  In this work, a novel method with an adaptive functional basis for reduced
order models (ROM) based on proper orthogonal decomposition (POD) is
introduced. The method is intended to be applied in particular to hydrocarbon
reservoir simulations, where a range of varying boundary conditions must be
explored. The proposed method allows us to update the POD functional basis
constructed for a specific problem setting in order to match varying boundary
conditions, such as modified well locations and geometry, without the necessity
to recalculate each time the whole set of basis functions. Such an adaptive
technique allows us to significantly reduce the number of snapshots required to
calculate the new basis, and hence reduce the computational cost of the
simulations. The proposed method was applied to a two-dimensional immiscible
displacement model, and simulations were performed using a high resolution
model, a classical POD reduced model, and a reduced model whose POD basis was
adapted to varying well location and geometry. Numerical simulations show that
the proposed approach allows us to reduce the required number of model
snapshots by a few orders of magnitude compared to a classical POD scheme,
without noticeable loss of accuracy of calculated fluid production rates. Such
an adaptive POD scheme can therefore provide a significant gain in
computational efficiency for problems where multiple or iterative simulations
with varying boundary conditions are required, such as optimization of well
design or production optimization.
