Reactor models continuous well-stirred model

In the second model (Fig. 2.16) the continuous well-stirred model, feed and product takeoff are continuous, and the reactor contents are assumed to he perfectly mixed. This leads to uniform composition and temperature throughout. Because of the perfect mixing, a fluid element can leave at the instant it enters the reactor or stay for an extended period. The residence time of individual fluid elements in the reactor varies. 

Solid catalysts can be conveniently studied in loop reactors, which allow measuring the rates by difference measurement across the catalyst bed. When operated continuously, they usually can be modelled as well-stirred tanks. Here the case of catalyst deactivation is studied. 

Stripper Remove of adsorbed hydrocarbons on the catalyst Continuously stirred-tank reactor (CSTR) with well-mixed model... 

Mixing Models. The assumption of perfect or micro-mixing is frequently made for continuous stirred tank reactors and the ensuing reactor model used for design and optimization studies. For well-agitated reactors with moderate reaction rates and for reaction media which are not too viscous, this model is often justified. Micro-mixed reactors are characterized by uniform concentrations throughout the reactor and an exponential residence time distribution function. 

A reactor model based on solid particles in BMF may be used for situations in which there is deliberate mixing of the reacting system. An example is that of a fluid-solid system in a well-stirred tank (i.e., a CSTR)-usually referred to as a slurry reactor, since the fluid is normally a liquid (but may also include a gas phase) the system may be semibatch with respect to the solid phase, or may be continuous with respect to all phases (as considered here). Another example involves mixing of solid particles by virtue of the flow of fluid through them an important case is that of a fluidized bed, in which upward flow of fluid through the particles brings about a particular type of behavior. The treatment here is a crude approximation to this case the actual flow pattern and resulting performance in a fluidized bed are more complicated, and are dealt with further in Chapter 23. 

The CSTR model, on the other hand, is based on a stirred vessel with continuous inflow and outflow (see Fig. 1.2). The principal assumption made when deriving the model is that the vessel is stirred vigorously enough to eliminate all concentration gradients inside the reactor (i.e., the assumption of well stirred). The outlet concentrations will then be identical to the reactor concentrations, and a simple mole balance yields the CSTR model equation ... 

Fig. 2.24. Model of a poorly agitated continuous stirred-tank reactor (a) Flow model fraction / of flow v by-passes only a fraction w of tank volume V is well-stirred (b) Equivalent C, curves for pulse input...

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 continuous stirred-tank reactor (CSTR) is a mathematical model that describes an important class of continuous reactors—continuous, steady, well-agitated tank reactors. The CSTR model is based on two assumptions ... 

In an attempt to explain the horatian oscillations due to the B-Z reaction in a well-stirred continuous flow reactor reported by R. A. Schmitz et al., Iwamoto and Seno (1981) proposed a reaction model and a two dimensional mathematical model. 

This reaction has been studied using batch reactors, perfectly stirred continuous reactors, tubular continuous reactors, BENSON type reactors, wall-less reactors and shock tubes. The reaction has been carried out at temperatures between 700 and 1300 K, at pressures of 0.1 Pa to 10 Pa and at reaction times of 10 s to 10 s. The effects of the nature and of the area of the reactor walls as well as those of various additives have also been studied. The diversity of the studies carried out by a dozen teams throughout the world, the particularly widespread range of operating conditions (600 K for the temperature, which represents 11 orders of magnitude for the rate of initiation, 8 orders of magnitude for the pressure and reaction duration) make the pyrolysis of neopentane into a model radical reaction. 

The configuration of the tissue engineering bioreactor and the culturing conditions can vary widely. One example is the well-stirred bioreactor where several scaffolds seeded with cells are fixed on needles and cultured in continuously stirred media. This is the so-called dynamic tissue culture method that has been shown to promote both cell proliferation and ECM component deposition in bioartificial tissues [137-139]. However, the aforementioned multiscale model can handle other reactor configurations by appropriately changing the boundary condition [2] of the diffusion-reaction problem. 

In order to reduce the number of free parameters (15 in the original model) as much as possible while still allowing for chaotic dynamics, we shall consider in the sequel a simplified version of the reactions in which k-2 = k-3 = k-4 = 0. The last two relations are also equivalent to supposing that A2 and A3 are continuously removed from the reactor. The rate equations in this limit read, assuming an ideal mixture and a well-stirred 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. 

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