Effect Of Wellbore Storage And Damage On The Transient Pressure Behavior Of Vertically Fractured Wells
Authors: Cinco-Ley Heber , Samaniego V. Fernando 
Published: December 2007

Abstract
A model recently presented by Cinco et al. for the transient pressure behavior of wells with finite conductivity vertical fractures was modified to include the effects of wellbore storage and fracture damage. An infinitesimal skin was considered around the fracture, and it was handled as a dimensionless factor defined as (pi/2)(wd/xf)[(k/kd) - 1].
It was found that the well behavior is importantly affected by the fracture damage. When plotted as a function of log pwD vs lot tD for short plotted as a function of log pwD vs lot tD for short times, results show flat, almost horizontal lines that later become concave upward curves asymptotically approaching the curve for undamaged fractures. This behavior is shown even by slightly damaged fractures. It also was found that important information about the fracture characteristics may not be determined when wellbore storage effects are present. present

Introduction
It has been shown that the increase in the productivity of a well created by hydraulic productivity of a well created by hydraulic fracturing depends on fracture characteristics, such as fracture conductivity, length, penetration, and also on a possible damage to the penetration, and also on a possible damage to the formation immediately surrounding the fracture. During the last few years, there has been a continuously increasing interest in the determination of the characteristics and orientation of fractures by means of transient pressure analysis. Most of these methods consider the fracture to be of infinite conductivity or of uniform flux; others consider finite conductivity fractures. Generally, these methods assume that there is no skin damage around the fracture. Evans proposed a pressure analysis technique considering fracture skin damage. He assumed the flow from the formation to the fracture to be linear, passing through two porous media in series, one being the damaged zone around the fracture and the other the undamaged formation. Ramey and Gringarten discussed the transient well behavior of vertically fractured wells with large wellbore storage, and suggested a matching technique for analyzing pressure data. Recently, Raghavan discussed pressure analysis techniques for vertically fractured wells, including the effects of wellbore storage and skin. He assumed the fracture to be of uniform flux, and presented general characteristics of the pressure transient behavior for these systems.
The purpose of this study is to present solutions for the transient wellbore pressure behavior of a well crossed by a finite conductivity vertical fracture, considering the effect of a damaged zone around the fracture and wellbore storage. It is also intended to show the general flow characteristics of these fractured systems.

MATHEMATICAL MODELS AND METHODS OF SOLUTION
The transient flow toward a well with a finite conductivity vertical fracture surrounded by a damaged zone was studied by using a modified version of the model presented by Cinco et al. The following assumptions were considered.An infinite, homogeneous, isotropic reservoir of permeability k, porosity phi, and thickness h.The formation is produced through a vertically fractured well. The wellbore is intersected by a fully penetrating vertical fracture of permeability kf, porosity cf, width w, and permeability kf, porosity cf, width w, and half-length xf. All production of fluid is via the fracture.There is a zone of reduced permeability caused by fracturing fluid loss around the fracture. This region has a permeability ks and width ws.The porous medium contains a slightly compressible fluid of viscosity mu and compressibility c.All formation, fracture and fluid properties are independent of pressure.Gravity effects are negligible and pressure gradients are small everywhere.