A Practical Two-Dimensional Model for Simulating Dry Gas Reservoirs with Bottom Water Drive
Authors: Givens James W. 
Published: December 2007

Abstract
This paper presents a single-phase two-dimensional model for simulating multiwell gas reservoirs with bottom water drive and water coning. Approximation techniques are used by the model to describe this two-phase three-dimensional problem. The model is primarily a numerical solution of the partial differential equation for two-dimensional unsteady-state flow of real gases through porous media. The permeabilities, thickness, porosity, viscosity, z-factor, and isothermal compressibility are treated as variables. The water influx is described by an approximate procedure that periodically calculates the net water encroachment and adjusts the reservoir thickness and pressure. Water coning at the producing wells is controlled by limiting the producing rates. The performance of a hypothetical reservoir is presented to show the effects of bottom water drive and water coning and to demonstrate the applicability of the model.

Introduction
The purpose of this paper is to present a simulation model that can be used to determine the effects of well density, producing rates, water influx, water coning, and rock and fluid properties on the depletion performance of gas reservoirs with bottom water drive. The selection of optimum development and operation programs for gas reservoirs requires that the effects of these parameters be thoroughly evaluated.

Review of Literature
Several methods for predicting the depletion performance of natural gas reservoirs have been published in the literature.1-5 Agarwal et al.1 used a material balance model to study the effects of water influx on natural gas recovery. On the basis of their calculations for edgewater-drive reservoirs, they concluded that recovery depends on (1) the production rate and manner of production,(2) the residual gas saturation in the water invaded zone, (3) the aquifer strength, (4) the permeability, and (5) the volumetric sweep efficiency of the encroaching water zone.
Carter2 and Quon et al.3 have presented analyses of numerical techniques for solving the partial differential equation for two-dimensional unsteady-state gas flow. Quon et al. found that the alternating direction explicit procedure (ADEP) had an advantage over the forward difference explicit (FOE) and the alternating direction implicit (ADI) procedures. Carter applied several numerical calculation methods to an example problem and concluded that methods of the Saul'ev type are stable for practical time step sizes and are advantageous over conventional explicit procedures.
Henderson et al.4 have presented a two-dimensional unsteady-state dry gas model with matching and predicting capabilities. The results of a reservoir study are presented to demonstrate the applicability of the model to a practical problem. The authors point out the necessity of using an unsteady-state multiwell model to analyze field performance adequately.
A two-phase two-dimensional model for predicting the recovery of gas from aquifer storage fields has been developed by Knapp et al.5 The model was used to study the effects of heterogeneity, aquifer strength, and gas production rates. These studies showed that gas recovery is a function of production rate, and aquifer strength, and heterogeneity. Their conclusions regarding production rate and aquifer strength agree with those of Agarwal et al.1

The Simulation Model
The simulation model is an approximate procedure for predicting the behavior of multiwell gas reservoirs with bottom water drive. The three main areas of the calculation procedure are (1) unsteady-state pressure calculations, (2) water influx calculations, and (3) water coning. Each of these areas will be discussed in detail before their role in the calculation procedure is discussed.