地下储层表征的不确定性及科学思维方法

由于地质的复杂性和资料的不完备性,地下储层表现为＂灰箱＂系统,表征结果存在着不确定性。基于系统论和科学哲学的方法,探讨了地下储层表征中不确定性的成因类型、内涵及解决方案,并论述了地下储层表征过程中所应重视的科学思维方法。地下储层表征中存在两类基本的不确定性类型：①随机不确定性,主要由局部预测整体（如应用多井资料进行井间储层预测）以及第二性资料的非完全映射（如应用地震资料预测储层）所致;②模糊不确定性,主要由储层概念模式认知不足所致。为了使表征结果逼近地质实际,除了正确应用和创新相关理论和方法外,需要具备科学的表征理念和思维,包括总体把握、分级约束,多科一体、地质为核,发散求索、聚焦论证,辩证思维、综合分析;同时,应正确理解和处理宏观与微观、绝对与相对、静态与动态、映射与多解、局部与整体、模糊与置信、确定与随机、个别与一般、复杂与简约、手工与自动等矛盾统一体的关系。     

自动识别多期断层擦痕的一种应力反演算法

由于地质历史上构造应力场的演变,多期断层擦痕数据的存在是应力反演所面临的普遍性问题.以往提出处理多期断层擦痕的应力反演算法都基于硬划分,忽视了数据自身的不确定性,并且一些只是传统的、处理一期断层擦痕的算法的简单延拓.在Fry (1999)的sigma空间里,同期断层擦痕向量具有统一的线性分布趋势,多期断层擦痕向量具有不同的线性分布趋势.在此基础上,本文提出利用模糊线性聚类法来识别多期断层擦痕向量的线性结构.这种算法不仅可以弥补以往算法的上述缺陷,还具有自动、直接、有效,且计算量也较小的优点.     

Response Surface Designs for Scenario Management and Uncertainty Quantification in Reservoir Production

Response surface experimental designs provide a framework for evaluating sensitivities and assessing uncertainties in reservoir-production forecasts for continuous parameters (i.e. permeability, flow rate, etc.). In this paper, the method is extended in order to integrate both continuous and discrete parameters (i.e. fault status: open/close, injection scheme: SWAG/WAG, etc.). This paper presents an appropriate experimental designs approach, notably the regression models associated with, and the statistical interpretation (sensitivity study, Monte Carlo simulations, etc.). The method has been successfully applied to a reservoir oil-production simulation problem. The objective was to define the best production scheme by optimizing the well-completion level. This application has highlighted the advantages of this new approach, both in terms of decreasing simulation cost and improving the interpretation quality.     

Characterization and Quantification of Uncertainty in?Coregionalization Analysis

Coregionalization analysis has been presented as a method of multi-scale analysis for multivariate spatial data. Despite an increasing use of this method in environmental and earth sciences, the uncertainty associated with the estimation of parameters in coregionalization analysis (e.g., sills and functions of sills) is potentially high and has not yet been characterized. This article aims to discuss the theory underlying coregionalization analysis and assess the robustness and limits of the method. A theoretical framework is developed to calculate the ergodic and fluctuation variance-covariance matrices of least-squares estimators of sills in the linear model of coregionalization. To adjust for the positive semidefiniteness constraint on estimated coregionalization matrices, a confidence interval estimation procedure for sills and functions of sills is presented. Thereafter, the relative importance of uncertainty measures (bias and variance) for sills and structural coefficients of correlation and determination is assessed under different scenarios to identify factors controlling their uncertainty. Our results show that the sampling grid density, the choice of the least-squares estimator of sills, the positive semidefiniteness constraint, the presence of scale dependence in the correlations, and the number and range of variogram models, all affect the level of uncertainty, sometimes through multiple interactions. The asymptotic properties of variogram model parameter estimators in a bounded sampling domain impose a theoretical limit to their accuracy and precision. Because of this limit, the uncertainty was found to be high for several scenarios, especially with three variogram models, and was often more dependent on the ratio of variogram range to domain extent than on the sampling grid density. In practice, in the coregionalization analysis of a real dataset, the circular requirement for sill estimates in the calculation of uncertainty measures makes the quantification of uncertainty very problematic, if not impossible. The use of coregionalization analysis must be made with due knowledge of the uncertainty levels and limits of the method.     

Characterization and Quantification of Uncertainty in Coregionalization Analysis

Coregionalization analysis has been presented as a method of multi-scale analysis for multivariate spatial data. Despite an increasing use of this method in environmental and earth sciences, the uncertainty associated with the estimation of parameters in coregionalization analysis (e.g., sills and functions of sills) is potentially high and has not yet been characterized. This article aims to discuss the theory underlying coregionalization analysis and assess the robustness and limits of the method. A theoretical framework is developed to calculate the ergodic and fluctuation variance-covariance matrices of least-squares estimators of sills in the linear model of coregionalization. To adjust for the positive semidefiniteness constraint on estimated coregionalization matrices, a confidence interval estimation procedure for sills and functions of sills is presented. Thereafter, the relative importance of uncertainty measures (bias and variance) for sills and structural coefficients of correlation and determination is assessed under different scenarios to identify factors controlling their uncertainty. Our results show that the sampling grid density, the choice of the least-squares estimator of sills, the positive semidefiniteness constraint, the presence of scale dependence in the correlations, and the number and range of variogram models, all affect the level of uncertainty, sometimes through multiple interactions. The asymptotic properties of variogram model parameter estimators in a bounded sampling domain impose a theoretical limit to their accuracy and precision. Because of this limit, the uncertainty was found to be high for several scenarios, especially with three variogram models, and was often more dependent on the ratio of variogram range to domain extent than on the sampling grid density. In practice, in the coregionalization analysis of a real dataset, the circular requirement for sill estimates in the calculation of uncertainty measures makes the quantification of uncertainty very problematic, if not impossible. The use of coregionalization analysis must be made with due knowledge of the uncertainty levels and limits of the method.     

A Strain-Rate Dependent Clay Constitutive Model with Parametric Sensitivity and Uncertainty Quantification

This paper presents a strain-rate dependent plastic constitutive model for clays. Based on the concepts of critical-state soil mechanics and bounding surface plasticity theory, the model reproduces the mechanical response of clays under triaxial and simple shear loading conditions. The model parameters are determined for Boston Blue Clay, London Clay and Kaolin Clay, and the performance of the model in simulating the mechanical response of these clays is demonstrated for low to medium strain rates. The sensitivity of each model parameter is checked by perturbing the calibrated values by ±20 %. Subsequently, a probabilistic analysis using Monte Carlo simulations is performed by treating the model parameters as random variables and the impact of the statistics of the parameters on the undrained shear strength is investigated.     

河道流量演算的一种新途径

系统地阐述了现行各种流量演算模型普遍存在系统偏差(注)及其造成的原因,根据河槽蓄泄特性提出了滞后出流流量演算模型及其解法.实例应用表明,该模型在实例河段优于反映非线性影响的马斯京根演算模型.     

地下多组分反应溶质运移数值模拟:地质资源和环境研究的新方法

地下多组分反应溶质运移数值模拟(RTM)是解释地球系统中的耦合过程和不同时空尺度对其影响的重要工具。RTM是研究地球科学基础理论、地质资源和环境等复杂地球化学过程的一个新方法,可用于如废物处置安全性评估、地下水污染研究、二氧化碳地质储存、金属矿床的地浸开采等的研究中。笔者首先回顾了反应溶质溶质运移模拟的发展历史,然后总结了反应溶质运移模拟的发展现状,再从耦合过程、空间尺度、裂隙和非均质介质处理角度说明了反应溶质运移模拟所面临的挑战。结合地下水质的演化、生物降解、CO2地质储存等具体实例讨论了反应溶质运移模拟的广泛应用前景,探讨了反应溶质运移模拟的未来发展方向。     

A Functional Data Analysis Approach to Surrogate Modeling in Reservoir and Geomechanics Uncertainty Quantification

Uncertainty quantification for geomechanical and reservoir predictions is in general a computationally intensive problem, especially if a direct Monte Carlo approach with large numbers of full-physics simulations is used. A common solution to this problem, well-known for the fluid flow simulations, is the adoption of surrogate modeling approximating the physical behavior with respect to variations in uncertain parameters. The objective of this work is the quantification of such uncertainty both within geomechanical predictions and fluid-flow predictions using a specific surrogate modeling technique, which is based on a functional approach. The methodology realizes an approximation of full-physics simulated outputs that are varying in time and space when uncertainty parameters are changed, particularly important for the prediction of uncertainty in vertical displacement resulting from geomechanical modeling. The developed methodology has been applied both to a subsidence uncertainty quantification example and to a real reservoir forecast risk assessment. The surrogate quality obtained with these applications confirms that the proposed method makes it possible to perform reliable time–space varying dependent risk assessment with a low computational cost, provided the uncertainty space is low-dimensional.     

Bayesian Gaussian Mixture Linear Inversion for Geophysical Inverse Problems

A Bayesian linear inversion methodology based on Gaussian mixture models and its application to geophysical inverse problems are presented in this paper. The proposed inverse method is based on a Bayesian approach under the assumptions of a Gaussian mixture random field for the prior model and a Gaussian linear likelihood function. The model for the latent discrete variable is defined to be a stationary first-order Markov chain. In this approach, a recursive exact solution to an approximation of the posterior distribution of the inverse problem is proposed. A Markov chain Monte Carlo algorithm can be used to efficiently simulate realizations from the correct posterior model. Two inversion studies based on real well log data are presented, and the main results are the posterior distributions of the reservoir properties of interest, the corresponding predictions and prediction intervals, and a set of conditional realizations. The first application is a seismic inversion study for the prediction of lithological facies, P- and S-impedance, where an improvement of 30% in the root-mean-square error of the predictions compared to the traditional Gaussian inversion is obtained. The second application is a rock physics inversion study for the prediction of lithological facies, porosity, and clay volume, where predictions slightly improve compared to the Gaussian inversion approach.     

新的瑞雷波多模式频散曲线反演目标函数

反演瑞雷波频散曲线能有效地获取横波速度和地层厚度,传统的多模式瑞雷波频散曲线反演需要正确的模式判别.然而,当地层中含有低速软弱夹层或高速硬夹层等复杂结构时,瑞雷波可能会出现"模式接吻"和"模式跳跃"等现象,这些现象极易造成模式误判,进而导致错误的反演结果;同时,传统的频散曲线反演方法需要进行求根运算,进而导致现有的瑞雷波非线性反演速度慢,运算时间长.鉴于此,对传统的Haskell-Thomson频散曲线正演模拟算法进行了改进,提出了一种新颖有效的目标函数.该目标函数直接利用实测频散曲线与迭代更新模型频散函数表面形状进行最佳拟合,无需将多模式频散数据归于特定的模式,可有效避免多模式瑞雷波频散曲线反演模式误识别;同时,该目标函数不需要求根运算,进而大大加快了非线性反演速度.基于粒子群优化算法,利用实际工作中经常遇到的3种典型理论地质模型和某一高速公路路基实测资料进行了理论模型试算和实例分析,检验了本文提出的瑞雷波多模式频散曲线反演新方法的有效性和实用性.      

流量过程线分割的新方法——应用分析

介绍了基于Horton下渗能力曲线的流量过程线分割的新方法的计算流程。选择猴子岩、西峡、东湾、王窑水库和尚义五个分属于不同气候区流域的降雨径流资料。采用该方法对流量过程线进行分割,并与现行的非线性水库假设分割法和数字滤波分割方法相比较。结果表明,该方法是具有物理机制的、客观的分割方法,分割的结果符合水文的基本规律,比其他两种方法更加合理,对于流域时段单位线和降雨径流关系的推求均有重要的意义。     

A Lattice Spring Model for Coupled Fluid Flow and Deformation Problems in Geomechanics

A lattice spring model is developed for coupled fluid flow and deformation problems. The model has an underlying structure consisting of particles connected by springs for the solid and fluid bubbles, connected by fluid pipelines for fluid flow. Formulations of the model to describe the coupled fluid flow and deformation behavior of a solid are derived. A few examples of consolidation problems are presented and compared with analytical solutions with good agreement being obtained, which means that the lattice model developed in this study can correctly simulate the coupled fluid flow and deformation response of a solid.     

起伏地形三维激电连续介质模型快速反演

为提高起伏地形三维激电数据的反演解释精度和处理效率,笔者开展了连续介质模型快速反演方法研究。针对起伏地形连续电性介质模型,提出了四面体单元电性参数分块线性连续变化的参数化方法。在反演中对模型参数施加光滑和背景约束信息,以提高反演的稳定性和分辨率。通过采用降低反问题的维数、压缩存储线性反演方程各矩阵的元素以及将互换原理和拟牛顿法相结合的方式计算偏导数矩阵等手段,可有效地加快反演的计算速度。最后,为验证反演方法的有效性,对2例地电模型进行反演试算,计算结果表明：反演耗费时间较少,仅迭代6次拟合差便趋于稳定,反演结果能较好地刻画异常体形态,编制的反演解释软件可用于实际生产。     

流量过程线分割的新方法--公式推导

针对现行流量过程线分割方法中存在着缺乏物理基础和客观的、科学的操作方法，以及其他的一些问题，提出了流量过程线的分割应遵循的三条基本原则，在此基础上提出流量过程线分割的新方法。该法通过流域的降雨资料和出口断面的流量资料，经推导得到Horton下渗能力曲线的三参数，并推导出地下净雨量在非饱和带运行时间公式和地下水汇流公式，从而对流域出口断面流量过程线进行分割。     

A Particle Tracking Model for Non-Fickian Subsurface Diffusion

In this paper, a new particle tracking technique is described which can simulate non-Fickian diffusion within porous media. The technique employs fractional Brownian motions (fBms), a generalization of regular Brownian motion. These random fractal functions allow both super- and subdiffusive particle paths to be produced and hence non-Fickian diffusion of the resulting panicle clouds can be modeled. In recent years, fBm trace functions have been used by many authors to reproduce self-affine random fields to simulate various porous media properties. In contrast, a method is detailed herein which uses self-similar spatial fBm trajectories to simulate directly non-Fickian behavior of the particle clouds. Although fractal trajectories have been previously suggested as the basis for possible methods of modeling non-Fickian diffusion, the authors believe that this paper contains the first algorithm to be presented which does not require an a priori knowledge of the end condition of the random walk and, more importantly, allows both a definable scaling exponent and (fractal) diffusion coefficient to be specified. The resulting non-Fickian diffusion using the new algorithm is illustrated and some applications are discussed. The purpose of this paper is to bring the potential usefulness of fBm trajectories in simulating non-Fickian processes within homogeneous media to the attention of numerical modelers active in the simulation of subsurface diffusive processes. The method has a particular environmental application in the simulation of the non-Fickian dispersion of groundwater contaminants through porous media.     

A New Methodology for Singularity Modelling in Flow Simulations in Reservoir Engineering

In this paper, numerical methods for flow simulation in the well vicinity are discussed. Flux truncation errors are analyzed on gridblocks near the well. Due to the singularity of the well, standard numerical schemes are not efficient for near well flow simulations. To improve simulation accuracy, a new methodology, using a change of coordinates to make near well pressure linear, is presented for the singularity modelling. Based on this new approach, two numerical schemes, a two-point flux approximation scheme and a multi-point one, are proposed. These schemes are accurate for the near well modelling and are suitable for any kinds of gridblocks.     

互相关系数自约束的重力三维反演与高效求解

本文将拟合残差计算所得的互相关系数作为先验信息,与深度加权函数同时引入到重力正则化反演的模型约束中,以提升反演结果的可靠性。针对三维反演中的大型线性方程组问题,引入阻尼LSQR （最小二乘QR分解）算法,结合等效几何格架技术,将大矩阵按照模型单元划分为若干个子矩阵进行存储与运算。理论模型计算结果表明：同时利用互相关系数和深度加权的模型自约束反演,能较清晰地反映真实异常体;基于分块矩阵的阻尼LSQR算法求解线性方程组较直接法节省了几千甚至上万倍的存储量,且计算速率提高了数倍,可在普通计算机上实现较大规模的反演计算。将其应用于云南芦子园铁铅锌铜多金属矿床隐伏花岗岩体定位,取得了良好的效果。