Statistical evaluation of hydraulic fracturing stress measurement parameters

Abstract

Statistical analysis of hydraulic fracturing field data enhances the objectivity of determining shut-in and fracture reopening pressures and fracture orientations. Using nonlinear regression analysis (NLRA), we isolate the closed-fracture segment of the pressure-time curve by fitting it to an exponential decay model. The shut-in pressure ( P s ) is expected to be in the range between P s epd−1 (the onset of the post fracture-closure segment) and P s epd− u (the pressure level of the best-fitting exponential curve extrapolated to the time of pump shut-off). We employ bilinear regression analysis to improve the objectivity of selecting P s from the pressure-decay rate vs pressure plot. The same analysis helps to identify P s in the pressure vs flowrate record obtained during steprate pressurization of the hydrofractured interval. We identify unambiguously the fracture reopening pressure ( P r ) by superposing the ascending portion of the pressure-time curves in the fracture-inducing cycle and a subsequent cycle. P r is the onset of deviation between the two curves, defined as the point where the difference in pressures is larger than a statistical “reference threshold”, provided the difference continues to increase from there on. Circular statistics and a sinusoidal curve-fitting method provide the means of objectively delineating the complete trace of induced hydrofractures from fragmented or splaying traces on the impression packer or on the borehole televiewer photograph. Examples of field hydraulic fracturing data and statistically determined pressures and fracture orientations are presented. A startling discovery was made in the course of determining P r , with our new technique: it appears to be very nearly equal to the estimated P s . A review of the literature shows that in a great number of cases P r and P s are indeed close to each other, which raises the question whether we are in fact reading the correct fracture reopening pressure.