Grain breakage criteria for discrete element models of sand crushing under one-dimensional compression

Frac sand consisting of quartz grains is widely used in hydraulic fracturing of tight shales to prop fractures open. However, the sand can be crushed by high compressive stress acting on the fractures and this reduces the fracture conductivity. In practice, a one-dimensional compression test is widely used to evaluate the crushing resistance of frac sand. This paper presents the results of discrete element modelling of sand crushing calibrated with laboratory data from one-dimensional compression tests. Three criteria for grain breakage that incorporate grain-size dependent particle strength and failure under shearing/tensile conditions were implemented and evaluated in PFC2D. An innovative aspect is linking the breakage of a clustered particle under multiple contacts in PFC2D to grain breakage criteria to examine the applicability of these breakage criteria in grain crushing. A macro-scale calibration demonstrates how incorporation of particle breakage algorithms can allow the PFC2D model to capture the change in particle size distribution as well as the non-linear stress-strain response of sand under high compressive stresses. The calibrated grain breakage criterion was used to study the crushing behaviour and permeability evolution of a mesh 20/40 Jordan frac sand.