Reactors with Mass Transfer Limitations

The MATLAB program requires you to write a function (m-file) that calculates the righthand side, given the input, which are the flow rates of all species. Thus, to solve the problem you would use the variables 

The function will have available to it the accumulated reactor volume Vr, and the local value = 1. 3 at the same reactor volume. You then calculate the concentrations at that 

The rates of reaction are then evaluated, and the function returns the numerical value of the right-hand side. You can complete this example by doing Problem 8.7 at the end of the chapter. 

The same considerations apply when using FEMLAB. The variables being solved for are now Fa, Fb, and Fc. In Options/Expressions/Subdomain Expressions you define equations for new variables ca, cb, and cc representing Eq. (8.42), and then use the same reaction rate expression (in terms of ca). The rest of the solution proceeds as before  

CHEMICAL REACTORS WITH MASS TRANSFER LIMITATIONS 

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CHEMICAL REACTORS WITH MASS TRANSFER LIMITATIONS... 

Reactor with mole changes and variable density, Chapter 8, p. 130. Chemical reactors with mass transfer limitations, Chapter 8, p. 131. Continuous stirred-tank reactors. Chapter 8, pp. 135, 136. 

Simulations show that, in order to achieve the same conversion degree of a fluidized bed membrane reactor without mass transfer limitations, the membrane area installed in the reactor needs to be increased 2.4 times with respect to the case without limitations as reported in the figure. Figure 10.10 shows that a decrease of 10 times in the mass transfer limitations is enough to reach the limit conversion required. 

In principle, the catalytic converter is a fixed-bed reactor operating at 500—620°C to which is fed 200—3500 Hters per minute of auto engine exhaust containing relatively low concentrations of hydrocarbons, carbon monoxide, and nitrogen oxides that must be reduced significantly. Because the auto emission catalyst must operate in an environment with profound diffusion or mass-transfer limitations (51), it is apparent that only a small fraction of the catalyst s surface area can be used and that a system with the highest possible surface area is required. 

Heat and mass transfer limitations are rarely important in the laboratory but may emerge upon scaleup. Batch reactors with internal variations in temperature or composition are difficult to analyze and remain a challenge to the chemical reaction engineer. Tests for such problems are considered in Section 1.5. For now, assume an ideal batch reactor with the following characteristics ... 

Many semibatch reactions involve more than one phase and are thus classified as heterogeneous. Examples are aerobic fermentations, where oxygen is supplied continuously to a liquid substrate, and chemical vapor deposition reactors, where gaseous reactants are supplied continuously to a solid substrate. Typically, the overall reaction rate wiU be limited by the rate of interphase mass transfer. Such systems are treated using the methods of Chapters 10 and 11. Occasionally, the reaction will be kinetically limited so that the transferred component saturates the reaction phase. The system can then be treated as a batch reaction, with the concentration of the transferred component being dictated by its solubility. The early stages of a batch fermentation will behave in this fashion, but will shift to a mass transfer limitation as the cell mass and thus the oxygen demand increase. 

Like enzymes, whole cells are sometime immobilized by attachment to a surface or by entrapment within a carrier material. One motivation for this is similar to the motivation for using biomass recycle in a continuous process. The cells are grown under optimal conditions for cell growth but are used at conditions optimized for transformation of substrate. A great variety of reactor types have been proposed including packed beds, fluidized and spouted beds, and air-lift reactors. A semicommercial process for beer used an air-lift reactor to achieve reaction times of 1 day compared with 5-7 days for the normal batch process. Unfortunately, the beer suffered from a mismatched flavour profile that was attributed to mass transfer limitations. 

This is explained by a possible higher activity of pure rhodium than supported metal catalysts. However, two other reasons are also taken into account to explain the superior performance of the micro reactor boundary-layer mass transfer limitations, which exist for the laboratory-scale monoliths with larger internal dimensions, are less significant for the micro reactor with order-of-magnitude smaller dimensions, and the use of the thermally highly conductive rhodium as construction material facilitates heat transfer from the oxidation to the reforming zone. 

When fluid velocities are high relative to the solid, mass transfer is rapid. However, in stagnant regions or in batch reactors where no provision is made for agitation, one may encounter cases where mass transfer limits the observed reaction rate. We should also note that in industrial practice pressure drop constraints may make it impractical to employ the exceedingly high velocities necessary to overcome the mass transfer resistance associated with highly active catalysts. 

Slurry Reactors. Slurry reactors are commonly used in situations where it is necessary to contact a liquid reactant or a solution containing the reactant with a solid catalyst. To facilitate mass transfer and effective catalyst utilization, the catalyst is usually suspended in powdered or in granular form. This type of reactor has been used where one of the reactants is normally a gas at the reaction conditions and the second reactant is a liquid, e.g., in the hydrogenation of various oils. The reactant gas is bubbled through the liquid, dissolves, and then diffuses to the catalyst surface. Obviously mass transfer limitations can be quite significant in those instances where three phases (the solid catalyst, and the liquid and gaseous reactants) are present and necessary to proceed rapidly from reactants to products. 

The use of immobilized cell reactors have shown improved biocatalyst stability, however, the specific rates of desulfurization have been much lower than for suspended cell (stirred) reactors. Mass transfer limitations have been significant resulting in lower rates. Thus, the activity is sacrificed to achieve stability. Further work in this area and improved immobilization matrices can help improve the activity along with the stability. 

Intraparticle Mass Transfer. One way biofilm growth alters bioreactor performance is by changing the effectiveness factor, defined as the actual substrate conversion divided by the maximum possible conversion in the volume occupied by the particle without mass transfer limitation. An optimal biofilm thickness exists for a given particle, above or below which the particle effectiveness factor and reactor productivity decrease. As the particle size increases, the maximum effectiveness factor possible decreases (Andrews and Przezdziecki, 1986). If sufficient kinetic and physical data are available, the optimal biofilm thickness for optimal effectiveness can be determined through various models for a given particle size (Andrews, 1988 Ruggeri et al., 1994), and biofilm erosion can be controlled to maintain this thickness. The determination of the effectiveness factor for various sized particles with changing biofilm thickness is well-described in the literature (Fan, 1989 Andrews, 1988)... 

It is important to be able to identify mass transfer limitations that occur when the reaction rate is high compared with the rate of mass transfer. For a heavily mass transfer limited reaction, preliminary experiments in a non optimised laboratory reactor... 

A rather new concept for biphasic reactions with ionic liquids is the supported ionic liquid phase (SILP) concept [115]. The SILP catalyst consists of a dissolved homogeneous catalyst in ionic liquid, which covers a highly porous support material (Fig. 41.13). Based on the surface area of the solid support and the amount of the ionic liquid medium, an average ionic liquid layer thickness of between 2 and 10 A can be estimated. This means that the mass transfer limitations in the fluid/ionic liquid system are greatly reduced. Furthermore, the amount of ionic liquid required in these systems is very small, and the reaction can be carried in classical fixed-bed reactors. 

Notice that in the mass-transfer-limited region increasing or reducing the concentration of reactant B will make httle difference in the reaction rate (or the reactor productivity) because the concentration of A in the liquid is so small. Likewise, increasing the reactor temperature will not give an exponential increase in reaction rate. The reaction rate may actually decrease with increasing temperature because of a decrease in the equihbrium solubihty of A at the gas-liquid interface. 

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