An Investigation of Pressure-Buildup Tests in Bounded Reservoirs
Authors: Cobb W.M. , Smith J.T. 
Published: December 2007

Two methods of pressure-buildup analysis for bounded reservoirs are analyzed. Pressure-buildup data for a variety of well locations within various rectangular drainage shapes are generated; the results are plotted according to both methods investigated; and the resulting curves are studied for diagnostic features and rules.

Introduction
One of the most important aspects of formation evaluation is the design, implementation, and interpretation of a pressure-buildup test. Basically, this test requires that a producing well be shut in and that the associated change in bottom-hole pressure be measured as a function of shut-in time. Muskat introduced the first interpretation method for these pressure data in 1937, but its significance was largely overlooked until the late 1940's. At that time, van Everdingen and Hurst revived interest in transient pressure analysis with their paper on the behavior of unsteady-state fluid flow in a porous media.
Miller-Dyes-Hutchinson (MDH) and Horner (HOR) in 1950 and 1951, respectively, published fundamental papers on interpretating wellbore pressure buildup papers on interpretating wellbore pressure buildup for the purpose of estimating formation permeability. Both these analysis procedures were similar in that they required a semilogarithmic plot of the test data. Miller et al. suggested that the buildup pressure, pws, be plotted against the logarithm of the time, Delta t, since the well was shut in. On the other hand, Horner suggested that the buildup pressure be plotted as a function of a time ratio, (t + Delta t)/Delta t, where t is the length of producing time before shut in. In both cases, the plotted data should result in a straight line with a slope inversely proportional to the mean formation permeability. Significantly, the Homer technique was developed for the buildup case of a constant production-rate well located in an infinitely large reservoir. production-rate well located in an infinitely large reservoir. The MDH method was developed for the case of a well located in the center of a closed (no-flow outer boundary) circular reservoir and produced to pseudosteady state before shut in. Accordingly, it is commonly believed that the Homer method is more applicable in new wells and that the MDH method is best suited for old wells.
In his original work, Horner showed that an extrapolation of the semilog straight line to a time ratio of unity would yield the initial reservoir pressure, pi, provided the production period was short. Moreover, he showed that, production period was short. Moreover, he showed that, for long production periods in a bounded reservoir, the straight line would extrapolate to a pressure p*. It is important to note that p* is not the initial pressure, pi, or the volumetric average pressure, p. However, if production time is short, then pi p p*. In 1954, Matthews-Brons-Hazebroek (MBH) presented correlations that relate p* to p for a variety of bounded reservoir shapes with wells located in a number of positions. To use these correlations to evaluate p accurately, it is necessary that the Homer semilog straight line be identified correctly.
The concept of formation damage, or skin factor, was introduced to transient pressure analysis by van Everdingen and Hurst. They discussed its effect on well behavior and presented methods for evaluating its presence. Probably the most reliable estimate of the skin factor is Probably the most reliable estimate of the skin factor is obtained from a pressure-buildup test. Specifically, the evaluation method makes use of the slope of the Homer or MDH semilog straight line.
JPT
P. 991