Stirred Tank Modeling Using Experimental Data

5-4 STIRRED TANK MODELING USING EXPERIMENTAL DATA 

Stirred tanks typically contain one or more impellers mounted on a shaft, and optionally, baffles and other internals. Although it is a straightforward matter to build a 3D mesh to contour to the space between these elements, the mesh must be built so that the solution of the flow field incorporates the motion of the impeller. This can be done in two ways. First, the impeller geometry can be modeled directly, or explicitly, and the grid and solution method chosen so as to incorporate the motion of the impeller using either a steady-state or time-dependent techniqne. This approach is discussed in detail in Section 5-5. Second, the motion of the impeller can be modeled implicitly, using time-averaged experimental velocity data to represent the impeller motion. The second approach is the subject of this section. 

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Polystyrene can be easily prepared by emulsion or suspension techniques. Harkins (1 ), Smith and Ewart(2) and Garden ( ) have described the mechanisms of emulsTon polymerization in batch reactors, and the results have been extended to a series of continuous stirred tank reactors (CSTR)( o Much information on continuous emulsion reactors Ts documented in the patent literature, with such innovations as use of a seed latex (5), use of pulsatile flow to reduce plugging of the tube ( ), and turbulent flow to reduce plugging (7 ). Feldon (8) discusses the tubular polymerization of SBR rubber wTth laminar flow (at Reynolds numbers of 660). There have been recent studies on continuous stirred tank reactors utilizing Smith-Ewart kinetics in a single CSTR ( ) as well as predictions of particle size distribution (10). Continuous tubular reactors have been examined for non-polymeric reactions (1 1 ) and polymeric reactions (12.1 31 The objective of this study was to develop a model for the continuous emulsion polymerization of styrene in a tubular reactor, and to verify the model with experimental data. 

The objeetive of the following model is to investigate the extent to whieh Computational Fluid Mixing (CFM) models ean be used as a tool in the design of industrial reaetors. The eommereially available program. Fluent , is used to ealeulate the flow pattern and the transport and reaetion of ehemieal speeies in stirred tanks. The blend time predietions are eompared with a literature eonelation for blend time. The produet distribution for a pair of eompeting ehemieal reaetions is eompared with experimental data from the literature. 

In the previous sections, the use of surfactants to increase the rate of desorption of hydrophobic organic contaminants was discussed. For the current study, several different surfactants were tested to determine whether the rate of TCE desorption from a peat soil could be increased. The effects of the surfactants on the rate of TCE desorption was tested using a continuous-flow stirred-tank reactor (CFSTR) methodology. The observed data were simulated using a distributed-rate kinetic desorption model. The parameters determined from the model simulation were then use to discern the effects of the surfactants on the rate of TCE desorption from the peat soil. The experimental methodology and the modeling procedure are now described in detail. 

An approximate technique to model the performance of an hollow fiber ILM for the removal of HNO, by coupled transport Is described by Noble and Danesl (110). The system was modeled as a series of ILM-contlnuous stirred tank reactor (CSTR) pairs. The approximate mathematical method used one adjustable parameter to predict steady-state nitric acid concentrations In good agreement with experimental data. 

Nitric acid removal from an aqueous stream was accomplished by continuously passing the fluid through a hollow fiber supported liquid membrane (SLM). The nitric acid was extracted through the membrane wall by coupled transport. The system was modeled as a series of (SLM)-continuous stirred tank reactor (CSTR) pairs. An approximate technique was used to predict the steady state nitric acid concentration in the system. The comparison with experimental data was very good. 

Type (b) models are at present the most useful, though still requiring more hydrodynamic data. A successful example considers the liquid and gas circulations in a stirred tank as loops of connected mixed zones (see Figure 15.23) with feed and offtake where appropriate. The zones can have different and gas hold-ups if these have been determined experimentally. The mean circulation flow and relevant number of zones have to be supplied from experiments, so the model is again not in itself predictive. However, the parameters have a physical meaning and so they are more amenable to scale-up. 

As can be seen in Figure 10.6 the model allows to change the number of continuously stirred tank reactors in both bubble and emulsion phases. These parameters can be used to investigate the effect of the degree of gas back-mixing in the bubble and emulsion phases. Moreover these are adjusting parameters to be evaluated through a model validation with experimental data. 

Another consideration in the case of gas-liquid mixtures is the impact of the impeller on gas bubble size. In an actual stirred tank, the momentum of the rotating impeller often acts to break up gas bubbles as they pass through the region. This reduces the bubble size and can lead to an increase in the gas hold-up as well as a change in the momentum exchange term (drag) between the phases. When experimental data are used, this phenomenon is missing from the formulation but can often be incorporated into the calculation if subroutines, written by the user, are available to modify the model in the commercial software. 

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