Packing and Drafting in Natural Gas Pipelines

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Summary Increasing and decreasing natural gas pipeline inventory (" packing" and "drafting" ) are examined mathematically. Any line segment's unsteady-state packing or drafting behavior depends on only two dimensionless parameters, packing or drafting behavior depends on only two dimensionless parameters, ( ) and ( ). The influence of ( ) is small, so that for any value of ( ) the behavior of all pipelines can be represented on a single plot; four such plots are shown for four different boundary conditions. Introduction Natural gas dispatchers use increase and decrease of the stored inventory of gas in their pipes as one method of matching time-varying demands with supplies, which generally have less time variation. In pipeline terminology, increasing the inventory (and hence the pressure) is called "line packing," while decreasing it is called "line drafting." This paper examines the limits of this procedure, asking both how much gas can be added to or subtracted from the inventory in a given pipeline segment, and how rapidly this can be accomplished. How Rapidly Can the Inventory Be Depleted or Restored? Although the questions of how large the inventory is and how much can be taken from it for any change in steady-state conditions can be answered very simply, the computation of how rapidly this can be accomplished requires a set of coupled partial differential equations and a numerical solution on a computer. Fortunately, as shown here, the nondimensional results can be summarized in ways that are fairly easy to use. Mathematical Theory It has been known since at least 1951 that the mathematical description of the unsteady-state flow of any gas in a long pipeline is governed by a material-balance equation, ............................(1) and a momentum-balance equation, ............................(2) The mass-balance and momentum equations, expressed with pressure, and mass flow rate, as dependent variables and length, and time, as independent variables and assuming that 's are much smaller than 's and ( / )'s, are ............................(3) and ........................... (4) respectively. The justification for dropping the terms as being much smaller than the others is that changes very slowly with changes in and other variables. JPT p. 655

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