Effect of a Linear Boundary on Interference and Pulse Tests - The Elliptical Influence Area

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Abstract
This paper discusses the effect of a linear, no-flow boundary on two-well interference and pulse tests. The effect of a boundary on the pulse-testing time lag and response amplitude is examined, and mathematical pulse-testing time lag and response amplitude is examined, and mathematical proof is given that the influence area for a two-well test is elliptical. proof is given that the influence area for a two-well test is elliptical. Introduction Pressure transient tests are used in the petroleum Pressure transient tests are used in the petroleum industry to measure or estimate characteristics of hydrocarbon reservoirs. Such tests include buildup, falloff, injectivity, interference, and pulse tests. Associated with these tests are measurements of pressures or pressure changes, times of measurements, and well flow rates. Different kinds of plots of pressure or pressure change vs time are used in pressure transient analysis to determine reservoir properties. Also associated with these tests is a transient properties. Also associated with these tests is a transient that propagates through the reservoir as the duration of the test increases. This leads to the concept of area of influence, which can be used to determine where in the reservoir the measurement of reservoir properties is taking place. Johnson et al. first described the pulse-testing procedure and established its terminology. Since then, several procedure and established its terminology. Since then, several investigators have advanced pulse-testing technology and methods of interpretation. Brigham and Kamal developed methods to determine reservoir properties from the time lag and the response amplitude. McKinley et al. applied pulse testing to obtain a detailed description of a heterogeneous, water-oil reservoir. Vela and McKinley defined the influence area and made a study of how heterogeneities affect pulse-test results. And Woods studied the pulse-test response of a two-zone reservoir. This paper is concerned with the effect of a linear, no-flow boundary on two-well interference and pulse tests. The paper consists of two parts. The first part discusses the effect of a boundary on the pulse-testing time lag and response amplitude. The second part (Appendix) proves mathematically that the influence area for a two-well test, defined by the effect of a boundary on the test, is elliptical. Effect of a No-Flow, Linear Boundary on Pulse-Testing Time Lag and Response Pulse-Testing Time Lag and Response Amplitude The effect of a no-flow, linear boundary on the pulse-test time lag and response amplitude was calculated for a reservoir with a simulated boundary where both the pulse length, Delta t, and the distance to the boundary, L, were varied. The method of images simulates a no-flow, linear boundary by placing an image well in such a way that the hypothetical boundary is the perpendicular bisector of the line connecting the real and image wells. If the production and/or injection schedules for the image and real wells are identical, then a no-flow condition will exist on a line that coincides with the hypothetical boundary. In the calculations, we simulated a boundary by placing an image well 2L ft behind the pulser and in line placing an image well 2L ft behind the pulser and in line with both the pulser and the responder (see Fig. 1). (Results in the Appendix show that the effect of this simulated boundary is the same as that for any boundary tangent to the ellipse defined by Eq. A-1.) To calculate pulse-test response, the Ei solution' was used for both the pulse-test response, the Ei solution' was used for both the image well and me real well (pulser). In every pulse test, the on-off ratio was 1. The pulse length was varied from 30 to 100 minutes, and the ratio of L to a (well spacing) was varied from 0 to 2.0. P. 947

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