Effects of External Boundaries on the Recognition of Reservoir Pinchout Boundaries by Pressure Transient Analysis

Effects of External Boundaries on the Recognition of Reservoir Pinchout Boundaries by Pressure Pinchout Boundaries by Pressure Transient Analysis Abstract Previous workers have shown that a semi-infinite reservoir with a pinchout Previous workers have shown that a semi-infinite reservoir with a pinchout boundary is characterized by spherical flow at long time. As a result, the presence of a pinchout should be recognizable from pressure-drawdown data presence of a pinchout should be recognizable from pressure-drawdown data by the appearance of a straight line on a graph of pressure vs. reciprocal square root of time. However, external boundaries of the system may be felt before spherical flow is established. This problem was studied by creating boundaries in the semi-infinite reservoir, using infinite-array superposition of the pinchout source function. Three partially closed systems were produced:two parallel, vertical boundaries normal to the pinchout,a vertical boundary opposite the pinchout, anda second pinchout, (2) a vertical boundary opposite the pinchout, and (3) a second pinchout opposite the first. Values of pressure vs. time have been pinchout opposite the first. Values of pressure vs. time have been calculated for each of these cases. It was found that the characteristic straight line begins at a time / = 5. This line would appear only if the external boundaries in the direction orthogonal to the pinchout were more than five times as distant from the well as the pinchout, and if boundaries in the direction parallel to the pinchout were more than eight times as distant. parallel to the pinchout were more than eight times as distant. Introduction Much of the current theory of pressure transient analysis was developed assuming a reservoir of uniform thickness with vertical external boundaries. In many reservoirs, however, the sand thins out to zero thickness on one or more sides. Only recently has the behavior of such pinchout boundaries been investigated. A diagram of such a system is shown pinchout boundaries been investigated. A diagram of such a system is shown in Fig. 1. By superposing line-source segments in a vertical plane passing through the well, Horne and Temeng derived an analytical solution to the diffusivity equation for a well in a semi-infinite reservoir with a pinchout boundary. They found that the system had the following pinchout boundary. They found that the system had the following characteristics.At early time, the solution is identical to the line-sourcesolution.At longer time, a spherical flow geometry is established. The transition occurs at the "cutoff time" ( ), which is a functionof the thickness of the sand ( ) and the angle of pinchout ( ).At very long time, the pressure drop at the well becomes constant. Like the cutoff time, the magnitude of the limiting pressure ( )is a function of and. The early-time and long-time behaviors disguise the presence of a pinchout and could result in misinterpretation of pressure transient test pinchout and could result in misinterpretation of pressure transient test data. If the test were terminated before the pinchout began to influence the pressure drop, the resulting data would be consistent with the assumption of a reservoir of constant thickness. A longer test, revealing the tendency to a constant value of pressure at infinite time, might lead to the mistaken inference of a constant-pressure boundary in the system. However, the spherical flow period at long time is peculiar to the pinchout system. Since spherical flow is characterized by the appearance pinchout system. Since spherical flow is characterized by the appearance of a straight line on a graph of pressure vs. reciprocal square root of time (p vs. 1/ ), Horne and Temeng suggested that such a graph be used to distinguish a pinchout boundary. They also determined that the slope of the straight line was related to the pinchout angle. From this, given the thickness of the sand at the well, the distance to the pinchout could be calculated. The application of this method to practical well testing is subject to two major limitations. First, the design of a test and the proper interpretation require some means to predict the onset of spherical flow. Second, the system will have other boundaries in addition to the pinchout because of the presence of sealing faults or active wells in the vicinity. Interference by these external boundaries will cause the pressure/time behavior to depart from the semi-infinite case; if the boundaries are too close, this departure may occur before spherical flow is established. By investigating these two limitations, it is possible to determine for a physical case whether spherical flow may be established in a practical physical case whether spherical flow may be established in a practical length of time and whether the geometric relationship between well, pinchout, and external boundaries is favorable to the acquisition of useful pinchout, and external boundaries is favorable to the acquisition of useful data. This information should be sufficient to demonstrate the practicality of recognizing and locating pinchouts through pressure transient analysis. SPEJ p. 427