Transient Sensitivity Analysis

With a series of continuations, solutions were computed at increasing temperatures up to 1400 K. In all cases the solution was obtained directly by Newton iteration, with no need for time stepping to assist convergence. Just in the vicinity of the turning point (around 1100 K), it is apparent that at least three of the solutions depart significantly from the true physical solution. 

In case 2 (middle panel of Fig. 15.9), the initial solution was also determined by beginning with an equilibrium estimate at a reactor temperature of T = 1200 K. Then, through a series of continuations, solutions were determined at temperatures down to 900 K. In this case the solutions are in reasonable agreement with the true solution, although there is some disagreement in the region around 1000 K. 

From these examples it is apparent that one needs to be cautious when using steady-state methods and continuation procedures near turning points. While the solutions may converge rapidly and even appear to be physically reasonable, there can be significant errors. Fortunately, a relatively simple time-stepping procedure can be used to identify the nonphysical solutions. Beginning from any of the solutions that are shown in Fig. 15.9 as shaded diamonds, a transient stirred-reactor model can be solved. If the initial solution (i.e., initial condition for the transient problem) is nonphysical, the transient procedure will march toward the physical solution. If the initial condition is the physical solution, the transient computational will remain stationary at the correct solution. 

Presume that a problem is described as an ordinary-differential-equation initial-value problem, such as the mass-action kinetics or plug-flow problems discussed earlier. In the standard form, such a problem might be written as 

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Figure 11 A. Transient chemically sensitive analysis of the effluent from a single catalyst [58].

Parametric sensitivity analysis showed that for nonreactive systems, the adsorption equilibrium assumption can be safely invoked for transient CO adsorption and desorption, and that intrapellet diffusion resistances have a strong influence on the time scale of the transients (they tend to slow down the responses). The latter observation has important implications in the analysis of transient adsorption and desorption over supported catalysts that is, the results of transient chemisorption studies should be viewed with caution, if the effects of intrapellet diffusion resistances are not properly accounted for. 

The advantage of ToF analyzers is their unlimited mass range for a sensitive analysis of large biomolecules or clusters of up to several millions of daltons and their ability to rapidly obtain mass spectra relevant for the fast analysis of transient signals.28 The latter property of analyzing... 

Gunawan, R., Jung, M.Y.L., Seebauer, E.G. and Braatz, R.D. (2003b) Parameter Sensitivity Analysis of Boron Activation and Transient Enhanced Diffusion in Silicon. J. Electrochem. Soc., 150, G758-G765. 

Modeling A, without consideration of land-use changes and the transient dynamics of clearance, agriculture, abandonment, and succession could contribute to the observed differences between modeled and measured A values. A sensitivity analysis of the importance of land-use change at a global scale is therefore necessary. Currently dynamic models are computer-intensive and coarser in PFT-specific-ness, but only future simulations with these models will be able to assess the long-term importance of memory effect and isotopic disequilibrium. 

A kinetics text with a strong theoretical bent that overviews transient kinetic methods and discusses data analysis issues such as error propagation and sensitivity analysis. 

Nakajo et al. [12] in 2006 carried out a numerical analysis, studying the effect of the temperature profile characteristics on the stress field of the cell components in a tubular SOFC design. Radial thermal gradients were of particular interest. A simplified WeibuU analysis was performed to evaluate the evolution of the probabiHty of survival of the cell components in steady and transient state. Sensitivity analysis... 

Kummer AM, Hierlemann A, Baltes H (2004) Tuning sensitivity and selectivity of complementary metal oxide semiconductor based capacitive chemical microsensors. Anal Chem 76 2470-2477 Kiunmer AM, Burg TP, Hierlemann A (2006) Transient signal analysis using complementary metal oxide semiconductor capacitive chemical microsensors. Anal Chem 78 279-290 Kurzawski P, Hagleitner C, Hierlemann A (2006) Detection and discrimination capabilities of a multitransducer single-chip gas sensor system. Anal Chem 78 6910-6920... 

Sappok A, Kamp C, Wong V (2012) Sensitivity Analysis of Ash Packing and Distribution in Diesel Particulate Filters to Transient Changes in Exhaust Conditions. SAE Int J Fuels Lubr 5(2) 733-750. doi 10.4271/2012-01-1093... 

Bieniasz LK, Diimmling S, Speiser B, Wiirde M (1998) Use of sensitivity analysis methods in the modeUing of electrochemical transients. Pent 2. Model expansion and model reduction. J Electroanal Chem 447 173-186... 

Essentially, each of the above systems has two widely different time scales. If the initial transient is not of interest, the systems can be projected onto a one-dimensional subspace. The subspace is invariant in that no matter where one starts, after a fast transient, all trajectories get attracted to the subspace in which A and B are algebraically related to each other. In essence, what one achieves is dimension reduction of the reactant space through time scale separation. For large, complex systems sueh as oil refining, it is difficult to use the foregoing ad hoc approaches to reduce system dimensionality manually. Computer codes are available for mechanism reduction by means of the QSA/QEA and sensitivity analysis. ... 

This is a typical flow increasing transient. The demand of the main coolant flow rate is assumed to rise stepwise up to 138% of the rated flow as is assumed in the feedwater control system failure of Japanese ABWRs. Since increase in the core coolant flow rate is mild in ABWRs due to the large recirculation flow, the feed-water flow rate is assumed to increase stepwise. This assumption is too conservative for the Super LWR. The main coolant flow rate is gradually increased by the control system in the safety analysis. The calculation results are shown in Fig. 6.31. The reactor power increases with the flow rate due to water density feedback. A scram signal is released when the reactor power reaches 120% of the rated power. The maximum power is 124% while the criterion is 182%. The increase in the pressure is small. The sensitivity analysis is summarized in Table 6.15. 

The data obtained is being used to test numerical procedures and codes. A sensitive analysis was performed and most sensitive parameters were identified. A representative group of transients were selected, in order to check computer models. Simulation models are in current development against a reference transient, without adjustment. When this contrast is clear, models will be compared against the representative group of transients. The information on specific models should be incorporated into CAREM modelling. 

Spectroscopic methods such as uv and fluorescence have rehed on the polyene chromophore of vitamin A as a basis for analysis. Indirectly, the classical Carr-Price colorimetric test also exploits this feature and measures the amount of a transient blue complex at 620 nm which is formed when vitamin A is dehydrated in the presence of Lewis acids. For uv measurements of retinol, retinyl acetate, and retinyl palmitate, analysis is done at 325 nm. More sensitive measurements can be obtained by fluorescence. Excitation is done at 325 nm and emission at 470 nm. Although useful, all of these methods suffer from the fact that the method is not specific and any compound which has spectral characteristics similar to vitamin A will assay like the vitamin... 

Limitations in the digitizer s dynamic range can be overcome by using multiple transient recorders operating at diflerent sensitivities, or by adding logarithmic preamplifiers in the detection system. From the preceding discussion it appears, however, that quantitative analysis is not the primary area of application of LIMS. Semiquantitative and qualitative applications of LIMS have been developed and are discussed in the remainder of this article. 

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