Practical Application of a Two-Dimensional Numerical Model for Gas Reservoir Studies
Authors: Henderson J.H. , Dempsey J.R , Nelson A.D. 
Published: December 2007

Abstract
A reservoir study was conducted using a general two-dimensional, single-phase, dry gas, unsteady-state model suitably altered from the academic form to the specific needs of the study. The two-dimensional, unsteady-state model was used because the conventional steady-state methods of prediction proved inadequate due to changes in simulated drainage volumes caused by variation in methods for calculating flow schedules. With the multi-well, two-dimensional model, the above effects of altering the production schedules can be adequately accounted for. Extensive changes were made in the model to reduce running time and duplicate field conditions. In the absence of good reservoir data, historical production decline performance of the wells was matched by manipulating reservoir parameters on successive runs. With the production histories matched, predictions were made for future performance under the alternate allocation schemes. Examples are given of the history-matching procedure and of the effect of two different allocation schemes on the predictions.

Introduction
The initial objective of this study was to evaluate the effect of changes in the method of allocating flow rates among a group of adjacent gas wells. It was felt that a change in the allocation scheme would alter the relative drainage volumes of the wells in question; it quickly became evident that the conventional method of extrapolating pressure decline curves to obtain pressures for calculating ability to produce (from the backpressure equation) was inadequate. The fundamental drawback to the conventional steady-state prediction method is that the slope of the pressure decline curve (determined in this study by approximately 20 annual pressure measurements) was "fixed" and predicted points could only follow the existing curve. Expected changes in the character of the pressure decline curve and the consequent effect on the well performance equations due to changing drainage volume for individual wells could only be evaluated by unsteady-state methods. A two-dimensional, dry gas, numerical reservoir model existed in academic form so it was decided to create a special modification. Two aims were then apparent: complete the reservoir study by matching past pressure-decline performance of the wells to obtain a good description of the reservoir on which to base performance predictions, and evaluate the wisdom of preserving the model in the academic form and modifying copies of the deck for special-purpose situations. This latter objective was important because of the need to satisfy ourselves and management that it was practical and technically desirable to use a technique as complicated as the two-dimensional model, yet not be required to build a huge library of seldom-used, special-situation models in advance. The mathematical model used for this study is given by the equation (Appendix A)
........(1)

Plan
The objective was to predict the performance of the wells relative to one another under alternate allocation schemes and evaluate the effects of modifying these schemes. To maintain minimum computing time requirements, yet give good definition in the numerical grid, a township containing 36 wells was chosen as the study area. The location was chosen so that runs could be started with pressure known to be a constant throughout the township. Reliable log and flow test data on well thickness and permeability were sparse. However, these wells have been on production for about 20 years and have well-defined pressure decline histories; therefore, it was decided to use the model to match calculated and measured pressures for individual wells by adjusting values of reservoir thickness and permeability to gas. Thus, with 20 or so points matched, it was felt that predictions of future performance could be made with confidence. Permeabilities from scattered pressure buildup tests were used for starting conditions.
JPT
P. 1127ˆ