Design of tubular reactors in recycle systems

The article presents an approach to design tubular reactors in recycle systems, based on non-linear analysis. A pseudo-homogeneous plug-flow reactor model is used. It is assumed that the separation unit delivers product and recycle streams with fixed composition. The stand-alone reactor has a unique stable steady state. The coupled reactor–separation–recycle system shows four types of conversion versus plant Damköhler number bifurcation diagrams. A feasible steady state exists only if the reactor volume exceeds a critical value. For isothermal reactor, the steady state is unique and stable. For non-isothermal reactor, one or two steady states are possible. In the second situation the low-conversion state is unstable. In some parameter regions, the unique state is unstable. The design should ensure state unicity and stability, which are favoured by large heat-transfer capacity, low coolant temperature and high reactor-inlet temperature. A case study demonstrates that these phenomena can be easily found in real plants.     

Nonlinear control of competitive mixed‐culture bioreactors via specific cell adhesion

A nonlinear control strategy is developed for competitive mixed‐culture bioreactors in which two cell populations compete for a common growth limiting substrate. A stream is periodically removed from the reactor, and the two cell populations are separated using specific cell adhesion. The steady state corresponding to the desired population fraction is stabilized by discarding faster growing cells and recycling slower growing cells to the reactor. The recycle loop must be operated periodically to allow regeneration of the adhesion column after each separation. As a result, the manipulated input is chosen as the sampling interval during which material is removed from the reactor. The nonlinear controller is designed using a simplified dynamic model that assumes continuous separation of the cell populations. The controller is implemented by calculating the sampling interval that leads to the same amount of material being removed from the reactor as that computed from the continuous control law. A nonlinear, closed‐loop observer is used to generate one‐time‐delay‐ahead predictions of the measured cell concentrations and the unmeasured substrate concentration. The efficacy of the proposed control strategy is evaluated via simulation.     

Fate of commensalistic cultures in identical coupled bioreactors

A comprehensive analysis of static and dynamic behavior of a mixed culture in two identical coupled bioreactors is presented considering anaerobic digestion involving acidogens (X) and methanogens (Y) as the example bioprocess. A single continuous culture may operate at up to seven steady states, including up to four coexistence steady states, with only one coexistence steady state being locally stable. The one-way interaction between X and Y allows for compartmentalization of the system for a stand-alone bioreactor and two coupled bioreactors into two subsystems, which facilitates the analysis of steady state types and stability characteristics of these and classification of dynamic behavior. The bioreactors in the two-reactor system are identical only in terms of feed composition and reactor space time. A two-reactor system may admit up to forty nine steady states, which are comprised of up to forty coexistence steady states, at least at very low interaction rate (R). The static and dynamic analysis of the two-reactor system is facilitated by appropriate grouping of large number of steady states arising for very low R into nine clusters. Numerical illustrations reveal the rich steady state structure of the bioprocess in coupled bioreactors. While a single bioreactor can operate at only one locally stable coexistence steady state, the coupled bioreactors can operate at up to five locally stable coexistence steady states over certain ranges of R. The two-reactor system is operationally more flexible and more robust vis-a-vis single reactor as concerns maintenance of mixed culture. Emergence of four additional steady state clusters and additional coexistence and partial washout steady states at intermediate R reveals that the coupled bioreactors are an example of a complex system.     

Theoretical analysis of inhibition effect on steady states of enzymatic membrane reactor with substrate and product retention for reaction producing weak acid

The aim of this study is to formulate a model of enzymatic membrane reactor (EMR), i.e., a continuous, stirred tank bioreactor with full enzyme recycle, for a reaction producing a weak acid, and to explore the effect of substrate and product inhibition of different mechanisms coupled with transport properties of the membrane on the static behaviour of the system. The inhibition of an enzyme by a substrate leads to the non-monotonicity of reaction rate expression with respect to the substrate concentration. If a product of enzymatic reaction, taking place in the EMR, influences the pH of a reaction mixture this is also the factor causing the non-monotonicity of the substrate and product dependent reaction rate. The character of these dependencies affects substantially the structure of the steady states of the reactor. The bifurcation diagrams, shown in the work, are of different characters depending on the bifurcation parameter. It has been found, that bifurcation diagrams for competitive and uncompetitive inhibition by a substrate differ in the number and position of bifurcation points. Steady states of multiplicity five have been localised in case of uncompetitive inhibition by the substrate at high affinity of the enzyme to this substrate. Retention of reagents, related to transport properties of a membrane, influences significantly the effectiveness of a process. A specially written software in Delphi™ has been used for the calculations.     

Dry anaerobic batch digestion of the organic fraction of municipal solid waste

Anaerobic digestion at high solid concentrations (dry anaerobic digestion) is an attractive method for the stabilization of solid organic wastes. A new concept for dry anaerobic batch digestion (BIOCEL) of the organic fraction of municipal solid waste is presented. The start up of a BIOCEL reactor was studied with several methods of process set up and operation. Dry anaerobic digestion of the pure undiluted organic fraction obtained from a shredding/separation process was not accelerated by partial spatial separation of substrate and methanogenic inoculum (granular sludge) or leachate recycle, or both. With these three methods after 30 days the high organic acids concentration and low pH in the reactor indicated a sour reactor, unable to establish significant methane production. When the organic fraction was digested in combination with compost addition (40% (w/w) of the initial solids) and leachate recycle, the stabilization rate increased significantly. Leachate recycling in combination with partial spatial separation of the substrate/compost mixture and the inoculum showed the shortest lag phase in the methane production and the shortest digestion time. When the digested residue of a completed digestion was applied as the methanogenic inoculum (40% (w/w) of the initial total solids) the digestion time was slightly shorter. It is concluded that dilution with compost had a positive effect on the start up of the dry anaerobic digestion and compensated for a suboptimal amount of initial methanogenic biomass. During the start up of dry anaerobic batch digestion of municipal solid waste the rapid recovery of methane formation from an initial overloading was observed and was found to be the result of a population shift in the methanogenic biomass and the existence of zones in the reactor with more optimal conditions (higher p H, lower organic acids concentration). The observed digestion time was 36 days. Recommendations are given to shorten the period needed, for complete digestion.     

Numerical and technological properties of bubble column bioreactors for aerobic processes

This paper describes the method of modelling and numerical simulation of bubble column bioreactors in which the process of aerobic biodegradation of carbonaceous substrate occurs. Such bioreactors belong to systems with distributed state variables. Determining steady states of such objects results in solving non-linear boundary-value problems.The bioreactors with axial dispersion and piston flow with biomass recirculation were analysed. The effectiveness of selected algorithms used to determine the steady states of such bioreactors were compared; the numerical properties of mathematical models of analysed bioreactors were specified, the branches of steady states in bioreactors with axial dispersion and piston flow were determined and the application areas of such bioreactors were defined.     

A FUNDAMENTAL ANALYSIS OF CONTINUOUS FLOW BIOREACTOR AND MEMBRANE REACTOR MODELS WITH TESSIER KINETICS

In this research we analyze the steady-state operation of a continuous flow bioreactor, with or without recycle, and an idealized or nonidealized continuous flow membrane reactor. The model extends to include a fixed bed reactor where a fraction of the biomass is detached by the flow. The reaction is assumed to be governed by Tessier growth kinetics. We show that a flow reactor with idealized recycle has the same performance as an idealized membrane reactor and that the performance of a nonidealized membrane reactor is identical to that of an appropriately defined continuous flow bioreactor with nonidealized recycle. The performance of all three reactor types can therefore be obtained by analyzing a flow reactor with recycle. The steady states of the recycle model are found and their stability determined as a function of the residence time. The performance of the reactor at large residence times is obtained.     

Kinetic analysis via mathematical modeling for ferrous iron oxidation in a class of SBR-type system

This paper analyses the oxidation of ferrous iron via chemical and biological means in a class of Sequential Batch Reactors (SBR-type). For this, a kinetic model for the study of iron oxidation system is proposed, followed by a parametric sensitivity analysis and a bifurcation analysis, which allow selecting the most influential kinetic parameters in order to ensure a suitable prediction capacity of the mathematical structure. The system consists of two SBR bioreactors, the first being used to produce hydrogen peroxide (H₂O₂) that is fed to a second reactor where the iron oxidation is carried out by chemical-biological processes. Model predictions were compared with experimental data for the production of H₂O₂ and for ferrous iron oxidation, finding suitable correlation coefficients (r²> 0.98) for each state variable. The bifurcation analysis showed the trajectories of the main variables, such as, biomass, H₂O₂ and ferrous iron, under the change of the most influential kinetic parameters. This analysis demonstrates the usefulness of the constructed model to predict the kinetic behaviour of the SBR-type process.     

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.     

Complex nonlinear behaviour of a fixed bed reactor with reactant recycle

The fixed bed reactor with reactant recycle investigated in this paper can exhibit periodic solutions. These solutions bifurcate from the steady state in a Hopf bifurcation. The Hopf bifurcation encountered at the lowest value of the inlet concentration turns the steady state unstable and marks the emergence of a stable periodic solution. This periodic solution in turn undergoes a period doubling leaving it unstable and giving rise to a stable period 2 solution. It is know that if the system possesses one period doubling it often also has the possibility of posessing a chaotic attractor. It is shown, that the dynamic behaviour of a fixed bed reactor with reactant recycle is much more complex than previously reported.     

PRODUCTION OF ETHANOL WITH SACCHAROMYCES CEREVISIAE IN A CONTINUOUS REACTOR Note III: an experimental, kinetic study with suspended, recycled biomass

By way of comparison with the kinetic investigation of the continuous production of ethanol in a tubular reactor with immobilized yeasts, a study was carried out of continuous fermentation in a stirred reactor, with final separation and recycling of the microorganisms. Flocculation with potassium ferrocyanide and zinc sulphate was used to separate the biomass. The maintenance of the metabolic activity was assessed. Next, discontinuous fermentation at various substrate and biomass concentrations was performed to determine the kinetics of glucose-ethanol transformation by flocculated and reinoculated Saccharomyces Cerevisiae.

Once again, the kinetic expression was a Michaelis-Menten equation, with un-competitive inhibition of the substrate and linear inhibition of the product.

The values observed for the various parameters were not very different from those for a biomass immobilized on an inert support or for a free biomass. Finally, the productivities of several types of reactor are compared.     

Two‐Parameter Continuation and Bifurcation Strategies for Oscillatory Behavior Elimination from a Zymomonas mobilis Fermentation System

Two‐parameter continuation and bifurcation analysis strategies were applied to deal with the oscillatory phenomena of a Zymomonas mobilis ethanol fermentation system. A structured verified non‐linear mathematical model considering the physiological limitations of microorganisms for a single continuous fermenter for ethanol production using Z. mobilis was built to identify the Hopf bifurcation (HB) points, which indicate the oscillatory behavior, using the inlet substrate concentration and the dilution rate as bifurcation parameters. The path of the HB points can be determined with different controlling operating parameters. It was found that with the addition of a small amount of cells or ethanol to the feed stream or by increasing the dilution rate, the oscillations could be eliminated and steady‐state behavior was attained. Using a two‐parameter continuation strategy, the Z. mobilis fermentation system could operate at steady state without oscillatory behavior.     

Effect of cholineacetyltransferase activity and choline recycle ratio on diffusion-reaction modeling,bifurcation and chaotic behavior of acetylcholine neurocycle and their relation to Alzheimer's and Parkinson's diseases

This paper is an extension of the previous two papers (Mustafa et al., 2009a, Mustafa et al., 2009b) on the modeling, simulation and analysis of bifurcation, dynamics, and chaotic characteristics of the acetylcholine (ACh) neurocycle. The effects of cholineacetyltransferase (ChAT) activity and choline recycle ratio as bifurcation parameters, on the system performance are studied through modifying the two-compartment model. It is found that as ChAT activity increases, ACh concentration in the model compartments increases continuously. The effect of choline recycle ratio shows that choline uptake represents the key role for providing choline as a substrate for ACh synthesis. It is found that the choline recycle ratio has a great influence on all state variables in both compartments. A detailed bifurcation and sensitive analyses over a wide range of ChAT activity and choline recycle ratio parameters are carried out in order to highlight the characteristics of ACh cholinergic system like non-linear dynamics and different solutions such as multiplicity of: stationery states as well as periodic and chaotic states. The relations between the results and the functions of ACh cholinergic neurons are investigated. A comparison between the results and other experimental and physiological measurements is performed. It is found that there is a good relation between cholinergic diseases such as Alzheimer's and Parkinson's diseases, and level of ACh in brains from one side and current results extracted from the disturbances in ChAT activity and choline recycle from the other side. It is found that choline recycled is the most critical factor in ACh processes in comparison with any of the following parameters: ChAT activity, as well as feed acetate and ACh concentrations.     

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.     

CSTR中生化反应振荡行为研究

考虑在生化反应中细胞收率系数Ｙｘ／ｓ随物料浓度变化这一事实，改进了原有的发酵动力学方程，同时首次运用分岔理论研究了乙醇连续发酵过程中存在的振荡现象。结果表明：在低糖浓度条件下，振荡的周期和幅值以及振荡出现的入口浓度阈值都将随着稀释率和入口糖浓度的变化而变化     

PRODUCTION OF ETHANOL WITH SACCHAROMYCES CEREVISIAE IN A CONTINUOUS REACTOR Note III: an experimental,kinetic study with suspended,recycled biomass

By way of comparison with the kinetic investigation of the continuous production of ethanol in a tubular reactor with immobilized yeasts, a study was carried out of continuous fermentation in a stirred reactor, with final separation and recycling of the microorganisms. Flocculation with potassium ferrocyanide and zinc sulphate was used to separate the biomass. The maintenance of the metabolic activity was assessed. Next, discontinuous fermentation at various substrate and biomass concentrations was performed to determine the kinetics of glucose-ethanol transformation by flocculated and reinoculated Saccharomyces Cerevisiae.

Once again, the kinetic expression was a Michaelis-Menten equation, with un-competitive inhibition of the substrate and linear inhibition of the product.

The values observed for the various parameters were not very different from those for a biomass immobilized on an inert support or for a free biomass. Finally, the productivities of several types of reactor are compared.     

Bulk copolymerization of styrene-acrylic esters: Some analysis and design considerations

A common framework for the analysis of styrene-acrylic ester systems has been developed by analyzing the pertinent kinetic information. This is shown to lead to a well defined strategy for the design of copolymerization reactors especially in the industrially relevant high conversion region. The existence of stable steady states and its influence on the system parameters has been illustrated for the case of a continuous stirred tank reactor (CSTR). A novel strategy of a CSTR operated with a recycle is proposed. This is shown to lead to an operation in the unique steady state with the added advantage of a high conversion and uniform copolymer composition. This would seem to be the first such analysis in the high conversion region.     

Design and Control of an Integrated 1,4‐Butanediol Dehydrogenation and Furfural Hydrogenation Plant

The design and plantwide control of an integrated plant, where the endothermic dehydrogenation of 1,4‐butanediol leading to γ‐butyrolactone and the exothermic hydrogenation of furfural leading to furfural alcohol and 2‐methyl furan are simultaneously performed in a single reactor, is presented. Analysis of the reactor‐separation‐recycle system shows that the reactions can be carried out using small hydrogen excess, in an adiabatic reactor, with reduced parameter sensitivity. The plant is flexible, allowing different production rates and a wide range of ratios between the furfural alcohol and 2‐methyl furan products. The additional separation of γ‐butyrolactone from the reaction mixture is easy. The conclusions are supported by rigorous steady‐state and dynamic simulations performed in AspenPlus and AspenDynamics.     

A comparative study of a fluidised bed reactor and a gas lift loop reactor for the ibe process: Part III. Reactor performances and scale Up

Continuous fermentations using Clostridium spp. DSM 2152 immobilised in calcium alginate beads to produce butanol and isopropanol from glucose were carried out in a fluidised bed reactor with liquid recycle (FBR, 10.9 dm³ working volume, 41 % solids) and in a gas lift loop reactor (GLR, 11.4 dm³ working volume, 32% solids). In the FBR in-situ produced non-coalescing gas bubbles had a negligible influence on the fluidisation pattern and the steady state results of the fermentation were in accordance with those predicted by a reactor model. The FBR was operated reliably for 5 weeks without decrease of activity. The GLR behaved as a three phase reactor because of the recycled fermentation gas. The steady state fermentation results were as predicted by the GLR model. Scale up to a 50 m³ FBR and a 65 m³ GLR led to development of a plug flow with recycle model for the FBR and a stirred tank model for the GLR. On the basis of overall reactor performance and ease of integration with a simultaneous product recovery the FBR is preferred to the GLR for application in a large scale butanol/isopropanol process using immobilised Clostridia spp.     

Steady‐state multiplicity in an adiabatic continuous stirred tank reactor with vapor recycle

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