 1])
test_vals = np.allclose((1 / salt_nacl.density_sol(param[:, 2])) * 1e3,
param[:, 3], 0, 1e-4)
self.assertTrue(test_vals)
def test_log_gamma(self):
# parameters in [temperature (C), molality, activity coefficient]
param = np.array([[25, 1, 0.605], [25, 0.1, 0.768], [25, 0.5, 0.650],
[25, 0.3, 0.687], [25, 2.0, 0.574], [50, 3.0, 0.584],
[50, 0.5, 0.646]])
# converting to [temperature (K), molality, activity coefficient]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
# testing params up to a precision of 10^-3
salt_kcl = kcl.KClPropertiesPabalanPitzer(param[:, 0],
1 / un.atm_2_bar(1))
test_vals = np.allclose(np.exp(salt_kcl.log_gamma(param[:, 1])),
param[:, 2], 0, 1e-3)
self.assertTrue(
test_vals,
str(np.exp(salt_kcl.log_gamma(param[:, 1]))) + " & " +
str(param[:, 2]))
def test_molar_volume(self):
# molar volume of water at [temperature(C), pressure(applied_bar), specific volume] Millero TABLE IV
param = np.array([[5, 0, 1.000036], [30, 0, 1.004369],
[75, 0, 1.025805], [35, 100, 1.001597],
[55, 300, 1.001642]])
# converting param to [temperature(K), pressure(atm), molar volume]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
# 1 atm = 1 applied_atm + 1, according to Millero
param[:, 1] = (param[:, 1] / un.atm_2_bar(1)) + 1
param[:,
2] = (param[:, 2] /
1e6) * fm.WaterPropertiesFineMillero(300).MolecularWeight
# testing molar volume up to a precision of 10^-11
wfm = fm.WaterPropertiesFineMillero(param[:, 0], param[:, 1])
test_vals = np.allclose(wfm.molar_volume(), param[:, 2], 0, 1e-11)
self.assertTrue(test_vals)
def test_osmotic_coeff(self):
# parameters in [temperature (C), molality, osmotic coefficient]
param = np.array([[25, 1, 0.899], [25, 0.1, 0.927], [25, 0.5, 0.901],
[25, 0.3, 0.907], [25, 2, 0.914], [50, 3, 0.954],
[50, 0.5, 0.903]])
# converting to [temperature (K), molality, osmotic coefficient]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
# testing params up to a precision of 10^-3
salt_kcl = kcl.KClPropertiesPabalanPitzer(param[:, 0],
1 / un.atm_2_bar(1))
test_vals = np.allclose(salt_kcl.osmotic_coeff(param[:, 1]),
param[:, 2], 0, 1e-3)
self.assertTrue(
test_vals,
str(salt_kcl.osmotic_coeff(param[:, 1])) + " & " +
str(param[:, 2]))
def test_apparent_molal_enthalpy(self):
# parameters in [temperature (C), molality, apparent relative molal enthalpy (kJ/mol)]
param = np.array([[25, 1.0, -0.06], [25, 0.1, 0.34], [25, 0.5, 0.24],
[25, 0.3, 0.33], [25, 2.0, -0.67], [25, 3.0, -1.21],
[50, 0.5, 0.79], [50, 3.0, 0.30], [50, 0.1, 0.59],
[50, 0.3, 0.75]])
# converting to [temperature (K), molality, apparent relative molal enthalpy (kJ/mol)]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
# testing params up to a precision of 10^-2
salt_kcl = kcl.KClPropertiesPabalanPitzer(param[:, 0],
(1 / un.atm_2_bar(1)))
test_vals = np.allclose(
salt_kcl.apparent_molal_enthalpy(param[:, 1]) / 1e3, param[:, 2],
0, 1e-2)
self.assertTrue(
test_vals,
str(salt_kcl.apparent_molal_enthalpy(param[:, 1]) / 1e3) + " & " +
str(param[:, 2]))
def test_params_der_p(self):
# pressure derivative parameters in [temperature (C), pressure (bar), [BV, 2CV]]
param = np.array([[70, 1, 3.513e-6, -1.22e-7],
[60, 1, 4.415e-6, -2.00e-7],
[90, 1, 2.577e-6, -6.02e-8],
[80, 400, 2.552e-6, -7.97e-8],
[60, 800, 3.062e-6, -2.00e-7]])
# converting to [temperature (K), pressure (atm), [bp, cp]]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
param[:, 1] = param[:, 1] / un.atm_2_bar(1)
param[:, 3] = param[:, 3] / 2
# testing params up to a precision of 10^-9
salt_nacl = nacl.NaClPropertiesRogersPitzer(param[:, 0], param[:, 1])
test_vals1 = np.allclose(salt_nacl.params_der_p[1], param[:, 2], 0,
1e-9)
test_vals2 = np.allclose(salt_nacl.params_der_p[4], param[:, 3], 0,
1e-9)
self.assertTrue(test_vals1)
self.assertTrue(test_vals2)
def test_molar_vol(self):
# parameters in [temperature (C), pressure (bar), molality, molar volume cm^3/mol]
param = np.array([[0, 196.62, 0.3331, 26.280],
[0, 196.62, 0.5009, 26.573],
[0, 196.62, 0.6693, 26.856],
[0, 196.62, 0.8360, 26.976],
[25, 196.62, 0.3331, 28.873],
[25, 196.62, 0.5009, 29.104],
[25, 196.62, 0.6693, 29.258],
[50, 196.62, 0.3331, 29.757],
[50, 196.62, 0.5009, 29.968],
[50, 196.62, 0.6693, 30.125]])
# converting to [temperature (K), pressure (atm), molality, molar volume m^3/mol]
param[:, 0] = un.celsius_2_kelvin(param[:, 0])
param[:, 1] = param[:, 1] / un.atm_2_bar(1)
param[:, 3] = param[:, 3] / 1e6
# testing params up to a precision of 10^-9
salt_kcl = kcl.KClPropertiesPabalanPitzer(param[:, 0], param[:, 1])
test_vals = np.allclose(salt_kcl.molar_vol(param[:, 2]), param[:, 3],
0, 1e-9)
self.assertTrue(
test_vals,
str(salt_kcl.molar_vol(param[:, 2])) + " & " + str(param[:, 3]))
def test_density_sol(self):
# parameters in [temperature (K), pressure (bar), molality, density of solution g/cm^3]
param = np.array([[323.90, 22.3, 0.0723, 0.99720],
[324.48, 22.3, 0.0723, 0.99699],
[324.24, 49.1, 0.0723, 0.99819],
[324.26, 98.3, 0.0723, 1.00020],
[294.21, 21.9, 0.1693, 1.01927],
[294.23, 23.1, 0.1693, 1.01924],
[293.84, 47.6, 0.1693, 1.02043],
[324.76, 47.5, 0.1693, 1.00917],
[325.27, 95.6, 0.1693, 1.01083],
[294.90, 95.2, 0.2503, 1.03156]])
# converting to [temperature (K), pressure (atm), molality, density of solution g/cm^3]
param[:, 1] = param[:, 1] / un.atm_2_bar(1)
# testing params up to a precision of 10^-5
salt_mgso4 = mgso4.MgSO4PropertiesPhutelaPitzer(
param[:, 0], param[:, 1])
test_vals = np.allclose((salt_mgso4.density_sol(param[:, 2])) / 1e3,
param[:, 3], 0, 1e-5)
self.assertTrue(
test_vals,
str((salt_mgso4.density_sol(param[:, 2])) * 1e3) + " & " +
str(param[:, 3]))
def test_density_sol(self):
# parameters in [temperature (K), pressure (bar), molality, density of solution g/cm^3]
param = np.array([[294.87, 20.2, 0.0578, 1.00608],
[325.16, 20.4, 0.0578, 0.99503],
[325.09, 20.5, 0.0578, 0.99507],
[295.18, 20.3, 0.0578, 1.00604],
[295.67, 48.8, 0.0578, 1.00717],
[325.01, 49.1, 0.0578, 0.99634],
[295.47, 95.3, 0.0578, 1.00928],
[325.08, 96.6, 0.0578, 0.99833],
[296.35, 20.0, 0.1085, 1.01207],
[294.85, 47.6, 0.1085, 1.01366]])
# converting to [temperature (K), pressure (atm), molality, density of solution g/cm^3]
param[:, 1] = param[:, 1] / un.atm_2_bar(1)
# testing params up to a precision of 10^-5
salt_na2so4 = na2so4.Na2SO4PropertiesPhutelaPitzer(
param[:, 0], param[:, 1])
test_vals = np.allclose((salt_na2so4.density_sol(param[:, 2])) * 1e3,
param[:, 3], 0, 1e-5)
self.assertTrue(
test_vals,
str((salt_na2so4.density_sol(param[:, 2])) * 1e3) + " & " +
str(param[:, 3]))
def __init__(self, tk, pa=1):
"""
constructor
:param tk: temperature in kelvin
:param pa: pressure in atmospheres
:instantiate: temperature, pressure, stoichiometry coefficients, Pitzer Parameters
"""
self.tk = tk
self.pa = pa
# Calculations MgSO4 parameters and coefficients
self.mat_stoich = np.array([[1, 1], [2, -2]])
self.m_ref = 5.550825
self.y_ref = 10
self.m_weight = 120.366
self.p_ref = np.array([self.m_weight, self.m_ref, self.y_ref])
# values for ion strength dependence and ion size constants in the extended Pitzer model
self.alpha_b1 = 1.4
self.alpha_b2 = 12.0
self.alpha_c1 = 0
self.alpha_c2 = 0
self.alpha_d1 = 0
self.alpha_d2 = 0
self.b_param = 1.2
self.ion_param = np.array([
self.alpha_b1, self.alpha_b2, self.alpha_c1, self.alpha_c2,
self.alpha_d1, self.alpha_d2, self.b_param
])
self.q = np.zeros(15)
self.q[0] = -7.97433e5
self.q[1] = 8.94735e3
self.q[2] = -3.78219e1
self.q[3] = 7.15424e-2
self.q[4] = -5.14523e-5
self.q[5] = 7.42784
self.q[6] = -6.12133e-2
self.q[7] = 1.77378e-4
self.q[8] = -1.82737e-7
self.q[9] = 2.06777e3
self.q[10] = -2.39043e1
self.q[11] = 1.03110e-1
self.q[12] = -1.96675e-4
self.q[13] = 1.40527e-7
self.q[14] = 1.18481e-4
# Pitzer Parameters
self.beta0 = 0
self.beta1 = 0
self.beta2 = 0
self.C0 = 0
self.C1 = 0
self.C2 = 0
self.D0 = 0
self.D1 = 0
self.D2 = 0
self.params = np.array([
self.beta0, self.beta1, self.beta2, self.C0, self.C1, self.C2,
self.D0, self.D1, self.D2
])
# Pitzer Parameters pressure derivative
self.pr = un.atm_2_bar(self.pa)
self.vp = self.q[0] / self.tk + self.q[1] + self.q[
2] * self.tk + self.q[3] * self.tk**2 + self.q[4] * self.tk**3
self.beta0_der_p = 0
self.beta1_der_p = self.q[5] / self.tk + self.q[
6] + self.q[7] * self.tk + self.q[8] * self.tk**2
self.beta2_der_p = self.q[9] / self.tk + self.q[
10] + self.q[11] * self.tk + self.q[12] * self.tk**2 + self.q[
13] * self.tk**3 + self.q[14] * self.pr
self.C0_der_p = 0
self.C1_der_p = 0
self.C2_der_p = 0
self.D0_der_p = 0
self.D1_der_p = 0
self.D2_der_p = 0
self.params_der_p = np.array([
self.vp, self.beta0_der_p, self.beta1_der_p, self.beta2_der_p,
self.C0_der_p, self.C1_der_p, self.C2_der_p, self.D0_der_p,
self.D1_der_p, self.D2_der_p
])
# Pitzer Parameters temperature derivative
self.beta0_der_t = 0
self.beta1_der_t = 0
self.beta2_der_t = 0
self.C0_der_t = 0
self.C1_der_t = 0
self.C2_der_t = 0
self.D0_der_t = 0
self.D1_der_t = 0
self.D2_der_t = 0
self.params_der_t = np.array([
self.beta0_der_t, self.beta1_der_t, self.beta2_der_t,
self.C0_der_t, self.C1_der_t, self.C2_der_t, self.D0_der_t,
self.D1_der_t, self.D2_der_t
])
super().__init__(tk, pa)
def __init__(self, tk, pa=1):
"""
constructor
:param tk: temperature in kelvin
:param pa: pressure in atmospheres
:instantiate: temperature, pressure, stoichiometry coefficients, Pitzer Parameters
"""
self.tk = tk
self.pa = pa
# Calculations nacl parameters and coefficients
self.mat_stoich = np.array([[1, 1], [1, -1]])
self.m_ref = 5.550825
self.y_ref = 10
self.m_weight = 74.5513
self.p_ref = np.array([self.m_weight, self.m_ref, self.y_ref])
# values for ion strength dependence and ion size constants in the extended Pitzer model
self.alpha_b1 = 2.0
self.alpha_b2 = 0
self.alpha_c1 = 0
self.alpha_c2 = 0
self.alpha_d1 = 0
self.alpha_d2 = 0
self.b_param = 1.2
self.ion_param = np.array([self.alpha_b1, self.alpha_b2, self.alpha_c1, self.alpha_c2, self.alpha_d1, self.alpha_d2, self.b_param])
self.q = np.array([[1.56152e3, 0.0],
[-1.69234e5, 0.0],
[-4.29918, 9.45015e-8],
[4.59233e-3, -2.90741e-10],
[-3.25686e4, 3.26205e-3],
[-6.86887, 8.39662e-7],
[7.35220e2, 0.0],
[2.02245e-2, -4.41638e-9],
[-2.15779e-5, 6.71235e-12],
[1.03212e2, -4.42327e-5],
[5.34941e-3, -7.97437e-10],
[-5.73121e-1, 0.0],
[-1.57862e-5, 4.12771e-12],
[1.66987e-8, -6.24996e-15],
[-7.22012e-2, 4.16221e-8]])
self.u = np.array([[-2.10289e-2, 2.208130e-1, 0.000000000],
[6.039670e-1, -4.61849000, 7.648910e-4],
[3.677680e-3, -4.10116e-2, 0.000000000],
[-7.05537e-6, 1.104450e-4, -1.12131e-8],
[1.979680e-9, -4.73196e-8, 1.72256e-11],
[-2.47588e-3, -2.74120e-2, 0.000000000],
[1.441600e-1, 3.328830e-1, -5.71188e-3]])
self.fl_1 = [6.771360e-4, 9.678540e-4, -4.12364e-5]
self.fg_1 = [4.808000e-2, 2.187520e-1, -3.94000e-4]
self.fl = [6.56838000e-4, 9.678540e-4, -4.12364e-5]
self.fg = [5.00380000e-2, 2.187520e-1, -3.94000e-4]
self.k_1 = [-2931.268116, 6353.355434, 28.17218000]
self.k_2 = [-33.95314300, 193.0040590, -0.12556700]
# Pitzer Parameters
self.tc = 298.15
def Fg(x):
f_1 = (self.u[0][x] * self.tk ** 2) / 6 + (self.u[1][x] * self.tk) / 2 + (self.u[2][x] * self.tk ** 2) * ((np.log(self.tk) / 2) - (5 / 12)) / 3
f_2 = (self.u[3][x] * self.tk ** 3) / 12 + (self.u[4][x] * self.tk ** 4) / 20 + self.u[5][x] * (self.tk / 2 + (3 * (227 ** 2)) / (2 * self.tk) + 227 * (self.tk - 227) * np.log(self.tk - 227) / self.tk)
f_3 = (-self.u[6][x]) * (2 * (647 - self.tk) * np.log(647 - self.tk) / self.tk + np.log(647 - self.tk))
f_4 = (-self.k_1[x]) / self.tk - self.fl[x] * ((self.tc ** 2) / self.tk) + self.k_2[x] + self.fg[x]
f_sum = f_1 + f_2 + f_3 + f_4
return f_sum
self.beta0 = Fg(0)
self.beta1 = Fg(1)
self.beta2 = 0
self.C0 = Fg(2)
self.C1 = 0
self.C2 = 0
self.D0 = 0
self.D1 = 0
self.D2 = 0
self.params = np.array([self.beta0, self.beta1, self.beta2, self.C0, self.C1, self.C2, self.D0, self.D1, self.D2])
# Pitzer Parameters pressure derivative
self.pr = self.pa * un.atm_2_bar(1)
self.pr_atm = un.atm_2_bar(1)
def Fv(x):
f_1 = self.q[0][x] + self.q[1][x] / self.tk + self.q[2][x] * self.tk + self.q[3][x] * self.tk ** 2 + self.q[4][x] / (647 - self.tk)
f_2 = self.pr * (self.q[5][x] + self.q[6][x] / self.tk + self.q[7][x] * self.tk + self.q[8][x] * self.tk ** 2 + self.q[9][x] / (647 - self.tk))
f_3 = (self.pr ** 2) * (self.q[10][x] + self.q[11][x] / self.tk + self.q[12][x] * self.tk + self.q[13][x] * self.tk ** 2 + self.q[14][x] / (647 - self.tk))
return f_1 + f_2 + f_3
self.vp = Fv(0)
self.beta0_der_p = Fv(1)
self.beta1_der_p = 0
self.beta2_der_p = 0
self.C0_der_p = 0
self.C1_der_p = 0
self.C2_der_p = 0
self.D0_der_p = 0
self.D1_der_p = 0
self.D2_der_p = 0
self.params_der_p = np.array([self.vp, self.beta0_der_p, self.beta1_der_p, self.beta2_der_p, self.C0_der_p, self.C1_der_p, self.C2_der_p, self.D0_der_p, self.D1_der_p, self.D2_der_p])
# Pitzer Parameters temperature derivative
def Fl(x):
f_1 = (self.u[0][x] * self.tk) / 3 + self.u[1][x] / 2 + self.u[2][x] * self.tk * (np.log(self.tk) - (1 / 3)) / 3
f_2 = (self.u[3][x] * self.tk ** 2) / 4 + (self.u[4][x] * self.tk ** 3) / 5
f_3 = (self.u[5][x] / (self.tk ** 2)) * (((self.tk - 227) ** 2) / 2 + 454 * (self.tk - 227) + (227 ** 2) * np.log(self.tk - 227))
f_4 = (self.u[6][x] / (self.tk ** 2)) * (-(647 - self.tk) + 1294 * np.log(647 - self.tk) + (647 ** 2) / (647 - self.tk))
f_5 = self.k_1[x] / (self.tk ** 2) + self.fl[x] * ((self.tc ** 2) / (self.tk ** 2))
return f_1 + f_2 + f_3 + f_4 + f_5
self.beta0_der_t = Fl(0)
self.beta1_der_t = Fl(1)
self.beta2_der_t = 0
self.C0_der_t = Fl(2)
self.C1_der_t = 0
self.C2_der_t = 0
self.D0_der_t = 0
self.D1_der_t = 0
self.D2_der_t = 0
self.params_der_t = np.array([self.beta0_der_t, self.beta1_der_t, self.beta2_der_t, self.C0_der_t, self.C1_der_t, self.C2_der_t, self.D0_der_t, self.D1_der_t, self.D2_der_t])
super().__init__(tk, pa)
def __init__(self, tk, pa=1):
"""
constructor
:param tk: temperature in kelvin
:param pa: pressure in atmospheres
:instantiate: temperature, pressure, stoichiometry coefficients, Pitzer Parameters
"""
self.tk = tk
self.pa = pa
# Calculations Na2SO4 parameters and coefficients
self.mat_stoich = np.array([[2, 1], [1, -2]])
self.m_ref = 5.550825
self.y_ref = 10
self.m_weight = 142.04
self.p_ref = np.array([self.m_weight, self.m_ref, self.y_ref])
# values for ion strength dependence and ion size constants in the extended Pitzer model
self.alpha_b1 = 2.0
self.alpha_b2 = 0
self.alpha_c1 = 0
self.alpha_c2 = 0
self.alpha_d1 = 0
self.alpha_d2 = 0
self.b_param = 1.2
self.ion_param = np.array([
self.alpha_b1, self.alpha_b2, self.alpha_c1, self.alpha_c2,
self.alpha_d1, self.alpha_d2, self.b_param
])
self.p = np.zeros(12)
self.p[0] = -5.11686e5
self.p[1] = 5.43000e3
self.p[2] = -2.18218e1
self.p[3] = 3.99915e-2
self.p[4] = -2.83513e-5
self.p[5] = 1.79274e-2
self.p[6] = 1.28610
self.p[7] = -1.06978e-2
self.p[8] = 2.96022e-5
self.p[9] = -2.70365e-8
self.p[10] = 4.59690e-1
self.p[11] = -1.31097e-3
# Pitzer Parameters
self.beta0 = 0
self.beta1 = 0
self.beta2 = 0
self.C0 = 0
self.C1 = 0
self.C2 = 0
self.D0 = 0
self.D1 = 0
self.D2 = 0
self.params = np.array([
self.beta0, self.beta1, self.beta2, self.C0, self.C1, self.C2,
self.D0, self.D1, self.D2
])
# Pitzer Parameters pressure derivative
self.pr = un.atm_2_bar(self.pa)
self.vp = self.p[0] / self.tk + self.p[
1] + self.p[2] * self.tk + self.p[3] * self.tk**2 + self.p[
4] * self.tk**3 + self.p[5] * self.pr
self.beta0_der_p = self.p[6] / self.tk + self.p[
7] + self.p[8] * self.tk + self.p[9] * self.tk**2
self.beta1_der_p = self.p[10] / self.tk + self.p[11]
self.beta2_der_p = 0
self.C0_der_p = 0
self.C1_der_p = 0
self.C2_der_p = 0
self.D0_der_p = 0
self.D1_der_p = 0
self.D2_der_p = 0
self.params_der_p = np.array([
self.vp, self.beta0_der_p, self.beta1_der_p, self.beta2_der_p,
self.C0_der_p, self.C1_der_p, self.C2_der_p, self.D0_der_p,
self.D1_der_p, self.D2_der_p
])
# Pitzer Parameters temperature derivative
self.beta0_der_t = 0
self.beta1_der_t = 0
self.beta2_der_t = 0
self.C0_der_t = 0
self.C1_der_t = 0
self.C2_der_t = 0
self.D0_der_t = 0
self.D1_der_t = 0
self.D2_der_t = 0
self.params_der_t = np.array([
self.beta0_der_t, self.beta1_der_t, self.beta2_der_t,
self.C0_der_t, self.C1_der_t, self.C2_der_t, self.D0_der_t,
self.D1_der_t, self.D2_der_t
])
super().__init__(tk, pa)
def __init__(self, tk, pa=1):
"""
constructor
:param tk: temperature in kelvin
:param pa: pressure in atmospheres
:instantiate: temperature, pressure, molecular weight, polarizability, dipole moment
"""
super().__init__(tk, pa)
# Calculations for density
self.t = self.tk - un.celsius_2_kelvin(0)
# pressure in applied bar according to Fine and Millero
self.y = un.atm_2_bar(self.pa - 1)
self.den1 = 0.9998396 + self.t * 18.224944e-3 - 7.922210e-6 * self.t**2 - 55.44846e-9 * self.t**3
self.den2 = 149.7562e-12 * self.t**4 - 393.2952e-15 * self.t**5
self.V0 = (1 + self.t * 18.159725e-3) / (self.den1 + self.den2)
self.B = 19654.320 + 147.037 * self.t - 2.21554 * self.t**2 + 1.0478e-2 * self.t**3 - 2.2789e-5 * self.t**4
self.a1 = 3.2891 - 2.3910e-3 * self.t + 2.8446e-4 * self.t**2 - 2.82e-6 * self.t**3 + 8.477e-9 * self.t**4
self.a2 = 6.245e-5 - 3.913e-6 * self.t - 3.499e-8 * self.t**2 + 7.942e-10 * self.t**3 - 3.299e-12 * self.t**4
# this in cm^3/gram
self.vol = self.V0 * (
1 - (self.y / (self.B + self.a1 * self.y + self.a2 * self.y**2)))
# density in kg/m^3
self.rt = 1e3 / self.vol
# Calculations for molar volume
self.molVol = 1e-3 * self.MolecularWeight / self.rt
# Calculations for dielectric constant
# convert from atmospheres to MPa
self.p_mpa = 1e-6 * un.atm_2_pascal(self.pa)
# coefficients
self.b = np.zeros(9)
self.b[0] = -4.044525e-2
self.b[1] = 103.6180
self.b[2] = 75.32165
self.b[3] = -23.23778
self.b[4] = -3.548184
self.b[5] = -1246.311
self.b[6] = 263307.7
self.b[7] = -6.928953e-1
self.b[8] = -204.4473
def g(x, y):
t1 = self.b[0] * y / x + self.b[1] / np.sqrt(x) + self.b[2] / (
x - 215) + self.b[3] / np.sqrt(x - 215)
t2 = self.b[4] / (self.tk - 215)**0.25
t3 = np.exp(self.b[5] / x + self.b[6] / x**2 + self.b[7] * y / x +
self.b[8] * y / x**2)
return 1 + 1e-3 * self.rt * (t1 + t2 + t3)
self.fac = un.one_over4pi_epsilon0() * 4 * np.pi * self.mu**2 / (
3 * un.k_boltzmann() * self.tk)
self.b_fac_0 = self.fac * g(self.tk, self.p_mpa)
self.b_fac_1 = self.alpha + self.b_fac_0
self.b_fac = self.rt * un.avogadro() * self.b_fac_1 / (
3.0 * self.MolecularWeight / 1000)
self.dielectricConstant = 0.25 * (
1 + 9 * self.b_fac +
3 * np.sqrt(1 + 2 * self.b_fac + 9 * self.b_fac**2))
# Calculations for compressibility
self.beta = self.V0 * (self.B - self.a2 * self.y**2) / (
self.vol * (self.B + self.a1 * self.y + self.a2 * self.y**2)**2)
self.comp = un.atm_2_bar(self.beta)
def __init__(self, tk, pa=1):
"""
constructor
:param tk: temperature in kelvin
:param pa: pressure in atmospheres
:instantiate: temperature, pressure, stoichiometry coefficients, Pitzer Parameters
"""
self.tk = tk
self.pa = pa
# Calculations MgCl2 parameters and coefficients
self.mat_stoich = np.array([[1, 2], [2, -1]])
self.m_ref = 5.550825
self.y_ref = 10
self.m_weight = 95.211
self.p_ref = np.array([self.m_weight, self.m_ref, self.y_ref])
# values for ion strength dependence and ion size constants in the extended Pitzer model
self.alpha_b1 = 2.0
self.alpha_b2 = 0
self.alpha_c1 = 0.4
self.alpha_c2 = 0.28
self.alpha_d1 = 0
self.alpha_d2 = 0
self.b_param = 1.2
self.ion_param = np.array([
self.alpha_b1, self.alpha_b2, self.alpha_c1, self.alpha_c2,
self.alpha_d1, self.alpha_d2, self.b_param
])
self.a = np.array([[[
-5.50111455e1, 7.2122055200e1, 5.924282400000, 0.000000000000,
0.000000000000, 4.0898005200e-2
],
[
1.5013032600e1, -1.771450850e1, -1.65126386000,
-1.02256042000, 0.000000000000, 0.0000000000000
],
[
-1.58107430e-1, 1.143971530e-1, 1.893998220e-2,
3.770186170e-2, -2.28040769e-3, -2.951198450e-4
],
[
2.304099190e-4, 0.000000000000, -2.99972128e-5,
-7.91682934e-5, 1.374258890e-5, 6.9100122700e-7
],
[
-1.31768095e-7, -1.43588435e-7, 1.891742910e-8,
5.913142580e-8, -1.94821902e-8, -5.32314849e-10
],
[
-1.26699609e-28, 1.72952766e-27, 0.00000000000,
0.000000000000, 1.04649784e-28, 3.979618090e-31
],
[
2.821974990e2, 3.41920714000e3, 5.4903020100e1,
-2.284930840e2, 0.000000000000, 0.0000000000000
]],
[[
0.00000000000, 0.0000000000000, 4.501140480e-2,
0.000000000000, 0.000000000000, 0.0000000000000
],
[
0.00000000000, 2.2844061200e-4, -1.08427926e-2,
0.000000000000, 0.000000000000, 0.0000000000000
],
[
8.396619600e-5, 0.000000000000, 7.410418640e-5,
-7.79259941e-5, 0.000000000000, 0.0000000000000
],
[
-4.60207270e-7, 0.000000000000, -5.99961498e-8,
4.286758760e-7, 0.000000000000, 0.0000000000000
],
[
6.21165614e-10, 0.000000000000, 0.000000000000,
-5.77509662e-10, 0.000000000000, 0.000000000000
],
[
8.43555937e-31, -1.77573402e-29, 0.00000000000,
0.000000000000, 0.000000000000, 0.0000000000000
],
[
0.000000000000, -2.2966887900e2, -4.6056284700,
0.000000000000, 0.000000000000, 0.0000000000000
]],
[[
0.000000000000, 0.0000000000000, 0.00000000000,
-5.13962051e-4, 0.000000000000, 0.0000000000000
],
[
0.000000000000, 0.0000000000000, 0.00000000000,
9.307611420e-5, 0.000000000000, 0.0000000000000
],
[
0.000000000000, -2.714850860e-7, 0.00000000000,
0.000000000000, 0.000000000000, 0.0000000000000
],
[
0.000000000000, 0.0000000000000, 0.00000000000,
0.000000000000, 0.000000000000, 0.0000000000000
],
[
0.000000000000, 0.0000000000000,
-1.39016981e-15, -7.43350922e-13,
0.000000000000, 0.0000000000
],
[
0.000000000000, 0.0000000000000, 0.00000000000,
0.000000000000, 0.000000000000, 0.0000000000000
],
[
-1.11176553000, 1.01000272e1, 1.40556304000e-1,
1.127215570000, 0.000000000000, 0.0000000000000
]]])
self.b = np.array([[
-1.17446972e4, 2.865416060e3, -2.279680760e1, 3.09897542e-2,
-1.92379975e-5, 1.674471870e-26, -1.91185804e6
],
[
0.00000000000, 0.00000000000, -4.00100143e-4,
0.00000000000, -2.43204343e-8, -6.04921882e-28,
1.080249060e5
],
[
0.00000000000, 1.19091585e-2, -4.19764987e-4,
7.93310194e-7, 0.000000000000, 0.0000000000000,
-1.66310231e3
]])
# Pitzer Parameters
self.pr = un.atm_2_pascal(self.pa) / 1e6
self.tc = 298.15
def Fg(x):
f_1 = self.a[0][0][x] + self.a[0][1][x] * np.log(
self.tk) + self.a[0][2][x] * self.tk + self.a[0][3][
x] * self.tk**2 + self.a[0][4][x] * self.tk**3 + self.a[0][
5][x] * self.tk**10 + self.a[0][6][x] / (
(647 - self.tk)**2)
f_2 = self.a[1][0][x] + self.a[1][1][x] * np.log(
self.tk) + self.a[1][2][x] * self.tk + self.a[1][3][
x] * self.tk**2 + self.a[1][4][x] * self.tk**3 + self.a[1][
5][x] * self.tk**10 + self.a[1][6][x] / (
(647 - self.tk)**2)
f_3 = self.a[2][0][x] + self.a[2][1][x] * np.log(
self.tk) + self.a[2][2][x] * self.tk + self.a[2][3][
x] * self.tk**2 + self.a[2][4][x] * self.tk**3 + self.a[2][
5][x] * self.tk**10 + self.a[2][6][x] / (
(647 - self.tk)**2)
return f_1 + f_2 * self.pr + f_3 * (self.pr**2) / 2
self.beta0 = Fg(0)
self.beta1 = Fg(1)
self.beta2 = 0
self.C0 = Fg(2)
self.C1 = Fg(3)
self.C2 = Fg(4)
self.D0 = Fg(5)
self.D1 = 0
self.D2 = 0
self.params = np.array([
self.beta0, self.beta1, self.beta2, self.C0, self.C1, self.C2,
self.D0, self.D1, self.D2
])
# Pitzer Parameters pressure derivative
def Fv(x):
f_2 = self.a[1][0][x] + self.a[1][1][x] * np.log(
self.tk) + self.a[1][2][x] * self.tk + self.a[1][3][
x] * self.tk**2 + self.a[1][4][x] * self.tk**3 + self.a[1][
5][x] * self.tk**10 + self.a[1][6][x] / (
(647 - self.tk)**2)
f_3 = self.a[2][0][x] + self.a[2][1][x] * np.log(
self.tk) + self.a[2][2][x] * self.tk + self.a[2][3][
x] * self.tk**2 + self.a[2][4][x] * self.tk**3 + self.a[2][
5][x] * self.tk**10 + self.a[2][6][x] / (
(647 - self.tk)**2)
return f_2 + f_3 * self.pr
def Fv_vp():
V_1 = self.b[0][0] + self.b[0][1] * np.log(
self.tk
) + self.b[0][2] * self.tk + self.b[0][3] * self.tk**2 + self.b[0][
4] * self.tk**3 + self.b[0][5] * self.tk**10 + self.b[0][6] / (
(647 - self.tk)**2)
V_2 = self.b[1][0] + self.b[1][1] * np.log(
self.tk
) + self.b[1][2] * self.tk + self.b[1][3] * self.tk**2 + self.b[1][
4] * self.tk**3 + self.b[1][5] * self.tk**10 + self.b[1][6] / (
(647 - self.tk)**2)
V_3 = self.b[2][0] + self.b[2][1] * np.log(
self.tk
) + self.b[2][2] * self.tk + self.b[2][3] * self.tk**2 + self.b[2][
4] * self.tk**3 + self.b[2][5] * self.tk**10 + self.b[2][6] / (
(647 - self.tk)**2)
return V_1 + V_2 * self.pr + V_3 * self.pr**2
self.vp = Fv_vp()
self.beta0_der_p = (
(Fv(0) / 1e6) * un.atm_2_pascal(1)) / un.atm_2_bar(1)
self.beta1_der_p = (
(Fv(1) / 1e6) * un.atm_2_pascal(1)) / un.atm_2_bar(1)
self.beta2_der_p = 0
self.C0_der_p = ((Fv(2) / 1e6) * un.atm_2_pascal(1)) / un.atm_2_bar(1)
self.C1_der_p = ((Fv(3) / 1e6) * un.atm_2_pascal(1)) / un.atm_2_bar(1)
self.C2_der_p = ((Fv(4) / 1e6) * un.atm_2_pascal(1)) / un.atm_2_bar(1)
self.D0_der_p = ((Fv(5) / 1e6) * un.atm_2_pascal(1)) / un.atm_2_bar(1)
self.D1_der_p = 0
self.D2_der_p = 0
self.params_der_p = np.array([
self.vp, self.beta0_der_p, self.beta1_der_p, self.beta2_der_p,
self.C0_der_p, self.C1_der_p, self.C2_der_p, self.D0_der_p,
self.D1_der_p, self.D2_der_p
])
# Pitzer Parameters temperature derivative
def Fl(x):
f_1 = self.a[0][1][x] / self.tk + self.a[0][2][
x] + 2 * self.a[0][3][x] * self.tk + 3 * self.a[0][4][
x] * self.tk**2 + 10 * self.a[0][5][
x] * self.tk**9 + 2 * self.a[0][6][x] / (
(647 - self.tk)**3)
f_2 = self.a[1][1][x] / self.tk + self.a[1][2][
x] + 2 * self.a[1][3][x] * self.tk + 3 * self.a[1][4][
x] * self.tk**2 + 10 * self.a[1][5][
x] * self.tk**9 + 2 * self.a[1][6][x] / (
(647 - self.tk)**3)
f_3 = self.a[2][1][x] / self.tk + self.a[2][2][
x] + 2 * self.a[2][3][x] * self.tk + 3 * self.a[2][4][
x] * self.tk**2 + 10 * self.a[2][5][
x] * self.tk**9 + 2 * self.a[2][6][x] / (
(647 - self.tk)**3)
return f_1 + f_2 * self.pr + f_3 * (self.pr**2) / 2
self.beta0_der_t = Fl(0)
self.beta1_der_t = Fl(1)
self.beta2_der_t = 0
self.C0_der_t = Fl(2)
self.C1_der_t = 0
self.C2_der_t = 0
self.D0_der_t = 0
self.D1_der_t = 0
self.D2_der_t = 0
self.params_der_t = np.array([
self.beta0_der_t, self.beta1_der_t, self.beta2_der_t,
self.C0_der_t, self.C1_der_t, self.C2_der_t, self.D0_der_t,
self.D1_der_t, self.D2_der_t
])
super().__init__(tk, pa)
def __init__(self, tk, pa=1):
"""
constructor
:param tk: temperature in kelvin
:param pa: pressure in atmospheres
:instantiate: temperature, pressure, stoichiometry coefficients, Pitzer Parameters
"""
self.tk = tk
self.pa = pa
# Calculations nacl parameters and coefficients
self.mat_stoich = np.array([[1, 1], [1, -1]])
self.m_ref = 5.550825
self.y_ref = 10
self.m_weight = 58.4428
self.p_ref = np.array([self.m_weight, self.m_ref, self.y_ref])
# values for ion strength dependence and ion size constants in the extended Pitzer model
self.alpha_b1 = 2.0
self.alpha_b2 = 0
self.alpha_c1 = 0
self.alpha_c2 = 0
self.alpha_d1 = 0
self.alpha_d2 = 0
self.b_param = 1.2
self.ion_param = np.array([
self.alpha_b1, self.alpha_b2, self.alpha_c1, self.alpha_c2,
self.alpha_d1, self.alpha_d2, self.b_param
])
self.cm = np.zeros(28)
self.cm[0] = 1.0249125e3
self.cm[1] = 2.7796679e-1
self.cm[2] = -3.0203919e-4
self.cm[3] = 1.4977178e-6
self.cm[4] = -7.2002329e-2
self.cm[5] = 3.1453130e-4
self.cm[6] = -5.9795994e-7
self.cm[7] = -6.6596010e-6
self.cm[8] = 3.0407621e-8
self.cm[9] = 5.3699517e-5
self.cm[10] = 2.2020163e-3
self.cm[11] = -2.6538013e-7
self.cm[12] = 8.6255554e-10
self.cm[13] = -2.6829310e-2
self.cm[14] = -1.1173488e-7
self.cm[15] = -2.6249802e-7
self.cm[16] = 3.4926500e-10
self.cm[17] = -8.3571924e-13
# exponent in 18 (19 in reference) is barely visible, it is 5 (confirmed)
self.cm[18] = 3.0669940e-5
self.cm[19] = 1.9767979e-11
self.cm[20] = -1.9144105e-10
self.cm[21] = 3.1387857e-14
self.cm[22] = -9.6461948e-9
self.cm[23] = 2.2902837e-5
self.cm[24] = -4.3314252e-4
self.cm[25] = -9.0550901e-8
self.cm[26] = 8.6926600e-11
self.cm[27] = 5.1904777e-4
self.qm = np.zeros(19)
self.qm[0] = 0.0765
self.qm[1] = -777.03
self.qm[2] = -4.4706
self.qm[3] = 0.008946
self.qm[4] = -3.3158e-6
self.qm[5] = 0.2664
# this value is not provided
self.qm[6] = 0
# this value is not provided
self.qm[7] = 0
self.qm[8] = 6.1608e-5
self.qm[9] = 1.0715e-6
self.qm[10] = 0.00127
self.qm[11] = 33.317
self.qm[12] = 0.09421
self.qm[13] = -4.655e-5
# this value is not provided
self.qm[14] = 0
self.qm[15] = 41587.11
self.qm[16] = -315.90
self.qm[17] = 0.8514
self.qm[18] = -8.3637e-4
# Pitzer Parameters
self.tc = 298.15
self.beta0_1 = self.qm[0] + self.qm[1] * (
1 / self.tk - 1 / self.tc) + self.qm[2] * np.log(self.tk / self.tc)
self.beta0_2 = self.qm[3] * (self.tk - self.tc) + self.qm[4] * (
self.tk**2 - self.tc**2)
self.beta0 = self.beta0_1 + self.beta0_2
self.beta1 = self.qm[5] + self.qm[8] * (
self.tk - self.tc) + self.qm[9] * (self.tk**2 - self.tc**2)
self.beta2 = 0
self.c_phi_1 = self.qm[10] + self.qm[11] * (
1 / self.tk - 1 / self.tc) + self.qm[12] * np.log(
self.tk / self.tc)
self.c_phi = self.c_phi_1 + self.qm[13] * (self.tk - self.tc)
self.C0 = self.c_phi / 2
self.C1 = 0
self.C2 = 0
self.D0 = 0
self.D1 = 0
self.D2 = 0
self.params = np.array([
self.beta0, self.beta1, self.beta2, self.C0, self.C1, self.C2,
self.D0, self.D1, self.D2
])
# Pitzer Parameters pressure derivative
self.pr = un.atm_2_bar(self.pa)
self.pr_atm = un.atm_2_bar(1)
self.vp_0 = self.cm[0] + self.cm[1] * self.tk + self.cm[
2] * self.tk**2 + self.cm[3] * self.tk**3
self.vp_1 = (self.pr - self.pr_atm) * (
self.cm[4] + self.cm[5] * self.tk + self.cm[6] * self.tk**2)
self.vp_2 = (self.pr - self.pr_atm)**2 * (self.cm[7] +
self.cm[8] * self.tk)
self.vp_sum = self.vp_0 + self.vp_1 + self.vp_2
self.bp_0 = self.cm[9] + self.cm[10] / (self.tk - 227) + self.cm[
11] * self.tk + self.cm[12] * self.tk**2 + self.cm[13] / (680 -
self.tk)
self.bp_1_1 = self.cm[14] + self.cm[15] / (
self.tk - 227) + self.cm[16] * self.tk + self.cm[17] * self.tk**2
self.bp_1 = (self.bp_1_1 + self.cm[18] /
(680 - self.tk)) * (self.pr - self.pr_atm)
self.bp_2_1 = self.cm[19] + self.cm[20] / (
self.tk - 227) + self.cm[21] * self.tk + self.cm[22] / (680 -
self.tk)
self.bp_2 = self.bp_2_1 * (self.pr - self.pr_atm)**2
self.beta0_der_p = self.bp_0 + self.bp_1 + self.bp_2
self.beta1_der_p = 0
self.beta2_der_p = 0
self.cq = self.cm[23] + self.cm[24] / (self.tk - 227) + self.cm[
25] * self.tk + self.cm[26] * self.tk**2 + self.cm[27] / (680 -
self.tk)
self.cp = 0.5 * self.cq
self.C0_der_p = self.cp
self.C1_der_p = 0
self.C2_der_p = 0
self.D0_der_p = 0
self.D1_der_p = 0
self.D2_der_p = 0
# calculates the molar volume at infinite dilution (vp)
# the factor 10 is the conversion from J to bar cm^3
self.ct = 10 * un.r_gas() * self.tk
# molar volume water in cm^3/mol
self.vol_water = 1e6 * bp.WaterPropertiesFineMillero(
self.tk, self.pa).molar_volume()
self.mv_i_0 = self.vp_sum / self.m_ref - self.y_ref * self.vol_water
self.mv_i_1 = -2 * bp.WaterPropertiesFineMillero(self.tk, self.pa).a_v(
) * (0.5 * np.log(1 + self.b_param * np.sqrt(self.m_ref)) /
self.b_param)
self.mv_i_2 = -2 * self.ct * (self.m_ref * self.beta0_der_p +
self.m_ref**2 * self.C0_der_p)
# this is in cm^3/mol
self.mv_i = self.mv_i_0 + self.mv_i_1 + self.mv_i_2
# return in SI m^3
self.molar_vol_infinite_dilution = 1e-6 * self.mv_i
# infinite molar volume, convert to cm^3/mol
self.vp = 1e6 * self.molar_vol_infinite_dilution
self.params_der_p = np.array([
self.vp, self.beta0_der_p, self.beta1_der_p, self.beta2_der_p,
self.C0_der_p, self.C1_der_p, self.C2_der_p, self.D0_der_p,
self.D1_der_p, self.D2_der_p
])
# Pitzer Parameters temperature derivative
self.beta0_der_t = 2 * self.qm[4] * self.tk + self.qm[
2] / self.tk - self.qm[1] / (self.tk**2) + self.qm[3]
self.beta1_der_t = 2 * self.qm[9] * self.tk + self.qm[8]
self.beta2_der_t = 0
self.c_phi_der_t = self.qm[12] / self.tk - self.qm[11] / (
self.tk**2) + self.qm[13]
self.C0_der_t = self.c_phi_der_t / 2
self.C1_der_t = 0
self.C2_der_t = 0
self.D0_der_t = 0
self.D1_der_t = 0
self.D2_der_t = 0
self.params_der_t = np.array([
self.beta0_der_t, self.beta1_der_t, self.beta2_der_t,
self.C0_der_t, self.C1_der_t, self.C2_der_t, self.D0_der_t,
self.D1_der_t, self.D2_der_t
])
super().__init__(tk, pa)
def test_atm_conversion(self):
# 1 atm = 101325 Pa
self.assertEqual(un.atm_2_pascal(1), 101325)
# 1 atm = 1.01325 bar
self.assertEqual(un.atm_2_bar(1), 1.01325)
def __init__(self, tk, pa=1):
"""
constructor
:param tk: temperature in kelvin
:param pa: pressure in atmospheres
:instantiate: temperature, pressure, molecular weight, polarizability, dipole moment
"""
super().__init__(tk, pa)
"""
Calculations for density
"""
self.t = self.tk - un.celsius_2_kelvin(0)
# pressure in applied bar according to Fine and Millero
self.y = un.atm_2_bar(self.pa - 1)
self.den1 = 0.9998396 + self.t * 18.224944e-3 - 7.922210e-6 * self.t ** 2 - 55.44846e-9 * self.t ** 3
self.den2 = 149.7562e-12 * self.t ** 4 - 393.2952e-15 * self.t ** 5
self.V0 = (1 + self.t * 18.159725e-3) / (self.den1 + self.den2)
self.B = 19654.320 + 147.037 * self.t - 2.21554 * self.t ** 2 + 1.0478e-2 * self.t ** 3 - 2.2789e-5 * self.t ** 4
self.a1 = 3.2891 - 2.3910e-3 * self.t + 2.8446e-4 * self.t ** 2 - 2.82e-6 * self.t ** 3 + 8.477e-9 * self.t ** 4
self.a2 = 6.245e-5 - 3.913e-6 * self.t - 3.499e-8 * self.t ** 2 + 7.942e-10 * self.t ** 3 - 3.299e-12 * self.t ** 4
# this in cm^3/gram
self.vol = self.V0 * (1 - (self.y / (self.B + self.a1 * self.y + self.a2 * self.y ** 2)))
# density in kg/m^3
self.rt = 1e3 / self.vol
# Calculations for molar volume
self.molVol = 1e-3 * self.MolecularWeight / self.rt
# Calculations for dielectric constant
# coefficients
self.U = np.zeros(9)
self.U[0] = 3.4279e2
self.U[1] = -5.0866e-3
self.U[2] = 9.4690e-7
self.U[3] = -2.0525
self.U[4] = 3.1159e3
self.U[5] = -1.8289e2
self.U[6] = -8.0325e3
self.U[7] = 4.2142e6
self.U[8] = 2.1417
self.D100 = self.U[0] * (np.exp(self.U[1] * self.tk + self.U[2] * self.tk ** 2))
self.C = self.U[3] + self.U[4] / (self.U[5] + self.tk)
self.B_dc = self.U[6] + (self.U[7] / self.tk) + self.U[8] * self.tk
self.dielectricConstant = self.D100 + self.C * np.log((self.B_dc + un.atm_2_bar(self.pa)) / (self.B_dc + 1000))
# dielectric constant derivative with respect to pressure
self.dielectricConstant_der_p = un.atm_2_bar(1) * self.C / (self.B_dc + (un.atm_2_bar(self.pa)))
# dielectric constant derivative with respect to temperature
self.val_1 = (un.atm_2_bar(self.pa) - 1000) * (self.U[3] * (self.U[5] + self.tk) + self.U[4]) * (self.U[8] * self.tk ** 2 - self.U[7])
self.val_2 = (self.U[5] + self.tk) * (self.U[6] * self.tk + self.tk * (self.U[8] * self.tk + 1000) + self.U[7]) * (self.tk * (un.atm_2_bar(self.pa) + self.U[8] * self.tk) + self.U[6] * self.tk + self.U[7])
self.val_3 = (self.U[4] * np.log((un.atm_2_bar(self.pa) + (self.U[7] / self.tk) + self.U[8] * self.tk + self.U[6]) / (1000 + (self.U[7] / self.tk) + self.U[8] * self.tk + self.U[6]))) / ((self.U[5] + self.tk) ** 2)
self.val_4 = (self.U[0] * np.exp(self.U[1] * self.tk + self.U[2] * self.tk ** 2)) * (2 * self.U[2] * self.tk + self.U[1])
self.dielectricConstant_der_t = -(self.val_1 / self.val_2) - self.val_3 + self.val_4
# Calculations for compressibility
self.beta = self.V0 * (self.B - self.a2 * self.y ** 2) / (
self.vol * (self.B + self.a1 * self.y + self.a2 * self.y ** 2) ** 2)
self.comp = un.atm_2_bar(self.beta)
# Calculations for osmotic coefficient
# Bjerrum length
self.l_b = un.e_square() / (un.k_boltzmann() * self.tk * self.dielectricConstant)
self.fac = 2 * np.pi * un.avogadro() * self.rt * self.l_b ** 3
self.osmotic_coefficient = np.sqrt(self.fac) / 3
# Calculations for apparent molal volume
# add a factor 1e6 and convert to Pascal (lat two parts of a_v_0)
self.a_v_0 = 2 * self.osmotic_coefficient * un.r_gas() * self.tk * 1e6 / un.atm_2_pascal(1)
self.a_v_1 = self.dielectricConstant
self.a_v_2 = 3 * self.dielectricConstant_der_p
self.a_v_3 = self.comp
self.app_molal_vol = self.a_v_0 * (self.a_v_2 / self.a_v_1 - self.a_v_3)
# Calculations for enthalpy coefficient
# thermal expansion coefficient
self.V0_der_1 = 2.85685e-14 * self.t ** 5 - 6.19212e-12 * self.t ** 4 + 1.41483e-9 * self.t ** 3
self.V0_der_2 = 3.10211e-7 * self.t ** 2 + 0.0000158444 * self.t - 0.0000681318
self.V0_der_3 = -3.93295e-13 * self.t ** 5 + 1.49756e-10 * self.t ** 4 - 5.54485e-8 * self.t ** 3
self.V0_der_4 = -7.92221e-6 * self.t ** 2 + 0.0182249 * self.t + 0.99984
self.V0_der = (self.V0_der_1 + self.V0_der_2) / ((self.V0_der_3 + self.V0_der_4) ** 2)
self.B_der = -0.000091156 * self.t ** 3 + 0.031434 * self.t ** 2 - 4.43108 * self.t + 147.037
self.a1_der = 3.3908e-8 * self.t ** 3 - 8.46e-6 * self.t ** 2 + 0.00056892 * self.t - 0.002391
self.a2_der = -1.3196e-11 * self.t ** 3 + 2.3826e-9 * self.t ** 2 - 6.998e-8 * self.t - 3.913e-6
self.aw_term_1 = (1 / self.vol) * self.V0_der
self.aw_term_2 = -((self.y * self.V0_der) / (self.vol * (self.B + self.a1 * self.y + self.a2 * self.y ** 2)))
self.aw_term_3 = self.y * self.V0 * ((self.B_der + self.y * self.a1_der + self.a2_der * self.y ** 2) / (self.vol * (self.B + self.a1 * self.y + self.a2 * self.y ** 2) ** 2))
self.aw = self.aw_term_1 + self.aw_term_2 + self.aw_term_3
# enthalpy coefficient
self.enthalpy_coefficient = -6 * self.osmotic_coefficient * un.r_gas() * self.tk * (1 + self.tk * (1 / self.dielectricConstant) * self.dielectricConstant_der_t + self.tk * (self.aw / 3))