Flow of concentrated suspensions through fractures: small variations in solid concentration cause significant in‐plane velocity variations

Abstract

AbstractFlow of high‐concentration suspensions through fractures is important to a range of natural and induced subsurface processes where fractures provide the primary permeability (e.g., mud volcanoes, sand intrusion, and hydraulic fracturing). For these flows, the simple linear relationship between pressure gradient and flow rate, which applies for viscous‐dominated flows of Newtonian fluids, breaks down. We present results from experiments in which a high concentration (50% by volume) of granular solids suspended in a non‐Newtonian carrier fluid (0.75% guar gum in water) flowed through a parallel‐plate fracture. Digital imaging and particle‐image‐velocimetry analysis provided detailed two‐dimensional maps of velocities within the fracture. Results demonstrate development of a strongly heterogeneous velocity field within the fracture. Surprisingly, we observed the highest velocities along the no‐flow boundaries of the fracture and the lowest velocities along the centerline of the fracture. Depth‐averaged simulations using a recently developed model of the rheology of concentrated suspensions of monodisperse solids in Newtonian carrier fluids reproduced experimental observations of pressure gradient versus flow rate. Results from additional simulations suggest that small (3%) variations in solid concentration within the fracture can lead to significant (factor of two) velocity variations within the fracture yet negligible changes in observed pressure gradients. Furthermore, the variations in solid concentration persist over the length of the fracture, suggesting that such heterogeneities may play a significant role in the transport of concentrated suspensions. Our results suggest that a simple fracture‐averaged conductivity does not adequately represent the transport of suspended solids through fractures, which has direct implications for subsurface suspension flows where small concentration variations are likely.