[SAFT-gamma mie] Errors with LLE calculation

[YouHyin]

Hello, Gustavo!
Your code has been helpful for my research, Thank you. However, I have encountered two major errors during LLE calculations:

In sgtpy\gammamie_mixtures\ares.py:491, while using Numpy's solve function to compute Xass, I encounter a "Singular matrix" error.

import numpy as np
from sgtpy import component, mixture, saftgammamie
from sgtpy.equilibrium import lle, tpd_minimas

def calculate_w_lle(amine_GC):
    # Define components using group contributions
    amine = amine_GC
    water = component(GC={'H2O': 1})
    
    # Create mixture and setup the SAFT-γ-Mie equation of state
    mix = amine + water
    mix.saftgammamie()
    eos = saftgammamie(mix)
    
    # Define molecular weights for mass fraction calculations (g/mol)
    MW_amine = eos.Mw[0]  # Molecular weight of TEA
    MW_H2O = eos.Mw[1]  # Molecular weight of water
    
    # Operating conditions
    T = 350.0  # temperature in K
    P = 1.01325e5  # pressure in Pa
    
    # Set up a range for z[0] values
    z0_values = np.linspace(1e-4, 1-1e-4, 1000)
    
    # Loop through z0_values to find the point where LLE starts to form
    for z0 in z0_values:
        z = np.array([z0, 1-z0])
        x0s, tpd0s = tpd_minimas(2, z, T, P, eos, stateW='L', stateZ='L')
        x0 = x0s[0]
        w0 = x0s[1]
        
        sol = lle(x0, w0, z, T, P, eos, full_output=True)
        x1, x2 = sol.X
        diff = np.abs(x1[0] - x2[0])
        
        if diff > 1e-3:
            # Calculate W_TEA at the first point where LLE is detected
            W_lle = z0 * MW_amine / (z0 * MW_amine + (1 - z0) * MW_H2O)
            return W_lle
    
    # If no LLE is formed, return None 
    return 1
    
amine_1=component(GC={'NH2': 1, 'CH2': 2})
W_solvent_optimal = calculate_w_lle(amine_1)

The error messages are as follows:

File ~\anaconda3\lib\site-packages\sgtpy\gammamie_mixtures\ares.py:491, in d2ares_drho(self, x, rho, temp_aux, Xass0)
    488 d2Dijklab_drho = self.kAB_kl * Fklab
    489 d2Dijklab_drho[self.indexABij] *= d2Iijklab_drho[self.indexAB_id]
--> 491 Xass = Xass_solver(rho, xjvk, DIJ, Dijklab, diagasso, Xass)
    492 CIJ = CIJ_matrix(rho, xjvk, Xass, DIJ, Dijklab, diagasso)
    493 dXass = dXass_drho(rho, xjvk, Xass, DIJ, Dijklab, dDijklab_drho, CIJ)

File ~\anaconda3\lib\site-packages\sgtpy\gammamie_mixtures\association_aux.py:152, in Xass_solver(rho, xjvk, DIJ, Dijklab, diagasso, Xass0)
    150 HIJ[diagasso] -= (xjvk + KIJXass)/Xass
    151 for i in range(15):
--> 152     dXass = np.linalg.solve(HIJ, -dQ)
    153     Xnew = Xass + dXass
    155     is_nan = np.isnan(Xnew)

File ~\anaconda3\lib\site-packages\numpy\linalg\linalg.py:409, in solve(a, b)
    407 signature = 'DD->D' if isComplexType(t) else 'dd->d'
    408 extobj = get_linalg_error_extobj(_raise_linalgerror_singular)
--> 409 r = gufunc(a, b, signature=signature, extobj=extobj)
    411 return wrap(r.astype(result_t, copy=False))

File ~\anaconda3\lib\site-packages\numpy\linalg\linalg.py:112, in _raise_linalgerror_singular(err, flag)
    111 def _raise_linalgerror_singular(err, flag):
--> 112     raise LinAlgError("Singular matrix")

LinAlgError: Singular matrix

In gammamie_mixtures\density_solver.py:91, within the density_topliss function, the value of rho_ub is calculated to be smaller than rho_lb, which causes an error.

amine_2=component(GC={'CH3': 1, 'CH2': 4, 'CH': 1, 'C': 1, 'H2O': 1, 'NH': 1}) W_solvent_optimal = calculate_w_lle(amine_2)

The error messages are as follows:

ValueError                                Traceback (most recent call last)
Cell In[9], line 2
      1 amine_2=component(GC={'CH3': 1, 'CH2': 4, 'CH': 1, 'C': 1, 'H2O': 1, 'NH': 1})
----> 2 W_solvent_optimal = calculate_w_lle(amine_2)

Cell In[3], line 33, in calculate_w_lle(amine_GC)
     30 x0 = x0s[0]
     31 w0 = x0s[1]
---> 33 sol = lle(x0, w0, z, T, P, eos, full_output=True)
     34 x1, x2 = sol.X
     35 diff = np.abs(x1[0] - x2[0])

File ~\anaconda3\lib\site-packages\sgtpy\equilibrium\lle.py:79, in lle(x0, w0, Z, T, P, model, v0, Xass0, K_tol, nacc, full_output)
     77     X0 = np.asarray(xes)
     78     beta0 = np.hstack([beta, 0.])
---> 79     out = multiflash(X0, beta0, equilibrio, Z, T, P, model, v, Xass,
     80                      K_tol, nacc, True)
     81     Xm, beta, tetha, v = out.X, out.beta, out.tetha, out.v
     83 X, W = Xm

File ~\anaconda3\lib\site-packages\sgtpy\equilibrium\multiflash.py:190, in multiflash(X0, betatetha, equilibrium, z, T, P, model, v0, Xass0, K_tol, nacc, full_output)
    187     lnphi[i], v[i], Xass[i] = model.logfugef_aux(X[i], temp_aux, P,
    188                                                  state, v[i], Xass[i])
    189     if np.any(np.isnan(lnphi[i])) or np.isnan(v[i]):
--> 190         lnphi[i], v[i], Xass[i] = model.logfugef_aux(X[i], temp_aux, P, state)
    192 lnK = lnphi[0] - lnphi[1:]
    193 error = np.sum((lnK - lnK_old)**2)

File ~\anaconda3\lib\site-packages\sgtpy\gammamie_mixtures\saftgammamie_mixture.py:1299, in saftgammamie_mix.logfugef_aux(self, x, temp_aux, P, state, v0, Xass0)
   1296 else:
   1297     rho0 = 1./v0
-> 1299 rho, Xass = self.density_aux(x, temp_aux, P, state, rho0, Xass0)
   1300 v = 1./rho
   1301 rhomolecular = Na * rho

File ~\anaconda3\lib\site-packages\sgtpy\gammamie_mixtures\saftgammamie_mixture.py:1022, in saftgammamie_mix.density_aux(self, x, temp_aux, P, state, rho0, Xass0)
    994 """
    995 density_aux(x, temp_aux, P, state)
    996 Method that computes the density of the mixture at given composition,
   (...)
   1019     computed fraction of nonbonded sites
   1020 """
   1021 if rho0 is None:
-> 1022     rho, Xass = density_topliss(state, x, temp_aux, P, Xass0, self)
   1023 else:
   1024     rho, Xass = density_newton(rho0, x, temp_aux, P, Xass0, self)

File ~\anaconda3\lib\site-packages\sgtpy\gammamie_mixtures\density_solver.py:91, in density_topliss(state, x, temp_aux, P, Xass0, saft)
     88 bracket = [rho_lb, rho_ub]
     89 if flag == 1:
     90     # Found inflexion point
---> 91     sol_inf = minimize_scalar(dPsaft_fun, args=(x, temp_aux, saft),
     92                               bounds=bracket, method='Bounded',
     93                               options={'xatol': 1e-1})
     94     rho_inf = sol_inf.x
     95     dP_inf = sol_inf.fun

File ~\anaconda3\lib\site-packages\scipy\optimize\_minimize.py:945, in minimize_scalar(fun, bracket, bounds, args, method, tol, options)
    942     if bounds is None:
    943         raise ValueError('The `bounds` parameter is mandatory for '
    944                          'method `bounded`.')
--> 945     res = _minimize_scalar_bounded(fun, bounds, args, **options)
    946 elif meth == 'golden':
    947     res = _recover_from_bracket_error(_minimize_scalar_golden,
    948                                       fun, bracket, args, **options)

File ~\anaconda3\lib\site-packages\scipy\optimize\_optimize.py:2253, in _minimize_scalar_bounded(func, bounds, args, xatol, maxiter, disp, **unknown_options)
   2250 x1, x2 = bounds
   2252 if not (is_finite_scalar(x1) and is_finite_scalar(x2)):
-> 2253     raise ValueError("Optimization bounds must be finite scalars.")
   2255 if x1 > x2:
   2256     raise ValueError("The lower bound exceeds the upper bound.")

ValueError: Optimization bounds must be finite scalars.

Could you provide some advice on how to resolve these issues?
Thank as always for your help.
Best wish!