Tanks-in-series

The leaching is 50—60°C without external heating. The cone-bottom tanks are equipped with a pipe from just above the solution level to near the bottom through which air is blown forming bubbles which lower the density of the slurry. These leach tanks, caHed Pachucas, are fairly efficient and are stiH popular although many plants employ mechanical agitators. Most plants use 3—5 tanks in series with acid and calcine being fed to the first and, in some cases, downstream from the first tank as weH. 

Disc Two well-mixed tanks in series with classified exit Well-mixed tank and plug-flow in series with fines bypass Sastry Loftus [Pmc. 5th Int. Symp. Agglom., IChemE, 623 (1989)1 Ennis, Personal communication (1986)... 

Comparison of Models Only scattered and inconclusive results have been obtained by calculation of the relative performances of the different models as converiers. Both the RTD and the dispersion coefficient require tracer tests for their accurate determination, so neither method can be said to be easier to apply The exception is when one of the cited correlations of Peclet numbers in terms of other groups can be used, although they are rough. The tanks-in-series model, however, provides a mechanism that is readily visualized and is therefore popular. 

In a single eontinuous flow stirred tank reaetor, a portion of the fresh feed eould exit immediately in the produet stream as soon as the reaetants enter the reaetor. To reduee this bypassing effeet, a numher of stirred tanks in series is frequently used. This reduees the prohahility that a reaetant moleeule entering the reaetor will immediately find its way to the exiting produet stream. The exit stream from the first stirred tank serves as the feed to the seeond, the exit stream from the seeond reaetor serves as the feed to the third, and so on. For eonstant density, the exit eoneentration or eonversion ean he solved hy eonseeutively applying Equation 5-158 to eaeh reaetor. The following derived equations are for a series of tliree stii+ed tanks (Figure 5-23) with eonstant volume Vr. 

For most types of kineties, the stepwise ehanges in eoneentration results in a smaller average reaetion rate than it would otherwise if the same feed materials were in a hateh or plug (tubular) reaetor. Therefore, to obtain the same output the volume of the reaetion spaee must be larger, and in some instanees mueh larger as in the ease where only a single tank is used. By arranging several tanks in series the... 

Eigure 8-25 shows the RTD of different numbers of tanks in series. As the number increases, the behavior of the system approaches that of a plug flow reactor. 

The number of tanks in series from the dimensionless varianee (Equation 8-45) from the traeer experiment is... 

N —> This indicates that the behavior of stirred tanks in series... 

The model consists of i -i- 1 stirred tanks in series, i of which have a common volume, and one of which has a smaller volume... 

Equations 8-109, 8-110, 8-111, and 8-112 are redueed to an ordinary tanks-in-series model when N = i and h = 0. For the equivalent number of ideal CSTRs, N is obtained by minimizing the residual sum of squares of the deviation between the experimental F-eurve and that predieted by Equation 8-109. The objeetive funetion is minimized from the expression... 

COMPARISION OF TANK IN SERIES (TIS) AND DISPERSION PLUG FLOW (DPF) MODELS... 

Both the tank in series (TIS) and the dispersion plug flow (DPF) models require traeer tests for their aeeurate determination. However, the TIS model is relatively simple mathematieally and thus ean be used with any kineties. Also, it ean be extended to any eonfiguration of eompartments witli or without reeycle. The DPF axial dispersion model is eomplex and therefore gives signifieantly different results for different ehoiees of boundary eonditions. 

Computer program PROGS 1 determines the number of tanks, the varianee, dispersion number, and the Peelet number from Hull and von Rosenberg data. The results of the simulation suggest that about three stirred tanks in series are equivalent to the RTD response eurve. Figure 8-44 shows the shows E(6), Fe p(6), and Fjy[gjgi(6) versus 6. 

If the reaetor is modeled as a tank-in-series (TIS) system, how many tanks are needed to represent this reaetor ... 

This chapter develops the techniques needed to analyze multiple and complex reactions in stirred tank reactors. Physical properties may be variable. Also treated is the common industrial practice of using reactor combinations, such as a stirred tank in series with a tubular reactor, to accomplish the overall reaction. 

Thus, aout/cim = 0.432 for the series combination. A single CSTR with twice the volume has ki ajn = 1. Equation (4.16) gives Uoutlam =0.5 so that the composite reactor with two tanks in series gives the higher conversion. 

Thus, the limit gives the same result as a piston flow reactor with mean residence time t. Putting tanks in series is one way to combine the advantages of CSTRs with the better yield of a PFR. In practice, good improvements in yield are possible for fairly small N. 

Number of tanks in series, N Value of kt to achieve a 1000-fold reduction in concentration Volume of the composite reactor relative to a PFR... 

Example 4.12 used N stirred tanks in series to achieve a 1000-fold reduction in the concentration of a reactant that decomposes by first-order kinetics. Show how much worse the CSTRs would be if the 1000-fold reduction had to be achieved by dimerization i.e., by a second order of the single reactant type. The reaction is irreversible and density is constant. 

Example 4.13 treated the case of a piston flow reactor inside a recycle loop. Replace the PER with two equal-volume stirred tanks in series. The reaction remains first order, irreversible, and at constant density. 

A continuous polymerization train consisting of two stirred tanks in series is used to copolymerize styrene, rx = 0.41, and acrylonitrile, vy = 0.04. The flow rate to the first reactor is 3000 kg/h and a conversion of 40% is expected. Makeup styrene is fed to the second reactor and a conversion of 30% (based on the 3000 kg/h initial feed) is expected there. What should be the feed composition and how much styrene should be fed to the second reactor if a copolymer containing 58 wt% styrene is desired ... 

Real reactors can have 0 < cr < 1, and a model that reflects this possibility consists of a stirred tank in series with a piston flow reactor as indicated in Figure 15.1(a). Other than the mean residence time itself, the model contains only one adjustable parameter. This parameter is called the fractional tubularity, Xp, and is the fraction of the system volume that is occupied by the piston flow element. Figure 15.1(b) shows the washout function for the fractional tubularity model. Its equation is... 

The Tanks-in-Series Model. A simple model having fuzzy first appearance times is the tanks-in-series model illustrated in Figure 15.2. The washout function is... 

FIGURE 15.2 The tanks-in-series model (a) physical representation (b) washout function. 

Example 15.14 Solve Zwietering s differential equation for the residence time distribution corresponding to two stirred tanks in series. Use second-order kinetics with ai ki = 5. 

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