Modeling the flow of non-Newtonian fluids in packed beds at the pore scale
Flow and transport in porous media are important in many science and engineering applications such as composite materials, subsurface water contamination, packed-bed reactors, and enhanced oil recovery. The general approach to modeling such processes is at the continuum scale. Semi-empirical expressions, such as Darcy's law, are substituted for velocity in the continuity equation, which is then coupled with a momentum, mass, and energy balance. While a continuum approach is acceptable in some cases, additional modeling is required for certain non-linear flows, such as multi-phase flows, inertial flows, non-Newtonian flows, and reactive flows. Pore-scale modeling is a first-principles approach to modeling flow and transport in porous media. In this work, network models that are physically representative of specific unconsolidated media are created. The networks can be used to model a wide range of flows, but the focus here is on polymers and suspensions that exhibit non-Newtonian behavior. The network models are used to model steady flow as well as displacement by less viscous fluids. The transient displacement is used to investigate important viscous fingering patterns. While simple boundary conditions are typically imposed in network modeling (e.g. a pressure gradient in one dimension), a more general approach has been developed where boundary conditions are also imposed by direct coupling to an adjacent continuum region. Important qualitative and quantitative results are obtained from the network model for non-Newtonian fluids. Preferential flow pathways form in the network due to the inherent heterogeneity and interconnectivity in porous media. Quantitative results of Darcy velocity versus applied pressure gradient show different behavior than semi-empirical models (analogous to Darcy's law) for non-Newtonian fluids. The transient displacement patterns for non-Newtonian fluids are also different than for Newtonian fluids. If the fluid exhibits a yield stress, a steady state is reached in which some of the original non-Newtonian fluid is left trapped in the network. The displacement patterns are affected by the boundary conditions, which can be determined from direct coupling to a continuum region.
porous media, pore-scale modeling, network modeling, non-newtonian flow, yield-stress fluids, packed beds
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