Analysis of Short-Time Buildup Data for Finite-Conductivity Fractures
Authors: Rosato N.D. , Bennett C.O. , Reynolds A.C. , Raghavan R. 
Published: December 2007

Summary
A finite-conductivity vertical fracture intersecting a well is considered. The well is produced at a constant rate or at a constant pressure and then is shut in. The pressure response during the buildup period and the pressure or rate response during the production period are obtained from a numerical model.
In this work we discuss the analysis of pressure buildup data following a short flow period. We present a buildup type curve to analyze pressure buildup data when the pressure (or rate) response is influenced by only the bilinear flow period. This type curve can be used to estimate the fracture flow capacity and a lower limit for the fracture half-length. It will be useful when the equivalent-time or the equivalent-drawdown concepts cannot be used.
We discuss strengths and limitations of the equivalent time method proposed in the literature. The theoretical basis for this procedure is provided.

Introduction
Virtually all type curves available in the literature are intended for analysis of drawdown data and thus can be used to analyze buildup data only if the producing time before shut-in is significantly longer than the buildup time. Although this limitation is stated in the literature as far back as 1970, the consequences of using the drawdown type curves to analyze pressure buildup data measured after a short flow period were documented only recently. Buildup type curves that take into account the influence of producing time also are presented in Ref. 1.
More recently, attempts have been made to bypass the buildup type curves and to use the drawdown curves directly. Raghavan et al. Suggests that buildup data can be converted to drawdown data and thus that the drawdown type curves can be used directly. This is the most accurate procedure available since it involves a minimum number of assumptions, but it does require that drawdown data be available unless Delta t/t less than 0.1 or Delta t/t &gt;1. The principal advantage of the method is that it allows analysis of buildup data when Delta t &gt;t. This is extremely important if the producing time before shut-in is small.
An alternative procedure suggested by Agarwal involves a modification of the time scale and is known as the equivalent-time method. Theoretically, the method is valid only if plane radial flow prevails. However, Agarwal was able to demonstrate empirically that this technique applies to fractured wells.
The principal objectives of this paper areto show that the normal form of the drawdown type curves for finite-conductivity fractured wells is inadequate to analyze buildup data following a short flow period,to present a modified version of these curves to analyze short-time data (drawdown or buildup),to present a buildup type curve suitable for analyzing data measured after a short production period,to discuss the strengths and limitations of the equivalent-time method, andto establish a theoretical basis for this procedure and to explain the empirical findings of Agarwal.
3 The buildup type curve presented here can be used to analyze tests in fractured wells when the response during the flow period is dominated by the bilinear flow regime. The type curve should prove useful when the other two methods suggested in the literature cannot (or should not) be used.

Definitions
All results given in this study are presented in terms of dimensionless variables. The dimensionless variables are defined in the following equations.
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