Nonisothermal Operations

It may not be realistic to use isothermal operation of a BR as a basis for design, particularly for a reaction that is strongly exothermic or endothermic. Although T may change considerably if left unattended, and may need to be controlled so that it does not go too high or too low, it need not be strictly constant Furthermore, in some cases, there may be advances, firm die point of view of kinetics, if T is allowed to increase in a controlled manner. 

In order to assess the design of both the reactor and the heat exchanger required to control T, it is necessary to use the material balance and the energy balance, together with information on rate of reaction and rate of heat transfer, since there is an interaction between T and /A. In this section, we consider two cases of nonisothermal operation adiabatic (Q = 0) and nonadiabatic (Q = 0). 

In adiabatic operation, there is no attempt to cool or heat the contents of the reactor (that is, there is no heat exchanger). As a result, T rises in an exothermic reaction and falls in an endothermic reaction. This case may be used as a limiting case for nonisothermal behavior, to determine if T changes sufficiently to require the additional expense of a heat exchanger and T controller. 

For an adiabatic system with Q = 0, the energy balance (12.3-16) becomes 

Substituting for (-rA)V from the material balance in terms of /A, equation 2.2-4, we obtain 

The simple ID reactor model (Eqs. (5.1)-(5.4)) was used to calculate the temperature profiles in both reactors. The gas properties were calculated following 

Reid et al, 1989, using pure component data from Himmelblau, 1974. As in the previous isothermal calculations the feed and wall temperature was fixed at 600 °C. 

In Fig. 5.8 are shown temperature profiles in both reactors. Because of the small reactor scale considered the maximum temperatures differ not much from the inlet values, but there are clear tendencies. 

It can be seen that in this particular case the different contact-time behavior results in a temperature maximum near the reactor inlet for the PBMR, while in the FBR the maximal temperature arises approximately in the middle of the catalyst bed. Predominantly, the residence time, rather than the transport through the membrane and therefore the oxygen supply, is responsible for these temperature profiles. It is instructive to inspect a wider range of operation conditions and to compare the two reactor concepts. 

The heat generation in the PBMR with high dosing rates through the membrane (Fts/Fss = 1/9) is more pronounced than in the FBR. This can be explained by the distinctly higher contact times of ethane near the reactor entrance, which favors the total oxidation and leads to undesired hot-spot formation. If the reaction heat could be removed more efficiently from the reaction zone, using e.g., a specific PBMR construction, this flow rate ratio could be attractive, because both ethylene selectivity and yield is higher in the PBMR than in the FBR (compare with Fig. 5.5). 

In this section, we formulate a ID model with interphase mass and heat transfer coefficients. These lumped models [103] describe the axial variation of concentration and temperature (which are averaged over the channel cross section). The diffusion processes in the transverse directions (represented by differential terms) are replaced by a transfer term, associated with a given driving force. The use of ID models is widespread throughout the literature on monoUth reactor modeling. Chen et al. [3] reviewed some specific appUcations including simulation of simultaneous heat transfer in monofith catalysts 

In steady-state and negligible axial diffusion in the monolith channel, the governing equations can be written in terms of four dependent variables, namely, the mixing-cup and surface concentrations ((c) and Cj ,y) and the equivalent quantities for temperature ((T) and T urj). The mixing-cup concentration is given by Equation 8.22, which can be defined similarly for fluid temperature as 

A consistent derivation of the ID model can be achieved by averaging the 2D mass and energy conservation equations (with a single transverse and axial coordinates) over the channel cross section. This results in 

The interphase coefficients for mass (A ) and heat h) transfer are made dimensionless into Sherwood and Nusselt numbers, both defined as 

The fully developed concentration (or temperature) profile discussed in Section 8.2.2 is characterized by a uniform value of Sherwood (or Nusselt) number, that is, independent of axial distance. Young and Finlayson [108] solved the heat and mass transfer problem numerically using the orthogonal collocation technique and calculated the asymptotic (for long distances) Sherwood and Nusselt numbers for several channel geometries. In terms of the analytical development that we have been presenting, it can be calculated for laminar flows from 

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Nonvolatile Solvents. In practice, some gases tend to Hberate such large amounts of heat when they are absorbed into a solvent that the operation caimot be assumed to be isothermal, as has been done thus far. The resulting temperature variations over the tower will displace the equiUbrium line on 2tj—x diagram considerably because the solubiUty usually depends strongly on temperature. Thus nonisothermal operation affects column performance drastically. 

Comparison of isothermal and nonisothermal policies revealed some interesting features of the polymer system. When M , values determine the isothermal policy, a nonisothermal operation reduces the minimum time compared to isothermal operation (by about 15%). However, when dead-end polymerization influences isothermal operation, a nonisothermal operation does not offer significant improvement. 

A dynamic differential equation energy balance was written taking into account enthalpy accumulation, inflow, outflow, heats of reaction, and removal through the cooling jacket. This balance can be used to calculate the reactor temperature in a nonisothermal operation. 

Nonisothermal reactors. Nonisothermal operation brings additional complexity to the superstructure approach1112. In the first instance, the optimum temperature... 

Kokossis A.C and Floudas C.A (1994) Optimization of Complex Reactor Networks - II Nonisothermal Operation, Chem Eng Sci, 49 1977. 

In this chapter, we first consider uses of batch reactors, and their advantages and disadvantages compared with continuous-flow reactors. After considering what the essential features of process design are, we then develop design or performance equations for both isothermal and nonisothermal operation. The latter requires the energy balance, in addition to the material balance. We continue with an example of optimal performance of a batch reactor, and conclude with a discussion of semibatch and semi-continuous operation. We restrict attention to simple systems, deferring treatment of complex systems to Chapter 18. 

For nonisothermal operation, the energy analysis, point (4) above, requires that the energy balance be developed for a complex system. The energy (enthalpy) balance previously developed for a BR, or CSTR, or PFR applies to a simple system (see equations 12.3-16,14.3-9, and 15.2-9). For a complex system, each reaction (i) in a specified network contributes to the energy balance (as (-AHRl)rt), and, thus, each must be accounted for in the equation. We illustrate this in the following example. 

In nonisothermal operations energy balances must be used in conjunction with material balances. Thus, as illustrated in Fig. 4.3, we have... 

This is the general equation showing the time required to achieve a conversion for either isothermal or nonisothermal operation. The volume of reacting fluid and the reaction rate remain under the integral sign, for in general they both change as reaction proceeds. 

In one form or another, Eqs. 2 to 5 have all been encountered in Chapter 3. They are applicable to both isothermal and nonisothermal operations. For the latter the variation of rate with temperature, and the variation of temperature with conversion, must be known before solution is possible. Figure 5.2 is a graphical representation of two of these equations. 

Sketch some possible r and 1/r versus Cao curves for an irreversible exothermic reaction for nonisothermal operation. Show that a CSTR becomes even more attractive for nonisothennal operation. 

In this and the previous chapters we considered the effects of nonisothermal operation on reactor behavior. The effects of nonisothermal operation can be dramatic, especially for exothermic reactions, often leading to reactor volumes many times smaller than if isothermal and often leading to the possibility of multiple steady states. Further, in nonisothermal operation, the CSTR can require a smaller volume for a given conversion than a PFTR. In this section we summarize some of these characteristics and modes of operation. For endothermic reactions, nonisothermal operation cools the reactor, and this reduces the rate, so that these reactors are inherently stable. The modes of operation can be classified as follows ... 

In the sequel, we will briefly review the approaches developed based on their classification (i) isothermal operation and (ii) nonisothermal operation. 

Kokossis and Floudas (1994) extended the MINLP approach so as to handle nonisothermal operation. The nonisothermal superstructure includes alternatives of temperature control for the reactors as well as options for directly or indirectly intercooled or interheated reactors. This approach can be applied to any homogeneous exothermic or endothermic reaction and the solution of the resulting MINLP model provides information about the optimal temperature profile, the type of temperature control, the feeding, recycling, and by-passing strategy, and the optimal type and size of the reactor units. 

This chapter presents an introduction to the key issues of reactor-based and reactor-separator-recycle systems from the mixed-integer nonlinear optimization perspective. Section 10.1 introduces the reader to the synthesis problems of reactor-based systems and provides an outline of the research work for isothermal and nonisothermal operation. Further reading on this subject can be found in the suggested references and the recent review by Hildebrandt and Biegler (1994). 

The last and most common nonmonotonic rate of reaction occurs under nonisothermal operation where the rate of reaction, even for a first-order reaction, is highly nonlinear, namely... 

Kokossis AC, Floudas CA. Optimization of complex reactor networks II. Nonisothermal operation. Chem Eng Sci 1994 49 1037. 

Those simplified models are often used together with simplified overall reaction rate expressions, in order to obtain analytical solutions for concentrations of reactants and products. However, it is possible to include more complex reaction kinetics if numerical solutions are allowed for. At the same time, it is possible to assume that the temperature is controlled by means of a properly designed device thus, not only adiabatic but isothermal or nonisothermal operations as well can be assumed and analyzed. 

A more quantitative analysis of the batch reactor is obtained by means of mathematical modeling. The mathematical model of the ideal batch reactor consists of mass and energy balances, which provide a set of ordinary differential equations that, in most cases, have to be solved numerically. Analytical integration is, however, still possible in isothermal systems and with reference to simple reaction schemes and rate expressions, so that some general assessments of the reactor behavior can be formulated when basic kinetic schemes are considered. This is the case of the discussion in the coming Sect. 2.3.1, whereas nonisothermal operations and energy balances are addressed in Sect. 2.3.2. 

For an isothermal run, the growth constant K may be evaluated by determining the initial and final weights of the seeds, the number of crystals, and the variation of supersaturation with time. Values of the growth constant obtained at several different temperatures may be used with Eq. (26) to predict nonisothermal operation. Palermo s work is in agreement with McCabe s (Ml) earlier work, for it is in essence an analysis limited to a single crystal size, rather than a distribution of sizes. 

The analysis presented so far has assumed an isothermal operation. In gas-liquid or gas-liquid solid reactions, two types of heat can cause nonisothermal operations. The absorption of gas can generate heat at the gas-liquid interface. This type of heat is commonly known as heat of solution. The reaction (in the... 

Development of a mathematical model for the gas-liquid-solid reactor where significant evaporation of the liquid occurs. The reaction could occur either only in liquid phase or in both liquid and gas phases. Both isothermal as well as nonisothermal operations should be considered. A practical example of such a reactor is the reactor used in high-severity hydrocracking operations. 

Discussion of the concepts and procedures involved in designing packed gas absorption systems shall first be confined to simple gas absorption processes without complications isothermal absorption of a solute from a mixture containing an inert gas into a nonvolatile solvent without chemical reaction. Gas and liquid are assumed to move through the packing in a plug-flow fashion. Deviations such as nonisothermal operation, multicomponent mass transfer effects, and departure from plug flow are treated in later sections. 

Nonisothermal Operation Some degree of temperature control of a reaction may be necessary. Figures 23-1 and 23-2 show some of the ways that may be applicable to homogeneous liquids. More complex modes of temperature control employ internal surfaces, recycles, split flows, cold shots, and so on. Each of these, of course, requires an individual design effort. 

The description of the nonisothermal batch reactor then involves Equation (9.3.1) and either Equation (9.3.9) or (9.3.11) for nonisothermal operation or Equation (9.3.12)... 

Figure 9.4.2 Dimensionless concentration and temperature profiles for adiabatic and nonisothermal operation, and are for adiabatic conditions while y,u and Q , are for nonisothermal operation.

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