Optimization of nonconventional wells under uncertainty using statistical proxies

The determination of the optimal type and placement of a nonconventional well in a heterogeneous reservoir represents a challenging optimization problem. This determination is significantly more complicated if uncertainty in the reservoir geology is included in the optimization. In this study, a genetic algorithm is applied to optimize the deployment of nonconventional wells. Geological uncertainty is accounted for by optimizing over multiple reservoir models (realizations) subject to a prescribed risk attitude. To reduce the excessive computational requirements of the base method, a new statistical proxy (which provides fast estimates of the objective function) based on cluster analysis is introduced into the optimization process. This proxy provides an estimate of the cumulative distribution function (CDF) of the scenario performance, which enables the quantification of proxy uncertainty. Knowledge of the proxy-based performance estimate in conjunction with the proxy CDF enables the systematic selection of the most appropriate scenarios for full simulation. Application of the overall method for the optimization of monobore and dual-lateral well placement demonstrates the performance of the hybrid optimization procedure. Specifically, it is shown that by simulating only 10% or 20% of the scenarios (as determined by application of the proxy), optimization results very close to those achieved by simulating all cases are obtained.     

绿片岩三轴流变力学特性的研究(Ⅰ):试验结果

为了解锦屏一级水电站坝基绿片岩的流变力学特性，采用岩石全自动流变伺服仪对绿片岩进行了三轴压缩流变试验。基于试验结果，研究了绿片岩在不同围压作用下的轴向应变以及侧向应变随时间的变化规律，讨论了流变特性对岩石应力一应变曲线的影响，探讨了不同应力水平下的轴向以及侧向流变速率变化趋势，分析了不同围压下流变的破裂机制，掌握了绿片岩三轴流变的基本规律，从而为该水电站工程流变数值分析时参数的辨识提供了可靠的依据。     

绿片岩三轴流变力学特性的研究(II):模型分析

首先,基于在岩石全自动流变伺服仪上得到的绿片岩三轴流变试验曲线,采用五元件线性粘弹性模型对表现为粘弹性流变特性的曲线进行了辨识,获得了绿片岩的粘弹性流变参数;然后,提出了一个新的非线性粘性元件,并将其与塑性体并联起来,得到一个新的非线性粘塑性体(NVPB),该体能充分反映岩石的加速流变特性:同时,将NVPB模型与五元件粘弹性模型串联起来,建立了一个新的岩石七元件非线性粘弹塑性流变模型。采用绿片岩加速流变全过程曲线,对提出的岩石七元件非线性粘弹塑性流变模型进行了辨识,得到了岩石七元件非线性粘弹塑性流变模型的材料参数。流变模型与试验结果的比较,显示了所建模型的正确性与合理性。     

Evaluation of the Reduction in Uncertainty Obtained by Conditioning a 3D Stochastic Channel to Multiwell Pressure Data

A stochastic channel embedded in a background facies is conditioned to data observed at wells. The background facies is a fixed rectangular box. The model parameters consist of geometric parameters that describe the shape, size, and location of the channel, and permeability and porosity in the channel and nonchannel facies. We extend methodology previously developed to condition a stochastic channel to well-test pressure data, and well observations of the channel thickness and the depth of the top of the channel. The main objective of this work is to characterize the reduction in uncertainty in channel model parameters and predicted reservoir performance that can be achieved by conditioning to well-test pressure data at one or more wells. Multiple conditional realizations of the geometric parameters and rock properties are generated to evaluate the uncertainty in model parameters. The ensemble of predictions of reservoir performance generated from the suite of realizations provides a Monte Carlo estimate of the uncertainty in future performance predictions. In addition, we provide some insight on how prior variances, data measurement errors, and sensitivity coefficients interact to determine the reduction in model parameters obtained by conditioning to pressure data and examine the value of active and observation well data in resolving model parameters.     

Propriétés fractales de la fragmentation et processus stochastiques de fracturation : approche géométrique 3D à l'aide du modèle ObsifracFractal properties of fragmentation and stochastic fracturing processes: geometrical 3D approach by OBSIFRAC model

A numerical rock fragmentation model was elaborated, producing a 3D puzzle of convex polyhedra, geometrically described in a database. In the first scenario, a constant proportion of blocks are fragmented at each step of the process and leads to fractal distribution. In the second scenario, division affects one random block at each stage of the process, and produces a Weibull volume distribution law. Imposing a minimal distance between the fractures, the third scenario reveals a power law. The inhibition of new fractures in the neighbourhood of existing discontinuities could be responsible for fractal properties in rock mass fragmentation. To cite this article: L. Empereur-Mot, T. Villemin, C. R. Geoscience 334 (2002) 127–133.     

固体介质中弹性波传播机制的细胞自动机有限深势阱模型

分析了采用细胞自动机研究波动问题的建模方法，针对一维、均匀、各向同性固体介质中弹性纵波的微观机制，借用一经典弹簧振子模型、细胞自动机格子气模型，以及量子力学中的无限深势阱模型，建立了一个细胞自动机有限深势阱模型，从量子力学角度出发，基于介观物理和纳米概念，以微观精子的德布罗意假设为基础，利用薛定谔方程，讨论了该模型中粒子（分子组）的振动速度与粒子物质波波速之间的联系，给出了模型中的波动方程，得出ζ＝Vp（ζ为粒子振动速度，Vp为物质波纵波波速）。同时还讨论了模型中粒子的大小和能量传递问题，引入引力场，得出了能量及引力势的量子化条件，另外，对声波速度、格子气粒子振动速度和本文模型中分子组振动速度进行了比较；还对本文模型中的粒子能量分布作了分析。     

Spatial variation of seismic motion induced by propagation of body waves

Spatial variation of earthquake ground motion is an important phenomenon that cannot be ignored in the design and safety of strategic structures. Several models have been developed to describe this variation using statistical, mathematical or physical approaches. The latter approach is not specific to an event. A recent contribution, which uses such an approach and called complete stochastic deamplification approach (CSDA), was developed [1]. The aim of this paper is to analyze the spatial variation of earthquake motion induced by the propagation of body waves using the CSDA. Coherency functions are evaluated for the cases of SH–SV–P waves propagating through stratified soil. Results obtained show that the variation of the coherency function is not the same for vertical and horizontal components and that the motion is more coherent at depth than at the free surface. In fact, we found that the rate of decrease with frequency and distance is not the same if P–SV waves propagate through stratified soil.     

Optimal placement of dampers and actuators based on stochastic approach

A general method is developed for optimal application of dampers and actuators by installing them at optimal location on seismic-resistant structures. The study includes development of a statistical criterion, formulation of a general optimization problem and establishment of a solution procedure. Numerical analysis of the seismic response in time-history of controlled structures is used to verify the proposed method for optimal device application and to demonstrate the effectiveness of seismic response control with optimal device location. This study shows that the proposed method for the optimal device application is simple and general, and that the optimally applied dampers and actuators are very efficient for seismic response reduction.     

钢筋砼摩擦耗能支撑框架结构的单元刚度和力学模型分析

为研究钢筋砼摩擦耗能支撑框架结构的动力反应性能 ,对其中的摩擦耗能器单元和框架杆单元的单元刚度和力学模型做了分析。钢筋砼摩擦耗能支撑单元由支撑杆单元和钢板—橡胶摩擦耗能器单元组成 ,支撑单元可取空间杆单元 ,摩擦耗能器单元为平面应力矩形单元。摩擦耗能器单元的剪切恢复力曲线为理想的弹塑性曲线 ,根据耗能器单元的力学模型 ,可确定其在每一时刻的刚度 ;框架结构空间杆单元的恢复力模型采用双线型模型 ,根据杆单元的力学模型 ,可确定其在每一时刻的刚度。并利用所编制的程序对十层单榀两跨空间普通框架和摩擦耗能支撑框架在地震作用下进行了弹塑性反应时程分析 ,结果表明耗能支撑框架的顶层最大位移明显小于普通框架     

河流水质风险评价的灰色-随机风险率方法

提出了量化影响河流水质的随机不确定性与灰色不确定性的水质超标灰色－随机风险率概念，建立了水质超标灰色－随机风险率评价模型。在水质单项参数评价模型中，将河流污染物浓度变量的分布处理成灰色概率分布，将污染物浓度超过水质类别标准值的风险率处理成灰色概率，即水质超标灰色－随机风险率。在水质综合评价模型中，河流水环境系统被考虑为担任某一使用可能的可靠性系统，而任意一种水质参数超标意味着河流水体使用功能不能得到应有的保证，也即表明水体综合评价超标，最后借鉴系统可靠性分析的理论和方法计算水质综合超标率。该方法应用于黄河花园口断面重金属污染风险评价。