Reservoir Reserve Tests
Authors: Jones L.G. 
Published: December 2007

Abstract
The objective of this paper is to present a better method for determining reservoir reserves of gas from extended drawdown test data. Means are proposed for conducting the test with or without the requirement of prior build-up to a static reservoir pressure. The test is based upon solutions to unsteady-state gas flow developed in an earlier paper and is believed to be superior to previous methods for determining reserves from flow-test data. The limitations of such tests are discussed, with emphasis on the subject of test duration. The test can supply useful information if the mechanics and limitations of it are understood. This type of in formation can be particularly valuable in deciding whether or not to drill offsets to producing wells.

Introduction
In the life of any gas or oil field, the engineer in charge must decide if certain wells need stimulation and whether or not to drill more wells in the field. Well production tests can aid in making these decisions. For instance, the value of stimulation can be estimated by determining formation permeability and the amount of well damage from drawdown or build-up tests. These tests are freely used in the oil industry. A less well-known type of analysis uses data from extended drawdown tests for determining reservoir reserves. Into this category fits the "reservoir limit test" of Jones, and the "reservoir reserve test" presented in this paper. The chief value of these tests is their ability to "see" reservoir boundaries and thus prevent costly dry holes. Methods for determining reserves of both gas and oil reservoirs were proposed in the work of Jones. His proposals appear sound for single-phase liquid flow. The generality of his work on gas flow is open to question, however, since the analysis is based upon solutions to liquid-flow equations. The test for gas reserves presented here is derived from unsteady-state gas-flow solutions presented in a previous paper. In deriving this reservoir reserve test, it has been assumed that all of the reservoir energy is provided by expansion of the reservoir fluid and that the reservoir is radially symmetrical. No mention has been made of the effects of deviations from Darcy's law such as quadratic (turbulent) flow and well damage. Since the terms representing these effects are function of rate only, since the rate is constant and since the data are plotted in a differential form, it seems reasonable that these terms will not affect the test results in any way. No attempt has been made to estimate the effects of water drive, faults, or other departures from an idealized and isolated reservoir. For a qualitative discussion of some of these effects, the reader is referred to a paper by Jones.

THEORY

POST EARLY TRANSIENT PERIOD
An equation relating well pressure and cumulative production for stabilized gas wells flowing at a constant rate was developed in Ref. 4. This equation is
LN c= (P - G ) - LN r ........(1)
where WD = dimensionless flow rate, Zavg = average compressibility factor, GD = dimensionless cumulative production, PiD = dimensionless initial pressure = pi/pi = 1, PwD = dimensionless well pressure = pw/pi, reD = dimensionless outer drainage radius = re/rw, C = correlation constant, pi = initial reservoir pressure, pw = well pressure, re = outer drainage radius of a well, andrw = well radius.2
Solving for 1 - pwD gives2 21 - pwD = 2GD - GD + WDZavg 1n(CreD) ..........(2)
Differentiation with respect to GD yields2d(1 - PwD )= 2 - 2GD = 2 (1 - GD) ...........(3)dGD
By definition,
GD = Gm/Gmi and dGD = dGm/Gmi,
where Gm = cumulative production in moles, andGmi = total number of moles in the reservoir. Thus,2d(1 -pwD ) -dPwD2 2 2Gm - PwD2 -.dGm dGm Gmt (Gmt)2 Gm...............................(4)
Normal field procedure is to measure and report gas production in standard cubic feet measured at 1-atm pressure and 60 F. Therefore, in using Eq. 4, it is convenient to convert Gm in moles to Gp in standard cubic feet. From the gas law,
PsVs = ZsnRTs.....................................(5)
where ps = pressure of the gas, standard conditions, Vs = volume of the gas, standard conditions, Zs = compressibility, standard conditions, n = moles of gas,
JPT
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