Transient-State Natural Gas Transmission in Gunbarrel Pipeline Networks

We study the energy consumption minimization problems of natural gas transmission in gunbarrel structured networks. In particular, we consider the transient-state dynamics of natural gas and the compressor’s nonlinear working domain and min-up-and-down constraints. We formulate the problem as a two-level dynamic program (DP), where the upper-level DP problem models each compressor station as a decision stage and each station’s optimization problem is further formulated as a lower-level DP by setting each time period as a stage. The upper-level DP faces the curse of high dimensionality. We propose an approximate dynamic programming (ADP) approach for the upper-level DP using appropriate basis functions and an exact approach for the lower-level DP by exploiting the structure of the problem. We validate the superior performance of the proposed ADP approach on both synthetic and real networks compared with the benchmark simulated annealing (SA) heuristic and the commonly used myopic policy and steady-state policy. On the synthetic networks (SNs), the ADP reduces the energy consumption by 5.8%–6.7% from the SA and 12% from the myopic policy. On the test gunbarrel network with 21 compressor stations and 28 pipes calibrated from China National Petroleum Corporation, the ADP saves 4.8%–5.1% (with an average of 5.0%) energy consumption compared with the SA and the currently deployed steady-state policy, which translates to cost savings of millions of dollars a year. Moreover, the proposed ADP algorithm requires 18.4%–61.0% less computation time than the SA. The advantages in both solution quality and computation time strongly support the proposed ADP algorithm in practice.