Abstract

This paper studies performance of gas wells producing from a reservoir containing several noncommunicating layers. Predictions were made with a newly developed simulator that performs a complete "nodal analysis" on each time step to determine flow capacity. The four categories of results given are; (1) the excellent correlation of predicted performance of 1- and 2-layer reservoirs with published data validates the novel mathematical approach used in our simulator, (2) for a 5-layer system comparison of simulated results to published values obtained with an analytical solution finds only partial agreement, (3) predicted recoveries after aggregating layers of differing permeability show that layer combinations must be chosen carefully to avoid large errors in predicted recovery and (4) the turbulence coefficient must be defined on a unit thickness basis to obtain correct results for layered systems.

Introduction

Predicting performance of gas reservoirs with non-communicating layers, which for brevity we refer to as layered reservoirs, is an important but complex problem. In this paper we present several such predictions made with a reservoir simulator, dubbed JRT (Joint Reservoir Trunkline simulator), that on each time step performs a nodal analysis to determine reservoir deliverability and change in reservoir pressure. The objective of the study was twofold; (1) to validate the accuracy of predictions made with JRT, this being necessary since the procedure used to rapidly solve simultaneously the complex set of mathematical equations describing behavior is a new and relatively untested approach and (2) to extend and expand the information in the literature relative to the performance of layered reservoirs.

Validity is confirmed by comparing JRTs results to those of Fetkovich. Special emphasis was given to validation because when we compared our results to those obtained by Lee using an analytical solution, we found only partial agreement, the major disagreement being relative to the accuracy of recovery predictions made after aggregating layers of different permeability. Results included for two example 5-layer systems show that improper aggregation of layers leads to large overestimates in economically recoverable reserves. Based on these results general guidelines are given for selecting layers to aggregate so that reasonable recovery predictions are obtained.

The literature is somewhat imprecise in specifying how formation thickness relates to turbulence coefficient, presumably because published methods for determining the coefficient from well tests all assume a single producing layer. We present computed results showing that for layered systems a specific turbulence coefficient (per unit thickness) must be defined and used in calculations to give consistent results. A mathematical proof of this conclusion is also given.

The Reservoir Simulator, JRT

In simulation jargon JRT uses a modified IMPES method to solve for reservoir deliverability, pressure and water saturation vs time. Although not required by the mathematical approach used, for reasons given elsewhere JRT currently includes only three computing cells per layer. This is of little import here; all computed results were obtained using one computing cell per layer to represent the drainage volume of the single well whose performance was being simulated.

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