Analysis Of Pressure Behaviour Of Hydraulically Fractured Vertical Wells By The Effective Hydraulic Fracture Length Concept
Authors: Malekzadeh D. , Khan F.U. , Day J.J. 
Published: March 2010

Abstract
This paper presents a new technique for analysing the performance of hydraulically fractured vertical wells in bounded reservoirs. The main objective is to present a new set of practical equations, based on the recently introduced concept in well testing, for evaluating the effective length of the hydraulic fracture, contributing to unrestricted production. It is determined that the performance of a hydraulically fractured vertical well with mechanical skin and fracture half-length xf1 can be substituted by the performance of a fractured well half-length of xf2 with no skin. New equations presented in this paper can be used to determine pseudo skin factor, effective fracture length, mechanical skin factor, shape factor, and productivity index of fractured vertical wells. The new equations and guidelines given in this paper can be used to determine the magnitude of formation damage around hydraulically fractured vertical wells and to evaluate the success of the stimulation treatment. An example based on simulated well test data is presented to illustrate the application of the new technique. The problems associated with the use of the finite-conductivity fracture model are discussed and it is recommended that the pressure transient data obtained on fractured vertical wells be analysed with effective hydraulic fracture length concept, in preference to the finite-conductivity fracture model.

Introduction
Hydraulic fracturing plays an important role in increasing the productivity of a damaged well or wells producing from low permeability formations. At the present time approximately 35 to 40% of all vertical wells drilled are hydraulically fractured and 25 to 30% of total US oil reserves have been exploited by this technique(l). The net increase in the oil reserve for North America as a result of hydraulic fracturing is believed to be about 8 billion barrels(l).
A hydraulic fracturing treatment should be designed based on reservoir properties, the economics of the well, well spacing, desired propped fracture length and desired productivity index increase (which depends on the areal extent of the fracture). In addition to mechanical properties of the rock, proppant concentration, viscosity and injection rate of the fracturing fluid, the leakoff of the fracturing fluid into the formation is also an important factor affecting the volume (or size) of the induced hydraulic fracture. Hydraulic fracturing models that predict the width, length, and height of the created fracture had been developed that take into account the above-mentioned parameters.
Pressure transient analysis of hydraulically fractured wells can be used to evaluate the performance of these wells. During the last three decades, extensive studies have been done to determine the fracture characteristics and formation properties using pressure transient analysis(2–9). These studies made it possible to analyse the entire pressure history of a well test, not just long time data as in conventional analysis. Determination of wellbore storage, skin and permeability can now be determined with the aid of statistical analysis. These studies presented solutions for the infinite-conductivity, uniform-flux and finite-conductivity fractures.