Uncertainty combustion analysis

Table 7-5 shows results for two of seven compounds sent to many labs to compare their performance in combustion analysis. For each compound, the first row gives the theoretical wt% for each element and the second row shows the measured wt%. Accuracy is excellent Mean wt% C, H, N, and S are usually within 0.1 wt% of theoretical values. The 95% confidence intervals for uncertainty for C for the first compound is 0.63 wt% and the uncertainty for the second compound is 0.33 wt%. The mean uncertainty for C listed in the bottom row of the table for all seven compounds in the study was 0.47 wt%. Mean 95% confidence intervals for H, N, and S are 0.24, 0.31, and 0.76 wt%, respectively. Chemists consider a result within 0.3 wt% of theoretical to be good evidence that the compound has the expected formula. This criterion can be difficult to meet for C and S with a single analysis because the 95% confidence intervals are larger than 0.3. 

Paper II presents a hypothetical method to indirectly measure the key quantities of a PBC, that is, the mass flow and the stoichiometry of the conversion gas, as well as the air excess numbers of the conversion and combustion system, defined in paper I. It also includes a measurement uncertainty analysis. 

This appendix presents a review of experimental work in the field of packed-bed combustion of biomass. It deals with the measurement methods used to analyse the thermochemical conversion of the biomass. This implies that thermochemical conversion studies of coal is outside the scope of this literature study. Wood stove research is not considered in this review either. Of special interest in this survey is the choice of sought physical quantities (target quantities) and measurands of interest in each study and how they are modelled and verified, and if uncertainty analysis is carried out. 

Stubington et al [6] presented a short descriptive model of how the ignition front rate and the combustion rate are determined. No mathematical models to calculate the ignition rate and the combustion rate are shown. However. As far as this author can understand, the calculation results are time average values, that is, no time instant values are obtained by the method used by Stubington. No uncertainty analysis was presented and no verification method was used. The methods used are unclearly defined. Consequently, the results would be difficult to reproduce. Nevertheless, the study includes interesting result. 

Koistinen et al [7] present a number of graphs on the grate fluxes (W/m, s). However, no theory of the method to calculate the grate effect was described. It must be based on the measured mass loss rate. Furthermore, no plots on the combustion rate (kg/m, s) are shown. Magnitudes of the air factor is presented, but no theory of how it is determined. No uncertainty analysis is carried out and no verification method is... 

Aho [8] presented a short descriptive model of the relationship between combustion heat rate and mass loss rate of bed. He applies the same method as Koistinen et al [7]. It is clear that the method used presents time average values of combustion heat rate. No verification method is applied and no uncertainty analysis is carried out. The... 

Often there are cases where the submodels are poorly known or misunderstood, such as for chemical rate equations, thermochemical data, or transport coefficients. A typical example is shown in Figure 1 which was provided by David Garvin at the U. S. National Bureau of Standards. The figure shows the rate constant at 300°K for the reaction HO + O3 - HO2 + Oj as a function of the year of the measurement. We note with amusement and chagrin that if we were modelling a kinetics scheme which incorporated this reaction before 1970, the rate would be uncertain by five orders of magnitude As shown most clearly by the pair of rate constant values which have an equal upper bound and lower bound, a sensitivity analysis using such poorly defined rate constants would be useless. Yet this case is not atypical of the uncertainty in rate constants for many major reactions in combustion processes. 

Detailed analysis of the spatial and temporal distribution of NO during the combustion phase yields information about the formation pathways involved. Nevertheless, as far as processes close to the flame front are concerned, there is a number of effects that cause uncertainties in the... 

The study of elementary reactions for a specific requirement such as hydrocarbon oxidation occupies an interesting position in the overall process. At a simplistic level, it could be argued that it lies at one extreme. Once the basic mechanism has been formulated as in Chapter 1, then the rate data are measured, evaluated and incorporated in a data base (Chapter 3), embedded in numerical models (Chapter 4) and finally used in the study of hydrocarbon oxidation from a range of viewpoints (Chapters 5-7). Such a mode of operation would fail to benefit from what is ideally an intensely cooperative and collaborative activity. Feedback is as central to research as it is to hydrocarbon oxidation Laboratory measurements must be informed by the sensitivity analysis performed on numerical models (Chapter 4), so that the key reactions to be studied in the laboratory can be identified, together with the appropriate conditions. A realistic assessment of the error associated with a particular rate parameter should be supplied to enable the overall uncertainty to be estimated in the simulation of a combustion process. Finally, the model must be validated against data for real systems. Such a validation, especially if combined with sensitivity analysis, provides a test of both the chemical mechanism and the rate parameters on which it is based. Therefore, it is important that laboratory determinations of rate parameters are performed collaboratively with both modelling and validation experiments. 

Application of formal uncertainty analysis to combustion systems has been very rare so far, and restricted to the utilization of local sensitivities. 

Possible reasons are the limited knowledge of the uncertainty of parameters, and the fact that global sensitivity methods are computationally very intensive. In the future, it is expected that both these limitations will be lifted and detailed uncertainty analyses will appear for combustion calculations. On the other hand, one of the main applications of sensitivity analysis has been to form a qualitative picture about which parameters should be known precisely in order to reproduce accurately a set of experimental observations. 

The A H (Nb20g, cr, 298.15 K) Investigations suffer from uncertainties concerning the polymorphic state of the samples employed and the oftentimes incomplete impurity analysis of the samples (1 ). There is considerable scatter in the following tabulation for the enthalpy of formation values, all of which are based on enthalpy of combustion studies. 

The homogeneity has been verified at the level of intake of 0.25 g. The method uncertainty was measured by seven replicate analysis of dissolutions of a coal CRM (NBS 1632a). F and Cl were determined by ion chromatography after oxygen combustion and absorption in water cooled in ice. No in-homogeneity was detected for fluorine. For Cl, a significant difference between the CV of the method and the CV between-bottles was demonstrated the very low Cl content led to a large uncertainty of measurements which could, however, not explain the differences observed in the within- and... 

One impediment to straightforward comparison is the lack of solid-phase enthalpies of formation for most low molecular weight molecules. Examination of the few examples for which there are both solid- and liquid-phase values shows, however, that the liquid- and solid-phase enthalpies of reaction do not vary too much, at least within the uncertainties of the steroid combustion measurements. We are additionally hampered by not having available enthalpies of formation for those small molecules which most resemble the steroid substructure. The prototype small molecules required for the analysis are primarily those of substituted five- or six-membered carbocyclic rings. Although the functional groups on the available prototypes and the steroids are identical, stereochemical aspects (such as axial vs. equatorial substituent positions) and their consequent interactions are different due to the differences in conformational flexibility of the monocyclic and polycyclic systems. The prototype molecules and their liquid-phase enthalpies of formation are listed in Table 3. 

The development of GC coupled via a combustion furnace to an IRMS (GC-C-IRMS) has allowed the analysis of individual compounds occurring at trace levels in very complex mixtures. Sometimes referred to as compound specific isotope analysis or isotope ratio monitoring MS (GC-irmMS), this technique has opened new fields of research in areas such as organic geochemistry, food science, medicine, nutrition, sport, forensic science, archaeology, soil science, and extraterrestrial science. The chromatographic separation in connection with the combustion of the analyte, however, exerts the strongest influence on the uncertainty of the measurement. Multidimensional GC (GC/GC) has also been coupled to IRMS for the authentication of flavor components. 

However, chemists were far less successful when they attempted to further analyze the extracted plant substances in order to establish knowledge about their elemental composition. Not only flour, which aroused Rousseau s objections, but all kinds of substances separated from plants or animals posed difficulties to elemental analysis. The pre-Lavoisierian chemists were well aware of these difficulties and of the uncertainty of their knowledge about the elemental composition of plant and animal materials. When they submitted different kinds of plant and animal materials to dry distillation—which was the standard analytical method for elemental analysis prior to Lavoisier s introduction of the combustion method—they always obtained very similar analytical products, such as empyreumatic oils, volatile acids, insipid waters, fixed salts, and earths. In 1749, Pierre Joseph Macquer described the problems with respect to the vegetable and animal oils. Based on elemental analysis by dry distillation, Macquer claimed that oils were composed of phlogiston, water, an acid, and a certain quantity of earth. Yet he also added that there may have been other principles contained in oils that had escaped his attention. The sole means that would have allowed chemists to be reassured about their analytical results—the resynthesis of the original compound from the analytical products—was barred in plant and animal chemistry as Macquer conceded ... 

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