Pressure Buildup Analysis For Wells Influenced By Fractures And Other Heterogeneities
Authors: Chen T. 
Published: March 2010

Abstract
A new approach has been devised to analyze pressure buildups in heterogeneous reservoirs. The proposed procedure is a modification of the semi-log straight line plotting of Horner analysis. It is also an improvement over the conventional type curve matching technique in that the effect of flow time, and the rate variations during drawdown, are incorporated. Applications of this procedure to analyze heterogeneities characterized by a linear boundary, natural fractures, and a vertical fracture demonstrate the strength of the approach.

Introduction
The Horner plot(1,2) has been used successfully in the analysis of buildups taken after constant rate drawdowns from infinite acting, homogeneous reservoirs. If all the underlying assumptions are valid, then a plot of shut-in pressure versus the logarithm of the Horner time group results in a straight line. Parametric estimations can be made from the slope and intercept of this line.
Any type of heterogeneity in the reservoir introduces deviations from linearity in such a plot. For mild near wellbore heterogeneities such as wellbore storage or skin, only the early time data is affected. If, however, the duration of the shut-in time is short, then the initial deviation from linearity may cause some uncertainty in determining the start of the semi-log straight line. Ramey(3) introduced the type curve matching technique to resolve this problem. It has been used mainly to detennine the start of the semi-log straight line. Homer analysis is still required for parametric estimation purposes.
In situations with more complex heterogeneities, the deviation from linearity in Homer plots is more serious. In some cases, such as pressure buildups taken from wells intersecting vertical fractures, the data points in a Horner plot curve continuously upward, making the choice of an appropriate semi-log straight line difficult, if not impossible. Clearly, Horner analysis is inadequate in these situations and, instead of being a supporting tool, type curves themselves are being used increasingly for parametric estimation.
Because most of the type curves are a dimensionless pressure solution to the constant rate drawdown boundary condition, their use for buildup analysis requires an extra assumption of the total flow time being much longer than the shut-in time. When this assumption is not valid, McKinley(4), and Raghaven(5) suggested using buildup type curves. Thus, from one single drawdown curve it is necessary to generate a number of buildup type curves for different flow times. As the number of drawdown type curves multiplies, the choice of a best match among the multitude of buildup curves is not an easy one.
Another problem associated with the constant rate assumption is that it can be impractical to maintain the rate constant during the field test. Bostic et. al.(6) attempted to modify the drawdown type curves to take into account rate variations. Their derivation, however, depends on an erroneous substitution of the measured pressure into the dimensionless pressure. Hence the subsequent derivation cannot be used.
Recently, Rosa and Horne(7), Kucuk et al.(8), and Lee and Brockenbrough(9) devised least squares optimization schemes to resolve the above-mentioned problems with type curve matching.