Planning and Analysis of Pulse-Tests

Abstract

Developed here are equations that approximate the pulse-test procedure and that, in turn, are plotted as simple graphs that can be used directly to design and analyze these tests. The necessary calculations require only 10 to 15 minutes. Introduction Pulse-testing is a fairly recent procedure that has received some attention in the last 2 years. In this method of testing, a well is pulsed with cycles of injection followed by shut-in, or production followed by shut-in. The pressure response to the cycles is then measured in an offset well. Articles in the literature1,2 discuss, to some extent, the theory of pulse-testing; but an engineer who wishes to analyze the results of such a test will find that he must make a number of tedious exponential integral calculations. The paper briefly covers the theoretical rationale behind pulse-testing, and then develops some approximate equations. As a result of these equations, two simple graphs are developed that can be used for design and analysis of pulse-tests. An example calculation is shown later in the text. General Response Theory Pulse-testing was first discussed by Johnson et al.l The concepts involved are fairly straightforward. Briefly, the bottom-hole pressure in a shut-in well will respond to production or injection cycles in an offset well. The magnitude and timing of the response depend on the flow rate, the permeability, porosity and thickness of the formation, and the compressibility and viscosity of the fluids that lie between the wells. Inhomogeneities, geometry and boundaries also affect the response, but these factors are not included in the scope of this paper, nor in the literature. The equations for the response are line-source solutions to the diffusivity equation. For instance, if a well is produced for a time ?t, then shut in, the equation for the pressure response in the shut-in well isEquation 1 Going further, if there are a number of cycles of production followed by shut-in, if each production rate is equal, and if each cycle lasts for an equal period of time (?t), then by superposition the equation for the pressure response becomesEquation 2 where N is the number of equal-length periods of production and shut-in (for instance, for one production and one shut-in period, N=2; Eq. 1). Eq. 2 is the same as cited by Johnson et al. Notice that each shut-in and production period is assumed equal. This is not necessary, but it is easier to handle theoretically and will be used throughout the rest of this paper. Also notice that Eqs. 1 and 2 are for production and shut-in. For continuity we will continue to speak of production; but the reader should realize that injection and shut-in will work equally well. We would merely reverse the signs.