Fracture pressure-slope analysis for TSOs in high-permeability formations

The relative popularity and success of the frac-pack technique in hydraulic fracturing has resulted in some misconceptions regarding the objective, procedure, and pressure analysis after a screenout. This paper addresses frac-pack procedures and the pressure response after a tip screenout (TSO). An analytical method has been developed for analyzing pressure-slope behavior after a TSO in high-permeability formations. These equations incorporate the first order parameters affecting the fracture pressure, rate of pressure change (derivative), and pressure-slope behaviors after a screenout. The fundamental equations for pressure-slope analysis are similar to those originally developed by Nolte for pressure-decline analysis. The major difference is that after the fracture stops propagating (i.e., after a TSO), the injection rate is not zero. Consequently, if the injection rate is greater than the leakoff rate, the fracture volume and net pressure (constant compliance) must increase. If the injection rate falls below the leakoff rate, the fracture net pressure must decrease. Although analytical equations will not replace 3D fracturing simulators normally used for design and real-time history matching, they do provide insight into the major parameters affecting pressure behavior after a TSO without running a numerical simulator. The analytical equations presented in this paper demonstrate why pressure slopes after a screenout are typically much greater than unity for low-efficiency fractures. A generalized set of equations is presented for analyzing the pressure-slope behavior after a screenout. Numerous graphs are provided that illustrate the parametric effects of fracture efficiency, spurt loss, and fracture net pressure at the time of a screenout on the pressure, derivative, and slope behaviors after a TSO. Comparisons of the analytical pressure-slope equations with a 3D fracturing simulator are presented to show the analysis' application. A new methodology of frac-pack post-analysis is presented using the pressure slope technique. This methodology uses the pressure slope during a screenout as a check on the minifracture and fracture efficiency. Two frac-pack cases with bottomhole data are analyzed with a 3D hydraulic fracturing simulator to illustrate the pressure-slope analysis for low efficiency fractures.