A detailed mathematical model of compressor stations and pipes is essential for optimizing the performance of the gas pipeline system. Most of the available literature on compressor station modeling is based on isothermal solutions for pipe flow, which is inadequate for our purposes. In the present work, the pipe flow is treated as nonisothermal unsteady one-dimensional compressible flow. This is accomplished by treating the compressibility factor as a function of pressure and temperature, and the friction factor as a function of Reynolds number. The solution method is the fully implicit finite difference method that provides solution stability, even for relatively large time steps. The compressors within the compressor station are modeled using centrifugal compressor map-based polynomial equations. This modeling technique permits the designation of different models of compressors in the compressor station. The method can be easily extended to include other types of compressors. Using this mathematical model as a basis, a nonlinear programing problem (NLP) is set up wherein the design variables are the compressor speeds and the objective function to be minimized is the total fuel consumption. The minimum acceptable throughput is imposed as a constraint. This NLP is solved numerically by a sequential unconstrained minimization technique, using the mathematical model of the system for the required function evaluations. The results show that this approach is very effective in reducing fuel consumption. An application of this methodology for selecting the number of compressors to be shut down for the most fuel-efficient operation is also presented. Our results further indicate that station-level optimization produces results comparable to those obtained by network-level optimization. This is very significant because it implies that the optimization can be done locally at the station level, which is computationally much easier.

1.
Botros
,
K. K.
,
Campbell
,
P. J.
,
Mah
,
D. B.
, 1989, “
Dynamic Simulation of Compressor Station Installations Including Control Systems
,”
21st Annual Meeting Pipeline Simulation Interest Group (PSIG)
Oct. 19–20
El Paso
, Texas.
2.
Botros
,
K. K.
,
Campbell
,
P. J.
, and
Mah
,
D. B.
, 1991, “
Dynamic Simulation of Compressor Station Operation Including Centrifugal Compressor and Gas Turbine
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
113
, April, pp.
300
311
.
3.
Botros
,
K. K.
, 1994, “
Transient Phenomena in Compressor Stations During Surge
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
116
, pp.
133
142
.
4.
Bryant
,
M.
, 1997, “
Complex Compressor Station Modeling
,”
29th Annual Meeting Pipeline Simulation Interest Group (PSIG)
, Oct. 15–17,
Tucson
.
5.
Stanley
,
R. A.
, and
Bohannan
,
W. R.
, 1977, “
Dynamic Simulation of Centrifugal Compressor Systems
,”
Proc. of Sixth Turbomachinery Symposium
, Texas A & M Univ., pp.
123
131
.
6.
Turner
,
W. J.
, and
Simonson
,
M. J.
, 1984, “
A Compressor Station Model for Transient Gas Pipeline Simulation
,”
16th Annual Meeting Pipeline Simulation Interest Group (PSIG)
, Oct. 18–19,
Chattanooga
.
7.
Turner
,
W. J.
, and
Simonson
,
M. J.
, 1985, “
Compressor Station Transient Flow Modeled
,”
Oil Gas J.
0030-1388, May 20, pp.
79
83
.
8.
Schultz
,
J. M.
, 1962, “
The Polytropic Analysis Of Centrifugal Compressors
,”
ASME J. Eng. Power
0022-0825, pp.
69
82
.
9.
Odom
,
F. M.
, 1990, “
Turorial on Modeling of Gas Turbine Driven Centrifugal Compressors
,”
22nd Annual Meeting Pipeline Simulation Interest Group (PSIG)
, Oct. 18–19,
Baltimore
.
10.
Carter
,
R. G.
, 1996, “
Compressor Station Optimization: Computational Accuracy and Speed
,”
28th Annual Meeting Pipeline Simulation Interest Group (PSIG)
, Oct. 23–25,
San Francisco
.
11.
Letnowski
,
F. W.
, 1993, “
Compressor Station Modeling in Networks
,”
25th Annual Meeting Pipeline Simulation Interest Group (PSIG)
, Oct. 14–15,
Pittsburgh
.
12.
Jenicek
,
T.
, and
Kralik
,
J.
, 1995, “
Optimized Control of Generalized Compressor Station
,”
27th Annual Meeting Pipeline Simulation Interest Group (PSIG)
, Oct. 18–20,
Albuquerque
.
13.
Botros
,
K. K.
, 1990, “
Thermodynamic Aspects of Gas Recycling During Compressor Surge Control
,”
ASME Proceeding Pipeline Engineering Symposium
, New Orleans,
ASME
, New York, pp.
57
65
.
14.
Boyd
,
E. A.
,
Scott
,
L. R.
, and
Wu
,
S.
, 1997, “
Evaluating the Quality of pipeline Optimization Algorithms
,”
29th Annual Meeting Pipeline Simulation Interest Group (PSIG)
, Oct. 15–17,
Tucson
.
15.
Carter
,
R.
, 1998, “
Pipeline Optimization: Dynamic Programming after 30Years
,”
30th Annual Meeting Pipeline Simulation Interest Group (PSIG)
, Oct. 28–30,
Denver
.
16.
Wu
,
S.
,
Rios-Mercado
,
R. Z.
,
Boyd
,
E. A.
, and
Scott
,
L. R.
, 2000, “
Model Relaxation for the Fuel Cost Minimization of Steady-State Gas Pipeline Networks
,”
Math. Comput. Modell.
0895-7177,
31
(
2-3
), pp.
197
220
.
17.
Cobos-Zaleta
,
D.
, and
Rios-Mercado
,
R. Z.
, “
A MINLP Model for a Minimizing Fuel Consumption on Natural Gas Pipeline Networks
,”
XI Latin-Ibero-American Conference on Operations Research
, Oct. 27–31,
Concepión
, Chile.
18.
Siregar
,
S.
,
Nababan
,
S. M.
,
Saragih
,
R.
,
Nuraini
,
N.
, and
Boestami
,
A.
, 2000, “
The Importance of Gas Pipeline Network Optimization
,”
Proc. of Sixth AEESEAP Triennial Conference
, Aug. 23–25,
Kuta
, Bali, Indonesia.
19.
Edgar
,
T. F.
,
Himmelblau
,
D.
, and
Bickel
,
T. C.
, 1978, “
Optimal Design of Gas Transmission Networks
,”
Society of Petroleum Engineers of ASME
, April, pp.
96
104
.
20.
Osiadacz
,
A. J.
, 1994, “
Dynamic Optimization of High Pressure Gas Networks Using Hierarchical Systems Theory
,”
26th Annual Meeting Pipeline Simulation Interest Group (PSIG)
, Oct. 13–14,
San Diego
.
21.
Issa
,
R. I.
, and
Spalding
,
D. B.
, 1972, “
Unsteady One-Dimensional Compressible Frictional Flow with Heat Transfer
,”
J. Mech. Eng. Sci.
0022-2542,
14
(
6
), pp.
365
369
.
22.
Deen
,
J. K.
, and
Reintsema
,
S. R.
, 1983, “
Modeling of High-Pressure Gas Transmission Lines
,”
Appl. Math. Model.
0307-904X,
7
, pp.
268
273
.
23.
Thorley
,
A. R. D.
, and
Tiley
,
C. H.
, 1987, “
Unsteady and Transient Flow of Compressible Fluids in Pipelines-A Review of Theoretical and Some Experimental Studies
,”
Int. J. Heat Fluid Flow
0142-727X,
8
(
1
), pp.
3
15
.
24.
Price
,
G. R.
,
McBrien
,
R. K.
,
Rizopolus
,
S. N.
, and
Golshan
,
H.
, 1996, “
Evaluating the Effective Friction Factor and Overall Heat Transfer Coefficient During Unsteady Pipeline Operation
,”
International Pipeline Conference
,
ASME
, New York, Vol.
2
, pp.
1175
1182
.
25.
Zemansky
,
M. W.
, 1968, “
Heat and Thermodynamics
,” 5th Edition,
McGraw Hill
.
26.
Kiuchi
,
T.
, 1994, “
An Implicit Method for Transient Gas Flow in Pipe Networks
,”
Int. J. Heat Fluid Flow
0142-727X,
15
(
5
), pp.
378
383
.
27.
Chapman
,
K. S.
, and
Abbaspour
,
M.
, 2003, “
Development of a Virtual Pipeline System Testbed Using Non-isothermal Transient Simulation
,”
GMC 2003 Conference
, Oct. 6–8,
Salt Lake City
.
28.
Abbaspour
,
M.
,
Chapman
,
K. S.
, and
Keshavarz
,
A.
, “
Non-isothermal Transient Gas Pipeline Simulation Using Fully Implicit Method
,”
Numer. Heat Transfer J.
(submitted).
29.
Abbaspour
,
M.
,
Chapman
,
K. S.
, and
Keshavarz
,
A.
, “
Dynamic modeling of non-isothermal gas pipeline system
,”
International Pipeline Conference, ASME
, IPC-0081, Oct. 4–8, 2004, Calgary, Canada.
30.
Fiacco
,
A. V.
, and
McCormick
,
G. P.
, 1968, “
Nonlinear Programming: Sequential Unconstrained Minimization Techniques
,”
Wiley
, New York.
You do not currently have access to this content.