Pressure Buildup Analysis: A Simplified Approach (includes associated papers 11862 and 11867 and 11925 and 11926 and 13676 )

Abstract

Summary Pressure transients are modeled by the logarithmic approximation of the exponential integral (Ei) function during the infinite-acting period. Use of the logarithmic approximation has been made for studying pressurebuildup, drawdown, and falloff behavior. The conventional methods of transient analyses have been applied successfully over the past 30 years for calculating permeability-thickness product and skin. Unfortunately, estimation of average reservoir pressure (p) from pressure buildup tests for closed systems has lacked the desired level of accuracy because of the uncertainties associate dwith the definition of drainage shape in field applications. A three-constante quation has been developed from the logarithmic approximation of the Eifunction to describe the transient pressure behavior. The equation developed traces a rectangular hyperbola, which is unique to the well at the time of testing. Because of the very nature of the equation, it is possible to extra polate a buildup curve beyond the infinite-acting period to obtain pdirectly regardless of the drainage shape and boundary conditions. Consequently, we always obtain a superior p estimate compared with the conventional methods, whose applications are often uncertain in actual cases. The proposed method also enables one to calculate the permeability-thickness product and skinwith accuracy comparable to the conventional methods. The theoretical validity and applicability of the method have been demonstrated by examples. Introduction The conventional methods of pressure buildup analysis are well known. These methods have been discussed in great detail by Ramey and Cobb for closed or no-flow boundary systems, and by Kumar and Ramey and Ramey et al. for constant-pressure boundary systems. A comprehensive review of these workscan be found in Ref 7. Horner's method of buildup analysis is by far the most popular in the petroleum industry. Ramey and Cobb and Cobb and Smith concluded that the Horner graph is superior to both the Miller-Dyes-Hutchinson(MDH) and Muskat graphs regardless of the producing time in closed systems. Even though determination of permeability-thickness product and skin are relatively straightforward, the estimation of static reservoir pressure remains somewhat difficult for a well that produces at pseudo steady state before shut-in. Horner's method requires correction of the extrapolated false pressure, p*, to obtain the static reservoir pressure, p, for closed reservoir boundaries. To correct p* for various reservoir drainage shapes, Mathews, Brons, and Hazebroek (MBH) generated dimensionless pressures as a function of dimensionless producing time. These MBH pressure function curves have been used extensively in the industry and are presented in Refs. 7, 10, and 11. Ramey and Cobb also suggest a method for extrapolating a Horner straight line to average reservoir pressure for a well producing at pseudo steady state in a known reservoir drainage boundary. Odeh and Al-Hussainy proposeda technique that correlates p* to p as a function of drainage shape. Likewise, the Dietz method of estimating p from an MDH plot also requires the knowledge of drainage shape. Once the pseudo steady-state flow is achieved, applicationof Slider's technique appears to be superior to the other methods just mentioned. The main advantage of Slider's desuper position method is that the reservoir shape definition no longer is required. JPT P. 178^