Indirect-error-based, Dynamic Upscaling of Multi-phase Flow in Porous Media

We propose an upscaling method that is based on dynamic simulation of a given model in which the accuracy of the upscaled model is continuously monitored via indirect measures of the error. If the indirect error measures are larger than a specified tolerance, the upscaled model is dynamically updated with approximate fine-scale information that is reconstructed by a multi-scale finite volume method (Jenny et al., JCP 217: 627--641, 2006). Upscaling of multi-phase flow entails detailed flow information from the underlying fine scale. We apply adaptive prolongation and restriction operators for the flow and transport equations in constructing an approximate fine-scale solution. This new method reduces the inaccuracy associated with traditional upscaling methods, which rely on prescribed boundary conditions in computing the upscaled variables. This dynamic upscaling algorithm is validated for incompressible two-phase flow in two dimensional heterogeneous domains. We demonstrate that the dynamically upscaled model achieves high numerical efficiency compared with fine-scale computations and also provides excellent agreement with reference fine-scale solutions.