Nineq1

Name:	Nineq1 - Three phase flash - ethanol, benzene and water mixture
Source:	Henley, E. J. and Rosen, E. M., Material and Energy Balance
	Computations, Wiley: New York, 1969
Reference/s
Model:	9 implicit equations, indep. variables x11, x12, x13, x21, x22, x23, V, L1 and L2
	Higher difficulty level
	Constraints: All the variables are bounded between zero and one
	Discontinuities:none
	Initial estimates: 1.(0.3, 0, 0.7, 0, 1, 0, 0.4, 0.55, 0.06) 2.(0.3, 0, 0.7, 0, 1, 0, 0.3, 0.6, 0.1);
	3.(0.3, 0.2, 0.5, 0.1, 0.7, 0.1, 0.3, 0.6, 0.1) 4.(0.3, 0.1, 0.6, 0.1, 0.7, 0.1, 0.3, 0.6, 0.1);
Solved by	Shacham, M., POLYMATH 5.1, build 19, April 4, 2001
Model Eqs.	Three phase flash - ethanol, benzene and water mixture |POLVER05_3
EXCEL FILE	f(x11)=x11*(L1+L2*k11/k21+V*k11)-0.23 #
TEXT FILE	f(x12)=x12*(L1+L2*k12/k22+V*k12)-0.27 #
POLYMATH FILE	f(x13)=x13*(L1+L2*k13/k23+V*k13)-0.5 #
	f(x21)=x21-x11*k11/k21 #
	f(x22)=x22-x12*k12/k22 #
	f(x23)=x23-x13*k13/k23 #
	f(V)=x11+x12+x13-1 #
	f(L1)=L1+L2+V-1 #
	f(L2)=x21+x22+x23-1 #
	T=63.7 #
	A12=1.6-217/(T+273) #
	A21=3.125-855/(T+273) #
	A13=0.63+23.3/(T+273) #
	A31=0.33+23.3/(273+T) #
	A23=1.54128+554/(T+273) #
	A32=-2.2534+1449/(T+273) #
	g11=10^(x12^2*(A12+2*x11*(A21-A12))+x13^2*(A13+2*x11*(A31-A13)) +x12*x13*(0.5*(A21+A12+A31+A13-A23-A32)+x11*(A21-A12+A31-A13) +(x12-x13)*(A23-A32)-(1-2*x11)*0.25)) #
	g21=10^(x22^2*(A12+2*x21*(A21-A12))+x23^2*(A13+2*x21*(A31-A13)) +x22*x23*(0.5*(A21+A12+A31+A13-A23-A32)+x21*(A21-A12+A31-A13) +(x22-x23)*(A23-A32)-(1-2*x21)*0.25)) #
	g22=10^(x23^2*(A23+2*x22*(A31-A23))+x21^2*(A21+2*x22*(A12-A21)) +x23*x21*(0.5*(A32+A23+A12+A21-A31-A13)+x22*(A32-A23+A12-A21) +(x23-x21)*(A31-A13)-(1-2*x22)*0.25)) #
	g12=10^(x13^2*(A23+2*x12*(A32-A23))+x11^2*(A21+2*x12*(A12-A21)) +x13*x11*(0.5*(A32+A23+A12+A21-A31-A13)+x12*(A32-A23+A12-A21) +(x13-x11)*(A31-A13)-(1-2*x12)*0.25)) #
	g13=10^(x11^2*(A31+2*x13*(A13-A31))+x12^2*(A32+2*x13*(A23-A32)) +x11*x12*(0.5*(A13+A31+A23+A32-A12-A21)+x13*(A13-A31+A23-A32) +(x11-x13)*(A12-A21)-(1-2*x13)*0.25)) #
	g23=10^(x21^2*(A31+2*x23*(A13-A31))+x22^2*(A32+2*x23*(A23-A32)) +x21*x22*(0.5*(A13+A31+A23+A32-A12-A21)+x23*(A13-A31+A23-A32) +(x21-x23)*(A12-A21)-(1-2*x23)*0.25)) #
	k12=10^(6.90565-1211.033/(T+220.79))*g12/760 #
	k22=10^(6.90565-1211.033/(T+220.79))*g22/760 #
	k11=10^(8.21337-1652.05/(T+231.48))*g11/760 #
	k21=10^(8.21337-1652.05/(T+231.48))*g21/760 #
	k13=10^(8.10765-1750.286/(T+235))*g13/760 #
	k23=10^(8.10765-1750.286/(T+235))*g23/760 #
	x11(0)=0.3
	x12(0)=0
	x13(0)=0.7
	x21(0)=0
	x22(0)=1
	x23(0)=0
	V(0)=0.4
	L1(0)=0.55
	L2(0)=0.06
Variable/function values	Variable	Value	f(x)
	x11	0.3	0.05590768
	x12	0	-0.27
	x13	0.7	-0.0372807
	x21	0	-0.0597063
	x22	1	1
	x23	0	-0.0073908
	V	0.400	0
	L1	0.550	0.01
	L2	0.06	0
	T	63.7
	A12	0.956
	A21	0.586
	A13	0.699
	A31	0.399
	A23	3.187
	A32	2.050
	g11	1.796
	g21	9.026
	g22	1
	g12	135.777
	g13	1.185
	g23	112.237
	k12	79.580
	k22	0.586
	k11	0.978
	k21	4.913
	k13	0.276
	k23	26.139
Solution 1	Variable	Value	f(x)
	x11	0.2253818399616	0
	x12	0.0042438488738	-5.55E-17
	x13	0.7703743111646	0
	x21	0.0960474647746	-2.78E-17
	x22	0.8916699617303	3.33E-16
	x23	0.0122825734951	-8.67E-18
	V	0.3838837845197	0
	L1	0.5483053023942	0
	L2	0.0678109130861	0
	T	63.7
	A12	0.9555093555094
	A21	0.5856474606475
	A13	0.6992010692011
	A31	0.3992010692011
	A23	3.1866616453817
	A32	2.0501343035343
	g11	2.1216976700662
	g21	4.9787063702737
	g22	1.0328151239404
	g12	217.0035383954700
	g13	1.1145870895998
	g23	69.9079278234338
	k12	127.1882800898110
	k22	0.6053448724202
	k11	1.1547431230150
	k21	2.7096824508485
	k13	0.2595803470200
	k23	16.2811182124574
Solution 2	Variable	Value	f(x)
	x11	0.2820991165743	-2.75E-11
	x12	0.0065405050490	-4.31E-11
	x13	0.7113603783767	-5.25E-11
	x21	1.09899657E-01	5.55E-17
	x22	0.8773341585418	5.44E-15
	x23	0.0127661842687	2.08E-17
	V	0.0000000277876	0
	L1	0.6974489843295	-4.88E-10
	L2	0.3025509883391	0
	T	63.7
	A12	0.9555093555094
	A21	0.5856474606475
	A13	0.6992010692011
	A31	0.3992010692011
	A23	3.1866616453817
	A32	2.0501343035343
	g11	1.8073616619912
	g21	4.6392786039280
	g22	1.0422697445961
	g12	139.8085992593810
	g13	1.1805963462842
	g23	65.7854724580141
	k12	81.9434347156137
	k22	0.6108863347806
	k11	0.9836643926371
	k21	2.5249474226313
	k13	0.2749534891607
	k23	15.3210241970905
Infeasible solution	Variable	Value	f(x)
	x11	0.5826079982548	4.83E-15
	x12	0.3426886603956	5.55E-17
	x13	0.0747033413497	-2.08E-14
	x21	2.02892710E-01	-1.94E-16
	x22	0.7836619231816	-3.33E-15
	x23	0.0134453670827	4.48E-16
	V	4.5989003044918	-2.22E-16
	L1	-1.5784710655727	-4.44E-16
	L2	-2.0204292389187	-1.11E-16
	T	63.7
	A12	0.9555093555094
	A21	0.5856474606475
	A13	0.6992010692011
	A31	0.3992010692011
	A23	3.1866616453817
	A32	2.0501343035343
	g11	1.0694730305672
	g21	3.0710001154022
	g22	1.1334643164870
	g12	2.5920111083090
	g13	8.0623827076193
	g23	44.7951285593662
	k12	1.5192076464611
	k22	0.6643365265981
	k11	0.5820653171848
	k21	1.6714050800311
	k13	1.8776783981976
	k23	10.4325046689882
Additional information	Convergence to the first solution from the first initial guess
	Convergence to the second solution from the second initial guess
	Most methods won't converge from the 3rd initial guess
	Convergence to the infeasible solution from the 4th initial guess