Reactor optimum temperature profile

Techniques for approaching optimum temperature profiles for exothermic reaction, (a) Adiabatic operation of reactors with interstage cooling, (b) Countercurrent heat exchange. (Adapted from Chemical Reaction Engineering, Second Edition, by O. Levenspiel. Copyright 1972. Reprinted by permission of John Wiley and Sons, Inc.)... 

If ki is less temperature-dependent that 2, the optimum temperature profile is one that starts off at a high temperature to get the first reaction going but then drops to prevent the loss of too much B. Figure 3.10 sketches typical optimum temperature and concentration profiles. Also shown in Fig. 3.10 as the dashed line is an example of an actual temperature that could be achieved in a real reactor. The reaction mass must be heated up to 7. We will use the optimum temperature profile as the setpoint signal. 

Although an optimum temperature profile may be specified from theoretical calculations, it may not be possible to achieve in practice. The maximum temperature which can be used is usually determined by the materials of reactor construction or the durability of a catalyst. Also, steep axial temperature gradients cannot be realised unless heat transfer rates are high. If heat transfer is poor and the overall process is exothermic, temperature programming of a single reactor may be impossible the reactor becomes virtually adiabatic. In cases such as these, staged reactors (discussed elsewhere in this volume) with intercoolers may be used as a compromise. 

A comparison was made between a reactor running at the optimum temperature profile and a two-stage adiabatic reactor the amount of catalyst required was calculated to be 2.3 times higher for the adiabatic reactor. Hence much less catalyst,... 

Figure 2.45 Optimum temperature profile and corresponding conversion profile for a WGS reactor with a steam reformate fee at an inititial composition of 9% CO, 9% C02, 36% H20 and 45% H2 [80] (by courtesy of W. E. TeGrotenhuis).

The purpose of the reactor design is to acquire the optimum reactor size. However, the ideal optimum reactor size (V/FAO)opt, is obtained by integrating the optimum temperature profile. That is,... 

The conversion and selectivity of the reaction can be decisively influenced by the design and the operation of the heat transfer circuit. The most obvious, although technically most complex solution, is to arrange different heat transfer circuits so as to achieve a stepwise approximation of an optimum temperature profile. The purposeful utilization of the temperature change of the heat transfer medium flowing through the reactor is technically simpler, and will be discussed here in connection with cocurrent or countercurrent cooling of a fixed-bed reactor with an exothermic reaction. 

R. Jackson and I. Coward, Optimum Temperature Profiles in Tubular Reactors, Chem. Eng. Sci., 20, 911 (1965). 

In an element of catalyst dW the production rate per unit mass is FdxjdW. Hence Eq. (12-1) states that optimum performance is attained in the element when Tp is at a maximum. For the entire reactor to operate at optimum conditions the rate should have its maximum permissible value at every axial position. This concept has been used to predict optimum temperature profiles for single exothermic reversible reactions. ... 

Integration along the length of the reactor gives the optimal temperature profile and the maximum exit conversion. The optimum temperature profiles were calculated for the different reactors and the... 

The absolute optimum temperature profile gives a considerable increase in conversion for all reactors with the maximum increase in conversion of 11.58% occuring for reactor IV. Obviously, such an operation must be non-adiabatic. The constrained optimal policy that takes into consideration the maximum allowable temperature of the catalyst gives results which are very close to those of the absolute optimum (e.g. increase of conversion over operating conversion of reactor IV being 10.49%). 

Chapter 6 introduced the concept of functional optimization. Several examples in that chapter addressed the problem of finding the optimum temperature profile, TwaiiCz), for a steady-state tubular reactor. Product transition strategies are also problems in functional optimization, but the functions to be determined are now functions of time such as ) and As suggested by the bang-bang strategy in Example... 

Curve B corresponds to a constant temperature in the reactor maintained at Tq, and curve A is for an optimum temperature profile. The shaded area represents the decrease in volume due to operation with the imposed optimum temperature profile. 

In industrial reactors, it is impractical to reach exactly this optimum temperature profile, as we would have to adjust appropriate locally adjusted values of the overall heat transfer coefficient and/or of the tem-... 

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