Hydraulic fracturing in a penny-shaped crack. Part I: Methodology and testing of frozen sand

Abstract

This work presents experimental data to determine the apparent fracture toughness, KQ, from hydraulic fracturing in a penny-shaped crack for frozen sand. An initial crack, represented by a circular plastic, is embedded in the specimen during the preparation with a pipe positioned perpendicular to the center of the circular crack in order to inject liquid into the penny-shaped crack. In determining the KQ, the first approach directly utilizes the penny-shaped crack stress-intensity factor (SIF), which requires the hydraulic pressure and crack radius dimension. The second approach combines the volume in the penny crack with the SIF, in which KQ is determined without using the crack radius dimension. The third approach (brittleness) explores the stress in the uncracked ligament to estimate the tensile strength (σt) and characteristic length (lch), which is related to the apparent fracture toughness. The KQ from these hydraulic fracturing approaches are validated via three-point bend (TPB) on notched and unnotched beams for frozen sand, using the same dimensions and preparation method. The hydraulic fracturing experimental results indicated that the values of KQ, σt, and lch for frozen sand are 0.22–0.66 MPa√m, 7.5–9.5 MPa, and 0.8–7.6 mm, respectively, which are comparable to the TPB results. An important outcome of this work allows for the determination or estimation of KQ, σt and lch for a material like methane hydrate in sand that is difficult to obtain using the standard test setup under the atmospheric conditions.