Bifurcation analysis of two continuous bioreactors operated in series with recycle

In this paper, bifurcation analysis has been carried out for two continuous bioreactors operated in series with recycle from the second reactor. The existence of multiplicity of steady states is analyzed by considering Contois growth kinetics in the process model. It was observed that there exist two possible steady states of which one is trivial (wash out condition). Stability analysis is carried out to determine the stability of these steady states and it was observed that both these steady states are unstable in nature. Bifurcation analysis has been carried out for substrate and biomass concentration with dilution rate as the bifurcation parameter. Effect of recycle ratio, substrate separation factor and biomass separation factor is studied and analyzed. It was observed that Hopf bifurcation occurs at a dilution rate of 1.0208 with purely imaginary Eigen values which showed that sustained oscillatory behavior exists in the substrate concentration of the second reactor. The significance of different bifurcation points and the operating conditions by considering biomass and substrate concentrations in each reactor is studied and it was observed that the bioreactors need to be operated at intermediate dilution rates to obtain improved conversion and yield.     

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.     

Periodic operation of biofilters. A concise model and experimental validation

Concise model of biofiltration based on a linear driving force concept, that takes into account adsorption of pollutant in the support phase and its biodegradation therein with the rate governed by a modified three-parameter Monod-type expression, was shown to be suitable to portray the transient behavior of biofilters arising from the periodic operation. Good agreement between simulations and experiments was obtained for the biodegradation of methyl-ethyl-ketone or n-butanol on a pre-selected bark bed in a broad range of operating conditions.     

Pareto-optimal solutions for multi-objective optimization of fed-batch bioreactors using nondominated sorting genetic algorithm

Many optimal control problems are characterized by their multiple performance measures that are often noncommensurable and competing with each other. The presence of multiple objectives in a problem usually give rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Evolutionary algorithms have been recognized to be well suited for multi-objective optimization because of their capability to evolve a set of nondominated solutions distributed along the Pareto front. This has led to the development of many evolutionary multi-objective optimization algorithms among which Nondominated Sorting Genetic Algorithm (NSGA and its enhanced version NSGA-II) has been found effective in solving a wide variety of problems. Recently, we reported a genetic algorithm based technique for solving dynamic single-objective optimization problems, with single as well as multiple control variables, that appear in fed-batch bioreactor applications. The purpose of this study is to extend this methodology for solution of multi-objective optimal control problems under the framework of NSGA-II. The applicability of the technique is illustrated by solving two optimal control problems, taken from literature, which have usually been solved by several methods as single-objective dynamic optimization problems.     

Control strategies for intermittently mixed, forcefully aerated solid-state fermentation bioreactors based on the analysis of a distributed parameter model

This paper tests different control strategies based on classic proportional integral derivative (PID) and advanced dynamic matrix control (DMC) algorithms for an intermittently stirred, forcefully aerated solid-state fermentation bioreactor. The study was done using a distributed parameter model to reproduce the main operating features of this type of bioreactor. There is predicted to be a remarkable improvement in the bioreactor productivity when control strategies are implemented. For this type of bioreactor, the temperature and water content of the substrate bed can be controlled by saturating the air at the air inlet but manipulating its temperature, coupled with a strategy of water replenishment when the water content of the bed falls below a threshold. Dynamic matrix control is superior to PID control; however, a specific convolution matrix for different stages of the fermentation is necessary due to the changing behavior of the system. This work shows the benefit of mathematical modeling, since the many different operating conditions investigated via simulations would not have been economically feasible to undertake experimentally with a large-scale bioreactor. The results obtained provide an excellent starting point for such large-scale experimental work.     

Understanding the scale-up of fermentation processes from the viewpoint of the flow field in bioreactors and the physiological response of strains

The production capability of a fermentation process is predominately determined by individual strains, which ultimately affected ultimately by interactions between the scale-dependent flow field developed within bioreactors and the physiological response of these strains. Interpreting these complicated interactions is key for better understanding the scale-up of the fermentation process. We review these two aspects and address progress in strategies for scaling up fermentation processes. A perspective on how to incorporate the multiomics big data into the scale-up strategy is presented to improve the design and operation of industrial fermentation processes.     

Modelling and optimisation of a transketolase-mediated carbon-carbon bond formation reaction

In this paper, we have integrated process characterisation and reaction kinetic data for a transketolase catalysed carbon-carbon bond formation to build a comprehensive reaction model. Based on the synthesis of erythrulose from β-hydroxypyruvate and glycolaldehyde, the model includes component degradation as a function of time and concentration as well as glycolaldehyde toxicity towards the enzyme. Using the ratio of initial substrate concentration as a process variable, simulations and analysis based on this model allowed process options to be evaluated. The model links bioconversion to upstream fermentation for enzyme production and downstream product purification and this could provide guidelines for process development.     

Nutrient transport in bioreactors for bone tissue growth: Why do hollow fibre membrane bioreactors work?

One of the main aims of bone tissue engineering is to produce three-dimensional soft bone tissue constructs of acceptable clinical size and shape in bioreactors. The tissue constructs have been proposed as possible replacements for diseased or dysfunctional bones in the human body through surgical transplantations. However, because of certain restrictions to the design and operation of the bioreactors, the size of the tissue constructs attained are currently below clinical standards. We believe that understanding the fluid flow and nutrient transport behaviour in the bioreactors is critical in achieving clinically viable constructs. Nevertheless, characterization of transport behaviour in these bioreactors is not trivial. As they are very small in size and operate under stringent conditions, in-situ measurements of nutrients are almost impossible. This issue has been somewhat resolved using computational modelling in previous studies. However, there is still a lack of certainty on the suitability of bioreactors. To address this issue we systematically compare the suitability of three bioreactors for growing bone tissues using mathematical modelling tools. We show how nutrient transport may be improved in these bioreactors by varying the operating conditions and suggest which bioreactor may be best suited for operating at high cell densities in order to achieve soft bone tissues of clinical size. The governing equations defined in our mathematical frameworks are solved through finite element method. The results show that the hollow fibre membrane bioreactor (HFMB) is able to maintain higher nutrient concentration during operation at high cell densities compared to the other two bioreactors, namely suspended tube and confined profusion type bioreactor. Our results show that by varying the operating conditions nutrient transport may be enhanced and the nutrient gradient can be substantially reduced. These are consistent with previous claims suggesting that the HFMB is suited for bone tissue growth at high cell densities.     

A MATHEMATICAL ANALYSIS OF A MEMBRANE BIOREACTOR CONTAINING A SLUDGE DISINTEGRATION SYSTEM

The activated sludge process is widely used to treat domestic and industrial wastewater. A significant drawback of this process is the production of “sludge”, the disposal of which can comprise a significant proportion of the total operating costs of a wastewater treatment plant. We analyze the steady-state operation of a membrane bioreactor system (MBR) incorporating a sludge disintegration unit (SDU) to reduce sludge production. We provide a qualitative understanding of the model by finding analytically the steady-state solutions of the model and determining its stability as a function of the residence time. In practice a target value of the mixed liquor suspended solids (MLSS) content within the membrane reactor is specified. Applying the mathematical technique of singularity theory we show that if the sludge disintegration factor is sufficiently high then the MLSS content is guaranteed to be below the target value. This model prediction, of key interest from a practical perspective, was not identified in the original investigation of this model, which relied upon numerical integration of the governing equations.     

Engineering and modeling of thin, adhesive, microbial biocatalytic coatings for high intensity oxidations in multi-phase microchannel bioreactors

A model-based investigation of the reactivity of a multi-phase microchannel bioreactor for the oxidation of d-sorbitol to l-sorbose by viable Gluconobacter oxydans entrapped in an adhesive, bilayer, and nano-porous latex coating has been performed. Using kinetics and mass-transfer information from literature, the overall productivity of a single microchannel was determined. For liquid and gas superficial velocities typical for monoliths and channel diameters smaller than 1000 μm, volumetric l-sorbose formation rates larger than 30 g l⁻¹ h⁻¹ were predicted. Since the system was approximately kinetically controlled any effort to increase the coating reactivity, for example by using thinner topcoats or improving cell viability should result in a further increase of the overall reactivity. These modeling studies should provide the basis for engineering of channel geometry, biocatalytic coating nano-porosity and thickness, coating stability, optimal reactivity and multi-phase channel flow properties for future microchannel bioreactors for high intensity microbial oxidations.     

Modelling the effect of temperature and time on the performance of a copper electrowinning cell based on reactive electrodialysis

A temperature- and time-dependent mathematical model for the operation of a laboratory-scale copper electrowinning cell based on reactive electrodialysis (RED) has been developed. The model is zero-dimensional. The cathodic reaction was copper electrodeposition and the anodic reaction was ferrous to ferric ion oxidation. The catholyte was aqueous cupric sulphate and the anolyte was aqueous ferrous sulphate, both in sulphuric acid. Catholyte and anolyte were separated by an electrodialytic anion membrane. The model predicts the effect of temperature and time on: (a) cathodic and anodic kinetics, (b) speciation of catholyte and anolyte, (c) transport phenomena in the electrolytes and (d) ion transport through the membrane. Model calibration and validation were carried out. Its predictions are in good agreement with experiments for: amount of deposited copper, amount of produced Fe(III) species, cell voltage and specific energy consumption.     

LP-based solution strategies for the optimal design of industrial water networks with multiple contaminants

This paper presents a new approach for the optimal design of water-using networks. Starting with a superstructure that accounts for all possible connections between water sources and water-using operations, different substructures are generated that consider all possible sequences of operations. Then, each operation is tackled one at a time, from the first to the last element in the sequence. This procedure has the advantage of replacing a nonlinear program (NLP) by a succession of linear programs (LP) that are solved for all operation sequences. Although part of the feasible region is lost in the process, the results have shown that the optimal solution is often obtained. The new procedure is at the same time a good approach of generating structurally different solutions that can be used as starting points for the full NLP. By doing this, local solutions can be avoided and the probability of finding the global optimal solution to the problem is increased. When compared to the standard initialization procedure that features a single starting point, the new approach is more efficient but substantially more demanding computationally. A trade-off can be reached by using the standard technique with multiple starting points originated from the possible operation sequences.     

The continuous self stirred tank reactor: measurement of the cracking kinetics of biomass pyrolysis vapours

The continuous self stirred tank reactor is a well known suitable device for studying the kinetics of high-temperature gas phase reactions. Temperature and composition are uniform at any point of the reactor, and for a given residence time, it is easy to calculate the values of kinetic constants from a very simple mathematical model. The aim of the present paper is to report the first experimental results obtained on the thermal cracking of vapours produced by the pyrolysis of biomass. The experiments are carried out between 836 and 1303 K and under mean residence times ranging from 0.3 to 0.5 s. The calculated activation energy and preexponential factor are in good agreement with those obtained by other authors operating in more usual devices, but needing the solving of more sophisticated models.     

Industrial fluidised bed direct reduction kinetics of hematite ore fines in H2 rich gases at elevated pressure

Reduction kinetics of iron ore fines were investigated under fluidised bed conditions with hydrogen-rich gas mixtures in the temperature range from 400 to 700 °C at a pressure of 10 bar. Kinetic parameters were determined for the reactions hematite to magnetite, magnetite to wuestite and wuestite to iron from experimental data. To be able to investigate the influence of both temperature and reducing gas composition on the reaction rate, a laboratory scale pressurised fluidised bed reactor was used which is able to apply process conditions close to those in industrial plants. Appropriate to heterogeneous reactions, a rate expression considering the specific surface area was derived. The time dependent function for the transient evolution of specific surface area was generated from measured mercury porosimetry data. Kinetic parameters such as frequency factor, energy of activation and reaction orders were determined for the consecutive reactions from hematite to magnetite, magnetite to wuestite and wuestite to iron by numerical integration and parameter estimation from measured rate data. A comparison to the evaluation of kinetic parameters without considering specific surface area confirm the results of this work.     

Classification and analysis of integrating frameworks in multiscale modelling

Chemical engineers are turning to multiscale modelling to extend traditional modelling approaches into new application areas and to achieve higher levels of detail and accuracy. There is, however, little advice available on the best strategy to use in constructing a multiscale model. This paper presents a starting point for the systematic analysis of multiscale models by defining several integrating frameworks for linking models at different scales. It briefly explores how the nature of the information flow between the models at the different scales is influenced by the choice of framework, and presents some restrictions on model—framework compatibility. The concepts are illustrated with reference to the modelling of a catalytic packed bed reactor.     

Nonlinear optimization of steel production using traditional and novel blast furnace operation strategies

The high energy requirements in primary steelmaking make this industrial sector a major contributor to the global emissions of carbon dioxide. Ways to suppress the use of fossil reductants and the emissions from the processes should therefore be developed. The present work applies simulation and optimization for studying the economic feasibility of recycling blast furnace top gas to the combustion zones after CO₂ stripping. The study comprises the unit processes in an integrated steel plant, paying special attention to the blast furnace and the preheating of the blast or the recycled top gas. The system is optimized with nonlinear programming with respect to some central variables under different CO₂ sequestration and emission costs, which yields information about the economic feasibility of the concept. It is demonstrated that the optimal states of the plant show complex transitions, where the costs play a decisive role. It is also shown that hot gas recycling with CO₂ capture and storage would dramatically reduce the harmful emissions from the process. The conditions under which top gas recycling is economically feasible are also reported, as well as the effect of omitting oil injection in a blast furnace with top gas recycling.     

Inference of chemical reaction networks

This paper demonstrates how, in principle, a chemical reaction mechanism (reaction network) can be inferred using relatively simple systematic mathematical and statistical analyses of experimental data obtained from chemical reactors. This method involves specifying a global ordinary differential equation (ODE) model structure capable of representing an entire set of possible chemical reactions. Mathematical and statistical tests are then used to reduce the ODE model structure to a subset of reactions. Finally, a model rationalisation procedure, relying on exploiting the basic rules of reaction chemistry, is used to obtain a consistent set of reactions which are combined to give the overall reaction network. The identification procedure is demonstrated for pure batch operation with a worked example using simulated noisy data from an extended Van de Vusse reaction network consisting of five species and four elementary reactions [Van de Vusse, J.G., 1964. Plug-flow type reactor versus tank reactor. Chemical Engineering Science 19, 994-997]. A further case study of a semi-batch (fed batch) system using simulated data from a simplified biodiesel system, with six chemical species involved in three elementary reactions, is provided. It is shown that the method is able to correctly identify the underlying structure of the network of chemical reactions and provide accurate estimates of the network rate constants.     

Flash pyrolysis of cellulose pellets submitted to a concentrated radiation: experiments and modelling

The image furnace technology has been applied to the study of the first steps of biomass flash pyrolysis. The experiments performed with small pellets of cellulose show that the reaction primarily passes through the intermediate of short lifetime liquid species (ILC). The quantitative study of the variations of the sample mass loss and of the mass of ILC reveals the existence of a transient period followed by a steady-state regime resulting from an equilibrium between cellulose decomposition into ILC and ILC vaporization. A mathematical model has been solved in parallel. The results agree very well with the experimental measurements and yield additional information on the temperatures of cellulose pyrolysis and of ILC vaporization.