def _Dew_P(self):
def f(P):
eq = self.__class__(self.T, P, self.mezcla)
return sum([x / k for k, x in zip(eq.Ki, self.fraccion)]) - 1.
P = fsolve(f, self.P.atm)
return unidades.Pressure(P, "atm")
def __init__(self, T, P, mezcla, **kwargs):
self.T = unidades.Temperature(T)
self.P = unidades.Pressure(P, "atm")
self.mezcla = mezcla
self.componente = mezcla.componente
self.fraccion = mezcla.fraccion
self.kwargs = kwargs
def TB_H_exceso(self, T, P):
"""Método de cálculo de la entalpía de exceso mediante la ecuación de estado de Trebble-Bishnoi"""
p = unidades.Pressure(P, "atm")
U = self.TB_U_exceso(T, P)
a, b, c, d, q1, q2 = self.TB_lib(T, P)
t = 1 + 6 * c / b + c**2 / b**2 + 4 * d**2 / b**2
if t >= 0:
v = self.TB_V(T, P).m3g * self.peso_molecular
return unidades.Enthalpy(
p * v - R / T / self.peso_molecular + U.Jg, "Jg")
else:
Z = self.TB_Z(T, P)
return unidades.Enthalpy(
R / self.peso_molecular * T * (Z - 1) + U.Jg, "Jg")
def fug(self, rho, T, nfirni=None):
if not nfirni:
tau = self.Tc / T
delta = rho / self.rhoc
fir, firt, firtt, fird, firdd, firdt, firdtt, nfirni = self._phir(
tau, delta)
f = []
FI = []
for xi, dn in zip(self.xi, nfirni):
f.append(
unidades.Pressure(xi * rho / self.M * R_atml * T * exp(dn),
"atm"))
FI.append(dn - log(self.Z))
return f, FI
def TB_Fugacidad(self, T, P):
"""Método de cálculo de la fugacidad mediante la ecuación de estado de Trebble-Bishnoi"""
a, b, c, d, q1, q2 = self.TB_lib(T, P)
z = self.TB_Z(T, P)
A = a * P / R_atml**2 / T**2
B = b * P / R_atml / T
u = 1 + c / b
t = 1 + 6 * c / b + c**2 / b**2 + 4 * d**2 / b**2
tita = abs(t)**0.5
if t >= 0:
lamda = log((2 * z + B * (u - tita)) / (2 * z + B * (u + tita)))
else:
lamda = 2 * arctan((2 * z + u * B) / B / tita) - pi
fi = z - 1 - log(z - B) + A / B / tita * lamda
return unidades.Pressure(P * exp(fi), "atm")
def calculo(self):
T = self.kwargs["T"]
rho = self.kwargs["rho"]
P = self.kwargs["P"]
v = self.kwargs["v"]
h = self.kwargs["h"]
s = self.kwargs["s"]
u = self.kwargs["u"]
x = self.kwargs["x"]
self.comp = []
for i in self.kwargs["componente"]:
c = self.componentes[i](eq="GERG", **self.kwargs)
self.comp.append(c)
self.id = self.kwargs["componente"]
self.xi = self.kwargs["fraccion"]
# Critic properties for mixture,
# eq. 7.9, 7.10 pag.125, Tabla 7.10 pag 136
bt = self.Prop_c["beta_t"]
bv = self.Prop_c["beta_v"]
gt = self.Prop_c["gamma_t"]
gv = self.Prop_c["gamma_v"]
c_T = zeros((len(self.comp), len(self.comp)))
c_rho = zeros((len(self.comp), len(self.comp)))
for i, cmpi in enumerate(self.comp):
for j, cmpj in enumerate(self.comp):
c_T[i, j] = 2 * bt[i][j] * gt[i][j] * (cmpi.Tc * cmpj.Tc)**0.5
c_rho[i, j] = 2*bv[i][j]*gv[i][j]/8. * \
(1./cmpi.rhoc**(1./3)+1./cmpj.rhoc**(1./3))**3
f_T = zeros((len(self.comp), len(self.comp)))
f_rho = zeros((len(self.comp), len(self.comp)))
dFT_ik = zeros((len(self.comp), len(self.comp)))
dFT_ki = zeros((len(self.comp), len(self.comp)))
dFrho_ik = zeros((len(self.comp), len(self.comp)))
dFrho_ki = zeros((len(self.comp), len(self.comp)))
for i, x_i in enumerate(self.xi):
for j, x_j in enumerate(self.xi):
f_T[i, j] = x_i * x_j * (x_i + x_j) / (bt[i][j]**2 * x_i + x_j)
f_rho[i,
j] = x_i * x_j * (x_i + x_j) / (bv[i][j]**2 * x_i + x_j)
dFT_ik[i, j] = x_j*(x_j+x_i)/(bt[i][j]**2*x_i+x_j) + \
x_j*x_i/(bt[i][j]**2*x_i+x_j) * \
(1-bt[i][j]**2*(x_j+x_i)/(bt[i][j]**2*x_i+x_j))
dFrho_ik[i, j] = x_j*(x_j+x_i)/(bv[i][j]**2*x_i+x_j) + \
x_j*x_i/(bv[i][j]**2*x_i+x_j) * \
(1-bv[i][j]**2*(x_j+x_i)/(bv[i][j]**2*x_i+x_j))
dFT_ki[j, i] = x_j*(x_j+x_i)/(bt[i][j]**2*x_j+x_i)+x_j*x_i / \
(bt[i][j]**2*x_j+x_i)*(1-(x_j+x_i)/(bt[i][j]**2*x_j+x_i))
dFrho_ki[j, i] = x_j*(x_j+x_i)/(bv[i][j]**2*x_j+x_i)+x_j*x_i /\
(bv[i][j]**2*x_j+x_i)*(1-(x_j+x_i)/(bv[i][j]**2*x_j+x_i))
sumai_v = sumaij_v = sumai_T = sumaij_T = m = 0
for i, componentei in enumerate(self.comp):
sumai_v += self.xi[i]**2 / componentei.rhoc
sumai_T += self.xi[i]**2 * componentei.Tc
m += self.xi[i] * componentei.M
for j, componentej in enumerate(self.comp):
if j > i:
sumaij_v += c_rho[i, j] * f_rho[i, j]
sumaij_T += c_T[i, j] * f_T[i, j]
self.rhoc = unidades.Density(1. / (sumai_v + sumaij_v))
self.Tc = unidades.Temperature(sumai_T + sumaij_T)
self.M = m # g/mol
self.R = unidades.SpecificHeat(R / self.M, "kJkgK")
Tcxi = rhocxi = []
for i, componentei in enumerate(self.comp):
sumav1 = sumat1 = 0
for k in range(i):
sumav1 += c_rho[k, i] * dFrho_ki[k, i]
sumat1 += c_T[k, i] * dFT_ki[k, i]
sumav2 = sumat2 = 0
for k in range(i + 1, len(self.xi)):
sumav2 += c_rho[i, k] * dFrho_ik[i, k]
sumat2 += c_T[i, k] * dFT_ik[i, k]
Tcxi.append(2 * self.xi[i] * componentei.Tc + sumat1 + sumat2)
rhocxi.append(2 * self.xi[i] / componentei.rhoc + sumav1 + sumav2)
self.Tcxi = Tcxi
self.rhocxi = rhocxi
if v and not rho:
rho = 1. / v
if T and x is not None:
pass
else:
if T and P:
rhoo = 2.
rho = fsolve(lambda rho: self._solve(rho, T)["P"] - P * 1e6,
rhoo)
elif T and rho:
pass
elif T and h is not None:
rho = fsolve(lambda rho: self._solve(rho, T)["h"] - h, 200)
elif T and s is not None:
rho = fsolve(lambda rho: self._solve(rho, T)["s"] - s, 200)
elif T and u is not None:
rho = fsolve(lambda rho: self._solve(rho, T)["u"] - u, 200)
elif P and rho:
T = fsolve(lambda T: self._solve(rho, T)["P"] - P * 1e6, 600)
elif P and h is not None:
rho, T = fsolve(
lambda par: (self._solve(par[0], par[1])["P"] - P * 1e6,
self._solve(par[0], par[1])["h"] - h),
[200, 600])
elif P and s is not None:
rho, T = fsolve(
lambda par: (self._solve(par[0], par[1])["P"] - P * 1e6,
self._solve(par[0], par[1])["s"] - s),
[200, 600])
elif P and u is not None:
rho, T = fsolve(
lambda par: (self._solve(par[0], par[1])["P"] - P * 1e6,
self._solve(par[0], par[1])["u"] - u),
[200, 600])
elif rho and h is not None:
T = fsolve(lambda T: self._solve(rho, T)["h"] - h, 600)
elif rho and s is not None:
T = fsolve(lambda T: self._solve(rho, T)["s"] - s, 600)
elif rho and u is not None:
T = fsolve(lambda T: self._solve(rho, T)["u"] - u, 600)
elif h is not None and s is not None:
rho, T = fsolve(
lambda par: (self._solve(par[0], par[1])["h"] - h,
self._solve(par[0], par[1])["s"] - s),
[200, 600])
elif h is not None and u is not None:
rho, T = fsolve(
lambda par: (self._solve(par[0], par[1])["h"] - h,
self._solve(par[0], par[1])["u"] - u),
[200, 600])
elif s is not None and u is not None:
rho, T = fsolve(
lambda par: (self._solve(par[0], par[1])["s"] - s,
self._solve(par[0], par[1])["u"] - u),
[200, 600])
else:
raise IOError
fio, fiot, fiott, fiod, fiodd, fiodt, fir, firt, firtt, fird, firdd,\
firdt, firdtt, nfioni, nfirni = self._eq(rho, T)
# Tabla 7.1 pag 127
tau = self.Tc / T
delta = rho / self.rhoc
self.T = unidades.Temperature(T)
self.rho = unidades.Density(rho)
self.v = unidades.SpecificVolume(1. / rho)
self.P = unidades.Pressure((1 + delta * fird) * self.R.JkgK * T * rho)
self.Z = 1 + delta * fird
self.s = unidades.SpecificHeat(self.R.kJkgK *
(tau * (fiot + firt) - fio - fir))
self.u = unidades.Enthalpy(self.R * T * tau * (fiot + firt))
self.h = unidades.Enthalpy(self.R * T * (1 + tau *
(fiot + firt) + delta * fird))
self.cp = unidades.SpecificHeat(
self.R * (-tau**2 * (fiott + firtt) +
(1 + delta * fird - delta * tau * firdt)**2 /
(1 + 2 * delta * fird + delta**2 * firdd)))
self.cv = unidades.SpecificHeat(-self.R * tau**2 * (fiott + firtt))
self.g = unidades.Enthalpy(self.R * T * (1 + fio + fir + delta * fird))
self.w = unidades.Speed(
(self.R * T *
(1 + 2 * delta * fird + delta**2 * firdd -
(1 + delta * fird - delta * tau * firdt)**2 / tau**2 /
(fiott + firtt)))**0.5)
f, FI = self.fug(rho, T, nfirni)
Ki, xi, yi, Q = self.flash()
self.x = unidades.Dimensionless(Q)
self.xl = xi
self.xv = yi
if self.kwargs["mezcla"]:
self.Pc = self.kwargs["mezcla"].Pc
self.Liquido = Fluid()
self.Gas = Fluid()
fiv = r_[yi] * r_[self.titaiv] * self.P
fil = r_[xi] * r_[self.titail] * self.P
# criterio de convergencia Eq 21
if sum((fil / fiv - 1)**2) < 1e-15 and (Q - Qo)**2 < 1e-15:
break
else:
Ki = r_[self.titail] / r_[self.titaiv]
return Ki, xi, yi, Q
id_GERG = [i.id for i in GERG.componentes]
if __name__ == "__main__":
# import doctest
# doctest.testmod()
T = unidades.Temperature(205, "F")
P = unidades.Pressure(315, "psi")
aire = GERG(T=T,
P=P,
componente=[0, 3, 4, 5, 7, 9],
fraccion=[0.26, 0.09, 0.25, 0.17, 0.11, 0.12])
# print "%0.1f %0.4f %0.3f %0.3f %0.5f %0.4f %0.2f" % (aire.T, aire.rho, aire.h.kJkg, aire.s.kJkgK, aire.cv.kJkgK, aire.cp.kJkgK, aire.w), aire.P.MPa
# aire=GERG([0], [1.], P=0.1, T=300)
# print "%0.1f %0.4f %0.3f %0.3f %0.5f %0.4f %0.2f" % (aire.T, aire.rho, aire.h.kJkg, aire.s.kJkgK, aire.cv.kJkgK, aire.cp.kJkgK, aire.w), aire.P.MPa
# aire=GERG([1], [1.], P=0.1, T=300)
# print "%0.1f %0.4f %0.3f %0.3f %0.5f %0.4f %0.2f" % (aire.T, aire.rho, aire.h.kJkg, aire.s.kJkgK, aire.cv.kJkgK, aire.cp.kJkgK, aire.w), aire.P.MPa
# aire=GERG([15], [1.], P=0.1, T=500)
# print "%0.1f %0.4f %0.3f %0.3f %0.5f %0.4f %0.2f" % (aire.T, aire.rho, aire.h.kJkg, aire.s.kJkgK, aire.cv.kJkgK, aire.cp.kJkgK, aire.w), aire.P.MPa