Viscosity Model Verification

Process modeling and simulation ate nevertheless extremely important tools in the design and evaluation of process control strategies for separation processes. There is a strong need, however, for better process mo ls for a variety of separations as well as process data with which to confirm tiiese models. Confidence in complex process models, especially those that can be used to study process dynamics, can come only from experimental verification of these models. This will require more sophisticated process sensors than those commonly available for temperature, pressure, pH, and differential pressure. Direct, reliable measurement of stream composition, viscosity, turbidity, conductivity, and so on is important not only for process model verification but also for actual process control applications. Other probes, which could be used to provide a better estimate of the state of the system, are needed to contribute to the understanding of the process in the same time frame as that of changes occurring in the process. 

The best verification of the mathematical model and calculation procedure comes from comparison with measurements in experimental models for which the parameters are known. Zhou and coworkers [1994] provide the first life-sized experimental model, designed to be similar to the human cochlea, but with fluid viscosity 28 times that of water to facilitate optical imaging. Results are shown in Figure 63.2 and Figure 63.3. Equation 63.13 gives rough agreement with the measurements. 

Many papers have been published in the last 20 years or so on modeling and simulation analysis of tubular reactors. It is difficult to make a clear statement on the validity of these analyses usually because of the lack of experimental verifications. When the velocity profile varies along the tube, a prediction of reactor performance is not much more complex theoretically, but its application to real systems is very difficult (if not impossible) because of lack of information on how the velocity profile changes along the tube at high monomer conversions (and viscosities). 

With a sophisticated software package, the verification of the default pure component model parameters can be performed fast and easily. Often the results can be judged graphically. Hopefully, in most cases the user will find good agreement between the calculated and the experimental data stored in the factual data bank. Eut sometimes also poor results may be obtained. As an example, the dynamic viscosity of hexafluorobenzene is shown in Figure 11.3. Deviations larger than 200% between calculated and experimental data are obtained. The reason for the poor results is that the parameters were fitted to predicted data and not to the data available in the literature. The deviation is caused by the fact that the chosen predictive method leads to poor dynamic viscosities for fluorine compounds. ... 

These models are also based on the Fickian equation (Lacey, 1954 Fan et al., 1990). The difficult part is the description of the diffusion coefficient for the diffusion model, which is a function of bubble size, its axial velocity, the particle density, particle size, the viscosity and density of the fluid, and the minimum fluidization velocity. When describing these models, experimentation is required for verification of the above parameters. Axial dispersion lakes place when the bubbles are rising in the bed, and horizontal dispersion when the bubbles burst. However, there exists evidence that horizontal dispersion also occurs as the bubbles form and move up the bed due to continuous displacement of the mass around the bubble. 

Simultaneously, the UP is an exciting phenomenon for the theory of electrochemical systems. Its modeling combines various types of theory and provides the results widely accepted in practice. Another remarkable aspect is the existence of UPs in a wide variety of systems with essentially different viscosity, permittivity, and molecular structure. This is always advantageous for theory verification. 

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