A MODEL ANALYSIS OF SAND INSERTION IN HYDRAULIC FRACTURES

Abstract

Hydraulic fracturing (fracking) is a well-stimulation technology to create large volume of fracture formation in rocks for gas and/or oil extraction. This technology has been applied to commercially exploit natural gas in unconventional shale reservoirs that contain immense quantity but low density of hydrocarbon sources. The productivity can be largely dependent on the connectivity of fractures that must stay open. However, upon initial hydraulic fracturing, the fractures would be closed due to high hydrostatic pressure deep inside the crust. Sand must be pumped into the fractures to keep them open. An in-depth understanding of the sand distribution and its dependence on operation parameters is essential to keep improving the flow conductivity and hence improving the fracking productivity. In the present study, a model is developed to analyze the sand motion along with hydraulic flow inside an opening crack. The crack opening profile is determined by the hydraulic pressure field meanwhile the hydraulic pressure field is in turn determined by the crack opening profile. They are described by the elastic fracture mechanics theory and the viscous gap flow theory, respectively, and are solved together. Upon the flow field, the sand transport problem is modeled with both inertia and convective effects taken into account. The thermal diffusion is also considered but determined to be trivial in comparison to those two effects. Parametric studies are carried out in terms of applied hydraulic pressure, fluid viscosity, and sand particle size. It is found that smaller sand particle size, lower fluid viscosity and higher hydraulic pressure can lead to greater depth of sand moving into a fracture. The sand insertion depth and quantity are sensitive to fluid viscosity only when the viscosity is low. The applied hydraulic pressure plays the most important role in moving sand into a fracture, probably because it determines the fracture opening gap. When the fracture is opened more with a higher hydraulic pressure, more sand can be moved in.