OCR Text |
Show calculation set. Details of the factorial design and response surface fitting are given elsewhere. [3] 8. Use the response surfaces to calculate target values that are then compared to measured values in an error function known as the objective function(O), which is then minimized. Here, 0 = l w [ l - calc/exper f. The values of the variables thus obtained are statistically the best values resulting from the universe of data considered as targets. 9. The result is a model faithful to both the fundamental kinetics and system data, one that can be reliably employed for modeling purposes. Not all data or targets are created equal. Some experiments are less trustworthy than others, which can be taken into account by weighting the targets differently (the term w ) in the objective function. The solution mapping paradigm allows the use of data of disparate types to refine rate parameters, thermochemistry or other parameters. Gaps or inconsistencies in the data set, and parameters which contribute large collective uncertainty and deserve more investigation, can be identified. A heuristic process and exercise of judgment is also involved in arriving at the final optimized mechanism in step 8 above. Several factors are at work. Foremost perhaps is the phenomenon of a shallow response surface, whereby the modeled target value only slowly changes with the rate constant(s) in the neighborhood of the suggested optimized solution. This effect occurs when the target sensitivities to a reaction are relatively low or parallel that of another. The optimization process will attempt to squeeze the last 0.001% decrease in O, but it makes no qualitative sense to require the mechanism to make the quantity and range of rate constant alterations to do so. Hence a significant part of the mechanism optimization process consists of locating these shallow or insignificant variables, and freezing their values at the baseline evaluated kinetic expressions. This involves some subjective judgment on how large an error to permit in the predicted target values. Sometimes variables optimize near their starting values, and thus need not be altered. W e have typically removed the majority of the variables from the final optimization. Version 1.2 altered 4 of the 30 rate constants considered, but of the 15 nitrogen kinetics reactions added to version 2.11, 10 additional ones were optimized. Work on version 3.0 has narrowed 98 variables down to 28. Additional factors to consider include the lack of a unique optimized mechanism, and the realization that errors in the data do require some subjective accommodation in the procedure given above. So it is also necessary to explore other possible combinations of rate parameters as optimization variables for groups of targets. A good example of multiple solution possibilities of similar quantitative agreement comes from our experience with the rate constants for O H + CO and H + 0 2 -» O + OH. Almost all targets are sensitive to one or both of these very important combustion reactions. Yet although the 3.0 optimization calculations suggest a lowering of these rates when they are included, the quality of target fits is not appreciably diminished by freezing them at their initial values (O increases 2%). OPTIMIZATION PROCESS To begin the chemical reaction mechanism development process, rate parameters and thermochemistry for the elementary reactions of methane oxidation and N O formation and reburning kinetics, 325 reactions of 53 species, were identified by critical evaluation of the basic 4 |