  Vertical equilibrium models have proven to be well suited for simulating
fluid flow in subsurface porous media such as saline aquifers with caprocks.
However, in most cases the dimensionally reduced model lacks the accuracy to
capture the dynamics of a system. While conventional full-dimensional models
have the ability to represent dynamics, they come at the cost of high
computational effort. We aim to combine the efficiency of the vertical
equilibrium model and the accuracy of the full-dimensional model by coupling
the two models adaptively in a unified framework and solving the emerging
system of equations in a monolithic, fully-implicit approach. The model domains
are coupled via mass-conserving fluxes while the model adaptivity is ruled by
adaption criteria. Overall, the adaptive model shows an excellent behaviour
both in terms of accuracy as well as efficiency, especially for elongated
geometries of storage systems with large aspect ratios.
