Threeq1

Name:	Threeq1 - Dew point of a nonideal binary mixture (isobutanol-water)
Source:	Henley, E. J. and Rosen, E. M., Material and Energy Balance
	Computations, Wiley: New York, 1969
Reference/s	Shacham, M., N. Brauner and M. Pozin, Computers chem. Engng., 22,321-323(1998)
Model:	3 implicit equations, indep. variables t, x1 and x2
	Average difficulty level
	Constraints: 0<=x1<=1, 0<=x2<=1
	Discontinuities: Undefined for t=-191.15 or t=-235
	Initial estimates: 1. t=100, x1=0.2, x2=0.8, 2. t=70, x1=0.5, x2=0.5;
	3. t=80, x1=0.2, x2=0.8 4. t=80, x1=0.5, x2=0.5
Solved by	Shacham, M., POLYMATH 5.1, build 19, April 3, 2001
Model Eqs.	Dew point of a nonideal binary mixture (isobutanol-water) |POLVER05_1
EXCEL FILE	f(t)=x1+x2-1 #
TEXT FILE	f(x1)=x1-y1/k1 #
POLYMATH FILE	f(x2)=x2-y2/k2 #
	y2=0.8 #
	y1=0.2 #
	p1=10^(7.62231-1417.9/(191.15+t)) #
	p2=10^(8.10765-1750.29/(235+t)) #
	B=0.7 #
	A=1.7 #
	gamma2=10^(B*x1*x1/((x1+B*x2/A)^2)) #
	gamma1=10^(A*x2*x2/((A*x1/B+x2)^2)) #
	k2=gamma2*p2/760 #
	k1=gamma1*p1/760 #
	t(0)=100
	x1(0)=0.2
	x2(0)=0.8
Variable/function values	Variable	Value	f(x)
	t	100	0.0000E+00
	x1	0.2	1.4093E-01
	x2	0.8	1.6744E-01
	y2	0.8
	y1	0.2
	p1	565.34
	p2	763.67
	B	0.7
	A	1.7
	gamma2	1.26
	gamma1	4.55
	k2	1.26
	k1	3.39
Solution	Variable	Value	f(x)
	t	93.96706523770	0.0000E+00
	x1	0.0078754574659	2.6021E-17
	x2	0.9921245425339	-6.66E-16
	y2	0.8
	y1	0.2
	p1	445.92824865560
	p2	612.47305384950
	B	0.7
	A	1.7
	gamma2	1.0005767327950
	gamma1	43.28155074142
	k2	0.8063503778230
	k1	25.39535015950
Additional Information	Some of the methods do not converge from initial guesses 3 and 4