Darcy's law and critical pressure drops for yield stress fracture flows

Abstract eng:
Using numerical computation, we explore the validity of lubrication/Hele-Shaw approaches for 2D channel flows of a Bingham fluid: effectively Darcy’s law. Wavy and linear profiles approximate a simple fracture and a shift between top/bottom walls adds tortuosity. The Darcy law estimate is valid as far as the geometry is long and thin, as expected. In other geometric ranges a major diversion occurs due to appearance of fouling layers, i.e. static fluid attached to the walls. Fouling gives an O(1) modification to the aperture, resulting in O(1) errors in Darcy law estimates. We show this can be improved. Second, we consider the critical pressure drop for the onset of flow, which is important in a variety of invasion/plugging and flow-back/cleaning applications. We study asymptotic behaviours and derive a simple toy model that gives good predictions for simple geometries. Illustrations are presented with more complex fractures.

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