Conditioning Fractal (fBm/fGn) Porosity and Permeability Fields to Multiwell Pressure Data

Stochastic fractal (fGn and fBm) porosity and permeability fields are conditioned to given variogram, static (or hard), and multiwell pressure data within a Bayesian estimation framework. Because fGn distributions are normal/second-order stationary, it is shown that the Bayesian estimation methods based on the assumption of normal/second-order stationary distributions can be directly used to generate fGn porosity/permeability fields conditional to pressure data. However, because fBm is not second-order stationary, it is shown that such Bayesian estimation methods can be used with implementation of a pseudocovariance approach to generate fBm porosity/permeability fields conditional to multiwell pressure data. In addition, we provide methods to generate unconditional realizations of fBm/fGn fields honoring all variogram parameters. These unconditional realizations can then be conditioned to hard and pressure data observed at wells by using the randomized maximum likelihood method. Synthetic examples generated from one-, two-, and three-dimensional single-phase flow simulators are used to show the applicability of our methodology for generating realizations of fBm/fGn porosity and permeability fields conditioned to well-test pressure data and evaluating the uncertainty in reservoir performance predictions appropriately using these history-matched realizations.     

An Initial Guess for the Levenberg–Marquardt Algorithm for Conditioning a Stochastic Channel to Pressure Data

A standard procedure for conditioning a stochastic channel to well-test pressure data requires the minimization of an objective function. The Levenberg–Marquardt algorithm is a natural choice for minimization, but may suffer from slow convergence or converge to a local minimum which gives an unacceptable match of observed pressure data if a poor initial guess is used. In this work, we present a procedure to generate a good initial guess when the Levenberg–Marquardt algorithm is used to condition a stochastic channel to pressure data and well observations of channel facies, channel thickness, and channel top depth. This technique yields improved computational efficiency when the Levenberg–Marquardt method is used as the optimization procedure for generating realizations of the model by the randomized maximum likelihood method.     

Conditioning Channel Meanders to Well Observations

Assessment of uncertainty in the performance of fluvial reservoirs often requires the ability to generate realizations of channel sands that are conditional to well observations. For channels with low sinuosity this problem has been effectively solved. When the sinuosity is large, however, the standard stochastic models for fluvial reservoirs are not valid, because the deviation of the channel from a principal direction line is multivalued. In this paper, I show how the method of randomized maximum likelihood can be used to generate conditional realizations of channels with large sinuosity. In one example, a Gaussian random field model is used to generate an unconditional realization of a channel with large sinuosity, and this realization is then conditioned to well observations. Channels generated in the second approach are less realistic, but may be sufficient for modeling reservoir connectivity in a realistic way. In the second example, an unconditional realization of a channel is generated by a complex geologic model with random forcing. It is then adjusted in a meaningful way to honor well observations. The key feature in the solution is the use of channel direction instead of channel deviation as the characteristic random function describing the geometry of the channel.     

A Multistep Methodology for Building a Stochastic Model of Gold Grades in the Disseminated and Complex Deposit of Casas Novas in Alentejo,Southern Portugal

This paper proposes a multistep approach for creating a 3D stochastic model of gold grades in a complex disseminated auriferous deposit located in the Alentejo region, southern Portugal. The approach involves the following steps: (i) the creation of a 3D low‐resolution vector object model of two geological domains that better discriminate gold grades; (ii) the definition of three intervals for gold grades (low, intermediate, and high values); (iii) the estimation of the probability of each grid block belonging to each interval constrained by the geological domains; (iv) the calculation of local conditional cumulative distribution functions (CCDFs) of gold grades, for each block, taking into account the geological domains and the borehole data; and finally (v) the simulation of images of gold grades. The results demonstrate the usefulness and accuracy of the proposed procedure, as they are in compliance with the conceptual model, the distribution laws are conditioned by the geological domains, and the transition of grades between domains is continuous.     

X射线荧光光谱法检测Au质量分数不确定度的评定——以样品Au750为例

为了使测量结果更加科学,其不确定度的评定就越来越重要。在运用X射线荧光光谱法检测贵金属质量分数的过程中,测量系统以标准曲线法为基础,测量仪器直接给出测量结果,故可将该测量方法等同于直接测量。以样品Au750为例,探讨了测量不确定度的评定过程与步骤。结果显示,该方法测量结果的不确定度来源主要与测量系统有关,其主要的不确定度分量有标准样品的给定值与误差、仪器的分辨率、准确度以及校准不确定度等,忽略了环境及操作不当的人为影响因素。该评定过程简化,评定方法趋干合理。     

钒酸铵容量法测定岩石矿物中铀的不确定度评定

根据核工业行业标准"硫酸亚铁还原/钒酸铵氧化滴定法测铀"(EJ267.2-84)进行不确定度评定。通过不确定度来源识别,不确定度分量的量化,并以标定好的钒酸铵溶液滴定铀质量分数,得出方法本身带来数据的不确定度。对整个过程的不确定度来源和大小进行分析研究,应用统计学基础对数据进行科学处理。报告出了不同铀质量分数的合成标准不确定度和扩展不确定度。     

硅钼蓝分光光度法测定钛铁矿中二氧化硅不确定度评定

对硅钼蓝分光光度法测定钛铁矿中SiO2含量的不确定度进行评估,建立了数学模型,认为测量过程中不确定度主要来源于标准物质、样品制备、曲线拟合,以及重复实验产生的不确定度.当SiO2平均含量为0.67%时,评定其扩展不确定度为0.05%(k=2).     

大气颗粒物样品波长色散X射线荧光光谱法无机元素测量结果不确定度评估

分析了用X射线荧光光谱法（XRF）测定大气颗粒物样品（TSP）中Al、Na、Cl、Mg、Cu、zn、Ca、S、Fe、Mn、K、Pb、Cd、Ba等无机元素结果的不确定度来源，对石英滤膜颗粒物样品无机元素含量测量不确定度进行了评估。计算结果表明，XRF测定中无机元素薄膜标样示值误差和工作曲线拟合误差是测量结果不确定度的主要来源。对计算测量不确定度的公式合成法和蒙特卡洛（Monte Carlo）模拟法的结果进行了比较，两种计算方法所得的结果一致。     

基于Monte Carlo模拟的三维剖面地质界线不确定性分析

三维剖面地质界线是构建三维地质结构模型的重要基础数据,其不确定性会影响三维模型的几何形态和属性分布。以单一分布为假设前提的统计学不确定性分析方法掩盖了其他概率分布特征对模型的影响。突破单一误差分布条件的假设前提,本文使用Monte Carlo方法模拟了不同概率分布情况下地质剖面数据中地质界线的抽样采集,以及地质界线空间分布的不确定性;依托地质界线空间位置与地质属性的耦合关系,提出了用地质属性概率分布实现地质界线空间不确定性的定量可视化,并结合实际地质剖面探讨了多种概率分布条件下地质界线的空间不确定性。实例研究表明,基于Monte Carlo模拟的不确定性分析方法可以突破单一误差分布假设条件,结合地质属性概率可充分揭示出建模数据的内在不确定性与模型外在要素形态之间的耦合关系。     

土壤中三氧化二铝测定结果的不确定度评定

讨论了影响三氧化二铝测定结果不确定度的各种因素,并评定了土壤样品中测定三氧化二铝结果的不确定度。采用EDTA络合、氟化钾置换、乙酸锌溶液滴定的测定方法,当三氧化二铝的含量为15.03%时,其扩展不确定度U=0.20%(Urel=1.4%,k=2)。     

FLAC3D在滑坡稳定性分析评价中的应用

本文以高治村滑坡为例,论述了FLAC3D在滑坡稳定性分析评价中的应用。作者首先介绍了FLAC3D的基本原理和主要流程,然后采用摩尔-库伦模型,对高治村滑坡在天然状态和暴雨状态下的变形和位移情况进行了数值模拟,模拟结果直观地显示了该坡体在上述两种状态下的塑性变形及水平方向位移的分布特征,清楚地显示了坡体内潜在的滑动面。文章根据数值模拟结果,对该滑坡的稳定性进行了分析和评价,对该滑坡的变形和破坏形式进行了研究和探讨。通过对该坡体的塑性变形与位移情况分析认为,该滑坡在天然状态下基本稳定;在连续高强度降雨状态下欠稳定,局部失稳滑塌的可能性很大,这与现场调查分析的结果一致。这个结果表明,利用FLAC3D进行滑坡稳定性分析和评价简单、可行,且更加直观、方便,具有传统极限平衡法所无法比拟的优势。     

火试金法测定铜精矿中金含量结果的不确定度评定

对火试金法测定铜精矿中金含量的结果进行不确定度评定。分析了铜精矿样品称量、铜精矿样品的不均匀性和配料处理,以及金粒称量等因素对金含量测量结果不确定度的影响,并得出火试金法测量铜精矿中金含量的扩展不确定度。     

多通道投影系统在三维城市地质成果演示中的应用

为了能将上海三维地质成果更好的展示,根据演示厅实际情况,上海地质调查研究院采用了三通道投影系统,在环屏幕上高分辨率地展示三维地质成果,实现了大场景的平面演示和虚拟三维投影之间的切换。     

气相色谱法测定地下水中六六六结果的不确定度评定

依照<测量不确定度评定与表示>,对气相色谱法测定地下水中六六六(HCH)四种单体结果进行了不确定度评定.分析了测量过程中引入的不确定度来源,包括提取液体积的量取、样品提取溶液的定容体积、分析仪器的进样量、标准系列溶液的测量以及仪器重复测定等分量引入不确定度及其各参数的采集和计算方法,最后合成标准不确定度,通过乘以95%概率下的扩展因子2,获得测量结果的扩展不确定度.     

半微量凯氏法测定土壤全氮量的不确定度评定

以半微量凯氏法测定土壤中全氮量为例，对测定结果的不确定度来源进行了详细分析，对测定过程中的主要不确定度分量进行了合理评定，包括样品和标准物质硼砂的称量引入的不确定度，硼砂的纯度引入的不确定度，容量瓶、移液管和滴定管的体积引入的不确定度．相关元素的摩尔质量引入的不确定度以及测量的重复性引入的不确定度。最后合成标准不确定度．通过乘以95％置信概率下的扩展因子2获得测量结果的扩展不确定度。     

硅钼黄分光光度法测定地下水中偏硅酸的不确定度评定

采用不确定度连续传递模型,对硅钼黄分光光度法测定地下水中偏硅酸(DZ/T0064.62—93)的不确定度进行评定。测量结果的不确定度主要来源于标准溶液引入的不确定度、曲线拟合产生的不确定度和测量过程引入的不确定度三部分,而二氧化硅和偏硅酸的摩尔质量不确定度较小,可以忽略不计。采用双误差回归的方式对标准曲线进行拟合,在对各个不确定度分量进行量化的基础上,通过合成得到测量结果的标准不确定度,再乘以95%置信概率下的扩展因子2,得到测量结果的扩展不确定度。     

Stochastic Modelling of the Impact of Flood Protection Measures Along the River Waal in the Netherlands

River flooding is a problem of international interest. In the past few years many countries suffered from severe floods. A large part of the Netherlands is below sea level and river levels. The Dutch flood defences along the river Rhine are designed for water levels with a probability of exceedance of 1/1250 per year. These water levels are computed with a hydrodynamic model using a deterministic bed level and a deterministic design discharge. Traditionally, the safety against flooding in the Netherlands is obtained by building and reinforcing dikes. Recently, a new policy was proposed to cope with increasing design discharges in the Rhine and Meuse rivers. This policy is known as the Room for the River (RfR) policy, in which a reduction of flood levels is achieved by measures creating space for the river, such as dike replacement, side channels and floodplain lowering. As compared with dike reinforcement, these measures may have a stronger impact on flow and sediment transport fields, probably leading to stronger morphological effects. As a result of the latter the flood conveyance capacity may decrease over time. An a priori judgement of safety against flooding on the basis of an increased conveyance capacity of the river can be quite misleading. Therefore, the determination of design water levels using a fixed-bed hydrodynamic model may not be justified and the use of a mobile-bed approach may be more appropriate. This problem is addressed in this paper, using a case study of the river Waal (one of the Rhine branches in the Netherlands). The morphological response of the river Waal to a flood protection measure (floodplain lowering in combination with summer levee removal) is analysed. The effect of this measure is subject to various sources of uncertainty. Monte Carlo simulations are applied to calculate the impact of uncertainties in the river discharge on the bed levels. The impact of the “uncertain” morphological response on design flood level predictions is analysed for three phenomena, viz. the impact of the spatial morphological variation over years, the impact of the seasonal morphological variation and the impact of the morphological variability around bifurcation points. The impact of seasonal morphological variations turns out to be negligible, but the other two phenomena appear to have each an appreciable impact (order of magnitude 0.05–0.1 m) on the computed design water levels. We have to note however, that other sources of uncertainty (e.g. uncertainty in hydraulic roughness predictor), which may be of influence, are not taken into consideration. In fact, the present investigation is limited to the sensitivity of the design water levels to uncertainties in the predicted bed level.     

电感耦合等离子体质谱法测定地下水中镉的不确定度评定

采用不确定度连续传递模型,对电感耦合等离子体质谱法测定地下水中镉元素的不确定度进行评定。其不确定度主要来源于标准溶液引入的不确定度、曲线拟合产生的不确定度和测量过程中引入的不确定度三部分。采用双误差回归的方式对标准曲线进行拟合,通过计算出各分量的不确定度,合成得到测量结果的总不确定度。     

酸碱滴定法测定天然石膏中碳酸盐的不确定度评定

对酸碱滴定法测定天然石膏中碳酸盐的结果进行不确定度评定。测量过程中的不确定度主要来源于样品制备过程引入的不确定度、滴定导致的不确定度、标定NaOH标准滴定溶液和HCl标准溶液引起的不确定度及重复性实验引起的不确定度等。合成各不确定度分量,并乘以扩展因子2得到扩展不确定度。对于CO₂平均含量为8.66%（质量分数）的天然石膏样品,其扩展不确定度为0.17%。     

榴辉岩中金红石物相二氧化钛含量测定的不确定度评定

通过对榴辉岩中金红石物相二氧化钛含量重复测定，建立数学模型，分析了测量过程的不确定度主要来源于样品制备的不确定度、标准物质引入的不确定度、曲线拟合中产生的不确定度．以及重复试验的不确定度。当二氧化钛平均含量为3．75％时，评定其扩展不确定度为0.16％。