Integration of local–global upscaling and grid adaptivity for simulation of subsurface flow in heterogeneous formations

We propose a methodology, called multilevel local–global (MLLG) upscaling, for generating accurate upscaled models of permeabilities or transmissibilities for flow simulation on adapted grids in heterogeneous subsurface formations. The method generates an initial adapted grid based on the given fine-scale reservoir heterogeneity and potential flow paths. It then applies local–global (LG) upscaling for permeability or transmissibility [7], along with adaptivity, in an iterative manner. In each iteration of MLLG, the grid can be adapted where needed to reduce flow solver and upscaling errors. The adaptivity is controlled with a flow-based indicator. The iterative process is continued until consistency between the global solve on the adapted grid and the local solves is obtained. While each application of LG upscaling is also an iterative process, this inner iteration generally takes only one or two iterations to converge. Furthermore, the number of outer iterations is bounded above, and hence, the computational costs of this approach are low. We design a new flow-based weighting of transmissibility values in LG upscaling that significantly improves the accuracy of LG and MLLG over traditional local transmissibility calculations. For highly heterogeneous (e.g., channelized) systems, the integration of grid adaptivity and LG upscaling is shown to consistently provide more accurate coarse-scale models for global flow, relative to reference fine-scale results, than do existing upscaling techniques applied to uniform grids of similar densities. Another attractive property of the integration of upscaling and adaptivity is that process dependency is strongly reduced, that is, the approach computes accurate global flow results also for flows driven by boundary conditions different from the generic boundary conditions used to compute the upscaled parameters. The method is demonstrated on Cartesian cell-based anisotropic refinement (CCAR) grids, but it can be applied to other adaptation strategies for structured grids and extended to unstructured grids.     

Accurate local upscaling with variable compact multipoint transmissibility calculations

We propose a new single-phase local upscaling method that uses spatially varying multipoint transmissibility calculations. The method is demonstrated on two-dimensional Cartesian and adaptive Cartesian grids. For each cell face in the coarse upscaled grid, we create a local fine grid region surrounding the face on which we solve two generic local flow problems. The multipoint stencils used to calculate the fluxes across coarse grid cell faces involve the six neighboring pressure values. They are required to honor the two generic flow problems. The remaining degrees of freedom are used to maximize compactness and to ensure that the flux approximation is as close as possible to being two-point. The resulting multipoint flux approximations are spatially varying (a subset of the six neighbors is adaptively chosen) and reduce to two-point expressions in cases without full-tensor anisotropy. Numerical tests show that the method significantly improves upscaling accuracy as compared to commonly used local methods and also compares favorably with a local–global upscaling method.     

Proceedings of the Third European Workshop on Vertebrate Palaeontology (Maastricht,May 6-9, 1998): Preface

Geologie en Mijnbouw -     

A tribute to Bert Boekschoten – Introduction

Geologie en Mijnbouw -     

The actinopterygian fish fauna of the Late Kimmeridgian and Early Tithonian ‘Plattenkalke’ near Solnhofen (Bavaria,Germany): state of the art

An overview is presented of the actinopterygian fishes from the Late Jurassic (Late Kimmeridgian and Early Tithonian) ‘Plattenkalke’ near Solnhofen (Solnhofen lithographic limestone), Bavaria, Germany. The fish fauna is very diverse, with the palaeonisciform Coccolepis, halecostomes such as Lepidotes, Heterostrophus, three genera of macrosemiids and six genera of pycnodontiforms, halecomorphs including two genera of caturids, two genera of amiids, Ophiopsis, ‘Furo’, Ionoscopus, Brachyichthys, Callopterus, Liodesmus, ?Lophiurus, five genera of pachycormids, three genera of pholidophorids, Pleuropholis, two genera of aspidorhynchids and eleven genera of basal teleosts. Although several groups have been subject of revision, most of the fauna remains poorly known. Study of this rich fauna will provide a lot of information on the phylogeny and interrelationships of halecostome fishes.

     

Bert Boekschoten: a biographical sketch

Geologie en Mijnbouw -