Uncertainty associated with

The timely acquisition of static and dynamic reservoir data is critical for the optimisation of development options and production operations. Reservoir data enables the description and quantification of fluid and rock properties. The amount and accuracy of the data available will determine the range of uncertainty associated with estimates made by the subsurface engineer. 

Each of the input parameters has an uncertainty associated with it. This uncertainty arises from the inaccuracy in the measured data, plus the uncertainty as to what the values are for the parts of the field for which there are no measurements. Take for example a field with five appraisal wells, with the following values of average porosity for a particular sand ... 

When providing input for the STOMP calculation a range of values of porosity (and all of the other input parameters) should be provided, based on the measured data and estimates of how the parameters may vary away from the control points. The uncertainty associated with each parameter may be expressed in terms of a probability density function, and these may be combined to create a probability density function for STOMP. 

PSCs are agreed with a schedule for exploration, appraisal and development, and production periods. During these times the terms of the PSC are usually fixed, thus reducing some of the uncertainties associated with tax and royalty systems where the royalty and tax rates may vary over the field lifetime. 

Starting with the quantum-mechanical postulate regarding a one-to-one correspondence between system properties and Hemiitian operators, and the mathematical result that only operators which conmuite have a connnon set of eigenfiinctions, a rather remarkable property of nature can be demonstrated. Suppose that one desires to detennine the values of the two quantities A and B, and that tire corresponding quantum-mechanical operators do not commute. In addition, the properties are to be measured simultaneously so that both reflect the same quantum-mechanical state of the system. If the wavefiinction is neither an eigenfiinction of dnor W, then there is necessarily some uncertainty associated with the measurement. To see this, simply expand the wavefiinction i in temis of the eigenfiinctions of the relevant operators... 

Athermal mixing is expected in the case of 61 - 62. Since polymers generally decompose before evaporating, the definition 6 = (AUy/V°) is not useful for polymers. There are noncalorimetric methods for identifying athermal solutions, however, so the 6 value of a polymer is equated to that of the solvent for such a system to estimate the CED for the polymer. The fact that a range of 6 values is shown for the polymers in Table 8.2 indicates the margin of uncertainty associated with this approach. 

Risk and uncertainty associated with each venture should translate, ia theory, iato a minimum acceptable net return rate for that venture. Whereas this translation is often accompHshed implicitly by an experienced manager, any formal procedure suffers from the lack of an equation relating the NRR to risk, as well as the lack of suitable risk data. A weaker alternative is the selection of a minimum acceptable net return rate averaged for a class of proposed ventures. The needed database, from a collection of previous process ventures, consists of NPV, iavestment, venture life, inflation, process novelty, decision (acceptance or rejection), and result data. 

Rules may represent either guidelines based on experience, or compact descriptions of events, processes, and behaviors with the details and assumptions omitted. In either case, there is a degree of uncertainty associated with the appHcation of the rule to a given situation. Rule-based systems allow for expHcit ways of representing and dealing with uncertainty. This includes the representation of the uncertainty of individual rules, as weU as the computation of the uncertainty of a final conclusion based on the uncertainty of individual rules, and uncertainty in the data. There are numerous approaches to uncertainty within the rule-based paradigm (2,35,36). One of these approaches is based on what are called certainty factors. In this approach, a certainty factor (CF) can be associated with variable—value pairs, and with individual rules. The certainty of conclusions is then computed based on the CF of the preconditions and the CF for the rule. For example, consider the foUowing example. 

The accuracy of absolute risk results depends on (1) whether all the significant contributors to risk have been analyzed, (2) the realism of the mathematical models used to predict failure characteristics and accident phenomena, and (3) the statistical uncertainty associated with the various input data. The achievable accuracy of absolute risk results is very dependent on the type of hazard being analyzed. In studies where the dominant risk contributors can be calibrated with ample historical data (e.g., the risk of an engine failure causing an airplane crash), the uncertainty can be reduced to a few percent. However, many authors of published studies and other expert practitioners have recognized that uncertainties can be greater than 1 to 2 orders of magnitude in studies whose major contributors are rare, catastrophic events. 

When managers are faced with the necessity of using QRA results on an absolute basis, they must respect the potentially large uncertainties associated with the numbers and use prudent and conservative interpretations of these results for their decisions. Absolute risk estimates in... 

Nuclear PSAs contain considerable uncertainty associated with the physical and chemical processes involved in core degradation, movement of the molten core in the reactor vessel, on the containment floor, and the response of the containment to the stresses placed upon it. The current models of these processes need refinement and validation. Because the geometry is greatly changed by small perturbations after degradation has commenced, it is not clear that the phenomcn.i can be treated. 

However, the data that are contributed to a generic failure rate data base are rarely for identical equipment and may represent many different circumstances. Generic data must be chosen carefully because aggregating generic and plant-specific data may not improve the statistical uncertainty associated with the final data point, owing to change in tolerance. 

A more interesting possibility, one that has attracted much attention, is that the activation parameters may be temperature dependent. In Chapter 5 we saw that theoiy predicts that the preexponential factor contains the quantity T", where n = 5 according to collision theory, and n = 1 according to the transition state theory. In view of the uncertainty associated with estimation of the preexponential factor, it is not possible to distinguish between these theories on the basis of the observed temperature dependence, yet we have the possibility of a source of curvature. Nevertheless, the exponential term in the Arrhenius equation dominates the temperature behavior. From Eq. (6-4), we may examine this in terms either of or A//. By analogy with equilibrium thermodynamics, we write... 

The nonspecialist reading Table 7-7 will probably be impressed by the substantial consistency among cti values evaluated by different methods, but the specialist tends to concentrate on the differences. There is one very interesting difference in Table 7-7, that for cti of alkyl groups based on Eq. (7-33) compared with cti based on the ionization of 3, the latter values showing practically no effect of inductive electron release and certainly no trend with increased branching. (The uncertainties associated with these substituent constants can be found in the original literature.) Swain... 

A UF of 10 is used when a LOAEL is used instead of a NOAEL. This factor is intended to account for the uncertainty associated with e.xtrapolating from LOAELs to NOAELs. 

Uncertainty on tlie other hand, represents lack of knowledge about factors such as adverse effects or contaminant levels which may be reduced with additional study. Generally, risk assessments carry several categories of uncertainly, and each merits consideration. Measurement micertainty refers to tlie usual eiTor tliat accompanies scientific measurements—standard statistical teclmiques can often be used to express measurement micertainty. A substantial aniomit of uncertainty is often inlierent in enviromiiental sampling, and assessments should address tliese micertainties. There are likewise uncertainties associated with tlie use of scientific models, e.g., dose-response models, and models of environmental fate and transport. Evaluation of model uncertainty would consider tlie scientific basis for the model and available empirical validation. 

Thus, tlie focus of tliis subsection is on qualitative/semiquantitative approaches tliat can yield useful information to decision-makers for a limited resource investment. There are several categories of uncertainties associated with site risk assessments. One is tlie initial selection of substances used to characterize exposures and risk on tlie basis of the sampling data and available toxicity information. Oilier sources of uncertainty are inlierent in tlie toxicity values for each substance used to characterize risk. Additional micertainties are inlierent in tlie exposure assessment for individual substances and individual exposures. These uncertainties are usually driven by uncertainty in tlie chemical monitoring data and tlie models used to estimate exposure concentrations in tlie absence of monitoring data, but can also be driven by population intake parameters. As described earlier, additional micertainties are incorporated in tlie risk assessment when exposures to several substances across multiple patliways are suimned. 

Quantitative risk analyses usually produces single-number estimates. Altliough tliere are sufficient uncertainties associated with tliese quantitative nmnerical values (see next Section) tliey seix e a valuable function. Tliese may be used to compare one risk witli anotlier in a quantitative sense or occasionally employed in an absolute sense. 

Our concepts of petroleum reserves and resources and their measurements are changing to reflect the uncertainty associated with these terms. Petroleum reseiwes have been largely calculated deterministically (i.e. single point estimates with the assumption of certainty). In the past decade, reseiwe and resource calculations have incorporated uncertainty into their estimates using probabilistic methodologies. One of the questions now being addressed are such as how certain arc you that the rcsciwcs you estimate arc the actual reseiwes and what is the range of uncertainty associated with that estimate New techniques arc required to address the critical question of how much petroleum we have and under what conditions it can be developed. 

Anyone making a measurement has a responsibility to indicate the uncertainty associated with it. Such information is vital to someone who wants to repeat the experiment or judge its precision. The three volume measurements referred to earlier could be reported as... 

Strategy Assume each student reported the mass in such a way as to indicate the uncertainty associated with the measurement Then follow a common sense approach. 

Each measuring device has limitations that fix its accuracy. Hence every individual observation has some uncertainty associated with it. Since every regularity of nature is discovered through observations, every regularity (law, rule, theory) has uncertainty attached to it. 

The high standard deviations are attributable to the uncertainties associated with powdered samples and with residues formed by evaporating solutions. 

The values of sA and. ru are not well defined by kinetic data.59 61 The wide variation in. vA and for MMA-S copolymerization shown in Table 7.5 reflects the large uncertainties associated with these values, rather than differences in the rate data for the various experiments. Partly in response to this, various simplifications to the implicit penultimate model have been used (e.g. rA3rBA= W- and -Va=- h)- These problems also prevent trends in the values with monomer structure from being established. 

The ITS-90 scale is designed to give temperatures T90 that do not differ from the Kelvin Thermodynamic Scale by more than the uncertainties associated with the measurement of the fixed points on the date of adoption of ITS-90 (January 1, 1990), to extend the low-temperature range previously covered by EPT-76, and to replace the high-temperature thermocouple measurements of IPTS-68 with platinum resistance thermometry. The result is a scale that has better agreement with thermodynamic temperatures, and much better continuity, reproducibility, and accuracy than all previous international scales. 

The uncertainties associated with the data base of an individual river basin are compounded when the intent is to provide a global perspective. This point is made in a recent bound volume of UNEP data in which a number of data interpretation limitations are sited. Quality of data varies from one individual reporting entity to another and the precision of the data is usually not possible to ascertain. Thus direct comparisons between data from one country, or even one laboratory to the next are not always possible. Since uncertainties associated with the data (variability, accuracy, precision, etc.) are often not specified, the significance of the data may be difficult to determine and no valid interpretation of the data may therefore be possible. It comes as no surprise that these and similar data from other data bases are often, if not usually, inadequate to establish cause and effect relationships. 

As with water solubility data, there is eonsiderable uncertainty associated with some of the log Wqw values reported in the lUCLID data sets, with impurities in the substances possibly contributing to increased water solubility and, hence, a lower than expeeted partition coefficient. 

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