Flow Test Analysis for a Well with Radial Discontinuity
Authors: Odeh A.S. 
Published: December 2007

Flow test data on a well with radial discontinuity in its drainage area can be interpreted so that the mobility of the zones and the radial distance to the discontinuity can be obtained.

Introduction
During the last few years, several authors have advanced mathematical solutions, both exact and approximate, to the pressure behavior of a well producing from a region bounded by a circular producing from a region bounded by a circular discontinuity. The most recent solutions were reported by Carter, and by Bixel and van Poollen. Carter solved the appropriate equations analytically. Bixel and van Poollen reported a numerical solution and provided correlation charts for the interpretation of provided correlation charts for the interpretation of flow tests; their method uses an overlay technique and is valid for wide ranges of mobility and storage capacity ratios. The mobility ratio is defined as the ratio between k/mu of the two zones, and the capacity ratio is defined as the ratio between c of the two zones.
We have developed independently an analytic solution, programmed for the CDC 1604, that agreed with Carter's. The same differential equation, assumptions, boundary, and initial conditions were used. We ran 30 drawdowns and 30 buildups of a unit capacity ratio and of varied mobility ratios. We also varied the radial distances to the discontinuity, and the radii of drainage. We examined the results and obtained correlations that were simple to apply and useful in flow test interpretation. The results and the correlations reported here in graphical form allow the determination of the mobility of the two zones and the radial distance to the discontinuity. They eliminate the need to fit field data to a curve as is required in the overlay technique. Thus, the advantages of the present correlations are that they require less effort and they provide a unique answer. They also provide guidelines for selecting the parts of the flow test plot to be used in the interpretations. Moreover, the results obtained from the programmed analytic solution define the time intervals where the approximate solution reported by Hurst and discussed by Larkin are applicable.
Normal buildup and drawdown plots resulted in an early straight line, a long transition zone and a late (second) straight line. However, the second straight line will not occur if the drainage radius is not at least 10 times the radial distance to the discontinuity. The mobility of the inner and outer zones can be calculated from the slopes of the first and second straight lines, respectively, by the normal methods of the flow test analysis. We found that the radial distance to the discontinuity may be determined from the abscissa value for the point of intersection of the extensions of the two straight lines. Results similar to some of these were reported by Adams et al.
The approximate solution compared favorably with the exact one during the first and second straightline periods. However, during the transition zone, deviation periods. However, during the transition zone, deviation occurred between the two solutions.

Discussion of Figures
Figs. 1 through 7 summarize the results of this investigation. On Figs. 3 through 7 there appears the equation of each respective plot. In this paper the mobility ratio M is defined as k(1) mu (2)/k(2) mu (1), where subscripts 1 and 2 refer respectively to the inner and outer zones, and dimensionless time = tD= 6.32 x 10(-3) k(1)t/phi mu cr(w)2.
JPT
P. 207