The Development, Testing And Application of an Efficient Steady State Gas Field Performance Evaluation Model
Authors: Agbi B. 
Published: March 2010

Abstract
Network theoretic concepts have been applied to the analysis and design of distribution network systems for some time. Notable applications include the analysis of water distribution networks, electrical network systems and, more recently, systems in the gas distribution industry. However, application ·of the technique to the simulation of natural gas field collection systems has been limited to the analysis of surface gathering configurations. This paper is an extension of this concept to allow for the inclusion of gas reservoirs and production strings.
The paper presents the matrix formulation of the problem to Include all components of a natural gas gathering system. The application of the N-dimensional Newton-Raphson technique to the solution of the resulting system of nonlinear algebraic equations is discussed, and it includes an outline of a procedure that ensures convergence without the need for acceleration parameters.
The application of the resulting model to an evaluation of the performance of a gas reservoir is given. The treatment includes, in addition to conventional analyses, the comprehensive evaluation of:the effect of liquid production on gathering and transmission line pressure drops; andthe effect of water influx on the performance and ultimate recovery from water-drive gas reservoirs.

INTRODUCTION
The increasing importance of natural gas in the energy supply spectrum demands comprehensive techniques for forecasting the future performance and deliverability of natural gas fields. The deliverability of natural gas fields is a function of pressure drops that occur in the reservoir, the production string and the surface facilities.
Although it is possible to isolate each of these pressure drop segments for independent evaluation, the over-all performance of the total system and consequent optimum production plan for a natural gas field can best be determined through an evaluation that simultaneously considers the effect of all three pressure drops. Network theory provides a comprehensive and efficient means of achieving this objective.

Literature Review
A number of papers have appeared in the literature dealing with the forecasting of gas field deliverability and associated reservoir and gathering system performance. Dempsey et al.(1) proposed an iterative solution of the problem which consisted of two so-called subglobal iteration loops involving independent solution of the equations for the surface system, the production string and the reservoir. A compatibility test was necessary to match pressures and flow rates between iteration steps.
The application of network theoretic concepts to the flow of fluid in networks has been reported in civil engineering literature(2,3) for water distribution systems and in electrical engineering literature for electrical networks(4,5,6). The formulation of problems using the concept of networks leads to a system of simultaneous algebraic equations. Iterative techniques must be used to obtain solutions to the unknowns when the system of equations is nonlinear.
Application of network theoretic concepts to the simulation of natural gas gathering systems was first reported by Stoner(7) and more recently by Berard and Eliason(8). Stoner reported covergence problems in the iterative procedure and proposed the use of a heuris