Flow of High Solid Volume Fraction Fluids through Fractures and around Obstructions

We present a set of experiments to investigate the development of solid volume fraction (φ) variations in the plane of a fracture in the direction perpendicular to the flow. We injected a concentrated suspension (φ = 0.5) into the same parallel fracture in all the experiments, however, each experiment included one or two thin-plate obstructions at different locations and orientations within the fracture. Though the development of φ-gradients in the plane of the fracture was not observed in the experimental system, we did observed a surprising transient behavior of these concentrated suspensions. A pressure transient was observed at all flow rates in all experiments and suggests that the solid volume fraction distribution across the fracture as well as the distribution in the plane of the fracture affect the pressure response to a given flow rate. This pressure transient is related to the timescale associated with a solid distribution front reaching the fracture and can have major implications when designing experiments or interpreting pressure data from field operations. The distribution of solids in concentrated suspensions is further complicated in fully three-dimensional geometries such as fractures. Across the fracture aperture, the fluid will develop a solid distribution with higher concentrations towards the centerline. This non-uniform solid distribution will induce variation in the effective μ that lead to nonlinear velocity gradients across the gap. As for flow along the fracture, Medina et al. recently flowed a multimodal concentrated suspension (φ=0.5) through a transparent fracture and observed a strongly two-dimensional flow field within the fracture. They observed particles near the walls moving significantly faster than particles travelling in the middle of the fracture. The velocity variation within the fracture was attributed to variations in φ, across the plane of the fracture, which was subsequently confirmed through numerical simulations [10]. However, the source of such concentration gradients in the plane of the fracture was not fully identified in their experiments. The goal of the present work is to investigate the formation of φgradients perpendicular to the flow direction, along the fracture plane. We present results from a set of four experiments in which we flowed a concentrated suspension (φ = 0.5) through the same parallel-sided fracture with different obstructions placed within the fracture. By varying the location and orientation of the obstruction we aimed to investigate the source of the previously observed φ variations [10]. The development of a φ-gradient would manifest itself through velocity fluctuations (i.e. a nonuniform velocity field), which we measure during experiments using optical techniques. We focus on conditions where suspended solids flow with the fluid, and we do not explore the regime where settling of solids within the fracture is important. 2. EXPERIMENTAL SETUP To explore the role of concentrated suspension rheology and fracture geometry we used an experimental apparatus that allows quantitative visualization of the entire flow field [10]. Here we briefly describe the experimental apparatus, the details of the fluid-solid mixture, and the procedure used to carry out the experiments. 2.1. Experimental Apparatus A rotating stand rigidly mounts a high-sensitivity chargecoupled device (CCD) camera (Photometrics Quantix KAF-6303e) above a monochromatic (red) LED panel (Fig. 1). Clamps secure the fracture cell to the stand between the light source and the camera. The fracture cell secures the fracture plates with a fixed space between the surfaces and allows light transmission through the entire flow field. The fracture surfaces (15 cm × 15 cm × 1.2 cm smooth glass plates) are separated by two aluminum shims which act as no-flow boundaries along the fracture edges and provide a uniform fracture aperture of ~0.3 cm. Two 2.5 cm-thick fused-quartz windows supported by 2.5 cm-thick aluminum frames clamp the fracture surfaces together (Fig. 1). An electronic controller synchronizes 65 ms pulses of the LED panel with exposure of the CCD to provide reproducible images of the fracture. The CCD camera uses 12-bit digitization of the measured intensities in images with a resolution of