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Abstract

A semianalytical solution was developed for the transient flow behavior of a reservoir with a well intersecting a partially-penetrating vertical fracture of finite conductivity. The transient pressure behavior of a well in this kind of system consists mainly of three flow periods:

  1. the early time,

  2. the infinite acting and

  3. the pseudoradial flow periods.

The results of this study show that the flow behavior of the partially-penetrating fracture during the early time period is equivalent to that of a totally- penetrating fracture. This period consists of a penetrating fracture. This period consists of a bilinear flow period for low conductivity fractures, and of a linear reservoir flow period for moderate to highly-conductive fractures.

The onset of the infinite-acting flow period is directly proportional to the square of the dimensionless fracture height, which is defined as the ratio between the fracture height and the fracture half length. The results show that as the value of this ratio becomes small, the infinite-acting flow period starts at very early times, such that the bilinear and the linear reservoir flow periods might not appear in the well response for practical values of time.

The approximate start of the pseudo-radial flow period does not depend significantly on the fracture period does not depend significantly on the fracture conductivity, an the fracture penetration ratio, or on the dimensionless fracture height, for moderate to highly conductive fractures, and for fracture penetration ratios larger than about 0.2. The effect penetration ratios larger than about 0.2. The effect of the dimensionless fracture height on the pressure response of a partially-penetrating fractured well becomes negligible for penetration ratios larger than about 0.8.

The vertical location of the fracture affects the behavior of the well only after the upper and/or lower boundaries of the reservoir become noticeable in the pressure response of the well. The same solutions are pressure response of the well. The same solutions are found for the early time and for the infinite-acting flow periods, until the boundary effects become evident.

Introduction

The effectiveness of hydraulic fracturing in increasing the productivity of damaged wells and wells located in low-permeability reservoirs has been recognized for many years.

It has been known for some time that data obtained from tests of fractured wells reflects the characteristics of the fractured well-reservoir system. Hence many studies have been undertaken to provide the means to evaluate the benefits of fracturing operations.

The effect of the conductivity of the fracture on the behavior of a fractured well-reservoir system was recognized early, and is reported in the works by van Poollen et al., Dyes et al:, McGuire and Sikora and Poollen et al., Dyes et al:, McGuire and Sikora and Prats. Steady-state results concerning the increase Prats. Steady-state results concerning the increase in productivity that a well would experience after fracturing were obtained by van Poolen et al., using a potentiometric model, by McGuire and Sikora, using an electric analog, and later by Prats through analytical procedures. Dyes et al. were mainly interested in the effect of fracturing on waterflooding operations. Their study was conducted using an electric analog.

Among subsequent works that contemplated the transient behavior of a vertically-fractured well were the work by Scott who used heat flow analogy, and a later work by Russell and Truitt who used a finite-difference formulation of the problem. Totally-penetrating fractures of infinite conductivity were considered in these studies.

Gringarten et al. obtained and analytical solution to the problem of transient flow of fluids towards fractured wells. Results were presented for the cases of wells with infinite conductivity and uniform flux vertical fractures. The method applied to solve these problems was based on the use of Green's and Source problems was based on the use of Green's and Source Functions whose usefulness in solving transient reservoir flow problems had been documented in a previous study. Type curves of the transient pressure previous study. Type curves of the transient pressure behavior of fractured wells were provided for use in type-curve matching procedures of well test data.

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