State multiplicity in PFR-separator-recycle polymerization systems

This article explores the non-linear behaviour of isothermal and non-isothermal plug-flow reactor (PFR)-separator-recycle systems, with reference to radical polymerization. The steady-state behaviour of six reaction systems of increasing complexity, from one-reactant first-order reaction to chain-growth polymerization, is investigated. In PFR-separator-recycle systems feasible steady states exist only if the reactor volume exceeds a critical value. For one-reaction systems, one stable steady state is born at a transcritical bifurcation. In case of consecutive-reaction systems, including polymerization, a fold bifurcation can lead to two feasible steady states. The transcritical bifurcation is destroyed when two reactants are involved. In addition, the thermal effects also introduce state multiplicity. When multiple steady states exist, the instability of the low-conversion branch sets a lower limit on the conversion achievable at a stable operating point. A low-density polyethylene process is presented as a real plant example.The results obtained in this study are similar to CSTR-separator-recycle systems. This suggests that the behaviour is dictated by the chemical reaction and flowsheet structure, rather than by the reactor type.     

Steady-state multiplicity in the autohumidification polymer electrolyte membrane fuel cell

“Ignition/extinction” phenomena and steady-state multiplicity were discovered in an autohumidification polymer electrolyte membrane fuel cell. At steady state, the water produced by the fuel cell reaction is balanced by water removal by the flowing reactant gas streams. Ignition, corresponding to a high fuel cell current, arises from positive feedback between the water produced by the reaction and the transport of protons in the membrane. A critical level of membrane hydration is required for ignition; insufficient membrane hydration will extinguish the fuel cell current. This new autocatalytic mechanism has an interesting analogy to the autothermal reactor.     

Suspension polymerisation of methyl methacrylate using sodium polymethacrylate as a suspending agent

Aqueous solutions of sodium polymethacrylate (PMA-Na) are used as suspending agents for the suspension polymerisation of methyl methacrylate. These aqueous polyelectrolyte solutions are viscous and they show a non-Newtonian shear thinning behaviour. The Sauter mean drop diameter decreases with increasing continuous-phase viscosity, but increases with increasing stirring speed. The maximum drop sizes follow the same trends. The Sauter mean diameter also decreases, initially, for increasing hold-up, reaches a minimum, and then increases with increasing hold-up. Taylor's theory of viscous break-up seems to be suitable to describe the breakage of the droplets.     

Transitional emulsion polymerisation: Zero-one to pseudo-bulk

The transitional behaviours of emulsion polymerisation for styrene and butyl acrylate (BA) monomers from zero-one to pseudo-bulk regime were mechanistically investigated. A dynamic mathematical model, which incorporates cross-over mechanism from zero-one to pseudo-bulk kinetics was developed for emulsion polymerisation and compared with experimental data for conversion, particle size and molar mass. Particles smaller than cross-over size follow zero-one kinetics and particles greater than cross-over size, they follow pseudo-bulk kinetics. In our mechanistic approach, particles nucleated from micelles, grow until the cross-over size is attained, based on zero-one kinetics, and subsequently continue to grow based on pseudo-bulk kinetics. Key findings from our work are that the developed transitional model predictions agree reasonably with experimental data on process and product attributes such as conversion, average molecular weight, molecular weight distribution (MWD), average particle size and particle size distribution (PSD). Optimal strategies for semibatch operation was developed using reaction temperature and monomer feed rate as process variables with specified initial conditions.     

Analysis of shear-induced coagulation in an emulsion polymerisation reactor using computational fluid dynamics

Shear-dependent coagulation is a costly problem for the latex manufacturing industry, due to product degradation and reactor downtime. In this study, a method for calculating the shear-dependent coagulation rate in emulsion polymerisation is developed. The method combines simple models for coagulation (only binary collisions being considered) with the effects of rheology on the flow field, using computational fluid dynamics (CFD) to solve the detailed flow field in the reaction vessel. By using the local shear rates (LSR), the method developed provides a more detailed and system-specific assessment compared with using an average shear rate (ASR) for calculating the coagulation rate. The difference in the predictions between the ASR and the proposed LSR method was investigated. It was found that the ASR and LSR methods predict different coagulation rates, especially for more sophisticated coagulation models where the coagulation rate is not linearly dependent on the shear rate. The LSR method was also used to study the effect of the rheology of the latex, of the impeller speed and of the reactor design on the coagulation rate. It was found that the LSR method is useful for providing both visual and numerical means to identify regions with elevated coagulation rates in the modelled reaction vessel. The treatment provides estimates of the amounts of coagulum formed on the vessel walls and on the impeller.     

Kinetics of catalytic reactions with two types of sites: nonuniform surfaces

Several aspects of heterogeneous catalytic kinetics over induced nonuniform surfaces are considered. The reaction mechanism is thought to occur through a surface collision of species, adsorbed on two distinct surface sites, which display nonuniform behavior. The expressions for rates of elementary reactions have been deduced within the framework of the surface electronic gas model, which accounts for the case of inhomogeneous surface. Equations for catalyst activity in the range of medium coverage have been derived and compared with the power-law model.     

General rate equations and their applications for cyclic reaction networks: multi-pathway systems

Many chemical reactions of industrial importance involve complex reaction pathways and networks; and the determinations of the reaction rate laws are very difficult. The accurate or proper rate expression is the most desired information in design phase however. In this study, the network reduction technique and the Bodenstein approximation of quasi-stationary behavior of reaction intermediates were systematically applied to derive general rate and instantaneous rate ratio equations for multi-pathway reaction networks in homogeneous catalysis or enzyme system. Multiple small reaction cycles in a main cycle, and multiple-pathways stemming from an intermediate and ending at different nodes in a cycle were considered. The general rate and rate ratio equations derived in this study are applicable for most homogeneous catalytic reactions and enzymatic reactions. Two examples of multi-pathway cyclic enzyme reaction were used to illustrate the applications of the general rate and rate ratio equations for network elucidation.     

The dynamic response of PEM fuel cells to changes in load

The dynamic response of the stirred tank reactor (STR) polymer electrolyte membrane (PEM) fuel cell has been explored over the temperature range of 35-. When the fuel cell was operated in the autohumidification mode the fuel cell current “ignited’’ when the membrane water content was greater than a critical level of ∼1.6 H₂O/SO₃, and it extinguished when the initial membrane water content was below this critical level. Above , two stable “ignited’’ states were observed at intermediate load resistances; these steady states corresponded to different levels of membrane hydration. At low load resistances only a single ignited steady state was observed with high membrane hydration, and at high load resistances only a single ignited steady state was observed with intermediate membrane hydration. Hysteresis between the two ignited states was observed; the steady state selected depended on the initial conditions in the fuel cell. The time constant for the fuel cell current to reach steady state after a change in the load resistance was ∼10³-. Below only one “ignited’’ state and the extinguished state were observed in the autohumidification fuel cell. After 3000 h of operation the STR PEM fuel cell current and effluent relative humidities oscillated autonomously between two membrane hydration states with a period of oscillation of ∼10,000 s. The oscillations showed abrupt transitions indicative of a capacitive switch. These complex dynamics of PEM fuel cell operation are associated with the membrane water uptake. It is hypothesized that water produced and swells the membrane, altering the interfacial membrane-electrode contact.     

Evaluating the performance of a cascade of two bioreactors

We investigate a reactor network consisting of two chemostats in series. Previous researchers have compared the performance of a two-reactor system against a single reactor having the same total residence time. In this paper, we suggest that it is more natural to compare the performance of a cascade against the optimal performance a single-reactor system having the same, or smaller, residence time.We consider a biological system in which the growth rate is given by a Monod expression with a variable yield coefficient. We find that it is possible for this model to obtain a significant increase in performance by using a two-reactor system. However for the two-reactor system the performance enhancements are achieved when the system reaches a time-invariant steady-state rather than under conditions which produce self-generated oscillations, which was the focus of interest of earlier researchers.     

Precipitation polymerisation of vinylidene fluoride in supercritical CO2 and real-time calorimetric monitoring

Vinylidene fluoride was polymerised in supercritical carbon dioxide. Power compensation calorimetry was used to monitor the polymerisation process on-line. The polymer product was found to have a low apparent-density, leading to an observed high solid content in the autoclave at low yields. In situ calorimetry showed a sharp transition of the heat transfer in the reactor, leading to a useful parameter for monitoring the polymerisation process. The stirring rate was found to have no effect on the molecular weight, but did modify the calorimetric traces and the morphology of the polymer. The polymerisation at a lower pressure resulted in a lower molecular weight product and a lower polymerisation rate.     

On the residence time distribution in reactors with non-uniform velocity profiles: The horizontal stirred bed reactor for polypropylene production

Horizontal stirred bed reactors for polypropylene production have a typical axial powder mixing pattern which is unique for polyolefin gas-phase reactors. The polymer, although adhering to the catalyst particles, has a shorter mean residence time and a broader residence time distribution than the catalyst. Both polymer and catalyst residence time distributions, strongly depend on the temporal catalyst activity profile. The powder mixing pattern in a horizontal stirred bed reactor results from two transport effects: the continuously increasing powder net flow in the downstream direction caused by the particle growth, and the simultaneous stirring flows with equal intensity in the up- and downstream directions. Both together lead to a residence time distribution of the reacting catalyst particles between fully backmixed and plug flow. A modelling approach is proposed which describes the axial flow contributions of stirring and polymerisation separately, and which is more accurate and flexible than simple cells-in-series models used in most papers so far. For large-scale reactors, residence time distributions are predicted from experimental pulse-response curves obtained in a miniaturised mixing model without reaction. Residence time distributions equivalent to “three to five” well-mixed reactors in a series reported in the literature are experimentally accessible only with difficulties under polymerising conditions. With the modelling approach proposed in this paper, the “reacting” RTD can be calculated on the basis of the cold-flow experimental data. We compare the proposed modelling concept with simple cells-in-series models by simulating catalyst yields, particle size distributions and catalyst transitions using two model catalysts with different activity profiles. The selection of the right modelling approach has indeed a significant influence on the simulation results, especially if the throughput or the axial velocity profile is changing and the catalyst is not deactivating.     

Steady state multiplicity in an UOP FCC unit with high-efficiency regenerator

The possibility of existence of multiple steady states in fluid catalytic cracking (FCC) units has a major impact in the supervision of these systems. The origins of these behaviours are usually due to the exothermicity of the catalyst regeneration reactions and to the strong interactions between the reactor and the regenerator system.Prior work has focused on modelling and control problems of different operating FCC units. However, none of these studies have considered a high-efficiency regenerator. This paper presents an analysis of the existence of output and input multiple steady states in an UOP FCC unit with a high-efficiency regenerator.The influence of unit disturbances and model uncertainties, such as coke composition and cracking enthalpy, in the output multiplicity, was studied and the results show that the high-efficiency regenerator exhibits at least three multiple output steady states and a maximum of five output steady states, in the operating range considered. Moreover, the state multiplicity analysis revealed that input multiplicity can be present in this FCC unit, depending on the choice of the control structure, and that operating the unit in full combustion mode can prevent instabilities due to input and output multiplicities. Therefore, these results can be used to guide the design of the most appropriate control structures in industrial applications. For the FCC unit with high-efficiency regenerator the most appropriate control structure corresponds to the control of the riser reactor temperature and the oxygen level in the flue gas, with the catalyst circulation rate and the combustion air flow rate, respectively.     

Semi-batch emulsion copolymerization of styrene and butyl acrylate for production of high solids content latexes: Experiments and mathematical model

Polymer latexes with high solids content exhibit several advantages such as lower costs of transport and storage and shorter drying and film formation times. To keep the apparent viscosity at satisfactory levels, the particle size distributions should be either broad or multimodal. In the present work, the production of high solid content latexes by emulsion copolymerization of styrene and butyl acrylate was studied in a semi-batch process in which the nucleation of a second population of particles is promoted by the instantaneous (shot) feeding of an additional charge of emulsifiers. Latexes of about 64 wt% of solids with bimodal particle size distributions and reasonably low apparent viscosity were produced. A representative mathematical model for the copolymerization processes that accounts for the changes in the particle size distribution that occurred in the process is presented, tested and validated with the experimental data measured during the experiments.     

Effects of thermal history on the polymerisation mechanism and network development in aromatic polybenzoxazines

The effect of heating rate (2, 8 and 15 K min^-1) during the initial stages of cure of 2,2-bis(3,4-dihydro-3-phenyl-2H-1,3-benzoxazine)propane is examined. The rate of heating has a marked effect on the observed modulus, measured by DMTA, with the higher heating rate giving rise to an increase in storage modulus of ca. 1000 MPa, although this is not accompanied by an increase in glass transition temperature. The thermal stability of the resulting polybenzoxazines also differs with the slower heating rate giving rise to less thermally stable structures. Data obtained from Raman spectroscopy (when combined with principal components analysis) suggest subtle changes in the mechanism during the early stages of reaction associated C–N–C and C–O moieties, some of which persist following a higher temperature postcure step leading to a crosslinked network with higher aliphatic character.     

Thermodynamic optimization of energy transfer in (bio)chemical reaction systems

The engineering science literature on energy-transfer processes (heat engines, heat pumps, etc.) for the production of mechanical energy, electricity, cold or heat has produced some remarkable results on maximum power and efficiency optimization. We have wondered in how far these results can be extended to include chemical reaction systems to describe living and possibly future-industrial energy-transfer systems. With elements of non-linear irreversible thermodynamics and chemical kinetics, we have arrived at some interesting results on optimizing the performance of chemical energy transfer. We discuss thermodynamic efficiency, energy-transfer rate, entropy-generation rate, and optimum-performance characteristics of (bio)chemical energy transfer.     

Nonlinear model reconstruction by frequency and amplitude response for a heterogeneous binary reaction in a chemostat

Here we present an analysis of a binary heterogeneous reaction in a chemostat for the particular case of reagents with unequal mass transfer coefficients. For fast irreversible kinetics, there are two potential steady states—the dispersed phase is preferentially populated by one reagent and essentially depleted of the other. The selection of which steady state occurs depends on the operating parameter which is the concentration ratio σ of the slower (B) to the faster (A) transferring reagent in the feed stream. The demarcation between these operating regimes is the critical value of this ratio:

     

Capillary reactor for cyclohexane oxidation with oxygen

Cyclohexane oxidation is the first step in the currently used technology for production of Nylon-6 and Nylon-6,6 which employs a two-stage process. In the first stage 80% selectivity to two main products, cyclohexanol and cyclohexanone (KA oil) is obtained at 4–8% cyclohexane conversion in staged bubble columns or stirred tanks. There have been reports that increased oxygen concentration in the gas phase or pure oxygen is beneficial to cyclohexane oxidation and this was confirmed in our previous study (Jevtic et al., 2009). To fully utilize this advantage here, we present a novel, safer capillary reactor for cyclohexane oxidation with pure oxygen. The discrepancy between the experimental and modeling results was attributed to lower than expected mass transfer achieved in the capillary. With a better design for gas–liquid mixing and contacting this type of a reactor could potentially become attractive for gas–liquid reactions of similar nature.     

Application of zeolite T membrane to vapor-permeation-aided esterification of lactic acid with ethanol

Zeolite T membranes were applied to vapor-permeation-aided esterification of lactic acid with ethanol. The hybrid process provided almost complete conversion within a short reaction time by removing water from the reaction mixture. Zeolite T membrane worked steadily for a long time. The reaction time-courses were described by a model based on the assumptions that the esterification obeyed second-order kinetics and the permeation flux of each component was proportional to its concentration in the reaction mixture. The final reaction liquid mixtures consisted mostly of ethyl lactate and ethanol with little ester of polylactic acids, although concentrated lactic acid solution was used as a source.     

Variant and invariant states for chemical reaction systems

Models of chemical reaction systems can be quite complex as they typically include information regarding the reactions, the inlet and outlet flows, the transfer of species between phases and the transfer of heat. This paper builds on the concept of reaction variants/invariants and proposes a linear transformation that allows viewing a complex nonlinear chemical reaction system via decoupled dynamic variables, each one associated with a particular phenomenon such as a single chemical reaction, a specific mass transfer or heat transfer. Three aspects are discussed, namely, (i) the decoupling of reactions and transport phenomena in open non-isothermal both homogeneous and heterogeneous reactors, (ii) the decoupling of spatially distributed reaction systems such as tubular reactors, and (iii) the potential use of the decoupling transformation for the analysis of complex reaction systems, in particular in the absence of a kinetic model.