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(Nature 386, 379-381 (1997)) Granular materials [1][2][3][4][5] size segregate when exposed to external periodic perturbations such as vibrations [6][7][8][9][10][11][12]. Moreover, mixtures of grains of different sizes spontaneously segregate in the absence of external perturbations: when a mixture is simply poured onto a pile, the large grains are more likely to be found near the base, while the small grains are more likely to be near the top [13][14][15][16][17][18][19][20]. Here, we report a novel spontaneous phenomenon arising when we pour a mixture between two vertical plates: the mixture spontaneously stratifies into alternating layers of small and large grains whenever the large grains have larger angle of repose than the small grains. In contrast, we find only spontaneous segregation when the large grains have smaller angle of repose than the small grains. The stratification is related to the occurrence of avalanches; during each avalanche the grains comprising the avalanche spontaneously stratify into a pair of layers, with the small grains forming a sublayer underneath the layer of large grains.Our experimental system consists of a vertical "quasitwo-dimensional" cell with a gap of 5 mm separating two transparent plates (made of plexiglass, or of glass) measuring 300 mm × 200 mm (see Fig. 1a). We choose this quasi-two-dimensional geometry since, by using this setup, the internal features of the avalanche process can be easily visualized, both statically and dynamically. To avoid the effects of electrostatic interaction with the wall, the wall is cleaned with an antistatic cleaner.In a first series of experiments, we close the left edge of the cell leaving the right edge free, and we pour, near the left edge, an equal-volume mixture of white glass beads (mean size 0.27 mm, spherical shape, and repose angle 26 o ), and red sugar crystals (typical size 0.8 mm, cubic shape, and repose angle 39 o ). Figure 1a shows the result of the first series of experiments. We note two features: (i) Spontaneous Stratification. We see the formation of alternating layers consisting of small and large grains-with a "wavelength" of about 1.2 cm.(ii) Spontaneous Segregation. We find that the smaller grains segregate near the left edge and the larger grains segregate furthest from it and near the base [13][14][15][16][17][18][19][20].In a second series of experiments, we confirmed the results of these initial experiments by testing for stratification and segregation using a mixture of grains of same density, consisting of fine sand (typical size 0.4 mm) and coarse sand (typical size 1 mm), suggesting that the density of the grains may not play an important role in stratification.In all the above experiments we used mixtures composed of two types of grain with different shape, and therefore with different angles of repose. In particular we obtain stratification (plus segregation) when we use larger cubic grains and smaller spherical grains: the angle of repose of the large species is then larger than the angle of repose o...

There is a need in the numerical simulation of reservoir performance to use average permeability values for the grid blocks. The permeability distributions to be averaged over are based on samples taken from cores and from logs using correlations between permeabilities and porosities and from other sources. It is necessary to use a suitable 'effective' value determined from this sample. The effective value is a single value for an equivalent homogeneous block. Conventionally, this effective value has been determined from a simple estimate such as the geometric mean or a detailed numerical solution of the single phase flow equation.If the permeability fluctuations are small then perturbation theory or effective medium theory (EMT) give reliable estimates of the effective permeability. However, for systems with a more severe permeability variation or for those with a finite fraction of nonreservoir rock all the simple estimates are invalid as well as EMT and perturbation theory.This paper describes a real-space renormalization technique which leads to better estimates than the simpler methods and is able to resolve details on a much finer scale than conventional numerical solution. Conventional simulation here refers to finite difference (or element) techniques for solving the single phase pressure equation. This requires the pressure and permeability at every grid point to be stored. Hence, these methods are limited in their resolution by the amount of data that can be stored in core. Although virtual memory techniques may be used they increase computer time. The renormalization method involves averaging over small regions of the reservoir first to form a new 'averaged permeability' distribution with a lower variance than the original. This pre-averaging may be repeated until a stable estimate is found. Examples are given to show that this is in excellent agreement with computationally more expensive numerical solution but significantly different from simple estimates such as the geometric mean.

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A 4.9 Mkm 2 region of the southwest Pacific Ocean is made up of continental crust. The region has elevated bathymetry relative to surrounding oceanic crust, diverse and silica-rich rocks, and relatively thick and low-velocity crustal structure. Its isolation from Australia and large area support its definition as a continent-Zealandia. Zealandia was formerly part of Gondwana. Today it is 94% submerged, mainly as a result of widespread Late Cretaceous crustal thinning preceding supercontinent breakup and consequent isostatic balance. The identification of Zealandia as a geological continent, rather than a collection of continental islands, fragments, and slices, more correctly represents the geology of this part of Earth. Zealandia provides a fresh context