Uncertainty accumulation

Table IV-1 contains the selected thermodynamic data of the auxiliary species and Table IV-2 the selected thermodynamic data of chemical reactions involving auxiliary species. The reason for listing both reaction data and entropies, enthalpies and Gibbs energies of formation is, as described in Chapter 111, that uncertainties in reaction data are often smaller than the derived, Af//° and AfG°, due to uncertainty accumulation during the calculations.

To this point we have learned to count the significant figures in a given number. Next, we must consider how uncertainty accumulates as calculations are carried out. The detailed analysis of the accumulation of uncertainties depends on the type of calculation involved and can be complex. However, in this textbook we will employ the following simple rules that have been developed for determining the appropriate number of significant figures in the result of a calculation. 

Because doing chemistry requires many types of calculations, we must consider what happens when we do arithmetic with numbers that contain uncertainties. It is important that we know the degree of uncertainty in the final result. Although we will not discuss the process here, mathematicians have studied how uncertainty accumulates and have designed a set of rules... 

Results of an analysis conducted on a hyphenated instrument are typically calculated from two or more experimental data sets, each of which carries some uncertainty due to random noise or experimental errors. It is therefore worthwhile determining the ways various uncertainties accumulate in the final output from a hyphenated instrument. For simplicity, let us assume that two in-line instruments measure two quantities jc and y which depend upon variables p, q, r for x, and s, t, u fory. 

Introduction and Commercial Application JUe objective of performing appraisal activities on discovered accumulations is to reduce the uncertainty in the description of the hydrocarbon reservoir, and to provide information with which to make a decision on the next action. The next action may be, for example, to undertake more appraisal, to commence development, to stop activities, or to sell the prospect. In any case, the appraisal activity should lead to a decision which yields a greater value than the outcome of a decision made in the absence of the information from the appraisal. The improvement in the value of the action, given the appraisal information, should be greater than the cost of the appraisal activities, otherwise the appraisal effort is not worthwhile. 

In determining an estimate of reserves for an accumulation, all of the above parameters will be used. When constructing an expectation curve for STOIIP, GIIP, or ultimate recovery, a range of values for each input parameter should be used, as discussed in Section 6.2. In determining an appraisal plan, it is necessary to determine which of the parameters contributes most to the uncertainty in STOIIP, GIIP, or UR. 

Many studies have reported a link between consumption of sunburned potatoes, ie, those exposed to the sun and having an accumulation of chlorophyll and solanine under the skin, with incidences of teratogenic effects and even death (59—61). Because sunburned potatoes in the commercial marketplace are relatively rare, and because the long-term effects of consumption of potatoes at the maximum estabUshed limits of solanine concentration are uncertain, there is equal uncertainty of the tme incidence of human toxicity (62). 

In most other cases, data on gains in mass due to the accumulation of corrosion products have little quantitative significance since there is usually a question as to how much of the corroded metal is represented in the corrosion products that remain attached to the specimen at a particular time. There are also uncertainties as to the chemical composition of corrosion products, which may consist of mixtures of several compounds with varying amounts of combined or uncombined water, depending on the humidity of the atmosphere at the time. 

A form of this approach has long been followed by RT Corporation in the USA. In their certification of soils, sediments and waste materials they give a certified value, a normal confidence interval and a prediction interval . A rigorous statistical process is employed, based on that first described by Kadafar (1982,), to produce the two intervals the prediction interval (PI) and the confidence interval (Cl). The prediction interval is a wider range than the confidence interval. The analyst should expect results to fall 19 times out of 20 into the prediction interval. In real-world QC procedures, the PI value is of value where Shewhart (1931) charts are used and batch, daily, or weekly QC values are recorded see Section 4.1. Provided the recorded value falls inside the PI 95 % of the time, the method can be considered to be in control. So occasional abnormal results, where the accumulated uncertainty of the analytical procedure cause an outher value, need no longer cause concern. 

That is, there would be a 10% error, or uncertainty, in the answer. Note that even though terms in the denominator have a negative exponent, the maximum error due to these terms is still cumulative, because a given error may be either positive or negative i.e., errors may either accumulate (giving rise to the maximum possible error) or cancel out (we should be so lucky ). 

And finally, additional research is needed on mercury accumulation and detoxification in comparatively pristine ecosystems. Key uncertainties in understanding the process of mercury uptake in aquatic ecosystems, for example, include relations between water chemistry and respiratory uptake, quantitative estimates of intestinal tract methylation and depuration, and degree of seasonal variability in mercury speciation and methylation-demethylation processes (Post et al. 1996). 

---