Recycle continuous-flow model

A real continuous-flow stirred tank will approximate a perfectly mixed CSTR provided that tmix h/i and tmix i. Mixing time correlations are developed using batch vessels, but they can be applied to flow vessels provided the ratio of throughput to circulatory flow is small. This idea is explored in Section 4.5.3 where a recycle loop reactor is used as a model of an internally agitated vessel. 

Methane can be oxidatively coupled to ethylene with very high yield using the novel gas recycle electrocatalytic or catalytic reactor separator. The ethylene yield is up to 85% for batch operation and up to 50% for continuous flow operation. These promising results, which stem from the novel reactor design and from the adsorptive properties of the molecular sieve material, can be rationalized in terms of a simple macroscopic kinetic model. Such simplified models may be useful for scale up purposes. For practical applications it would be desirable to reduce the recycle ratio p to lower values (e.g. 5-8). This requires a single-pass C2 yield of the order of 15-20%. The Sr-doped La203... 

The following scheme was suggested as a possible network model to describe a real electrolytic processes. Reactors 1 and 2 are continuous-flow stirred-tank electrolytic reactors (CSTER), reactor 3 is a reactor for the recycling electrolyte and reactor 4 is collector in which no electrolytic process takes place. 

Modify the above program to model the case of a discontinuous five-stage extraction cascade, in which a continuous flow of aqueous phase L is passed through the cascade. The solvent is continuously recycled through the cascade and also through a solvent holding tank, of volume Vs, as shown below. This problem of a stagewise discontinuous extraction process has been solved analytically by Lelli (1966). 

The second mode of CSTR operation is that used by Thien (17) and by Li and Shrier (10). Here, both the external phase and the LM emulsion are in a continuous flow mode. The reactor effluents are sent to gravity settlers where the exterior phase is separated from the emulsion phase. The emulsion phase is then demulsified to recover the product followed by remulsification and recycle back to the reactor. Hatton and Wardius (48) have developed the advancing front model for the analysis of such staged LM operations. Thien (17) employed this scheme to remove the amino acid L-phenylalanine from simulated fermentation broth (dilute aqueous solution). 

Recycling effluent through a thin-film continuous flow electrophoresis (CFE) chamber allows virtually complete separation of a binary feed with negligible dilution of products and permits throughput to be increased by 0(100-10,000) over present thin-film CFE devices. An approximate model of recycle CFE is developed for the high Peclet number regime and solved analytically. The solution is used to characterize the behavior of a recycle CFE device. 

As the main responsible for the changes in the material balance, the chemical reactor must be modelled accurately from this point of view. Basic flowsheeting reactors are the plug flow reactor (PFR) and continuous stirred tank reactor (CSTR), as shown in Fig. 3.17. The ideal models are not sufficient to describe the complexity of industrial reactors. A practical alternative is the combination of ideal flow models with stoichiometric reactors, or with some user programming. In this way the flow reactors can take into account the influence of recycles on conversion, while the stoichiometric types can serve to describe realistically selectivity effects, namely the formation of impurities, important for separations. Some standard models are described below. 

Continuous flow stirred-tank reactors are normally just what the name implies tanks into which reactants flow and from which a product stream is removed on a continuous basis. CFSTRs, CSTRs, C-star reactors, and backmix reactors are only a few of the names applied to the idealized stirred-tank flow reactor model. We will use the letters CSTR in this book. The virtues of a stirred-tank reactor lie in its simplicity of construction and the relative ease with which it may be controlled. These reactors are used primarily for carrying out liquid phase reactions in the organic chemicals industry, particularly for systems that are characterized by relatively slow reaction rates. If it is imperative that a gas phase reaction be carried out under efficient mixing conditions similar to those found in a stirred-tank reactor, one may employ a tubular reactor containing a recycle loop. At sufficiently high recycle rates, such systems approximate the behavior of stirred tanks. In this section we are concerned with the development of design equations that are appropriate for use with the idealized stirred-tank reactor model. 

Models for a continuous reactor without recycle will be identical with those developed for the batch reactor. We will therefore confine ourselves to a continuous reactor with recycle. Although the low conversion per pass make the hydrodynamic classification of the reactor of little significance, it will still be convenient to develop the continuous reactor model on the basis of a plug-flow reactor. 

For example, different fermentation schemes have been developed for the production of ethanol. Conventional batch, continuous, cell recycle and immobilized cell processes, as well as membrane, extraction and vacuum processes, which selectively remove ethanol from the fermentation medium as it is formed, were compared on identical bases using a consistent model for yeast metabolism (Maiorella et al., 1984). The continuous flow stirred tank reactor (CSTR) with cell recycle, tower and plug flow reactors all showed similar cost savings of about 10% compared to batch fermentation. Cell recycle increases cell density inside the fermentor, which is important in reducing fermentation cost. 

In this example, a fluidised biofilm sand bed reactor for nitrification, as investigated by Tanaka et al. (1981), is modelled as three tanks-in-series with a recycle loop (Fig. 1). With continuous operation, ammonium ion is fed to the reactor, and the products nitrite and nitrate exit in the effluent. The bed expands in volume because of the constant circulation flow of liquid upwards through the bed. Oxygen is supplied external to the bed in a well-mixed gas-liquid absorber. 

The older modular simulation mode, on the other hand, is more common in commerical applications. Here process equations are organized within their particular unit operation. Solution methods that apply to a particular unit operation solve the unit model and pass the resulting stream information to the next unit. Thus, the unit operation represents a procedure or module in the overall flowsheet calculation. These calculations continue from unit to unit, with recycle streams in the process updated and converged with new unit information. Consequently, the flow of information in the simulation systems is often analogous to the flow of material in the actual process. Unlike equation-oriented simulators, modular simulators solve smaller sets of equations, and the solution procedure can be tailored for the particular unit operation. However, because the equations are embedded within procedures, it becomes difficult to provide problem specifications where the information flow does not parallel that of the flowsheet. The earliest modular simulators (the sequential modular type) accommodated these specifications, as well as complex recycle loops, through inefficient iterative procedures. The more recent simultaneous modular simulators now have efficient convergence capabilities for handling multiple recycles and nonconventional problem specifications in a coordinated manner. 

In this section the model for a continuous evaporative crystallizer is discussed. The crystallizer is of the draft tube baffled (DTB) type and is equiped with a fines removal system consisting of a large annular zone on the outside of the crystallizer (see Figure 1). In order to vary the dissolved fines flow without changing the cut-size of the fines removal system, the flow in the annular zone is kept constant and the flow in the dissolving system is varied by changing the recycle flow rate. The model assumptions are ... 

One might intuitively expect that infinite recycle rates associated with a system as described by eqn. (61) would produce a completely well-mixed volume with concentration independent of location. This is indeed so and under these conditions, the performance tends to that of an equal sized CSTR. At the other extreme, when R is zero, PFR performance pertains. Fractional conversions at intermediate values of R may be determined from Fig. 14. The specific form of recycle model considered is thus seen to be continuously flexible in describing flow mixing between the PFR and CSTR extremes just as was the tanks-in-series model. The mean and variance of this model are given by eqns. (62) and (63) and these may be used for moments matching purposes of the type illustrated in Example 6. 

Continuous lactic acid production from whey permeate is carried out in a process that consists of three separate operations in (1) a bioreactor, (2) an ultrafiltered (UF) model, and (3) an ED cell. With the UF process, recycling of all or part of the biomass is achieved. It is also possible to separate low molecular weight metabolites, such as sodium lactate, resulting from lactose fermentation. This product can then be extracted and concentrated continuously by ED. A disadvantage of continuous lactic acid production is, however, that it tends to clog the ultrafiltration membranes, which restricts permeate flow (Bazinet, 2004). 

A recycle reactor is a mathematical model describing a steady plug-flow reactor where a portion of the outlet is recycled to the Met, as shown schematically in Figure 9.5. Although this reactor configuration is rarely used in practice, the recycle reactor model enables us to examine the effect of mixing on the operations of continuous reactors. In some cases, the recycle reactor is one element of a complex reactor model. Below, we analyze the operation of a recycle reactor wifii multiple chemical reactions, derive its design equations, and discuss how to solve fiiem. 

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