Twoeq10

Name:	Twoeq10 - Correlation of liquid-liquid equilibrium data
Source:	Shacham, M., pp. 891-923 in A. W. Westerberg and H. H. Chien (Eds),
	Proc. of FOCAPD 2, CACHE Publications, Ann Arbor, Michigan, 1984.
Reference/s	Shacham, M., Computers Chem. Engng. 9(2), 103 (1985).
Model:	2 implicit equations, indep. variables t12 and t21
	Average difficulty level
	Constraints:none
	Discontinuities: none in the region of interest
	Initial estimates:1. t12=t21=0.1; 2. t12=t21=1; 3. t12=t21=0.10; 4. t12=t21=15;
	4. Ca=0.2, T=560; 5. Ca=0.5, T=560
Solved by	Shacham, M., POLYMATH 5.1, build 19, April 3, 2001
Model Eqs.	Correlation of liquid-liquid equilibrium data |POLVER05_1
EXCEL FILE	f(t12) = 1/(x1*x2)-2*t21*c2/((x1+x2*c1)^3)-2*t12*c4/((x2+x1*c3)^3) #
TEXT FILE	f(t21) = (x1-x2)/((x1*x2)^2)+6*t21*c2*(1-c1)/((x1+x2*c1)^4) +6*t12*c4*(c3-1)/((x2+x1*c3)^4) #
POLYMATH FILE	c1=exp(-alpha*t21) #
	c2=exp(-2*alpha*t21) #
	c3=exp(-alpha*t12) #
	c4=exp(-2*alpha*t12) #
	x2=1-x1 #
	alpha=0.4 #
	x1=0.5 #
	t12(0)=1
	t21(0)=10
Variable/function values	Variable	Value	f(x)
	t12	0.1	3.608155692
	t21	0.1	0
	alpha	0.40
	c1	0.96
	c2	0.92
	c3	0.9608
	x1	0.5000
	c4	0.92
	x2	0.50
Solution 1	Variable	Value	f(x)
	t12	1.6043843214350	2.2204E-16
	t21	1.6043843214350	0.0000E+00
	alpha	0.4
	c1	0.5263685066391
	c2	0.2770638047815
	c3	0.5263685066391
	x1	0.5
	c4	2.770638048E-01
	x2	0.5
Solution 2	Variable	Value	f(x)
	t12	2.9353711137400	8.8818E-16
	t21	2.9353711137400	0.0000E+00
	alpha	0.4
	c1	0.3090820678822
	c2	0.0955317246863
	c3	0.3090820678822
	x1	0.5
	c4	9.553172469E-02
	x2	0.5
Additional information	Convergence to the 1st solution from the 1st and 2nd initial guesses
	convergence to the 2nd solution from the 3rd initial guess. Most
	methods won't converge from the 4th initial guess.

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