Mass transfer steps

Because this mass-transfer step is so vital, conventional dead-end operation of ultrafilters is veiy rare. There are many ways to depolarize a membrane. Cross-flow is by far the most common. Turbulent flow is more common than laminar flow. 

The difficulty disappears when the mixing and mass transfer steps are fast compared with the reaction steps. The contents of the reactor remain perfectly mixed even while new ingredients are being added. Compositions and reaction rates will be spatially uniform, and a flow term is simply added to the mass balance. Instead of Equation (2.30), we write... 

Solution Under the assumption of intrinsic kinetics, all mass transfer steps are eliminated, and the reaction rate is determined by Steps 4-6. The simplest possible version of Steps 4-6 treats them all as elementary, irreversible reactions ... 

The appearance of this heterogeneous form for the rate expression reflects the presence of a mass transfer step in series with the reaction step. If the parameter values are known, this ODE for bi i) can be integrated subject to the initial condition that bi=(bi)o at t = 0. The result can then be used to find a (f). 

From a reaction engineering viewpoint, semiconductor device fabrication is a sequence of semibatch reactions interspersed with mass transfer steps such as polymer dissolution and physical vapor deposition (e.g., vacuum metallizing and sputtering). Similar sequences are used to manufacture still experimental devices known as NEMS (for nanoelectromechanical systems). 

It is important to appreciate the fact that when two or more reaction rates are to be compared and/or combined, they should be defined in the same manner. For instance, if it is required to combine a mass transfer step and a reaction step, then the rates corresponding to both should be defined in an identical manner. Since the mass transfer rate by definition is the flow of material per unit time normal to a unit surface... 

Next, as an example of combining nonlinear rate expressions one could consider the same reaction as before, assuming that the reaction is of the second order with respect to the gas phase reactant g. In this case, for the mass transfer step, one has... 

To be able to combine the chemical step with the mass transfer steps in simple fashion, we must replace the above awkward rate equation with a first-order approximation, as follows ... 

Mass transfer steps are essential in any multiphase reactor because reactants must be transferred from one phase to another. When we consider other multiphase reactors in later chapters, we will see that mass transfer rates fiequently control these processes. In this chapter we consider a simpler example in the catalytic reactor. This is the first example of a multiphase reactor because the reactor contains both a fluid phase and a catalyst phase. However, this reactor is a very simple multiphase reactor because the catalyst does not enter or leave the reactor, and reaction occurs only by the fluid reacting at the catalyst surface. 

Essential mass transfer steps between phases always accompany reaction steps, and these frequently control the overall rate of the chemical reactions. 

If the second reactant 5 is in high concentration (Hquids have much hi er densities than gases even at high pressures) and the reaction is not limited by its mass transfer, then this becomes a pseudo-first-order reaction r" = k"CA. If all mass transfer steps are fast compared to the reaction, then this problem would simplify to be identical to the tube waU catalytic reactor, which gave... 

Most industrial reactors involve multiple phases, and mass transfer steps between phases are essential and usually control the overall rates of process. 

Due to the ionic nature of cephalosporin molecules, the interfacial chemical reaction may in general be assumed to be much faster than the mass transfer rate in the carrier facilitated transport process. Furthermore, the rate controlling mass transfer steps can be assumed to be the transfer of cephalosporin anion or its complex, but not that of the carrier. The distribution of the solute anion at the F/M and M/R interfaces can provide the equilibrium relationship [36, 69]. The equilibrium may be presumably expressed by the distribution coefficients, mf and m at the F/M and M/R interfaces, respectively and these are defined as... 

In three-phase systems, two interfaces exist, i.e. the gas bubble-liquid interface and the liquid-solid interface and thus, four mass-transfer steps and the corresponding films are involved in the process (Figure 3.3)... 

The process of drying while applying spraying solution is a critical unit operation. This mass transfer step was previously discussed. The temperature, humidity, and volume of the process air determines the drying capacity. If the... 

In Eqn. 5.3-1, rj is the effectiveness factor of the catalyst with respect to the dissolved gaseous reactant and the temperature of the outer surface. The rate of reaction within the catalyst pores is comprised in rj. R is the reaction rate expressed in moles of gaseous reactant, A, per unit of bubble-free liquid, per unit of time. Reaction is irreversible. In equation (1) it has not been assumed that the gas is pure gas A, its concentration in the bubbles being Cg. Also, Henry s law for the gas is assumed and written as in Eqn. 5,3-4. Using Henry s law, Eqn. 5.3-4, the intermediate concentrations (Cs, CL) can be eliminated using the above system of equations. This provides an expression of the global rate in terms of an apparent constant, ko, that contains the various kinetic and mass transfer steps. Therefore, the observed rate can be written as ... 

In these types of laboratory reactor, the flow of the liquid is very carefully controlled so that, although the mass transfer step is coupled with the chemical reaction, the mass transfer characteristics can be disentangled from the reaction kinetics. For some reaction systems, absorption of the gas concerned may be studied as a purely physical mass transfer process in circumstances such that no reaction occurs. Thus, the rate of absorption of C02 in water, or in non-reactive electrolyte solutions, can be measured in the same laboratory contactor as that used when the absorption is accompanied by the reaction between C02 and OH ions from an NaOH solution. The experiments with purely physical absorption enable the diffusivity of the gas in the liquid phase DL to be calculated from the average rate of absorption per unit area of gas-liquid interface NA and the contact time te. As shown in Volume 1, Chapter 10, for the case where the incoming liquid contains none of the dissolved gas, the relationship is ... 

As Fig. 4.15 demonstrates, the two mass transfer steps, gas to liquid and liquid to solid, and then the chemical reaction, take place in series. This means that in the steady state each must proceed at the same rate as the overall process. Continuing then on the basis of unit volume of dispersion, and using the reactant concentrations shown in Fig. 4.15, with the gas-liquid and liquid-solid film mass transfer coefficients kL and ks shown in Fig. 4.20, the overall rate 91, may be written as ... 

Fig. 4.22. Trickle-bed reactor, (a) Schematic diagram showing individual mass transfer steps for a hydrogenation process (b) profile of dissolved hydrogen in the liquid flowing down the column, calculated in Example 4.8...

Immobilization can influence biocatalytic reactions in two different ways (i) through a change in effective reaction parameters (pH value, charge density, and hydro-phobicity) or (ii) through a change in the rate-limiting step away from the biocatalytic step towards either preceding or successive mass-transfer steps. 

Use a test method that has been validated to ensure correct identification and selective, accurate measurement of the analyte of interest Establish the bias associated with the mass transfer steps (digestion, extraction, evaporation, derivatisa-tion etc.) by measuring the recovery of spikes and by... 

These results could suggest that what has been traditionally been described as "biphasic" behavior may reflect a combination of chemical reaction and mass transfer effects, with each limiting xylan reaction and removal at different stages or modes of operation. This effect might be better described by a model that incorporates reaction of solids to form soluble species as a function of temperature and acid concentration coupled with a second mass transfer step that is affected by flow. On this basis, we plan to investigate whether the pore leaching model could be simplified and adapted in this way to better describe hemicellulose hydrolysis. 

The heart of the pilot plant study normally involves varying the speed over two or three steps with a given impeller diameter. The analysis is done on a chart, shown in Fig. 36. The process result is plotted on a log-log curve as a function of the power applied by the impeller. This, of course, implies that a quantitative process result is available, such as a process yield, a mass transfer absorption rate, or some other type of quantitative measure. The slope of the line reveals much information about likely controlling factors. A relatively high slope (0.5-0.8) is most likely caused by a controlling gas-liquid mass transfer step. A slope of 0, is usually caused by a chemical reaction, and a further increase of power is not reflected in the process improvement. Point A indicates where blend time has been satisfied, and further reductions of blend time do not improve the process performance. Intermediate slopes on the order of 0.1-0.4, do not indicate exactly which mechanism is the major one. Possibilities are shear rate factors, blend time requirements, or other types of possibilities. 

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