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BRITGAS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME BRITGAS
* Problem :
* *********
* A simple high pressure gas network problem for British Gas.
* Invented Data, but real network.
* 23 node network, 8 hour operation.
* Source:
* N. Gould, private communication,March 1990.
* SIF input: N. Gould, March 1990.
* classification OOI2-RN-450-360
* Period is the number of time periods
IE HOURS 8
IE NODES 23
* Define problem parameters
RE THETA 0.75
RE A 1.0
RE B 1.0
RE ALPHA 1.8539
RE DT 1.0
* Define a few helpful parameters
IE 0 0
IE 1 1
RE ONE 1.0
RE -ONE -1.0
RM -THETA THETA -1.0
RA OMEGA -THETA 1.0
RM -OMEGA OMEGA -1.0
R/ 1/DT ONE DT
VARIABLES
DO T 0 HOURS
* P(J,) = pressure at node J at time T
DO J 1 NODES
X P(J,T)
ND
* flows along pipes connecting nodes (network dependent)
* Q(I,J,T) = flow from node I to node J at time T
DO T 0 HOURS
X Q1, 2, (T)
X Q1, 17,(T)
X Q2, 3, (T)
X Q4, 5, (T)
X Q5, 6, (T)
X Q7, 8, (T)
X Q8, 9, (T)
X Q8, 10,(T)
X Q8, 11,(T)
X Q11,12,(T)
X Q12,13,(T)
X Q13,14,(T)
X Q13,15,(T)
X Q15,16,(T)
X Q17,18,(T)
X Q18,19,(T)
X Q20,21,(T)
X Q21,22,(T)
X Q22,23,(T)
ND
DO T 1 HOURS
* flows through machines connecting nodes (network dependent)
* F(I,J,T) = flow from node I to node J at time T
X F3, 4, (T)
X F5, 7, (T)
X F19,20,(T)
* compressor ratios (network dependent)
* R(I,J,T) = compressor ratio between node I to node J at time T
X R3, 4, (T)
X R5, 7, (T)
X R19,20,(T)
ND
DO T 1 HOURS
* the input supply at node 1
X IN1,(T)
* the output supplies at nodes 16 and 23
X OUT16,(T)
X OUT23,(T)
ND
GROUPS
* Define objective function group
N OBJ
DO T 1 HOURS
IA S T -1
* mass balance at nodes
ZE M1,(T) Q1, 17,(T) -THETA
ZE M1,(T) Q1, 2, (T) -THETA
ZE M1,(T) IN1,(T) ONE
ZE M1,(T) Q1, 17,(S) -OMEGA
ZE M1,(T) Q1, 2, (S) -OMEGA
ZE M2,(T) Q2, 3, (T) -THETA
ZE M2,(T) Q1, 2, (T) THETA
ZE M2,(T) Q2, 3, (S) -OMEGA
ZE M2,(T) Q1, 2, (S) OMEGA
ZE M3,(T) F3, 4, (T) -ONE
ZE M3,(T) Q2, 3, (T) THETA
ZE M3,(T) Q2, 3, (S) OMEGA
ZE M4,(T) Q4, 5, (T) -THETA
ZE M4,(T) F3, 4, (T) ONE
ZE M4,(T) Q4, 5, (S) -OMEGA
ZE M5,(T) Q5, 6, (T) -THETA
ZE M5,(T) F5, 7, (T) -ONE
ZE M5,(T) Q4, 5, (T) THETA
ZE M5,(T) Q5, 6, (S) -OMEGA
ZE M5,(T) Q4, 5, (S) OMEGA
ZE M6,(T) Q5, 6, (T) THETA
ZE M6,(T) Q5, 6, (S) OMEGA
ZE M7,(T) Q7, 8, (T) -THETA
ZE M7,(T) F5, 7, (T) ONE
ZE M7,(T) Q7, 8, (S) -OMEGA
ZE M8,(T) Q8, 9, (T) -THETA
ZE M8,(T) Q8, 10,(T) -THETA
ZE M8,(T) Q8, 11,(T) -THETA
ZE M8,(T) Q7, 8, (T) THETA
ZE M8,(T) Q8, 9, (S) -OMEGA
ZE M8,(T) Q8, 10,(S) -OMEGA
ZE M8,(T) Q8, 11,(S) -OMEGA
ZE M8,(T) Q7, 8, (S) OMEGA
ZE M9,(T) Q8, 9, (T) THETA
ZE M9,(T) Q8, 9, (S) OMEGA
ZE M10,(T) Q8, 10,(T) THETA
ZE M10,(T) Q8, 10,(S) OMEGA
ZE M11,(T) Q11,12,(T) -THETA
ZE M11,(T) Q8, 11,(T) THETA
ZE M11,(T) Q11,12,(S) -OMEGA
ZE M11,(T) Q8, 11,(S) OMEGA
ZE M12,(T) Q12,13,(T) -THETA
ZE M12,(T) Q11,12,(T) THETA
ZE M12,(T) Q12,13,(S) -OMEGA
ZE M12,(T) Q11,12,(S) OMEGA
ZE M13,(T) Q13,14,(T) -THETA
ZE M13,(T) Q13,15,(T) -THETA
ZE M13,(T) Q12,13,(T) THETA
ZE M13,(T) Q13,14,(S) -OMEGA
ZE M13,(T) Q13,15,(S) -OMEGA
ZE M13,(T) Q12,13,(S) OMEGA
ZE M14,(T) Q13,14,(T) THETA
ZE M14,(T) Q13,14,(S) OMEGA
ZE M15,(T) Q15,16,(T) -THETA
ZE M15,(T) Q13,15,(T) THETA
ZE M15,(T) Q15,16,(S) -OMEGA
ZE M15,(T) Q13,15,(S) OMEGA
ZE M16,(T) Q15,16,(T) THETA
ZE M16,(T) Q15,16,(S) OMEGA
ZE M16,(T) OUT16,(T) -ONE
ZE M17,(T) Q17,18,(T) -THETA
ZE M17,(T) Q1, 17,(T) THETA
ZE M17,(T) Q17,18,(S) -OMEGA
ZE M17,(T) Q1, 17,(S) OMEGA
ZE M18,(T) Q18,19,(T) -THETA
ZE M18,(T) Q17,18,(T) THETA
ZE M18,(T) Q18,19,(S) -OMEGA
ZE M18,(T) Q17,18,(S) OMEGA
ZE M19,(T) F19,20,(T) -ONE
ZE M19,(T) Q18,19,(T) THETA
ZE M19,(T) Q18,19,(S) OMEGA
ZE M20,(T) Q20,21,(T) -THETA
ZE M20,(T) F19,20,(T) ONE
ZE M20,(T) Q20,21,(S) -OMEGA
ZE M21,(T) Q21,22,(T) -THETA
ZE M21,(T) Q20,21,(T) THETA
ZE M21,(T) Q21,22,(S) -OMEGA
ZE M21,(T) Q20,21,(S) OMEGA
ZE M22,(T) Q22,23,(T) -THETA
ZE M22,(T) Q21,22,(T) THETA
ZE M22,(T) Q22,23,(S) -OMEGA
ZE M22,(T) Q21,22,(S) OMEGA
ZE M23,(T) Q22,23,(T) THETA
ZE M23,(T) Q22,23,(S) OMEGA
ZE M23,(T) OUT23,(T) -ONE
* compressor ratio constraints.
ZE C3, 4, (T)P4,(T) -ONE
ZE C5, 7, (T)P7,(T) -ONE
ZE C19,20,(T)P20,(T) -ONE
* Panhandle pipe equations (nonlinear)
XE P1, 2, (T)
XE P1, 17,(T)
XE P2, 3, (T)
XE P4, 5, (T)
XE P5, 6, (T)
XE P7, 8, (T)
XE P8, 9, (T)
XE P8, 10,(T)
XE P8, 11,(T)
XE P11,12,(T)
XE P12,13,(T)
XE P13,14,(T)
XE P13,15,(T)
XE P15,16,(T)
XE P17,18,(T)
XE P18,19,(T)
XE P20,21,(T)
XE P21,22,(T)
XE P22,23,(T)
ND
CONSTANTS
* The constants for the mass balance equations (guesses).
DO T 1 HOURS
*X BRITGAS M1,(T) -8.0
X BRITGAS M2,(T) 1.0
X BRITGAS M6,(T) 1.0
X BRITGAS M10,(T) 1.0
X BRITGAS M13,(T) 1.0
X BRITGAS M15,(T) 1.0
*X BRITGAS M16,(T) 1.0
X BRITGAS M17,(T) 1.0
X BRITGAS M18,(T) 1.0
X BRITGAS M21,(T) 1.0
X BRITGAS M22,(T) 1.0
*X BRITGAS M23,(T) 1.0
ND
BOUNDS
* All flows and pressures are positive
* compressor ratio bounds
* crmax = maximum compressor ratio (guess)
RE CRMAX 10.0
* flows along pipes connecting nodes (network dependent)
* Q(I,J,T) = flow from node I to node J at time T
DO T 0 HOURS
XL BRITGAS Q1, 2, (T)1.0D-16
XL BRITGAS Q1, 17,(T)1.0D-16
XL BRITGAS Q2, 3, (T)1.0D-16
XL BRITGAS Q4, 5, (T)1.0D-16
XL BRITGAS Q5, 6, (T)1.0D-16
XL BRITGAS Q7, 8, (T)1.0D-16
XL BRITGAS Q8, 9, (T)1.0D-16
XL BRITGAS Q8, 10,(T)1.0D-16
XL BRITGAS Q8, 11,(T)1.0D-16
XL BRITGAS Q11,12,(T)1.0D-16
XL BRITGAS Q12,13,(T)1.0D-16
XL BRITGAS Q13,14,(T)1.0D-16
XL BRITGAS Q13,15,(T)1.0D-16
XL BRITGAS Q15,16,(T)1.0D-16
XL BRITGAS Q17,18,(T)1.0D-16
XL BRITGAS Q18,19,(T)1.0D-16
XL BRITGAS Q20,21,(T)1.0D-16
XL BRITGAS Q21,22,(T)1.0D-16
XL BRITGAS Q22,23,(T)1.0D-16
ND
DO T 1 HOURS
ZL BRITGAS R3, 4, (T) ONE
ZL BRITGAS R5, 7, (T) ONE
ZL BRITGAS R19,20,(T) ONE
ZU BRITGAS R3, 4, (T) CRMAX
ZU BRITGAS R5, 7, (T) CRMAX
ZU BRITGAS R19,20,(T) CRMAX
ND
START POINT
XV BRITGAS 'DEFAULT' 1.0
ELEMENT TYPE
EV HPOWER F R
EV PROD PI R
EV RATIO P
EV SQUARE P
EV PANHAN Q PL
EV PANHAN PR
ELEMENT USES
DO T 1 HOURS
* horsepower at compressors
XT H3, 4, (T)HPOWER
ZV H3, 4, (T)R R3, 4, (T)
ZV H3, 4, (T)F F3, 4, (T)
XT H5, 7, (T)HPOWER
ZV H5, 7, (T)R R5, 7, (T)
ZV H5, 7, (T)F F5, 7, (T)
XT H19,20,(T)HPOWER
ZV H19,20,(T)R R19,20,(T)
ZV H19,20,(T)F F19,20,(T)
* compressor ratios
XT C3, 4, (T)PROD
ZV C3, 4, (T)R R3, 4, (T)
ZV C3, 4, (T)PI P3,(T)
XT C5, 7, (T)PROD
ZV C5, 7, (T)R R5, 7, (T)
ZV C5, 7, (T)PI P5,(T)
XT C19,20,(T)PROD
ZV C19,20,(T)R R19,20,(T)
ZV C19,20,(T)PI P19,(T)
ND
* for the mass balance constraint at each node
DO T 0 HOURS
DO J 1 NODES
XT R(J,T) RATIO
ZV R(J,T) P P(J,T)
ND
DO T 1 HOURS
* For the panhandle constraints along each pipe
DO J 1 NODES
XT S(J,T) SQUARE
ZV S(J,T) P P(J,T)
OD J
XT P1, 2, (T)PANHAN
ZV P1, 2, (T)PL P1,(T)
ZV P1, 2, (T)PR P2,(T)
ZV P1, 2, (T)Q Q1, 2, (T)
XT P1, 17,(T)PANHAN
ZV P1, 17,(T)PL P1,(T)
ZV P1, 17,(T)PR P17,(T)
ZV P1, 17,(T)Q Q1, 17,(T)
XT P2, 3, (T)PANHAN
ZV P2, 3, (T)PL P2,(T)
ZV P2, 3, (T)PR P3,(T)
ZV P2, 3, (T)Q Q2, 3, (T)
XT P4, 5, (T)PANHAN
ZV P4, 5, (T)PL P4,(T)
ZV P4, 5, (T)PR P5,(T)
ZV P4, 5, (T)Q Q4, 5, (T)
XT P5, 6, (T)PANHAN
ZV P5, 6, (T)PL P5,(T)
ZV P5, 6, (T)PR P6,(T)
ZV P5, 6, (T)Q Q5, 6, (T)
XT P7, 8, (T)PANHAN
ZV P7, 8, (T)PL P7,(T)
ZV P7, 8, (T)PR P8,(T)
ZV P7, 8, (T)Q Q7, 8, (T)
XT P8, 9, (T)PANHAN
ZV P8, 9, (T)PL P8,(T)
ZV P8, 9, (T)PR P9,(T)
ZV P8, 9, (T)Q Q8, 9, (T)
XT P8, 10,(T)PANHAN
ZV P8, 10,(T)PL P8,(T)
ZV P8, 10,(T)PR P10,(T)
ZV P8, 10,(T)Q Q8, 10,(T)
XT P8, 11,(T)PANHAN
ZV P8, 11,(T)PL P8,(T)
ZV P8, 11,(T)PR P11,(T)
ZV P8, 11,(T)Q Q8, 11,(T)
XT P11,12,(T)PANHAN
ZV P11,12,(T)PL P11,(T)
ZV P11,12,(T)PR P12,(T)
ZV P11,12,(T)Q Q11,12,(T)
XT P12,13,(T)PANHAN
ZV P12,13,(T)PL P12,(T)
ZV P12,13,(T)PR P13,(T)
ZV P12,13,(T)Q Q12,13,(T)
XT P13,14,(T)PANHAN
ZV P13,14,(T)PL P13,(T)
ZV P13,14,(T)PR P14,(T)
ZV P13,14,(T)Q Q13,14,(T)
XT P13,15,(T)PANHAN
ZV P13,15,(T)PL P13,(T)
ZV P13,15,(T)PR P15,(T)
ZV P13,15,(T)Q Q13,15,(T)
XT P15,16,(T)PANHAN
ZV P15,16,(T)PL P15,(T)
ZV P15,16,(T)PR P16,(T)
ZV P15,16,(T)Q Q15,16,(T)
XT P17,18,(T)PANHAN
ZV P17,18,(T)PL P17,(T)
ZV P17,18,(T)PR P18,(T)
ZV P17,18,(T)Q Q17,18,(T)
XT P18,19,(T)PANHAN
ZV P18,19,(T)PL P18,(T)
ZV P18,19,(T)PR P19,(T)
ZV P18,19,(T)Q Q18,19,(T)
XT P20,21,(T)PANHAN
ZV P20,21,(T)PL P20,(T)
ZV P20,21,(T)PR P21,(T)
ZV P20,21,(T)Q Q20,21,(T)
XT P21,22,(T)PANHAN
ZV P21,22,(T)PL P21,(T)
ZV P21,22,(T)PR P22,(T)
ZV P21,22,(T)Q Q21,22,(T)
XT P22,23,(T)PANHAN
ZV P22,23,(T)PL P22,(T)
ZV P22,23,(T)PR P23,(T)
ZV P22,23,(T)Q Q22,23,(T)
ND
GROUP USES
* objective function = sum of power generated at compressors.
* zi (inlet compressibility) and k are constants (guesses)
RE K 1.0
RE ZI 1.0
R* K*ZI K ZI
DO T 1 HOURS
ZE OBJ H3, 4, (T) K*ZI
ZE OBJ H5, 7, (T) K*ZI
ZE OBJ H19,20,(T) K*ZI
* compressor ratio constraints
XE C3, 4, (T)C3, 4, (T)
XE C5, 7, (T)C5, 7, (T)
XE C19,20,(T)C19,20,(T)
ND
* mass balance constraints
* v = volume coefficient for mass around node (guess)
*RD V 0.0
RE V 1.0
R* V/DT V 1/DT
RM -V/DT V/DT -1.0
DO T 1 HOURS
IA S T -1
DO J 1 NODES
ZE M(J,T) R(J,T) V/DT
ZE M(J,T) R(J,S) -V/DT
ND
* Pressure drop equations
* H = friction coefficient (guess)
RE H 0.01
*RD H 0.1
RM -H H -1.0
DO T 1 HOURS
ZE P1, 2, (T)S1,(T) ONE
ZE P1, 2, (T)S2,(T) -ONE
ZE P1, 2, (T)P1, 2, (T) -H
ZE P1, 17,(T)S1,(T) ONE
ZE P1, 17,(T)S17,(T) -ONE
ZE P1, 17,(T)P1, 17,(T) -H
ZE P2, 3, (T)S2,(T) ONE
ZE P2, 3, (T)S3,(T) -ONE
ZE P2, 3, (T)P2, 3, (T) -H
ZE P4, 5, (T)S4,(T) ONE
ZE P4, 5, (T)S5,(T) -ONE
ZE P4, 5, (T)P4, 5, (T) -H
ZE P5, 6, (T)S5,(T) ONE
ZE P5, 6, (T)S6,(T) -ONE
ZE P5, 6, (T)P5, 6, (T) -H
ZE P7, 8, (T)S7,(T) ONE
ZE P7, 8, (T)S8,(T) -ONE
ZE P7, 8, (T)P7, 8, (T) -H
ZE P8, 9, (T)S8,(T) ONE
ZE P8, 9, (T)S9,(T) -ONE
ZE P8, 9, (T)P8, 9, (T) -H
ZE P8, 10,(T)S8,(T) ONE
ZE P8, 10,(T)S10,(T) -ONE
ZE P8, 10,(T)P8, 10,(T) -H
ZE P8, 11,(T)S8,(T) ONE
ZE P8, 11,(T)S11,(T) -ONE
ZE P8, 11,(T)P8, 11,(T) -H
ZE P11,12,(T)S11,(T) ONE
ZE P11,12,(T)S12,(T) -ONE
ZE P11,12,(T)P11,12,(T) -H
ZE P12,13,(T)S12,(T) ONE
ZE P12,13,(T)S13,(T) -ONE
ZE P12,13,(T)P12,13,(T) -H
ZE P13,14,(T)S13,(T) ONE
ZE P13,14,(T)S14,(T) -ONE
ZE P13,14,(T)P13,14,(T) -H
ZE P13,15,(T)S13,(T) ONE
ZE P13,15,(T)S15,(T) -ONE
ZE P13,15,(T)P13,15,(T) -H
ZE P15,16,(T)S15,(T) ONE
ZE P15,16,(T)S16,(T) -ONE
ZE P15,16,(T)P15,16,(T) -H
ZE P17,18,(T)S17,(T) ONE
ZE P17,18,(T)S18,(T) -ONE
ZE P17,18,(T)P17,18,(T) -H
ZE P18,19,(T)S18,(T) ONE
ZE P18,19,(T)S19,(T) -ONE
ZE P18,19,(T)P18,19,(T) -H
ZE P20,21,(T)S20,(T) ONE
ZE P20,21,(T)S21,(T) -ONE
ZE P20,21,(T)P20,21,(T) -H
ZE P21,22,(T)S21,(T) ONE
ZE P21,22,(T)S22,(T) -ONE
ZE P21,22,(T)P21,22,(T) -H
ZE P22,23,(T)S22,(T) ONE
ZE P22,23,(T)S23,(T) -ONE
ZE P22,23,(T)P22,23,(T) -H
ND
OBJECT BOUND
* Solution
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS BRITGAS
TEMPORARIES
R A
R B
R HALFB
R ALPHA
R BETA
R SUM
R RATIO
R BETARA
R BETARF
R ABSLQ
R POWER1
R POWER2
M ABS
GLOBALS
* compresibility coefficients (guesses)
A A 1.0D+0
A B 1.0D+0
A HALFB 5.0D-1 * B
INDIVIDUALS
* horse power from compressor
T HPOWER
A BETA 0.22D+0
A RATIO ABS( R ) ** BETA
A BETARA BETA * RATIO
A BETARF BETARA * F
F F * ( RATIO - 1.0D+0 )
G R BETARF / R
G F RATIO - 1.0D+0
H R R BETARF * ( BETA - 1.0D+0 ) / ( R * R )
H F R BETARA / R
* product of pi and r
T PROD
F PI * R
G PI R
G R PI
H PI R 1.0D+0
* ratio of p over a + b p
T RATIO
A SUM A + B * P
F P / SUM
G P A / SUM ** 2
H P P - 2.0D+0 * A * B / SUM ** 3
* square of p
T SQUARE
F P * P
G P P + P
H P P 2.0D+0
* panhandle term
T PANHAN
A ALPHA 1.8539D+0
A SUM A + HALFB * ( PL + PR )
A ABSLQ ABS( Q )
A POWER1 ABSLQ ** ALPHA
A POWER2 ABSLQ ** ( ALPHA - 1.0D+0 )
F SUM * POWER1
G Q ALPHA * SUM * POWER2
G PL HALFB * POWER1
G PR HALFB * POWER1
H Q Q ALPHA * ( ALPHA - 1.0D+0 ) *
H+ SUM * ABSLQ ** ( ALPHA - 2.0D+0 )
H Q PL HALFB * ALPHA * POWER2
H Q PR HALFB * ALPHA * POWER2
ENDATA