When pressure buildup data are plotted on semilogarithmic coordinates, several straight lines can be obtained, even though theoretical considerations indicate that only one straight line should appear. Thus, an engineer is faced with the problem of choosing one of these straight lines to estimate formation permeability, average reservoir pressure, and flow efficiency. During the past few years, methods have been suggested whereby an engineer may extricate himself/herself from this quandary.
In this paper we consider a few field examples which demonstrate the correct procedure one may follow to choose a straight line. Methods to identify after flow, the presence of a fracture, and the existence of boundaries are discussed. The advantages and limitations of the various methods are also discussed.
The pressure buildup test is the most common of transient well tests. The procedure, as shown in Figure 1, consists of flowing the well at a constant rate, q, for a time, t, and then shutting-in the well for a time, delta t, while measuring the bottom-hole pressure during the shut-in period. pressure during the shut-in period. There are a substantial number of papers written on the subject of pressure transient analysis. The objective of this paper is to promote the combined and simultaneous use of the traditional semilogarithmic techniques with the newer log-log method.
The two best approaches of pressure buildup analysis are the Horner and the Miller, Dyes, Hutchinson methods. The Horner method involves plotting the bottom-hole shut-in pressure, VS. plotting the bottom-hole shut-in pressure, VS. the logarithm of the time ratio (tp + delta t)/delta t, while the Miller-Dyes-Hutchinson (MDH) procedure involves plotting pws vs. the logarithm of delta t. Here, tp is plotting pws vs. the logarithm of delta t. Here, tp is the producing time prior to shut-in and delta t is the shut-in time. These methods show that such a graph should yield a straight line, whose slope is inversely proportional to the permeability-thickness product, proportional to the permeability-thickness product, kh, as illustrated in Figure 2. Other parameters such as wellbore damage or stimulation, average reservoir pressure, and distance to the nearest boundary can be pressure, and distance to the nearest boundary can be obtained from a Horner or MDH graph.
The main problem in analyzing pressure buildup data is that, often, when buildup data are plotted on semilogarithmic coordinates, several straight lines can be obtained, even though theoretical considerations indicate that only one straight line should appear. Thus, the engineer is faced with the problem of choosing one of these straight lines for analysis, or concluding that the reservoir is heterogeneous; in the latter case, the conventional procedures suggested in the literature are not applicable. The appearance of several straight lines, or even a smooth curve, may be due to near wellbore effects such as afterflow, and/or fractures intersecting the wellbore. This paper is concerned with the identification of the proper straight line, if such a straight line exists. The methods suggested here should also be helpful in answering such questions as:
Has the test run long enough to get the straight line needed to obtain formation permeability, skin factor, and average reservoir pressure?
Is the reservoir heterogeneous?
Is a more complex procedure or reservoir simulator (computer approach) needed to analyze the data?
What special precautions should be taken or what improvements can be made when the test is rerun at a later date?
PRELIMINARY CONSIDERATIONS PRELIMINARY CONSIDERATIONS To establish a basis for discussion, let us consider two gas well tests shown in Figure 3 where buildup data have been plotted as suggested by Horner. Since these are gas wells, we use p2, rather than p. From Figure 3, we see two similarities between the two graphs. First, two well-defined straight lines can be seen on both tests—a straight line with a shallow slope, followed by a second straight line with a much steeper slope. Either line on each test could be used to estimate formation permeability. Secondly, on both tests the slope of the second straight line is twice that of the first.