Pressure Transient Behavior Of The Uniform Flux Finite Capacity Fracture
Authors: Hanley Edward J. , Bandyopadhyay Pratip 
Published: December 2007

Abstract
A relatively simple semi-analytical model is developed for a well in a square with a fully penetrating fracture. Building upon this unit system with penetrating fracture. Building upon this unit system with uniform flux at the fracture face, the effects of storage, fracture length, fracture capacity, formation properties and reservoir boundaries are investigated.
New type curves which simultaneously incorporate concepts of uniform flux and finite fracture capacity are presented for both the constant flow rate and constant terminal pressure cases. The results of this study compare favorably with appropriate published data.
The practical application of the theoretical results to pressure transient testing of fractured wells is emphasized. The dominant flow regimes and their dimensionless time durations are identified for specification of appropriate data analysis methods. The result is establishment of a systematic method for evaluation of hydraulic fracture effectiveness. Furthermore, the technique can be readily applied for generating the corresponding well performance forecast. The utility of the method is demonstrated using real field data.

Introduction
With the accelerating demand for domestic natural gas and oil, the use of large hydraulic fracture treatments for stimulation of low permeability reservoirs has become a common practice. Improved diagnostic techniques are needed for evaluating the effectiveness of these treatments. More precise post-stimulation assessment will allow for better control of design for future treatments. Also, accurate characterization of the fractured well is needed for performance forecasting and optimal reservoir development. Conventional fracture analysis methods are inadequate for evaluation of large propped fractures in tight formations. The application of these methods in such situations has often produced incorrect results.
The concept of the finite capacity fracture has done much to improve understanding of the influence of large hydraulic fractures upon well performance and pressure transient behavior. The characteristic flow pressure transient behavior. The characteristic flow behavior of the finite capacity fractured well has been discussed in the literature and type curves have been published for the evaluation of fracture effectiveness. published for the evaluation of fracture effectiveness. Practical considerations, however, have limited Practical considerations, however, have limited the use of available type curves and theoretical predictive methods. The finite capacity type curves predictive methods. The finite capacity type curves suffer from a lack of uniqueness. Indiscriminate use of these curves will produce erroneous results. While it has been demonstrated that a reliable analysis may be performed through a judicious application of type curves and analytical methods it is recognized that a better understanding of the characteristic fractured well flow behavior is needed. This knowledge can be acquired through development of relatively simple system models. With very sophisticated models, insight into the problem is often lost through the complexity of the solution.
In the present study, a tractable model is developed to describe the physics of the fractured well system. The model is based upon the drawdown behavior of a well intercepted by a finite capacity fracture where a uniform flux is maintained at the fracture face. Effects of storage, formation properties, fracture properties and reservoir boundaries are considered. Emphasis is placed upon the practical application of the Uniform Flux Finite Capacity Fracture (UFFCF) model to pressure transient testing and analysis.

THEORETICAL DEVELOPMENT
The basic unit in the UFFCF model is a well in a closed square reservoir intersected by a finite capacity vertical fracture. The fracture fully penetrates the reservoir height and width. This unit system is shown schematically in Figure 1.