Analysis and evaluation of gas well tests for wells intersected by finite conductivity hydraulic fractures

A single-phase two-dimensional mathematical model was used for analyzing the behavior of a gas well intersecting a finite conductivity vertical fracture at the center of a closed square gas reservoir. Turbulent flow in both the fracture and the formation was included in the model. The analysis of the simulated well tests at constant mass rate at the sand face showed that the early portions of log m(p) vs. log t_f plots do not display the characteristic one-half slope line when the dimensionless fracture conductivity (F_CD) is less than 416. Instead, the plots display much smaller slopes, regardless of fracture length, flow rate, formation permeability, and initial reservoir pressure. The time required to reach the radial behavior constant slope line on m(p_wf) vs. log t_f plot was found to increase with: (1) increasing fracture conductivity (F_CD); (2) increasing fracture length; (3) decreasing formation permeability; and (4) increasing flow rate. Turbulent flow is found to be most significant inside the fracture. The square-root time method [m(p) vs. t μc_g] during the linear flow period yields a good estimate of the quantity kx² when fracture conductivity (F_CD)≥416. In addition, this method could be used to estimate kx² when F_CD>5 if the linear flow period inside the fracture can be defined. Finally, this paper shows that high-conductivity fractures are more important as a design criterion than the length of the fracture.