Basic Research Needs for Geosciences - Energetics Meetings and ...

GRAND CHALLENGE: SIMULATION OF MULTISCALE GEOLOGIC SYSTEMS FOR ULTRA-LONG TIMESCoupling methods used for different scalesThe mathematical models for each fundamental length scale are reasonably well understood(Figure 36). However, the link between models and their parameters at different scales is largelymissing. Geologic characterization models are usually constructed using sparse data, which comefrom different sources, have different spatial and temporal coverage and resolution, and are ofvarying quality and information content. Uncertainty in the characterization leads to uncertaintyin forward predictions of dynamic behavior. The development of techniques that couple differentscales and different physics incorporating stochasticity requires the four following aspects.1. Methodology concept and computationalScaling over a range of fundamental scales can be achieved through a combination of numericalapproaches:• Via coupling of models, each tuned for computation at specific scales. (e.g., lattice-Boltzmann computations feeding accurate, computed, pore-scale parameter information intoa network flow model, which in turn feeds computed core-scale parameter information into acontinuum-scale model.) This direction requires an understanding of accurate “informationpassing” (Fish 2006) from one model to the next; that is, from one scale to the next.• Via efficient means for solving very large systems of equations on high performancecomputers. New adaptive hierarchical and multilevel methods are essential. It is a criticalneed to migrate the computational geoscience community towards petascale computingfacilities and software capable of utilizing such hardware.• Via “adaptive upscaling” techniques (local upscaling, model hybridization) that applyspatially variable resolution dynamically over the domain of computation (resolve fine scaleslocally).2. Mathematical theoryThe mathematical challenges to subsurface modeling require much more detailed informationfrom microscale phenomena:• The development of techniques that couple different scales and different physics in the samesimulation, e.g., precalculated or adaptively computed parameterization of the coarse scalerepresentation (Weinan et al. 2003; Kevrekidis et al. 2003).• Development of techniques that seamlessly integrate nonseparable scales (Caffarelli et al.1996; Owhadi and Zhang 2007).• Solution of hybrid systems of differential equations.• Stochastic formulations, e.g., the development of Probability Density Functions (PDFs) ofthe dynamic properties of interest (Pope 2000), development of statistical moment equations(Dagan 1985; Neuman 1990, 1994; Zhang 2002; Li and Tchelepi 2003), smart Monte Carlo(Sarma et al. 2005), and discrete network approximation (Borcea and Papanicolaou 1998;Berlyand and Kolpakov 2001).Basic Research Needs for Geosciences: Facilitating 21 st Century Energy Systems 101