A Computer Simulation of Gas Flow in Long Pipelines

A computer program has been developed to simulate a gas transmission line operating under transient conditions. The program was developed by application of the basic mass and momentum balance equations. The nonlinear equations thus obtained were transformed by the method of characteristics and finite-difference techniques to make them suitable for machine computation. Three tests of the computer program were made. In each of these, the initial condition was assumed to be steady-state flow, the inlet density was held constant at the initial condition, and the outlet mass flow rate was varied with time. One test was theoretical in nature, but the others were made for direct comparison with actual field data. Results of the tests are presented in graphical form. Introduction Theoretical investigations of the transient flow of gas in long pipelines have been limited in number. In 1951, Olds and Sage developed a graphical method of solving the nonlinear flow equations describing transient gas flow in a long pipeline. Research in this field at the U. of Oklahoma was initiated by Nelson in 1956. Nelson utilized a computer to solve numerical equations involving a lengthy trial-and-error procedure, and his results have been reported in the literature. It does not seem likely that Nelson's method can be extended to the analysis of transient behavior of pipeline networks; therefore, the investigation to be discussed in this paper was undertaken to improve and extend the previous work. The following discussion presents, briefly:the basic differential equations governing transient flow,transformation of these equations into a form suitable for machine computation,role of boundary conditions in the calculations,a very brief description of the computer program which was developed to simulate the pipeline andresults of tests of the computer program. DEVELOPMENT OF EQUATIONS BASIC DIFFERENTIAL EQUATIONS The isothermal flow of fluids can be adequately described by the mass and momentum balance equations as applied to the system under consideration. Using as a system a section of pipe having a differential length, the continuity equations were developed as follows. Mass balance: .......................(1) Momentum balance: .......................(2) where p = gas density, G = mass flow rate of gas, x = distance along pipe from system inlet, t = time from start of time interval of interest, gc = gravitational constant, R = gas constant T = gas temperature, absolute, M = gas molecular weight, D = pipe diameter, and f = Moody friction factor. The following assumptions are involved in the development of Eqs. 1 and 2: constant temperature, rod-like flow, negligible effect of changes in elevation, no chemical or atomic reactions, single-phase fluid, pipe has constant cross-sectional area, and ideal gas. SPEJ P. 297^