Determination Of The Orientation Of A Finite Conductivity Vertical Fracture By Transient Pressure Analysis
Authors: Cinco-Ley Heber , Samaniego V. F. 
Published: December 2007

Abstract
A method is presented for the determination of the orientation of fully penetrating vertical fractures by means of analysis of transient pressure data recorded at the active well and at two observation wells due to production or injection at the active fractured well. The fracture is considered to be of finite conductivity. The method discussed in thus work is an extension of the method of Uraiet et al. for the determination of compass orientation of vertical fractures. They considered uniform flux fractures. Results of this study show that when the pressure interference data, on the presence of finite pressure interference data, on the presence of finite conductivity fractures, are matched to the uniform flux-type curves, a match may not be obtained correctly.

Introduction
It is important to know the flow patterns created after a number of wells in a reservoir have been hydraulically fractured. This is of prime interest for enhanced recovery projects. Also, the development of low-permeability reservoirs using fracturing techniques requires an accurate knowledge of the dimensions and orientation of the fractures. This is essential for well spacing purposes if interference effects are to be minimized.
Several methods have been suggested for determining the orientation of fractures. Elkins and Skov discussed a method for the determination of the orientation of natural fractures in a reservoir. They considered the fractured system (the reservoir) to be of anisotropic permeability and used the line-source solution to find the orientation of the major fracture trend. Reynolds et al. and Fraser and Pettit presented a method to obtain data about the fractures presented a method to obtain data about the fractures by means of an inflatable formation packer. They could get information about the type of fracture, vertical, horizontal or inclined, and the penetration and orientation. Pierce et al. described a way to us use pulse testing to determine the fracture length and orientation. Power et al. showed how acoustic, seismic, and surface electric-potential measurements can be applied to detect fracture orientation. Recently, Uraiet et al. discussed a method for determining the fracture orientation using transient pressure data recorded at the active fractured well, pressure data recorded at the active fractured well, production or injection, and at the observation wells. production or injection, and at the observation wells. They considered the fracture to be of uniform flux.
The purpose of this study is to extend the method recently presented by Uraiet et al. to the case of finite conductivity fractures, and provide type curves for the analysis of pressure interference data. It is also intended to show what kind of problems may arise when pressure interference data, created by an active finite conductivity fractured well, are matched to the uniform flux-type curves.

MATHEMATICAL FORMULATION
The mathematical model considered in thus study is the finite conductivity vertical fracture model of Cinco et al. It is assumed that the porous medium is isotropic, homogeneous, horizontal, of uniform thickness h, permeability k, and porosity phi. All formation properties are assumed to be independent of pressure. The reservoir contains a slightly pressure. The reservoir contains a slightly compressible fluid of compressibility c and viscosity mu, both properties being constant. Fluid is produced through properties being constant. Fluid is produced through a vertically fractured well intersected by a fully penetrating finite conductivity fracture of penetrating finite conductivity fracture of half length xf, width w, and permeability kf. These fracture characteristics are constants and fluid entering the wellbore comes only via the fracture.
The system defined under the above assumptions is shown in Fig. 1.
It is also assumed that gravity effects are negligible and that Darcy flow occurs in the porous medium and in the fracture.
It can be shown that the dimensionless pressure drop at a point (xD, yD) in the reservoir, created by the fractured active well can be expressed approximately by the following equation.
PD(XD,YD,TDM) = PD(XD,YD,TDM) =