  We study two-phase flow for Darcy and Brinkman regimes. To reduce the
computational complexity for flow in vertical equilibrium various simplified
models have been suggested. Examples are dimensional reduction by vertical
integration, the multiscale model approach in [Guo et al., 2014] or the
asymptotic approach in [Yortsos, 1995]. The latter approach uses a geometrical
scaling. We show the efficiency of the approach in asymptotically flat domains
for Darcy regimes. Moreover, we prove that it is vastly equivalent to the
multiscale model approach.
  We apply then asymptotic analysis to the two-phase flow model in Brinkman
regimes. The limit model is a single nonlocal evolution law with a
pseudo-parabolic extension. Its computational efficiency is demonstrated using
numerical examples. Finally, we show that the new limit model exhibits
overshoot behaviour as it has been observed for dynamical capillarity laws
[Hassanizadeh and Gray, 1993].
