Well-Test Analysis for Vertically Fractured Wells
Authors: Raghavan R. , Cady Gilbert V. , Ramey Henry J. 
Published: December 2007

This paper fills in some existing gaps in knowledge of the behavior ofvertically fractured wells under buildup testing conditions. It describes thegeneral characteristics of all common buildup graphs that deal with such wells. The soundness of the best approaches is substantiated: a Horner-type graph issuperior for determining permeability thickness, and a Muskat graph, properlyused, is permeability thickness, and a Muskat graph, properly used, isapplicable for determining fully static pressure.

Introduction
The pressure behavior of vertically fractured wells is of great interestbecause of the large number of wells that have been hydraulically fractured. Even though much is known about the mechanics of artificial fracturing, theperformance of wells with fractures is imperfectly understood. Studies of thiscase have been based on analytical, analog, and digital methods. Of the severalinvestigations of vertically fractured wells, the most important was conductedby Russell and Truitt, whose primary objective was to provide methods toanalyze performance of vertically fractured wells for transient andpseudosteady-state flow. They considered a homogeneous isotropic reservoir inthe form of a closed square completely filled with a slightly compressibleliquid of constant viscosity. Pressure gradients were assumed to be smalleverywhere, and gravity effects were neglected. The plane of the fracture waslocated symmetrically within the reservoir and parallel to one of the sides ofthe square boundary. The fracture extended throughout the vertical extent ofthe formation, and production was at a constant rate and was assumed to comeonly through the fracture. Russell and Truitt generated dimensionless pressureat the well as a function of dimensinless time and fracture penetration for awell producing in a reservoir like that described above. They analyzed pressurebuildup behavior by means of a Horner graph and found that significantcorrections were required to obtain correct values of permeability-thicknessproduct. The correction became more important as the fracture penetration(length) increased. They recommended that penetration (length) increased. Theyrecommended that the Muskat graph be used to obtain average pressure. Russelland Truitt indicated that they were interested in the effect of producing timeon pressure buildup analysis. However, all of their remarks seem to relateexclusively to wells that have been produced to pseudosteady state. Also, nomention was made of the pseudosteady state. Also, no mention was made of theshut-in times required to obtain the proper straight line. Thus even though theRussell and Truitt paper provides important information in the form ofdimensionless provides important information in the form of dimensionlesspressure-time data, the interpretations provided in their pressure-time data, the interpretations provided in their paper are limited. Fortunately, a recentstudy presents paper are limited. Fortunately, a recent study presents generalempirical methods that can be used to explore all useful characteristics of thecommon buildup analyses graphically. These methods will be applied to determinecorrect analytical procedures for the vertically fractured well.

Transient Flow Information
As already mentioned, Russell and Truitt have presented pressure drawdowndata for a vertically presented pressure drawdown data for a verticallyfractured well in the center of a closed square.
JPT
P. 1014