Twoeq5a

Name:	Twoeq5a - Van Laar eqs. coeff. from azeotropic data (ethanol - n heptane) - 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 A and B
	Average difficulty level
	Constraints: A>0, B>0
	Discontinuities: Undefined for A=0 or B=0, may be undefined for some
	negative values of A or B.
	Initial estimates: 1. A=0.5, B=0.5; 2. A=1, B=1; 3. A=5, B=5; 4. A=8, B=2
Solved by	Shacham, M., POLYMATH 5.1, build 19, April 2, 2001
Model Eqs.	Van Laar eqs. coeff. from azeotropic data (ethanol - n heptane) - 1st form. |POLVER05_3
EXCEL FILE	f(A) = log(gamma1)-A*x2^2/(A*x1/B+x2)^2 #
TEXT FILE	f(B) = log(gamma2)-B*x1^2/(x1+B*x2/A)^2 #
POLYMATH FILE	t=70.9 #
	pw1=49 #
	x1=(pw1/46.07)/(pw1/46.07+(100-pw1)/100.2) #
	P2=10^(6.9024-1268.115/(216.9+t)) #
	P1=10^(8.04494-1554.3/(222.65+t)) #
	gamma1=760/P1 #
	x2=1-x1 #
	gamma2=760/P2 #
	g1calc=10^(A*x2^2/(A*x1/B+x2)^2) #
	g2calc=10^(B*x1^2/(x1+B*x2/A)^2) #
	A(0)=1.0
	B(0)=1.0
Variable/function values	Variable	Value	f(x)
	A	1	2.5957E-02
	B	1	-7.2785E-02
	t	70.9
	pw1	49
	x1	0.6763
	P2	313.4462
	P1	562.4721
	gamma1	1.3512
	x2	0.3237
	gamma2	2.4247
	g1calc	1.2728
	g2calc	2.8671
Solution	Variable	Value	f(x)
	A	0.7580768059470	-2.4980E-16
	B	1.1249034445330	-1.6098E-15
	t	70.9
	pw1	49
	x1	0.6763396823691
	P2	313.4462149790
	P1	562.4720681541
	gamma1	1.3511782060470
	x2	0.3236603176309
	gamma2	2.4246584060710
	g1calc	1.3511781866300
	g2calc	2.4246581829110
Additional information	Most methods won't converge from the 4th initial guess