Scaling parameters experimental determination

In order to determine rigorously the process parameters, a few relevant parameters are to be experimentally determined on a laboratory scale column. 

Fitzgerald et al. (1984) measured pressure fluctuations in an atmospheric fluidized bed combustor and a quarter-scale cold model. The full set of scaling parameters was matched between the beds. The autocorrelation function of the pressure fluctuations was similar for the two beds but not within the 95% confidence levels they had anticipated. The amplitude of the autocorrelation function for the hot combustor was significantly lower than that for the cold model. Also, the experimentally determined time-scaling factor differed from the theoretical value by 24%. They suggested that the differences could be due to electrostatic effects. Particle sphericity and size distribution were not discussed failure to match these could also have influenced the hydrodynamic similarity of the two beds. Bed pressure fluctuations were measured using a single pressure point which, as discussed previously, may not accurately represent the local hydrodynamics within the bed. Similar results were... 

When comparing an experimentally determined RTD with the theoretical predictions of a flow-mixing model so as to determine some unknown parameters in that model, it is not the absolute time scale of the two curves... 

Engineers commonly use dimensionless ratios such as the Reynolds number and the lift coefficient to help understand complex experimental data, organize equations and model building, and relate model testing in a wind tunnel to that of a prototype flight. This kind of analysis is called dimensional analysis because it uses the dimensional nature of important variables to derive dimensionless parameters that determine the scaling properties of a physical system. 

In Fig. 1.10 [31], the experimentally determined instability wavelength is plotted versus d (at a constant applied voltage), reflecting the non-linear scaling predicted by Eq. 1.15. To compare data obtained for varying experimental parameters (hp, d, ep, U, y), it is useful to introduce rescaled coordinates. Assuming a characteristic field strength Id) = LIqo =... 

Equation 4.35 shows that the concentration deviations based on a linearization analysis of the rate laws in Eqs. 1.54a and 1.54c will decay to zero exponentially ( relax ) as governed by the two time constants, r, and r2. These two parameters, in turn, are related to the rate coefficients for the coupled reactions whose kinetics the rate laws describe (Eqs. 4.36c-4.36e and 4.38). If the rate coefficients are known to fall into widely different time scales for each of the coupled reactions, their relation to the time constants can be simplified mathematically (Eq. 4.39 and Table 4.3). Thus an experimental determination of the time constants leads to a calculation of the rate coefficients.20 In the example of the metal complexation reaction in Eq. 1.50, with the assumptions that the outer-sphere complexation step is much faster than the inner-sphere complexation step and that dissociation of the inner-sphere complex is negligible (k b = 0 in Eq. 1.54c), the results for tx and r2 in the first row of Table 4.3 can be applied. The expression for tx indicates that measurements of this parameter as a function of differing equilibrium concentrations of the complexing metal and ligand will produce a straight line whose slope is kf and whose y-intercept is kb. The measured values of l/r2 at these same two equilibrium concentrations then lead to a calculation of kf. 

The resulting set of 10 equations, assuming toroidal symmetry and replacing the radial component of the ion momentum balance equation by an ad hoc diffusions ansatz (likewise the other radial transport coefficients are replaced by ad hoc anomalous expressions) is the basis for most current edge plasma simulation models. These anomalous ad-hoc coefficients are free model parameters. They, and their empirical scalings, can be determined by comparison with experimental plasma profile data, if one can be sure that all other terms in the equations, and in particular the source terms Sm resulting from atomic and molecular processes, are accurately known and implemented. 

Note again that the quantitative values associated with hardness and softness in this article are based wholly on experimentally determined log stability constant differences determined in aqueous solutions at room temperature. The values are not absolute addition of more metal ions might extend the scales in either direction. Small differences between metal ions should not be overinterpreted. The relative difference scales are linear in log stability constant, stretching from very hard at one end to very soft at the other. As hardness decreases, softness correspondingly increases, and vice versa. These practical scales are difficult to relate to that of Pearson, where absolute hardness values are derived from gas-phase parameters, and softness is the reciprocal of hardness. ... 

The successful design of industrial reactors lies primarily with the reliability of the experimentally determined parameters used in the scale-up. Consequently, it is imperative to design equipment and experiments that will generate accurate and meaningful data. Unfortunately, there is usually no single comprehensive laboratory reactor that could be used for aU types of reactions and catalysts. In this section we discuss the various types of reactors that can be chosen to obtain the kinetic parameters for a specific reaction system. We closely follow the excellent strategy presented in the article by V. W. Weekman of Mobd Oil. The criteria used to evaluate various types of laboratory reactors are listed in Table 5-3. 

The performance of lab-scale BSR modules in the SCR of NO can be predicted with an error of ca. 10% by four relatively simple mathematical models, whose parameters were determined via independent experiments. As expected, the LCF and the LCR model generally underpredict the conversion, whereas the CB model generally overestimates it. The CBS model gives the most accurate prediction of the NO conversion On the average, the predicted conversion deviates ca. 5% (relative) from the experimentally determined value. Such deviations can be attributed to stochastic variations in the experiments. 

Practical problems in the estimation of the lipophilicity of araliphatic and aliphatic compoimds led to the / hydrophobicity scales of Rekker and Leo/Hansch. However, all such descriptor scales depend on experimental determinations. New molecular descriptors were developed from scratch, starting with the work of Randic, Kier and Hall, i.e. the various molecular connectivity parameters %. Later the electrotopological state parameters and the Todeschini WHIM parameters were added. Whereas topological descriptors are mathematical constructs that have no unique chemical meaning, they are clearly related to some physicochemical properties and are suited to the description of compound similarities in a quantitative manner. Thus, despite several critical comments in the past, they are now relatively widely used in QSAR studies. Only a meaningless and excessive application in quantitative models, as far as the number of tested and included variables is concerned, still deserves criticism. 

This test has a similar basis to the PAC predictions described previously. In this case the kinetic parameters are determined using a small-scale GAC column, run over several hours. The equilibrium parameters are used in the HSDM to fit the experimental column data and the derived kinetic parameters are then applied to predict the adsorption in the column under different conditions of flow, initial concentration, etc. [10]. 

A wastewater flowrate of 180 m /day has a TOC (total organic carbon level) of 200 mg/L. A flxed-bed GAC adsorption column wiU be used to reduce the maximum effluent concentration to 8 mg/L. A breakthrough curve. Figure 7.12, has been obtained from an experimental pilot column operated at 2(BV)/hr. Other data concerning the pilot column are mass of carbon = 4.13 kg, water flowrate = 15 L/hr, and packed carbon density = 400 kg/m. Using the scale-up approach, determine the values of the following parameters for the design column ... 

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