Utilizing Ultrasonic Waves in the Investigation of Contact Stresses, Areas, and Embedment of Spheres in Manufactured Materials Replicating Proppants and Brittle Rocks

In the oil and gas industry, hydraulic fracturing (HF) is a common application to create additional permeability in unconventional reservoirs. Using proppant in HF requires understanding the interactions with rocks such as shale, and the mechanical aspects of their contacts. However, these studies are limited in literature and inconclusive. Therefore, the current research aims to apply a novel method, mainly ultrasound, to investigate the proppant embedment phenomena for different rocks. The study used proppant materials that are susceptible to fractures (glass) and others that are hard and do not break (steel). Additionally, the materials used to represent brittle shale rocks (polycarbonate and phenolic) were based on the ratio of elastic modulus to yield strength (E/Y). A combination of experimental and numerical modeling was used to investigate the contact stresses, deformation, and vertical displacement. The results showed that the relation between the stresses and ultrasound reflection coefficient follows a power-law equation, which validated the method application. From the experiments, plastic deformation was encountered in phenolic surfaces despite the corresponding contacted material. Also, the phenolic stresses showed a difference compared to polycarbonate for both high and low loads, which is explained by the high attenuation coefficient of phenolic that limited the quality of the reflected signal. The extent of vertical displacements surrounding the contact zone was greater for the polycarbonate materials due to the lower E/Y, while the phenolic material was limited to smaller areas not exceeding 50% of polycarbonate for all tested load conditions. Therefore, the study confirms that part of the contact energy in phenolic material was dissipated in the plastic deformation, indicating greater proppant embedment, and leading to a loss in fracture conductivity for rocks of higher E/Y.