Fiveq1

Name:	Fiveq1 - Steady state operation of an exothermic CSTR
Source:	Smith, C. A. and Corripio, A. B., Principles and Practice of Authomatic
	Process Control, John Wiley, 1985
Reference/s
Model:	5 implicit equations, indep. variables ca, t1, tc, b, y
	Average difficulty level
	Constraints: ca>=0, 0<=b<=1, 0<=y<=1
	Discontinuities: Undefined for t1=-273.15
	Initial estimates: 1. (1, 100,50,0.4, 0.25)); 2.(0.5, 50, 25, 0.1, 0.1);
	3.(0.2, 20, 10, 0.01, 0.01); 4. (2, 200, 150, 0.8, 0.8)
Solved by	Shacham, M., POLYMATH 5.1, build 19, April 19, 2001
Model Eqs.	Steady state operation of an exothermic CSTR |POLVER05_3
EXCEL FILE	f(ca) = F*(2.88-ca)/V-k*ca*ca #
TEXT FILE	f(t1) = F*(66-t1)/V-dhr*k*ca*ca/(rho*cp)-u*a*(t1-tc)/(V*rho*cp) #
POLYMATH FILE	f(tc) = u*a*(t1-tc)/(1.82*1000*4184)-fc*(tc-27)/1.82 #
	f(b) = ((t1-80)/20-b)/20 #
	f(y) = (m-y)/taui #
	k=0.0744*exp(-1.182e7/(8314.39*(t1+273.16))) #
	fc = 0.02*50^(-m) #
	m = y+kc*(10/20-b) #
	F=0.0075 #
	V=7.08 #
	dhr=-9.86e7 #
	rho=19.2 #
	cp=1.815e5 #
	u=3550 #
	a=5.4 #
	taui=600 #
	kc=1 #
	ca(0)=1
	t1(0)=100
	tc(0)=50
	b(0)=0.4
	y(0)=0.25
Variable/function values	Variable	Value	f(x)
	ca	1	0.00034
	t1	100	-0.02823
	tc	50	0.06160
	b	0.4	0.03
	y	0.25	0.00017
	k	0.00165
	fc	0.00509
	m	0.35
	kc	1
	F	0.0075
	V	7.08
	dhr	-98600000
	rho	19.2
	cp	181500
	u	3550
	a	5.4
	taui	600
Solution	Variable	Value	f(x)
	ca	1.1206138931808	2.17E-19
	t1	90	-6.94E-18
	tc	54.8512245178517	1.39E-17
	b	0.5	0
	y	0.3172119884117	0
	k	0.0014841478215
	fc	0.0057822430439
	m	0.3172119884117
Additional information	Some algorithms won't converge from initial guesses 2 and 3