Characterization of Reactor Performance

In the preceding sections, the stoichiometric relationships used to quantify the operation of chemical reactors were expressed in terms of extensive quantities (moles, molar flow rates, reaction extents, etc.) whose numerical values depend on the basis selected for the calculation. In most applications, it is convenient to define intensive dimensionless quantities that characterize the operation of chemical reactors and provide quick measures of the reactor performance. In this section, we define and discuss some common stoichiometric quantities used in reactor analysis. 

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Different reactor networks can give rise to the same residence time distribution function. For example, a CSTR characterized by a space time Tj followed by a PFR characterized by a space time t2 has an F(t) curve that is identical to that of these two reactors operated in the reverse order. Consequently, the F(t) curve alone is not sufficient, in general, to permit one to determine the conversion in a nonideal reactor. As a result, several mathematical models of reactor performance have been developed to provide estimates of the conversion levels in nonideal reactors. These models vary in their degree of complexity and range of applicability. In this textbook we will confine the discussion to models in which a single parameter is used to characterize the nonideal flow pattern. Multiparameter models have been developed for handling more complex situations (e.g., that which prevails in a fluidized bed reactor), but these are beyond the scope of this textbook. [See Levenspiel (2) and Himmelblau and Bischoff (4).]... 

In a general sense, the characterization of the performance of the microtechnology-based equipment is not a process analytical problem and is the responsibility of the hardware developer since there are many variables that need to be characterized for proper design and operation of the device. These include flow distribution to the multiple channels, chemical component mixing and heat transfer rates, to name just a few. For example, Schouten has demonstrated the care needed to characterize and model gas-phase reactor systems that he and his colleagues design (e.g. [6]). 

For instance, in order to characterize the mixing performance of any transparent reactor, the reaction of discoloration of an iodine solution with sodium thiosulfate could be used according to the following reaction scheme ... 

A detailed characterization of micro mixing and reaction performance (combined mixing and heat transfer) for various small-scale compact heat exchanger chemical reactors has been reported [27]. The superior performance, i.e. the process intensification, of these devices is evidenced and the devices themselves are benchmarked to each other. 

The homogeneously catalyzed oxidation of butyraldehyde to butyric acid is a well-characterized gas/Hquid reaction for which kinetic data are available. It thus serves as a model reaction to evaluate mass transfer and reactor performance in general for new gas/liquid micro reactors to be tested. This reaction was particularly used to validate a reactor model for a micro reactor [9, 10]. 

Establishing the process sensitivity with respect to the above-mentioned factors is crucial for further scale-up considerations. If the sensitivity is low, a direct volume scale-up is allowed and the use of standard batch reactor configurations is permitted. However, many reactions are characterized by a large thermal effect and many molecules are very sensitive to process conditions on molecular scale (pH, temperature, concentrations, etc.). Such processes are much more difficult to scale up. Mixing can then become a very important factor influencing reactor performance for reactions where mixing times and reaction times are comparable, micromixing also becomes important. 

To understand how such computer packages function, consider the simple flowsheet in Figure 13.13a. This involves an isomerization of Component A to Component B. The mixture of A and B from the reactor is separated into relatively pure A, which is recycled, and relatively pure B, which is the product. No byproducts are formed and the reactor performance can be characterized by its conversion. The performance of the separator is to be characterized by the recovery of A to the recycle stream (rA) and recovery of B to the product (rB). 

Several age-distribution functions may be used (Danckwerts, 1953), but they are all interrelated. Some are residence-time distributions and some are not. In the discussion to follow in this section and in Section 13.4, we assume steady-flow of a Newtonian, single-phase fluid of constant density through a vessel without chemical reaction. Ultimately, we are interested in the effect of a spread of residence times on the performance of a chemical reactor, but we concentrate on the characterization of flow here. 

In this chapter, we consider nonideal flow, as distinct from ideal flow (Chapter 13), of which BMF, PF, and LF are examples. By its nature, nonideal flow cannot be described exactly, but the statistical methods introduced in Chapter 13, particularly for residence time distribution (RTD), provide useful approximations both to characterize the flow and ultimately to help assess the performance of a reactor. We focus on the former here, and defer the latter to Chapter 20. However, even at this stage, it is important to realize that ignorance of the details of nonideal flow and inability to predict accurately its effect on reactor performance are major reasons for having to do physical scale-up (bench —> pilot plant - semi-works -> commercial scale) in the design of a new reactor. This is in contrast to most other types of process equipment. 

A mathematical model for nonideal flow in a vessel provides a characterization of the mixing and flow behavior. Although it may appear to be an independent alternative to the experimental measurement of RTD, the latter may be required to determine the parameters) of the model. The ultimate importance of such a model for our purpose is that it may be used to assess the performance of the vessel as a reactor (Chapter 20). 

The performance of a reactor for a fluid (A) + solid (B) reaction may be characterized by /B obtained for a given feed rate (FBo) and size of reactor the latter is related to the holdup (WB) of solid in the reactor, whether the process is continuous or batch (fixed... 

Applying the equipment shown in Fig. 13 (Section III.B) the authors performed a simultaneous analysis of the reaction products leaving the MAS NMR rotor reactor by on-line gas chromatography and an NMR characterization of the compounds adsorbed on the catalyst under steady-state conditions. These investigations showed that the intensity of the signals at ca. 80 ppm correlates with the yields of MTBE determined by gas chromatography (60). An increase of the reaction temperature of the exothermic synthesis of MTBE from 333 to 353 K, led to a simultaneous... 

For reactions characterized by high values of Q, the onset of a thermal explosion can be controlled by adjusting the batch time, tt, the explosion occurs if t, > and does not in the opposite case. Hence, the reactor performance shows a typical on-off behavior, being characterized by either complete or negligible reactant conversion. It follows that reactions of interest must be carried out under explosion conditions, provided that the reactor vessel withstands the final internal pressure and the thermal shock caused by the sudden temperature increase. A similar map can be drawn with reference to undesired secondary reactions and, in this respect, operative parameters must be adjusted in order to avoid the ignition stage within the batch length. 

The polymerization of ethylene to yield low density polyethylene (LDPE) is performed in vessel reactors at high pressures (1000 2500 kg/cm2) and in the temperature range between 150 and 300°C. Two main features characterize these type of reactors a) the very high power input per unit volume required to maintain good mixing conditions in the reaction zone and b) the absence of appreciable heat exchange, so that the reactor can be considered practically adiabatic. 

In a previous work (5), it was shown that the effect of mixing on reactor performances is very important. In particular, it was discussed that a) the mixing inside the reactor can be characterized by a recirculating flow rate caused by the impeller in the reaction zone, and that b) an imperfectly mixed reactor requires a higher initiator consumption per polymer produced than a perfectly mixed one operating at the same conditions. 

Sizing of the absorption column started from a base case that assumed complete recovery of FeEDTA2- in the bioreactor. Then, sensitivity studies provided the values of the G/L interfacial area and of the absorber volume giving maximum performance. The values of the two Damkohler numbers characterizing reactor performance were found after relaxing the assumption of complete FeEDTA2-recovery. Finally, the specification of NO concentration in the purified gases was checked, for different feed conditions. 

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