Direct forecasting of reservoir performance using production data without history matching

The conventional paradigm for predicting future reservoir performance from existing production data involves the construction of reservoir models that match the historical data through iterative history matching. This is generally an expensive and difficult task and often results in models that do not accurately assess the uncertainty of the forecast. We propose an alternative re-formulation of the problem, in which the role of the reservoir model is reconsidered. Instead of using the model to match the historical production, and then forecasting, the model is used in combination with Monte Carlo sampling to establish a statistical relationship between the historical and forecast variables. The estimated relationship is then used in conjunction with the actual production data to produce a statistical forecast. This allows quantifying posterior uncertainty on the forecast variable without explicit inversion or history matching. The main rationale behind this is that the reservoir model is highly complex and even so, still remains a simplified representation of the actual subsurface. As statistical relationships can generally only be constructed in low dimensions, compression and dimension reduction of the reservoir models themselves would result in further oversimplification. Conversely, production data and forecast variables are time series data, which are simpler and much more applicable for dimension reduction techniques. We present a dimension reduction approach based on functional data analysis (FDA), and mixed principal component analysis (mixed PCA), followed by canonical correlation analysis (CCA) to maximize the linear correlation between the forecast and production variables. Using these transformed variables, it is then possible to apply linear Gaussian regression and estimate the statistical relationship between the forecast and historical variables. This relationship is used in combination with the actual observed historical data to estimate the posterior distribution of the forecast variable. Sampling from this posterior and reconstructing the corresponding forecast time series, allows assessing uncertainty on the forecast. This workflow will be demonstrated on a case based on a Libyan reservoir and compared with traditional history matching.     

Optimistic bias and the consistency of hurricane track forecasts

Forecast graphics depicting a hurricane track and uncertainty cone have become pervasive in the communication of hurricane risk. This study examined whether the effect of hurricane tracks on risk perception is influenced by the consistency and optimistic bias. Specifically, it focused on the differences between forecasts that remain consistent compared to those that veer away for a forecast period. To answer the research question, this study conducted online surveys in which respondents from two coastal universities were asked risk perception questions based on a series of forecast graphics. Other variables measured included dispositional optimism, general hurricane risk perception, and hurricane information use. Optimistic bias was calculated from two of the risk perception questions. Results did not indicate strong support for an influence of optimistic bias or changing forecast track on risk perception. There was limited evidence that a veering track scenario may lead to differences in risk judgments about another location, but most measures of personal risk estimation were not influenced by the track. Dispositional optimism was not related to optimistic bias or many of the risk perception variables tested, including general hurricane risk perception. There did appear to be an interaction between track scenario and optimistic bias with more relationships being significant among those who received the consistent track scenario.     

Probabilistic comparative analysis between design rules of a shallow foundation safety

ABSTRACT

A fact that is generally overlooked in many geotechnical uncertainty analyses is that input data of the model may be correlated. While this correlation may influence the system response, epistemic uncertainties i.e. lack of knowledge of this correlation appears as a risk factor. This paper discusses how a negative correlation between cohesion (c’) and friction angle (Ø’) with their associated uncertainties can influence both the bearing resistance of a shallow strip foundation footing and the estimation of its safety. A probabilistic approach that considers both the negative correlation and the uncertainty is used in this work as a reference. This method is compared to Eurocode 7 variants that do not for the correlation. These variants, resistance and material factoring methods appears to be more or less conservative depending on the negative correlation degree between (c’–Ø), their associated uncertainties and soil configurations. Finally, the proposed probabilistic comparison shows that the material factoring method is more conservative than the resistance one.     

贝叶斯概率水文预报系统在中长期径流预报中的应用

采用贝叶斯概率水文预报理论制订水电站水库中长期径流预报模型,以概率分布的形式定量地描述水文预报的不确定度,探索概率水文预报理论及其应用价值。采用气象因子灰关联预报模型处理输入因子的不确定度,将实时气象信息和历史水文资料有效结合,突破传统确定性预报方法在信息利用和样本学习方面的局限性,以提高水文预报的精确度。以丰满水电厂水库为例对所建模型进行检验,模拟计算结果表明,该模型与确定性径流预报方法相比,不仅有利于决策人员定量考虑不确定性,而且在期望意义上提高了径流预报精度,具有较高的应用价值。     

Choosing a rockfall barrier with the Precautionary Principle: a quantitative approach

The paper illustrates an approach for implementing the Precautionary Principle in risk management, exemplified by a procedure aimed at choosing the height of a rockfall barrier protecting a railway stretch. Risk is expressed by the frequency f of blocks hitting the railway—i.e. by the ratio between the number of blocks reaching the railway and the number of blocks falling from the slope—assessed through software simulation of the falling of the blocks. The height from which a block may fall is considered to be the main uncertainty factor in risk estimation, which translates into uncertainty as to the level of risk, as every simulation shows that more than one impact frequency is possible. Such uncertainty justifies the precautionary approach to the design of the barrier, and is represented mathematically by means of possibility and probability distribution functions. The distributions make it possible to express the degree of precaution related to a barrier as the level of confidence, in terms of necessity or probability measures—that can be placed on the fact that, because of the barrier, the impact frequency, although uncertain, will not exceed what is acceptable. It will be shown that the degree of precaution takes quite different values if possibility theory is used instead of probability theory. Finally some simple cost/benefit analyses, that explicitly and quantitatively consider the degree of precaution, are exemplified.     

Model for Estimation of Time and Cost for Tunnel Projects Based on Risk Evaluation

Summary. In the planning and procurement phases of tunnelling projects, numerous decisions have to be made regarding tender price and budget. Many case studies have shown that, in practice, the predicted costs and time schedules are often exceeded. This paper describes a study of the various risk factors in machine tunnelling and their differing impacts on cost and time. It has been concluded from the study that it is important to make a clear distinction between normal cost and time, and the undesirable events that cause exceptional cost and time. Existing decision-aid estimation models consider variation of the risk factors, but do not consider normal cost or time separately from undesirable events. Usually, estimations of project cost and time are made in a deterministic manner, but this does not allow one to consider uncertainty in cost and time variables. However, if the variables are treated probabilistically, the total cost of tunnelling can be expressed as a distribution curve, and a decision can be made on the tunnelling method by comparing the respective cost and time distributions. Based on such decisions, the budget and tender price can be determined separately, both by the client and contractor respectively. To meet the demands placed on decision-making for tender and procurement for currently favoured construction-contracting methods, a new model for estimating tender price and budget has been developed, and is described in this paper. This estimating technique has been applied to a case study of the Grauholz Tunnel. The predictions obtained from the estimation model are shown to be realistic, as the total construction cost and time obtained from the model correspond fairly well to the actual construction cost and time. The separate estimation of normal cost and time and exceptional cost and time contribute to the clarity of the results. The use of the proposed model also shows that the tunnelling method most suitable for the actual geological and hydrogeological conditions can be selected by this method.     

Methods for probabilistic assessments of geologic hazards

Although risk analysis today is considered to include three separate aspects (1) identifing sources of risk, (2) estimating probabilities quantitatively, and (3) evaluating consequences of risk, here only estimation of probabilities for natural geologic events, processes, and phenomena is addressed. Ideally, evaluation of potential future hazards includes an objective determination of probabilities that have been derived from past occurrences of identical events or components contributing to complex processes or phenomena. In practice, however, data which would permit objective estimation of those probabilities of interest may not be adequate, or may not even exist.Another problem that arises normally, regardless of the extent of data, is that risk assessments involve estimating extreme values. Probabilities are required for events that are the greatest or rarest because they commonly will have the greatest consequences; the largest, or rarest, events always fall in tails of frequency distributions. Rarely are extreme values accurately predictable even when an empirical frequency distribution is established well by data.In the absence of objective methods for estimating probabilities of natural events or processes, subjective probabilities for the hazard must be established through Bayesian methods, expert opinion, or Delphi methods. Alternative solutions may involve consequence analysis which may demonstrate that, although an event may occur, its consequences are sufficiently small that it safely may be ignored or by establishing bounds which may demonstrate that although probabilities are not known they cannot exceed a maximum value that is sufficiently small so that associated risk may be considered to be negligible.Uncertainty of every probability determination must be stated for each component of an event, process, or phenomenon. These uncertainties also must be propagated through the quantitative analysis so that a realistic estimate of total uncertainty can be associated with each final probability estimate for a geologic hazard.This paper was presented (by title) at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.     

Quantifying impacts of forecast uncertainties on predicted storm surges

In this paper, we propose a framework for quantifying risks, including (1) the effects of forecast errors, (2) the ability to resolve critical grid features that are important to accurate site-specific forecasts, and (3) a framework that can move us toward performance-based/cost-based decisions, within an extremely fast execution time. A key element presently lacking in previous studies is the interrelationship between the effects of combined random errors and bias in numerical weather prediction (NWP) models and bias and random errors in surge models. This approach examines the number of degrees of freedom in present forecasts and develops an equation for the quantification of these types of errors within a unified system, given the number of degrees of freedom in the NWP forecasts. It is shown that the methodology can be used to provide information on the forecasts and along with the combined uncertainty due to all of the individual contributions. A potential important benefit from studies using this approach would be the ability to estimate financial and other trade-offs between higher-cost “rapid” evacuation methods and lower-cost “slower” evacuation methods. Analyses here show that uncertainty inherent in these decisions depends strongly on forecast time and geographic location. Methods based on sets of surge maxima do not capture this uncertainty and would be difficult to use for this purpose. In particular, it is shown that surge model bias can play a dominant role in distorting the forecast probabilities.     

Risk analysis for flood-control structure under consideration of uncertainties in design flood

This study presents a risk analysis model to evaluate the failure risk for the flood-control structures in the Keelung River due to the uncertainties in the hydrological and hydraulic analysis, including hydrologic, hydraulic, and geomorphologic uncertainty factors. This study defines failure risk as the overtopping probability of the maximum water level exceeding the levee crown, and the proposed risk analysis model integrates with the advanced first-order and second-moment (AFOSM) method to calculate the overtopping probability of levee system. The proposed model is used to evaluate the effects of the freeboard and flood-diversion channel on the flood-control ability of the levees in the Keelung River, which were designed based on the 3-day, 200-year design rainfall event. The numerical experiments indicate that the hydrologic uncertainty factors have more effect on the estimated maximum water level than hydraulic and geomorphologic uncertainty factors. In addition, the freeboard and the flood-diversion channel can effectively reduce the overtopping probability so as to significantly enhance the flood-control capacity of the levee system in the Keelung River. Eventually, the proposed risk analysis successfully quantifies the overtopping risk of the levee system under a scenario, the increase in the average 200-year rainfall amount due to climate change, and the results could be useful when planning to upgrade the existing levee system.     

基于不确定性分析框架的动态环状河网水质模型——以温州市温瑞塘河为例

以温州市温瑞塘河为背景,基于不确定性分析的框架,开发了动态环状河网水质模型。用HSY(Hornberger,Spear and Young)算法作水质参数的不确定性分析,求得模型参数的空间分布,从而提高模型使用的可靠性、降低决策的风险度。模型由水量子模型及水质子模型两部分组成:水量子模型采用圣维南方程并用四级解法求解;水质子模型采用CSTR(Continuously Stirred Tank Reactor)模型的机理,并结合环状河网特征作了修正,由于只需解常微分方程,因而避免了矩阵求解,显著提高了计算效率,使得用HSY算法进行不确定性分析成为可能。模型选取温州市温瑞塘河流域的鹿城区河网进行了首次应用,用HSY算法率定水质参数并讨论了参数的不确定性。对参数率定结果进行验证,结果比较理想。最后简要讨论了参数不确定性传递。     

Application and Verification of Joint Probability Method in Potential Forecast for Severe Convective Weather in Anhui Province

In consideration of large uncertainties in severe convective weather forecast, ensemble forecasting is a dynamic method developed to quantitatively estimate forecast uncertainty. Based on ensemble output, joint probability is a post-processing method to delineate key areas where weather event may actually occur by taking account of the uncertainty of several important physical parameters. An investigation of the environments of little rainfall convection and strong rainfall convection from April to September (warm season) during 2009-2015 was presented using daily disastrous weather data, precipitation data of 80 stations in Anhui province and NCEP Final Analysis (FNL) data. Through ingredients-based forecasting methodology and statistical analysis,four convective parameters characterizing two types of convection were obtained, respectively, which were used to establish joint probability forecasting together with their corresponding thresholds. Using the ECMWF ensemble forecast and observations from April to September during 2016-2017, systematic verification mainly based on ROC and case study of different weather processes were conducted. The results demonstrate that joint probability method is capable of discriminating little rainfall convection and non-convection with comparable performance for different lead times, which is more favorable to identifying the occurrence of strong rainfall convection. The joint probability of little rainfall convection is a good indication for the occurrence of regional or local convection, but may produce some false alarms. The joint probability of strong rainfall convection is good at indicating regional concentrated short-term heavy precipitation as well as local heavy rainfall. There are also individual missing reports in this method, and in practice, 10% can be roughly used as joint probability threshold to achieve relative high TS score. Overall, ensemble-based joint probability method can provide practical short-term probabilistic guidance for severe convective weather.     

Bi-level optimization for risk-based regional hurricane evacuation planning

Almost all engineering evacuation models define the objective as minimizing the time required to clear the region or total travel time, thus making an implicit assumption that who will or should evacuate is known. Conservatively evacuating everyone who may be affected may be the best strategy for a given storm, but there is a growing recognition that in some places that strategy is no longer viable and in any case, may not be the best alternative by itself. Here, we introduce a new bi-level optimization that reframes the decision more broadly. The upper level develops an evacuation plan that describes, as a hurricane approaches, who should stay and who should leave and when, so as to minimize both risk and travel time. The lower level is a dynamic user equilibrium (DUE) traffic assignment model. The model includes four novel features: (1) it refocuses the decision on the objectives of minimizing both risk and travel time; (2) it allows direct comparison of more alternatives, including for the first time, sheltering-in-place; (3) it uses a hurricane-scenario-based analysis that explicitly represents the critically important uncertainty in hurricane track, intensity, and speed; and (4) it includes a new DUE algorithm that is efficient enough for full-scale hurricane evacuation applications. The model can be used both to provide an evacuation plan and to evaluate a plan’s performance in terms of risk and travel time, assuming the plan is implemented and a specified hurricane scenario then actually occurs. We demonstrate the model with a full-scale case study for Eastern North Carolina.     

耦合长期预报的跨流域引水受水水库调度模型

为提高跨流域引水工程受水水库引水有效性,研究了耦合长期径流预报信息的跨流域引水受水水库调度模型。首先选取汛期径流预报信息,采用径流预报概率修正先验概率来描述径流的不确定性,建立了贝叶斯随机动态规划模型(BSDP-LTF)。然后将模型应用于碧流河水库,并与仅考虑径流相关的随机动态规划模型(SDP-I)、仅考虑长期预报信息的随机动态规划模型(SDP-LTF)进行比较。比较结果得出在供水保证率基本一致且不增加调度风险的情况下,BSDP-LTF模型相比SDP-I、SDP-LTF模型,可分别减少引水8.2%、4.1%。表明贝叶斯随机动态规划模型BSDP-LTF有效改进了径流描述,提高了跨流域引水的有效性。     

Method of Data Reduction and Uncertainty Estimation for Platinum-Group Element Data Using Inductively Coupled Plasma-Mass Spectrometry

A data reduction method is described for determining platinum-group element (PGE) abundances by inductively coupled plasma-mass spectrometry (ICP-MS) using external calibration or the method of standard addition. Gravimetric measurement of volumes, the analysis of reference materials and the use of procedural blanks were all used to minimise systematic errors. Internal standards were used to correct for instrument drift. A linear least squares regression model was used to calculate concentrations from drift-corrected counts per second (cps). Furthermore, mathematical manipulations also contribute to the uncertainty estimates of a procedure. Typical uncertainty estimate calculations for ICP-MS data manipulations involve: (1) Carrying standard deviations from the raw cps through the data reduction or (2) calculating a standard deviation from multiple final concentration calculations. It is demonstrated that method 2 may underestimate the uncertainty estimate of the calculated data. Methods 1 and 2 do not typically include an uncertainty estimate component from a regression model. As such models contribute to the uncertainty estimates affecting the calculated data, an uncertainty estimate component from the regression must be included in any final error calculations. Confidence intervals are used to account for uncertainty estimates from the regression model. These confidence intervals are simpler to calculate than uncertainty estimates from method 1, for example. The data reduction and uncertainty estimation method described here addresses problems of reporting PGE data from an article in the literature and addresses both precision and accuracy. The method can be applied to any analytical technique where drift corrections or regression models are used.     

淮河息县站流量概率预报模型研究

应用美国天气局采用的由Roman Krzysztofowicz开发的贝叶斯统计理论建立概率水文预报理论框架，即以分布函数形式定量地描述水文预报不确定度，研究了淮河息县站流量概率预报模型。理论和经验表明，概率预报至少与确定性预报一样有价值，特别当预报不确定度较大时，概率预报比现行确定性预报具有更高的经济价值。     

Analysis of Time of Occurrence of Earthquakes: A Functional Data Approach

There is no single method available for estimating the seismic risk in a given area, and as a result most studies are based on some statistical model. If we denote by Z the random variable that measures the maximum magnitude of earthquakes per unit time, the seismic risk of a value m is the probability that this value will be exceeded in the next time units, that is, R(m)=P(Z>m). Several approximations can be made by adjusting different theoretical distributions to the function R, assuming different distributions for the magnitude of earthquakes. A related method used to treat this problem is to consider the difference between the times of occurrence of consecutive earthquakes, or inter-event times. The hazard function, or failure rate function, of this variable measures the instantaneous risk of occurrence of a new earthquake, supposing that the last earthquake happened at time 0. In this paper, we will consider the estimation of the variable that measures the inter-event time and apply nonparametric techniques; that is, we do not consider any theoretical distribution. Moreover, because the stochastic process associated with this variable can sometimes be non-stationary, we condition each time by the previous ones. We then work with a multidimensional estimation, and consider each multidimensional variable as a functional datum. Functional data analysis deals with data consisting of curves or multidimensional variables. Nonparametric estimation can be applied to functional data, to describe the behavior of seismic zones and their associated instantaneous risk. The applications of estimation techniques are shown by applying them to two different regions and data catalogues: California and southern Spain.     

岩土工程风险分析及应用综述

系统分析了岩土工程不确定性的根源及其分析方法,总结了降低不确定性的途径。系统评述了岩土参数随机场估计、随机变量描述方法以及模型不确定性研究。对几类典型岩土工程问题的风险分析方法、研究现状及其工程应用进行了总结。对目前岩土工程风险理论及其应用的前沿问题进行了研究和展望。研究指出岩土工程风险分析待研问题主要有：系统的风险源辨识方法包括风险源辨识的可视化研究,不确定性因子的合理描述研究,极限状态包括失效模式的仿真研究,不确定性计算包括应用信息融合技术数据挖掘技术研究,目标可靠度研究,风险转嫁风险交换的量化及风险跟踪的实施研究,风险的反分析研究等。展望岩土工程风险分析与应用：风险分析反映了对工程设计的综合性要求,表现了安全与经济的统一;定量风险分析作为决策工具或传统设计的补充,可给决策者提供更多的辅助评价信息,提高了结果的置信程度;但现在能描述的还只是“随机性的确定性模式”,工程师们只有使用“保守的”选择,以适应和弥补不完全的认识与有限的资料的条件。     

Forecasting flood disasters using an accelerated genetic algorithm: Examples of two case studies for China

This article discusses a rescaled range analysis model, titled AGA-R/S, that is based on an accelerated genetic algorithm. The parameter a, Hurst index of rescaled range analysis, and the recurrent time of disaster in the next time-period, were directly computed using an accelerated genetic algorithm developed by the authors. As case studies, using the AGA-R/S model, a forecast was made of the tendency for change in a time series of annual precipitation for the city of Jinhua, China. The model also forecast flooding-disaster in the city of Wuzhou, China. Results indicate that it is a relatively efficient technique to forecast the change-tendency of flood and disaster time series using the AGA-R/S model. When time series is utilized, forecasted error of the AGA-R/S model is less than with a linear least square method. The Hurst indexes of the two cities are from 0.23 to 0.24, which indicates that these time series are fractal and relatively long-term. Their fractional Brownian motion shows anti-persistence. AGA-R/S has application in forecasting the change-tendency of other natural disaster for specific time series.     

Seismic Hazard and Risk Assessment for Tulbagh,South Africa: Part I – Assessment of Seismic Hazard

In this part of our study the probabilistic seismic hazard analysis (PSHA) for Tulbagh was performed. The applied procedure is parametric and consists essentially of two steps. The first step is applicable to the area in the vicinity of Tulbagh and requires an estimation of the area-specific parameters, which, in this case, is the mean seismic activity rate, , the Gutenberg-Richter parameter, b, and the maximum regional magnitude, m_max. The second step is applicable to the Tulbagh site, and consists of parameters of distribution of amplitude of the selected ground motion parameter. The current application of the procedure provides an assessment of the PSHA in terms of peak ground acceleration (PGA) and spectral acceleration (SA). The procedure permits the combination of both historical and instrumental data. The historical part of the catalogue only contains the strongest events, whereas the complete part can be divided into several subcatalogues, each assumed complete above a specified threshold of magnitude. In the analysis, the uncertainty in the determination of the earthquake was taken into account by incorporation of the concept of `apparent magnitude'. The PSHA technique has been developed specifically for the estimation of seismic hazard at individual sites without the subjective judgement involved in the definition of seismic source zones, when the specific active faults have not been mapped or identified, and where the causes of seismicity are not well understood. The results of the hazard assessment are expressed as probabilities that specified values of PGA will be exceeded during the chosen time intervals, and similarly for the spectral accelerations. A worst case scenario sketches the possibility of a maximum PGA of 0.30g. The results of the hazard assessment can be used as input to a seismic risk assessment.     

Uncertainty Analysis for Assessing Leakage Through Water Tunnels: A Case from Nepal Himalaya

Water leakage problems in unlined or shotcrete lined water tunnels are not new issues. In many occasions severe water leakage problems have been faced that not only have reduced the stability of the rock mass, but also have caused valuable water to be lost from it, causing safety risk as well as huge economic loss to the projects. Hence, making tunnels water tight plays an important role in improving stability and safety of underground excavations. The real challenge is however accurate prediction and quantification of possible water leakage, so that cost consequences can be incorporated during planning of a water conveying tunnel project. The main purposes of this paper are to analyze extensive data on leakage test carried out through exploratory drillhole used to define the need for pre-injection grouting of Khimti headrace tunnel and to carry out probabilistic approach of uncertainty analysis based on relationship established between leakage, hydrostatic head and selected Q-value parameters. The authors believe that the new approach regarding uncertainty analysis of leakage presented in this paper will improve the understanding of leakage characteristics of the rock mass, and hope this will lead to a better understanding concerning quantification of possible water leakage from unlined and shotcrete lined water tunnels.