Image-based Stokes flow modeling in bulk proppant packs and propped fractures under high loading stresses

Rock fracturing, followed by proppant injection, has been used for years to improve oil and gas production rates in low permeability reservoirs and is now a routine part of producing from low-permeability resources such as a shales and tight sands. While field data makes clear the effectiveness of this technique, there is still much room to improve on the science, including how the proppant-filled fracture system responds to changes in loading stress and the corresponding impact on the proppant structure and fracture width, which affect permeability and conductivity. Here, we use high-resolution x-ray computed tomography (XCT) to image two unsaturated rock/fracture/proppant systems: one with shale, one with Berea sandstone. Both systems were imaged under a series of stress levels typical of producing reservoirs. The resulting XCT images were segmented, analyzed for structural and porosity changes, and then used for image-based flow modeling of Stokes flow using both finite element (FEM) and Lattice Boltzmann (LBM) methods. The images and quantitative grain analysis showed expected changes as stress increased: rearrangement of the packing structure, corresponding reduction in porosity, and some embedding at rock walls to a depth of less than 0.5 times the proppant diameter. The shale system exhibited more embedding than the Berea system. At the highest stress in the Berea system (20 kpsi or 138 MPa), individual proppant particles failed and the broken particles caused significant loss of permeability. For the shale system, the embedding had a significant effect on the simulated permeability/fracture conductivity. Simulation results for each of the loadings showed that permeability is less sensitive to loading than experimental (vendor-reported) permeability values, but also show reasonable agreement at 8 kpsi (55 MPa) for both systems. Another somewhat surprising result is that fracture permeability for the single-layer proppants confined between shale is similar to what would be predicted from bulk proppant results, despite the significantly different flow geometry in the monolayer fracture.