Twoeq4a

Name:	Twoeq4a - Wilson coeff. from azeotropic data (ethyl alcohol - n hexane) - 1st form
Source:	Cutlip, M. B. and Shacham, M, Problem Solving in Chemical
	Engineering with Numerical Methods (2nd Ed.), Prentice Hall Inc.,
Reference/s
Model:	2 implicit equations, indep. variables G12 and G21
	Average difficulty level
	Constraints: G12>=0, G21>=0
	Discontinuities: Undefined for G12<0 or G21<0
	Initial estimates: 1. G12=0.1, G21=0.1; 2.G12=0.5, G21=0.5; 3. G12=0.8, G21=0.8
Solved by	Shacham, M., POLYMATH 5.1, build 19, April 2, 2001
Model Eqs.	Wilson coeff. from azeotropic data (ethyl alcohol - n hexane) - 1st form |POLVER05_1
EXCEL FILE	f(G21) = ln(gamma2)+ln(t2)+x1*(G12*t2-G21*t1)/(t1*t2) #
TEXT FILE	f(G12) = ln(gamma1)+ln(t1)-x2*(G12*t2-G21*t1)/(t1*t2) #
POLYMATH FILE	t=58.7 #
	pw1=21 #
	x1=(pw1/46.07)/(pw1/46.07+(100-pw1)/86.18) #
	P2 = 10^(6.87776-1171.53/(224.366+t)) #
	P1 = 10^(8.04494-1554.3/(222.65+t)) #
	gamma2=760/P2 #
	gamma1=760/P1 #
	x2=1-x1 #
	t1=x1+x2*G12 #
	t2=x2+x1*G21 #
	g2calc=exp(-ln(t2)-x1*(G12*t2-G21*t1)/(t1*t2)) #
	g1calc=exp(-ln(t1)+x2*(G12*t2-G21*t1) /(t1*t2)) #
	G21(0)=0.5
	G12(0)=0.5
Variable/function values	Variable	Value	f(x)
	G21	0.5	1.9504E-01
	G12	0.5	3.2233E-01
	t	58.7
	pw1	21
	x1	0.3321
	P2	548.3315
	P1	331.5158
	gamma2	1.3860
	gamma1	2.2925
	x2	0.6679
	t1	0.6661
	t2	0.8339
	g2calc	1.1404
	g1calc	1.6608
Solution	Variable	Value	f(x)
	G21	0.3017535930592	-1.8874E-15
	G12	0.0785888476379	1.1935E-15
	t	58.7
	pw1	21
	x1	0.3321117719491
	P2	548.3315489669
	P1	331.5158092912
	gamma2	1.3860227474270
	gamma1	2.2925000217180
	x2	0.6678882280509
	t1	0.3846003381426
	t2	0.7681041485338
	g2calc	1.3860227916690
	g1calc	2.2924999769100
Additional Information	If started farther from the solution (see 3rd initial estimate)
	most methods yield negative G12 or G21 values leading to an execution error.
	A constrained method which keeps G12 and G21 positive throughout the
	iterations should be used.