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Renormalization of miscible flow functions. (English) Zbl 0708.76133

Summary: We present a numerical renormalization study of two-phase, viscous fingering flow in a uniform two-dimensional porous medium. Iterating our procedure gives the effective flow parametrization appropriate to successively larger scales and enables us to compute flow functions that can be used to simulate kilometre-sized oil reservoirs, starting from functions appropriate to 10cm core samples. We parametrize the local flow in terms of the fractional and total flows across a block as functions of the average composition and pressure gradient across the block. From numerical simulations on a fine grid, we measure the corresponding flow functions for larger blocks: these show only limited statistical scatter and so allow us to define a renormalization. We discuss the range of physically significant fractional flow and total mobility functions, and find evidence for non-trivial fixed point behaviour of these functions in the fingering instability regime.

MSC:

76S05 Flows in porous media; filtration; seepage
76T99 Multiphase and multicomponent flows
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