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RESEARCH PAPERS

# Transient Optimization in Natural Gas Compressor Stations for Linepack Operation

[+] Author and Article Information
M. Abbaspour

Gregg Engineering, Inc., 403 Julie Rivers Drive, Sugar Land, TX 77479

P. Krishnaswami

Department of Mechanical and Nuclear Engineering, Kansas State University, 3002 Rathbone Hall, Manhattan, KS 66506

K. S. Chapman

National Gas Machinery Laboratory, Kansas State University, 3002 Rathbone Hall, Manhattan, KS 66506

J. Energy Resour. Technol 129(4), 314-324 (Aug 03, 2007) (11 pages) doi:10.1115/1.2790983 History: Received August 23, 2006; Revised August 03, 2007

## Abstract

One of the key factors in the operation of a natural gas pipeline network is the linepack in the network. The desired operation of the network as derived from estimated receipts and deliveries is expressed in terms of the desired linepack profile that must be maintained. The compressor stations in the pipeline network are then operated in a manner that generates this linepack profile. Generally, the operating points selected for the units in the compressor stations are based on experience and experimentation and are therefore not optimal. In this paper, we present a systematic approach for operating the units of a compressor station to meet a specified linepack profile. The first step in developing this approach is the derivation of a numerical method for analyzing the flow through the pipeline under transient nonisothermal conditions. We have developed and verified a fully implicit finite difference formulation that provides this analysis capability. Next, the optimization of the compressor stations is formulated as a standard nonlinear programing problem in the following form: Find the values in the design variable vector denoted by $b=[b1,b2,…,bn]T$, to minimize a given objective function $F(b)$, subject to the constraints $gj(b)⩽0$, $j=1,…,m$. Here, $n$ is the number of operational parameters whose optimal value is to be determined, while $m$ is the number of operational constraints that must be enforced. In our formulation, the design variables are chosen to be the operating speeds of the units in the compressor stations, while the objective function is taken to be the average fuel consumption rate over the interval of interest, summed over all units. The constraint functions $gj(b)$ are formulated suitably to ensure that operational limits are met at the final solution that is obtained. The optimization problem is then solved using a sequential unconstrained minimization technique (SUMT), in conjunction with a directed grid search method for solving the unconstrained subproblems that are encountered in the SUMT formulation. The evaluation of the objective function and constraint functions at each step of the optimization is done by using the fully implicit analysis method mentioned above. A representative numerical example has been solved by the proposed approach. The results obtained indicate that the method is very effective in finding operating points that are optimal with respect to fuel consumption. The optimization can be done at the level of a single unit, a single compressor station, a set of compressor stations, or an entire network. It should also be noted that the proposed solution approach is fully automated and requires no user involvement in the solution process.

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## Figures

Figure 8

Variation of compressor speeds for transient optimization with 30min subintervals (Case 4)

Figure 9

Variation of pressure for transient optimization in every 30min

Figure 7

Average fuel consumption of system for different time periods

Figure 6

Variation of isentropic efficiency with respect to operating time for each compressor

Figure 5

Variation of fuel consumption with respect to operating time for each compressor

Figure 4

Variation of discharge temperature with respect to operating time

Figure 3

Variation of pressure at different points of system with respect to operating time

Figure 2

Mass flow rate at different points in the system with respect to operating time

Figure 1

Schematic of compressor stations

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