On the dynamic behaviour of a class of homogeneous continuous stirred tank polymerization reactors

The steady state and dynamic behaviour of two typical vinyl polymerizations (polymethylmethacrylate and polystyrene with AIBN) carried out in a CSTR has been analyzed. Both the cases of constant and dynamically varying initiator concentration were treated for a wide range of reactor operating conditions. The results show that multiple steady states are possible even under isothermal conditions, but only unstable limit cycles appear possible for the systems studied.     

Dynamic simulation of propylene polymerization in continuous flow stirred tank reactors

The dynamic operation of an ideal continuous-flow stirred tank slurry reactor for propylene polymerization has been studied. A simple model is developed, which could be used for optimal computer control using advanced strategies. Step increases in input feed rates of propylene, solvent, and catalyst are used as the stimuli or forcing functions. It is assumed that the volume of the slurry in the reactor is maintained constant during the period. Responses of three output variables are studied, namely, monomer concentration in the liquid, volume-fraction of solids in the exiting slurry, and average mass fraction of catalyst in the exiting macroparticles. It is found that the transients last for about five times the mean residence time of the reactor. Competing effects of changes in the diffusional resistance, number density of catalyst particles, and washout and dilution effects lead to interesting dynamic results.     

Simulation of reversible nylon-66 polymerization in homogeneous continuous-flow stirred tank reactors

Experimental data of Ogata¹ has been curve-fitted to obtain the forward and reverse rate constants for nylon-66 polymerization. Its molecular weight distribution (MWD) has been simulated in homogeneous continuous-flow stirred tank reactors (HCSTR) for 11 h of residence time when the reaction mass is very close to equilibrium. The set of algebraic equations have been solved using Brown's algorithm,² which was found to be more efficient compared to the Gauss-Jordon techniques of solution. The MWD thus obtained is compared with our earlier simulation of the molecular weight distribution from batch reactors³ and was found to differ significantly. In HCSTR, the weight fraction distribution does not undergo a maximum and the polydispersity index ρ of the polymer formed is much higher than that obtained from batch reactors. The number and weight average of the polymer formed in HCSTR is found to be significantly lower.     

On the dynamic behavior of continuous stirred tank reactors

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.     

Effect of multiple feeds on a termination-free polymerization in continuous stirred tank reactors

The effect of monomer and initiator feeds to each of a series of continuous stirred tank reactors (CSTR) on the molecular weight distributions, average molecular weight, polymer production rate, and initiator and monomer conversions is studied for the termination-free polymerization system. For initiator feed concentrations less than 0.001 mole/liter, the distribution becomes narrower as the polymer progresses from reactor 1 to reactor 3. But for concentrations of initiator of 0.01 mole/liter, the distribution may be broadened from reactor 1 to reactor 3. The broadening of the distribution results in the production of a lower molecular weight polymer.     

On the detailed dynamics of coupled continuous stirred tank reactors

The dynamic behaviour of coupled parallel and serial arrays of cells is analysed. Phenomena such as synchrnization of oscillations at a common frequency, rhythm splitting, amplitude amplification, jump between oscillatory regimes and quasi-periodic oscillations of a torus type have been observed for an autocatalytic reaction with product inhibition. The possibility of steady-state operation driven by the coupling of two cells, each of which is oscillatory by itself, has been detected. The configuration of the cell arrays does not change the bifurcation pattern drastically.     

Forced oscillations in continuous flow stirred tank reactors with nonlinear step growth polymerization

The self-step growth polymerization of RA_f monomers in homogeneous, continuous flow stirred tank reactors (HCSTRs) is simulated under conditions of periodic feed concentration (with frequency ω and amplitude α). By having periodic operation, the polydispersity index of the polymer is found to increase by about 35% over the values at steady state. Periodic operation of HCSTRs is found to lead to gelation only for certain values of the frequency and the dimensionless residence time τ^*. Gelling envelopes have been obtained to give conditions under which HCSTRs should be operated. These envelopes can be described in terms of two critical dimensionless residence times, τ and τ such that nongelling operation is always ensured when τ^* < τ. For τ^* > τ, periodic operation always leads to gelation, and HCSTRs cannot be used. For τ < τ^* < τ, the gelling behavior is found to depend on the functionality f, amplitude α, and the dimensionless residence time τ^*.     

Fed-batch operation of stirred reactors

Numerical algorithm for the computation of the dependence of periodic solutions on parameters in fed-batch or periodically operating reactors is described. Results for the simulation of a simple model of anaerobic digester and of a first order exothermic reaction are then discussed and various types of m-periodic solutions are presented. The possibility of existence of chaotic solutions is also illustrated.     

ABA block copolymers without tapering by isokinetic living anionic polymerization in a series of stirred tank reactors

Equations for the molecular weight distribution and the average molecular weights of a living anionic polymerization with very rapid or slow initiation are presented for a series of stirred tank reactors. It is shown that polydispersity of the polymer in the last vessel of a cascade takes for nearly complete conversion of monomer then a minimum, when the reaction is performed isokinetically with concern to monomer conversion, i.e. when monomer conversion in each vessel of a cascade of n tanks is 1/n. Now, polydispersity of the polymer in the mth vessel of the cascade (1 ≤ m ≤ n) is D_m = 1 + 1/m. Values of all systems variables needed for isokinetic control of the polymerization may be precalculated from kinetic models. For vessels of equal size and with equal residence times reaction temperature is suggested as control variable increasing stepwise from vessel to vessel. The proposed procedure was checked for the systems styrene/n-butyllithium/toluene, styrene/s-butyllithium/benzene, and isoprene/s-butyllithium/n-heptane. A satisfying agreement between calculated and measured values of the objectives monomers conversion, number average molecular weight, and polydispersity was found. It is proposed to use the described procedure for the preparation of ABA block copolymers with negligible tapering between the blocks by living anionic polymerization in a series of stirred tank reactors.     

Dynamics of a cascade of two continuous stirred tank polymerization reactors with a binary initiator mixture

The dynamic behavior of two continuous stirred tank reactors in series has been investigated for free radical solution polymerization of styrene with a binary mixture of two initiators having different thermal decomposition activities. For a wide range of initiator feed composition, both reactors exhibit quite complex nonlinear steady state and transient behavior. When the reactor residence time is used as a bifurcation parameter, the second reactor can have up to five steady states. For certain range of reactor operating conditions, bifurcations to various types of periodic solutions have been observed, such as Hopf bifurcation, isolas, period doubling, period-doubling cascade, and homoclinics. The effects of other reactor variables, such as total initiator concentration, coolant temperature, and reactor volume ratio on the reactor dynamics, are illustrated to show the complex dynamic behavior of the two-reactor system catalyzed by a mixture of t-butyl perbenzoate and benzoyl peroxide.     

Optimal hybrid modeling approach for polymerization reactors using parameter estimation techniques

The dynamics of polymerization catalytic reactors have been investigated by many researchers during the past five decades; however, the emphasis of these studies was directed towards correlating process model parameters using empirical investigation based on small scale experimental setup and not on real process conditions. The resulting correlations are of limited practical use for industrial scale operations. A statistical study for the relative correlation of each of the effective process parameters revealed the best combination of parameters that could be used for optimizing the process model performance. Parameter estimation techniques are then utilized to find the values of these parameters that minimize a predefined objective function. Published real industrial scale data for the process was used as a basis for validating the process model. To generalize the model, an artificial neural network approach is used to capture the functional relationship of the selected parameters with the process operating conditions. The developed ANN-based correlation was used in a conventional fluidized catalytic bed reactor (FCR) model and simulated under industrial operating conditions. The new hybrid model predictions of the melt-flow index and the emulsion temperature were compared to industrial measurements as well as published models. The predictive quality of the hybrid model was superior to other models. The suggested parameter estimation and modeling approach can be used for process analysis and possible control system design and optimization investigations.     

The modeling of batch and continuous emulsion polymerization reactors. Part II: Comparison with experimental data from continuous stirred tank reactors

A detailed model for emulsion polymerization is compared with extensive data from continuous stirred tank reactors. Model predictions are compared with both steady-state and dynamic data, for polymerization of styrene, methyl methacrylate, and vinyl acetate. Good agreement between model and experiment is achieved with one set of parameters and without any data fitting. The results show that the model is capable of predicting all of the experimentally observed phenomena including steady-state multiplicity, sustained oscillations, ignition and extinction dynamics, and overshoot during start-up.     

Periodic regimes of continuous stirred tank reactors

The scheme of analysis of the dynamic behaviour of continuous stirred tank reactors is developed. All classes of possible phase plots and their position in the parameter space are established for the case of the nth order exothermic reaction.     

Scale-up of continuous flow stirred tank reactors

A model of a continuous flow stirred tank reactor based on laboratory experiments successfully describes the behavior of a pilot plant reactor. This model simulates the pilot plant performance over the full range of operating conditions: at high impeller speeds where performance approaches that of a perfectly mixed reactor and at low impeller speeds where performance significantly differs from perfect mixing. The micro-mixed feed model divides the continuous flow stirred tank reactor into a small micro-mixed impeller zone and a large macro-mixer.     

An analytical solution of the molecular weight distribution of reversible step growth polymerization in homogeneous continuous flow stirred tank reactors

Mole balance for the molecular weight distribution in homogeneous continuos-flow stirred tank reactors (HCSTRs) for reversible step-growth polymerization has been written. The relation for the moment generating function G is found to be a nonlinear ordinary differential equation and has been solved analytically. The solution of the MWD of the polymer formed is shown to be valid even if the condensation product is removed. At equilibrium, the solution reduces to the Flory distribution. The computations show that the polydispersity of the polymer first increases with the residence time θ of the reactor, but, for large θ, it reduces to the equilibrium value after undergoing a maximum.     

Pattern formation in interacting continuous stirred tank reactors

The dynamic behavior of coupled continuous stirred tank reactors in which the nonisothermal Langmuir-Hinshelwood type reactions occur, exhibits several types of pattern formation. The regular and irregular multipeak patterns are detected for the endothermic reaction of a Langmuir-Hinshelwood type when the heat communication between the neighboring cells is larger than the mass interaction. These observations may imply the possible existence of spatial structure in a matrix of catalysis, the non-uniform distribution of concentration and temperature in packed bed reactors, and corrugated propagating fronts in combustion problems.