Numerical simulation of pollution and oil spill spreading by the stochastic discrete particle method

The features of the stochastic discrete particle method are discussed as applied to the simulation of pollutant advection and diffusion in a turbulent flow and to the spread of a thin film of a viscous substance (oil) on the surface of water. The diffusion tensor in the former problem depends on the scale of the pollution cloud, and the diffusivity in the latter problem depends nonlinearly on the desired function. For pollution dispersion by a turbulent flow, a stochastic discrete particle algorithm is constructed in the case when the diffusion tensor corresponds to the Richardson 4/3 law. The numerical and analytical results are shown to agree well. The problem of oil film spreading is described by a quasilinear advection-diffusion equation. For this problem, a random walking algorithm is constructed in which the variance of the walking particle step depends on the desired function. For both instantaneous and time-continuous sources of pollutants, the solution produced by the stochastic discrete particle method agrees well with the analytical and/or numerical solutions to the test problems under consideration.     

A nonlinear test case for the finite element method in two-phase flow

The ability of the finite element method to compute the motion of sharp interfaces in two-phase flow is examined by applying it to a test problem for which an analytical solution can be found. The problem is one of imbibition, the nonlinear diffusion of a fixed amount of water into an oil filled porous medium and can be solved exactly by similarity and the separation of variables method used by Boyer. The finite element program used was of the Galerkin type and employed a self-adaptive time stepping algorithm with both linear and quadratic isoparametric triangular elements. Results are presented for both elements and show that there is little difficulty in this type of diffusion problem in following the oil-water interface to accuracies of 2 or 3 percent.     

Evolutionary computation for automatic Web service composition: an indirect representation approach

Web services have become increasingly popular in recent years, and they are especially suitable to the process of Web service composition, which is when several services are combined to create an application that accomplishes a more complex task. In recent years, significant research efforts have been made on developing approaches for performing Quality of Service -aware Web service composition. Evolutionary computing (EC) techniques have been widely used for solving this problem, since they allow for the quality of compositions to be optimised, meanwhile also ensuring that the solutions produced have the required functionality. Existing EC-based composition approaches perform constrained optimisation to produce solutions that meet those requirements, however these constraints may hinder the effectiveness of the search. To address this issue, a novel framework based on an indirect representation is proposed in this work. The core idea is to first generate candidate service compositions encoded as sequences of services. Then, a decoding scheme is developed to transform any sequence of services into a corresponding feasible service composition. Given a service sequence, the decoding scheme builds the workflow from scratch by iteratively adding the services to proper positions of the workflow in the order of the sequence. This is beneficial because it allows the optimisation to be carried out in an unconstrained way, later enforcing functionality constraints during the decoding process. A number of encoding methods and corresponding search operators, including the PSO, GA, and GP-based methods, are proposed and tested, with results showing that the quality of the solutions produced by the proposed indirect approach is higher than that of a baseline direct representation-based approach for twelve out of the thirteen datasets considered. In particular, the method using the variable-length sequence representation has the most efficient execution time, while the fixed-length sequence produces the highest quality solutions.     

Simulation of suspended substance transport on the continental shelf: Horizontal dispersion

Suspended substance dispersion in a water body is simulated in the case when the spread area is considerably larger than the depth of the water body. A model of horizontal dispersion of pollutants is formulated and analyzed. Numerical approaches to the computation of suspended substance dispersion in a water body are discussed. A meshless stochastic numerical algorithm is proposed that combines the advantages of two well-known techniques, namely, the discrete cloud method and the stochastic discrete particle method. The performance the method and its features are demonstrated by comparing numerical results with the exact solution to the model problem of turbulent dispersion of a pollution plume produced by a continuous source of suspension.     

整体压裂裂缝导流能力与储层渗透率匹配关系研究

针对低渗透油藏存在非达西渗流的问题,建立了整体压裂三维油水两相油藏和裂缝系统的数学模型,并采用有限差分法进行求解.利用建立的数学模型,针对不同储层渗透率级别,研究裂缝导流能力对油井产能的影响.结果表明:在各级储层渗透率级别下,随着裂缝导流能力的增加,采油强度逐渐增加,但增加的幅度越来越小.在此基础上,引入采油强度变化率的概念,确定了不同储层渗透率级别下裂缝导流能力与采油强度变化率的关系,进而得到不同储层渗透率级别下的最佳裂缝导流能力.为合理、高效开发低渗透油藏提供技术支持与保障.     

An Introduction to Constant Curvature Spaces in the Commutative (Segre) Quaternion Geometry

It is known that complex numbers can be associated with plane Euclidean geometry and their functions are successfully used for studying extensions of Euclidean geometry, i.e., non-Euclidean geometries and surfaces differential geometry. In this paper we begin to study the constant curvature spaces associated with the geometry generated by commutative elliptic-quaternions and we show how the “mathematics” they generate allows us to introduce these spaces and obtain the geodesic equations without developing a complete mathematical apparatus as the one developed for Riemannian geometry.     

化学驱粘性指进微观渗流模拟研究

化学驱是提高原油采收率的重要方法,化学剂的加入使得地下流体粘度界面张力发生变化,粘性指进演变特征更为复杂.基于格子玻尔兹曼伪势多相流模型,综合考虑油水两相间相互作用、聚合物增粘与非牛顿特性、表面活性剂传质扩散作用及降低界面张力机理,建立了化学驱微观渗流格子玻尔兹曼模拟方法.基于数值模拟方法了研究二维单通道内粘性指进发展...     

A variety of (3 + 1)‐dimensional Burgers equations derived by using the Burgers recursion operator

A new variety of (3 + 1)‐dimensional Burgers equations is presented. The recursion operator of the Burgers equation is employed to establish these higher‐dimensional integrable models. A generalized dispersion relation and a generalized form for the one kink solutions is developed. The new equations generate distinct solitons structures and distinct dispersion relations as well. Copyright © 2014 John Wiley & Sons, Ltd.     

洼38块特稠油油藏流-固-热三场耦合规律研究

近年来,随着石油的不断开发开采,在研究高压注水,稠油热采等涉及到温度剧烈变化的研究领域中,油藏工作者难以通过经典的渗流力学理论和传统的油藏数值模拟方法得到有效、合理的解释,必须考虑到温度场、渗流场、应力场三场相互影响、相互作用、相互变化等相关变化因素.基于考虑热弹性的岩石应力一应变关系、地下流体运动定律、能量守恒定律,建立包括油水两相渗流控制方程、岩石变形体控制方程、温度场控制方程的稠油油藏三场耦合数学模型,运用全耦合算法实现同时求解所有耦合方程组,研究了应用有限元分析软件ADINA进行三场耦合规律的建模过程与方法.以小洼油田洼38块为例研究三场耦合规律.结果表明:距离井筒越近,其总位移、温度场、应力场、渗流场及岩石物性参数越会产生明显的变化;距离井筒越远,其变化越不明显.距离井筒越近的储层温度变化越剧烈,而距离井筒越远的储层温度变化越缓;井筒周围的温度变化呈现倒置漏斗形状,随着注水的不断进行,漏斗会逐渐平缓;最后储层各点的温度会平衡在同一温度水平线上,达到平衡状态.模型较为真实的模拟油藏实际开采情况.     

$${\tt surveillance}$$: An R package for the monitoring of infectious diseases

Public health surveillance of emerging infectious diseases is an essential instrument in the attempt to control and prevent their spread. This paper presents the R package “surveillance”, which contains functionality to visualise routinely collected surveillance data and provides algorithms for the statistical detection of aberrations in such univariate or multivariate time series. For evaluation purposes, the package includes real-world example data and the possibility to generate surveillance data by simulation. To compare algorithms, benchmark numbers like sensitivity, specificity, and detection delay can be computed for a set of time series. Package motivation, use and potential are illustrated through a mixture of surveillance theory, case study and R code snippets.     

A path probability approach to the solute transport problem

An alternative solute transport algorithm, termed the path probability approach, is presented. The method may be more effective than typical finite methods in some numerical solution problems. The method differs from predominant numerical techniques in that the conventional conservation differential is replaced by a series of equations defining solute migration in terms of a finite number of representative particle position histories and corresponding probabilities. The governing physical assumptions applied in model development are conditionally consistent with those of conventional Lagrangian and Eulerian conceptualizations, but mathematical expression and development of the problem differ from traditional approaches. The method represents dispersion orthogonal to the primary axis of advective transport explicitly, according to arbitrary user-defined probability functions; longitudinal dispersion effects result from the existence of velocity shear effects along the primary axis of movement. It is possible to incorporate Fickian dispersive processes, and thereby reproduce results obtainable with traditional stream tube models; but non-Fickian alternatives can also be explored. Simulation results of the path probability model are compared to analogous results from a representative finite difference model for a hypothetical test flow channel. The comparison demonstrated the ability of the new model to effectively generate simulation results with a computational effeciency considerably higher than conventional techniques under the conditions tested.     

Pre- and post-processing for the finite element method

The finite element method provides a powerful procedure to mathematically model physical phenomena. The technique is numerically formulated and is effectively used on a broad range of computers. The method has increased in both popularity and functionality with the development of user friendly pre- and post-processing software. Pre-processing software is used to create the model, generate an appropriate finite element grid, apply the appropriate boundary conditions, and view the total model. Post-processing provides visualization of the computed results. This paper addresses the pertinent issues of pre- and post-processing for finite element analysis. It reviews the capabilities that are provided by pre- and post-processors and suggests enhancements and new features that will likely be developed in the near future.     

Explanation of exceptional values in multi-dimensional business databases

In this paper, we describe an extension of the OnLine Analytical Processing (OLAP) framework with causal explanation, offering the possibility to automatically generate explanations for exceptional cell values. This functionality can be built into conventional OLAP databases using a generic explanation formalism, which supports the work of managers in diagnostic processes. The central goal is the identification of specific knowledge structures and reasoning methods required to construct computerized explanations from multi-dimensional data and business models. The methodology was tested on a case study involving the comparison of financial figures of a firm’s business units. The findings suggest improved decision-making by managers because the current tedious and error-prone manual analysis process is enhanced by automated problem identification and explanation generation. It is also noted that this novel methodology has general utility for decision-support systems, for example, for automated diagnosis in the financial and accountancy domain.     

On‐site surrogates for large‐scale calibration

Motivated by a computer model calibration problem from the oil and gas industry, involving the design of a honeycomb seal, we develop a new Bayesian methodology to cope with limitations in the canonical apparatus stemming from several factors. We propose a new strategy of on‐site design and surrogate modeling for a computer simulator acting on a high‐dimensional input space that, although relatively speedy, is prone to numerical instabilities, missing data, and nonstationary dynamics. Our aim is to strike a balance between data‐faithful modeling and computational tractability in a calibration framework—tailoring the computer model to a limited field experiment. Situating our on‐site surrogates within the canonical calibration apparatus requires updates to that framework. We describe a novel yet intuitive Bayesian setup that carefully decomposes otherwise prohibitively large matrices by exploiting the sparse blockwise structure. Empirical illustrations demonstrate that this approach performs well on toy data and our motivating honeycomb example.     

Solitary fluid transients in rectangular ducts with transverse magnetic fields

Summary This paper treats a fluid hammer wave which is propagating into a fully developed MHD duct flow and which is produced by suddenly closing a valve at some cross section of a rectangular, insulating duct with a uniform transverse, applied magnetic field. The Mach and magnetic Reynolds numbers are assumed to be small, while the Hartmann number is assumed to be large. For a small interaction parameter, the electromagnetic effects on the fluid hammer wave are small and consist of both dispersion and dissipation. The dispersion is cumulative and becomes larger for large time, while the dissipation remains small for all time.Résumé Cet article traite de l'onde de choc produite par la fermeture subite d'une vanne et qui se propage dans un fluide conducteur d'electricité s'écoulant dans une conduite isolante de section rectangulaire à laquelle est appliqué un champ magnétique transversal et homogène. On admet que le nombre de Reynold magné tique et le nombre de Mach sont petits, alors que le nombre de Hartmann est grand. Pour des faibles valeurs du paramètre d'interaction, les effets électromagnétiques sur l'onde de choc sont petits et comprennent une dispersion et une dissipation. La dispersion est cummulative et augmente avec le temps, alors que la dissipation reste toujours petite.     

Assessment of an Eulerian CFD model for prediction of dilute droplet dispersion in a turbulent jet

The turbulent dispersion of non-evaporating droplets in an axisymmetric round jet issuing from a nozzle is investigated both experimentally and theoretically. The experimental data set has a well-defined inlet boundary with low turbulence intensity at the nozzle exit, so that droplet dispersion is not affected by the transport of nozzle-generated fluctuating motion into the jet, and is influenced solely by turbulence in the gas phase produced in the shear layer of the jet. This data set is thus ideal for testing algebraic models of droplet fluctuating motion that assume local equilibrium with the turbulence in the gas phase. Moreover, the droplet flux measurements are sufficiently accurate that conservation of the total volume flow of the droplet phase has been demonstrated. A two-fluid turbulence modelling approach is adopted, which uses the k–ε turbulence model and a simple algebraic model that assumes local equilibrium to predict the fluid and droplet turbulent correlations, respectively. We have shown that the k–ε turbulence model lacks generality for predicting the spread of momentum in jets with and without a potential core. However, in general, the model predicts the radial dispersion of droplets in the considered turbulent jet with reasonable accuracy over a broad range of droplet sizes, once deficiencies in the k–ε turbulence model are taken into account.     

Fluctuating Powder-Driven Pulsed Water Jet

A study is made of the internal ballistics of a powder-driven pulsed water jet which generates a fluctuating, high velocity stream of liquid. The velocity fluctuations are caused by the use of a light piston which, together with the gases produced by the powder, forms an oscillating system. Calculations of the water jet parameters in the nonstationary and quasistationary approximations are compared. It is shown that the period of the stream velocity fluctuations depends on the initial pressure of the gases produced by the powder, the masses of the piston and water, and the geometry of the apparatus. The period of the fluctuations estimated in a linear approximation for instantaneous powder burnup is in good agreement with the quasistationary calculations.     

横观各向同性材料的剪切模量

本文提出了一个决定横观各向同性材料的独立剪切模量的新的简单方法.给出了数学公式和推导及其解,也提出了测定仪器及其测定结果.本法曾用Green河岩层的油页岩试验过,这种油页岩就是横观各向同性材料.本文结果也和其它近似结果并和声学试验法的结果比较过.本文也用已知剪切模量的材料来校核本文的测定方法.     

Numerical Modeling of Pollutant Dispersion and Oil Spreading by the Stochastic Discrete Particles Method

We consider two applications of the stochastic discrete particles method. The first one is concerned with the dispersion of a passive pollutant by a turbulent stream with a scale dependent diffusion coefficient. The second application deals with the problem of an oil spill spreading on the water surface described by transport–diffusion equation with a nonlinear diffusion coefficient. For the first problem we develop a discrete particles algorithm provided the diffusion coefficient obeys Richardson's "4/3" law and show good correspondence with the numerical and analytical results. The second problem is more involved and we develop a heuristic procedure based on the standard discrete particles random walk algorithm updating the dependence of each particle step variance on the dependent function. The obtained solution coincides well with analytical and direct one-dimensional finite-difference solutions both for instantaneous and continuous oil release.     

An improved numerical simulator for different types of flows in porous media

We develop an improved numerical simulator for subsurface compressible flows through porous media with point sources and sinks, which are governed by different equations of state. Computational experiments show that the simulator can generate stable simulation for different types of incompressible or compressible flows involving light or heavy components in porous media with point sources and sinks, large mobility ratios, discontinuous permeabilities and porosities, and anisotropic dispersion in tensor form, even though very large time steps and spatial grids are used. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 343–362, 2003.