  Upscaling the effect of heterogeneities in porous media is crucial for
macroscopic flow predictions, with widespread applications in energy and
environmental settings. In this study, we derive expressions for the upscaled
flow properties of a porous medium with a vertical heterogeneity, using a
combination of asymptotic analysis and numerical simulations. Then, we use
these upscaled expressions to describe the dynamic flooding of an aquifer,
where the classic Buckley-Leverett formulation is modified to account for
heterogeneities. In particular, we show that heterogeneities can modify
flooding speeds significantly, and we discuss the implications of these results
in the case of carbon dioxide sequestration.
