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Utility systems operational planning optimization based on pipeline network simulation
16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering W. Marquardt, C. Pantelides (Editors) © 2006 Published by Elsevier B.V.
Utility systems operational planning optimization based on pipeline network simulation Luo X.L. a, Hua B.a, Zhang B.J. a, Lu M.L. b
aThe Key Lab of Enhanced Heat Transfer and Energy Conservation, Ministry of Education of China, South China University of Technology, Guangzhou, 510640, China bAspen Technology Inc. 10 Canal Park, Cambridge, MA 02141, USA
Abstract In this paper, an analysis on the negative impact of steam parameters change on utility system and process operations is conducted, which is not reported previously. In order to avoid the impact, a method that integrates utility system operational planning optimization with pipeline network simulation has been developed. A multiperiod mixed integer non-linear programming (MINLP) model is developed and a decomposed iteration algorithm is applied to solve this model, which is demonstrated in an industrial case study.
Keywords: Utility system; Optimization; Pipeline network; Simulation; MINLP 1. I N T R O D U C T I O N Utility system is an important part of the process industry and several efforts on the design and operation of utility system have been reported. Papoulias and Grossmann (1983) described mixed integer linear programming (MILP) model for the optimization of the structure and parameter of utility system under fixed demand. Hui and Natori (1996) presented a mixed-integer formulation of multiperiod design and operational planning for utility system and discussed the industrial application of this problem. Oliveira Francisco (2004) extended the multiperiod synthesis and operational planning model by including the global emissions of atmospheric pollutants issues coming from the fuels burning. However, most of these efforts assume fixed steam and power demand from processes and emphasize on the utility production and distribution, and none of them consider the utility parameters change within the pipeline network. In fact, the steam parameters usually fluctuate greatly when steam passes through pipeline network. Some of the steam branches reaching the process users are degraded greatly and fail to meet the requirement and even impact the process operation. Therefore steam sources parameters or flowrates must be increased to overcome the above problem. Inevitably, the operation of the whole utility system deviated from the initial conditions and the optimal schedule without involving pipeline network simulation was not the optimal solution. This paper presents a method that integrates utility system operational planning optimization with pipeline network simulation and a multiperiod mixed integer non-linear programming (MINLP) model is developed. The MINLP model involves a large number of continuous, discrete decisions variables, non-linear constraints and is difficult to solve. A decomposed iteration approach is applied to solve this problem and the optimal solution can be reached within a reasonable time. A case study shows that using the proposed method, significant savings can be obtained by optimizing the utility system operation at no capital investment as well as steady and safety process operation can be ensured.
489
490
X.L. Luo et al.
2. PROBLEM
FORMULATION
The utility system operational planning problem is modeled with a complex M1NLP model that is an extension of the multiperiod models described by Iyer and Grossmann (1997). The objective function includes the fixed and variable costs of equipments, costs of purchased power and steam for each period as well as the changeover costs between periods. Following are the objective function and the constraint equations of the proposed utility system multiperiod operational planning optimization problem. Objective function MinCost = Z Z CEF, × Y,t + Z Z ( Z FF"it X C j~ + ,
.
,
.
i
(1)
CWF,t ×Cow +C, x Z O , t ) + Z C w ×WF t + Z Z c s r t
t
×SFrt
r
The mass balance of equipment n
ZF.,in,t-ZF~,out,t -0 in
(2)
n~S,t~T
out
The energy balance of equipment n Im,,,u,u,,,,,wq
~
~_~F.,in,,hns.,t-ZX.,ou,,,h.,out,t-W.t-S..h.~ , - 0 in
.~ N,t~ V
(3)
out
The equipment capacity bounds
L < F F n ,in m
n ,
i. , t < f~ uF n ,in B
~-~ L < Fn,out,t < ~-~ uF n ,out F n ,out ~ ~
(4)
n~N,t~T n~ N,t~
T
(5)
The power and steam demand constraints t~ T
(6)
r ~ R, t ~ T
(7)
The equipment changeover constraints ZO ., > Y., - Y.,t_I n ~ N,t ~ T
(8)
The fuel supply bounds constraints F F nit <- ~-~ UFi,,
(9)
WFt + Z
Wnt
~ DWt
n
SF~, + ~ S.n >- D S ~, n
i~I,t~T
n
Steam enthalpy is the function of pressure and temperature h- f (P,T) Pressure drop in pipej in period t
~ (j~ 4 0 •11 ejd 1.25 J ~ dj j P jt .... ke K j Temperature drop in pipej in period t •c.(dj + 26oj + 26j). (Tj,. . . . . - - T a ) L j ATj, dj +260j +26j dj +260j +26j 1 In + 22j .m j, . Cp,j, dj + 260j %, .m j, . Cp,j, Ap jt = 0.811
mj,
P jt ....
(lO) je J, te T
(11)
j ~ J,t ~ T
(12)
"
Steam flowrate of pipej that pass through node d in period t
) - mdjt --0 d ~ D,t ~ T J Steam sink parameter bounds constraints
(13)
Utility Systems Operational Planning Optimization
491
P~ < Psi < P f
s~ S,t~ T
(14)
T~L < T~t < Tsu
s ~ S, t ~ T
(15)
The improved drive turbine model involves steam parameters change (Liu Jinping, 2002) W - a + b. mr,ac t - mr,ac t (Z~l" Kae 1 + A T 1 • KAr 1)
(16)
The calculated steam heat flowrate considered parameters change m ~,,a~t - f (P~,, T~t, m ~t,dem )
S ~ S, t ~ T
(17)
3. M O D E L S O L V I N G S T R A T E G Y It usually fails to guarantee robust convergence and global optimality if the MINLP model presented above is applied directly. Fortunately, it is possible to overcome this difficulty by decomposing the problem into two sub-problems and solve them by a three-step iteration algorithm developed in this paper. One sub-problem is utility system operational planning optimization (USOPO) that involves the MILP model as illustrated from Eqs.(1) to Eqs.(9). The other sub-problem is pipeline network simulation (PNS) that involves non-linear model as illustrated from Eqs.(10) to Eqs.(13). To solve this model, the first step of the proposed algorithm solves the USOPO problem (MILP model) under fixed utility demand and steam parameters. This is followed by the second step of rigorous PNS (non-linear model) and the steam parameters are calculated for every sink. In the third step, the steam sink parameters are checked and the steam source parameters or fiowrates are adjusted according to Eqs. (16) and (17). The linear optimization of the first step is repeated, followed again by the pipeline network simulation of the second step. It iterates until the problem converges. This is illustrated in Figure 1 where k denotes the iteration times. The global optimality of the MILP model and the rigorous of pipeline network simulation guarantee the global optimality of the decomposition algorithm. Besides, the algorithm is characterized by rapid convergence of no more than five iterations to reach reasonably small error levels. In this paper, the USOPO problem model is developed using the General Algebraic Modeling System-GAMS and solved using Cplex while the PNS problem is solved using PIPEPHASE 8.1 package. Begin ) I MILP Optimization I ÷ [Pipe network simmulation I [ Adjust source param eters 1 P ..... T ...... I ÷
N
[Adjust . . . . . . fl . . . . t . . . . .~.
-~y
(End)
Fig. 1 The solving procedure of utility system optimization
492
X..L. L u o e t al.
4. C A S E S T U D Y Figure 2 shows the flowsheet of the utility system and the pipeline network of a Chinese oil refinery. Table 1 gives the data of steam source parameters and fiowrates for the operation of the utility plant in a year horizon consisting of three periods of equal length. In table 1, the symbol "/" denotes that the data is under calculating. The estimated demand of steam flowrate of each sink in each period is illustrated as mest in Table 3. The utility system component model (Luo XiangLong, 2006) is applied in this case.
gSTq 777N crSN L011.
L 02.1,
.oo
~
L15
_
~lkL 13
6
_
HPHC
[
[
Gas Sep
Acrylic Fibres Plant
MTBE
Utility Plant
Condenser
Lube Plant
Polymer Plant
Fig.2 The flowsheet of utility system and pipe network of an oil refinery Using the proposed method and algorithm, the optimal results are obtained in the third iteration. The minimum annual cost is $9,286,328 and more than $800,000 is saved compare with the planning schedule made by the refinery. The optimal utility operational planning results are illustrated in Table 2 where mori and mopti denote the optimal flowrates schedule before and after pipeline network simulation respectively. The simulated steam sink parameters and flowrates in each period are illustrated as Pact, Tact, mact in Table 3. Table 2 also shows that the utility optimal planning schedule changes greatly even though the steam demand does not increase very much. And the steam sources parameters need not to change in this case but the steam sinks parameters do change a lot as shown in Table 3. Table 1 The steam sources parameters and flowrates P ......
Tsource
m ...... (tflil)
(MPa)
(°C)
1
2
3
MP
3.43
430
/
/
/
P01
Mp
1.02
285
73
45
40
P01
LP
3.39
425
50
60
50
P02
LP
1.00
290
43
45
46
Source
Steam
B1, B2, B3
Table 2 The utility system optimization result comparison
Utility Systems Operational Planning Optimization
Period
mori
(t/h)
B1
B2
B3
T1
T2
T3
493
Vl
mopti
(t/h)
B1
B2
B3
T1
T2
T3
V1
1
60
0
130
85
85
27.4
8
60
0
130
85.0
85
21.9
5.5
2
0
0
130
82
0
0
28
0
30
130
52.6
85
20.0
0
3
60
0
0
41
0
22.0
0
60
0
0
40.0
0
11.5
0
Table 3 The estimated and simulated steam parameters and flowrates demand by steam sinks Sink
Steam
mest(t/h)
Pact(MPa)
Tact(°C)
1
2
3
1
2
3
1
85
80
69
3.34
3.34
3 . 3 5 418
mact(t/h)
2
3
1
2
3
418
416
8 7 . 5 8 2 . 4 71.0
P02
MP
P03
LP
50
40
15
0.90
0 . 9 5 0.99
280
286
286
5 0 . 5 40.1
15.1
P04
LP
50
45
25
0 . 9 3 0 . 9 5 0.98
277
276
264
5 0 . 5 45.5
25.5
P05
LP
55
50
30
0 . 7 8 0.86
0.96
276
274
265
5 5 . 5 50.6
30.6
P06
LP
40
30
10
0.80
0.88
0.97
276
272
251
40.3
30.4
10.3
P07
LP
50
40
25
0.72
0.84
0 . 9 5 266
261
247
5 0 . 5 40.9
25.9
5. C O N C L U S I O N This paper presents a new method to overcome the negative impact of steam parameters change in the pipeline network. A decomposed iteration algorithm is presented to solve the complex multiperiod mixed integer non-linear programming problem. A case study shows that using the proposed method the optimal operational planning schedule can be obtained in a reasonable time as well as steady and safety process operation can be ensured. Compared with the previous efforts, the method presented in this paper brings the optimization much closer to the real engineering operation, and the scheduling is more applicable. Besides, if power demand is considered, more significant benefits can be expected by applying the proposed method. ACKNOWLEDGEMENTS
The authors wish to acknowledge the financial supports from the Major State Basic Research Development Program (G2000026307). NOMENCLATURE
Sets I/i N/n D/d
set of fuel J/j set of pipe set of equipment S/s set of steam sink set of pipeline network node K/k
T/t R/r
set of period set of steam main level set of pipe local resistance
Parameters a, b C:~
Cw CEFn
model coefficients unit price of fuel i unit price of purchased power maintain cost of equipment n
C~w Cn C~r dj.
unit price of cold water equipment startup cost unit price of steam of level r diameter of pipej
X.L. Luo et al.
494
DWt
T~ DSrt K~p1
K~n mst, dem ~'~Fn, i / ~'~Fn, ou L ~'~Fn, in U ~'~Fn, out U ~"~Fi,t v
pL, p U
power demand in period t L/ length of pipej surrounding temperature rio/ thickness of pipej insulation thickness of pipej e/ roughness of pipe j demand of steam of level r in period t specific decreased power production for the inlet pressure drop specific decreased power production for the inlet temperature drop steam flowrate demand of sink s before steam parameters change in period t lower bound of inlet steam rate of equipment n lower bound of outlet steam rate of equipment n upper bound of inlet steam rate of equipment n upper bound of outlet steam rate of equipment n upper bound flowrate of fuel i in period t lower and upper bound of steam temperature of sink s lower and upper bound of steam temperature of sink s heat conductivity of insulation of pipe j local resistance coefficient of pipe j
Binary variable Ynt ZOnt
1 if equipment n operate in period t; 0 otherwise 1 if equipment n incurs startup cost in period t; 0 otherwise
Variable
Cp,jt ~t n, in, t n, out, t
CWF.t FFnit hn, in, t
hn,out,t hnrt roT,act
Is, SFrt Snrt
T~, Tjt, aver
W., aj~ Pjt, aver
AP1
AT1
steam specific in pipe j in period t W power production of turbine steam flowrate of pipej in period t WFt purchased power in period t stream flowrate enter equipment n in period t stream flowrate exit equipment n in period t cold water flowrate of unit n in period t flowrate of fuel i that equipment n consumes in period t specific enthalpy of stream that enter equipment n in period t specific enthalpy of stream that exit equipment n in period t steam enthalpy of level r produced in equipment n steam flowrate demand of turbine after steam parameters change steam pressure of sink s in period t purchased steam flowrate of level r in period t steam production rate of level r in equipment n in period t steam temperature of sink s in period t average steam temperature of pipe j in period t power production of equipment n in period t heat exchange coefficient between insulation of pipe j and surrounding average steam density in pipe j in period t pressure drop of steam enter turbine temperature drop of steam enter turbine
REFERENCE Papoulias, S. A, Grossmann, I. E, 1983, A structural optimisation approach in process synthesis--l: utility systems. Comput. Chem. Engng, 19:481-488 Chi-Wai Hui,Yukikazu Natori, 1996, An industrial application using mixed-integer programming technique: a multiperiod utility system model. Comput. Chem. Engng, 20(Supplement 2): 1577-1582.
Utility Systems Operational Planning Optimization
495
A. P. Oliveira Francisco, H. A. Matos, 2004, Multiperiod synthesis and operational planning of utilitysystems with environmental concerns, Comput. Chem. Engng, 2004, 28: 745-753. Iyer, R.. and Grossmann, I. E., 1997, Optimal multiperiod operational planning for utility systems. Computers and Chemical Engineering, 21 (8), 787-800. Liu Jinping, 2002, Study on the Theory and Application of Hierarchical modeling of Steam Power System in Process Industry, Ph.D thesis, SCUT ,China. LUO XiangLong, HUA Ben and ZHANG BingJian, 2006, Optimal multiperiod operational planning for steam power system of petrochemical industry, Computers and applied chemistry, 23 (1): 41-45.
Utility systems operational planning optimization based on pipeline network simulation Luo X.L. a, Hua B.a, Zhang B.J. a, Lu M.L. b
aThe Key Lab of Enhanced Heat Transfer and Energy Conservation, Ministry of Education of China, South China University of Technology, Guangzhou, 510640, China bAspen Technology Inc. 10 Canal Park, Cambridge, MA 02141, USA
Abstract In this paper, an analysis on the negative impact of steam parameters change on utility system and process operations is conducted, which is not reported previously. In order to avoid the impact, a method that integrates utility system operational planning optimization with pipeline network simulation has been developed. A multiperiod mixed integer non-linear programming (MINLP) model is developed and a decomposed iteration algorithm is applied to solve this model, which is demonstrated in an industrial case study.
Keywords: Utility system; Optimization; Pipeline network; Simulation; MINLP 1. I N T R O D U C T I O N Utility system is an important part of the process industry and several efforts on the design and operation of utility system have been reported. Papoulias and Grossmann (1983) described mixed integer linear programming (MILP) model for the optimization of the structure and parameter of utility system under fixed demand. Hui and Natori (1996) presented a mixed-integer formulation of multiperiod design and operational planning for utility system and discussed the industrial application of this problem. Oliveira Francisco (2004) extended the multiperiod synthesis and operational planning model by including the global emissions of atmospheric pollutants issues coming from the fuels burning. However, most of these efforts assume fixed steam and power demand from processes and emphasize on the utility production and distribution, and none of them consider the utility parameters change within the pipeline network. In fact, the steam parameters usually fluctuate greatly when steam passes through pipeline network. Some of the steam branches reaching the process users are degraded greatly and fail to meet the requirement and even impact the process operation. Therefore steam sources parameters or flowrates must be increased to overcome the above problem. Inevitably, the operation of the whole utility system deviated from the initial conditions and the optimal schedule without involving pipeline network simulation was not the optimal solution. This paper presents a method that integrates utility system operational planning optimization with pipeline network simulation and a multiperiod mixed integer non-linear programming (MINLP) model is developed. The MINLP model involves a large number of continuous, discrete decisions variables, non-linear constraints and is difficult to solve. A decomposed iteration approach is applied to solve this problem and the optimal solution can be reached within a reasonable time. A case study shows that using the proposed method, significant savings can be obtained by optimizing the utility system operation at no capital investment as well as steady and safety process operation can be ensured.
489
490
X.L. Luo et al.
2. PROBLEM
FORMULATION
The utility system operational planning problem is modeled with a complex M1NLP model that is an extension of the multiperiod models described by Iyer and Grossmann (1997). The objective function includes the fixed and variable costs of equipments, costs of purchased power and steam for each period as well as the changeover costs between periods. Following are the objective function and the constraint equations of the proposed utility system multiperiod operational planning optimization problem. Objective function MinCost = Z Z CEF, × Y,t + Z Z ( Z FF"it X C j~ + ,
.
,
.
i
(1)
CWF,t ×Cow +C, x Z O , t ) + Z C w ×WF t + Z Z c s r t
t
×SFrt
r
The mass balance of equipment n
ZF.,in,t-ZF~,out,t -0 in
(2)
n~S,t~T
out
The energy balance of equipment n Im,,,u,u,,,,,wq
~
~_~F.,in,,hns.,t-ZX.,ou,,,h.,out,t-W.t-S..h.~ , - 0 in
.~ N,t~ V
(3)
out
The equipment capacity bounds
L < F F n ,in m
n ,
i. , t < f~ uF n ,in B
~-~ L < Fn,out,t < ~-~ uF n ,out F n ,out ~ ~
(4)
n~N,t~T n~ N,t~
T
(5)
The power and steam demand constraints t~ T
(6)
r ~ R, t ~ T
(7)
The equipment changeover constraints ZO ., > Y., - Y.,t_I n ~ N,t ~ T
(8)
The fuel supply bounds constraints F F nit <- ~-~ UFi,,
(9)
WFt + Z
Wnt
~ DWt
n
SF~, + ~ S.n >- D S ~, n
i~I,t~T
n
Steam enthalpy is the function of pressure and temperature h- f (P,T) Pressure drop in pipej in period t
~ (j~ 4 0 •11 ejd 1.25 J ~ dj j P jt .... ke K j Temperature drop in pipej in period t •c.(dj + 26oj + 26j). (Tj,. . . . . - - T a ) L j ATj, dj +260j +26j dj +260j +26j 1 In + 22j .m j, . Cp,j, dj + 260j %, .m j, . Cp,j, Ap jt = 0.811
mj,
P jt ....
(lO) je J, te T
(11)
j ~ J,t ~ T
(12)
"
Steam flowrate of pipej that pass through node d in period t
) - mdjt --0 d ~ D,t ~ T J Steam sink parameter bounds constraints
(13)
Utility Systems Operational Planning Optimization
491
P~ < Psi < P f
s~ S,t~ T
(14)
T~L < T~t < Tsu
s ~ S, t ~ T
(15)
The improved drive turbine model involves steam parameters change (Liu Jinping, 2002) W - a + b. mr,ac t - mr,ac t (Z~l" Kae 1 + A T 1 • KAr 1)
(16)
The calculated steam heat flowrate considered parameters change m ~,,a~t - f (P~,, T~t, m ~t,dem )
S ~ S, t ~ T
(17)
3. M O D E L S O L V I N G S T R A T E G Y It usually fails to guarantee robust convergence and global optimality if the MINLP model presented above is applied directly. Fortunately, it is possible to overcome this difficulty by decomposing the problem into two sub-problems and solve them by a three-step iteration algorithm developed in this paper. One sub-problem is utility system operational planning optimization (USOPO) that involves the MILP model as illustrated from Eqs.(1) to Eqs.(9). The other sub-problem is pipeline network simulation (PNS) that involves non-linear model as illustrated from Eqs.(10) to Eqs.(13). To solve this model, the first step of the proposed algorithm solves the USOPO problem (MILP model) under fixed utility demand and steam parameters. This is followed by the second step of rigorous PNS (non-linear model) and the steam parameters are calculated for every sink. In the third step, the steam sink parameters are checked and the steam source parameters or fiowrates are adjusted according to Eqs. (16) and (17). The linear optimization of the first step is repeated, followed again by the pipeline network simulation of the second step. It iterates until the problem converges. This is illustrated in Figure 1 where k denotes the iteration times. The global optimality of the MILP model and the rigorous of pipeline network simulation guarantee the global optimality of the decomposition algorithm. Besides, the algorithm is characterized by rapid convergence of no more than five iterations to reach reasonably small error levels. In this paper, the USOPO problem model is developed using the General Algebraic Modeling System-GAMS and solved using Cplex while the PNS problem is solved using PIPEPHASE 8.1 package. Begin ) I MILP Optimization I ÷ [Pipe network simmulation I [ Adjust source param eters 1 P ..... T ...... I ÷
N
[Adjust . . . . . . fl . . . . t . . . . .~.
-~y
(End)
Fig. 1 The solving procedure of utility system optimization
492
X..L. L u o e t al.
4. C A S E S T U D Y Figure 2 shows the flowsheet of the utility system and the pipeline network of a Chinese oil refinery. Table 1 gives the data of steam source parameters and fiowrates for the operation of the utility plant in a year horizon consisting of three periods of equal length. In table 1, the symbol "/" denotes that the data is under calculating. The estimated demand of steam flowrate of each sink in each period is illustrated as mest in Table 3. The utility system component model (Luo XiangLong, 2006) is applied in this case.
gSTq 777N crSN L011.
L 02.1,
.oo
~
L15
_
~lkL 13
6
_
HPHC
[
[
Gas Sep
Acrylic Fibres Plant
MTBE
Utility Plant
Condenser
Lube Plant
Polymer Plant
Fig.2 The flowsheet of utility system and pipe network of an oil refinery Using the proposed method and algorithm, the optimal results are obtained in the third iteration. The minimum annual cost is $9,286,328 and more than $800,000 is saved compare with the planning schedule made by the refinery. The optimal utility operational planning results are illustrated in Table 2 where mori and mopti denote the optimal flowrates schedule before and after pipeline network simulation respectively. The simulated steam sink parameters and flowrates in each period are illustrated as Pact, Tact, mact in Table 3. Table 2 also shows that the utility optimal planning schedule changes greatly even though the steam demand does not increase very much. And the steam sources parameters need not to change in this case but the steam sinks parameters do change a lot as shown in Table 3. Table 1 The steam sources parameters and flowrates P ......
Tsource
m ...... (tflil)
(MPa)
(°C)
1
2
3
MP
3.43
430
/
/
/
P01
Mp
1.02
285
73
45
40
P01
LP
3.39
425
50
60
50
P02
LP
1.00
290
43
45
46
Source
Steam
B1, B2, B3
Table 2 The utility system optimization result comparison
Utility Systems Operational Planning Optimization
Period
mori
(t/h)
B1
B2
B3
T1
T2
T3
493
Vl
mopti
(t/h)
B1
B2
B3
T1
T2
T3
V1
1
60
0
130
85
85
27.4
8
60
0
130
85.0
85
21.9
5.5
2
0
0
130
82
0
0
28
0
30
130
52.6
85
20.0
0
3
60
0
0
41
0
22.0
0
60
0
0
40.0
0
11.5
0
Table 3 The estimated and simulated steam parameters and flowrates demand by steam sinks Sink
Steam
mest(t/h)
Pact(MPa)
Tact(°C)
1
2
3
1
2
3
1
85
80
69
3.34
3.34
3 . 3 5 418
mact(t/h)
2
3
1
2
3
418
416
8 7 . 5 8 2 . 4 71.0
P02
MP
P03
LP
50
40
15
0.90
0 . 9 5 0.99
280
286
286
5 0 . 5 40.1
15.1
P04
LP
50
45
25
0 . 9 3 0 . 9 5 0.98
277
276
264
5 0 . 5 45.5
25.5
P05
LP
55
50
30
0 . 7 8 0.86
0.96
276
274
265
5 5 . 5 50.6
30.6
P06
LP
40
30
10
0.80
0.88
0.97
276
272
251
40.3
30.4
10.3
P07
LP
50
40
25
0.72
0.84
0 . 9 5 266
261
247
5 0 . 5 40.9
25.9
5. C O N C L U S I O N This paper presents a new method to overcome the negative impact of steam parameters change in the pipeline network. A decomposed iteration algorithm is presented to solve the complex multiperiod mixed integer non-linear programming problem. A case study shows that using the proposed method the optimal operational planning schedule can be obtained in a reasonable time as well as steady and safety process operation can be ensured. Compared with the previous efforts, the method presented in this paper brings the optimization much closer to the real engineering operation, and the scheduling is more applicable. Besides, if power demand is considered, more significant benefits can be expected by applying the proposed method. ACKNOWLEDGEMENTS
The authors wish to acknowledge the financial supports from the Major State Basic Research Development Program (G2000026307). NOMENCLATURE
Sets I/i N/n D/d
set of fuel J/j set of pipe set of equipment S/s set of steam sink set of pipeline network node K/k
T/t R/r
set of period set of steam main level set of pipe local resistance
Parameters a, b C:~
Cw CEFn
model coefficients unit price of fuel i unit price of purchased power maintain cost of equipment n
C~w Cn C~r dj.
unit price of cold water equipment startup cost unit price of steam of level r diameter of pipej
X.L. Luo et al.
494
DWt
T~ DSrt K~p1
K~n mst, dem ~'~Fn, i / ~'~Fn, ou L ~'~Fn, in U ~'~Fn, out U ~"~Fi,t v
pL, p U
power demand in period t L/ length of pipej surrounding temperature rio/ thickness of pipej insulation thickness of pipej e/ roughness of pipe j demand of steam of level r in period t specific decreased power production for the inlet pressure drop specific decreased power production for the inlet temperature drop steam flowrate demand of sink s before steam parameters change in period t lower bound of inlet steam rate of equipment n lower bound of outlet steam rate of equipment n upper bound of inlet steam rate of equipment n upper bound of outlet steam rate of equipment n upper bound flowrate of fuel i in period t lower and upper bound of steam temperature of sink s lower and upper bound of steam temperature of sink s heat conductivity of insulation of pipe j local resistance coefficient of pipe j
Binary variable Ynt ZOnt
1 if equipment n operate in period t; 0 otherwise 1 if equipment n incurs startup cost in period t; 0 otherwise
Variable
Cp,jt ~t n, in, t n, out, t
CWF.t FFnit hn, in, t
hn,out,t hnrt roT,act
Is, SFrt Snrt
T~, Tjt, aver
W., aj~ Pjt, aver
AP1
AT1
steam specific in pipe j in period t W power production of turbine steam flowrate of pipej in period t WFt purchased power in period t stream flowrate enter equipment n in period t stream flowrate exit equipment n in period t cold water flowrate of unit n in period t flowrate of fuel i that equipment n consumes in period t specific enthalpy of stream that enter equipment n in period t specific enthalpy of stream that exit equipment n in period t steam enthalpy of level r produced in equipment n steam flowrate demand of turbine after steam parameters change steam pressure of sink s in period t purchased steam flowrate of level r in period t steam production rate of level r in equipment n in period t steam temperature of sink s in period t average steam temperature of pipe j in period t power production of equipment n in period t heat exchange coefficient between insulation of pipe j and surrounding average steam density in pipe j in period t pressure drop of steam enter turbine temperature drop of steam enter turbine
REFERENCE Papoulias, S. A, Grossmann, I. E, 1983, A structural optimisation approach in process synthesis--l: utility systems. Comput. Chem. Engng, 19:481-488 Chi-Wai Hui,Yukikazu Natori, 1996, An industrial application using mixed-integer programming technique: a multiperiod utility system model. Comput. Chem. Engng, 20(Supplement 2): 1577-1582.
Utility Systems Operational Planning Optimization
495
A. P. Oliveira Francisco, H. A. Matos, 2004, Multiperiod synthesis and operational planning of utilitysystems with environmental concerns, Comput. Chem. Engng, 2004, 28: 745-753. Iyer, R.. and Grossmann, I. E., 1997, Optimal multiperiod operational planning for utility systems. Computers and Chemical Engineering, 21 (8), 787-800. Liu Jinping, 2002, Study on the Theory and Application of Hierarchical modeling of Steam Power System in Process Industry, Ph.D thesis, SCUT ,China. LUO XiangLong, HUA Ben and ZHANG BingJian, 2006, Optimal multiperiod operational planning for steam power system of petrochemical industry, Computers and applied chemistry, 23 (1): 41-45.