Mixing Rules at Pore and Fracture Junctions

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9405837 Wilson We propose to use a mathematical model and laboratory experiments to elucidate the mixing rule at the pore body or fracture junction scale. Traditional models have assumed that tracers or contaminants entering one of these junctions are either well mixed, or follow flowlines through the junction. A cellular automata numerical model and a machined Lucite experimental micromodel are proposed to investigate the hypothesis that there is a range of mixing rules between these limits. The Peclet number would be used to position in flow between diffusion control leading to the well mixed rule, and advection control, with contaminants never leaving a flowline. A pore or fracture junction Peclet Number is defined as the mean advective velocity times pore/fracture size, divided by the diffusion coefficient. At high velocities and high Peclet Numbers there is little mixing across the dividing stream line, yielding advective control. At small velocities and Peclet numbers diffusion dominates, resulting in complete mixing. We hypothesize that the transition between these limits spans about an order of magnitude of Peclet numbers, and occurs near a Peclet number of 1. Lattice gas automata (LGA) and /or lattice Boltzman methods will be used to numerically simulate flow and transport simultaneously. These methods work well for Peclet numbers near one, but a new algorithm has been developed to efficiently model dilute solutions of non-homogeneous fluids in order to economically vary Peclet number over a large range, while holding Reynolds number constant. The experimental approach employs a Lucite physical micromodels of a junctions, consisting of four intersecting channels. In order to accommodate the expected range of Peclet numbers the low Reynolds number, and reasonable experimental time constants, the channels and flow rates must be quite small. At low flow rates and Peclet numbers the experiment is very sensitive to leaks, temperature fluctua tions, and other problems. We built a preliminary version of the experiment to elucidate and solve each of these problems. The cellular automata simulations and the physical micromodel will be used to explore mixing with different combinations of entering and exiting flow rates, and with different junction geometries. We will then work with other investigators to apply the rules to percolation network models of porous systems, and various fracture network systems, to determine the spatial distribution of mixing rules, and their effect on mechanical and macro-dispersion calculations. Through collaborations we will simulate miscible displacement experiments in the networks, with mixing, no-mixing and adaptive mixing rules, to further investigate the range of mixing conditions.