Rapid simulation of multiple radially growing hydraulic fractures using an energy‐based approach

The goal of hydraulic fracturing stimulation of horizontal wells is typically to generate uniform, simultaneously growing hydraulic fractures from 3 to 6 initiation/entry sites that are spaced within a certain interval of the wellbore comprising a so‐called stage. Because of the stress interaction among growing hydraulic fractures, however, it is hard to attain simultaneous growth of all hydraulic fractures. While models have been proven useful for devising mitigation strategies of these so‐called stress‐shadow effects, the required simulations are so computationally expensive that optimization is possible only in the simplest cases. Here, we present an approximate (energy‐based) model capable of running an entire simulation in 1–2s, which is about one million times faster than the benchmark model. The approach is built on asymptotic solutions to approximate growth of radial hydraulic fractures, a far field approximation for the stress shadow interactions among growing hydraulic fractures, and coupling the effect of the stress shadow to fracture growth via a global energy balance equation. We show very close agreement in predictions of the lengths of each fracture in the array between the approximate model and the benchmark model, thus verifying that the new approximate model is useful for optimization of hydraulic fracture design. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance of quasilinear elastic constitutive models in simulation of geosynthetic encased columns

Past numerical simulations of geosynthetic encased columns (GECs) using different versions of the quasilinear elastic hyperbolic model for the encased granular material have, in certain cases, yielded unrealistic results. In this paper the cause of such results is investigated by performing three-dimensional finite element analyses of GECs in soft clay, utilizing three common functional forms of the hyperbolic model for the encased granular material. Results indicate that one form of the hyperbolic model can predict an unrealistic lateral response for GECs during application of load to the column. In addition, the inability of hyperbolic models to properly account for soil behavior near failure compromises their ability to realistically capture the behavior of encased granular soil in GECs. Modeling the behavior of soil near failure is essential for properly simulating the behavior of GECs, as soil shear failure is necessary to mobilize the tensile stresses in the encasement and improve the stress–displacement response of the GEC. Although this type of hyperbolic model behavior was demonstrated for the specific case of encased soil in a GEC, the limitations of the hyperbolic model described herein apply equally to other geotechnical problems in which some portion of the soil mass is at or near failure.     

Failure and size effect for notched and unnotched concrete beams

Modelling failure in geomaterials, concrete or other quasi‐brittle materials and proper accounting for size effect, geometry and boundary effects are still pending issues. Regularised failure models are capable of describing size effect on specimens with a specific geometry, but extrapolations to other geometries are rare, mostly because experimental data presenting size effect for different geometries and for the same material are lacking. Three‐point bending fracture tests of geometrically similar notched and unnotched specimens are presented. The experimental results are compared with numerical simulations performed with an integral‐type non‐local model. Comparisons illustrate the shortcomings of this classical formulation, which fails to describe size effect over the investigated range of geometries and sizes. Finally, experimental results are also compared with the universal size effect law. Copyright © 2013 John Wiley & Sons, Ltd.     

A quantitative approach to fluvial facies models: Methods and example results

Traditional facies models lack quantitative information concerning sedimentological features: this significantly limits their value as references for comparison and guides to interpretation and subsurface prediction. This paper aims to demonstrate how a database methodology can be used to generate quantitative facies models for fluvial depositional systems. This approach is employed to generate a range of models, comprising sets of quantitative information on proportions, geometries, spatial relations and grain sizes of genetic units belonging to three different scales of observation (depositional elements, architectural elements and facies units). The method involves a sequential application of filters to the knowledge base that allows only database case studies that developed under appropriate boundary conditions to contribute to any particular model. Specific example facies models are presented for fluvial environmental types categorized on channel pattern, basin climatic regime and water‐discharge regime; the common adoption of these environmental types allows a straightforward comparison with existing qualitative models. The models presented here relate to: (i) the large‐scale architecture of single‐thread and braided river systems; (ii) meandering sub‐humid perennial systems; (iii) the intermediate‐scale and small‐scale architecture of dryland, braided ephemeral systems; (iv) the small‐scale architecture of sandy meandering systems; and (v) individual architectural features of a specific sedimentary environment (a terminal fluvial system) and its sub‐environments (architectural elements). Although the quantification of architectural properties represents the main advantage over qualitative facies models, other improvements include the capacity: (i) to model on different scales of interest; (ii) to categorize the model on a variety of environmental classes; (iii) to perform an objective synthesis of many real‐world case studies; (iv) to include variability‐related and knowledge‐related uncertainty in the model; and (v) to assess the role of preservation potential by comparing ancient‐system and modern‐system data input to the model.     

Estimating Co2 Source/Sink Distributions Within A Rice Canopy Using Higher-Order Closure Model

Source/sink strengths and vertical fluxdistributions of carbon dioxide within and above arice canopy were modelled using measured meanconcentration profiles collected during aninternational rice experiment in Okayama, Japan (IREX96). The model utilizes an Eulerian higher-orderclosure approach that permits coupling of scalar andmomentum transport within vegetation to infer sourcesand sinks from mean scalar concentration profiles; theso-called `inverse problem'. To compute the requiredvelocity statistics, a Eulerian second-order closuremodel was considered. The model well reproducedmeasured first and second moment velocity statisticsinside the canopy. Using these modelled velocitystatistics, scalar fluxes within and above the canopywere computed and compared with CO<sub>2</sub>eddy-correlation measurements above the canopy. Goodagreement was obtained between model calculations offluxes at the top of the canopy and measurements. Close to the ground, the model predicted higherrespiratory fluxes when the paddy was drained comparedto when it was flooded. This is consistent with thefloodwater providing a barrier to diffusion ofCO<sub>2</sub> from the soil to the atmosphere. TheEulerian sources and flux calculations were alsocompared to source and flux distributions estimatedindependently using a Lagrangian Localized Near Fieldtheory, the first study to make such a comparison.Some differences in source distributions werepredicted by these analyses. Despite this, thecalculated fluxes by the two approaches compared wellprovided a closure constant, accounting for theinfluence of `near-field' sources in the Eulerian fluxtransport term, was given a value of 1.5 instead ofthe value of 8 found in laboratory studies.     

Sediment‐rich meltwater plumes and ice‐proximal fans at the margins of modern and ancient tidewater glaciers: Observations and modelling

Turbid meltwater plumes and ice‐proximal fans occur where subglacial streams reach the grounded marine margins of modern and ancient tidewater glaciers. However, the spacing and temporal stability of these subglacial channels is poorly understood. This has significant implications for understanding the geometry and distribution of Quaternary and ancient ice‐proximal fans that can form important aquifers and hydrocarbon reservoirs. Remote‐sensing and numerical‐modelling techniques are applied to the 200 km long marine margin of a Svalbard ice cap, Austfonna, to quantify turbid meltwater‐plume distribution and predict its temporal stability. Results are combined with observations from geophysical data close to the modern ice front to refine existing depositional models for ice‐proximal fans. Plumes are spaced ca 3 km apart and their distribution along the ice front is stable over decades. Numerical modelling also predicts the drainage pattern and meltwater discharge beneath the ice cap; modelled water‐routing patterns are in reasonable agreement with satellite‐mapped plume locations. However, glacial retreat of several kilometres over the past 40 years has limited build‐up of significant ice‐proximal fans. A single fan and moraine ridge is noted from marine‐geophysical surveys. Closer to the ice front there are smaller recessional moraines and polygonal sediment lobes but no identifiable fans. Schematic models of ice‐proximal deposits represent varying glacier‐terminus stability: (i) stable terminus where meltwater sedimentation produces an ice‐proximal fan; (ii) quasi‐stable terminus, where glacier readvance pushes or thrusts up ice‐proximal deposits into a morainal bank; and (iii) retreating terminus, with short still‐stands, allowing only small sediment lobes to build up at melt‐stream portals. These modern investigations are complemented with outcrop and subsurface observations and numerical modelling of an ancient, Ordovician glacial system. Thick turbidite successions and large fans in the Late Ordovician suggest either high‐magnitude events or sustained high discharge, consistent with a relatively mild palaeo‐glacial setting for the former North African ice sheet.     

A model for the three-dimensional evolution of continental rift basins,north-east Africa

Large areas of north-east Africa were dominated by regional extension in the Late Phanerozoic. Widespread rifting occurred in the Late Jurassic, with regional extension culminating in the Cretaceous and resulting in the greatest areal extent and degree of interconnection of the west, central and north African rift systems. Basin reactivation continued in the Paleocene and Eocene and new rifts probably formed in the Red Sea and western Kenya. In the Oligocene and Early Miocene, rifts in Kenya, Ethiopia and the Red Sea linked and expanded to form the new east African rift system.This complex history of rifting resulted in failed rift basins with low to high strain geometries, a range of associated volcanism and varying degrees of interaction with older structures. One system, the Red Sea rift, has partially attained active seafloor spreading. From a comparison of these basins, a general model of three-dimensional rift evolution is proposed. Asymmetrical crustal geometries dominated the early phases of these basins, accompanied by low angle normal faulting that has been observed at least locally in outcrop. As rifting progressed, the original fault and basin forms were modified to produce larger, more through-going structures. Some basins were abandoned, others experienced reversals in regional dip and, in general, extension and subsidence became focused along narrower zones near the rift axes. The final transition to oceanic spreading was accomplished in the Red Sea by a change to high angle, planar normal faulting and diffuse dike injection, followed by the organization of an axial magma chamber.     

A Study of Global Change Population and Economic System Risk Forming Mechanism and Assessment

Global climate change featured with warming has created serious challenge to world sustainable development and human security. It has become an important consensus of the international society to assess global change risk at the global scale and carry out tailored governance and risk-based adaptation. National Key Research and Development Program “Study on global change population and economic system risk forming mechanism and assessment” aims at quantitatively predicting future global climate change and population and economic system exposure and vulnerability change, developing global change population and economic system risk assessment model based on complex system dynamics, synthesizing risk assessment model with proprietary intellectual property rights, assess global change population and economic system risk of the near and mid future at the global scale, and compiling the atlas of global change population and economic system risk. The outcomes intend to serve the participation of global risk governance and international climate negotiation, and to provide scientific support to the implementation of international disaster risk reduction strategy.     

Lagrangian Stochastic Models For Turbulent Dispersion In The Atmospheric Boundary Layer

A one-particle three-dimensional stochastic Lagrangian model fortransport of particles in a horizontally-homogeneous atmosphericsurface layer with arbitrary one-point probability density functionof Eulerian velocity fluctuations is suggested. A uniquely definedLagrangian stochastic model in the class of well-mixed models isconstructed from physically plausible assumptions. These assumptionsare: (i) in the neutrally stratified horizontally homogeneous surface layer, the vertical motion is mainly controlled by eddies whose size is of order of the current height; and (ii), the streamwise drift term is independent of the crosswind velocity. Numerical simulations for neutral stratification have shown a good agreement of our model with the well-known Thomson's model, with Flesch and Wilson's model, and with experimental measurements as well. However there is a discrepancy of these results with the results obtained by Reynolds' model.     

Estimation for partially observed Markov processes

Many stochastic process models for environmental data sets assume a process of relatively simple structure which is in some sense partially observed. That is, there is an underlying process (X_n, n 0) or (X_t, t 0) for which the parameters are of interest and physically meaningful, and an observable process (Y_n, n 0) or (Y_t, t 0) which depends on the X process but not otherwise on those parameters. Examples are wide ranging: the Y process may be the X process with missing observations; the Y process may be the X process observed with a noise component; the X process might constitute a random environment for the Y process, as with hidden Markov models; the Y process might be a lower dimensional function or reduction of the X process. In principle, maximum likelihood estimation for the X process parameters can be carried out by some form of the EM algorithm applied to the Y process data. In the paper we review some current methods for exact and approximate maximum likelihood estimation. We illustrate some of the issues by considering how to estimate the parameters of a stochastic Nash cascade model for runoff. In the case of k reservoirs, the outputs of these reservoirs form a k dimensional vector Markov process, of which only the kth coordinate process is observed, usually at a discrete sample of time points.