Mixing Equations in Various Geometries

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Abstract
Summary: In flow through porous media, the mixing characteristics of the flowing fluids are often defined by the diffusivity equation. Solutions of this equation are available for linear flow, and close approximations are available for radial flow. In this paper, one of the radial flow approximation methods has been generalized to a variety of geometries. The solution is assumed to be in the form of an error function; and equations are derived for the standard deviation—i.e., the argument of the error function. By breaking the flow system into segments and by repeated use of these solutions, mixing can be calculated in a large variety of flow systems. For example, equations can be used to calculate tracer flow behavior in reservoirs and mixing in vertical miscible displacement.

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