The Effect of Horizontal Hydraulic Fracturing On Well Performance
Authors: Hartsock J.H. , Warren J.E. 
Published: December 2007

Abstract
Because of the extensive utilization of hydraulic fracturing for the stimulation of low-productivity wells, the two related problems of fracture design and evaluation have become economically significant and, as a consequence, have motivated this investigation. The producing characteristics of horizontally fractured wells were studied to determine the fracture configuration that should be employed as the basis for the design of the treatment and to develop a method that can be used to establish the degree to which the design objectives have been achieved. The equations which describe the steady-state flow of a single-phase fluid into, and through, a finite-capacity fracture were solved numerically for an idealized reservoir-fracture model. The numerical results were used to obtain an apparent skin effect for each combination of the parameters considered. Based on the computed results, subject to the limitations implied by the assumptions that were made, the following general conclusions were drawn.For a radius of drainage at least four times as large as the radius of the fracture, an apparent skin effect that is independent of the radius of drainage can be calculated.The productivity of the hydraulically fractured system, relative to that of the unfractured well, can be determined from the apparent skin effect and can be used to establish design objectives.In the evaluation of a fracture job, it is not possible to determine both the radius of the fracture and its flow capacity uniquely from the apparent skin effect; an independent determination of one of the quantities is necessary.

Introduction
Although hydraulic fracturing has been employed as a method for stimulating the productivity of literally hundreds of thousands of wells during the past 10 years. It is only in the last few years that improvements in fracture design and fracturing technique have combined to increase the probability of obtaining a successful treatment to such an extent that the mechanics of the method may be considered to be standardized. From an economic point of view, however, two related questions must be satisfactorily answered before hydraulic fracturing can be used in the most profitable manner. The two questions are the following.For a particular well in a given formation, what are the optimum design specifications for the fracture treatment?Have the design objectives been achieved by the fracture treatment?
The significance of these questions has been recognized, and some attempts to obtain answers have been made. Howard, et al, endeavored to determine the optimum treatment, based on maximizing profits, for any given formation; unfortunately, this work was based on a crude method for approximating the productivity of a well. Carter and Tracy utilized the same approximation to study the effect of fracturing on the behavior of a well producing by virtue of a solution-gas drive. Electrolytic models were used by van Poollen to investigate the variation in productivity due to fracturing; however, only a limited number of results were presented. Later, from the same model results, van Poollen, et al, attempted to justify an approximate expression for determining the productivity of a fractured well. It is quite apparent that there is a definite lack of the practical information necessary for specifying the optimum fracture configuration to be considered for design purposes. The only detailed attempt to develop a procedure for evaluating the result of a given fracture treatment appears to be that of van Dam and Horner. These authors described a technique for analyzing pressure build-down data, obtained immediately after fracturing, to determine the final fracture volume, the final fracture porosity, the fracture area, the fracture thickness and the in situ fluid loss of the fracturing fluid. While this approach should be useful whenever acceptable pressure measurements are available, it does not yield a value for the flow capacity of the fracture. Since the problems of fracture design and evaluation are inversely related, it should he sufficient to study the effect of the fracture configuration on the performance of a well. The primary objective of this investigation is to evolve a technique for computing the desired solutions. The secondary objective is to analyze these computed results in order to prescribe a method for evaluating fracture treatments.
JPT
P. 1050^