Uncertainty Analysis In Geomodeling: How Much Should We
GUSS14 - 29Uncertainty Analysis in Geomodeling: How Much Should WeKnow About What We Don’t Know?Y. Zee Ma, Schlumberger, Denver CO, USAThis paper has been selected for presentation for the 2014 Gussow Geosciences Conference. The authors of this material have been cleared by all interestedcompanies/employers/clients to authorize the Canadian Society of Petroleum Geologists (CSPG), to make this material available to the attendees of Gussow 2014and online.depositional systems and natural fracturing of subsurfacesystems, and applications of probabilistic methods. It hasevolved from fragmentary pieces into a discipline ofgeoscience applications for the petroleum industry, fromuniversity research to value-added resource developments,from 2D mapping of structures and reservoir properties to 3Dgeocellular representations of hydrocarbon reservoirs, andfrom dealing with discipline-specific problems to integratedmultidisciplinary reservoir modeling.ABSTRACTAs the demand for hydrocarbon resources continues togrow, reservoir modeling and uncertainty analysis havebecome increasingly important for optimizing fielddevelopment. Optimal valuation and exploitation of a fieldrequires a realistic description of the reservoir, which in turnrequires reservoir characterization and modeling, andquantification of the uncertainty by integrating multidisciplinary data. An integrated approach for reservoirmodeling helps bridge the traditional disciplinary divides andtear down interdisciplinary barriers, leading to betterhandling of uncertainties, and improvement of reservoirmodeling for its use in the petroleum industry. Uncertaintyanalysis should be conducted for investigational analyses, andfor decision analysis under uncertainty and risk. Constructinga realistic reservoir model, and reducing and quantifying theuncertainty are the topics discussed in this article.The division of tasks between geologists and reservoirengineers in the early time was that geologists explored arbons from the reservoirs. This separation of thetasks was based on the low usage of fossil fuel relative to theamount of the resources in the ground and high reservoirquality of formations. As hydrocarbon consumption hasdramatically increased worldwide, reservoir management hasbecome more and more important. Integration of geologywith reservoir engineering has become critical for betterreservoir management (Haldorsen and Lake, 1984, Ma et al,2008), especially for unconventional reservoirs (Du et al.,2011; Cipolla et al., 2012).INTRODUCTIONReservoir characterization and modeling have seensignificant leaps in the last two to three decades, driven bythe development of computational horsepower, advances inseismic technology, logging tools, geological understanding ofGeology has traditionally been considered as descriptive,although some quantitative branches including geophysics,1
mathematical geology and geostatistics have significantlyincreased the breadth of geoscience. We believe that in thefuture, most geoscientists will conduct geologic or reservoirmodeling as routine work. By performing geologic modeling,geoscientists can test and quantify their geologic conceptsand hypotheses. In doing so, they use data to prove ordisprove the concepts, and use statistics and geostatistics toresolve inconsistencies in various data and integrate them ina coherent manner (Ma, 2010). As a result of theconvergence of descriptive geology and quantitative geology,geoscientists need to use the modeling as a process forunderstanding the reservoir, not just producing a numericmodel. The convergence should make reservoir modeling asynonym of reservoir characterization.RESERVOIR MODELINGReservoir management and field development planningare important for maximizing the economics of the field,which requires accurate reservoir characterization. Reservoirmodeling was the missing link between geosciences andreservoir engineering in field development before the mid1980s. Since then reservoir characterization has shownsignificant values in identifying both prolific and marginalreservoirs, extending the production life of existing fields andincreasing the hydrocarbon recovery of reservoirs. Successfulreservoir characterization projects typically show high degreeof integration. In fact, reservoir modeling is the best way tointegrate all the data and disciplines, and the only way inwhich all the data and interpretations come together into asingle 3D numeric representation of a reservoir. Inintegration, the data include not only quantitative data suchas well-logs, cores, and seismic data, but also the geologicconcepts and descriptive interpretations (Mallet, 2002; Ma,2009; Cao et al., 2014).Why build a reservoir model?“A good model can advance fashion by ten years.”Yves Saint-LaurenThe essence of reservoir modeling lies in using all theavailable data to build an accurate reservoir representationthat is fit-for-purpose to the field’s development needs. In asignificant hydrocarbon resource asset, a good reservoirmodel can be an essential element for increasing theproduction and extending the field development life foryears.The most common use of reservoir models is to provide a3D numeric input to reservoir simulation. Reservoir modelingand simulation provide a basis for maximizing economic valuefor field development and operational decisions. The typicalmotivation for reservoir simulation is to increase profitabilitythrough better reservoir management. These includedevelopment plans for new fields and depletion strategies formature fields. Reservoir modeling and simulation can addressliquid (oil, and water) and gas volume forecasting, declineanalysis, infill drilling uplift, secondary or tertiary recoveryoptions, well management strategies, water/gas handlingstrategies and facility constraints, contact movement, liquiddropout, reservoir surveillance strategies, injection strategies,and well and completion designs. Reservoir modeling andsimulation can also be used for reserve confirmation, equitydetermination, or support for funding large projects.Traditional mapping and cross-section methods workedrelatively well for homogeneous reservoirs, but they tend tooverestimate sweep efficiency for heterogeneous reservoirs.These methods may significantly under- or over-estimate inplace hydrocarbon resources because they lack 3Dexamination of reservoir heterogeneities. Reservoir modelingand simulation provide powerful tools for more accuratereservoir description and hydrocarbon production forecasting(Dubrule, 1989; Yu et al., 2011), and can help reservoirmanagement and field development. Accurate reserveassessment through reservoir modeling and simulation couldhelp reduce cost and increase recovery.A reservoir is the result of geologic processes and is notrandomly generated. However, the complexity of subsurfacereservoir properties coupled with limited data leads tosubstantial uncertainty in a reservoir model. Uncertaintiescan be mitigated by gaining more information and/or usingbetter science and technology. How much uncertainty shouldbe mitigated depends on the needs of decision analysis forreservoir management and the cost of information.Uncertainty analysis should be conducted for investigationalanalyses, and for decision analysis under uncertainty and risk.Knowing what needs to be known and what can be knownshould be the main focal points of uncertainty analysis inreservoir modeling.2
Besides reservoir simulation, reservoir modeling itselfcan be used as support for reservoir surveillance activities,such as monitoring fluid contacts and reservoir pressures,analyzing fault transmissibility and performing productionfault seal analysis. It can also be used for an accuratedetermination of stock-tank original oil in place (STOOIP), forexample, by incorporating capillary pressure effects, newopportunity identification and prioritization, well planningand well placement optimization, visualization andcommunication of the detailed 3-D reservoir architecture andproperties between various disciplines, reviewing data andtheir quality controls, resolving inconsistencies betweenvarious disciplines, support for time lapse seismic analyses,for example, by identifying bypassed oil, and reservoiruncertainty and risk analysis.Cases for building a reservoir modelReservoir modeling generally brings significant value thatis higher than its cost, and the majority of reservoir modelingprojects have been successful. For individual reservoirs, theasset team needs to assess the cost, benefits, and availabilityof skills to decide if a reservoir model should be built. Thefollowing criteria are important considerations in decidingwhether a model will be constructed. A reservoir simulation study is planned. The field is a major asset that warrants a significantreservoir management and depletion planning effort. Reservoir performance is not well understood due tocomplex geology, fluid, etc. Significant drilling or workover activity is planned. Reserves need a confirmation through accurate STOOIPdetermination and history-matched simulation to comparewith other studies, such as material balance, and declinecurve analysis. A secondary recovery plan may be warranted. Manage risk by evaluating multiple scenarios andrealizations based on sensitivity of important parameters. Guide the operations team in selecting well locations usinga living/evergreen model. Identify the need, type and value of additional data. Rapidly feed decision-making information. Understand the reservoir system before hydrocarbonproduction to improve the cost effectiveness of theproject. Reduce the chance for dry holes by feeding informationback to the operations team. Update the development plan and reserve.Reservoir modeling is critical to rapid successfulcommercialization of discovered and undevelopedhydrocarbon resources, as well as to optimizing depletion ofmature fields. As a rapidly growing discipline, reservoirmodeling has become an integral part of the field assetmanagement. For large and capital-intensive developmentprojects, reservoir modeling and simulation have almostbecome a necessity. Even for small to medium reservoirs,modeling and simulation can enhance efficient development,and depletion planning, and potentially increase reserves andyield cost saving. Modeling can also help in moving staticresources to reserves.In some cases using traditional 2D mapping methods,reserves have originally been grossly overestimated, leadingto false optimism. Expensive modern platforms may beinstalled, but later may be found under used because of theover-estimation of the resource. On the other hand, somelarge oil fields have been mistakenly farmed out because ofthe underestimation of the resource by traditional methods,leading to false pessimism. In many of these cases, reservoirmodeling could have helped make the decisions moreobjectively and realistically.How should the model be built?A reservoir is complex in its geometry as well as in thevariability of its rock properties. Yet improving hydrocarbonrecovery requires detailed and accurate descriptions ofreservoir properties. Integrated modeling attempts toimprove quantitative reservoir descriptions by incorporatinggeologic knowledge, well data and seismic data. Properintegration of diverse data can help build a more realisticgeologic model and reduce the uncertainty in describing thereservoir properties. Geologic modeling provides us with anReservoir modeling is a critical link between seismicinterpretation and reservoir simulation. Without reservoirmodeling, integrated approaches to E&P solution andaccurate reservoir evaluation are almost impossible. Buildinga reservoir model used to be very costly, but availability ofincreasingly versatile and sophisticated software packageshas made reservoir modeling much more efficient andaffordable.3
excellent platform for uncertainty analysis in reservoircharacterization.object-based modeling approaches provide tools forintegrating diverse data and analyzing uncertainty associatedwith the description of the reservoir. Integration is one of themost important characteristics of modeling, as shown inFigure 1.A model should be built according to business and/ortechnical needs, i.e., fit-for-purpose, optimally using theavailable data, and conveying the uncertainty of reservoirgeology and production. With the complexity of reservoirgeology and limited data, building a model that exactlyreplicates every detail of the subsurface is impossible.However, it is possible to build a model that fits technical andbusiness needs by optimally integrating all the available data.The objective of the model needs to be realistic based onneeds, available technology, data quantity and quality, andtimeline.Capabilities for building models in all stages of fielddevelopment are important considerations. As the objectiveschange through time and business stage, a reservoir modelmust address business or technical needs (volumetrics,reservoir compartments, and production driving mechanism,targeting wells, and aiding drilling decisions etc.), so it cannothave everything. Models are different for exploration,discovery, development, early production, and mature anddepletion stages. However, the model should be updateable,allowing for rapid updates as more data become available.Initial modeling should be simple so that it enables an earlyevaluation. As more data become available, modeling canincorporate more complexity.Figure 1 Illustration of integrated reservoir modelingUNCERTAINTY ANALYSIS“I’d rather be vaguely right than precisely wrong.”A reservoir model typically includesJohn M. Keynes Structural and stratigraphic models Lithofacies modelsReservoirs are not random; they were depositedgeologically and evolved into hydrocarbon-bearing entities.There is no uncertainty in a reservoir; there is onlyuncertainty in our understanding and description of itbecause of the subsurface complexity—and thus the difficultyin formulating a complete and precise description. Thesubsurface complexity and limited data make the reservoircharacterization and modeling complex and indeterministic,which explains the large uncertainty space in managing ahydrocarbon resource project (Massonnate, 1997). Petrophysical property models Dynamic simulation modelsThe structural model deals with how the major geologicalelements are in play for reservoir architecture, and how thesedifferent elements are related in space. Facies are the rockproperties that reflect the depositional characteristics, suchas facies relationships, stacking patterns, and stratalgeometry. Petrophysical properties are descriptions of finescale characteristics of the reservoir, typically includingporosity, fluid saturations, and permeability. Dynamicsimulation model generally represents a coarse grid thatcontains all the necessary reservoir properties that definereservoir volumetrics, and flow properties. Geostatistical andUncertainty is ubiquitous in reservoir characterization,and it exists in various disciplines, including 4Seismic processingInterpretations of faults and horizonsTime-to-depth conversionStructural modelling
drilling technology project sometimes becomes an economicfailure for these reasons.Petrophysical analysisGeological interpretationFluid contact determinationSpatial and frequency distributions of reservoirpropertiesFault transmisibilitiesPressure/volume/temperature and saturation modelProduction and drilling scenariosEconomic parametersQuantification of uncertainty should consider as many aspossible uncertainty factors to approach the total uncertaintyspace. Uncertainty of each factor also should be correctlyrepresented by a statistical distribution. Where uncertaintyincreases as more data are introduced, the original model didnot include all uncertainty factors in the first place andconsequently underrepresented the true uncertainty. Whendata that correlate with the target variable are introducedinto the modeling, the uncertainty space can be narrowed. Ifthe uncertainties in the input factors are reduced, theuncertainty space will be narrowed.It is a paradox that sometimes uncertainty appears toincrease as more data becomes available (Ma, 2011). In fact,in these cases the uncertainty space was not correctlydefined and the uncertainty model was overly simplified. Toreconcile them, further analysis is warranted, includingacquiring additional data and mitigation of sampling bias ifpresent (discussed later) to adequately define the correctspace of uncertainty.Data integration and uncertainty analysis“We don’t see things as they are, we see things as we are.”Anais NinWe don’t analyze uncertainty for the sake of uncertainty.Describing uncertainty generally is not the ultimate goal of aproject; reducing it and/or managing it is the goal. Thequestion is, “How much should we try to know about what wedon’t know?” Subsurface complexity, coupled with limiteddata, prevents us from completely describing every detail ofthe heterogeneities. Our main emphasis in reservoirmodeling should be to define relevant objectives that impactthe business decision, and to find realistic solutionsaccordingly.Three approaches can be used to reduce uncertainty:using additional direct information or hard data, e.g., welldata; capitalizing on relatable indirect information or softdata, such as seismic data and geological concepts; andemploying robust inference and prediction methods. Theseapproaches should be integrated coherently in applicationswhenever possible. We show the effectiveness of theseapproaches in this section using various geostatistical andother analytical methods for data integration and uncertaintyassessment.A pitfall is to reduce the model uncertainty at all costs. Insome cases reducing the model uncertainty actually increasesthe true uncertainty because the process increases theconceptual uncertainty without being noticed. For example,integrating more data should logically always decrease themodel uncertainty, but actual uncertainty might increase ifthe data are inaccurate.Because the purpose of uncertainty analysis is reducingand managing it, we must first fully exploit the available dataand build a baseline or technically most sound model. Inmany projects, multiple realizations of the reservoir modelare generated before the data are fully explored, which is nota good practice. Here we show an example of incorporatinggeological principles into the model, which requires anunderstanding and objective interpretation of the physicalsetup.Reservoir modeling provides an efficient platform forperforming uncertainty analysis related to field development.A double goal of uncertainty analysis is to quantify andreduce the uncertainty. This is critical because optimalreservoir management, including production forecasting andoptimal depletion, requires knowledge of the reservoircharacterization uncertainties for business decision analysis.Resource development projects frequently fail because of thefailure to study subsurface heterogeneity and of the lack ofuncertainty analysis for resource estimates and riskmitigation in the reservoir management process. A successfulOne of the best examples of the importance ofunderstanding the physical setup in applying probability isthe Monty Hall problem (Rosenhouse, 2009), of which manyresearchers get the answer wrong, not because they do notknow how to calculate the conditional probability, butbecause they mis-interpret the physical setup. The MontyHall problem shows the importance of discerning the non-5
randomness from a seemingly “random” event in a physicalprocess.In reservoir characterization and modeling, trueintegration is very important, just assembling a group with ageologist, a geophysicist, a petrophysicist, and a reservoirengineer doesn’t mean it will be an integrated team. In somecases, a team of heterogeneous skills is like the old tale aboutthe blind men and the elephant. One grabs his long trunk,one touches his large ears, and one pats his broad side; eachcomes away with a totally different conclusion. The geologistmay think it is all about reservoir geology; the geophysicistclaims it is all about rock physics; the reservoir engineerdeems that the bottom line is economics. They are all right,and they are all wrong, simply because they are all partial. Inthe end, the integrated project may become disintegrated.The best solution lies in optimally integrating everythingwhile resolving the inconsistencies between different dataand capitalizing on values from different disciplines.Figure 2 shows an example of comparing a facies modelthat is not constrained to the conceptual depositional modelinterpreted using geological knowledge and a facies modelthat has integrated the geological knowledge. The conceptualdepositional characteristics can be objectively interpretedand quantified through propensity analysis and incorporatedin the facies modeling by use of probability maps or cubes(Ma et al., 2009). Moreover, two different methods,sequential indicator simulation and truncated Gaussianmethod, were used to build these facies models, whichillustrates the inference uncertainty in modeling. Withoutunderstanding the physical setup, it is difficult to objectivelydevelop a conceptual depositional model, and accuratelyconstruct the reservoir model.Facies(c)(a)(b)(d)Figure 2 Facies modeling example. (a) Facies data at 8 wells. (b) Facies model built with Sequential Indicator Simulation(SIS). (c) Facies model built with SIS using geological prior knowledge or a conceptual depositional model. (d) Faciesmodel built with truncated Gaussian simulation using geological prior knowledge or a conceptual depositional model.6
Figure 3 shows an example of a reservoir modelconstructed using several different approaches. Althoughwell-log porosity data are honored as a result of usingGaussian Random Function Simulation, or GRFS (Gutjahr etal., 1997), conditional to the data in building the model, theyare not enough to constrain the porosity model to berealistic, partly because of the lateral trend or nonstationarityin the porosity data, as the different facies have differentporosity histograms (discussed later) and the depositionalfacies model shows distinct spatial transitions (Figure 2).This is also reflected by the lateral variogram (Figure 3b).The seismic attribute has a similar lateral trend, and it issignificantly correlated to the porosity, with a correlationcoefficient equal to 0.705 (Figure 3f). By using CollocatedCosimulation (CoCosim), the lateral trend is quite wellintegrated in the model (Figure 3g). CoCosim can deal withnonstationarity better than single variable simulation throughthe correlation between the primary and secondary variableswhen the trend is reflected in the secondary variable.(e)(a)(b)(f)(c)(g)(d)Figure 3 Illustration of uncertainty reduction through integration. (a) Porosity data from wireline logs at 8 wells. (b) Lateral variogramfor the well-log porosity that shows a nonstationary linear trend. (c) Vertical variogram. (d) Porosity model built using GaussianRandom Function Simulation (GRFS) with a spherical variogram. (e) Seismic attribute. (f) Crossplot between seismic attribute in (c) andwell log porosity in (a). (g) Porosity model built using Collocated Co-simulation (CoCosim) by integrating the well-log porosity in (a) andseismic attribute in (e). Both models in (d) and (g) were built with the variograms in (b) and (c).7
Spatial uncertainty, frequency uncertainty and their impacton volumetrics and field developmentmodels in Figures 4b and 4e have approximately a 20% bias;the hydrocarbon saturation can have a similar magnitude ofbias; so the in-place hydrocarbon volume can be biased morethan 40% as the fluid volume compounds the biases inporosity and fluid saturation.Statistics that have great impact on reservoir modelingand resource evaluation include frequency statistics andspatial statistics (Ma et al., 2008). Frequency statistics isespecially important for the overall heterogeneity and massbalance; spatial statistics is especially important in describingthe continuity, local heterogeneity, facies pattern, andconnectivity of the reservoir properties (Journel and Alabert,1990). These two schools should be coupled in reservoirmodeling and uncertainty analysis (Ma et al., 2011).Reproduction of the histogram in stochastic simulation issuch an issue that involves both frequency and spatialstatistics, and it has drawn significant attention (Soares,2001; Robertson et al., 2006). However, honoring thehistogram of the data is generally not a good idea when asampling bias exists (Ma, 2010).On the other hand, two reservoir properties, such asporosity and hydrocarbon saturation, are sometimes biasedin different directions, one over-estimation and oneunderestimation, with a similar magnitude. Then theestimated hydrocarbon volume may appear correct in thereservoir model. This is a composite error of false positiveand false negative (Ma, 2010), which will cause problems inreservoir dynamic simulation and production forecasting.Uncertainty quantification and reduction are highlyrelated. Optimally, quantifying uncertainty is a process ofreducing it, because the best use of all the availableinformation reduces the uncertainty compared to not fullyusing the data. Figure 5a shows an example of hydrocarbonpore volume (HCPV) uncertainty quantification based on themodel realizations, in which the P50 model honors thestatistics of the well-log porosity without mitigation of thesampling bias.Figure 4a shows a good histogram match between theporosity model in Figure 3g and the well-log porosity data.But the model is actually biased as a result of the samplingbias in the wells. The same can be said to the model in Figure3d. Specifically, more wells were drilled in the eastern part,wherein reef facies are dominant and porosity is generallyhigher. Propensity analysis and subsequent facies modelingcan mitigate sampling bias, such as the models in Figures 2cand 2d. Thus, use of such a facies model as a constraint to theporosity model enables the mitigation of sampling bias.Figure 5b shows an example of HCPV uncertaintyquantification based on the model realizations, in which theP50 model honors the statistics of the well-log porosity afterdiscounting the sampling bias and constraining the model tothe facies model. The sensitivity was mainly focused on theporosity, and thus the uncertainty range of the HCPVs is notlarge. However, comparing the two HCPV uncertaintyhistograms, P10 of the reservoir model without discountingthe sampling bias is greater than the P90 model with itsmitigation of the sampling bias.Figures 4b and 4c show two porosity model realizationsgenerated using GRFS–based collocated cosimulationconstrained to the facies model in Figure 2d and the seismicattribute (Figure 3e). Although the histogram of the modeldoes not match the well-log porosity histogram (Figure 4d),the histogram matches between the model and the data areactually good for each facies (Figures 4e, 4g, 4i). On the otherhand, although the global histogram match between themodel and the data is good for the model without mitigationof the sampling bias (Figure 3g), the histogram matches arenot good for each facies (Figures 4f, 4h, 4j).How the model is built impacts not only the globalvolumetrics but also the spatial distribution of pore andhydrocarbon volumetrics. This has implications for thepositioning of future wells and field development planningstrategies. Figure 6 compares the average spatialdistributions of the two HCPVs based on the two models usedfor HCPV computation in Figure 5. The field developmentplanning should be different for these two different HCPVspatial distributions.When a sampling bias is present and is not accountedfor, it produces an estimation bias in all the petrophysicalmodels, often in the same direction (over- orunderestimation), and can result in a systematic error in theestimated in-place hydrocarbon volumes. The porosity8
(a)(b)(e)(f)(g)(h)(i)(j)(c)Figure 4 Comparing reservoir models that handle spatial andfrequency uncertainties. (a) Histogram of the porositymodel in Figure 3g (Blue) compared to the well-log datahistogram (green). (b) Porosity model built using CoCosimconstrained to the facies model in Figure 3d and the seismicattribute in Figure 4e. (c) Same as (a) but with a differentrandom seed. (d) Histogram of the porosity model in Figure4b (blue) compared to the well-log data histogram (green).(e)-(j) Histogram comparisons by facies between theporosity model (blue) in (b), porosity model (blue) in Figure3g and the well-log data (green). (e) and (f) for reef, (g) and(h) for tidal flat, and (i) and (j) for lagoon.(d)9
(a)(a)(b)Figure 6 Average HCPV maps. (a) Based on the reservoirmodel without propensity analysis and no conditioning tothe seismic attribute (Figure 3e). (b) Based on the reservoirmodel with propensity analysis, mitigation of sampling bias,and conditioning to the seismic attribute.Known knowns, known unknowns and unknown unknownsIn uncertainty and risk evaluation, three categories ofvariables can be distinguished: known knowns, knownunknowns and unknown unknowns, to use the terminologyof Rumsfeld (Girard and Girard, 2009, p. 54). Here we will usethese terms loosely by extending the meanings for reservoirmodeling. Known knowns include core and wireline logmeasurements, histograms of reservoir properties from coreand wireline logs (e.g., green histogram in Figure 4a),empirical correlations between reservoir properties (e.g.,Figure 3f). Known unknowns, in its original meaning, implythe variables that we know that we don’t know, but we mayuse them loosely for the variables that we know a little, butnot fully; for example, the conceptual depositional modelthat is typically interpreted from limited data and generalgeo
convergence of descriptive geology and quantitative geology, geoscientists need to use the modeling as a process for understanding the reservoir, not just producing a numeric model. The convergence should make reservoir modeling a synonym of reservoir characterization. Reservoir management and field development planning
1.1 Measurement Uncertainty 2 1.2 Test Uncertainty Ratio (TUR) 3 1.3 Test Uncertainty 4 1.4 Objective of this research 5 CHAPTER 2: MEASUREMENT UNCERTAINTY 7 2.1 Uncertainty Contributors 9 2.2 Definitions 13 2.3 Task Specific Uncertainty 19 CHAPTER 3: TERMS AND DEFINITIONS 21 3.1 Definition of terms 22 CHAPTER 4: CURRENT US AND ISO STANDARDS 33
73.2 cm if you are using a ruler that measures mm? 0.00007 Step 1 : Find Absolute Uncertainty ½ * 1mm 0.5 mm absolute uncertainty Step 2 convert uncertainty to same units as measurement (cm): x 0.05 cm Step 3: Calculate Relative Uncertainty Absolute Uncertainty Measurement Relative Uncertainty 1
fractional uncertainty or, when appropriate, the percent uncertainty. Example 2. In the example above the fractional uncertainty is 12 0.036 3.6% 330 Vml Vml (0.13) Reducing random uncertainty by repeated observation By taking a large number of individual measurements, we can use statistics to reduce the random uncertainty of a quantity.
Uncertainty in volume: DVm 001. 3 or 001 668 100 0 1497006 0 1 3 3. %. % .% m m ª Uncertainty in density is the sum of the uncertainty percentage of mass and volume, but the volume is one-tenth that of the mass, so we just keep the resultant uncertainty at 1%. r 186 1.%kgm-3 (for a percentage of uncertainty) Where 1% of the density is .
economic policy uncertainty index, while the trade policy uncertainty index is used in Section 5. Concluding remarks follow. 2. Literature on policy uncertainty and trade There is a large body of theoretical and empirical work that studies the impact of uncertainty, and of policy
Measurement Uncertainty Approach 10 ISOGUM -ISO Guide to the Expression of Uncertainty Determine the uncertainty components based on the model: Isolate each component in the model that is anticipated to cause variation in the measured results. Calculate the sensitivity coefficients: Sensitivity coefficients are multipliers that are used to convert uncertainty
Dealing with Uncertainty: A Survey of Theories and Practices Yiping Li, Jianwen Chen, and Ling Feng,Member, IEEE Abstract—Uncertainty accompanies our life processes and covers almost all fields of scientific studies. Two general categories of uncertainty, namely, aleatory uncertainty and epistemic uncertainty, exist in the world.
Example risk assessment for food preparation, cooking and service This example risk assessment applies to restaurants, cafés, sandwich bars, pubs, takeaways or hotel kitchens.
