[SAFT-Gamma-Mie] Question about VLLE for binary mixture

[YouHyin]

Hello, I'm trying to reproduce the following paper's a binary mixture of water and triethylamine (TEA) VLLE results (Figure.3) using sgtpy.
Using the example code, I have created the following code.

Paper : Lee, Y. S., Galindo, A., Jackson, G., & Adjiman, C. S. (2023). Enabling the direct solution of challenging computer-aided molecular and process design problems: Chemical absorption of carbon dioxide. Computers & Chemical Engineering, 174, 108204.

import numpy as np
import matplotlib.pyplot as plt
from sgtpy import component, mixture, saftgammamie
from sgtpy.equilibrium import vlleb

TEA = component(GC={'CH3': 3, 'CH2': 3,'N': 1})
water = component(GC={'H2O':1})

mix = TEA + water

mix.saftgammamie()
eos = saftgammamie(mix)

# phase equilibria conditions
T = 365.  # K
P = 0.101e6  # Pa
z = np.array([0.15, 0.85])

from sgtpy.equilibrium import tpd_min
# initial guess for the composition of the trial phase
w0 = np.array([0.9, 0.1])
x0, tpx0 = tpd_min(w0, z, T, P, eos, stateW = 'L', stateZ = 'L')
# initial guess for the composition of the trial phase
w0, tpw0 = tpd_min(w0, z, T, P, eos, stateW = 'L', stateZ = 'L')
y0 = np.array([0.2, 0.8])
y0, tpv0 = tpd_min(w0, z, T, P, eos, stateW = 'V', stateZ = 'L')

from sgtpy.equilibrium import vlleb
# initial guesses for aqueous, organic and vapor phase composition obtained from tpd minimization
# calculation at fixed temperature
P0 = 1.01325e5  # Pa
vlleb(x0, w0, y0, P0, T, 'T', eos, full_output=True)

# initial guesses for aqueous, organic and vapor phase composition obtained from tpd minimization
# calculation at fixed pressure
T0 =  363.  # K
sol = vlleb(x0, w0, y0, T0, P, 'P', eos, full_output=True)

from sgtpy.equilibrium import bubbleTy, lle
from sgtpy.equilibrium import vlleb
# three phase equilibria computation
sol = vlleb(x0, w0, y0, T0, P, 'P', eos, full_output=True)
Xhaz,  Whaz, Yhaz, Thaz = sol.X, sol.W, sol.Y, sol.T

n = 100

# VLE zone 1
x1 = np.linspace(0, Xhaz[0], n)
XI = np.array([x1, 1-x1])
YI = np.zeros_like(XI)
TI = np.zeros(n)

vxI = np.zeros(n)
vyI = np.zeros(n)
i = 0
T0 = 373.
sol = bubbleTy(XI[:, i], T0, XI[:, i], P, eos, full_output = True)
YI[:, i], TI[i] = sol.Y, sol.T
vxI[i], vyI[i] = sol.v1, sol.v2
for i in range(1, n):
    sol = bubbleTy(YI[:, i-1], TI[i-1], XI[:, i], P, eos, full_output=True, v0=[vxI[i-1], vyI[i-1]])
    YI[:, i], TI[i] = sol.Y, sol.T
    vxI[i], vyI[i] = sol.v1, sol.v2
    
# VLE zone 2
w1 = np.linspace(Whaz[0], 1, n)
XII = np.array([w1, 1-w1])
YII = np.zeros_like(XII)
TII = np.zeros(n)
vxII = np.zeros(n)
vyII = np.zeros(n)

i = 0
sol = bubbleTy(Yhaz, Thaz, XII[:, i], P, eos, full_output = True)
YII[:, i], TII[i] = sol.Y, sol.T
vxII[i], vyII[i] = sol.v1, sol.v2

for i in range(1, n):
    sol = bubbleTy(YII[:, i-1], TII[i-1], XII[:, i], P, eos, full_output = True, v0=[vxII[i-1], vyII[i-1]])
    YII[:, i], TII[i] = sol.Y, sol.T
    vxII[i], vyII[i] = sol.v1, sol.v2

# LLE calculation
Tll =  np.linspace(Thaz,  290, n)
Xll = np.zeros([2, n])
Wll = np.zeros([2, n])

vxll = np.zeros(n)
vwll = np.zeros(n)

i = 0 
Z = (Xhaz+Whaz)/2
sol = lle(Xhaz, Whaz, Z, Tll[i], P, eos, full_output=True)
Xll[:, i], Wll[:, i] = sol.X
vxll[i], vwll[i] = sol.v

for i in range(1, n):
    Z = (Xll[:, i-1] + Wll[:, i-1])/2
    sol = lle(Xll[:, i-1], Wll[:, i-1], Z, Tll[i], P, eos, full_output=True, v0=[vxll[i-1], vwll[i-1]])
    Xll[:, i], Wll[:, i] = sol.X
    vxll[i], vwll[i] = sol.v

fig = plt.figure(figsize=(5,5))
ax = fig.add_subplot(111)
ax.plot(XI[0], TI, color = 'b')
ax.plot(YI[0], TI, color = 'b')

ax.plot(XII[0], TII, color = 'b')
ax.plot(YII[0], TII, color = 'b')

ax.plot(Xll[0], Tll, color = 'b')
ax.plot(Wll[0], Tll, color = 'b')

ax.plot([Xhaz[0], Yhaz[0], Whaz[0]], [Thaz, Thaz, Thaz], 'o-', color = 'b')


ax.tick_params(direction='in')
ax.set_xlabel('$x_1, y_1$')
ax.set_ylabel('T / K')
ax.set_ylim([280, 400])
ax.set_xlim([0, 1])

Result :

The figure I want to reproduce :

As a result, there seems to be a problem with the LLE prediction.
What would be the best way to set z and the values of w0, z0, and y0 in this code?
Thanks as always for your help!
I look forward to your response.

[gustavochm]

Hi YouHyin,

I think there is a problem in your initial guesses for the VLLE. If you get the VLLE correctly you can easily construct the whole diagram. See below.

Edit: Initializing the VLLE is not trivial. Ideally you want to have z what is between the VLLE line. Then you can minimize the tpd to obtain possible initial guesses.

import numpy as np
import matplotlib.pyplot as plt
from sgtpy import component, mixture, saftgammamie
from sgtpy.equilibrium import vlleb, bubbleTy, lle
from sgtpy.equilibrium import tpd_minimas


TEA = component(GC={'CH3': 3, 'CH2': 3,'N': 1})
water = component(GC={'H2O':1})

mix = TEA + water

mix.saftgammamie()
eos = saftgammamie(mix)

P = 0.101e6 # Pa

# obtaining three phase equilibria
T0 = 350. # K

z = np.array([0.6, 0.4])
x0s, tpd0s = tpd_minimas(2, z, T0, P, eos, stateW='L', stateZ='L')
y0s, tpd0 = tpd_minimas(1, z, T0, P, eos, stateW='V', stateZ='L')

x0 = x0s[0]
w0 = x0s[1]
y0 = y0s[0]

sol_vlle = vlleb(x0, w0, y0, T0, P, 'P', eos, full_output=True)
Xhaz,  Whaz, Yhaz, Thaz = sol_vlle.X, sol_vlle.W, sol_vlle.Y, sol_vlle.T

#######

n = 100

# VLE zone 1
x1 = np.linspace(0, Xhaz[0], n)
XI = np.array([x1, 1-x1])
YI = np.zeros_like(XI)
TI = np.zeros(n)

vxI = np.zeros(n)
vyI = np.zeros(n)
i = 0
T0 = 373.
sol = bubbleTy(XI[:, i], T0, XI[:, i], P, eos, full_output = True)
YI[:, i], TI[i] = sol.Y, sol.T
vxI[i], vyI[i] = sol.v1, sol.v2
for i in range(1, n):
    sol = bubbleTy(YI[:, i-1], TI[i-1], XI[:, i], P, eos, full_output=True, v0=[vxI[i-1], vyI[i-1]])
    YI[:, i], TI[i] = sol.Y, sol.T
    vxI[i], vyI[i] = sol.v1, sol.v2

# VLE zone 2
w1 = np.linspace(Whaz[0], 1, n)
XII = np.array([w1, 1-w1])
YII = np.zeros_like(XII)
TII = np.zeros(n)
vxII = np.zeros(n)
vyII = np.zeros(n)

i = 0
sol = bubbleTy(Yhaz, Thaz, XII[:, i], P, eos, full_output = True)
YII[:, i], TII[i] = sol.Y, sol.T
vxII[i], vyII[i] = sol.v1, sol.v2

for i in range(1, n):
    sol = bubbleTy(YII[:, i-1], TII[i-1], XII[:, i], P, eos, full_output = True, v0=[vxII[i-1], vyII[i-1]])
    YII[:, i], TII[i] = sol.Y, sol.T
    vxII[i], vyII[i] = sol.v1, sol.v2

# LLE calculation
Tll =  np.linspace(Thaz,  310, n)
Xll = np.zeros([2, n])
Wll = np.zeros([2, n])

vxll = np.zeros(n)
vwll = np.zeros(n)

i = 0 
Z = (Xhaz+Whaz)/2
sol = lle(Xhaz, Whaz, Z, Tll[i], P, eos, full_output=True)
Xll[:, i], Wll[:, i] = sol.X
vxll[i], vwll[i] = sol.v

for i in range(1, n):
    Z = (Xll[:, i-1] + Wll[:, i-1])/2
    sol = lle(Xll[:, i-1], Wll[:, i-1], Z, Tll[i], P, eos, full_output=True, v0=[vxll[i-1], vwll[i-1]])
    Xll[:, i], Wll[:, i] = sol.X
    vxll[i], vwll[i] = sol.v

I hope that helps,

Gustavo

[YouHyin]

Thank you so much. Thanks to your advice and code, it helped me a lot.