* Nonsharp separation of propane, isobutane, n-butane and isopentane
* Aggarwal and Floudas (1990)

* Sets
SET i /1*54/;
SET j /0*3/;
SET l /1*3/;
SET m /1*3/;

* Parameters
PARAMETER a(j,l)  
         / '0'.'1'     0.31569
           '0'.'2'     0.96926
           '0'.'3'     0.40281
           '1'.'1'     -0.0112812
           '1'.'2'     -0.0413393
           '1'.'3'     -0.0119785
           '2'.'1'     0.0072698
           '2'.'2'     0.0228203
           '2'.'3'     0.0082055
           '3'.'1'     0.0064241
           '3'.'2'     0.0257035
           '3'.'3'     0.009819/;

PARAMETER b(l,m)  
         / '1'.'1'     0.0016446
           '1'.'2'     0.0015625
           '1'.'3'     -0.001748
           '2'.'1'     0.0018611
           '2'.'2'     0.0091604
           '2'.'3'     -0.0002583
           '3'.'1'     0.001262
           '3'.'2'     0.0076758
           '3'.'3'     -0.0004691/;

* A, B, C, D denote propane, isobutane, n-butane and isopentane respectively
* Fi denotes the flowrate of stream i (kgmol/h) 
* xji denotes the mole fraction of component j in stream i
* Refer to Figure 5.7 in the test problem collection.
VARIABLES
	 F1  
	 F2  
	 F3  
	 F4  
	 F5  
	 F6  
	 F7  
	 F8  
	 F9  
	 F10  
	 F11  
	 F12  
	 F13  
	 F14  
	 F15  
	 F16  
	 F17  
	 F18  
	 F19  
	 F20  
	 F21  
	 F22  
	 F23  
	 F24  
	 F25  
	 F26  
	 F27  
	 F28  
	 F29  
	 F30  
	 F31  
	 F32  
	 xA6  
	 xB6  
	 xC6  
	 xD6  
	 xA7  
	 xB7  
	 xA10  
	 xB10  
	 xC10  
	 xD10  
	 xA15  
	 xB15  
	 xC15  
	 xD15  
	 xA16
	 xB16
	 xC16
	 xB20
	 xC20
	 xD20
	 xA24
	 xB24
	 xC24
	 xD24
	 xA25  
	 xB25  
	 xC25  
	 xD25  
	 xC30  
	 xD30  
     objval    Automatically generated objective function variable;

FREE VARIABLES    objval;


EQUATIONS
	 g1  
	 g2  
	 g3  
	 g4  
	 g5  
	 g6  
	 g7  
	 g8  
	 g9  
	 g10  
	 g11  
	 g12  
	 g13  
	 g14  
	 g15  
	 g16  
	 g17  
	 g18  
	 g19  
	 g20  
	 g21  
	 g22  
	 g23  
	 g24  
	 g25  
	 g26  
	 g27  
	 g28  
	 g29  
	 g30  
	 g31  
	 g32  
	 g33  
	 g34  
	 g35  
	 g36  
	 g37  
	 g38  
	 g39  
	 g40  
	 g41  
	 g42  
	 g43  
	 g44  
	 g45  
	 g46  
	 g47  
	 g48  
	 g49  
	 g50  
	 g51  
	 g52  
	 g53  
	 g54  
	 f Objective function;

f  .. objval =e= a('0','1')+(a('1','1')+0.85*a('2','1')+a('3','1')
                +b('1','1')*xA6+b('2','1')*xB6+b('3','1')*xC6)*F6
				+a('0','2')+(a('1','2')+0.85*a('2','2')+0.85*a('3','2')
				+b('1','2')*xA15+b('2','2')*xB15+b('3','2')*xC15)*F15
				+a('0','3')+(a('1','3')+a('2','3')+0.85*a('3','3')
				+b('1','3')*xA24+b('2','3')*xB24+b('3','3')*xC24)*F24;
g1  .. F1+F2+F3+F4+F5 =e= 600;
g2  .. F6-F1-F17-F26 =e= 0;
g3  .. F15-F2-F11-F27 =e= 0;
g4  .. F24-F3-F12-F21 =e= 0;
g5  .. F7-F8-F9 =e= 0;
g6  .. F10-F11-F12-F13-F14 =e= 0;
g7  .. F16-F17-F18-F19 =e= 0;
g8  .. F20-F21-F22-F23 =e= 0;
g9  .. F25-F26-F27-F28-F29 =e= 0;
g10  .. F30-F31-F32 =e= 0;
g11  .. F13*0 =e= 0;
g12  .. F7*xA7-0.85*F6*xA6 =e= 0;
g13  .. F16*xB16-0.85*F15*xB15 =e= 0;
g14  .. F25*xC25-F24*xC24 =e= 0;
g15  .. F10*xB10-F6*xB6 =e= 0;
g16  .. F20*xC20-0.85*F15*xC15 =e= 0;
g17  .. F30*xD30-0.85*F24*xD24 =e= 0;
g18  .. F6*xA6-F7*xA7-F10*xA10 =e= 0;
g19  .. F6*xB6-F7*xB7-F10*xB10 =e= 0;
g20  .. F6*xC6-F10*xC10 =e= 0;
g21  .. F6*xD6-F10*xD10 =e= 0;
g22  .. F15*xA15-F16*xA16 =e= 0;
g23  .. F15*xB15-F16*xB16-F20*xB20 =e= 0;
g24  .. F15*xC15-F16*xC16-F20*xC20 =e= 0;
g25  .. F15*xD15-F20*xD20 =e= 0;
g26  .. F24*xA24-F25*xA25 =e= 0;
g27  .. F24*xB24-F25*xB25 =e= 0;
g28  .. F24*xC24-F25*xC25-F30*xC30 =e= 0;
g29  .. F24*xD24-F25*xD25-F30*xD30 =e= 0;
g30  .. 0.25*F1+F17*xA16+F26*xA25-F6*xA6 =e= 0;
g31  .. 0.333*F1+F17*xB16+F26*xB25-F6*xB6 =e= 0;
g32  .. 0.167*F1+F17*xC16+F26*xC25-F6*xC6 =e= 0;
g33  .. 0.25*F1+F26*xD25-F6*xD6 =e= 0;
g34  .. 0.25*F2+F11*xA10+F27*xA25-F15*xA15 =e= 0;
g35  .. 0.333*F2+F11*xB10+F27*xB25-F15*xB15 =e= 0;
g36  .. 0.167*F2+F11*xC10+F27*xC25-F15*xC15 =e= 0;
g37  .. 0.25*F2+F11*xD10+F27*xD25-F15*xD15 =e= 0;
g38  .. 0.25*F3+F12*xA10-F24*xA24 =e= 0;
g39  .. 0.333*F3+F12*xB10+F21*xB20-F24*xB24 =e= 0;
g40  .. 0.167*F3+F12*xC10+F21*xC20-F24*xC24 =e= 0;
g41  .. 0.25*F3+F12*xD10+F21*xD20-F24*xD24 =e= 0;
g42  .. 0.25*F4+F8*xA7+F13*xA10+F18*xA16+F28*xA25 =e= 50;
g43  .. 0.222*F4+F8*xB7+F13*xB10+F18*xB16+F22*xB20+F28*xB25 =e= 100;
g44  .. 0.167*F4+F13*xC10+F18*xC16+F22*xC20+F28*xC25+F31*xC30 =e= 40;
g45  .. 0.25*F4+F13*xD10+F22*xD20+F28*xD25+F31*xD30 =e= 100;
g46  .. xA6+xB6+xC6+xD6 =e= 1;
g47  .. xA7+xB7 =e= 1;
g48  .. xA10+xB10+xC10+xD10 =e= 1;
g49  .. xA15+xB15+xC15+xD15 =e= 1;
g50  .. xA16+xB16+xC16 =e= 1;
g51  .. xB20+xC20+xD20 =e= 1;
g52  .. xA24+xB24+xC24+xD24 =e= 1;
g53  .. xA25+xB25+xC25+xD25 =e= 1;
g54  .. xC30+xD30 =e= 1;

* Bounds
F1.LO = 0; F1.UP = 600;
F2.LO = 0; F2.UP = 600;
F3.LO = 0; F3.UP = 600;
F4.LO = 0; F4.UP = 600;
F5.LO = 0; F5.UP = 600;
F6.LO = 0; F6.UP = 600;
F7.LO = 0; F7.UP = 600;
F8.LO = 0; F8.UP = 600;
F9.LO = 0; F9.UP = 600;
F10.LO = 0; F10.UP = 600;
F11.LO = 0; F11.UP = 600;
F12.LO = 0; F12.UP = 600;
F13.LO = 0; F13.UP = 600;
F14.LO = 0; F14.UP = 600;
F15.LO = 0; F15.UP = 600;
F16.LO = 0; F16.UP = 600;
F17.LO = 0; F17.UP = 600;
F18.LO = 0; F18.UP = 600;
F20.LO = 0; F20.UP = 600;
F19.LO = 0; F19.UP = 600;
F21.LO = 0; F21.UP = 600;
F22.LO = 0; F22.UP = 600;
F23.LO = 0; F23.UP = 600;
F24.LO = 0; F24.UP = 600;
F25.LO = 0; F25.UP = 600;
F26.LO = 0; F26.UP = 600;
F27.LO = 0; F27.UP = 600;
F28.LO = 0; F28.UP = 600;
F29.LO = 0; F29.UP = 600;
F30.LO = 0; F30.UP = 600;
F31.LO = 0; F31.UP = 600;
F32.LO = 0; F32.UP = 600;
xA6.LO = 0; xA6.UP = 1;
xB6.LO = 0; xB6.UP = 1;
xC6.LO = 0; xC6.UP = 1;
xD6.LO = 0; xD6.UP = 1;
xA7.LO = 0; xA7.UP = 1;
xB7.LO = 0; xB7.UP = 1;
xA10.LO = 0; xA10.UP = 1;
xB10.LO = 0; xB10.UP = 1;
xC10.LO = 0; xC10.UP = 1;
xD10.LO = 0; xD10.UP = 1;
xA15.LO = 0; xA15.UP = 1;
xB15.LO = 0; xB15.UP = 1;
xC15.LO = 0; xC15.UP = 1;
xD15.LO = 0; xD15.UP = 1;
xA16.LO = 0; xA16.UP = 1;
xB16.LO = 0; xB16.UP = 1;
xC16.LO = 0; xC16.UP = 1;
xB20.LO = 0; xB20.UP = 1;
xC20.LO = 0; xC20.UP = 1;
xD20.LO = 0; xD20.UP = 1;
xA24.LO = 0; xA24.UP = 1;
xB24.LO = 0; xB24.UP = 1;
xC24.LO = 0; xC24.UP = 1;
xD24.LO = 0; xD24.UP = 1;
xA25.LO = 0; xA25.UP = 1;
xB25.LO = 0; xB25.UP = 1;
xC25.LO = 0; xC25.UP = 1;
xD25.LO = 0; xD25.UP = 1;
xC30.LO = 0; xC30.UP = 1;
xD30.LO = 0; xD30.UP = 1;

* Starting point (global solution)
* F1.L = 161.99; F2.L = 115.49; F3.L = 93.68; F4.L = 60.20;
* F5.L = 168.62; F6.L = 161.99; F7.L = 34.42; F8.L = 0;
* F9.L = 34.42; F10.L = 127.57; F11.L = 0; F12.L = 0;
* F13.L = 127.57; F14.L = 0; F15.L = 115.49; F16.L = 64.46;
* F17.L = 0; F18.L = 64.46; F19.L = 0; F20.L = 51.04;
* F21.L = 51.04; F22.L = 0; F23.L = 0; F24.L = 144.72;
* F25.L = 100.27; F26.L = 0; F27.L = 0; F28.L = 0;
* F29.L = 100.27; F30.L = 44.45; F31.L = 44.45; F32.L = 0;
* xA6.L = 0.250; xB6.L = 0.333; xC6.L = 0.167; xD6.L = 0.250;
* xA7.L = 1.000; xB7.L = 0;
* xA10.L = 0.048; xB10.L = 0.423; xC10.L = 0.212; xD10.L = 0.317;
* xA15.L = 0.250; xB15.L = 0.333; xC15.L = 0.167; xD15.L = 0.250;
* xA16.L = 0.448; xB16.L = 0.507; xC16.L = 0.045; xB20.L = 0.113;
* xC20.L = 0.321; xD20.L = 0.566;
* xA24.L = 0.162; xB24.L = 0.256; xC24.L = 0.221; xD24.L = 0.361;
* xA25.L = 0.234; xB25.L = 0.369; xC25.L = 0.319; xD25.L = 0.078;
* xC30.L = 0; xD30.L = 1;

MODEL test /ALL/;
SOLVE test USING NLP MINIMIZING objval;