Determining Barrier Distance from Transient Well Test Data
Authors: Peres Alvaro M. M. 
Published: December 2007

Abstract
Wellbore storage, short producing times and variable rate effects usually make the identification and computation of the well-to-fault distance from well test data a difficult task. The semilog method is, by far, the most popular method to estimate the fault distance. Several approximated formulae applicable to semilog methods are widely used in field practice. Sometimes, however, these equations have been used out of their range of applicability. Such practice introduces an error which can be eliminated by a correction factor derived in this work. The resulting new equations are very accurate, yet simple enough for field applications. New equations for determining fault distance for variable rate tests are also provided. The new equations are based on the well known superposition time function, therefore the proposed expressions can be applied directly to field data without any extra computation. One of the major difficulties of the semilog methods is the proper selection of the straight lines. In this work, a plot of the pressure to pressure derivative ratio [Δp/(2Δp')] versus the logarithm of time is used to identify the semilog straight lines. This plot also allows an independent estimate for the fault distance and skin factor. For the wellbore storage case, the pressure to pressure derivative ratio presents a distinct behavior when a sealing fault exists near a well. It is also shown that the existent wellbore storage and skin type curves for infinite reservoirs can be used to calculate the fault distance. Field examples are presented to illustrate the use and the reliability of the new analysis procedure.

Introduction
It has been recognized that a proper identification and location of a flow barrier near a well is a fundamental information for field development and secondary recovery project design. This paper considers the analysis of transient pressure data from a well near a single sealing fault. Several techniques to determine the distance to a barrier from transient tests have appeared in the technical literature over the last 45 years. This paper reviews some of these previous works and presents new methods that improve our ability to detect and estimate the barrier/fault distance. The first procedure to estimate the distance to a fault from a transient test was due to Homer. Ref. 1 has shown that a semilog plot of the shut-in pressure of a well near a sealing fault yields two straight lines. The reservoir permeability and skin factor are obtained from the first semilog straight line, whereas the extrapolation of the second straight line to infinite shut-in time provides the reservoir pressure. An interesting feature of this plot is that the second semilog straight line has twice the slope of the first straight line. Homer also presented a procedure to estimate the fault distance from the intersection point of these two straight lines. Using the logarithm approximation to the integral exponential function in Homer's procedure, Dolan, Einarsen and Hill derived a simple formula to estimate the fault distance from a buildup test. Park Jones has shown that a drawdown test also presents two semilog straight lines for a well near a fault. Ref. 3 also derived a formula based on the intersection time of the semilog straight lines. Davis and Hawkins indicated that Park Jones' formula can also be used to estimate the barrier distance from a buildup test when the producing time is much larger than the shut-in time. Standing tried to improve the accuracy of Davis and Hawkins' formula for short producing times by adding a correction factor. Gray used a synthetic buildup data to evaluate different methods to determine fault distance. Ref. 6 concluded that Homer's procedure becomes less accurate as the producing time is reduced, whereas the Davis and Hawkins formula gives acceptable accuracy for buildup tests even for cases where such formula is applied out of its range of validity. Gray has also shown that the derivation of Standing's correction factor has a conceptual mistake, leading to wrong fault distance calculation. Tippie and van Poollen considered the producing time effect on the buildup pressure response.