Product yields, uncertainty

Yang, Y.-J., W. R. Stockwell, and J. B. Milford, Effect of Chemical Product Yield Uncertainties on Reactivities of VOCs and Emissions from Reformulated Gasolines and Methanol Fuels, Environ. Sci. TechnoL, SO, 1392-1397 (1996). 

Ns new constraints to represent the Ns number of scenarios dealing with yield uncertainty are introduced for each product whose yield is uncertain, with the general form of the new constraints given by ... 

Table 6.2 Scenario formulation for uncertainty in prices, market demands, and product yields.

There was also great uncertainty of the production yields for SHEs. Closely related to the fission probability of SHEs in the ground-state, the survival of the compound nuclei formed after complete fusion was difficult to predict. Even the best choice of the reaction mechanism, fusion or transfer of nucleons, was critically debated. However, as soon as experiments could be performed without technical limitations, it turned out that the most successful methods for the laboratory synthesis of heavy elements are fusion-evaporation reactions using heavy-element targets, recoil-separation techniques, and the identification of the nuclei by generic ties to known daughter decays after implantation into position-sensitive detectors [13-15],... 

Further insight into the reaction mechanism can be obtained from consideration of the conversion dependence of product ratios. These can provide more reliable information than normal selectivity plots since, although these ratios are subject to the uncertainties in the individual product yields, their accuracy is not affected by the larger uncertainty in the calculated conversion levels. Moreover, the variation in product yield ratios with conversion can provide a clearer insight into the course of secondary reactions. 

Now let us look at the same problem at an angle of realistic expectations. We have to confess that at the current stage of understanding micro- and macro-kinetic aspects of alkane oxidation it is practically impossible to anticipate a precise quantitative description and prediction of the system behavior, product yields, etc. This is not only due to our limited ability to build an adequate model, but also because of a limited accuracy and significant uncertainty in the parameters of any real experiment (see Sections IV.A and IV.B for a detailed analysis). 

The raw GC data was converted into compositional data using the internal standard method with either N2 or Kr as the reference species. Once the species compositions were determined, values for the reactant conversion, product selecti-vities, and product yields were evaluated using the standard expressions. Errors in these parameters were calculated by closing the mass balance on the reaction. This was done by comparing the feed gas composition with the measured product gas compositions. Large errors in the mass balance (> 5%) were indicative of physical problems with the system, which were typically attributed to leaks. Smaller errors (< 5%) were caused by uncertainties in the GC molar response factors as well as fluctuations in flow rates of the MFCs on the Feed Gas Mixing Board. 

Extensions of this model have been developed, for instance, to take into account the exchange interaction [32]. However, the facts that such refined models require more parameters, that the uncertainty of these parameters is usually rather large, and that the observables, product yields or spin polarizations, are only global effects, tend to reduce their practical value. 

A typical comparison of this type has been shown in Table I. The cited peak retention data show that our (NPGS + DBPH) and (C9GROT + C7ACRY) columns exhibit different selectivities toward polar and nonpolar halocarbons. The measured product yields are in quantitative agreement within the allowed radioactive statistical measurement uncertainties. Products having > 0.2% yields are easily detected, and expected species other than those reported are routinely monitored. 

Mechanistic Uncertainties and Errors. Mass-balance mechanism yield consistency tests are definitive only to the extent that complementary changes in the product yield distributions have been monitored. To illustrate the nature of this limitation, we recall that stable and activated nascent products are formed from F-for-F Reaction 18 via respective Reactions 24 and 25. Because the yield from Reaction 25 is not subject to decomposition, no (P/Z) interdependence is possible between these contributions to Y(CH3CHF F). Chemical intuition thus provides the only basis for assigning the species from Reactions 24 and 25 to the same primary reaction channel (25,34,45). 

Here, mathematically the uncertainties are variances. The minimum value of this product yields the minimum energy uncertainty which can never be surpassed... 

For applications we have first to specify universes and fuzzy sets in them. The universe X that is to be specified could be the wavelength, energy or a product yield. The uncertainty of the appearance of the variables could be modeled by a fuzzy set A. As a special case of a fuzzy set we will regard a fuzzy measurement or fuzzy observation. Here ix(x) indicates the degree by which x is to be examined as a result of our actual measurement. The membership function that should be used depends on the application problem. The following practical hints can be given, cf. Otto ... 

A similar study by Ou et al. (2015) evaluated the techno-economic analysis of transportation fuels via HTL of defatted microalgae (Ou et al., 2015). Similar conclusions were drawn in regards to the minimum fuel selling price (MFSP), which was calculated as 679 /m. A sensitivity analysis revealed that the price is most sensitive to the HTL product yield, highlighting the importance of conversion performance. The feedstock cost was also a major uncertainty toward the MFSP which was also highlighted by the study at the PNNL. 

A tabulation of the ECPSSR cross sections for proton and helium-ion ionization of Kand L levels in atoms can be used for calculations related to PIXE measurements. Some representative X-ray production cross sections, which are the product of the ionization cross sections and the fluorescence yields, are displayed in Figure 1. Although these A shell cross sections have been found to agree with available experimental values within 10%, which is adequate for standardless PKE, the accuracy of the i-shell cross sections is limited mainly by the uncertainties in the various Zrshell fluorescence yields. Knowledge of these yields is necessary to conven X-ray ionization cross sections to production cross sections. Of course, these same uncertainties apply to the EMPA, EDS, and XRF techniques. The Af-shell situation is even more complicated. 

The production of the agrochemical 6 (Scheme 5.7) is carried out batchwise via a three-step protocol. Mass balancing has been conducted for three stages of development Laboratory-, pilot- and operation scale. An LCA was available for the operation stage only. A description of this LCA including data sources and data acquisition methods was published by Geisler et al. (product A in reference [9] corresponds to product 6 here). Many parameters in the Life-Cycle Inventory (LCI) are estimated, especially utihty demands and yields of processes for the production of precursors. Uncertainty in these estimations was illustrated in a... 

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