Publications

Hydraulic fracturing uses substantial amounts of proppants to keep the fracture open. The arrangement of proppants inside the fracture depends on several parameters that are included in the pad stage, slurry stage, and rock properties. Lower amounts of proppants can be placed close to the fracture tip due to the limited fracture width. Therefore, only one layer of proppants might form, either as a compacted monolayer or a less compacted partial monolayer. The interaction of rock and proppant during drawdown can lead to proppant embedment in ductile formations, and proppant or rock crushing in brittle formations. Both cases cause a loss of fracture conductivity which directly impacts well productivity. A better understanding of the relationship that exists between proppants and rocks can allow better treatment designs. This interaction is investigated in this study through the development of a semi-analytical model. This model uses the basis of contact mechanics for sphere–plane interactions to find the deformation profile of the fracture. Different parameters were considered in this study including, proppant size, concentration, and arrangement. The results were compared with an existing analytical model and a numerical model. The simulation results suggest that using non-uniform proppant sizes in a fractured rock can have a significant impact on the crushing and embedment of proppants. Furthermore, a mixture of proppant sizes can provide better fracture conductivity results for the cases considered in this study. The ultimate compressive strength of the larger-sized proppants is a critical parameter in the success of this design.