Error in Square System: Pivot too small

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Janet

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Mar 25, 2016, 3:02:30 PM3/25/16

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Hello, I need help on solving this error I had when I'm doing my project. I've previously made 4 separate gams files for each unit (reactor, flash vessel, distillation 1, distillation 2) I needed for the project and they run successfully on their own files.

Now I need to combine the codes into one gams file and I have problem combining the reactor and flash vessel as the error "Pivot too small" keeps coming up. I have no problem combining both distillation files and I need to combine my reactor with my flash before combining with the distillation columns.

I have no problem running the file until eq17, but when I input eq18 the error came and I'm confused as to why it happened and how to fix it as they run perfectly on their own separate files

this is the .lst file

1 SETS i components /A,B,C,D,E/

2 j reactions /1,2/

3 m /AA, AB, AC/

4 ;

6 POSITIVE VARIABLES

7 *reactor

8 F(i) mole flowrate of component i at REACTOR EXIT [mol s-1]

9 F0A feed mole flowrate of component A propylene INTO REACTOR

[mol s-1]

10 F0B feed mole flowrate of component B benzene INTO REACTOR [m

ol s-1]

11 VR reactor volume [L]

12 k(j) reaction rate constant [L mol-1 s-1]

13 FRout_total total flowrate at REACTOR EXIT [mol s-1] same as FLASH FE

14 zflash(i) mole composition at REACTOR OUTLET and INTO FLASH

16 *relative volatility

17 RVflash(i) relative volatility of component i wrt component D

18 *flash

19 OSFflash(i) overhead split fraction

20 TotalVflowrate total vapour flowrate

21 TotalLflowrate total liquid vapour flowrate

22 Vflowrate(i) vapour flowrate

23 yflash(i) vapour fraction

24 Lflowrate(i) liquid flowrate

25 xflash(i) liquid fraction

26 ;

28 VARIABLE

29 EP_L3 economic potential level 3 [mil£ per year]

30 TACflash TAC of flash vessel [mil£ per year]

31 ;

33 TABLE Antoine(i,m) Antoine coefficients

34 AA AB AC

35 A 6.81960 785.000 247.000

36 B 6.90565 1211.033 220.790

37 C 6.93666 1460.793 207.777

38 D 7.03004 1703.400 200.033

39 E 6.80398 803.810 246.990

40 ;

42 PARAMETERS

43 *reactor

44 Ea(j) activation energy [J mol-1]

45 /1 55500

46 2 55400/

47 A(j) pre-exponential factor [L mol-1 s-1]

48 /1 3500

49 2 290/

50 Treactor reactor temperature [K] /713.15/

51 R gas constant [J mol-1 K-1] /8.314/

52 beta(j) model parameter [mol2 L-2]

53 /1 2.78

54 2 1.67/

55 FFB fresh feed benzene at the very start of the process [mol s-1] /27

.78/

56 xA conversion of A /0.6/

58 *flash vessel

59 Tflash flash temperature [K] /373.15/

60 Pvap_flash(i) vapour pressure at flash vessel [mmHg]

61 Nflash number of stages in flash vessel /1/

63 *D1

64 TD1 distillation column 1 temperature /423.15/

65 Pvap_D1(i) vapour pressure for distillation column 1

66 *light key = lightest component found in significant quantiies in the bott

om product

67 *heavy key = heaviest component found in significant quatities in the dist

illate product

68 xLK_DD1 light key (benzene) fraction at distillate /0.99/

69 xHK_DD1 heavy key (cumene) fraction at distillate /0.01/

70 xLK_BD1 light key (benzene) fraction at bottom /0.01/

71 xHK_BD1 heavy key (cumene) fraction at bottom /0.99/

72 xLK_FD1 light key (benzene) fraction at feed /0.422/

74 *D2

75 TD2 distillation column 2 temperature /463.15/

76 Pvap_D2(i) vapour pressure for distillation column 2

77 *light key = lightest component found in significant quantiies in the bott

om product

78 *heavy key = heaviest component found in significant quatities in the dist

illate product

79 xLK_DD2 light key (cumene) fraction at distillate /0.99/

80 xHK_DD2 heavy key (PDIB) fraction at distillate /0.01/

81 xLK_BD2 light key (cumene) fraction at bottom /0.01/

82 xHK_BD2 heavy key (PDIB) fraction at bottom /0.99/

83 xLK_FD2 light key (cumene) fraction at feed /0.887/

84 ;

86 Pvap_flash(i) = (10**(Antoine(i,'AA')-Antoine(i,'AB')/(Tflash+Antoine(i,'A

C'))));

87 Pvap_D1(i) = (10**(Antoine(i,'AA')-Antoine(i,'AB')/(TD1+Antoine(i,'AC'))))

;

88 Pvap_D2(i) = (10**(Antoine(i,'AA')-Antoine(i,'AB')/(TD2+Antoine(i,'AC'))))

;

89 ;

91 EQUATIONS

92 *reactor

93 eq1 mass balance A (propylene)

94 eq2 mass balance B (benzene)

95 eq3 mass balance C (cumene)

96 eq4 mass balance D (PDIB)

97 eq5 mass balance E (propane)

98 eq6 total flowrate of component i out of reactor

99 eq7(j) Arrhenius equation [L mol-1 s-1]

100 eq8 benzene recycled

101 eq9 conversion of propylene

102 eq10(i) mole composition

103 eqEP_L3 economic potential level 3

104

105 *flash

106 eq11(i) relative volatility of component i wrt component B

107 eq12(i) overhead split fraction to find vapour flowrate

108 eq13 propylene recovery

109 eq14 cumene recovery

110 eq15 PDIB recovery

111 eq16 propane recovery

112 eq17 total vapour flowrate

113 eq18(i) vapour flowrate for each component

114 eq19(i) mass balance for each component

115 eq20 total liquid flowrate

116 eq21(i) liquid flowrate for each component

117 eqTACflash TAC of flash vessel

118 ;

119

120 *reactor

121 eq1.. F('A') =e= F0A*exp((-VR/F0A)*beta('1')*(k('1')+k('2')));

122 eq2.. F('B') =e= F0B*exp((-VR/F0A)*beta('2')*k('1'));

123 eq3.. F('C') =e= F0A*exp((-VR/F0A)*beta('1')*k('2'))-F0A*exp((-VR/F0A)

*beta('1')*k('1'));

124 eq4.. F('D') =e= F0A-F0A*exp((-VR/F0A)*beta('2')*k('2'));

125 eq5.. F('E') =e= (F0A/19);

126 eq6.. FRout_total =e= sum(i,F(i));

127 eq7(j).. k(j) =e= A(j)*exp(-Ea(j)/(R*Treactor));

128 *add the benzene recycle stream, DflowD1('B'), from D1 after combining eve

rything in eq8

129 eq8.. F0B =e= FFB;

130 eq9.. xA =e= (F0A-F('A'))/(F0A);

131 eq10(i).. zflash(i)*FRout_total =e= F(i);

132 eqEP_L3.. EP_L3 =e= ((31610.24 - (927.971/(0.95*xA)))*5760/1000000) - (1.

9*VR);

133

134 *flash

135 eq11(i).. RVflash(i) =e= Pvap_flash(i)/Pvap_flash('B');

136 eq12(i).. OSFflash(i)*(zflash(i)*FRout_total) =e= Vflowrate(i);

137 eq13.. OSFflash('A') =e= ((RVflash('A')**Nflash)*OSFflash('B'))/(1+((RVfla

sh('A')**Nflash)-1)*OSFflash('B'));

138 eq14.. OSFflash('C') =e= ((RVflash('C')**Nflash)*OSFflash('B'))/(1+((RVfla

sh('C')**Nflash)-1)*OSFflash('B'));

139 eq15.. OSFflash('D') =e= ((RVflash('D')**Nflash)*OSFflash('B'))/(1+((RVfla

sh('D')**Nflash)-1)*OSFflash('B'));

140 eq16.. OSFflash('E') =e= ((RVflash('E')**Nflash)*OSFflash('B'))/(1+((RVfla

sh('E')**Nflash)-1)*OSFflash('B'));

141 eq17.. sum(i,Vflowrate(i)) =e= TotalVflowrate;

142 eq18(i).. yflash(i)*TotalVflowrate =e= Vflowrate(i);

143 eq19(i).. zflash(i)*FRout_total =e= Lflowrate(i) + yflash(i)*TotalVflowrat

144 eq20.. sum(i,Lflowrate(i)) =e= TotalLflowrate;

145 eq21(i).. xflash(i)*TotalLflowrate =e= Lflowrate(i);

146 eqTACflash.. TACflash =e= (0.01*FRout_total);

147

148 F0A.l = 100000/3600;

149 F.FX('C') = 90000/3600;

150 OSFflash.FX('B') = 0.3;

151

152 MODEL Project /All/;

153 SOLVE Project using CNS;

COMPILATION TIME = 0.002 SECONDS 3 MB 24.6.1 r55820 WIN-VS8

GAMS 24.6.1 r55820 Released Jan 18, 2016 WIN-VS8 x86 32bit/MS Windows 03/25/16 16:24:28 Page 2

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Equation Listing SOLVE Project Using CNS From line 153

---- eq1 =E= mass balance A (propylene)

eq1.. F(A) - (1)*F0A + (0)*VR + (0)*k(1) + (0)*k(2) =E= 0 ;

(LHS = -27.7777777777778, INFES = 27.7777777777778 ****)

---- eq2 =E= mass balance B (benzene)

eq2.. F(B) + (0)*F0A - (1)*F0B + (0)*VR + (0)*k(1) =E= 0 ; (LHS = 0)

---- eq3 =E= mass balance C (cumene)

eq3.. F(C) + (0)*F0A + (0)*VR + (0)*k(1) + (0)*k(2) =E= 0 ;

(LHS = 25, INFES = 25 ****)

---- eq4 =E= mass balance D (PDIB)

eq4.. F(D) + (0)*F0A + (0)*VR + (0)*k(2) =E= 0 ; (LHS = 0)

---- eq5 =E= mass balance E (propane)

eq5.. F(E) - 0.0526315789473684*F0A =E= 0 ;

(LHS = -1.46198830409357, INFES = 1.46198830409357 ****)

---- eq6 =E= total flowrate of component i out of reactor

eq6.. - F(A) - F(B) - F(C) - F(D) - F(E) + FRout_total =E= 0 ;

(LHS = -25, INFES = 25 ****)

---- eq7 =E= Arrhenius equation [L mol-1 s-1]

eq7(1).. k(1) =E= 0.301180046021959 ; (LHS = 0, INFES = 0.301180046021959 ****)

eq7(2).. k(2) =E= 0.0253793741894551 ;

(LHS = 0, INFES = 0.0253793741894551 ****)

---- eq8 =E= benzene recycled

eq8.. F0B =E= 27.78 ; (LHS = 0, INFES = 27.78 ****)

---- eq9 =E= conversion of propylene

eq9.. (0.036)*F(A) + (0)*F0A =E= -0.6 ; (LHS = -1, INFES = 0.4 ****)

---- eq10 =E= mole composition

eq10(A).. - F(A) + (0)*FRout_total + (0)*zflash(A) =E= 0 ; (LHS = 0)

eq10(B).. - F(B) + (0)*FRout_total + (0)*zflash(B) =E= 0 ; (LHS = 0)

eq10(C).. - F(C) + (0)*FRout_total + (0)*zflash(C) =E= 0 ;

(LHS = -25, INFES = 25 ****)

REMAINING 2 ENTRIES SKIPPED

---- eqEP_L3 =E= economic potential level 3

eqEP_L3.. 1.9*VR + EP_L3 =E= 172.697591242105 ;

(LHS = 0, INFES = 172.697591242105 ****)

---- eq11 =E= relative volatility of component i wrt component B

eq11(A).. RVflash(A) =E= 4.86529599749014 ;

(LHS = 0, INFES = 4.86529599749014 ****)

eq11(B).. RVflash(B) =E= 1 ; (LHS = 0, INFES = 1 ****)

eq11(C).. RVflash(C) =E= 0.359254684025443 ;

(LHS = 0, INFES = 0.359254684025443 ****)

REMAINING 2 ENTRIES SKIPPED

---- eq12 =E= overhead split fraction to find vapour flowrate

eq12(A).. (0)*FRout_total + (0)*zflash(A) + (0)*OSFflash(A) - Vflowrate(A) =E=

0 ; (LHS = 0)

eq12(B).. (0)*FRout_total + (0)*zflash(B) + (0)*OSFflash(B) - Vflowrate(B) =E=

0 ; (LHS = 0)

eq12(C).. (0)*FRout_total + (0)*zflash(C) + (0)*OSFflash(C) - Vflowrate(C) =E=

0 ; (LHS = 0)

REMAINING 2 ENTRIES SKIPPED

---- eq13 =E= propylene recovery

eq13.. - (0.428571428571429)*RVflash(A) + OSFflash(A) + (0)*OSFflash(B) =E= 0 ;

(LHS = 0)

---- eq14 =E= cumene recovery

eq14.. - (0.428571428571429)*RVflash(C) + (0)*OSFflash(B) + OSFflash(C) =E= 0 ;

(LHS = 0)

---- eq15 =E= PDIB recovery

eq15.. - (0.428571428571429)*RVflash(D) + (0)*OSFflash(B) + OSFflash(D) =E= 0 ;

(LHS = 0)

---- eq16 =E= propane recovery

eq16.. - (0.428571428571429)*RVflash(E) + (0)*OSFflash(B) + OSFflash(E) =E= 0 ;

(LHS = 0)

---- eq17 =E= total vapour flowrate

eq17.. - TotalVflowrate + Vflowrate(A) + Vflowrate(B) + Vflowrate(C)

+ Vflowrate(D) + Vflowrate(E) =E= 0 ; (LHS = 0)

---- eq18 =E= vapour flowrate for each component

eq18(A).. (0)*TotalVflowrate - Vflowrate(A) + (0)*yflash(A) =E= 0 ; (LHS = 0)

eq18(B).. (0)*TotalVflowrate - Vflowrate(B) + (0)*yflash(B) =E= 0 ; (LHS = 0)

eq18(C).. (0)*TotalVflowrate - Vflowrate(C) + (0)*yflash(C) =E= 0 ; (LHS = 0)

REMAINING 2 ENTRIES SKIPPED

---- eq19 =E= mass balance for each component

eq19(A).. (0)*FRout_total + (0)*zflash(A) + (0)*TotalVflowrate + (0)*yflash(A)

- Lflowrate(A) =E= 0 ; (LHS = 0)

eq19(B).. (0)*FRout_total + (0)*zflash(B) + (0)*TotalVflowrate + (0)*yflash(B)

- Lflowrate(B) =E= 0 ; (LHS = 0)

eq19(C).. (0)*FRout_total + (0)*zflash(C) + (0)*TotalVflowrate + (0)*yflash(C)

- Lflowrate(C) =E= 0 ; (LHS = 0)

REMAINING 2 ENTRIES SKIPPED

---- eq20 =E= total liquid flowrate

eq20.. - TotalLflowrate + Lflowrate(A) + Lflowrate(B) + Lflowrate(C)

+ Lflowrate(D) + Lflowrate(E) =E= 0 ; (LHS = 0)

---- eq21 =E= liquid flowrate for each component

eq21(A).. (0)*TotalLflowrate - Lflowrate(A) + (0)*xflash(A) =E= 0 ; (LHS = 0)

eq21(B).. (0)*TotalLflowrate - Lflowrate(B) + (0)*xflash(B) =E= 0 ; (LHS = 0)

eq21(C).. (0)*TotalLflowrate - Lflowrate(C) + (0)*xflash(C) =E= 0 ; (LHS = 0)

REMAINING 2 ENTRIES SKIPPED

---- eqTACflash =E= TAC of flash vessel

eqTACflash.. - 0.01*FRout_total + TACflash =E= 0 ; (LHS = 0)

GAMS 24.6.1 r55820 Released Jan 18, 2016 WIN-VS8 x86 32bit/MS Windows 03/25/16 16:24:28 Page 3

G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m

Column Listing SOLVE Project Using CNS From line 153

---- F mole flowrate of component i at REACTOR EXIT [mol s-1]

F(A)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

1 eq1

-1 eq6

(0.036) eq9

-1 eq10(A)

F(B)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

1 eq2

-1 eq6

-1 eq10(B)

F(C)

(.LO, .L, .UP, .M = 25, 25, 25, 0)

1 eq3

-1 eq6

-1 eq10(C)

REMAINING 2 ENTRIES SKIPPED

---- F0A feed mole flowrate of component A propylene INTO REACTOR [mol s-1]

F0A

(.LO, .L, .UP, .M = 0, 27.7777777777778, +INF, 0)

(-1) eq1

(0) eq2

(0) eq3

(0) eq4

-0.0526 eq5

(0) eq9

---- F0B feed mole flowrate of component B benzene INTO REACTOR [mol s-1]

F0B

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(-1) eq2

1 eq8

---- VR reactor volume [L]

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq1

(0) eq2

(0) eq3

(0) eq4

1.9 eqEP_L3

---- k reaction rate constant [L mol-1 s-1]

k(1)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq1

(0) eq2

(0) eq3

1 eq7(1)

k(2)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq1

(0) eq3

(0) eq4

1 eq7(2)

---- FRout_total total flowrate at REACTOR EXIT [mol s-1] same as FLASH FEED

FRout_total

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

1 eq6

(0) eq10(A)

(0) eq10(B)

(0) eq10(C)

(0) eq10(D)

(0) eq10(E)

(0) eq12(A)

(0) eq12(B)

(0) eq12(C)

(0) eq12(D)

(0) eq12(E)

(0) eq19(A)

(0) eq19(B)

(0) eq19(C)

(0) eq19(D)

(0) eq19(E)

-0.01 eqTACflash

---- zflash mole composition at REACTOR OUTLET and INTO FLASH

zflash(A)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq10(A)

(0) eq12(A)

(0) eq19(A)

zflash(B)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq10(B)

(0) eq12(B)

(0) eq19(B)

zflash(C)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq10(C)

(0) eq12(C)

(0) eq19(C)

REMAINING 2 ENTRIES SKIPPED

---- RVflash relative volatility of component i wrt component D

RVflash(A)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

1 eq11(A)

(-0.4286) eq13

RVflash(B)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

1 eq11(B)

RVflash(C)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

1 eq11(C)

(-0.4286) eq14

REMAINING 2 ENTRIES SKIPPED

---- OSFflash overhead split fraction

OSFflash(A)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq12(A)

1 eq13

OSFflash(B)

(.LO, .L, .UP, .M = 0.3, 0.3, 0.3, 0)

(0) eq12(B)

(0) eq13

(0) eq14

(0) eq15

(0) eq16

OSFflash(C)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq12(C)

1 eq14

REMAINING 2 ENTRIES SKIPPED

---- TotalVflowrate total vapour flowrate

TotalVflowrate

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

-1 eq17

(0) eq18(A)

(0) eq18(B)

(0) eq18(C)

(0) eq18(D)

(0) eq18(E)

(0) eq19(A)

(0) eq19(B)

(0) eq19(C)

(0) eq19(D)

(0) eq19(E)

---- TotalLflowrate total liquid vapour flowrate

TotalLflowrate

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

-1 eq20

(0) eq21(A)

(0) eq21(B)

(0) eq21(C)

(0) eq21(D)

(0) eq21(E)

---- Vflowrate vapour flowrate

Vflowrate(A)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

-1 eq12(A)

1 eq17

-1 eq18(A)

Vflowrate(B)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

-1 eq12(B)

1 eq17

-1 eq18(B)

Vflowrate(C)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

-1 eq12(C)

1 eq17

-1 eq18(C)

REMAINING 2 ENTRIES SKIPPED

---- yflash vapour fraction

yflash(A)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq18(A)

(0) eq19(A)

yflash(B)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq18(B)

(0) eq19(B)

yflash(C)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq18(C)

(0) eq19(C)

REMAINING 2 ENTRIES SKIPPED

---- Lflowrate liquid flowrate

Lflowrate(A)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

-1 eq19(A)

1 eq20

-1 eq21(A)

Lflowrate(B)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

-1 eq19(B)

1 eq20

-1 eq21(B)

Lflowrate(C)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

-1 eq19(C)

1 eq20

-1 eq21(C)

REMAINING 2 ENTRIES SKIPPED

---- xflash liquid fraction

xflash(A)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq21(A)

xflash(B)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq21(B)

xflash(C)

(.LO, .L, .UP, .M = 0, 0, +INF, 0)

(0) eq21(C)

REMAINING 2 ENTRIES SKIPPED

---- EP_L3 economic potential level 3 [mil£ per year]

EP_L3

(.LO, .L, .UP, .M = -INF, 0, +INF, 0)

1 eqEP_L3

---- TACflash TAC of flash vessel [mil£ per year]

TACflash

(.LO, .L, .UP, .M = -INF, 0, +INF, 0)

1 eqTACflash

GAMS 24.6.1 r55820 Released Jan 18, 2016 WIN-VS8 x86 32bit/MS Windows 03/25/16 16:24:28 Page 4

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Model Statistics SOLVE Project Using CNS From line 153

MODEL STATISTICS

BLOCKS OF EQUATIONS 23 SINGLE EQUATIONS 48

BLOCKS OF VARIABLES 17 SINGLE VARIABLES 50

NON ZERO ELEMENTS 155 NON LINEAR N-Z 90

DERIVATIVE POOL 20 CONSTANT POOL 19

CODE LENGTH 240

FIXED EQUATIONS 48 FREE VARIABLES 48

GENERATION TIME = 0.004 SECONDS 4 MB 24.6.1 r55820 WIN-VS8

EXECUTION TIME = 0.004 SECONDS 4 MB 24.6.1 r55820 WIN-VS8

GAMS 24.6.1 r55820 Released Jan 18, 2016 WIN-VS8 x86 32bit/MS Windows 03/25/16 16:24:28 Page 5

G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m

Solution Report SOLVE Project Using CNS From line 153

S O L V E S U M M A R Y

MODEL Project

TYPE CNS

SOLVER CONOPT FROM LINE 153

**** SOLVER STATUS 1 Normal Completion

**** MODEL STATUS 5 Locally Infeasible

RESOURCE USAGE, LIMIT 0.001 1000.000

ITERATION COUNT, LIMIT 1 2000000000

EVALUATION ERRORS 0 0

CONOPT 3 24.6.1 r55820 Released Jan 18, 2016 VS8 x86 32bit/MS Windows

C O N O P T 3 version 3.17A

Bagsvaerdvej 246 A

DK-2880 Bagsvaerd, Denmark

** Warning ** The number of nonlinear derivatives equal to zero

in the initial point is large (= 53 percent).

A better initial point will probably help the

optimization.

Pre-triangular equations: 12

Post-triangular equations: 2

** Error in Square System: Pivot too small.

CONOPT time Total 0.001 seconds

of which: Function evaluations 0.000 = 0.0%

1st Derivative evaluations 0.000 = 0.0%

**** ERRORS/WARNINGS IN EQUATION eq10(B)

1 error(s): Pivot too small.

**** ERRORS/WARNINGS IN VARIABLE yflash(A)

1 error(s): Pivot too small.

LOWER LEVEL UPPER

---- EQU eq1 . -27.778 . INFES

---- EQU eq2 . -27.780 . INFES

---- EQU eq3 . 25.000 . INFES

---- EQU eq4 . . .

---- EQU eq5 . -1.462 . INFES

---- EQU eq6 . . .

eq1 mass balance A (propylene)

eq2 mass balance B (benzene)

eq3 mass balance C (cumene)

eq4 mass balance D (PDIB)

eq5 mass balance E (propane)

eq6 total flowrate of component i out of reactor

---- EQU eq7 Arrhenius equation [L mol-1 s-1]

LOWER LEVEL UPPER

1 0.301 0.301 0.301

2 0.025 0.025 0.025

LOWER LEVEL UPPER

---- EQU eq8 27.780 27.780 27.780

---- EQU eq9 -0.600 -1.000 -0.600 INFES

eq8 benzene recycled

eq9 conversion of propylene

---- EQU eq10 mole composition

LOWER LEVEL UPPER

A . . .

B . . . DEPND

C . -25.000 . INFES

D . . .

E . . .

LOWER LEVEL UPPER

---- EQU eqEP_L3 172.698 . 172.698

eqEP_L3 economic potential level 3

---- EQU eq11 relative volatility of component i wrt component B

LOWER LEVEL UPPER

A 4.865 4.865 4.865

B 1.000 1.000 1.000

C 0.359 0.359 0.359

D 0.155 0.155 0.155

E 4.377 4.377 4.377

---- EQU eq12 overhead split fraction to find vapour flowrate

LOWER LEVEL UPPER

A . . .

B . . .

C . . .

D . . .

E . . .

LOWER LEVEL UPPER

---- EQU eq13 . . .

---- EQU eq14 . . .

---- EQU eq15 . . .

---- EQU eq16 . . .

---- EQU eq17 . . .

eq13 propylene recovery

eq14 cumene recovery

eq15 PDIB recovery

eq16 propane recovery

eq17 total vapour flowrate

---- EQU eq18 vapour flowrate for each component

LOWER LEVEL UPPER

A . . .

B . . .

C . . .

D . . .

E . . .

---- EQU eq19 mass balance for each component

LOWER LEVEL UPPER

A . . .

B . . .

C . . .

D . . .

E . . .

LOWER LEVEL UPPER

---- EQU eq20 . . .

eq20 total liquid flowrate

---- EQU eq21 liquid flowrate for each component

LOWER LEVEL UPPER

A . . .

B . . .

C . . .

D . . .

E . . .

LOWER LEVEL UPPER

---- EQU eqTACflash . -0.250 .

eqTACflash TAC of flash vessel

---- VAR F mole flowrate of component i at REACTOR EXIT [mol s-1]

LOWER LEVEL UPPER

A . . +INF

B . . +INF

C 25.000 25.000 25.000

D . . +INF

E . . +INF

LOWER LEVEL UPPER

---- VAR F0A . 27.778 +INF

---- VAR F0B . 27.780 +INF

---- VAR VR . . +INF

F0A feed mole flowrate of component A propylene INTO REACTOR [mol s-1]

F0B feed mole flowrate of component B benzene INTO REACTOR [mol s-1]

VR reactor volume [L]

---- VAR k reaction rate constant [L mol-1 s-1]

LOWER LEVEL UPPER

1 . 0.301 +INF

2 . 0.025 +INF

LOWER LEVEL UPPER

---- VAR FRout_tot~ . 25.000 +INF

FRout_total total flowrate at REACTOR EXIT [mol s-1] same as FLASH FEED

---- VAR zflash mole composition at REACTOR OUTLET and INTO FLASH

LOWER LEVEL UPPER

A . . +INF

B . . +INF

C . . +INF

D . . +INF

E . . +INF

---- VAR RVflash relative volatility of component i wrt component D

LOWER LEVEL UPPER

A . 4.865 +INF

B . 1.000 +INF

C . 0.359 +INF

D . 0.155 +INF

E . 4.377 +INF

---- VAR OSFflash overhead split fraction

LOWER LEVEL UPPER

A . 0.676 +INF

B 0.300 0.300 0.300

C . 0.133 +INF

D . 0.062 +INF

E . 0.652 +INF

LOWER LEVEL UPPER

---- VAR TotalVflo~ . . +INF

---- VAR TotalLflo~ . . +INF

TotalVflowrate total vapour flowrate

TotalLflowrate total liquid vapour flowrate

---- VAR Vflowrate vapour flowrate

LOWER LEVEL UPPER

A . . +INF

B . . +INF

C . . +INF

D . . +INF

E . . +INF

---- VAR yflash vapour fraction

LOWER LEVEL UPPER

A . . +INF DEPND

B . . +INF

C . . +INF

D . . +INF

E . . +INF

---- VAR Lflowrate liquid flowrate

LOWER LEVEL UPPER

A . . +INF

B . . +INF

C . . +INF

D . . +INF

E . . +INF

---- VAR xflash liquid fraction

LOWER LEVEL UPPER

A . . +INF

B . . +INF

C . . +INF

D . . +INF

E . . +INF

LOWER LEVEL UPPER

---- VAR EP_L3 -INF . +INF

---- VAR TACflash -INF . +INF

EP_L3 economic potential level 3 [mil£ per year]

TACflash TAC of flash vessel [mil£ per year]

**** REPORT SUMMARY : 6 INFEASIBLE (INFES)

SUM 107.420

MAX 27.780

MEAN 17.903

1 DEPENDENT (DEPND)

2 ERRORS ( ****)

EXECUTION TIME = 0.002 SECONDS 2 MB 24.6.1 r55820 WIN-VS8

USER: GAMS Development Corporation, Washington, DC G871201/0000CA-ANY

Free Demo, 202-342-0180, sa...@gams.com, www.gams.com DC0000

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