A multiscale method for distributed parameter estimation with application to reservoir history matching

A method for multiscale parameter estimation with application to reservoir history matching is presented. Starting from a given fine-scale model, coarser models are generated using a global upscaling technique where the coarse models are tuned to match the solution of the fine model. Conditioning to dynamic data is done by history-matching the coarse model. Using consistently the same resolution both for the forward and inverse problems, this model is successively refined using a combination of downscaling and history matching until model-matching dynamic data are obtained at the finest scale. Large-scale corrections are obtained using fast models, which, combined with a downscaling procedure, provide a better initial model for the final adjustment on the fine scale. The result is thus a series of models with different resolution, all matching history as good as possible with this grid. Numerical examples show that this method may significantly reduce the computational effort and/or improve the quality of the solution when achieving a fine-scale match as compared to history-matching directly on the fine scale.     

The quantifiable clinothem – types,shapes and geometric relationships in the Plio‐Pleistocene Giant Foresets Formation,Taranaki Basin,New Zealand

The understanding of how clinoforms develop is approached based on shape and dimensions, correlation between geometric parameters, and internal characteristics of clinothems bounded by clinoform surfaces in high‐resolution 2D seismic data from the Giant Foresets Formation, Taranaki Basin, offshore New Zealand. The study subdivides the observed clinothems to identify nine types: 1. Oblique 2. Tangential oblique 3. Tangential oblique chaotic 4. Sigmoidal symmetrical 5. Sigmoidal divergent 6. Sigmoidal chaotic 7. Asymmetrical top‐heavy 8. Asymmetrical bottom‐heavy 9. Complex. Accommodation is a dominant control on the type of clinothem that develops, whereby limited accommodation promotes clinothems with significant shelf‐edge advance and low trajectory angles, while increasing accommodation promotes higher trajectory angles and increased deposition on the shelf. Further variations in shape, slope and deposition are influenced by many factors of which sediment influx appears be a fundamental driver. Sigmoidal clinothems tend to show a strong relationship between their maximum thickness and average thickness, their overall slope and maximum foreset angle, along with a high correlation between average thickness and toe advance. This suggests that they distribute sediment in a manner that may be possible to predict and quantify. The increasing steepness of the foreset slope from bottom‐heavy to symmetrical to top‐heavy clinothems, respectively, is dominantly the result of decreasing sediment influx. The clinothems with the steepest slopes, along with chaotic clinothems, are associated with comparatively large toe advance suggesting a strong link between over‐steepened slopes and/or collapse, and processes promoting sediment deposition along the basin floor. Apart from toe advance, the two types of chaotic clinothems develop differently from each other, and from their assumed parent‐clinothem. Tangential oblique chaotic forms steepen, and shelf‐edge advance is limited, suggesting upper slope collapse. Sigmoidal chaotic clinothems have comparatively higher shelf‐edge advance, lower shelf‐edge trajectories and gentler slopes and profiles, suggesting different processes are responsible for their development and resulting shape.     

A generalized cubic equation of state with application to pure CO<Subscript>2</Subscript> injection in aquifers

A generalized cubic equation of state is given. The Peng-Robinson and the Soave-Redlich-Kwong equations are special cases of this equation. The generalized equation of state is precisely as simple and computationally efficient as these classical equations. Through comparison with the Span-Wagner equation for CO ₂, we obtain an improved density accuracy in predefined temperature-pressure domains. The generalized equation is then verified through two relevant examples of CO ₂ injection and migration. Comparisons are made with other standard cubic EOS in order to show the range of solutions obtained with less accurate EOS.     

Interpretation of well-cell pressures on stretched hexagonal grids in numerical reservoir simulation

Peaceman’s equivalent well-cell radius for 2D Cartesian grids has been generalized to 2D uniform Voronoi grids consisting of stretched hexagons in an isotropic medium. An analytical expression for the equivalent well-cell radius for infinitely fine grids is derived. The derivation is performed by comparison of analytical and numerical solution for boundary value problems with one or two wells. Since the well-cell radius varies slowly with the grid fineness, the found formula can be considered representative for all grid sizes.     

Effects of estuarine mudflat formation on tidal prism and large-scale morphology in experiments

Human interference in estuaries has led to increasing problems of mud, such as hyper-turbidity with adverse ecological effects and siltation of navigation channels and harbours. To deal with this mud sustainably, it is important to understand its long-term effects on the morphology and dynamics of estuaries. The aim of this study is to understand how mud affects the morphological evolution of estuaries. We focus on the effects of fluvial mud supply on the spatial distribution of mudflats and on how this influences estuary width, depth, surface area and dynamics over time. Three physical experiments with self-forming channels and shoals were conducted in a new flume type suitable for tidal experiments: the Metronome. In two of the experiments, we added nutshell grains as mud simulant, which is transported in suspension. Time-lapse images of every tidal cycle and digital elevation models for every 500 cycles were analysed for the three experiments. Mud settles in distinct locations, forming mudflats on bars and sides of the estuary, where the bed elevation is higher. Two important effects of mud were observed: the first is the slight cohesiveness of mud that causes stability on bars limiting vertical erosion, although the bank erosion rate by migrating channels is unaffected. Secondly, mud fills inactive areas and deposits at higher elevations up to the high-water level and therefore decreases the tidal prism. These combined effects cause a decrease in dynamics in the estuary and lead to near-equilibrium planforms that are smaller in volume and especially narrower upstream, with increased bar heights and no channel deepening. This trend is in contrast to channel deepening in rivers by muddier floodplain formation. These results imply large consequences for long-term morphodynamics in estuaries that become muddier due to management practices, which deteriorate ecological quality of intertidal habitats but may create potential area for marshes. © 2018 The Authors. Earth Surface Processes and Landforms Published by John Wiley & Sons Ltd.     

Late Devensian ice‐marginal features in the central North Sea – processes and chronology

Palaeoglaciological reconstructions of the North Sea sector of the last British Ice Sheet have, as other shelf areas, suffered from a lack of dates directly related to ice‐front positions. In the present study new high‐resolution TOPAS seismic data, bathymetric records and sediment core data from the Witch Ground Basin, central North Sea, were compiled. This compilation made it possible to map out three ice‐marginal positions, partly through identification of terminal moraines and partly through location of glacial‐fed debrisflows. The interfingering of the distal parts of the glacial‐fed debrisflows with continuous marine sedimentation enabled the development of a chronology for glacial events based on previously published and some new radiocarbon dates on marine molluscs and foraminifera. From these data it is suggested that after the central Witch Ground Basin was deglaciated at c. 27 cal. ka BP, the eastern part was inundated by glacial ice from the east in the Tampen advance at c. 21 cal. ka BP. Subsequently, the basin was inundated by ice from northeast during the Fladen 1 (c. 17.5 cal. ka BP) and the Fladen 2 (16.2 cal. ka BP) events. It should be emphasized that the Fladen 1 and 2 events, individually, may represent dynamics of relatively small lobes of glacial ice at the margin of the British Ice Sheet and that the climatic significance of these may be questioned. However, the Fladen Events probably correlate in time with the Clogher Head and Killard Point re‐advances previously documented from Ireland and the Bremanger event from off western Norway, suggesting that the British and Fennoscandian ice sheets both had major advances in their northwestern parts, close to the northwestern European seaboard, at this time.     

The concept of cryo-conditioning in landscape evolution

Recent accounts suggest that periglacial processes are unimportant for large-scale landscape evolution and that true large-scale periglacial landscapes are rare or non-existent. The lack of a large-scale topographical fingerprint due to periglacial processes may be considered of little relevance, as linear process-landscape development relationships rarely can be substantiated. Instead, periglacial landscapes may be classified in terms of specific landform associations. We propose “cryo-conditioning”, defined as the interaction of cryotic surface and subsurface thermal regimes and geomorphic processes, as an overarching concept linking landform and landscape evolution in cold regions. By focusing on the controls on processes, this concept circumvents scaling problems in interpreting long-term landscape evolution derived from short-term processes. It also contributes to an unambiguous conceptualization of periglacial geomorphology. We propose that the development of several key elements in the Norwegian geomorphic landscape can be explained in terms of cryo-conditioning.     

Multiscale mass conservative domain decomposition preconditioners for elliptic problems on irregular grids

Multiscale methods can in many cases be viewed as special types of domain decomposition preconditioners. The localisation approximations introduced within the multiscale framework are dependent upon both the heterogeneity of the reservoir and the structure of the computational grid. While previous works on multiscale control volume methods have focused on heterogeneous elliptic problems on regular Cartesian grids, we have tested the multiscale control volume formulations on two-dimensional elliptic problems involving heterogeneous media and irregular grid structures. Our study shows that the tangential flow approximation commonly used within multiscale methods is not suited for problems involving rough grids. We present a more robust mass conservative domain decomposition preconditioner for simulating flow in heterogeneous porous media on general grids.