A Method for Computing Pressure Behavior and Volume of Gas-Storage Reservoirs
Authors: Glass E.D. , Hessing R.C. 
Published: December 2007

Abstract
The volume of gas in storage reservoirs may be computed from estimates of hydrocarbon pore volume and gas density. However, both are difficult to estimate accurately. Further, no adequate method has been presented for estimating reservoir performance during operation for volumetric gas-storage reservoirs. Normally, gas-storage reservoirs exhibit small pressure gradients in the area containing the storage wells, even under conditions of maximum injection or withdrawal. A zone of low permeability usually surrounds, and is in communication with, the permeable zone which causes the storage reservoir to exhibit a definite pressure lag, as evidenced by lack of pressure stabilization after extended periods of shut-in. An analysis is presented for determining pore volume and gas in place, and for predicting future reservoir behavior of such reservoirs. The mathematical development is presented and a solution is shown for an operating storage reservoir.

Introduction
Depleted gas reservoirs are often used for gas storage. The reservoir usually contains a permeable area in which numerous storage wells are located. The permeable zone permits high deliverability and injectivity with relatively small pressure loss. However, pressure equilibrium may not be attained even after long periods of shut-in because of the fact that the permeable zone is in communication with an adjacent tight section. Most of these gas-storage reservoirs are sand lenses, such as ancient beaches or offshore bars. The areal geometry of these reservoirs is normally such that flow in the tight zone will be approximately linear, and the solutions presented here should apply.

Discussion
For purposes of this paper, a gas-storage reservoir is considered to consist of a volume of permeable rock in communication with tight rock, all of which is surrounded by an impermeable barrier. Pressure gradients across the permeable zone are small due to low flow resistance and well density. Hence, the permeable zone is considered to be at a uniform pressure which is only a function of time as gas is injected or withdrawn. The tight zone is considered to be linear with uniform permeability and porosity, and the pressure in the tight zone is a function of both position and time. Two solutions for flow in this system are used to define the reservoir and determine its properties. The first solution is for an infinite linear tight zone in communication with the permeable zone. The expression for constant gas-withdrawal rate is
............................(1)
where c is the constant. The expression is derived in the Appendix.
The second solution is for a finite tight zone in communication with the permeable zone. An adequate solution may be adapted from Carslaw and Jaeger, as shown in the Appendix.
............................(2)
L where b = and the 's are the roots of the DL expression L cot (L) + = 0.D
Eqs. 1 and 2 are superposed to account for varying rates of production or injection and are used to fit gas-storage field reservoir history. The solution for the infinite case, Eq. 1, is first applied to field data for early times following a shut-in period. Constants BD and c are obtained by a least-squares fit of pressure and rate data. After the pressure wave from gas injection or withdrawal reaches the external boundary of the tight zone, the infinite solution will no longer apply and pressure behavior should be more nearly represented by Eq. 2 for a gas reservoir in communication with a finite linear tight zone.
JPT
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