Relative impact of advective and dispersive processes on the efficiency of POD-based model reduction for solute transport in porous media

09/2016

Relative impact of advective and dispersive processes on the efficiency of POD-based model reduction for solute transport in porous media

Friday 19th February 2016

Rizzo, C.B.; de Barros, F.P.J.; Perotto, S.; Oldani, L.; Guadagnini, A.

We study the applicability of a model order reduction technique to the cost-effective solution of transport of passive scalars in porous media. Transport dynamics is modeled through the advection-dispersion equation (ADE) and we employ Proper Orthogonal Decomposition (POD) as a strategy to reduce the computational burden associated with the numerical solution of the ADE. Our application of POD relies on solving the governing ADE for selected time intervals, termed snapshots. The latter are then employed to achieve the desired model order reduction. The problem dynamics require alternating, over diverse time scales, between the solution of the full numerical transport model, as expressed by the ADE, and its reduced counterpart, constructed through the selected snapshots. We explore the way the selection of these time scales is linked to the Péclet number characterizing transport under steady-state flow conditions taking place in two-dimensional homogeneous and heterogeneous porous media. We find that the length of the time scale within which the POD-based reduced model solution provides accurate results tends to increase with decreasing Péclet number. This suggests that the effects of local scale dispersive processes facilitate the POD method to capture the salient features of the system dynamics embedded in the selected snapshots. Since the dimension of the reduced model is much lower than that of the full numerical model, the methodology we propose enables one to accurately simulate transport at a markedly reduced computational cost.