An Investigation of Fracture Asymmetry on the Pressure Response of Fractured Wells
Authors: Berumen Sergio , Rodriguez Fernando , Tiab Djebbar 
Published: December 2007

Abstract
This paper presents an investigation of the pressure response on hydraulically fractured wells flowing at constant flow rate through an asymmetric vertical fracture. The pressure behavior of wells intercepting asymmetric fractures of both infinite and finite conductivity was investigated by solving numerically and analytically the mathematical model. New solutions of the dimensionless wellbore pressure under production at constant flow rate are developed and are presented in terms of an asymmetry factor ξ. New curves for these systems were generated and the deviation from the classical solution was readily detected. Some qualitative criteria to interpret the intensity of this effect are provided. Results of our investigation demonstrate that the relative position of the well in the fracture, i.e. the asymmetry condition, is an important consideration for the fracture characterization. Simulated pressure well tests indicated that at early times for fractures of moderate conductivity (CD &lt; 5) the characteristic slope of one fourth is present, except for those cases of intense asymmetry (0.85 &lt; ξ ≤ 1) where no evidence of straight line having one fourth slope was observed. However, it was also detected that at intermediate fracture conductivities (5 &lt; CD &lt; 50), even the case of complete asymmetry shows the characteristic slope of one fourth. It was also observed that as the asymmetry factor increases the end of the bilinear flow occurs earlier. The tabular solutions presented in this paper describe quantitatively the pressure behavior of fractured wells producing from asymmetric fractures for a wide range of asymmetry conditions. Our results are relevant in improving the fracture characterization of fractured wells as well as in the design of fracturing operations.

Introduction
Virtually all previous theoretical analyses of fractured wells have used the same restrictive assumptions used by Gringarten et. al, Cinco et. al, Wong et. al and Tiab postulating a symmetrically homogeneous fracture frame. A few studies of the fracture asymmetry for fractured wells are available, while many others are available for the behavior of the symmetric fractures.
The relevance of fracture asymmetry to pressure analysis was first discussed by Crawford and Landrum forty two years ago, but its significance in fracturing design applications has not yet been fully recognized. Demonstration of asymmetry effects in transient pressure analysis have also been made recently by Rodriguez et. al and Resureicao y Rodriguez. Among other evidences of this phenomenon, we would like to cite the fact that perforating scheme in wells, some heterogeneities along with the stress field gradients of developed reservoirs may be responsible of the presence of asymmetric fractures.
This work is concerned with the analysis of fracture asymmetry effect on the pressure response of fracture wells. Solutions for this case are presented in tabular form for various asymmetry factors. The analysis is based on the numerical and analytical solutions to this problem, assuming constant conductivity and Darcy flow conditions.