Model calculations, sensitization

Sensitivity analysis is a method used to evaluate the impact of a single variable or a group of variables on the results from a model calculation. Sensitivity analysis may be used to determine which parameters in a calculation have the greatest influence on the results such that greater emphasis is placed on characterizing these parameters. Moreover, the results from these analyses may be used to identify ways to improve the overall predictive capability of the model by reducing the uncertainty in the parameters that have the greatest influence on the outcome. Sensitivity analysis may be applied to the risk assessment process in order to identify those variables that dominate risk estimates as well as those that are relatively unimportant. 

The above example is a simple one, and it can be seen that the individual items form part of the chain in the production system, in which the items are dependent on each other. For example, the operating pressure and temperature of the separators will determine the inlet conditions for the export pump. System modelling may be performed to determine the impact of a change of conditions in one part of the process to the overall system performance. This involves linking together the mathematical simulation of the components, e.g. the reservoir simulation, tubing performance, process simulation, and pipeline behaviour programmes. In this way the dependencies can be modelled, and sensitivities can be performed as calculations prior to implementation. 

Model is sensitive to the method used to calculate reaeration. Only the Velz method gave segment-by-segment reaeration inputs which resulted in good agreement of predicted and observed DO profiles. 

Fig. 16-4 pH sensitivity to SO4- and NH4. Model calculations of expected pH of cloud water or rainwater for cloud liquid water content of 0.5 g/m. 100 pptv SO2, 330 ppmv CO2, and NO3. The abscissa shows the assumed input of aerosol sulfate in fig/m and the ordinate shows the calculated equilibrium pH. Each line corresponds to the indicated amoimt of total NH3 + NH4 in imits of fig/m of cloudy air. Solid lines are at 278 K, dashed ones are at 298 K. The familiar shape of titration curves is evident, with a steep drop in pH as the anion concentration increases due to increased input of H2SO4. (From Charlson, R. J., C. H. Twohy and P. K. Quinn, Physical Influences of Altitude on the Chemical Properties of Clouds and of Water Deposited from the Atmosphere." NATO Advanced Research Workshop Acid Deposition Processes at High Elevation Sites, Sept. 1986. Edinburgh, Scotland.)... 

In order to test the sensitivity of the model, calculations for adsorbed proplyene were repeated with the assumed value of vf 517 cm-1. This increase of 24% in the value of vf caused vf to increase to 1220 cm-1, a change of 1% in frequency. By way of contrast, if the angle was changed by 4%, the change in the calculated value of vf was 50 cm-1 (4%). Thus, the calculations depend little on the assumed bending frequency but provide a sensitive criteria for the angle. The value of 120°, the ideal value for a ir-allyl, provides the best fit to the data. The value of the stretching... 

Values of AEG calculated on the basis of the effective mass model are sensitive to the height of the barrier present at the surface of the confined structures [De4, Xu2]. For the case of oxidized PS, it is obvious that the silicon crystallites are embedded in a wide-gap material. In the case of a hydrogen termination of the crys-... 

Further studies examining time-variable behavior of PCBs in the Twelve Mile Creek-Lake Hartwell system and sensitivity of model calculations to various system parameters are presently being performed. The steady-state modeling results presented in this chapter, however, provide a reasonable base for an initial assessment of the fate of PCBs in the Twelve Mile Creek-Lake Hartwell system. The cumulative removals of PCBs from the system by volatilization and burial are shown as percents of the total PCB... 

Because the spectral irradiance 1(1) enters in this definition, the correction factor is a function of total ozone (Q) and solar zenith angle (6), which are the main parameters that determine 1(1). It is obvious from (2), that /ri expresses actually the relative change in the weighted integral when the instrument s sensitivity is used as weighting function instead of the CIE, Because of the involvement of 1(1) in relative sense, 1(1) can be determined from model calculations, as far as total ozone and SZA are known. In practice, lookup tables can be constructed for each instrument, defining the correction factor fd, as functions of total ozone and SZA. These tables can be used thereafter for the conversion of the broadband detectors radiometric output to CIE weighted eiythemal irradiance. 

As we shall discuss below, it is also more straightforward to calculate the relative intensity of vibrational modes observed by inelastic neutron scattering than in electron-energy-loss and optical spectroscopies. The relative intensity of the modes, as well as their frequency, can then be used to identify the atomic displacement pattern or eigenvector of the mode. We shall also see through examples of model calculations how the relative intensity of surface vibratory modes is sensitive to the orientation of the adsorbed molecule and the strength and location of its bond to the surface. 

Model calculations that include at least some of the reactions we have discussed for the syntheses of complex molecules have been performed in the last several years. Both steady-state and chemical time dependent models have been published. Unfortunately, as models include more and more complex species, they become more and more sensitive in their predictions to small changes. As an example, consider two models that in their predictions of the abundances of one-carbon-atom hydrocarbons differ by a factor of 3. This factor is not considered to be a major one in the field of interstellar chemistry. However, since the two-carbon-atom hydrocarbons are formed by reactions between one-carbon atom species, the model will differ in their predictions for the abundances of the larger hydrocarbons by a factor of 9. As one can easily discern, the situation becomes worse as the size of the hydrocarbons increase. Given this extreme sensitivity, modelers should attempt to make sure that at each stage of molecular complexity, they consider all depletion mechanisms and do not overestimate the abundances of the complex molecules that are intermediates in the formation of still more complex species. Unless this is done, models can become in our view overly optimistic about the growth of complexity in the interstellar medium. 

The authors [98] note sensitivity to the ignition temperature and the Cone Calorimeter irradiance, at which the experimental data were obtained. Comparison of model calculations and experimental data are presented for five different tests. The model calculations matched the experimental HRR least closely for Material B, and most closely for Material C. Figure 20.8 shows the model calculations and experimental data for these two cases. 

The sensitivity of Wn to chemical factors can be appreciated through a simple model calculation based on Eq. 6.53. Perhaps the least complicated expression for the interparticle potential energy is the large-separation approximation.38... 

Two experimental runs were performed. The H2S- and CO2 mole fluxes were obtained from the measured concentration curves by numerical differentiation and are plotted in figure 8a,b together with penetration and film model calculations. It is evident that forced desorption can be realized under practical conditions and can be predicted by the model. In general, measured H2S mole fluxes are between the values predicted by the models, whereas the CO2 forced desorption flux is larger than calculated by the models. The CO2 absorption flux, on the other hand, can correctly be calculated by the models. This probably implies that the rate of the reverse reaction, incorporated in equation (5), is underestimated. Moreover, it should be kept in mind that especially the results of the calculations in the forced desorption range are very sensitive to indirectly obtained parameters (diffusion, equilibrium constants and mass transfer coefficients) and the numerical differentiation technique applied. 

Finally, the numerical results obtained with the present model are sensitive to the input data and since these are subject to rather large uncertainties only the over-all pattern of the results is probably of significance. The general applicability of the pattern to other alkali halides cannot be assessed on the basis of calculations for a single crystal. It is hoped that the investigation of other alkali halides will clarify this point. 

Model calculations have been carried out using a variety of parameter values and some relative values are given in Table 2 appropriate to Sn02 (m = 0.2m0, es = 10) and TiOs (m = 8mo,es = 173) and assuming that the last two exponential terms in eqn. (255) are unity at both potentials. It is evident from these figures that the tunneling current is very sensitive indeed to the bulk properties of the semiconductor, a result also reported experimentally [124],... 

The interest in atmospheric environmental problems has stimulated a great deal of laboratory research on chemical kinetics. New research tools, especially lasers, have aided in increasing the quantity and quality of data. A major problem that is limiting the development of this research area is that often the reactions that need to be studied are not easily identified. For example, it is not possible to assess the effect of a reaction on model calculations until one has an estimate of the rate coefficient. Also it is not possible to tell which previous studies may be in error. One must speculate on reactions to which model predictions are very sensitive or for which there are inconsistencies in the data. 

Optimization of internal engine combustion in respect of fuel efficiency and pollutant minimization requires detailed insight in the microscopic processes in which complex chemical kinetics is coupled with transport phenomena. Due to the development of various pulsed high power laser sources, experimental possibilities have expanded quite dramatically in recent years. Laser spectroscopic techniques allow nonintrusive measurements with high temporal, spectral and spatial resolution. New in situ detection techniques with high sensitivity allow the measurement of multidimensional temperature and species distributions required for the validation of reactive flow modeling calculations. The validated models are then used to And optimal conditions for the various combustion parameters in order to reduce pollutant formation and fuel consumption. 

Figure 3 Plot of atmospheric CO2 versus time for the Phanerozoic, as calculated via the GEOCARB model, showing sensitivity to the rise of large vascular land plants. Rqo is the ratio of the mass of CO2 at some past time to that for the pre-industrial present. The ratios plants/bare refer to the relative rates of CO2 consumption via weathering in the presence of vascular plants versus prevascular ground cover ( bare ).

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