Series of stirred tanks model

Packed, Tray, and Spray Towers Packed and tray towers have been discussed in the subsection Mass Transfer in Sec. 5. Typically, the gas and liquid are countercurrent to each other, with the liquid flowing downward. Each phase may be modeled using a PFR or dispersion (series of stirred tanks) model. The model is solved numerically... 

Series-of-stirred-tanks model The series-of-stirred-tanks model (often referred to as the cell model) is perhaps the simplest type of stagewise model for the backmix reactor. In this model, the reactor is represented by a series of perfectly mixed stages. The degree of backmixing is characterized by the number of stages the... 

Interpretation of Response Data by the Series-of-stirred-tanks Model... 

In the series-of-stirred-tanks model the actual reactor is simulated by n ideal stirred tanks in series. The total volume of the tanks is the same as the volume of the actual reactor. Thus for a given flow rate the total mean residence time is also the same. The mean residence time per tank is 8Jn. Figure 6-lOu describes the situation. The objective is to find the value of n for which the response curve of the model would best fit the response curve for the actual reactor. To do this the relation between (C/Co)stcp should be developed. 

SECTION 6-6 INTERPRETATION OF RESPONSE DATA BY THE SERIES-OF-STIRRED-TANKS MODELS 259... 

Figure 6-lOh is a plot of Eq. (6-33) for various values of n. The similarity between Figs. 6-8 and 6-10 indicates that the axial-dispersion and series-of-stirred-tanks models give the same general shape of response curve. The analogy is exact for = 1, for this curve in Fig. 6-1 Oh agrees exactly with that in Fig. 6-8 for infinite dispersion, DJuL = oo both represent the behavior of an ideal stirred-tank reactor. Agreement is exact also at the other extreme, the plug-flow reactor ( = oo in Fig. 6-1 Oh and DjuL = 0 in Fig. 6-8). The shapes of the curves for the two models are more nearly the same the larger the value of n.

The series-of-stirred-tanks model could not represent the RTD for the laminar-flow reactor shown in Fig. 6-7. However, the RTD data given in Example 6-2 can be simulated approximately. The dashed curve in Fig. 6-1 Oh is a plot of this RTD. While no integer value of n coincides with this curve for all 6/6, the curve for = 5 gives approximately the correct shape. Comparison of the fit in Figs. 6-9 and 6-lOh indicates that about the same... 

Example 6-7 Using the series-of-stirred-tanks model to simulate the RTD of the reactor described in Example 6-2, predict the conversion for a first-order reaction for which k = 0.1 sec and 0 = 10 sec. 

SECTION 6-10 CONVERSION ACCORDING TO THE SERIES-OF-STIRRED-TANKS MODEL... 

Figure 6. Schematic representation of series of stirred tanks model (oell model).

Non-ideal mixing conditions in a reactor can often be modelled as combinations of tanks and tubes. Here a series of stirred tanks are used to simulate a tubular, by-passing condition. 

The use of the tanks-in-series model for packed beds can be more strongly justified. The fluid can be visualized as moving from one void space to another through the restrictions between particles. If the fluid in each void space were perfectly mixed, the mixing could be represented by a series of stirred tanks each with a size the order of magnitude of the particle. This has been discussed in detail by Aris and Amundson (A14). The fluid in the void spaces is not perfectly mixed, and so an efficiency of mixing in the void spaces has to be introduced (C6). This means that the analogy is somewhat spoiled and the model loses some of its attractiveness. In laminar flow the tanks-in-series model may be still less applicable. 

In this case, Vr is the volume of each individual reactor in the battery. In modeling a reactor, n is empirically determined based on the extent of reactor backmixing obtained from tracer studies or other experimental data. In general, the number of stages n required to approach an ideal PFR depends on the rate of reaction (e.g., the magnitude of the specific rate constant k for the first-order reaction above). As a practical matter, the conversion for a series of stirred tanks approaches a PFR for n > 6. 

I suggest that where performance problems are found in large continuous plants, then an analysis of the flow distribution in particular sections of the system can be made by constructing models of performance in which the results are compared with those from combinations of plug flow reactors and various series of stirred tanks. Obviously an infinite series of small stirred tanks is equivalent to a plug flow reactor. 

Figure 2. Mass transfer models for a batch ideal tank contactor (a), a continuous-co-current-flow multi-stage fluidised-bed contactor (b), and a packed column contactor (c) the last two modelled by a series of stirred tanks.

A stirred-tank model has been proposed, (Daly, 1980), to model the mixing behavior of an air-solid, spouted, fluidised-bed reactor. The central spout is modelled as two tanks in series, the top fountain as a further tank and the down flowing annular region of the bed as 6 equal tanks in series. It is assumed that a constant fraction of the total solids returns from each stage of the annular region into the central two tank region, as depicted below. 

We have discussed the tanks-in-series model in the sense that the composition in the system was constant over a cross-section. Recently Deans and Lapidus (D12) devised a three-dimensional array of stirred tanks, called a finite-stage model, that was able to take radial as well as axial mixing into account. Because of the symmetry, only a two-dimensional array is needed if the stirred tanks are chosen of different sizes across the radius and are properly weighted. By a geometrical argument. Deans and Lapidus arrived at the following equation for the (i, j) tank ... 

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