Dynamic Upscaling of Multiphase Flow in Porous Media via Adaptive Reconstruction of Fine Scale Variables

Lee, Seong Hee (Chevron ETC) | Wang, Xiaochen (Stanford University) | Zhou, Hui (Stanford University) | Tchelepi, Hamdi A.


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 error-measures. If the indirect measures are bigger 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 a detailed flow information in the underlying fine scale. We apply adaptive prolongation and restriction operators for flow and transport equations in constructing an approximate fine scale solution. This new method eliminates inaccuracy associated with the traditional upscaling method which relies on prescribed inaccurate boundary conditions in computing upscaled variables. The new upscaling algorithm is validated for two-phase, incompressible flow in two dimensional porous media with heterogeneous permeabilities. It is demonstrated that the dynamically upscaled model achieves high numerical efficiency than the fine-scale models and also provides an excellent agreement with the reference solution computed from fine-scale simulation.