START-UP TIME IN TUBULAR REACTORS WITH AXIAL DISPERSION

In the modeling of nonideal reactors the axial dispersion model is one of the most used (Butt, 1980). Boundary conditions for a tubular reactor with axial dispersion were extensively analyzed (Danckwerts, 1953, Wehner and Wilhelm, 1965, Van Cauwen-berghe, 1966, Choi and Perlmutter, 1976, Deckwer and Mahlmann, 1976) Similarly, the steady state behaviour of the reactor when simple or complex reactions take place was also studied by several authors (Deckwer et al. 1972, Wan and Ziegler, 1973). However, the transient behaviour was only analyzed for simple kinetics expressions (Fan and Ahn, 1963, Sawinsky artd Hunek, 1977, Godslave and Chang, 1980)

In the present work, the time necessary to reach the steady state or start-up time is determined for single and complex reversible reactions. The analysis presented is also valid in case there is a change in feed concentration (feed upset, etc.)     

Dynamics of a CSTR for styrene polymerization initiated by a binary initiator system

The steady state and dynamic behavior of a continuous stirred tank reactor has been analyzed for free radical solution polymerization of styrene initiated by a mixture of two initiators having different thermal stabilities. From the steady state analysis of the reactor model with a mean residence time as a bifurcation parameter, four unique regions of steady state solutions are identified in an operating parameter space for a given initiator feed composition. A variety of complex bifurcation behavior such as multiple steady states, Hopf bifurcation and limit cycles have been observed and their stability characteristics have been analyzed. The effects of feed initiator composition and the concentration of the initiator in the feed stream on the reactor dynamics are also presented.     

Dynamics of a continuous stirred tank reactor for styrene polymerization initiated by a binary initiator mixture. II: Effect of viscosity dependent heat transfer coefficient

The dynamic behavior of the solution polymerization of styrene in a continuous stirred tank reactor is analyzed with a mixture of tert-butyl perbenzoate and benzoyl peroxide as an initiator system. In the modeling of the reactor, a viscosity dependent reactor wall heat transfer coefficient is used to account for the changing heat transfer efficiency as monomer conversion and polymer molecular weight increase. The steady state and bifurcation behaviors have been investigated with the reactor residence time, initiator feed composition, initiator concentration, feed solvent volume fraction, and coolant temperature as bifurcation parameters. Unlike the reactors with constant heat transfer coefficient, the present system exhibits relatively simple steady state and dynamic bifurcation behaviors. Oscillatory behavior is observed only when the solvent volume fraction in the feed exceeds 0.2. The dynamic simulation of the reactor also indicates that a feedback temperature controller may fail to maintain the reactor temperature when the heat transfer coefficient changes as a result of process disturbances.     

Effect of kinetic regime and axial dispersion on the dynamic response of counter flow extractive reactors

Plug flow as well as axial dispersion dynamic models for counter-flow extractive reactors are formulated and solved to investigate the frequency response characteristics of such reactors. The reactions considered are taken to be either infinitely fast, taking place at the interface between the two phases or within a thin film in one of the phases, or slow taking place in the bulk of one of the phases. The results demonstrate the effect of the kinetic regime as well as axial dispersion (Peclet number) of the continuous phase on the dynamic behaviour of the two phase reactor. For the plug flow case (Pe → ∞) it is shown that for some input-output relations the kinetic regime affects the functional forms of the transfer functions. The complex transfer functions are approximated, using simple fitting techniques, to simpler ones suitable for the design of the reactor's control loops. For the axial dispersion case the results show that the continuous phase Peclet number affects the frequency response of the reactor in a complicated manner giving rise, for some input-output relations and small values of the Peclet number, to complex oscillations in both amplitude ratio and phase angle.     

BEHAVIOUR OF AN ADIABATIC PACKED BED REACTOR PART 2: MODELLING

The steady state and dynamic behaviour of an adiabatic packed bed reactor for the selective hydrogenation of mixtures of ethyne and ethene is studied. A heterogeneous model with axial dispersion of heat is solved numerically by means of a fully implicit discretisation scheme. From an analysis of the inlet and outlet boundary conditions, it follows that in order to avoid an influence of the type of boundary condition on the reactor behaviour, sufficiently long inert zones before and after the active bed should be present. Using preliminary kinetic expressions adapted from Mcn'shchikov ct al. (1975), the model calculations show a reasonable agreement with the experiments performed in a laboratory scale reactor and demonstrate the importance influence of small amounts of carbon monoxide both on the steady state as well as on the transient behaviour of the reactor. However, using the rate expressions derived from our own kinetic experiments in a Berty reactor, the behaviour under runaway conditions and the transition from non-runaway to runaway conditions can not be described well. Several factors that contribute to this discrepancy are discussed. This work shows that, in particular for a complex reaction system such as the selective hydrogenation of ethyne in ethene, the limited accuracy of the kinetic model and kinetic parameters dominates the precision attainable with packed bed reactor models.     

Unsteady tubular reactors—time variable flow and inlet conditions

Unsteady flow in a tubular reactor with inlet concentration of reactant that depends on time and position is studied.It is shown that the coefficients which arise in the expression for the axial flux are different from those which occur in the dispersion model when heterogeneous reactions occur. Therefore a new inlet boundary condition expression is derived. This inlet condition is used to solve for the steady state reactant concentration distribution.     

Dispersion models of unsteady tubular reactors

Axial dispersion in time-variable laminar flow in a tubular reactor is analyzed using an exact procedure for the case of a homogenous first-order reaction. For the first time since the Taylor Dispersion model was originally introduced for the modeling of reactors, its validity is examined over a wide range of the reaction rate parameter by comparison against an exact analysis. It is shown that a constant coefficient dispersion model can be obtained from first principles for large values of time only for initial distribution problems; however, this simple approximate model also is reasonably good for describing concentration distributions for the present inlet distribution problem for slow reactions and for axial locations sufficiently far away from the inlet. For rapid reactions, while the dispersion model is inaccurate in describing axial concentration distributions, it is surprisingly good for predicting the reactor length required for complete conversion. In contrast to the conclusion of a recent article, it will be shown that the dispersion coefficient is independent of the reaction rate constant.     

Steady state multiplicity behavior of an isothermal axial dispersion fixed-bed reactor with nonuniformly active catalyst

An isothermal, heterogeneous fixed-bed reactor packed with nonuniformly active catalyst pellets where a biomolecular Langmuir-Hinshelwood reaction occurs, is studied using an axial dispersion model. A catalyst activity distribution given by a Dirac delta function, where the active catalyst is deposited at a specific location within the pellet, is considered. This includes the common case of externally coated pellets with external mass transfer resistance. The steady state multiplicity behavior of this reactor, and its limiting cases: CSTR, PFR and pseudohomogeneous axial dispersion, are examined in detail. The nonlinearity of the reaction kinetics provides two sources of multiplicity, through the heterogeneous nature of the reactor and the presence of axial dispersion in the fluid phase. Their roles in determining reactor multiplicity behavior are fully explored. It is shown that this system can admit at most nine steady state solutions. The limiting behavior of the heterogeneous axial dispersion model as Pe → 0 or ∞ is not represented fully by the CSTR or PFR models because of ignition phenomenon. Finally, the effects of mixing on reactor conversion are discussed.     

MeOH to DME in bubbling fluidized bed: Experimental and modelling

Methanol dehydration over a ZSM‐5 containing catalyst was studied in a fluidized bed reactor. At temperatures ranging from 250 to 325°C, methanol conversion varied from 30% at a contact times of 0.14 s and approached 100% of the equilibrium conversion at a contact time starting from 10 s. Sequential and parallel reactions were negligible at low temperatures while hydrocarbon formation became appreciable at 325°C. Online gas analysis by mass spectrometry provided real‐time measurements at a frequency of 4.4 Hz that allowed for fast determination of steady‐state conditions. Gas phase residence time distribution (RTD) measurements indicated that axial dispersion was essentially negligible at short contact times with a shallow bed of catalyst. With longer residence times, the flow pattern could be approximated by six continuously stirred‐tank reactors (CSTR) in series. Both the simple 1D hydrodynamic model and a detailed multi‐zone fluidized model were used to interpret the experimental data to derive a kinetic expression for the dehydration of methanol to di‐methyl ether (DME). The expression includes the reverse reaction that is most often neglected in the literature. The reaction data were best fit with the kinetics based on the 1D model. The fluidized bed is a viable reactor type for kinetic measurements of highly exothermic reactions where hotspots and radial and axial temperature gradients are problematic in fixed beds.     

Multiplicity of steady states in fluidized bed reactors—V: The effect of catalyst decay

A simplified two-phase model is used to investigate the behaviour of non-isothermal fluidized bed reactors experiencing catalyst decay. The investigation shows that for highly exothermic reaction it is almost always desirable to operate the reactor at the middle unstable steady state, since it gives higher accumulative yield than both the high and the low temperature steady states. A simple feedback control scheme with time varying set point is suggested to stabilize the middle steady state. The dynamic behaviour and stability of the system is investigated for the open-loop reactor (uncontrolled) and the closed loop reactor (controlled).     

Modeling of chemical reactors—XXXI: The one-phase backflow cell model used for simulation of tubular adiabatic reactors

The backflow cell model is used to simulate steady state operation of a tubular adiabatic reactor. The model proposed embraces different mechanism of axial dispersion of heat and mass. It will be shown that the backflow cell model may be used for approximation of the dispersion model. While there are differences in qualitative behavior of simple cell and dispersion models, the backflow cell model gives results which are in agreement with the dispersion model. The model may be used for simulation of steady-state behavior of tubular homogeneous and heterogeneous reactors.     

Stationary spatially periodic and aperiodic solutions in membrane reactors

The formation of stationary spatially patterns is analysed for a detailed reaction mechanism of the oxidative dehydrogenation of ethane. In the first step, a simple steady-state model of an ideal plug flow membrane reactor is investigated by numerical bifurcation analysis. The model shows a complex nonlinear behaviour including period doubling bifurcations and aperiodic spatial patterns. In the next step, the influence of axial heat dispersion is studied. Finally, a more detailed model of a fixed bed membrane reactor is considered. It is found that pattern formation is possible under operation conditions realisable in a laboratory reactor.     

Entwurf und Betrieb eines Rohrreaktors mit enger Verweilzeitverteilung

In process engineering the residence time is an important design parameter, and a narrow residence time distribution is advantageous to avoid possible by-products in complex chemical reactions. A good radial mixing with low axial dispersion provides a narrow residence time distribution in a tube reactor. The axial dispersion of laminar flow in a straight tube is very high and generates a wide residence time distribution. However, secondary flows improve the radial mixing, which are investigated in this paper for curved tube reactors. Design notes for good radial mixing and geometric designs of tube reactors with baffles are presented.     

A STUDY OF THE HIGH PRESSURE POLYETHYLENE TUBULAR REACTOR

As an example of the free radical polymerization reactor we have conducted a theoretical study of the high pressure polyethylene tubular reactor with cooling from the jacket. The plug flow model including the axial dispersion is considered with as well as without the steady state assumption for the active intermediates. We observe that the axial dispersion has negligible effect on the reactor performance and that the steady slate assumption is quite reasonable. The performance of the reactor is characterized by the exit monomer conversion, the peak temperature and the number and weight average degrees of polymerization, and the effects of various operating conditions are extensively investigated. Finally, an optimal temperature policy that would maximize the exit monomer conversion is determined by means of the Maximum Principle.     

Start-up procedures for continuous flow emulsion polymerization reactors

Experiments have been carried out using a continuous flow back-mixed emulsion polymerization reactor. Styrene was used as monomer. Particular attention was given to the effects of start-up procedure on reactor behaviour. Steady feed rates were not always accompanied by steady conversions of monomer. In some cases, especially at high initiator concentrations, oscillations occurred in the conversion. For a given feed composition and space time changes i start-up procedure could affect both transient and long term reactor behaviour. In some cases eventual conversions could be tripled by changing the sta procedure. When conversions reached a high and near-constant value, significant increases in the average size of polymer particles could still occur. T was accompanied by an increase in the average number of radicals per particle. The results cannot be described by simple reactor models and it is sugge that more than one process for particle formation might be operative.     

Polymerization of styrene in a continuous filled tubular reactor

Free radical solution polymerization of styrene has been studied using a binary mixture of symmetrical bifunctional initiators in a filled tubular reactor packed with static mixers. Owing to intensive radial mixing induced by the static mixers, a near plug flow pattern was obtained in the reactor with some axial dispersion effect. The axial mass dispersion coefficient was determined from the residence time distribution experiment and a dynamic axial dispersion model has been developed and solved to investigate steady state and transient behavior of the filled tubular reactor. With a solvent volume fraction of 0.3, the monomer conversion up to 70% was obtained without fouling problems in the temperature range 90 to 120°C. The experimental filled tubular reactor was operated under various reaction conditions and a reasonably good agreement between the model and the experimental data was obtained without using any adjustable parameters.     

Simulation of catalytic fluidized bed reactors by a transient axial dispersion model with invariant physical properties and nonlinear chemical reactions

This paper presents a transient axial dispersion model for an isothermal, catalytic fluidized bed reactor, which is frequently employed in synthetic production processes including coal gasification and liquefaction. A non-linear chemical reaction is considered to occur in the reactor. This model of a fluidized bed reactor takes into account the axial dispersion in the three phases, bubble, cloud-wake and emulsion. The physical properties along the axial coordinate are invariant in the model. Transient characteristics of the gas reactant, and the length of the transient period have been examined based on the model. The model compares favorably with experimental data in the steady state condition.     

Mathematical modelling of fluidized bed reactors—III: Axial dispersion model

An axial dispersion model has been developed for a continuous fluidized bed catalytic reactor with a cocurrent flow of the emulsion phase gas and the catalyst particles. The influence of some parameters on multiplicity of steady states has been reported. Several examples illustrating the transient behavior of the system are presented. In cases where three steady states are possible it appears that the intermediate steady state is unstable, while the lower and the upper steady states are locally stable. It was noted that the initial temperature of the emulsion phase is a predominant factor in determining which steady state will be approached.     

Modeling of chemical reactors—XXX: Steady-state analysis of combined axial and gas-to-solid heat and mass transfer in a tubular adiabatic reactor

The topic of interest in this paper is the behaviour of a dispersion model which embraces external gas-to-solid heat and mass transfer. Two methods of solution of transport equations-shooting technique and parameter mapping method are suggested. The effect of governing parameters on the occurrence of multiple steady states is investigated. It is shown that multiple steady states can be caused by two factors: axial dispersion and external gas-to-solid heat and mass transfer. If the interphase heat and mass transfer is responsible for the multiple steady states then an infinite number of steady states may exist. Under certain conditions hot spot temperatures may be expected in an adiabatic reactor.