Wave propagation in a general anisotropic poroelastic medium: Biot’s theories and homogenisation theory

Anisotropic wave propagation is studied in a fluid-saturated porous medium, using two different approaches. One is the dynamic approach of Biot’s theories. The other approach known as homogenisation theory, is based on the averaging process to derive macroscopic equations from the microscopic equations of motion. The medium considered is a general anisotropic poroelastic (APE) solid with a viscous fluid saturating its pores of anisotropic permeability. The wave propagation phenomenon in a saturated porous medium is explained through two relations. One defines modified Christoffel equations for the propagation of plane harmonic waves in the medium. The other defines a matrix to relate the relative displacement of fluid particles to the displacement of solid particles. The modified Christoffel equations are solved further to get a quartic equation whose roots represent complex velocities of the four attenuating quasi-waves in the medium. These complex velocities define the phase velocities of propagation and quality factors for attenuation of all the quasi-waves propagating along a given phase direction in three-dimensional space. The derivations in the mathematical models from different theories are compared in order to work out the equivalence between them. The variations of phase velocities and attenuation factors with the direction of phase propagation are computed, for a realistic numerical model. Differences between the velocities and attenuations of quasi-waves from the two approaches are exhibited numerically.     

Utility Efficient Frontier: An Application in the Oil and Gas Industry

Current practice shows that the use of portfolio and utility theory is very low among petroleum companies. This article advocates the use of both portfolio theory and utility theory as decision-making tools to improve performance of oil and gas companies. We introduce a model that can be practically used and applied in the oil and gas industry. This model generates an optimized, efficient portfolio and, at the same time, enables the decision maker to incorporate his risk attitude and policy. This can only be done by combining both the portfolio theory and utility theory through an approach called the utility mean-variance model. A typical oil portfolio optimization problem is investigated by applying both portfolio and utility theories. Through the utility mean-variance model, an efficient frontier that captures decision maker risk attitude is achieved.     

Dual models of pore spaces

We present a model for pore spaces that consists of two parts related by duality: (1) a decomposition of an open polyhedral pore space into open contractible pore bodies separated by relatively open interfaces and (2) a pore network that is homotopy equivalent to the pore space. The dual model is unique and free of parameters, but it relies on regularity conditions for the pore space. We show how to approximate any pore space by the interior of a polyhedral complex such that the regularity conditions are fulfilled. Thus, we are able to calculate the dual model from synthetic porous media and images of real porous media. The pore bodies are unions of relatively open Delaunay cells with respect to the corners of the pore boundary, and the pore network consists of certain at most two-dimensional (2D) Voronoi cells with respect to the corners of the pore boundary. The pore network describes the neighborhood relations between the pore bodies. In particular, any relatively open 2D Delaunay face f separating two pore bodies has a unique (relatively open) dual network edge. In our model, f is a pore throat only if it is hit by its dual network edge. Thus, as opposed to widespread intuition, any pore throat is convex, and adjacent pore bodies are not necessarily separated by pore throats. Due to the duality between the pore network and the decomposition of the pore space into pore bodies it is straightforward to store the geometrical properties of the pore bodies [pore throats] as attributes of the dual network vertices [edges]. Such an attributed network is used to perform 2D drainage simulations. The results agree very well with those from a pore-morphology based modeling approach performed directly on the digital image of a porous medium. Contractibility of the pore bodies and homotopy equivalence of the pore space and the pore network is proven using discrete Morse theory and the nerve theorem from combinatorial topology.     

Nonlinear determinism in river flow: prediction as a possible indicator

Whether or not river flow exhibits nonlinear determinism remains an unresolved question. While studies on the use of nonlinear deterministic methods for modeling and prediction of river flow series are on the rise and the outcomes are encouraging, suspicions and criticisms of such studies continue to exist as well. An important reason for this situation is that the correlation dimension method, used as a nonlinear determinism identification tool in most of those studies, may possess certain limitations when applied to real river flow series, which are always finite and often short and also contaminated with noise (e.g. measurement error). In view of this, the present study addresses the issue of nonlinear determinism in river flow series using prediction as a possible indicator. This is done by (1) reviewing studies that have employed nonlinear deterministic methods (coupling phase‐space reconstruction and local approximation techniques) for river flow predictions and (2) identifying nonlinear determinism (or linear stochasticity) based on the level of prediction accuracy in general, and on the prediction accuracy against the phase‐space reconstruction parameters in particular (termed as the ‘inverse approach’). The results not only provide possible indications to the presence of nonlinear determinism in the river flow series studied, but also support, both qualitatively and quantitatively, the low correlation dimensions reported for such. Therefore, nonlinear deterministic methods are a viable complement to linear stochastic ones for studying river flow dynamics, if sufficient caution is exercised in their applications and in interpreting the outcomes. Copyright © 2006 John Wiley & Sons, Ltd.     

基于矩阵论的空间相似变换分析

根据空间相似变换的线性化公式，利用矩阵论分析误差方程的系数矩阵，给出求解空间相似变换参数所需控制点的具体要求。     

江苏省锡山市西部地区地下水资源计算模型研究

从地下水运动均衡原理的角度分析江苏省锡山市西部地区第Ⅱ承压含水层天然和现状开采条件下的地下水均衡要素.揭示了该区地下水开采与地面沉降的关系,其中现状开采条件下的75%～80%的开采量来自于粘性土层的压密水量.根据地面沉降的发生机理剖析地面沉降严重发育地区忽略地面沉降影响因子建立的地下水资源计算模型中存在的问题针对存在的问题,提出了地下水可开采资源合理的计算方法,并对融有地面沉降影响因子的地下水资源计算模型的可实现性进行了分析.