Parameter Identification in Liquid-Liquid Equilibrium Modeling of Food-Related Thermodynamic Systems Using Flower Pollination Algorithms

Table 2: Results of LLE parameter identification in selected ternary and quaternary systems using FPA and MFPA and closure equations with different parameter elimination.

		RMSD for NRTL model		RMSD for UNIQUAC model
Thermodynamic system	Parameter Elimination	FPA-C	MFPA-C	FPA-C	MFPA-C
water + levulinic acid + dimethyl succinate	A₁₂	0.0087	0.0021	0.0065	0.0018
	A₂₁	0.0098	0.0013	0.0072	0.0028
	A₁₃	0.0086	0.0035	0.0068	0.0016
	A₃₁	0.0094	0.0018	0.0078	0.0011
	A₂₃	0.0092	0.0017	0.0069	0.0026
	A₃₂	0.0084	0.0023	0.0085	0.0036
water + levulinicacid + glutarate	A₁₂	0.0092	0.0018	0.0070	0.0025
	A₂₁	0.0082	0.0021	0.0052	0.0013
	A₁₃	0.0078	0.0040	0.0061	0.0013
	A₃₁	0.0075	0.0032	0.0054	0.0018
	A₂₃	0.0073	0.0015	0.0047	0.0026
	A₃₂	0.0083	0.0020	0.0045	0.0035
palm oil + palmitic acid + (ethanol 93.9% + water 6.10%)	3 parameters A_ij	0.0092^a	0.0078^b	0.0088^c	0.0032^d
limonene + carvone + (ethanol 76.36% + water 23.64%)	3 parameters A_ij	0.0072^e	0.0037^f	0.0081^g	0.0041^h

^aThe best eliminated parameters are: A₁₂, A₃₁, A₃₂;

^bThe best eliminated parameters are: A₁₂, A₁₄, A₂₃;

^cThe best eliminated parameters are: A₁₃, A₃₄, A₄₁;

^dThe best eliminated parameters are: A₂₃, A₂₄, A₃₄;

^eThe best eliminated parameters are: A₂₄, A₃₁, A₃₄;

^fThe best eliminated parameters are: A₂₃, A₃₄, A₄₁;

^gThe best eliminated parameters are: A₂₁, A₃₂, A₄₁;

^hThe best eliminated parameters are: A₁₃, A₁₄, A₄₃.