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This paper was prepared for the Society of Petroleum Engineers Gas Technology Symposium to be held in Omaha, Nebr. Sept. 15–16, 1966. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon requested to the Editor of the appropriate journal, provided agreement to give proper credit is made.
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This paper attacks the problem of computing transient flow in gas pipeline networks by means of finite differences and digital computation. Pressure (P) and flow (Q) are assumed to he dependent upon a single space variable (x) along the pipe and on the time (t). A greatly simplified but generally accepted mathematical model consistent, of a system of nonlinear partial differential equations is the point of departure:
Following simple changes of variable (w = p2, v = Q2), the problem is reduced to the solution of:
A stable predictor-corrector method of finite difference approximation due to Jim Douglas, Jr. and B.R. Jones, Jr. is employed to reduce the computation to the solution of a system of linear algebraic equations (matrix inversion). The incorporation of initial conditions, boundary conditions, and internal flow conservation equations, all of which in finite difference form become linear algebraic equations, results in a single matrix equation for the calculation of pressures and flows in the pipeline network.
The computation of transient flow in gas pipeline networks is complicated mathematically by the nonlinearity of the governing partial differential equations. This is in marked contrast, of course, to the situation in steady state flow, where the corresponding equations, at least in their simplest form, have exact mathematical solutions. The mathematical model we assume has resulted from a number of simplifications, including the neglect of altitude and temperature variation. Although it is beyond the scope of this note to discuss the validity and significance of these simplifications, it is generally believed that the equations we will discuss are an accurate first order description of the actual physical system.