Twoeq5b

Name:	Twoeq5b - Van Laar eqs. coeff. from azeotropic data (ethanol - n heptane) - 2nd 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) - 2nd form. |POLVER05_3
EXCEL FILE	f(A)=log(gamma1)*(A*x1/B+x2)^2-A*x2^2 #
TEXT FILE	f(B)=log(gamma2)*(x1+B*x2/A)^2-B*x1^2 #
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	0.7580768919420	1.3878E-17
	B	1.1249035089540	-1.1102E-16
	t	70.9
	pw1	49
	x1	0.6763396823691
	P2	313.4462149790
	P1	562.4720681541
	gamma1	1.3511782060470
	x2	0.3236603176309
	gamma2	2.4246584060710
	g1calc	1.3511782060470
	g2calc	2.4246584060710
False solution	Variable	Value	f(x)
	A	-0.0000004247588	4.8039E-07
	B	0.0000008929642	5.3593E-06
	t	70.9
	pw1	49
	x1	0.6763396823691
	P2	313.4462149790
	P1	562.4720681541
	gamma1	1.3511782060471
	x2	0.3236603176309
	gamma2	2.4246584060714
	g1calc	0.9732505120701
	g2calc	1.0579343014792
Additional information	Some methods converge to the false solution from the 4th
	initial estimate