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Transient flow of natural gas in pipelines is simulated without neglecting the inertia term. The governing equations constitute a nonhomogeneous hyperbolic set of first-order quasilinear partial differential equations. The first-order, three-point, explicit Godunov scheme and the second-order, five-point, total variation diminishing (TVD) scheme are used to solve this set of equations. Two examples are simulated. The first is the propagation of a slow transient, with 24-hour cycle, in a 45-mile long, 8-in. inside diameter (ID) transmission pipeline, while the second is propagation of a fast transient in a 24-in., 300-ft long pipe. Comparisons between the predicted results and the measured data are fairly good and appear to be better than the predictions reported in the literature. This suggests that the mathematical model presented in the present study, which includes the inertia term in the momentum equation, is more realistic and the numerical schemes used are more robust.

Summary Based on mass and momentum balance, a rigorous analytical equation is derived for compressible fluid flow in pipelines. This equation gives a functional relationship between flow rate, inlet pressure, and outlet pressure. It is very useful in design calculations where any of these variables need to be estimated if the others are given. The equation can be used for any pipeline topology and configuration, including size and orientation. A number of problems of engineering importance are studied with this equation. They include bottomhole pressure (BHP) calculations in gas wells, gas injection calculations, and long-distance gas pipeline design calculations. The excellent agreement between predicted results and field data, with this equation for this wide variety of problems and conditions, demonstrate the efficacy of this equation for engineering applications. Simple computer programs, in both FORTRAN and BASIC, are developed to handle these applications. The BASIC program can be run on any programmable calculator with 3 kilobytes of memory. Introduction The problem of compressible fluid flow through pipelines and conduits has been studied by many investigators. In the natural gas industry, the problems of interest fall into two categories: gas pipeline flow calculations and gas-well calculations. Because of the differing sets of assumptions usually invoked, these two problems have been treated as almost mutually exclusive in the literature. For pipelines, the most commonly used equations for these calculations are the Weymouth equation and the Panhandle equations. For BHP prediction in gas wells, the most popular methods are those developed by Sukkar and Cornell and Cullender and Smith. Basically, the Weymouth and Panhandle equations are derived for gas flow in horizontal and slightly inclined pipelines. For slightly inclined pipes, the elevation change is accounted for by simply adding the static head of the gas column to the pressure difference calculation. While this may be adequate for small elevation changes, as obtained in gas pipelines, it is inadequate in gas wells where the pipe is either vertical or nearly vertical. The reason is that, in this case, the gravity term is sufficiently significant to affect fluid velocity and hence the friction term.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractA multi-mechanistic flow environment is the result of the combined action of a Darcian flow component (the macroscopic flow of the phase due to pressure gradients) and a Fickian-like or diffusive flow component (diffusive flow due to molecular concentration gradients) taking place in a hydrocarbon reservoir. The present work presents the framework needed for the assessment of the impact of multimechanistic flow on systems where complex fluid behaviorsuch as that of retrograde gas-condensate fluids-requires the implementation of compositional reservoir simulators. Due to the complex fluid behavior nature of gas-condensate fluids, a fully-implicit (IMPISC-type) compositional model is implemented and the model is used for the study of the isothermal depletion of naturally fractured retrograde gas reservoirs. In these systems, especially those tight systems with very low permeability (k < 0.1 md), bulk fluid flow as predicted by Darcy's law might not take place despite the presence of large pressure gradients. The use of an effective diffusion coefficient in the gas phase-which accounts for the combined effect of the different diffusion mechanisms that could take place in a porous medium-and its relative contribution to fluid recovery is discussed. The compositional tracking capabilities of the model are tested and the conditions where Fickian flow can be the major player in recovery predictions and considerably overcome the flow impairment to gas flow posed by the eventual appearance of a condensate barrier-typical of gas-condensate systems-are investigated. Finally, a mapping that defines different domains where multimechanistic flow can be expected in compositional simulators of retrograde gas-condensate reservoirs is presented.

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Pressure and temperature variations of natural gas flows in a pipeline may cause partial gas condensation. Fluid phase behavior and prevailing conditions often make liquid appearance inevitable, which subjects the pipe flow to a higher pressure loss. This study focuses on the hydrodynamic behavior of the common scenarios that may occur in natural gas pipelines. For this purpose, a two-fluid model is used. The expected flow patterns as well as their transitions are modeled with emphasis on the low-liquid loading character of such systems. In addition, the work re-examines previous implementations of two-flow model for gas-condensate flow.

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