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Multiplicity and Stability of Chemical Reactors with Evaporative Cooling
Abstract
This work characterizes the dynamic behavior of reactors with evaporative cooling. The process under consideration is a continuous stirred tank reactor used to carry out an exothermic irreversible first-order reaction with heat removal through the wall as well as by partial evaporation of the reacting liquid followed by return of the condensate to the reactor. Bifurcation analysis is used to classify the stability character and the types of multiplicity and oscillatory behavior to be expected. A variety of practical situations is examined, including cases of volatile reactant, volatile or nonvolatile product (liquid or solid), and volatile solvent. For a fixed vapor flowrate to the condenser, the dynamic structure of reactors with evaporative cooling is qualitatively similar to the case with wall cooling alone. Other cases show significantly different structures. Cases with five steady states and two regions of three steady states are found with evaporative cooling operation, and for some conditions even seven steady states may be possible. A rich variety of dynamic behavior is predicted.
Dynamic model development and control of an existing operating industrial continuous bulk free radical styrene polymerization process are carried out to evaluate the performance of auto-refrigerated CSTRs (continuous stirred tank reactors). One of the most difficult tasks in polymerization processes is to control the high viscosity reactor contents and heat removal. In this study, temperature control of an auto-refrigerated CSTR is carried out using an alternative control scheme which makes use of a vacuum system connected to the condenser and has not been addressed in the literature (i.e. to the best of our knowledge). The developed model is then verified using some experimental data of the real operating plant. To show the heat removal potential of this control scheme, a common control strategy used in some previous studies is also simulated. Simulation results show a faster dynamics and superior performance of the first control scheme which is already implemented in our operating plant. Besides, a nonlinear model predictive control (NMPC) is developed for the polymerization process under study to provide a better temperature control while satisfying the input/output and the heat exchanger capacity constraints on the heat removal. Then, a comparison has been also made with the conventional proportional-integral (PI) controller utilizing some common tuning rules. Some robustness and stability analyses of the control schemes investigated are also provided through some simulations. Simulation results clearly show the superiority of the NMPC strategy from all aspects.
Titanium silicalite (TS-1), discovered in 1979, proved to be a valuable catalyst for a number of different oxidation reactions with hydrogen peroxide. This section provides a personal, historical account of the discovery of TS-1 and of the industrial development of the first commercial process that exploited its catalytic properties: the oxidation of phenol to produce a mixture of hydroquinone and catechol. Details on the process features are also provided. Brief information is also disclosed on early development of other processes.
This study illustrates the optimization of the O-arylation step of fluoxetine hydrochloride (1) synthesis. In the
entire process, this is the most critical step that dictates the yield and quality of the product. The highlight of the process is the concept of evaporative cooling that was employed in manipulating the above highly exothermic reaction by introducing toluene as the cosolvent. The evaporative cooling not only aided in getting an efficient procedure but also increased the yield of 1 and simplified the work-up procedure. This was a protective approach adopted for process safety, considering the worst-case scenario in the plant.
The multiplicity features of a continuous stirred tank reactor with vapor recycle have been studied for a dimerization reaction with second-order kinetics. Such reaction systems are common in the polymer industry. The aim of the analysis is to provide a simple design methodology that will ensure safe operation of the reactor. It is shown that solutions with and without vapor recycle exist. The bifurcation set for the system is calculated, and 11 different bifurcation diagrams arise. A linear relationship exists between the system parameter values, when these are normalized by their values at the ignition point. This leads to a simple method for defining a safe operating point for the system under a defined disturbance. © 2012 American Institute of Chemical Engineers AIChE J, 59: 553–559, 2013
Evaporative cooling is an attractive mechanism for heat removal in polymerization reactors where fast, exothermic reactions and high viscosities complicate other means of heat removal. In this work we consider the effect that the mechanism has on the dynamics of a well mixed tank reactor for solution free-radical polymerization of styrene. Continuation and stability analysis reveals the existence of isola structures and oscillatory behavior at typical industrial conditions as well as strong coupling of the degree of evaporative cooling with important parameters like residence time, feed initiator concentration, jacket temperature, and reactor size. Further analysis is performed to try to understand the impact that this behavior has on practical aspects such as reactor design, scale-up, and operation.
A continuous stirred tank reactor subject to random fluctuations in flow rate and inlet temperature was simulated on a hybrid computer. The stochastic response of the reactor about unique stable deterministic steady states was studied as a function of the damping coefficient and response time of the deterministic system and the power spectrum of the stochastic input. It was found that the stochastic response could be classified into categories similar to those used for forced periodic systems according to the relationship between the deterministic system response time and the 90% cut-off frequency of the stachastic input. The nature of the stochastic response is predictable for relatively low frequency inputs but unexpected results may occur at intermediate frequencies. The magnitude of reactor state fluctuations was seen to be dependent on the deterministic damping coefficient. The distribution of reactor states was studied as a function of input process variance and it was found that the distribution can become bimodal even when the associated deterministic steady state is unique.The concept of stochastic stability is discussed and several practical stochastic stability definitions are proposed. The stochastic stability of the random systems was seen to be well described by the stochastic regions of operation predicted by the input process power spectrum and the deterministic system response time. The input variance levels necessary to produce stochastic instability can be estimated in the Quasi Steady region of operation. It was found that exposure of an autonomous limit cycle about a unique unstable deterministic steady state to high frequency random inputs may lead to effective stabilization.
Experiments are reported on the reaction of methanol vapour with hydrogen chloride to give methyl chloride and water in a two phase stirred tank reactor. The reactants enter and the products leave, as vapours but the reaction takes place in a concentrated aqueous solution of zinc chloride. The system may reach a steady state, display limit-cycle behaviour or overflow depending on the conditions. A theoretical analysis indicates that one or two equilibrium points can occur which have dynamic characteristics in accord with the observed behaviour. In applying Bendixson's Theorem particular attention must be paid to the boundedness constraints.
The dynamic behavior of the continuous stirred tank reactor is analysed and classified for a variable reactor residence time. Although earlier work, treating the bifurcation to limit cycles and steady states with changing Damköhler number, yields a complete description of the problem, the evolution of multiple steady states and limit cycles is much more bizarre as the reactor residence time varies. In addition, it is the reactor residence time which is most easily varied experimentally so that the present results are more readily compared with experiment. Plots are given to show the influence of system parameters on the reactor behavior.
Autorefrigerated or evaporatively cooled chemical reactors use the heat of vaporization to remove the heat generated by exothermic chemical reactions. Liquid in the reactor is at its bubblepoint. The vapor boiled from the liquid is condensed in a heat exchanger and the condensate is returned to the reactor. One of the major advantages of this type of reactor is that the area for heat transfer is not limited by reactor size because the heat exchanger can be specified to be any desired size. This aids in scale-up since heat-transfer area can be scaled directly with reactor volume and heat generation. Despite their widespread use in industry, little has appeared in the literature dealing with this type of reactor. This paper presents a quantitative study of temperature control of boiling-liquid reactors. The effects of conversion and activation energy are explored. The major contribution of this paper is a demonstration that the condenser heat-transfer area required for dynamic stability can be an order of magnitude larger than that suggested by conventional steady-state heat-transfer design heuristics.
Many highly exothermic gas-liquid reactions are carried out with a vaporizing solvent, which after condensation is returned to the reactor. In this way the liberated reaction heat for a large part is absorbed by the cooling water flowing through the condenser. In order to determine the influence of this evaporation on the behaviour of an agitated gas-liquid tank reactor a model second order reaction was studied. The temperature dependence of the enhancement factor is strongly affected by the solvent evaporation. The influence of several design and operation parameters such as liquid residen time, dilution of reactant with solvent, air excess in the gas phase and reactor pressure on the conversion and the reactor pressure is demonstrated. Multiplicity for the chosen model reaction will only occur under rather severe conditions. The theory developed is applied to an industrial air oxidati of a hydrocarbon.
The types of dynamic behavior possible for a single first order reaction carried out in a stirred tank reaction are classified according to values of the parameters and plots in parameter space used to define the various possibilites. Analytic criteria are developed which predict the existence and stability character of limit cycles as a function of the system parameters. The types of dynamic behavior predicted are illustrated by numerical computation of the temperature and concentration trajectories. Several kinds of new jump phenomena for this problem are observed and explained in terms of the parameter space plots. The theory and analysis methods can be easily generalized to other types of reaction systems.
The objective of this paper is to present a continuous stirred-tank model for processes in which a liquid is sprayed into a gas. In this model a uniform spray of droplets enters the reactor along with one or more gaseous reactants. Both the droplets and the gas are taken to be well-mixed in the reactor. The droplets evaporate and the resulting vapors combine homogeneously with the gaseous reactants. In the multicomponent case the droplets contain a mixture of two or more miscible components. Steady state and transient equations are derived, and the numerical methods of solution are discussed. Steady states are calculated for two-component systems of heptane-octane and hydrazine-water and for a three-component system of heptane-octane-nonane, with oxygen as the gaseous reactant in each case. In addition, a study is made of several parameters of the heptane-octane system. Stability is determined by calculating transients for selected perturbations from the steady states. Incorporated in the reactor model is an analytic model for the fluxes of vapors from a multicomponent droplet which exhibits the augmentation of transfer of one vapor due to the net flux of the remaining vapors. Also presented is an approximate model for the multicomponent spray reactor which gives good results for small droplets and requires only a fraction of the effort needed to solve the complete set of equations.
This is an analytical study of the influence of viscosity on the temperature control of a well-mixed continuous reactor producing polystyrene via thermal polymerization of styrene monomer. Three temperature control schemes are considered: (1) heat removal by cooling coils and a cooling jacket, (2) heat removal by vaporization and reflux of styrene and the solvent (autorefrigeration), (3) heat removal by a pump-around loop with external heat exchanger. In the coil/jacket-cooled reactor, the heat-transfer coefficient drops off dramatically with conversion, leading to a narrow operating range for controllability. This factor also reduces the potential for multiple steady states. The autorefrigerated reactor permits a broad range of temperature control with reflux of the condensed vapor and shows no potential for multiple steady states. Finally, the reactor cooled by the external pump-around loop and heat exchanger can provide the most robust temperature control with recirculation rate as an additional control parameter.
Removal of the exothermic heat of chemical reactons by autorefrigeration (vaporization of a liquid phase) is frequently used in continuous and batch chemical reactors. The vapor thus generated is usually liquified in a condenser and the condensate returned to the reactor.
This paper studies the effects of the formation of an inert gas by‐product on the stability and control of batch autorefrigerated reactors.
Stability is shown to be strongly influenced by the production of these inerts because their buildup in the condenser reduces heat removal capacity. Inert buildup can be reduced by venting, but excessive venting results in a loss of not only inerts but also of the volatile components in the system. This leads to higher reactor temperaturs, faster reaction rates and instability.
Digital simulation of a numerical example illustrates the effects of various parameters.
This paper discusses the effects of imperfect mixing on the stability of autorefrigerated chemical reactors. Mixing is shown to strongly influence stability in these evaporatively-cooled systems. A modified van Heerdensteady state stability analysis is presented. Computer simulation of a typical system illustrates the occurrence ofrunaways and local hot spots. Both continuous stirred tank reactors and batch reactors are considered.
The purpose of this paper is to consider the well agitated continuous reactor from the standpoint of stability of the steady state. It has been shown in the past that chemical-reaction systems may be unstable in the sense that on slight perturbation they tend to move to a more stable state or that they are stable in their steady states, small perturbations being self-correcting so that the system possesses autoregulation. In this paper methods of developing criteria for the quantitative determination of stability or instability or presented and applied to some simple problems. In order that the effect of large perturbations on the system may be determined, complete solutions of the rigorous equations are obtained on the analogue computer (R.E.A.C.). A complete plot of reaction paths in the concentration-temperature plane may be obtained in this manner. Because of the nonlinearity of the system one cannot predict with certainty what steady state will be approached after a given large perturbation, multiple steady states being assumed possible. From the phase plot of reaction paths the regions in the plane which lead to certain steady states are delineated. Also it is shown that the natural behavior of a reactor is not to approach an unstable state. So far as the reactor is concenrned, the unstable state does not exist. The stability of the system is important to the engineer, as control will be easy or difficult and product quality will be satisfactory or not depending upon the relative stability of the steady state. An unstable state would require more elaborate control than a stable state.
Stability of exothermic chemical reactors with cooling jackets or internal cooling coils has been extensively studied by steady state, phase plane, and linear analysis techniques. The purpose of this paper is to apply these techniques to the frequently encountered case of autorefrigerated or boiling liquid reactors. In these reactors the exothermic heat of reaction is removed, not by conductive and convective heat transfer, but by vaporization of a liquid phase or, more generally, by any kind of endothermic change in phase.
Open-loop and closed-loop stability of a continuous stirre-tank autorefrigerated reactor is studied. General equations are derived and illustrated by numerical examples.
Both constant and variable latent heats of vaporization are considered. A particularly interesting aspect of autorefrigerated reactor stability is operation near the critical temperature. Since the latent heat approaches zero, instability of the system is increased, representing a form of positive feedback in a chemical system.
Photocopy. Thesis (Ph. D.)--University of Wisconsin--Madison, 2000. Includes bibliographical references (p. 244-251).
Reactor Steady State Multiplic-ity and Stability. In Chemical Reaction and Reactor Engineering
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Modeling Dynamic Behavior, and Control of Chemi-cal Reactors with Evaporative Cooling ReceiVed for reView
- Z Soló
Soló, Z. Modeling Dynamic Behavior, and Control of Chemi-cal Reactors with Evaporative Cooling. Ph.D. Thesis, Department of Chemical and Biological Engineering, University of Wisconsin-Madison, 2000. ReceiVed for reView January 11, 2008 ReVised manuscript receiVed March 17, 2008 Accepted March 24, 2008 IE800044B Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9039
Reactor Steady State Multiplicity and Stability. InChemical Reaction and Reactor Engineering;Carberry
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