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How granular media behave when invaded by a fluid is a question of fundamental scientific importance. While extensive literature exists for the two limiting cases when the granular media either behave as rigid porous media or are dispersed in a fluid to form a dilute suspension, the process in dense granular media where grain displacements occur as a result of fluid flow is still poorly understood. Fundamental understanding of the injection process in dense granular media is also critical to many engineering applications, e.g., hydraulic fracturing and water flooding in unconsolidated formations and drill cuttings reinjection.

Granular media such as sands can be considered either as a nonlinear deformable solid or as a non-Newtonian fluid with a yield stress (a viscoelastic mixture of particles and fluid). We therefore hypothesized that the behaviors of dense granular media when invaded by a fluid could be both solid-like, similar to hydraulic fracturing, and fluid-like, similar to viscous fingering (a Saffman-Taylor type of instability). There must be transitions from solid-like behaviors to fluid-like behaviors under certain conditions.

During this report period, we have successfully verified such a conceptual hypothesis via physical experiments. The experimental set up was based on a Hele-Shaw cell-like configuration. The Hele-Shaw cell consists of two transparent PMMA plates with an adjustable gap size. The cell was filled with dense dry sands, Ottawa F110, and can be considered as a plane strain representation of the granular media. The fluid was injected from the center of the bottom plate. Aqueous glycerin solutions at various weight concentrations were used as the invading fluid. The experiments were designed so that the capillary effect was negligible.

By adjusting the fluid viscosity via the weight concentration of the glycerin solutions and by changing the flow velocity via the flow rate and the gap size, we can identify four distinct displacement patterns or failure/flow regimes, namely, i) simple radial flow, ii) infiltration- (or leak off) dominated regime, iii) grain displacement-dominated regime, and iv) viscous fingering-dominated regime. Given the same granular media properties, the displacement patterns evolve from i) to iv) as the product of viscosity and flow velocity increases. In the simple radial flow regime, fluid only permeates through the granular media and no fluid channels are created. In the infiltration-dominated regime, fluid channels (or fractures) develop near the inlet. However, the permeation fronts remain circular and are not affected by the growth of the fluid channels (or fractures). In the grain displacement-dominated regime, the permeation fronts now reflect the propagation of the fluid channels and the channels are much wider. The behavior of the media in the viscous fingering-dominated regime resembles that of fluid-fluid invasion for flow in porous media. The behaviors of the granular media in regimes (i)-(iii) are more solid-like while the behavior in regime (iv) is more fluid-like. We may argue that these failure/flow patterns emerge as a result of competition among different forms of energy dissipation, i.e., viscous dissipation in the infiltration process, mechanical dissipation via grain displacement and viscous dissipation for flow through thin channels.

From the start of the project in January 2010, funding from PRF has supported two graduate students, one in Spring 2010 and the other in Summer 2010. For the next report period, we will focus on analyzing the images from the experiments and to model the experiments numerically.