Calculation of Gas Recovery Upon Ultimate Depletion of Aquifer Storage
Authors: Knapp Roy M. , Henderson James H. , Dempsey John R. , Coats Keith H. 
Published: December 2007

Abstract
The recovery of cushion gas upon ultimate depletion of an aquifer storage reservoir dependent upon reservoir heterogeneity, aquifer strength, production rate, and fluid and rock properties. This study illustrates the use of multi-dimensional, two-phase, compressible fluid flow calculations to simulate the depletion. Results that illustrate the non-exhaustive examination of the effects of heterogeneity. The multi-dimensional type of calculation employed appears necessary to reliably estimate recoverable cushion gas for any particular reservoir.

Introduction
When the use of aquifer storage for natural gas is contemplated, the capital cost of such a venture must be closely estimated to evaluate properly the feasibility of such a proposal. It is relatively simple to account for lease acquisition, drilling, well completion and surface facility costs. Determining the cost of the unrecoverable cushion gas is difficult, and this portion of the investment can be the largest item in the total required to develop an aquifer storage field. Think paper describes a study made at Northern Natural Gas Co. to evaluate a technique that has application to this problem.
Two basic factors determine the percentage of nonrecoverable cushion gas: water invasion efficiency and average pressure level at abandonment. Invasion efficiency is defined here as the average water saturation in the reservoir at time of abandonment. This efficiency is dependent upon reservoir heterogeneity, gas production rate, and fluid and rock properties such as density, viscosity, relative permeability, capillary pressure and residual gas saturation the lowest saturation at which gas will flow under a potential gradient during displacement by water.
Earlier work related to this problem of gas recovery treated the effects of aquifer strength, production rate. and several other factors on ultimate recovery from gas producing fields. In that work the reservoir was assumed to be homogeneous with uniform pressure, and water invasion efficiency was assumed.
In this paper a computerized model is described and applied to simulate the displacement of gas by water during ultimate storage field depletion. This simulation yields unsteady-state pressure and saturation distributions throughout the reservoir during depletion. These distributions give water invasion efficiency and average pressure level, which in turn determine the percentage of cushion gas not recoverable at abandonment. The calculations simulate multi-dimensional, two-phase, compressible fluid flow and account for effects of reservoir heterogeneity, production rate, aquifer strength, well completion interval and fluid and rock properties.
Three hypothetical reservoirs of different heterogeneities are treated, including one considered representative of a zone in the Redfield Storage field. For each reservoir, results are presented as percentage of cushion gas recovered for various aquifer strengths and gas production rates.

The Simulation Model
A calculational technique described by Douglas, Peaceman and Rachford was applied recently by Coats and Richardson to the problem of water displacement by gas during initial growth of an aquifer storage reservoir. The technique simulates two-dimensional, two-phase, incompressible fluid flow in reservoirs. A similar method was used in this study to simulate the two-dimensional, compressible gas-water displacement during ultimate depletion of an aquifer storage field.
The calculations are based on continuity equations for both fluid phases and Darcy's law including relative permeability. These are combined to give the basic equations of flow, Eqs. 1a and 1b.(1a)
(1b) JPT
P. 1129ˆ