Seveneq1

Name:	Seveneq1 - Chemical Equilibrium
Source:	Carnahan, B., Luther, H. A. and Wilkes, J. O., Applied Numerical Methods
	Wiley, New York, 1969
Reference/s	Shacham, M., pp. 891-923 in A. W. Westerberg and H. H. Chien (Eds),
	Proc. of FOCAPD 2, CACHE Publications, Ann Arbor, Michigan, 1984.
	Bullard, L. G. and Biegler, L. T., Computers Chem. Engng. 15(4), 239 (1991).
Model:	7 implicit equations, indep. variables x1 to x7
	Lower difficulty level
	Constraints: xi are nonnegative for I=1,2,…7
	Discontinuities: Undefined for x7=0
	Initial estimates: 1. (0.5,0,0,0.5,0,0.5,2); 2.(0.2, 0.2, 0.2, 0.2, 0.2, 0.5, 0.2);
	3. (0.22,0.075, 0.001, 0.58, 0.125, 0.435, 2.35)
Solved by	Shacham, M., POLYMATH 5.1, build 19, April 6, 2001
Model Eqs.	Chemical Equilibrium |POLVER05_1
EXCEL FILE	f(x1) = 0.5*x1+x2+0.5*x3-x6/x7 #
TEXT FILE	f(x2) = x3+x4+2*x5-2/x7 #
POLYMATH FILE	f(x3) = x1+x2+x5-1/x7 #
	f(x4) = -28837*x1-139009*x2-78213*x3+18927*x4+8427*x5 +13492/x7-10690*x6/x7 #
	f(x5) = x1+x2+x3+x4+x5-1 #
	f(x6) = 400*x1*x4^3-1.7837e5*x3*x5 #
	f(x7) = x1*x3-2.6058*x2*x4 #
	x1(0)=0.5
	x2(0)=0
	x3(0)=0
	x4(0)=.5
	x5(0)=0
	x6(0)=0.5
	x7(0)=2
Variable/function values	Variable	Value	f(x)
	x1	0.5	0
	x2	0	-0.5
	x3	0	0
	x4	0.50	-881.5
	x5	0	0
	x6	0.50	25
	x7	2.00	0
Solution	Variable	Value	f(x)
	x1	0.3228708394765	0
	x2	0.0092235435392	0
	x3	0.0460170909606	0
	x4	0.6181716750708	2.27E-12
	x5	0.0037168509528	-1.11E-16
	x6	0.5767153959355	-3.55E-15
	x7	2.9778634507910	-3.47E-18
Infeasible solution	Variable	Value	f(x)
	x1	0.4569305530947	2.78E-17
	x2	-0.0004071984094	2.78E-17
	x3	-0.0021251991567	-4.16E-17
	x4	0.9151719085274	1.36E-12
	x5	-0.3695700640561	0
	x6	2.6105450054500	-2.84E-14
	x7	11.5004273301600	1.08E-19
Additional information	Some methods converge to the infeasible solution from initial guess No.3