A Method for Analyzing Pulse Tests Considering Wellbore Storage and Skin Effects

Abstract

Summary. Pulse testing is used to determine the transmissivity and storativity of a reservoir. A pulse test is conducted by creating a series of flow-rate changes at an active (pulsing) well and observing the pressure response at a nearby observation (responding) well. Previous studies have shown that wellbore storage and skin effects should be accounted for when analyzing a pulse test. This study presents the data required for the analysis and design of pulse tests considering wellbore storage and skin effects at the pulsing or responding well, for tests run with unequal producing and shut-in periods. Before this study, data were limited to tests run with equal producing and shut-in periods. The use of unequal producing and shut-in periods is necessary to optimize test design and analysis. To reduce the amount of data required in this method, a new correlation is used and a set of regression coefficients is provided. A field example is included to illustrate how to use this method. Introduction The method of pulse testing was introduced into the petroleum literature by Johnson et al. in 1966. A pulse test is an interference test whereby pressure transients caused by short perturbations in flow rate at the active well are transmitted through the porous formation to an observation well and the observed pressure response is analyzed for reservoir transmissivity and storativity. An important advantage of pulse testing compared with conventional interference testing is that a pulse test provides a diagnostic response that can easily be distinguished from other reservoir trends and noise. Several investigators have shown that pulse-test data can be strongly affected by wellbore storage. In a recent study, Ogbe and Brigham concluded that the interpretation of pulse-test data without accounting for wellbore storage and skin effects can result in significant error. They proposed a method for correcting pulse-test values for wellbore storage and skin effects. However, the correction factors presented were limited to pulse tests run with equal producing and shut-in periods. In an earlier study, Kamal and Brigham showed that to optimize test time and pulse-response amplitude, a pulse test should be conducted with unequal producing and shut-in periods. The desire to optimize pulse-test time and amplitude, as well as to correct pulse-test data for wellbore storage and skin effects, creates the need to produce the correction factors for pulse tests run with pulse ratios other than 0.5. The purpose of this paper is to provide these correction factors for values of pulse ratios ranging from 0.3 to 0.7. In addition, this paper will investigate the validity of applying the new dimensionless wellbore storage correlation proposed by Ogbe and Brigham to pulse testing. A similar correlation, suggested by Ehlig-Economides and Ayoub, combines several dimensionless variables--i.e., wellbore storage, skin effect(s), and the distance between the active and observation wellsinto one dimensionless group. In their work on conventional interference testing, Ogbe and Brigham showed that the new correlation allowed us to display on a single graph most of the type curves required for the analysis of interference tests with wellbore storage and skin effects at one well. In this paper, we will attempt to extend the data-reduction capability of this correlation to produce the dimensionless data for analyzing storage-dominated pulse tests conducted with unequal pulsing and shut-in periods. Model Description The pulse-test model used is described extensively in Ref. 4. The model considers two line-source (vanishing-radius) wells in an infinitely large, homogeneous system, and the pressure response at the observation well is given bywhereNote that the pressure solution given in Eq. 1 is in Laplace space and the term L is the Laplace-space time variable. The responding well pressure response created by alternately producing and shuting in the active well can be determined by superposition of Eq. 1:where pwD1 is the pressure obtained from the inverse Laplace transformation of Eq. 1. Eq. 1 was inverted numerically with the Stehfest algorithm. Eq. 3 was used to calculate the dimensionless-pulse-test response curves similar to Fig. 1. With Eqs. 1 and 3 and the computational algorithm presented by Ogbe and Brigham, values of dimensionless response amplitude and time lag were calculated for the first four pulses. As shown in Fig. 1, the first four pulses are referred to as the first peak pulse, the first inverse pulse, the second peak pulse, and the second inverse pulse, respectively. For example, to obtain the dimensionless time lag of the first peak pulse (Fig. 1), we used SPEFE P. 743^