CSTR periodically operated

Yu (13) simulated a periodically operated CSTR for the thermal polymerization of styrene and found the MWD to increase at low frequencies but all effects were damped out at higher frequencies because of the limited heat transfer which occurs relative to the thermal capacity of industrial scale reactors. 

One of the few attempts to examine a polymerization reactor in periodic operation experimentally is the work of Spitz, Laurence and Chappelear (X6)who reported the influence of periodicity in the initiator feed to the bulk polymerization of styrene in a CSTR. To induce periodicity the initiator feed was pulsed on-and-off and the reactor output compared with steady-state operation with the same time-averaged initiator input. 

The My, D and conversions observed for the free-radically initiated polymerization of MMA produced in a periodically operated CSTR... 

Hoffman, U. Schadlich, H. K. 1986 The influence of reaction orders and of changes in the total number of moles on the conversion in a periodically operated CSTR. Chem. Engng Sci. 41(11), 2733-2738. 

The results Illustrated by Figures 3 and 4 resemble those obtained in the Berty recycle reactor under similar conditions. The space-mean, time average rates for the fixed-bed reactor were only about 50% of those measured in the Berty reactor, because, of course the former reactor achieved conversions high enough for the back reaction to become important. The significance of these observations is that 1) CSTR and differential reactors, widely used for laboratory studies, seem to reflect performance improvements obtainable with fixed-bed, integral reactor which resemble commercial units, and 2) improvement from periodic operation are still observed even tfien reverse reactions become important. 

Under ideal condition, when an isothermal CSTR is operating at steady state (SS) in a totally micro-mixing condition, the PS produced will be homogeneous having a perfect 2.0 polydispersity (the Schultz-Flory distribution). Deviations from ideality have been theoretically studied by operating CSTR processes under non-steady state conditions with forced periodic operation [70]. The effects of an independent sinusoidal forcing of the monomer and the initiator feed concentrations results in theoretical control of the polydispersity. 

Consider the CSTR described in Example 6.7 (p. 164) but under periodic operation in which the objective is to minimize... 

Consider a CSTR under periodic operation governed by the state equations dyi... 

Intermediate periodic operation lies between both extremes and covers systems in which the response time is of the same order as the imposed function cycle time so that resonance is possible. Here the state of the mechanism changes dynamically and is not directly related to the environmental conditions at the moment considered. Intermediate periodic operations encompass semibatch periodic operations, selectivity in periodically forced CSTRs, cycled reactors with heterogeneous catalysts, and non-steady-state biofilm reactors (e.g., Rittmann and McCarty, 1981). Lag, overshoot phenomena, and oscillations can typically occur. Biological reactor operation will basically fall into this latter class of operation, and balanced growth must be distinguished from steady-state growth (Barford et al., 1982). 

Aris et al. have primarily analyzed whether the steady-state multiplicity features in a CSTR arising from a cubic rate law also can arise for a series of successive bimolecular reactions [26]. Aris et al. have showed that the steady-state equations for a CSTR with bimolecular reactions scheme reduces to that with a cubic reaction scheme when two parameters e(=k,Cg/k j) and K(=kjC /k j) arising in system equations for the bimolecular reactions tend to zero. Aris et al. have shown that the general multiplicity feature of the CSTR for bimolecular reactions is similar to that of the molecular reactions only at smaller value of e and K. The behavior is considerably different at larger values of e and K. Chidambaram has evaluated the effect of these two parameters (e and K) on the periodic operation of an isothermal plug flow reactor [18]. 

The feasibility of increasing the selectivity of the Fischer-Tropsch synthesis by periodic operation is investigated. The process is modeled in a dynamic form using a CSTR reactor. The dynamic behavior of the model corresponds with in literature reported experimental results. The simulation results show a 20% increase in selectivity to Diesel range products compared to the best steady-state solution using a blockprofile. The profile has a cycle time of 1.1 O seconds and consists of a base composition of almost pure carbon monoxide and a pulse of 95% hydrogen and 5% carbon monoxide during 10.8% of the cycle time. 

The effect of periodic operation on the performance of the catalyst can be examined most clearly if the applied concentration change is immediately and fully felt by the catalyst. This situation is reached by defining a small amount of catalyst in a well-mixed reactor (CSTR) with large flow rates resulting in high space velocities. 

This study explores the potential of periodic operation for the Fischer-Tropsch synthesis aiming at Diesel range products. The approach followed is modeling the process in a dynamic form using a simple CSTR reactor configuration. The kinetic scheme is based on steady-state data reported in literature. The steady-state behavior is in agreement with experimental observations reported earlier by various research groups. 

Compositional modulation has been practiced for the FT synthesis in catalytic reactors [126]. It was found that the cyclic feeding of synthesis gas (CO/IT2) had an influence on the selectivity of the FT products. In the early studies, only low conversions could be utilized due to the exothermic nature of the reaction. It was concluded that for an iron catalyst, the methane selectivity increased with periodic operation as did the molar ratio of alkene/alkane. Higher conversion studies were conducted in a CSTR, and it was found that periodic operation had an influence on the selectivity of the products from the FT synthesis using an iron catalyst [127]. First, there was a decrease in the alpha value for synthesis with increasing period. In addition, the alkane/alkene ratio increased with an increase in the period. There was a change in the CO2 production but this could be attributed to the change in CO conversion and not the... 

Cyclic Runs. Having established the inlet ratio of H2 Buta-diene for which the steady-state yield is maximised for a given residence time, the cyclic runs were carried out such that the mean value of the feed compositions were as near as possible to their optimum steady-state values. The mole fractions of H2 and Butadiene were cycled out of phase in a symmetrical square wave fashion. Such symmetrical wave forms need not be the optimum periodic operation. Indeed, Farhad Pour et al. (7 ) demonstrated theoretically that it was possible to obtain further improvement in the selectivity of series-parallel reactions in a CSTR when asymmetrical rather than symmetrical square waves are considered. Theoretically the search for the optimum wave modulation, or the number of switches over one cycle time, can be computed by search methods or optimisation routines. However, in this work we arbitrarily limited ourselves to symmetrical square waves which are 180 out of phase accepting that such a configuration may, indeed, be quite far from the optimum periodic mode. 

In order to allow integration of countercurrent relations like Eq. (23-93), point values of the mass-transfer coefficients and eqiiilibrium data are needed, over ranges of partial pressure and liquid-phase compositions. The same data are needed for the design of stirred tank performance. Then the conditions vary with time instead of position. Because of limited solubihty, gas/liquid reactions in stirred tanks usually are operated in semibatch fashion, with the liquid phase charged at once, then the gas phase introduced gradually over a period of time. CSTR operation rarely is feasible with such systems. 

The rate of polymerization with styrene-type monomers is directly proportional to the number of particles formed. In batch reactors most of the particles are nucleated early in the reaction and the number formed depends on the emulsifier available to stabilize these small particles. In a CSTR operating at steady-state the rate of nucleation of new particles depends on the concentration of free emulsifier, i.e. the emulsifier not adsorbed on other surfaces. Since the average particle size in a CSTR is larger than the average size at the end of the batch nucleation period, fewer particles are formed in a CSTR than if the same recipe were used in a batch reactor. Since rate is proportional to the number of particles for styrene-type monomers, the rate per unit volume in a CSTR will be less than the interval-two rate in a batch reactor. In fact, the maximum CSTR rate will be about 60 to 70 percent the batch rate for such monomers. Monomers for which the rate is not as strongly dependent on the number of particles will display less of a difference between batch and continuous reactors. Also, continuous reactors with a particle seed in the feed may be capable of higher rates. 

Example 14.1 shows how an isothermal CSTR with first-order reaction responds to an abrupt change in inlet concentration. The outlet concentration moves from an initial steady state to a final steady state in a gradual fashion. If the inlet concentration is returned to its original value, the outlet concentration returns to its original value. If the time period for an input disturbance is small, the outlet response is small. The magnitude of the outlet disturbance will never be larger than the magnitude of the inlet disturbance. The system is stable. Indeed, it is open-loop stable, which means that steady-state operation can be achieved without resort to a feedback control system. This is the usual but not inevitable case for isothermal reactors. 

In this chapter, we develop the basis for design and performance analysis for a plug flow reactor (PFR). Like a CSTR. a PFR is usually operated continuously at steady-state, apart from startup and shutdown periods. Unlike a CSTR, which is used primarily for liquid-phase reactions, a PFR may be used for either gas-phase or liquid-phase reactions. 

The results represented in Figure 4.17 are obtained when the system is operated as a CSTR with Q = 6 mL/h. It can be seen that after the transient hme, oscillatory output signals with a period time of 40 min are obtained and they are represented by the concentration profiles of Si, S2, A, and B. Thus, this system converts the sharp input signals to oscillatory signals with the same period of time of the input signal (40 min) but with different amplitudes. Very similar behavior is observed when a PFR is considered (n = 5), and these results are presented in Figure 4.18. 

Sincic and Bailey (1977) relaxed the assumption of only one stable attractor for a given set of operating conditions and showed examples of some possible exotic responses in a CSTR with periodically forced coolant temperature. They also probed the way in which multiple steady states or sustained oscillations in the dynamics of the unforced system affect its response to periodic forcing. Several theoretical and experimental papers have since extended these ideas (Hamer and Cormack, 1978 Cutlip, 1979 Stephanopoulos et al., 1979 Hegedus et al., 1980 Abdul-Kareem et al., 1980 Bennett, 1982 Goodman et al., 1981, 1982 Cutlip et al., 1983 Taylor and Geiseler, 1986 Mankin and Hudson, 1984 Kevrekidis et al., 1984). 

The principal advantage of continuous reaction vessels is that they operate (after an initial transient period) under steady-state conditions that are conducive to the formation of a highly uniform and well-regulated product. In this section, we shall confine the discussion to continuous stirred-tank reactors (CSTRs). These reactors are characterized by isothermal, spatially uniform operation. 

Conventional flow reactors operate at steady state. This requirement involves the stabilization of the composition of the reacting mixture and of the temperature of the mass of the reactor vessel and, in the case of CSTRs and BRs, of the reactor internals. The achievement of this condition usually requires long periods of stabilization before a steady state is assured. It is not uncommon for a CSTR to take a day to reach stability at a new reaction condition. The situation may be somewhat better in the case of changes in feed rate and/or reactant composition without a change in reactor temperature, although in principle all transients in CSTRs decay exponentially and take forever to complete. 

The basic TS mode of operation involves experiments, each consisting of a number of runs. Each run consists of operating the reactor over a period of time while the temperature of the feed, and usually of the reactor surroundings, is varied in some way. During each run, frequent (continuous if possible) measurements of temperature and conversion are made at the outlet conditions, i.e. of product drawn off from a TS-BR, or of product exiting a TS-PFR or TS-CSTR. Rates will later be calculated from this raw data obtained at the exit conditions present at the moment of sampling. 

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