Steady-state simulation and fuel cost minimization of gas pipeline networks

Natural gas, driven by pressure, is transported through pipeline networks. As it flows over distances through a network, energy, and so pressure, is lost due to both the friction of pipes and heat transfer between the gas and its environment. The lost energy of the gas is periodically added at the compressor stations which are installed in the network. These compressor stations consume about 3-5% of the transported gas. This transportation cost is significant because the amount of gas being transported worldwide is huge. According to the U.S. petroleum statistics, the U.S. natural gas consumption in 1996 was 21.9* {dollar}rm Tcfspdag.{dollar} Suppose the average transportation cost is 4%, then the actual amount of the gas supplied was 22.81 Tcf, and so the transportation cost was 0.91 Tcf, or, in U.S. dollars, {dollar}4.86spddagger{dollar} billion dollars. Thus, a 1% savings on the transportation cost is worth of 48.6 million dollars. On the other hand, reports from gas industry experts, see (29), show that, "The rigorous optimization of operations should save at least 20% of the fuel (consumed in gas transportation)." These make the problem of how to minimize the fuel cost for the gas pipeline networks significantly important.; The mathematical model of the fuel cost minimization problem could be very complicated by the existence of both complex network structures and sophisticated compressor stations.; In the real world, a typical compressor station itself could have several identical or different types of compressor units installed with various configurations. Operating a compressor station means turning on or off some or all of those units and setting the speeds for the units turned on. It turns out that, for a specific requirement to a compressor station, there are several different ways to operate the station to achieve the given requirement, each with the fuel cost different from the other. This implies that there is a subproblem which deals with minimizing fuel cost within a single compressor station. A mathematical model of minimizing fuel cost for a single compressor station has been studied by Wu, Boyd, and Scott in (30).; The focus of the thesis, however, is on the problem of minimizing the fuel cost for gas pipeline networks. Thus, the variables associated with compressor stations must also satisfy the network flow constraints. In this work, we have established a complete mathematical model of the steady-state flow for gas pipeline networks. By making use of the results from graph theory and functional analysis, we have proved the uniqueness and existence of the solution to a system of nonlinear algebraic equations arising from pipeline network flows. Based on the result, a network decomposition method is introduced which greatly reduces the size and simplifies the difficulty of the problem. We also have developed a lower bound procedure to find good lower bounds of the solution to the problem. Finally, a few sample data of gas pipeline networks are established and numerical experiments with these data have been carried out. ftn*Data are cited from Independent Petroleum Association of America (IPAA), http://www.ipaa.org/ {dollar}rmspdag1 Tcf = 10sp{lcub}12{rcub}{dollar} cubic feet {dollar}spddagger{dollar}According to IPAA, the commercial price in 1996 was {dollar}5.33/Mcf, where 1 {dollar}Mcf = 10 sp3{dollar} cubic feet.