TY - JOUR

T1 - Laboratory measurement of tip and global behavior for zero - toughness hydraulic fractures with circular and blade-shaped (PKN) geometry

AU - Xing, Pengju

AU - Yoshioka, Keita

AU - Adachi, Jose

AU - El-Fayoumi, Amr

AU - Bunger, Andrew P.

PY - 2017/4/21

Y1 - 2017/4/21

N2 - The tip behavior of hydraulic fractures is characterized by a rich nesting of asymptotic solutions, comprising a formidable challenge for the development of efficient and accurate numerical simulators. We present experimental validation of several theoretically-predicted asymptotic behaviors, namely for hydraulic fracture growth under conditions of negligible fracture toughness, with growth progressing from early-time radial geometry to large-time blade-like (PKN) geometry. Our experimental results demonstrate: 1) existence of a asymptotic solution of the form w ∼ s3/2 (LEFM) in the near tip region, where w is the crack opening and s is the distance from the crack tip, 2) transition to an asymptotic solution of the form w ∼ s2/3 away from the near-tip region, with the transition length scale also consistent with theory, 3) transition to an asymptotic solution of the form w ∼ s1/3 after the fracture attains blade-like (PKN) geometry, and 4) existence of a region near the tip of a blade-like (PKN) hydraulic fracture in which plane strain conditions persist, with the thickness of this region of the same order as the crack height.

AB - The tip behavior of hydraulic fractures is characterized by a rich nesting of asymptotic solutions, comprising a formidable challenge for the development of efficient and accurate numerical simulators. We present experimental validation of several theoretically-predicted asymptotic behaviors, namely for hydraulic fracture growth under conditions of negligible fracture toughness, with growth progressing from early-time radial geometry to large-time blade-like (PKN) geometry. Our experimental results demonstrate: 1) existence of a asymptotic solution of the form w ∼ s3/2 (LEFM) in the near tip region, where w is the crack opening and s is the distance from the crack tip, 2) transition to an asymptotic solution of the form w ∼ s2/3 away from the near-tip region, with the transition length scale also consistent with theory, 3) transition to an asymptotic solution of the form w ∼ s1/3 after the fracture attains blade-like (PKN) geometry, and 4) existence of a region near the tip of a blade-like (PKN) hydraulic fracture in which plane strain conditions persist, with the thickness of this region of the same order as the crack height.

KW - Fluid-driven fractures

KW - Hydraulic fracturing

KW - Asymptotic analysis

U2 - 10.1016/j.jmps.2017.04.013

DO - 10.1016/j.jmps.2017.04.013

M3 - Article

VL - 104.2017

SP - 172

EP - 186

JO - Journal of the mechanics and physics of solids

JF - Journal of the mechanics and physics of solids

SN - 0022-5096

IS - July

ER -