Mix Reactors in Series

Taking the terms with an exponential term to solve for 2 and the terms without an exponential term to solve for results in 

An estuary or river will not be completely mixed, but will have some mixing that goes with the convective transport velocity. Complete mix reactors-in-series respond to a first-order reaction in the manner given in Example 6.5. 

EXAMPLE 6.5 Steady-State reactors-in-series with a first-order sink 

From equation (E6.5.6) we can see that, for any numbered reactor n, the concentration leaving the reactor, C would be 

In the next example, we will compare a complete mixed reactor with a first-order degradation reaction at steady state for a plug flow reactor and a series of smaller complete mixed reactors. 

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Fig. 8. Combined flow reactor models (a) parallel flow reactors with longitudinal diffusion (diffusivities can differ), (b) internal recycle—cross-flow reactor (the recycle can be in either direction), comprising two countercurrent plug-flow reactors with intercormecting distributed flows, (c) plug-flow and weU-mixed reactors in series, and (d) 2ero-interniixing model, in which plug-flow reactors are parallel and a distribution of residence times dupHcates that...

The reaction takes place at low temperature (40-60 °C), without any solvent, in two (or more, up to four) well-mixed reactors in series. The pressure is sufficient to maintain the reactants in the liquid phase (no gas phase). Mixing and heat removal are ensured by an external circulation loop. The two components of the catalytic system are injected separately into this reaction loop with precise flow control. The residence time could be between 5 and 10 hours. At the output of the reaction section, the effluent containing the catalyst is chemically neutralized and the catalyst residue is separated from the products by aqueous washing. The catalyst components are not recycled. Unconverted olefin and inert hydrocarbons are separated from the octenes by distillation columns. The catalytic system is sensitive to impurities that can coordinate strongly to the nickel metal center or can react with the alkylaluminium derivative (polyunsaturated hydrocarbons and polar compounds such as water). 

Figure 6.4 Notation for a system of N equal-size mixed reactors in series.

Complete mix reactors Plug flow or complete mix reactors in series... 

EXAMPLE 6.6 Degradation in various systems modeled by one complete mixed reactor, one plug flow reactor, and several complete mixed reactors-in-series... 

The compound formaldehyde is biodegrading in several systems simultaneously (1) a lake, modeled as a complete mix reactor (2) an estuary, modeled as three complete mixed reactors in series (3) a large river, modeled as 10 complete mixed reactors in series, and a small stream, modeled as a plug flow reactor. What is the nondimensional reaction/residence time, k p, that is required for each of these systems to reach a degradation of 50%, 90%, 99%, and 99.9% ... 

For a single complete mix reactor, we found that there is little difference in the nondimensional response to a front versus a pulse. This will not be the case for a series of complete mix reactors. Let us assume that we have four complete mix reactors in series, each with a volume Yi and a residence time, tn, as illustrated in Figure 6.5. Then, for a pulse input, we have the boundary conditions ... 

Complete Mix Reactors-in-Series. The number of complete mix reactors-in-series that should be applied to fit the tracer curve can be found from an application of equation (6.13) ... 

The complete mix reactor-in-series model resulted in degradation to 4% of the initial trichloroethylene concentration. 

Deflnitions. The basic elements of Markov chains associated with Eq.(2-24) are the system, the state space, the initial state vector and the one-step transition probability matrix. Considering refs.[26-30], each of the elements will be defined in the following with special emphasize to chemical reactions occurring in a batch perfectly-mixed reactor or in a single continuous plug-flow reactor. In the latter case, which may simulated by perfectly-mixed reactors in series, all species reside in the reactor the same time. 

The Danckwerts model [92] regards a plug flow reactor and a ideal back-mixed reactor in series (Fig. 1.23). In case A the pipe reactor is preceded by the stined tank and in case B the reverse is the case. 

Another way of assessing the effect of axial dispersion is to use the model of n perfectly mixed reactors in series. Since the theory for dispersion in packed beds predicts Pe = 2 if the gas is mixed between each layer of particles, n L/dp. For n > 10, the conversion is almost the same as for a plug-flow reactor, as was shown in Figure 3.9. 

Figure 10.2.b-2 Economic optimum choice of number of perfectly mixed reactors in series. 

Consider two perfectly mixed reactors in series. For a given total volume, determine optimal distribution of the sub-volumes for (a) first-order reaction, (b) second-order reaction. 

Consider a number of mixed reactors in series, with a liquid containing reactant B flowing through it. A gas, containing reactant A is introduced in each reactor. 

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