CSTR, mass transfer model

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

One of the simplest models for convective mass transfer is the stirred tank model, also called the continuously stirred tank reactor (CSTR) or the mixing tank. The model is shown schematically in Figure 2. As shown in the figure, a fluid stream enters a filled vessel that is stirred with an impeller, then exits the vessel through an outlet port. The stirred tank represents an idealization of mixing behavior in convective systems, in which incoming fluid streams are instantly and completely mixed with the system contents. To illustrate this, consider the case in which the inlet stream contains a water-miscible blue dye and the tank is initially filled with pure water. At time zero, the inlet valve is opened, allowing the dye to enter the... 

We have used CO oxidation on Pt to illustrate the evolution of models applied to interpret critical effects in catalytic oxidation reactions. All the above models use concepts concerning the complex detailed mechanism. But, as has been shown previously, critical. effects in oxidation reactions were studied as early as the 1930s. For their interpretation primary attention is paid to the interaction of kinetic dependences with the heat-and-mass transfer law [146], It is likely that in these cases there is still more variety in dynamic behaviour than when we deal with purely kinetic factors. A theory for the non-isothermal continuous stirred tank reactor for first-order reactions was suggested in refs. 152-155. The dynamics of CO oxidation in non-isothermal, in particular adiabatic, reactors has been studied [77-80, 155]. A sufficiently complex dynamic behaviour is also observed in isothermal reactors for CO oxidation by taking into account the diffusion both in pores [71, 147-149] and on the surfaces of catalyst [201, 202]. The simplest model accounting for the combination of kinetic and transport processes is an isothermal continuously stirred tank reactor (CSTR). It was Matsuura and Kato [157] who first showed that if the kinetic curve has a maximum peak (this curve is also obtained for CO oxidation [158]), then the isothermal CSTR can have several steady states (see also ref. 203). Recently several authors [3, 76, 118, 156, 159, 160] have applied CSTR models corresponding to the detailed mechanism of catalytic reactions. 

Many working groups have modeled the performance of diesel particulate traps during the past few decades. Concentrated parameter models (CSTR assumption) have been applied for the evaluation of formal kinetic models and model parameters. The formal kinetic parameters lump the heat and mass transfer effects with the reaction kinetics of the complicated reaction network of diesel soot combustion. Those models and model parameters were used for the characterization of the performance of different filter geometries and filter materials, as well as of the performance of a variety of catalytically active coatings and fuel additives [58],... 

One important oscillating system—namely, the methylamine decomposition on noble metal wires (24,143,227,228)—belongs to this class of ther-mokinetic blocking/reactivation models. This reaction is unique in several ways. It is the only endothermic oscillator (-1-150 kJ/mol), and it is the only unimolecular reaction that displays oscillations caused by sur ce effects. [The oscillating N2O decomposition, reported by Hugo (5) in 1968, does not oscillate because of the instability of the surface reaction, but rather due to the instability of a CSTR when certain heat and mass transfer conditions exist. Any reaction with similar rate and heat effects would oscillate under such circumstances.] This reaction is also the most vigorous oscillator yet observed and displays frequencies of up to 10 Hz and amplitudes approaching 500 K. Moreover, because the reaction oscillates at temperatures of around 1000 K, the oscillations can actually be observed visually as the metal catalyst heats and cools. 

However, each set of factors entering in to the rate expression is also a potential source of scaleup error. For this, and other reasons, a fundamental requirement when scaling a process is that the model and prototype be similar to each other with respect to reactor type and design. For example, a cleaning process model of a continuous-stirred tank reactor (CSTR) cannot be scaled to a prototype with a tubular reactor design. Process conditions such as fluid flow and heat and mass transfer are totally different for the two types of reactors. However, results from rate-of-reaction experiments using a batch reactor can be used to design either a CSTR or a tubular reactor based solely on a function of conversion, -r ... 

Industrial reactors are usually more complex than the simple simulator library models. Real reactors usually involve multiple phases and have strong mass transfer, heat transfer, and mixing effects. The residence time distributions of real reactors can be determined by tracer studies and seldom exactly match the simple CSTR or PFR models. 

After extracting the kinetic parameters, selected results for CO oxidation over were used to analyze the effect of non-uniform temperature and velocity distributions on the conversion of CO. In order to determine the optimum number of multiple CSTR s to capture the behavior of a PFR, the rate law of Oh and Carpenter (14) for the NO+CO reaction was used to model a monolith channel as a CSTR in series. The results indicated that it was sufficient to use 5 reactors in series to capture the performance of the PFR behavior in the NO+CO reaction The cells of a monolith reactor were taken as independent parallel reactors ignoring the mass transfer and diffusion through the ceramic pores. The axial and radial temperature and velocity profiles collected from the literature(4,5) are used to calculate the... 

Consider the dynamics of an isothermal CSTR followed by a simple (single stage) separating unit (e.g., an extractor, crystallizer, or a settler). The reaction is reversible, A B, and the effluent stream from the separator, which is rich in unreacted material, is recycled. It is assumed that the reaction rate is first order, the equilibrium relationship for the separator is linear, and the rate of mass transfer between the phases in the separator could be written in terms of mass transfer coefficient and a linear driving force. Making certain that you define all your terms carefully, show that the dynamic model for the plant can be put into the following form ... 

It is important to remember that a simulation results are only as good as the mathematical models on which those are based. However, there are still many items that are neglected or treated insufficiently in mathematical models, such as ageing and deactivation of the catalyst and the stability of the products under actual production conditions. Many commercial flowsheeting programs still rely totally on idealistic behaviour. Many programs have only very limited number of reactor types like tube and CSTR. Common multiphase reactors where mass transfer phenomena also plays important role are missing. Also idealized separation models are common. 

The same conclusion can be attained via the PFR evaluation. The respective data from the ProCell unit (gray cycles) are located in Fig. 4.16 significantly lower than Sherwood numbers evaluated with the CSTR assumption, because back-mixing reduces the efficiency of interface heat and mass transfer and, thus, leads to lower values of transfer coefficients, if taken into account in such coeffidents instead of being considered in the balance equation of the model. For the reference case of the conventional fluidized bed, so-called apparent Sherwood numbers (Shapp) must be used in combination with the PFR model (Groenewold and Tsotsas, 1999). 

Figure 13 Coke conversions predicted for 14 m dia x 10 m tall catalyst regenerator (75) as a function of dense bed height with and without freeboard region (Fbr) included a) Dense bed modelled as single-phase CSTR b) Orcutt model (17,18) c) as in (b) only with lower interphase mass transfer predicted by Kunil and Levenspiel (20). dp 60 pm.

Models of BCR can be developed on the basis of various view points. The mathematical structure of the model equations is mainly determined by the residence time distribution of the phases, the reaction kinetics, the number of reactive species involved in the process, and the absorption-reaction regime (slow or fast reaction in comparison to mass transfer rate). One can anticipate that the gas phase as well as the liquid phase can be either completely backmixed (CSTR), partially mixed, as described by the axial dispersion model (ADM), or unmixed (PFR). Thus, it is possible to construct a model matrix as shown in Fig. 3. This matrix refers only to the gaseous key reactant (A) which is subjected to interphase mass transfer and undergoes chemical reaction in the liquid phase. The mass balances of the gaseous reactant A are the starting point of the model development. By solving the mass balances for A alone, it is often possible to calculate conversions and space-time-yields of the other reactive species which are only present in the liquid phase. Heat effects can be estimated, as well. It is, however, assumed that the temperature is constant throughout the reactor volume. Hence, isothermal models can be applied. 

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