Mixing and reactions in porous media: Closures for predicting effectiveness factor

Abstract:

Mixing in porous media is a complex and poorly understood process. In this work, we focus on the process of microscale mixing and the development of a local volume-averaged advection-dispersion-reaction equation, where the microscale configuration of a reacting mixture (where two components must mix to create reaction) is an important quantity for predicting the effective rate of reaction. Although such a system is simple from the transport perspective, it has a sufficiently rich structure that the mixing and reaction dynamics are still reasonably complex. It also provides a model structure where the influence of microscale configuration can be understood in detail.

In this work, we focus on (1) development of the upscaled advection-dispersion-reaction equation (via volume averaging) for a system in which two chemical components must mix to react, and (2) identification of a closure scheme from which the effective rate of reaction can be predicted. In particular, we examine mixing at a simple interface, and construct approximate methods to predict the (generally transient) effectiveness factor. By providing an explicit closure for the advection-dispersion-reaction problem, additional physical content is provided about how the scalar dissipation relates to the effective rate of reaction due to mixing.