Comparison of fast algorithms for estimating large-scale permeabilities of heterogeneous media

The problem of upscaling permeability data from the core to the reservoir grid block scale for input into flow simulators is addressed. Two fast, approximate algorithms which have been suggested for this purpose—one based on random walks and the other on real-space renormalisation group methods—are compared using the results of numerical tests performed on 30 different heterogeneous permeability realisations in 3-D. The results show that random walks outperform renormalisation for this problem, being computationally more efficient and demonstrating significantly better accuracy for particular cases.