Experimental characterization of time-dependent mechanical behaviours of frac sand at high compressive stresses and implication on long-term proppant conductivity

Abstract

This paper experimentally examines the time-dependent mechanical behaviours of frac sand at high compressive stresses. A series of instant and sustained one-dimensional compression tests was performed on Jordan sand, White sand, and Genoa sand, and three grain size distributions for each frac sand were tested. The acoustic emission events related to sand crushing were monitored by piezoelectric sensors for understanding sand breakage during compression. The results show that Genoa sand with 25% weaker anorthite mineral grains show much more grain breakage and higher plastic and creep strains at high compressive stresses than the pure quartz Jordan and White sand. Wider grain size distributions tend to result in larger plastic strains than narrower size distributions but provide better crushing resistance and smaller creep deformation. Cyclic and creep load stages only slightly increase grain breakage compared with instant loads, but result in higher plastic and creep strains. Two creep stages were found in the time-dependent deformation of sand and can be satisfactorily depicted with the Riemann–Liouville fractional calculus model at different stress levels, with sand’s fractional derivative of increases from 0.28 to 0.35 as sand grains are gradually crushed. Lower viscosity coefficients are found in Genoa (~ 15e4 MPa*s) than White and Jordan sand (> 20e4 MPa*s). The time-dependent deformation of sand proppant has a significant implication on the long-term conductivity of sand packs, which can reduce the hydraulic conductivity by about 40%–90% after a one-year duration. The results warrant considering frac sand’s long-term deformation when choosing frac sand as proppants in hydraulic fracturing.

Article Highlights

• Weaker Genoa sand shows 50–150% higher plastic and creep strains than Jordan and White sand at high compression.

• Wider grain size distributions result in larger plastic but smaller strains creep in sand at sustained loads.

• Creep strain is depicted by fractional calculus with an increased derivative from 0.28 to 0.35 as sand is crushed.