Nonisothermal effects

Fig. 15. Correlation of effective average slope m of nonisothermal equilibrium line (concentrated part of absorber) equilibrium line concave downward. The...

Problem Solving Methods Most, if not aU, problems or applications that involve mass transfer can be approached by a systematic-course of action. In the simplest cases, the unknown quantities are obvious. In more complex (e.g., iTmlticomponent, multiphase, multidimensional, nonisothermal, and/or transient) systems, it is more subtle to resolve the known and unknown quantities. For example, in multicomponent systems, one must know the fluxes of the components before predicting their effective diffusivities and vice versa. More will be said about that dilemma later. Once the known and unknown quantities are resolved, however, a combination of conservation equations, definitions, empirical relations, and properties are apphed to arrive at an answer. Figure 5-24 is a flowchart that illustrates the primary types of information and their relationships, and it apphes to many mass-transfer problems. 

Nonisothermal hquid-phase processes may be driven by changes in feed temperature or heat addition or withdrawal through a column wall. For these, heats of adsorption and pressure effects are generally of less concern. For this case a suitable energy balance is... 

In order to get a quantitative idea of the magnitude of the effects of these temperature variations on molecular structure and morphology an experimental study was undertaken. Two types of polymerizations were conducted. One type was isothermal polymerization at fixed reaction time at a series of temperatures. The other type was a nonisothermal polymerization in the geometry of a RIM mold. Intrinsic viscosities, size exclusion chromotograms (gpc) and differential scanning calorimetry traces (dsc) were obtained for the various isothermal products and from spatially different sections of the nonisothermal products. Complete experimental details are given below. 

The molecular weight and morphological variations are in themselves interesting. Seeking a quantitative explanation for them, and for the observed MWD effects, is quite challenging however. We have noted, first of all, that in all cases, not just the nonisothermal samples, the MWD is broader than can be predicted by the model developed in a previous section. 

The theory of nonisothermal effectiveness is sufficiently well advanced to allow order-of-magnitude estimates for rj. The analysis requires simultaneous... 

FIGURE 10.3 Nonisothermal effectiveness factors for first-order reactions in spherical pellets. (Adapted from Weisz, P. B. and Hicks, J. S., Chem. Eng. Sci., 17, 265 (1962).)... 

Do an order-of-magnitude calculation for the nonisothermal effectiveness factor. 

In this paper we present a meaningful analysis of the operation of a batch polymerization reactor in its final stages (i.e. high conversion levels) where MWD broadening is relatively unimportant. The ultimate objective is to minimize the residual monomer concentration as fast as possible, using the time-optimal problem formulation. Isothermal as well as nonisothermal policies are derived based on a mathematical model that also takes depropagation into account. The effect of initiator concentration, initiator half-life and activation energy on optimum temperature and time is studied. 

In this paper we formulated and solved the time optimal problem for a batch reactor in its final stage for isothermal and nonisothermal policies. The effect of initiator concentration, initiator half-life and activation energy on optimum temperature and optimum time was studied. It was shown that the optimum isothermal policy was influenced by two factors the equilibrium monomer concentration, and the dead end polymerization caused by the depletion of the initiator. When values determine optimum temperature, a faster initiator or higher initiator concentration should be used to reduce reaction time. 

In order to reduce the disparities in volume or space time requirements between an individual CSTR and a plug flow reactor, batteries or cascades of stirred tank reactors ard employed. These reactor networks consist of a number of stirred tank reactors confiected in series with the effluent from one reactor serving as the input to the next. Although the concentration is uniform within any one reactor, there is a progressive decrease in reactant concentration as ohe moves from the initial tank to the final tank in the cascade. In effect one has stepwise variations in composition as he moves from onfe CSTR to another. Figure 8.9 illustrates the stepwise variations typical of reactor cascades for different numbers of CSTR s in series. In the general nonisothermal case one will also en-... 

ILLUSTRATION 12.4 EFFECTIVENESS FACTOR DETERMINATION FOR A NONISOTHERMAL CATALYST PELLET-EXOTHERMIC REACTION... 

The reactor feed mixture was "prepared so as to contain less than 17% ethylene (remainder hydrogen) so that the change in total moles within the catalyst pore structure would be small. This reduced the variation in total pressure and its effect on the reaction rate, so as to permit comparison of experiment results with theoretical predictions [e.g., those of Weisz and Hicks (61)]. Since the numerical solutions to the nonisothermal catalyst problem also presumed first-order kinetics, they determined the Thiele modulus by forcing the observed rate to fit this form even though they recognized that a Hougen-Watson type rate expression would have been more appropriate. Hence their Thiele modulus was defined as... 

There are several factors that may be invoked to explain the discrepancy between predicted and measured results, but the discrepancy highlights the necessity for good pilot plant scale data to properly design these types of reactors. Obviously, the reaction does not involve simple first-order kinetics or equimolal counterdiffusion. The fact that the catalyst activity varies significantly with time on-stream and some carbon deposition is observed indicates that perhaps the coke residues within the catalyst may have effects like those to be discussed in Section 12.3.3. Consult the original article for further discussion of the nonisothermal catalyst pellet problem. 

Grant and coworkers [8] studied the dehydration kinetics of piroxicam monohydrate using both model-free and model-fitting approaches in an effort to understand the effects of lattice energy and crystal structure. The dehydration kinetics was found to differ when determined under isothermal and nonisothermal conditions. Ultimately, the dehydration behavior of piroxicam monohydrate was determined by details of the crystal structure, which was characterized by an absence of channels and a complicated hydrogen-bonding network, and ab initio calculations proved useful in understanding the structural ramifications of the dehydration process. 

It is obvious that nonisothermal conditions induced by microwave heating lead to very different results from those obtained under conventional heating conditions. In summary microwave effects like superheating, selective heating and hot spots, can all be characterized by temperature gradients ranging from macroscopic to molecular scale dimensions. 

Step 3. Adjust the concentration for a nonisothermal release. The Britter-MacQuaid model provides an adjustment to the concentration to account for nonisothermal release of the vapor. If the original concentration is C, then the effective concentration is given by... 

The chief cases that are the subject of the problems here are zero, first and second order in spheres, slabs and cylinders with sealed flat ends, problems P7.03.03 to P7.03.ll. A summary of calculations of effectiveness is in P7.03.02. The correlations are expressed graphically and either analytically or as empirical curve fits for convenience of use with calculator or computer. A few other cases are touched on L-H type rate equation, conical pores and changes in volume. Nonisothermal reactions are in another section. 

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