def getZfromPT(self, _P: float, _T: float):
a = 1.0
b = np.real(self._numf_a0(_P, _T))
c = np.real(self._numf_a1(_P, _T))
d = np.real(self._numf_a2(_P, _T))
roots = np.asarray(solve_cubic(a, b, c, d))
real_values = roots[roots > 0]
return real_values
def bi(self, i):
zeta_c = (0.32903 - 0.076799 * self.mix[i].omega +
0.0211947 * self.mix[i].omega**2)
r = np.atleast_1d(
solve_cubic(1, 2 - 3 * zeta_c, 3 * zeta_c**2, -zeta_c**3))
omega_b = np.min(r[r >= 0])
return omega_b * (R_IG * self.mix[i].Tc) / self.mix[i].Pc
def _calc_a_and_b(T: float, Tc: float, Pc: float, w: float):
Bc = 0.25989 + w * (-0.0217 + 0.00375 * w)
bs = solve_cubic(6.0 * w + 1.0, 3.0, 3.0, -1.0, x0=Bc)
Bc = np.min([x for x in bs if x > 0])
zeta_c = 1.0 / (3.0 * (1.0 + w * Bc))
omega_b = Bc * zeta_c
omega_a = (1.0 - zeta_c * (1.0 - Bc)) ** 3
b = omega_b * R_IG * Tc / Pc
a = omega_a * (R_IG * Tc) ** 2 / Pc
return a, b
def getZfromPT(self, P, T, y):
A = self.thetam(y, T) * P / (R_IG * T)**2
B = self.bm(y) * P / (R_IG * T)
_a = 1.0
_b = -(1.0 - B)
_c = A - 3 * B * B - 2.0 * B
_d = -(A * B - B * B - B**3)
roots = np.asarray(solve_cubic(_a, _b, _c, _d))
real_values = roots[roots > 0]
return real_values
def getZfromPT(self, P, T, y):
A = self.thetam(y, T) * P / (R_IG * T)**2
B = self.bm(y) * P / (R_IG * T)
a = 1.0
b = -1.0
c = A - B * (1 + B)
d = -A * B
roots = np.asarray(solve_cubic(a, b, c, d))
real_values = roots[roots > 0]
return real_values
def _calc_a_b_c(i: int, T: float, substances):
w = substances[i].omega
Pc = substances[i].Pc
Tc = substances[i].Tc
zeta_c = 0.32903 - 0.076799 * w + 0.0211947 * w ** 2
omega_c = 1.0 - 3.0 * zeta_c
c = omega_c * R_IG * Tc / Pc
r = np.atleast_1d(solve_cubic(1, 2 - 3 * zeta_c, 3 * zeta_c ** 2, -zeta_c ** 3))
omega_b = np.min(r[r >= 0])
omega_a = (
3 * zeta_c ** 2 + 3 * (1 - 2 * zeta_c) * omega_b + omega_b ** 2 + 1 - 3 * zeta_c
)
a = omega_a * (R_IG * Tc) ** 2 / Pc
b = omega_b * (R_IG * Tc) / Pc
return a, b, c
def thetai(self, i, T):
F = 0.452413 + 1.30982 * self.mix[i].omega - 0.295937 * self.mix[
i].omega**2
zeta_c = (0.32903 - 0.076799 * self.mix[i].omega +
0.0211947 * self.mix[i].omega**2)
r = np.atleast_1d(
solve_cubic(1, 2 - 3 * zeta_c, 3 * zeta_c**2, -zeta_c**3))
omega_b = np.min(r[r >= 0])
omega_a = (3 * zeta_c**2 + 3 * (1 - 2 * zeta_c) * omega_b +
omega_b**2 + 1 - 3 * zeta_c)
alpha = (1 + F * (1 - (T / self.mix[i].Tc)**0.5))**2
return alpha * omega_a * (R_IG * self.mix[i].Tc)**2 / self.mix[i].Pc
def getZfromPT(self, P, T, y):
b = self.bm(y)
theta = self.thetam(y, T)
delta = b
_Bl = b * P / (R_IG * T)
_deltal = delta * P / (R_IG * T)
_thetal = theta * P / (R_IG * T)**2
_epsilonl = 0
a = 1.0
b = _deltal - _Bl - 1
c = _thetal + _epsilonl - _deltal * (_Bl + 1)
d = -(_epsilonl * (_Bl + 1) + _thetal * _Bl)
roots = np.asarray(solve_cubic(a, b, c, d))
real_values = roots[roots > 0]
return real_values
def _getZfromPT_helper(
b: float,
theta: float,
delta: float,
epsilon: float,
T: float,
P: float,
R_IG: float,
):
Bl = b * P / (R_IG * T)
deltal = delta * P / (R_IG * T)
epsilonl = epsilon * np.power(P / (R_IG * T), 2)
thetal = theta * P / np.power(R_IG * T, 2)
_b = deltal - Bl - 1.0
_c = thetal + epsilonl - deltal * (1.0 + Bl)
_d = -(epsilonl * (Bl + 1.0) + Bl * thetal)
roots = np.array(solve_cubic(1.0, _b, _c, _d))
real_values = roots[roots >= 0]
return real_values
def getZfromPT(self, P, T, y):
b = self.bm(y)
theta = self.thetam(y, T)
delta = 0
epsilon = 0
_Bl = b * P / (R_IG * T)
_deltal = delta * P / (R_IG * T)
_thetal = theta * P / (R_IG * T)**2
_epsilonl = epsilon * (P / (R_IG * T))**2
# coefficients Z**3 + a0*Z**2 + a1*Z + a2 = 0
_a0 = _deltal - _Bl - 1
_a1 = _thetal + _epsilonl - _deltal * (_Bl + 1)
_a2 = -(_epsilonl * (_Bl + 1) + _thetal * _Bl)
roots = np.asarray(solve_cubic(1.0, _a0, _a1, _a2))
real_values = roots[roots > 0]
return real_values
def getZfromPT(self, P, T, y):
A = self.thetam(y, T) * P / (R_IG * T)**2
B = self.bm(y) * P / (R_IG * T)
c = self.cm(y)
b = self.bm(y)
delta = b + 2 * c
epsilon = c * (b + c)
theta = self.thetam(y, T)
_Bl = b * P / (R_IG * T)
_deltal = delta * P / (R_IG * T)
_thetal = theta * P / (R_IG * T)**2
_epsilonl = epsilon * (P / (R_IG * T))**2
a = 1.0
b = _deltal - _Bl - 1
c = _thetal + _epsilonl - _deltal * (_Bl + 1)
d = -(_epsilonl * (_Bl + 1) + _thetal * _Bl)
roots = np.asarray(solve_cubic(a, b, c, d))
real_values = roots[roots > 0]
return real_values
def _initialize(self):
if self.eosValue == "van_der_waals_1890":
thetas = []
self.b = 0
for i in range(self.n):
self.b += (0.125 / (self.Pcs[i] /
(R_IG * self.Tcs[i]))) * self.y[i]
thetas.append(0.42188 * (R_IG * self.Tcs[i])**2 / self.Pcs[i])
self._calculate_theta_mixture(thetas)
self.delta = 0.0
self.epsilon = 0.0
elif self.eosValue == "redlich_and_kwong_1949":
thetas = []
self.b = 0
for i in range(self.n):
self.b += (0.08664 / (self.Pcs[i] /
(R_IG * self.Tcs[i]))) * self.y[i]
thetas.append(
(0.42748 * (R_IG * self.Tcs[i])**2 / self.Pcs[i]) /
(self.T / self.Tcs[i])**0.5)
self._calculate_theta_mixture(thetas)
self.delta = self.b
self.epsilon = 0.0
elif self.eosValue == "wilson_1964":
thetas = []
self.b = 0
for i in range(self.n):
self.b += (0.08664 / (self.Pcs[i] /
(R_IG * self.Tcs[i]))) * self.y[i]
a = 0.42748 * (R_IG * self.Tcs[i])**2 / self.Pcs[i]
alpha = (self.T /
self.Tcs[i]) * (1 + (1.57 + 1.62 * self.omegas[i]) *
(1.0 / (self.T / self.Tcs[i]) - 1.0))
thetas.append(a * alpha)
self._calculate_theta_mixture(thetas)
self.delta = self.b
self.epsilon = 0.0
elif self.eosValue == "soave_1972":
thetas = []
self.b = 0
for i in range(self.n):
self.b += (0.08664 / (self.Pcs[i] /
(R_IG * self.Tcs[i]))) * self.y[i]
a = 0.42748 * (R_IG * self.Tcs[i])**2 / self.Pcs[i]
alpha = (1.0 + (0.48 + 1.574 * self.omegas[i] -
0.176 * self.omegas[i]**2) *
(1.0 - (self.T / self.Tcs[i])**0.5))**2
thetas.append(a * alpha)
self._calculate_theta_mixture(thetas)
self.delta = self.b
self.epsilon = 0.0
elif self.eosValue == "peng_and_robinson_1976":
thetas = []
self.b = 0
for i in range(self.n):
self.b += self.y[i] * (0.07780 / (self.Pcs[i] /
(R_IG * self.Tcs[i])))
self.symb_bm += (self.symb_ys[i]) * (0.07780 /
(self.Pcs[i] /
(R_IG * self.Tcs[i])))
_tmpthetas = ((1.0 + (0.37464 + 1.54226 * self.omegas[i] -
0.2699 * self.omegas[i]**2) *
(1.0 - (self.T / self.Tcs[i])**0.5))**
2) * (0.45724 *
(R_IG * self.Tcs[i])**2 / self.Pcs[i])
thetas.append(_tmpthetas)
self._calculate_theta_mixture(thetas)
self._symb_calculate_theta_mixture(thetas)
self.delta = 2 * self.b
self.symb_deltam = 2 * self.symb_bm
self.epsilon = -self.b * self.b
self.symb_epsilonm = -self.symb_bm**2
elif self.eosValue == "peneloux_et_al_1982":
thetas = []
self.b = 0
c = 0
for i in range(self.n):
a = 0.42748 * (R_IG * self.Tcs[i])**2 / self.Pcs[i]
c += (0.40768 * (R_IG * self.Tcs[i] / self.Pcs[i]) *
(0.00385 + 0.08775 * self.omegas[i])) * self.y[i]
self.b += (0.08664 / (self.Pcs[i] /
(R_IG * self.Tcs[i]))) * self.y[i]
alpha = (1.0 + (0.48 + 1.574 * self.omegas[i] -
0.176 * self.omegas[i]**2) *
(1.0 - (self.T / self.Tcs[i])**0.5))**2
thetas.append(a * alpha)
self.b = self.b - c
self._calculate_theta_mixture(thetas)
self.delta = self.b + 2 * c
self.epsilon = c * (self.b + c)
elif self.eosValue == "patel_and_teja_1982":
thetas = []
self.b = 0
c = 0
for i in range(self.n):
F = 0.45241 + 1.30982 * self.omegas[
i] - 0.295937 * self.omegas[i]**2
zeta_c = (0.32903 - 0.076799 * self.omegas[i] +
0.0211947 * self.omegas[i]**2)
r = np.atleast_1d(
solve_cubic(1, 2 - 3 * zeta_c, 3 * zeta_c**2, -zeta_c**3))
omega_b = np.min(r[r >= 0])
omega_c = 1 - 3 * zeta_c
omega_a = (3 * zeta_c**2 + 3 * (1 - 2 * zeta_c) * omega_b +
omega_b**2 + 1 - 3 * zeta_c)
c += self.y[i] * omega_c * R_IG * self.Tcs[i] / self.Pcs[i]
self.b += self.y[i] * omega_b * R_IG * self.Tcs[i] / self.Pcs[i]
alpha = (1 + F * (1 - (self.T / self.Tcs[i])**0.5))**2
a = omega_a * (R_IG * self.Tcs[i])**2 / self.Pcs[i]
thetas.append(a * alpha)
self._calculate_theta_mixture(thetas)
self.delta = self.b + c
self.epsilon = -self.b * c
elif self.eosValue == "adachi_et_al_1983":
thetas = []
self.b = 0
c = 0
b1, b2, b3 = 0, 0, 0
for i in range(self.n):
b1 += self.y[i] * (R_IG * self.Tcs[i] *
(0.08974 - 0.03452 * self.omegas[i] +
0.00330 * self.omegas[i]**2) / self.Pcs[i])
b2 += self.y[i] * (R_IG * self.Tcs[i] *
(0.03686 + 0.00405 * self.omegas[i] -
0.01073 * self.omegas[i]**2 +
0.00157 * self.omegas[i]**3) / self.Pcs[i])
b3 += self.y[i] * (R_IG * self.Tcs[i] *
(0.154 + 0.14122 * self.omegas[i] -
0.00272 * self.omegas[i]**2 -
0.00484 * self.omegas[i]**3) / self.Pcs[i])
a = ((R_IG * self.Tcs[i])**2 *
(0.44869 + 0.04024 * self.omegas[i] + 0.01111 *
self.omegas[i]**2 - 0.00576 * self.omegas[i]**3) /
self.Pcs[i])
alpha = (1 + (0.407 + 1.3787 * self.omegas[i] -
0.2933 * self.omegas[i]**2) *
(1.0 - (self.T / self.Tcs[i])**0.5))**2
thetas.append(a * alpha)
self.b = b1
self._calculate_theta_mixture(thetas)
self.delta = b3 - b2
self.epsilon = -b2 * b3
elif self.eosValue == "soave_1984":
thetas = []
self.b = 0
self.epsilon = 0
for i in range(self.n):
self.b += (0.08333 / (self.Pcs[i] /
(R_IG * self.Tcs[i]))) * self.y[i]
self.epsilon += (0.001736 / (self.Pcs[i] /
(R_IG * self.Tcs[i]))**2 *
self.y[i])
a = 0.42188 * (R_IG * self.Tcs[i])**2 / self.Pcs[i]
alpha = (
1.0 +
(0.4998 + 1.5928 * self.omegas[i] -
0.19563 * self.omegas[i]**2 + 0.025 * self.omegas[i]**3) *
(1.0 - (self.T / self.Tcs[i])**0.5))**2
thetas.append(a * alpha)
self._calculate_theta_mixture(thetas)
self.delta = self.b
elif self.eosValue == "adachi_et_al_1985":
thetas = []
self.b = 0
c = 0
for i in range(self.n):
a = ((R_IG * self.Tcs[i])**2 *
(0.43711 + 0.02366 * self.omegas[i] + 0.10538 *
self.omegas[i]**2 + 0.10164 * self.omegas[i]**3) /
self.Pcs[i])
self.b += self.y[i] * (
(R_IG * self.Tcs[i]) *
(0.08779 - 0.02181 * self.omegas[i] -
0.06708 * self.omegas[i]**2 + 0.10617 * self.omegas[i]**3)
/ self.Pcs[i])
c += self.y[i] * ((R_IG * self.Tcs[i]) *
(0.0506 + 0.04184 * self.omegas[i] +
0.16413 * self.omegas[i]**2 -
0.03975 * self.omegas[i]**3) / self.Pcs[i])
alpha = (
1 +
(0.4406 + 1.7039 * self.omegas[i] -
1.729 * self.omegas[i]**2 + 0.9929 * self.omegas[i]**3) *
(1 - (self.T / self.Tcs[i])**0.5))**2
thetas.append(a * alpha)
self._calculate_theta_mixture(thetas)
self.delta = 2 * c
self.epsilon = -c**2
elif self.eosValue == "stryjek_and_vera_1986":
thetas = []
self.b = 0
for i in range(self.n):
self.b += self.y[i] * (0.07780 / (self.Pcs[i] /
(R_IG * self.Tcs[i])))
self.symb_bm += (self.symb_ys[i]) * (0.07780 /
(self.Pcs[i] /
(R_IG * self.Tcs[i])))
k0 = (0.378893 + 1.48971530 * self.omegas[i] -
0.17131848 * self.omegas[i]**2 +
0.0196554 * self.omegas[i]**3)
k1 = 0
name = self.mix.substances[i].Name
if name == "hexadecane":
k1 = 0.02665
elif name == "hexane":
k1 = 0.05104
elif name == "cyclohexane":
k1 = 0.07023
elif name == "methane":
k1 = -0.00159
elif name == "benzene":
k1 = 0.07019
Tr = self.T / self.Tcs[i]
k = k0 + k1 * (1 + Tr) * (0.7 - Tr)
_tmpthetas = ((1.0 + (k) * (1.0 - (self.T / self.Tcs[i])**0.5))
**2) * (0.45724 *
(R_IG * self.Tcs[i])**2 / self.Pcs[i])
thetas.append(_tmpthetas)
self._calculate_theta_mixture(thetas)
self._symb_calculate_theta_mixture(thetas)
self.delta = 2 * self.b
self.symb_deltam = 2 * self.symb_bm
self.epsilon = -self.b * self.b
self.symb_epsilonm = -self.symb_bm**2
elif self.eosValue == "twu_et_al_1995":
thetas = []
self.b = 0
for i in range(self.n):
self.b += (self.y[i] * (R_IG * self.Tcs[i]) * 0.0777960739039 /
self.Pcs[i])
a = (R_IG * self.Tcs[i])**2 * 0.457235528921 / self.Pcs[i]
alpha0 = (self.T / self.Tcs[i])**(
-0.171813) * 2.718281828459045235360**(
0.125283 * (1 - (self.T / self.Tcs[i])**1.77634))
alpha1 = (self.T / self.Tcs[i])**(
-0.607352) * 2.718281828459045235360**(
0.511614 * (1 - (self.T / self.Tcs[i])**2.20517))
alpha = alpha0 + self.omegas[i] * (alpha1 - alpha0)
thetas.append(a * alpha)
self._calculate_theta_mixture(thetas)
self.delta = self.b * 2
self.epsilon = -self.b**2
elif self.eosValue == "ahlers_gmehling_2001":
thetas = []
self.b = 0
c = 0
for i in range(self.n):
a = 0.45724 * (R_IG * self.Tcs[i])**2 / self.Pcs[i]
alpha = (1.0 + (0.37464 + 1.54226 * self.omegas[i] -
0.2699 * self.omegas[i]**2) *
(1.0 - (self.T / self.Tcs[i])**0.5))**2
gamma = 246.78 * self.Zcs[i]**2 - 107.21 * self.Zcs[i] + 12.67
n = -74.458 * self.Zcs[i] + 26.966
beta = 0.35 / (0.35 + (n * np.abs(
(self.T / self.Tcs[i]) - alpha))**gamma)
cc = ((0.3074 - self.Zcs[i]) * R_IG * (self.T / self.Tcs[i]) /
self.Pcs[i])
c += (cc * beta) * self.y[i]
self.b += self.y[i] * 0.07780 / (self.Pcs[i] /
(R_IG * self.Tcs[i]))
thetas.append(a * alpha)
self._calculate_theta_mixture(thetas)
self.b = self.b - c
self.delta = self.b * 2
self.epsilon = -self.b * self.b + 4 * self.b * c - 2 * c**2
elif self.eosValue == "gasem_et_al_pr_2001":
thetas = []
self.b = 0
for i in range(self.n):
a = 0.45724 * (R_IG * self.Tcs[i])**2 / self.Pcs[i]
self.b += self.y[i] * 0.07780 / (self.Pcs[i] /
(R_IG * self.Tcs[i]))
alpha = (1.0 + (0.386590 + 1.50226 * self.omegas[i] -
0.1687 * self.omegas[i]**2) *
(1.0 - (self.T / self.Tcs[i])**0.5))**2
thetas.append(a * alpha)
self._calculate_theta_mixture(thetas)
self.delta = 2 * self.b
self.epsilon = -self.b**2
elif self.eosValue == "gasem_et_al_twu_2001":
thetas = []
self.b = 0
for i in range(self.n):
a = 0.45724 * (R_IG * self.Tcs[i])**2 / self.Pcs[i]
self.b += self.y[i] * 0.07780 / (self.Pcs[i] /
(R_IG * self.Tcs[i]))
alpha0 = (self.T / self.Tcs[i])**(
-0.207176) * 2.718281828459045235360**(
0.092099 * (1 - (self.T / self.Tcs[i])**1.94800))
alpha1 = (self.T / self.Tcs[i])**(
-0.502297) * 2.718281828459045235360**(
0.603486 * (1 - (self.T / self.Tcs[i])**2.09626))
alpha = alpha0 + self.omegas[i] * (alpha1 - alpha0)
thetas.append(a * alpha)
self._calculate_theta_mixture(thetas)
self.delta = 2 * self.b
self.epsilon = -self.b**2
elif self.eosValue == "gasem_et_al_2001":
thetas = []
self.b = 0
for i in range(self.n):
a = 0.45724 * (R_IG * self.Tcs[i])**2 / self.Pcs[i]
self.b += self.y[i] * 0.07780 / (self.Pcs[i] /
(R_IG * self.Tcs[i]))
A = 2.0
B = 0.836
C = 0.134
D = 0.508
E = -0.0467
Tr = self.T / self.Tcs[i]
w = self.omegas[i]
alpha = 2.718281828459045235360**((A + B * Tr) *
(1.0 - Tr**(C + w *
(D + E * w))))
thetas.append(a * alpha)
self._calculate_theta_mixture(thetas)
self.delta = 2 * self.b
self.epsilon = -self.b**2
else:
raise ValueError(
"Equation of state doesn't exists in the current database")