of the reactor frequently, if not always, determines the economics and, hence, the commercial feasibility of the process. To achieve high efficiency of the reactor, it must be designed according to the specific reaction system concerned, namely, the kinetics of the reaction.

Chemical reactors have also been classified according to the design features. There are tank reactors, tubular reactors, tower reactors, and fluidized reactors. Most of these reactors have found their uses in biological and biochemical processes. The most popular reactor used in biological and biochemical processes has been the tank reactor. The majority of the industrial fermentation process, waste products-treatment processes, and food-cooking processes use tank reactors. For factories making a repertoire ofhun-dreds of products each at a small scale, the tanks are versatile and flexible, and batch operation is the one of choice. However, a batch process is inherently harder to control than a continuous one, even with the advent of computercoupled control systems. The right decision between batch and continuous operation depends on the relative magnitude of labor and capital costs. What is best for a developed country is not necessarily good for a developing one.

In the following, the performances of distinctive reactors in continuous operation are discussed. For the sake of simplicity in mathematical analyses of the reactor performances, these reactors can be categorized into two ideal reactors: well-mixed (back-mixed or stirred tank) and plug-flow reactors, according to the flow patterns in the reactors. In a well-mixed reactor, it is assumed that there is no concentration distribution in the reactor; if the process is continuous, there is no distribution of residence time among the elements of fluid (or substrate) leaving the reactor tank. Under such a condition (complete mixing), the rate is constant throughout the reactor, and there is no need for a differential equation describing the change in concentration or conversion between the inlet and outlet streams. A simple material balance is sufficient. In a plug-flow reactor (wherein no longitudinal mixing but complete radial mixing is assumed), the concentration of the substrate varies longitudinally and so does the rate of the reaction (unless the reaction is of zero order with respect to the substrate concentration). In such a case, a differential equation is needed to express the performance of the reactor, and the performance of the reactor can be obtained by integrating the equation. Due to such differences in reactor features for well-mixed and plug-flow reactors, other things being equal, when a reaction is substrate inhibitory, it is desirable to use a well-mixed reactor. On the other hand, if the reaction is product inhibitory, it is desirable to use a plug-flow reactor. In most occasions, the selection of either a well-mixed or a plug-flow reactor depends mainly on the kinetics of the reaction concerned. In general, if a first-order enzymatic reaction is free of substrate and product inhibition, the amount of enzyme required for 99% conversion in a well-mixed reactor is 21 times that required for a plug-flow reactor. The ratio of the amount of the enzyme required (ECSTR/EPFR) becomes four to one when 90% conversion is desired. Consequently, other things being equal, for a first-order enzymatic reaction, it is advisable to use a plug-flow reactor rather than a well-mixed reactor.

The growth of cells is a self-catalytic process. The plot of cell growth rate versus cell concentration follows a bell-shaped curve with an optimum. In such processes, if the reaction rate in the reactor never reaches the maximum rate, theoretically the use of one single well-mixed reactor is superior to the use of a plug-flow reactor. This is based on the comparison of the efficiency of the reactors in carrying out a specific conversion under identical environmental conditions. If the cultivation of cell tissue is the purpose of a fermentation process, either in a batch or continuous process, the rate of cell growth in the fermenter usually does not exceed the maximum rate during the process. This is one of the reasons why a mechanically stirred-tank reactor with air dispersed into liquid medium by sparging is the most typical industrial fermenter, although the production of secondary metabolites and enzymes from fermentation processes usually includes the growth of microorganisms beyond the exponential phase. This type of process usually warrants a two-stage process, and theoretically the use of a stirred-tank reactor followed by a plug-flow reactor is most desirable (33). The most obvious difficulty of using a plug-flow reactor is the maintenance of the flow pattern, especially under aeration requirements.

Another aspect of the discussion of reactor kinetics is the use of immobilized enzymes in various reactor types for biocatalytic conversions. Free enzymes can be used in these reactors, except that a rather large amount of energy will have to be spent on the retention of enzymes usually through the use of ultrafilters. Basically, enzymes are expensive materials; because they are catalysts, their reusability is logical, provided it is economical to do so. Immobilization of enzymes seems to be the answer to this question. Although some of the immobilization processes are quite elaborate and potentially expensive, many are quite simple and effective (8,10).

The efficiency of a reactor used for immobilized enzymes depends on the following factors: mass-transfer resistances (external and internal), enzyme-loading factor, enzyme stability, substrate contact efficiency, and so on. In selecting reactors to house immobilized enzymes, these factors must be considered. As an example, the selection of a reactor for glucose isomerase is discussed. There are three types of immobilized glucose isomerase: immobilized cell-free glucose isomerase (8,9,34,35), immobilized cells with intracellular glucose isomerase (10), and free cells with intracellular glucose isomerase (36,37). As has been pointed out for immobilized glucose isomerase reactors (35) and as a general rule, for higher-order reactions or Michaelis-Menten kinetics with a high value of KM, when high conversion is desired, much more enzyme is required in the continuous stirred-tank reactor than in the plug-flow reactor. The choice of a plug-flow reactor is also partly due to the fact that the intrinsic reaction kinetics there are equilibrium controlled. The Keg value of the isomerization reaction is close to the value of one at most operating temperatures. The concentration of product cannot be neglected in the rate expression. Applying reversible Michaelis-Menten kinetics to glucose-fructose conversion, the resulting rate expression is

where K is equilibrium constant (PIS at equilibrium), S is the glucose concentration, P is the fructose concentration, Km and KP are constants, v is the reaction rate, and VM is equal to (£)totai times k, the maximum reaction rate. This rate expression can be looked upon as one derived from the product-inhibition model, and, as discussed before, the use of a plug-flow reactor is more efficient for this type of reaction. In published data on immobilized glucose isomerase, mass-transfer resistances were not found to be limiting factors. Both internal and external resistances were found to be negligible. In accordance with this, it has been found that the activation energy of immobilized and soluble glucose isomerase are close, 15.7 and 14.5 kcal/g ~ mol, respectively (35). Due to the lack of mass-transfer resistances in this case, it is advisable to use an immobilized whole-cell system instead of an immobilized enzyme system, provided that the cells are fully induced and are high in glucose isomerase concentration (8).

In batch reactors, concentrations of reactant(s) and product(s) are a function of time. So batch processes are transient processes. Continuous processes, on the other hand, can be in either transient or steady state. There are two types of steady state in continuous operations: volumetric steady state and concentration steady state. Other things being equal, a volumetric steady state is a prerequisite for reaching a concentration steady state. Mathematically, steady state means that the variable (volume or concentration) is not changing with respect to time, dV/dt or dC/dt = 0. In operation, volume invariance can be achieved mechanically; for biological systems, concentration steady state, such as constant cell concentration, is difficult to achieve. In reality, dC/dt = + or —10% of the mean is a good criterion for reaching the steady state of cell cultures (38).

Deviations from ideal reactors are common in practice. Many real reactors behave in between a well-mixed and a plug-flow reactor. A column reactor is closer to a plug-flow reactor, a tank reactor to a well-mixed reactor, and a fluidized-bed reactor is a hybrid of the two ideal reactors. A series of well-mixed reactors can be operated to perform like a plug-flow reactor. An extruder is closer to a plug-flow than a well-mixed reactor. These arguments can be evaluated by looking at the residence time distributions of various reactors.

An extruder is like a pump. It is a versatile reactor, capable of performing other operations in concert with its pumping function. For instance, extruders can be used as a mixer and as reactors to make pasta, pet foods, instants, confectioneries, and snacks and can be used to determine spices. Extrusion is a typical continuous process that has the potential of steady-state operation with high productivities. The engineering analysis of an extrusion process is a difficult task. Chemical and physical changes of materials that occur in extruders are the results of solid (powdery) or semisolid interactions under limited-moisture contents. The initiation, or activation, of such changes can be done by thermal energy input or mechanical energy input. In addition to changes at the molecular level, extruders are also most effective in rendering size reductions to affect changes at the particle level. All these changes are important in determining the product quality, especially in texture-related features. The kinetics of chemical and physical changes of starch and other food ingredients in extrusion process are difficult to study because of the highly nonideal environment, as opposed to gas or dilute solution, and the complication of transport processes (heat, mass, and momentum transfers) coupling with reaction kinetics. The idea of predicting the performance of an extruder by using transport coupled kinetic models is a desirable one. The task of correlating product qualities, such as specific texture, flavor, or color, to the performance of an extruder is a difficult one. Certainly innovative ideas are needed to achieve such a goal.

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