Periodic operation of bioreactors for autocatalytic reactions with Michaelis-Menten kinetics

The performance of an isothermal tubular bioreactor carrying out autocatalytic reactions obeying Michaelis-Menten Kinetics is analyzed for improvement in the average yield of product B. Under steady-state condition, the reactor is shown to exhibit input multiplicities in the yield of B with the mean residence time. Simulation results show that a significant improvement in the average yield of B is obtained under feed substrate concentration cycling. The two values of mean residence time giving identical yield under conventional steady-state operation is shown to give distinctly different behaviour under periodic operation. The lower value of the residence time gives improved average yield of B. The performances of the reactor with power law kinetics and that with the Michaelis-Menten kinetics show distinct average yield under periodic operation even though steady-state operation gives identical yield.     

Optimal design for CSTR's in series using reversible Michaelis-Menten reactions

An analytical expression is derived for the optimal design of a series of CSTR's performing reversible Michaelis-Menten kinetics in the liquid phase. The optimal design is based on minimum overall volume ofN reactors in series required to achieve a certain degree of substrate conversion. The reversible Michaelis-Menten equation is also able to explain competitive product inhibition and irreversible Michaelis-Menten kinetics. The reversible Michaelis-Menten kinetics covers three types of enzymatic reactions depending on the values of the rate constant for the forward (k _s) and reverse (k _p) reactions. An optimum design is obtained in the three cases ofK _s=K_p, K_s>K_p andK _s<K_p. The minimum overall reactors volume is compared with the more convenient equal-sized CSTR's. The effect of enzyme deactivation on the minimum overall reactors volume is investigated. The performance of a series of CSTR's is compared with plug-flow reactor. Glucose isomerization which exhibits reversible Michaelis-Menten kinetics is used as a model system for optimization.     

Optimal design for CSTR's in series performing enzymatic lactose hydrolysis

Analytical expressions are derived for the optimal design (based on minimum overall reactors volume) of a series of N CSTR's performing enzymatic lactose hydrolysis. It is assumed that lactose hydrolysis obeys Michaelis-Menten kinetics with competitive product (galactose) inhibition and no enzyme deactivation occurs. The optimum design of a cascade of ideally mixed reactors are compared with equal size reactors and with plug flow reactor required for a given overall degree of lactose conversion. The effect of operating parameters such as temperature, lactose initial (feed) concentration and conversion, enzyme and product initial concentration on the optimal overall holding time are also investigated. Optimization results for a series of N CSTR's up to five are obtained and compared with plug flow reactor.     

Optimization of glucose isomerase reactor: optimum operating temperature mode

The optimum temperature operation mode required to achieve high fructose productivity is studied for immobilized glucose isomerase (GI) packed bed reactor. In this study, the reactor design equation based on reversible Michaelis-Menten kinetics assumes both thermal enzyme deactivation and substrate protection. The optimization problem is formulated as a discretized constrained nonlinear programming problem (NLP). The formulation is expressed in terms of maximization of fructose productivity as the objective function subject to reactor design equation, kinetic parameter equations, substrate protection factor equation and feasibility constraints. The constraints are discretized along the reactor operating period by employing piecewise polynomial approximations. Approximately 7% improvement in terms of fructose productivity is achieved when running the reactor at the optimum decreasing temperature operation mode as compared to the constant optimum isothermal operation.     

Effects of operating parameters on performances of nitrification and denitrification processes

Nitrification and denitrification of synthetic wastewater was studied by using two reactors in series. An activated sludge unit was used for nitrification followed by a downflow biofilter (packed column) for denitrification. A glucose solution was fed to the denitrification column to supply carbon source. Effects of important process variables such as sludge age, hydraulic residence time and feed ammonium concentration on system's performance were investigated. Effluent ammonium-nitrogen (NH4-N) concentration decreased with increasing sludge age and hydraulic residence time and remained constant for sludge age and hydraulic residence times greater than 12 d and 15 h, respectively. Feed ammonium-nitrogen concentration above 200 mg/l resulted in significant levels of NH4-N in the effluent at Š_c = 15 d and Š_H = 12 h in nitrification. Performance of denitrification stage was not satisfactory for feed NO₃-N concentrations above 150 mg N/l resulting in significant effluent NO₃-N levels at hydraulic residence time of Š_H = 6 h.     

Optimum temperature operation mode for glucose isomerase reactor operating at constant glucose conversion

The optimum temperature operation mode required to achieve constant outlet glucose conversion is determined for immobilized glucose isomerase continuous packed bed reactor. The reactor design equation assumes reversible Michaelis-Menten kinetics with both enzyme deactivation and substrate protection. An increasing temperature profiles are determined for different operating periods, residence times and glucose conversions. The temperature increase with time is very small at low degree of glucose conversion and at relatively long residence time. The temperature rise with time increases at high degree of conversion and at relatively short residence time.     

Determination of multiple steady states in an enzyme kinetics involving two substrates in a CSTR

The multiple steady states in an isothermal, constant-density CSTR involving two-substrates, enzyme- catalyzed reactions is determined by a zero eigenvalue analysis. The hysteresis and bistability occurs for a certain range of the rate constant of product formation from a ternary complex, k_ES1S2MP+E. A two-parameter (k_ES1S2MP+E, k_0MS1) bifurcation diagram for several different values of flow rate k_S1̂ is also presented. It shows that, to maintain the existence of the steady state multiplicity under a fixed flow rate, the larger the rate constant k_ES1S2MP+E is, the larger the feed concentration of a substrate is required and the wider the range of that exists. To maintain the existence of the steady state multiplicity for a lower flow rate, it is required to reduce the feed concentration of substrates.     

Process development of continuous hydrogen production by Enterobacter aerogenes in a packed column reactor

Hydrogen bioproduction from agro-industrial residues by Enterobacter aerogenes in a continuous packed column has been investigated and a complete reactor characterization is presented. Experimental runs carried out at different residence time, liable of interest for industrial application, showed hydrogen yields ranging from 1.36 to 3.02 mmol_H2mmol^у_glucose or, in other words, from 37.5% to 75% of the theoretical hydrogen yield. A simple kinetic model of cell growth, validated by experimental results and allowing the prediction of biomass concentration profile along the reactor and the optimization of superficial velocity, is suggested. By applying the developed approach to the selected operative conditions, the identification of the optimum superficial velocity v_0,opt of about 2.2 cm h^у corresponding to the maximum hydrogen evolution rate H£_2g,max, was performed.     

On the optimum distribution of enzyme feed in a cascade of CSTR's performing an enzyme-catalyzed reaction with deactivation

A search for the optimum fractional distribution of an enzyme-rich stream to the various reactors of a cascade of CSTR's was implemented. A theoretical analysis, laid out in dimensionless form and based on the assumptions that the system is operated under steady state conditions, the enzyme undergoes first order deactivation, and the reaction catalyzed by the enzyme follows Michaelis-Menten kinetics, is reported. The objective function utilised is the minimisation of the overall volume of the cascade, and analytical expressions are obtained for the concentration of active enzyme and substrate in the outlet stream from each reactor. It is found that the best option is to add the whole enzyme-rich stream to the first reactor in the cascade irrespective of the operating and kinetic parameters of the system.     

Experimental behavior of a whole cell immobilized dextransucrase biocatalyst in batch and packed bed reactors

Dextransucrases from Leuconostoc mesenteroides have been used to produce a diversity of controlled structure oligosaccharides with potential industrial applications. This is the case of !(1̄) branched glucooligosaccharides produced by L. mesenteroides NRRL B-1299 dextransucrase. In order to establish an industrial scale process with the immobilized enzyme, a biocatalyst was produced by whole cell entrapment in alginate beads. The main physical and physicochemical properties of the biocatalyst were determined and the hydrodynamic behavior in a packed bed reactor studied. It was possible to produce spherical beads of 0.2 cm diameter containing the insoluble part of L. mesenteroides culture (cells and insoluble polymer) with an activity of 4 IU/g. Immobilization yield reached 93% with an effectiveness factor of 0.995 for particles of d_p < 0.2 cm. Due to the complexity of dextransucrase mechanism and kinetics, data obtained from initial rate measurements failed to describe the results obtained from the batch and continuous reactors. Therefore, apparent K_M and V_max data were used for the reactor modeling. It was found that under the conditions studied, the reaction rate was controlled by external mass transfer limitations.     

Optimal temperature policy for immobilized enzyme packed bed reactor performing reversible Michaelis-Menten kinetics using the disjoint policy.

The optimal temperature policy that maximizes the time-averaged productivity of a continuous immobilized enzyme packed bed reactor is determined. This optimization study takes into consideration the enzyme thermal deactivation with substrate protection during the reactor operation. The general case of reversible Michaelis-Menten kinetics under constant reactor feed flow rate is assumed. The corresponding nonlinear optimization problem is solved using the calculus of variations by applying the disjoint policy. This policy reduces the optimization problem into a differential-algebraic system, DAE. This DAE system defines completely the optimal temperature-time profiles. These profiles depend on the kinetic parameters, feed substrate concentration, operating period, and the residence time and are characterized by increasing form with time. Also, general analytical expressions for the slopes of the temperature and residual enzyme activity profiles are derived. An efficient solution algorithm is developed to solve the DAE system, which results into a one-dimensional optimization problem with simple bounds on the initial feed temperature. The enzymatic isomerization of glucose into fructose is selected as a case study. The computed productivities are very close to that obtained by numerical nonlinear optimization with simpler problem to solve. Moreover, the computed conversion profiles are almost constant over 90% of the operating periods, thus producing a homogeneous product.     

Kinetics of a hollow fiber dehydrogenase reactor

A hollow fiber module was used as a reactor for conversion of ethanol to acetaldehyde in the presence of horse liver alcohol dehydrogenase as catalyst. Mass transport rates for NAD⁺, the overall acetaldehyde generation rate, catalyst effectiveness factors, and the overall order of the reaction with respect to NAD⁺ concentration were measured. A coupled-substrate reactor with continuous in situ regeneration of cofactor was also examined. Two substrates of opposite redox state were added simultaneously to the feed stream. NADH and acetaldehyde concentrations were monitored in the effluent stream. The cofactor recycle number, or ratio of moles of product to moles of NADH produced, exceeded 10,000 under certain conditions. While decreasing the NAD⁺ concentration in the feed stream decreased reactor productivity somewhat, it greatly enhanced the ratio of product formed per mole of NAD⁺ fed to the reactor. It is suggested that high cofactor costs in dehydrogenase reactors may be overcome with efficient in situ regeneration and secondary recovery and recycling of cofactor from the process stream.     

Feasibility of culturing C2C12 mouse myoblasts on glass microcarriers in a continuous stirred tank bioreactor

Commercial culturing of mammalian cell lines is increasing in importance as more biological products unique to mammals are being produced in genetically altered mammalian cells. Most mammalian cells are anchorage dependent, so they must be cultured on a support matrix. This limitation, along with the requirement of a low shear environment, severely effects the scale-up of bench-scale culture systems. The need to culture mammalian cells on a support matrix limits the increase in cell population to a factor of 10-20 before growth virtually stops due to contact inhibition. Commercial culturing systems for anchorage dependent cells are batch processes because of the combination of contact inhibition and support matrix requirements. Development of a continuous bioreactor system could allow both unlimited scale-up and continuous cell-mass production. To design a continuous reactor, a mathematical model to predict the reactor performance should be developed. This paper addresses the development of a mathematical model for predicting continuous bioreactor performance. It was found that anchorage dependent C2C12 mouse myoblast cells, a continuous cell line, followed Monod kinetics for glucose consumption and cell mass production in batch flask experiments, with w_max = 0.040 hr^у and K_m = 2.5 mM. Furthermore, it was found that these parameters could be used to predict the glucose consumption in a continuous bioreactor operated with constant feed of seeded microcarriers operated at two different residence times. The success of this model implies the possibility of developing a continuous cell harvesting and reinoculation system using a microcarrier bioreactor to produce cell mass.     

Wine vinasses treatments by ozone and an activated sludge system in continuous reactors

In this work wine vinasses have been treated separately by means of a chemical ozonation and a biological aerobic degradation in an activated sludge system, and later by means of a combined process which consisted of an aerobic pretreatment followed by an ozonation treatment, in continuous reactors in all cases. In the ozonation experiments, the hydraulic retention time and the ozone partial pressure were varied leading to substrate removals in the range 4.4-16%, with increases in this removal when both operating variables were increased. A kinetic study, which combines mixed flow reactor model for the liquid phase and plug flow reactor model for the gas phase, allows to determine the rate constant for the ozone reaction and the consumption ratio, which are k_O3 = 3.6 l/(g COD · h) and b = 22.5 g COD degraded/mol O₃ consumed. The aerobic degradation experiments were conducted in the activated sludge system with variations in the retention time and influent organic substrate concentration in the wastewater. A modified Contois model applied to the experimental results leads to the determination of the kinetic parameters of that model: K₁ = 5.43 l/g VSS and q_max = 6.29 g COD/(g VSS · h). Finally, the combined process reveals an improvement in the efficiency of the ozonation stage due to the previous aerobic treatment with increases in the substrate removal reached and in the rate constant obtained, the last one being k_O3 = 5.6 l/(g COD · h).     

Evaluation of the effectiveness factor along immobilized enzyme fixed-bed reactors: Design of a reactor with naringinase covalently immobilized into glycophase-coated porous glass

A design equation is presented for packed-bed reactors containing immobilized enzymes in spherical porous particles with internal diffusion effects and obeying reversible one-intermediate Michaelis-Menten kinetics. The equation is also able to explain irreversible and competitive product inhibition kinetics. It allows the axial substrate profiles to be calculated and the dependence of the effectiveness factor along the reactor length to be continuously evaluated. The design equation was applied to explain the behavior of naringinase immobilized in Glycophase-coated porous glass operating in a packed-bed reactor and hydrolyzing both p-nitrophenyl-alpha-L-rhamnoside and naringin. The theoretically predicted results were found to fit well with experimentally measured values.     

A novel split-cylinder airlift reactor for fed-batch cultures

Conventional airlift reactors are not adequate to carry out variable volume processes since it is not possible to achieve a proper liquid circulation in these reactors until the liquid height is higher than that of the downcomer. To carry out processes of variable volume, the use of a split-cylinder airlift reactor is proposed, in the interior of which two multi-perforated vertical baffles are installed in order to provide several points of communication between the reactor riser and downcomer. This improves the liquid circulation and mixing at any liquid volume. In fed-batch cultures, it is important to know how liquid height affects the hydrodynamic characteristics and the volumetric oxygen transfer coefficient since this impacts on the kinetic behavior of any fermentation. Thus, in the present work, the effect of the liquid height on the mixing time, the overall gas hold-up, and the volumetric oxygen transfer coefficient of the proposed airlift reactor were determined. The mixing time was increased and the volumetric oxygen transfer coefficient decreased due to the increase of the liquid height in the reactor in all the superficial gas velocities tested, which corresponded to a pseudohomogeneous flow regime. The experimental values of the mixing time and the mass-transfer coefficient were properly described through correlations in which the U_GR/H_L ratio was used as the independent variable. Thus, this variable might be used to describe the hydrodynamic behavior and the oxygen transfer coefficient of airlift reactors when such reactors are used in processes where the liquid volume changes with time. However, these correlations are useful for the particular device and for the particular operating conditions at which they were obtained. These empirical correlations are useful to understand some factors that influence the mixing time and volumetric oxygen transfer coefficient, but such correlations do not have a sufficient predictive potential for a satisfactory reactor design. The overall gas hold-up values were not significantly affected when the liquid height was lower than the downcomer height. However, the values decreased abruptly when the reactor was operated with liquid heights over the downcomer height, especially at high superficial gas velocities.     

A modeling study of anaerobic biofilm systems: II. Reactor modeling

A rigorous steady-state model of anaerobic biofilm reactors taking into account acid-base and gas-phase equilibria in the reactor in conjunction with detailed chemical equilibria and mass transfer in acetate-utilizing methanogenic biofilms is presented. The performances of ideal completely stirred tank reactors (CSTRs) and plug-flow reactors, as well as reactors with nonideal hydraulic conditions, are simulated. Decreasing the surface loading rate increases the acetate removal efficiency, while decreasing the influent pH and increasing the buffering capacity improves the removal efficiency only if the bulk pH of the reactor shifts toward more optimal values between 6.8 to 7.0. The reactor can have negative or positive removal efficiencies depending on the start-up conditions. The respiration coefficient plays a critical role in determining the minimum influent pH required for reactor recovery after failure. Having multiple CSTRs-in-series generally increases the overall removal efficiency for the influent conditions investigated. Monitoring of the influent feed quality is critical for plug-flow reactors, becasue failure of the initial sections of the reactor may cause a cascading effect that may lead to a rapid reactor failure. (c) 1995 John Wiley & Sons, Inc.     

Study of microencapsulated urease in a continuous feed,stirred tank reactor

Urease, (urea amidohydrolase, EC 3.5.1.5) co-encapsulated with haemoglobin in cellulose nitrate membranes was found to exhibit apparent Michaelis-Menten kinetics; however, a steadily increasing apparent Michaelis-Menten constant over the lifetime of the preparation was observed. The activity of the enzyme in a continuous feed stirred tank reactor (CSTR) was investigated and correlated with a mathematical model derived from basic Michaelis-Menten kinetics. Plots relating substrate conversion to feed substrate concentration and tank reactor capacity were constructed and found to be accurate to less than 15% error under the experimental conditions studied.     

Optimal design of a number of membrane reactors in series using Michaelis-Menten one-substrate reversible kinetics

Summary Exact analytical expressions are derived for the optimal design (minimum overall reaction volume) of N perfectly mixed membrane reactors in series carrying out an enzyme catalysed Michaelis-Menten, one-substrate/one-product reversible reaction. The equations enable the direct calculation of the smallest total reactor volume needed for a given overall conversion degree. Results show that when substrate rejection is present, membrane reactors perform better compared with continuous stirred tank reactors.     

Prediction of continuous reactors performance based on batch reactor deactivation kinetics data of immobilized lipase

Experiments on deactivation kinetics of immobilized lipase enzyme fromCandida cylindracea were performed in stirred batch reactor using rice bran oil as the substrate and temperature as the deactivation parameter. The data were fitted in first order deactivation model. The effect of temperature on deactivation rate was represented by Arrhenius equation. Theoretical equations were developed based on pseudo-steady state approximation and Michaelis-Menten rate expression to predict the time course of conversion due to enzyme deactivation and apparent half-life of the immobilized enzyme activity in PFR and CSTR under constant feed rate policy for no diffusion limitation and diffusion limitation of first order. Stability of enzyme in these continuous reactors was predicted and factors affecting the stability were analyzed.