Evaluating Effective Properties of Linear Aquifers
Authors: Gomaa Ezzat E. 
Published: December 2007

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
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Abstract
This paper describes a method by which effective aquifer properties can be evaluated from production and pressure history of properties can be evaluated from production and pressure history of linear reservoir-aquifer systems. Effective aquifer properties include: water permeability, type of boundary condition, dimensions, and total pore space.
In this method, use is made of the straight line relationship between production and water influx terms in the material balance equation. Cumulative water influx is expressed as a continuous function of time using either Duhamel's Formula or the Convolution Integral. This procedure for evaluating water influx eliminates the need for dimensionless influx tables. Expressions are obtained for different boundary conditions existing at the aquifer's outer boundary. These expressions are arranged in a form that allows evaluation of aquifer properties from the solution of the material balance equation by a trial and error technique. The correct ratio of effective water permeability to the square of the aquifer length when used with the correct type of boundary condition should give a straight line plot for the production versus water influx terms in the material balance equation. This ratio and the slope of the line are used to calculate the effective properties of the system. The method is illustrated on actual reservoir-aquifer systems whose characteristics allow the linearity assumption.

Introduction
Many water driven reservoirs are associated with aquifers which can be best described as linear. Analysis of water influx into such a reservoir should be more accurate if the aquifer associated with it is completely defined. A linear aquifer is completely defined in terms of its effective properties which include effective permeability to water, type of boundary condition, dimensions and total pore space. In general, reliable values for these properties are not known and the analyses are carried out using values assumed from the available core and geological data. Cores are usually taken from the reservoir and chances are that they may not be representative of the aquifer rock. Geological data for the aquifer are usually limited and include many uncertainties. In this paper a technique is presented for evaluating the effective values of these properties from production and pressure history.
Miller analyzed the performance of infinite and finite sealed linear aquifers and developed equations and curves for evaluating water influx. Nabor and Barham modified Miller's equations and reduced them to a form which yields a single working curve.