In fractured reservoirs characterized by low matrix permeability,fracture networks control the main fluid flow paths.However,in layered reservoirs,the vertical extension of fractures is often restricted to single laye...In fractured reservoirs characterized by low matrix permeability,fracture networks control the main fluid flow paths.However,in layered reservoirs,the vertical extension of fractures is often restricted to single layers.In this study,we explored the effect of changing marl/shale thickness on fracture extension using comprehensive field data and numerical modeling.The field data were sampled from coastal exposures of Liassic limestone-marl/shale alternations in Wales and Somerset(Bristol Channel Basin,UK).The vertical fracture traces of more than 4000 fractures were mapped in detail.Six sections were selected to represent a variety of layer thicknesses.Besides the field data also thin sections were analyzed.Numerical models of fracture extension in a two-layer limestone-marl system were based on field data and laboratory measurements of Young's moduli.The modeled principal stress magnitude σ3 along the lithological contact was used as an indication for fracture extension through marls.Field data exhibit good correlation(R^2=0.76) between fracture extension and marl thickness,the thicker the marl layer the fewer fractures propagate through.The model results show that almost no tensile stress reaches the top of the marl layer when the marls are thicker than 30 cm.For marls that are less than 20 cm,the propagation of stress is more dependent on the stiffness of the marls.The higher the contrast between limestone and marl stiffness the lower the stress that is transmitted into the marl layer.In both model experiments and field data the critical marl thickness for fracture extension is ca.15-20 cm.This quantification of critical marl thicknesses can be used to improve predictions of fracture networks and permeability in layered rocks.Up-or downsampling methods often ignore spatially continuous impermeable layers with thicknesses that are under the detection limit of seismic data.However,ignoring these layers can lead to overestimates of the overall permeability.Therefore,the understanding of how fractures propagate and terminate through impermeable layers will help to improve the characterization of conventional reservoirs.展开更多
Empirical research is playing a significant role in software engineering （SE）, and it has been applied to evaluate software artifacts and technologies. There have been a great number of empirical research articles p...Empirical research is playing a significant role in software engineering （SE）, and it has been applied to evaluate software artifacts and technologies. There have been a great number of empirical research articles published recently. There is also a large research community in empirical software engineering （ESE）. In this paper, we identify both the overall landscape and detailed implementations of ESE, and investigate frequently applied empirical methods, targeted research purposes, used data sources, and applied data processing approaches and tools in ESE. The aim is to identify new trends and obtain interesting observations of empirical software engineering across different sub-fields of software engineering. We conduct a mapping study on 538 selected articles from January 2013 to November 2017, with four research questions. We observe that the trend of applying empirical methods in software engineering is continuously increasing and the most commonly applied methods are experiment, case study and survey. Moreover, open source projects are the most frequently used data sources. We also observe that most of researchers have paid attention to the validity and the possibility to replicate their studies. These observations are carefully analyzed and presented as carefully designed diagrams. We also reveal shortcomings and demanded knowledge/strategies in ESE and propose recommendations for researchers.展开更多
First introduced in[2],the lumped particle framework is a flexible and numerically efficient framework for the modelling of particle transport in fluid flow.In this paper,the framework is expanded to simulate multicom...First introduced in[2],the lumped particle framework is a flexible and numerically efficient framework for the modelling of particle transport in fluid flow.In this paper,the framework is expanded to simulate multicomponent particle-laden fluid flow.This is accomplished by introducing simulation protocols tomodel particles over a wide range of length and time scales.Consequently,we present a time ordering scheme and an approximate approach for accelerating the computation of evolution of different particle constituents with large differences in physical scales.We apply the extended framework on the temporal evolution of three particle constituents in sandladen flow,and horizontal release of spherical particles.Furthermore,we evaluate the numerical error of the lumped particle model.In this context,we discuss the Velocity-Verlet numerical scheme,and show how to apply this to solving Newton’s equations within the framework.We show that the increased accuracy of the Velocity-Verlet scheme is not lost when applied to the lumped particle framework.展开更多
This paper presents a lumped particle model for simulating a large number of particles.The lumped particle model is a flexible framework in modeling particle flows,embodying fundamental features that are intrinsic in ...This paper presents a lumped particle model for simulating a large number of particles.The lumped particle model is a flexible framework in modeling particle flows,embodying fundamental features that are intrinsic in particle laden flow,including advection,diffusion and dispersion.In this paper,the particles obey a simplified version of the Bassinet-Boussinesq-Oseen equation for a single spherical particle.However,instead of tracking the individual dynamics of each particle,a weighted spatial averaging procedure is used where the external forces are applied to a“lump”of particles,from which an average position and velocity is derived.The temporal evolution of the particles is computed by partitioning the lumped particle into smaller entities,which are then transported throughout the physical domain.These smaller entities recombine into new particle lumps at their target destinations.For particles prone to the effects of Brownian motion or similar phenomena,a symmetric spreading of the particles is included as well.Numerical experiments show that the lumped particle model reproduces the effects of Brownian diffusion and uniform particle transport by a fluid and gravity.The late time scale diffusive nature of particle motion is also reproduced.展开更多
This paper presents an extension of the lumped particle model in[1]to include the effects of particle collisions.The lumped particle model is a flexible framework for the modeling of particle laden flows,that takes in...This paper presents an extension of the lumped particle model in[1]to include the effects of particle collisions.The lumped particle model is a flexible framework for the modeling of particle laden flows,that takes into account fundamental features,including advection,diffusion and dispersion of the particles.In this paper,we transform a binary collision model and concepts from kinetic theory into a collision procedure for the lumped particle framework.We apply this new collision procedure to investigate numerically the role of particle collisions in the hindered settling effect.The hindered settling effect is characterized by an increase in the effective drag coefficient CD that influences each particle in the flow.This coefficient is given by CD=(1−φ)−nC∗D,whereφis the volume fraction of particles,C∗D is the drag coefficient for a single particle,and n≃4.67 for creeping flow.We obtain an approximation for CD/C∗D by calculating the effective work done by collisions,and comparing that to the work done by the drag force.In our numerical experiments,we observe a minimal value of n=3.0.Moreover,by allowing high energy dissipation,an approximation for the classical value for creeping flow,n=4.7,is reproduced.We also obtain high values for n,up to n=6.5,which is consistent with recent physical experiments on the sedimentation of sand grains.展开更多
We describe and evaluate a numerical solution strategy for simulating surface acoustic waves(SAWs)through semiconductor devices with complex geometries.This multi-physics problem is of particular relevance to the desi...We describe and evaluate a numerical solution strategy for simulating surface acoustic waves(SAWs)through semiconductor devices with complex geometries.This multi-physics problem is of particular relevance to the design of SAW-based quantum electronic devices.The mathematical model consists of two coupled partial differential equations for the elastic wave propagation and the electric field,respectively,in anisotropic piezoelectric media.These equations are discretized by the finite element method in space and by a finite difference method in time.The latter method yields a convenient numerical decoupling of the governing equations.We describe how a computer implementation can utilize the decoupling and,via object-oriented programming techniques reuse independent codes for the Poisson equation and the linear time-dependent elasticity equation.First we apply the simulator to a simplified model problem for verifying the implementation,and thereafter we show that the methodology is capable of simulating a real-world case from nanotechnology,involving SAWs in a geometrically non-trivial device made of Gallium Arsenide.PACS:02.70.Dh,41.20.Jb,46.25.Hf Key words:Finite element method,piezoelectric surface acoustic waves,Gallium Arsenide.展开更多
基金supported by the Deutsche Forschungsgemeinschaft(DFG,grant PH 189/2-1)
文摘In fractured reservoirs characterized by low matrix permeability,fracture networks control the main fluid flow paths.However,in layered reservoirs,the vertical extension of fractures is often restricted to single layers.In this study,we explored the effect of changing marl/shale thickness on fracture extension using comprehensive field data and numerical modeling.The field data were sampled from coastal exposures of Liassic limestone-marl/shale alternations in Wales and Somerset(Bristol Channel Basin,UK).The vertical fracture traces of more than 4000 fractures were mapped in detail.Six sections were selected to represent a variety of layer thicknesses.Besides the field data also thin sections were analyzed.Numerical models of fracture extension in a two-layer limestone-marl system were based on field data and laboratory measurements of Young's moduli.The modeled principal stress magnitude σ3 along the lithological contact was used as an indication for fracture extension through marls.Field data exhibit good correlation(R^2=0.76) between fracture extension and marl thickness,the thicker the marl layer the fewer fractures propagate through.The model results show that almost no tensile stress reaches the top of the marl layer when the marls are thicker than 30 cm.For marls that are less than 20 cm,the propagation of stress is more dependent on the stiffness of the marls.The higher the contrast between limestone and marl stiffness the lower the stress that is transmitted into the marl layer.In both model experiments and field data the critical marl thickness for fracture extension is ca.15-20 cm.This quantification of critical marl thicknesses can be used to improve predictions of fracture networks and permeability in layered rocks.Up-or downsampling methods often ignore spatially continuous impermeable layers with thicknesses that are under the detection limit of seismic data.However,ignoring these layers can lead to overestimates of the overall permeability.Therefore,the understanding of how fractures propagate and terminate through impermeable layers will help to improve the characterization of conventional reservoirs.
基金This work was supported by the National Natural Science Foundation of China under Grant Nos. 61672078 and 61732019, and the National Key Research and Development Program of China under Grant No. 2018YFB1004202.
文摘Empirical research is playing a significant role in software engineering （SE）, and it has been applied to evaluate software artifacts and technologies. There have been a great number of empirical research articles published recently. There is also a large research community in empirical software engineering （ESE）. In this paper, we identify both the overall landscape and detailed implementations of ESE, and investigate frequently applied empirical methods, targeted research purposes, used data sources, and applied data processing approaches and tools in ESE. The aim is to identify new trends and obtain interesting observations of empirical software engineering across different sub-fields of software engineering. We conduct a mapping study on 538 selected articles from January 2013 to November 2017, with four research questions. We observe that the trend of applying empirical methods in software engineering is continuously increasing and the most commonly applied methods are experiment, case study and survey. Moreover, open source projects are the most frequently used data sources. We also observe that most of researchers have paid attention to the validity and the possibility to replicate their studies. These observations are carefully analyzed and presented as carefully designed diagrams. We also reveal shortcomings and demanded knowledge/strategies in ESE and propose recommendations for researchers.
基金The presented work was funded by a research grant from Statoil.
文摘First introduced in[2],the lumped particle framework is a flexible and numerically efficient framework for the modelling of particle transport in fluid flow.In this paper,the framework is expanded to simulate multicomponent particle-laden fluid flow.This is accomplished by introducing simulation protocols tomodel particles over a wide range of length and time scales.Consequently,we present a time ordering scheme and an approximate approach for accelerating the computation of evolution of different particle constituents with large differences in physical scales.We apply the extended framework on the temporal evolution of three particle constituents in sandladen flow,and horizontal release of spherical particles.Furthermore,we evaluate the numerical error of the lumped particle model.In this context,we discuss the Velocity-Verlet numerical scheme,and show how to apply this to solving Newton’s equations within the framework.We show that the increased accuracy of the Velocity-Verlet scheme is not lost when applied to the lumped particle framework.
文摘This paper presents a lumped particle model for simulating a large number of particles.The lumped particle model is a flexible framework in modeling particle flows,embodying fundamental features that are intrinsic in particle laden flow,including advection,diffusion and dispersion.In this paper,the particles obey a simplified version of the Bassinet-Boussinesq-Oseen equation for a single spherical particle.However,instead of tracking the individual dynamics of each particle,a weighted spatial averaging procedure is used where the external forces are applied to a“lump”of particles,from which an average position and velocity is derived.The temporal evolution of the particles is computed by partitioning the lumped particle into smaller entities,which are then transported throughout the physical domain.These smaller entities recombine into new particle lumps at their target destinations.For particles prone to the effects of Brownian motion or similar phenomena,a symmetric spreading of the particles is included as well.Numerical experiments show that the lumped particle model reproduces the effects of Brownian diffusion and uniform particle transport by a fluid and gravity.The late time scale diffusive nature of particle motion is also reproduced.
文摘This paper presents an extension of the lumped particle model in[1]to include the effects of particle collisions.The lumped particle model is a flexible framework for the modeling of particle laden flows,that takes into account fundamental features,including advection,diffusion and dispersion of the particles.In this paper,we transform a binary collision model and concepts from kinetic theory into a collision procedure for the lumped particle framework.We apply this new collision procedure to investigate numerically the role of particle collisions in the hindered settling effect.The hindered settling effect is characterized by an increase in the effective drag coefficient CD that influences each particle in the flow.This coefficient is given by CD=(1−φ)−nC∗D,whereφis the volume fraction of particles,C∗D is the drag coefficient for a single particle,and n≃4.67 for creeping flow.We obtain an approximation for CD/C∗D by calculating the effective work done by collisions,and comparing that to the work done by the drag force.In our numerical experiments,we observe a minimal value of n=3.0.Moreover,by allowing high energy dissipation,an approximation for the classical value for creeping flow,n=4.7,is reproduced.We also obtain high values for n,up to n=6.5,which is consistent with recent physical experiments on the sedimentation of sand grains.
文摘We describe and evaluate a numerical solution strategy for simulating surface acoustic waves(SAWs)through semiconductor devices with complex geometries.This multi-physics problem is of particular relevance to the design of SAW-based quantum electronic devices.The mathematical model consists of two coupled partial differential equations for the elastic wave propagation and the electric field,respectively,in anisotropic piezoelectric media.These equations are discretized by the finite element method in space and by a finite difference method in time.The latter method yields a convenient numerical decoupling of the governing equations.We describe how a computer implementation can utilize the decoupling and,via object-oriented programming techniques reuse independent codes for the Poisson equation and the linear time-dependent elasticity equation.First we apply the simulator to a simplified model problem for verifying the implementation,and thereafter we show that the methodology is capable of simulating a real-world case from nanotechnology,involving SAWs in a geometrically non-trivial device made of Gallium Arsenide.PACS:02.70.Dh,41.20.Jb,46.25.Hf Key words:Finite element method,piezoelectric surface acoustic waves,Gallium Arsenide.
