  Efficient multiphysics models that can adapt to the varying complexity of
physical processes in space and time are desirable for modeling fluid migration
in the subsurface. Vertical equilibrium (VE) models are simplified mathematical
models that are computationally efficient but rely on the assumption of instant
gravity segregation of the two phases, which may not be valid at all times or
at all locations in the domain. Here, we present a multiphysics model that
couples a VE model to a full multidimensional model that has no reduction in
dimensionality. We develop a criterion that determines subdomains where the VE
assumption is valid during simulation. The VE model is then adaptively applied
in those subdomains, reducing the number of computational cells due to the
reduction in dimensionality, while the rest of the domain is solved by the full
multidimensional model. We analyze how the threshold parameter of the criterion
influences accuracy and computational cost of the new multiphysics model and
give recommendations for the choice of optimal threshold parameters. Finally,
we use a test case of gas injection to show that the adaptive multiphysics
model is much more computationally efficient than using the full
multidimensional model in the entire domain, while maintaining much of the
accuracy.
