Constant rate solutions for a fractured well with an asymmetric fracture

This paper presents solutions for 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. The new solutions developed for the dimensionless wellbore pressure under production at constant flow rate 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 indicated that at early times for fractures of moderate conductivity (CD<5) the characteristic slope of one fourth is present, except for cases of strong asymmetry (0.85<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<CD<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. Our results are relevant in improving the fracture characterization of fractured wells.