Optimization of Operating Temperature for Continuous Immobilized Glucose Isomerase Reactor with Pseudo Linear Kinetics

In this work, the optimal operating temperature for the enzymatic isomerization of glucose to fructose using a continuous immobilized glucose isomerase packed bed reactor is studied. This optimization problem describing the performance of such reactor is based on reversible pseudo linear kinetics and is expressed in terms of a recycle ratio. The thermal deactivation of the enzyme as well as the substrate protection during the reactor operation is considered. The formulation of the problem is expressed in terms of maximization of the productivity of fructose. This constrained nonlinear optimization problem is solved using the disjoint policy of the calculus of variations. Accordingly, this method of solution transforms the nonlinear optimization problem into a system of two coupled nonlinear ordinary differential equations (ODEs) of the initial value type, one equation for the operating temperature profile and the other one for the enzyme activity. The ODE for the operating temperature profile is dependent on the recycle ratio, operating time period, and the reactor residence time as well as the kinetics of the reaction and enzyme deactivation. The optimal initial operating temperature is selected by solving the ODEs system by maximizing the fructose productivity. This results into an unconstrained one‐dimensional optimization problem with simple bounds on the operating temperature. Depending on the limits of the recycle ratio, which represents either a plug flow or a mixed flow reactor, it is found that the optimal temperature of operation is characterized by an increasing temperature profile. For higher residence time and low operating periods the residual enzyme activity in the mixed flow reactor is higher than that for the plug flow reactor, which in turn allows the mixed flow reactor to operate at lower temperature than that of the plug flow reactor. At long operating times and short residence time, the operating temperature profiles are almost the same for both reactors. This could be attributed to the effect of substrate protection on the enzyme stability, which is almost the same for both reactors. Improvement in the fructose productivity for both types of reactors is achieved when compared to the constant optimum temperature of operation. The improvement in the fructose productivity for the plug flow reactor is significant in comparison with the mixed 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.     

Optimal Bioreactor Operational Policies for the Enzymatic Hydrolysis of Sugarcane Bagasse

The consolidation of the industrial production of second-generation (2G) bioethanol relies on the improvement of the economics of the process. Within this general scope, this paper addresses one aspect that impacts the costs of the biochemical route for producing 2G bioethanol: defining optimal operational policies for the reactor running the enzymatic hydrolysis of the C6 biomass fraction. The use of fed-batch reactors is one common choice for this process, aiming at maximum yields and productivities. The optimization problem for fed-batch reactors usually consists in determining substrate feeding profiles, in order to maximize some performance index. In the present control problem, the performance index and the system dynamics are both linear with respect to the control variable (the trajectory of substrate feed flow). Simple Michaelis–Menten pseudo-homogeneous kinetic models with product inhibition were used in the dynamic modeling of a fed-bath reactor, and two feeding policies were implemented and validated in bench-scale reactors processing pre-treated sugarcane bagasse. The first approach applied classical optimal control theory. The second policy was defined with the purpose of sustaining high rates of glucose production, adding enzyme (Accellerase® 1500) and substrate simultaneously during the reaction course. A methodology is described, which used economical criteria for comparing the performance of the reactor operating in successive batches and in fed-batch modes. Fed-batch mode was less sensitive to enzyme prices than successive batches. Process intensification in the fed-batch reactor led to glucose final concentrations around 200 g/L.     

Optimization of operating temperature for continuous glucose isomerase reactor system

The Optimal temperature control policy for an immobilized glucose isomerase reactor system was studied. This optimization study takes into consideration the enzyme deactivation during the continuous reactor operation. The Kinetic parameters including reduced Michaelis–Menten constant (K?_m), reduced maximum reaction rate (V?_m), equilibrium constant (K_e), and enzyme deactivation constant (k_d) and their functional relationships to temperature were determined experimentally. The optimization problem was formulated in terms of maximization of fructose productivity as the objective function. The optimization problem was solved by making use of a maximum principle and the control vector iteration method. Approximately optimal temperature control policy was employed as compared with the reactor operation at an optimum constant temperature.     

Optimum design of a series of CSTRs performing reversible Michaelis-Menten kinetics: a rigorous mathematical study

The optimum design of a given number of CSTRs in series performing reversible Michaelis-Menten kinetics in the liquid phase assuming constant activity of the enzyme is studied. In this study, the presence of product in the feed stream to the first reactor, as well as the effect of the product intermediate concentrations in the downstream reactors on the reaction rate are investigated. For a given number of N CSTRs required to perform a certain degree of substrate conversion and under steady state operation and constant volumetric flow rate, the reactor optimization problem is posed as a constrained nonlinear programming problem (NLP). The reactor optimization is based on the minimum overall residence time (volume) of N reactors in series. When all the reactors in series operate isothermally, the constrained NLP is solved as an unconstrained NLP. And an analytical expression for the optimum overall residence time is obtained. Also, the necessary and sufficient conditions for the minimum overall residence time of N CSTRs are derived analytically. In the presence of product in the feed stream, the reversible Michaelis-Menten kinetics shows competitive product inhibition. And this is, because of the increase in the apparent rate constant K^' _m that results in a reduction of the overall reaction rate. The optimum total residence time is found to increase as the ratio (‚₀) of product to substrate concentrations in the feed stream increases. The isomerization of glucose to fructose, which follows a reversible Michaelis-Menten kinetics, is chosen as a model for the numerical examples.     

Optimal fishery policy: An equilibrium solution with irreversible investment

Optimal fishery policy has been derived using several different models of varying biological realism. Policy has either been assumed to be non-time-varying and static optimization techniques have been applied or dynamic techniques have been used and have in some cases resulted in constant policy. Botsford (1981) showed by applying dynamic optimization techniques to several biologically realistic models (i.e. models that included size structure and either density or food dependent growth and recruitment rates) that the constant policy solution found for simpler, less realistic models was not possible. He concluded that optimal policy was a time-varying, possibly pulse-fishing policy. We show here that when the maximum allowed fishing mortality is low enough a different kind of constant policy is optimal for these realistic models. Interpretation of this condition requires explicit consideration of fixed capital costs in addition to operating costs. Practical considerations indicate that this constant policy would apply only to fisheries with high fixed capital costs.     

Analysis of substrate protection of an immobilized glucose isomerase reactor

The effect of substrate protection on enzyme deactivation was studied in a differential bed and a packed bed reactor using a commercial immobilized glucose isomerase (Swetase, Nagase Co.). Experimental data obtained from differential bed reactor were analyzed based on Briggs-Haldane kinetics in which enzyme deactivation accompanying the protection of substrate was considered. The deactivation constant of the enzyme-substrate complex was found to be about half of that of the free enzyme. The mathematical analysis describing the performance of a packed bed reactor under the considerations of the effects of substrate protection, diffusion resistance, and enzyme deactivation was studied. The system equations for the packed bed reactor were solved using an orthogonal collocation method. The presence of substrate protection and the diffusion effect within the enzyme particles resulted in an axial variation of effectiveness factor, eta(D), along the length of the packed bed. The axial distribution profile of eta(D) was found to be dependent on the operation temperature, Based on the effect of substrate protection, a better substrate feed policy could be theoretically found for promoting productivity in long-term operation. (c) 1993 John Wiley & Sons, Inc.     

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.     

Productivity improvement of recombinant <Emphasis Type="Italic">Escherichia coli</Emphasis> fermentation via robust optimization

A nonlinear model of a recombinant Escherichia coli producing porcine growth hormone (pGH) fermentation was developed. The model was used to calculate a glucose feeding and temperature strategy to optimize the production of pGH. Simulations showed that the implementation of optimal feed and temperature profiles was sensitive to the maximum specific growth rate, and a mismatch could result in excessive acetate production and a significant reduction in pGH yield. An optimization algorithm was thus developed, using feedback control, to counter the effects of uncertainty in the specific growth rate and thus determine an optimal operating strategy for pGH production. This policy was experimentally implemented in a 10 L fermenter and resulted in a 125% increase in productivity over the previous best experimental result with this system—in spite of significant plant-model mismatch.     

Nonisothermal immobilized enzyme reaction in a packed-bed reactor

Summary This work investigates the reaction behavior of immobilized enzymes in a packed-bed reactor. The effect of heat generation due to exothermic enzyme reaction is considered. Conservations of substrate and energy constitute two coupled nonlinear partial differential equations which are simultaneously solved by a numerical method. It is found that substrate conversion is generally increased at higher temperature. However, the extent of temperature heavily depends on the magnitude of the dimensionless Michaelis constant which is defined as the ratio of Michaelis constant to inlet substrate concentration. At low dimensionless Michaelis constant, substrate conversion is considerably affected by temperature, but at high dimensionless Michaelis constant, the temperature effect is negligibly small. It is also found that maximum bulk temperature of reaction mixtures occurs around a dimensionless reactor length of 1.3 for the case with high substrate conversion.     

Optimization of feeding profile for baker's yeast production by dynamic programming

An optimal substrate feeding for an industrial scale fed-batch fermenter is determined through iterative dynamic programming in order to maximize the cell-mass production and to minimize the ethanol formation. An experimentally validated rigorous dynamic model comprises constraints in the optimization problem. A new objective function is proposed to accommodate the competing requirements of maximum yeast production and minimum ethanol formation. The objective function is maximized with iterative dynamic programming with respect to the sugar feed rate. Results prove the effectiveness of dynamic programming for solving such high-dimensional and nonlinear optimization problems, and the resulting optimal policy indicates that considerable increase in yeast production in fed-batch fermenters can be achieved while minimizing the undesired by-product, ethanol.     

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.     

Performance of the continuous glucose isomerase reactor system for the production of fructose syrup

Glucose isomerase in the form of heat-treated whole-cell enzyme prepared from Streptomyces phaeochromogenus follows the reversible single-substrate reaction kinetics in isomerization of glucose to fructose. Based on the Kinetic constants determined and the mathematical model of the reactor system developed, the preformance of a plug-flow-type continuous-enzyme reactor system was studied experimentally and also simulated with the aid of a computer for the ultimate objective of optimization of the glucose isomerase reactor system. The enzyme decay function for both the enzyme storage and during the use in the continuous reactor, was found to follow the first-order decay kinetics. When the enzyme decay function is taken into consideration, the ideal homogeneous enzyme reactor kinetics provided a satisfactory working model without further complicatin of the mathematical model, and the results of computer simulation were found to be in good agreement with the experimental results. Under a given set of constraints the performance of the continuous glucose isomerase reactor system can be predicted by using the computer simulation method described in this paper. The important parameters studied for the optimization of reactor operation were enzyme loading, mean space time of the reactor, substrate feed concentration, enzyme decay constants, and the fractional conversion, in addition to the kinetic constants. All these parameters have significant effect on the productivity. Some unique properties of the glucose isomerization reaction and its effects on the performance of the continuous glucose isomerase reactor system have been studied and discussed. The reaction kinetics of glucose isomerase and the effects of both the enzyme loading and the changes in reaction rate within a continuous reactor on the productivity are all found to be of particular importance to this enzyme reactor system.     

Mathematical modeling of diffusion and reaction in the hydrolysis of vegetable protein in an immobilized enzyme recycle reactor

Experimental investigation is by far the most effective approach for studying the behavior of physical systems. However, an enzymatic solubilization of vegetable protein is a complex combination of intrinsic problems, of which many are not easily adaptable to experimental investigation. Experimental designs to study enzyme vegetable protein reactions yield data which describe the extramembraneous activity of the immobilized enzyme. In a continuous recycle immobilized enzyme reactor, the microenvironment concentration of the substrate or product in the membrane phase, or the concentrations along the reactor axial length in the bulk phase are not discernible to the experimenter. However, the knowledge of such concentration profiles is important in weighing the significance of such factors as intermembrane diffusion, enzyme loading, wet membrane size, and the mode of operation of the reactor. The simulation of mathematical models, which describe the physical system within the constraints imposed, yields information which is vital to the understanding of the process occurring in the reactor. The kinetics and diffusion of an immobilized thermophilic Penicillium duponti enzyme at pH 3.4-3.7 and 50 degrees C was modeled mathematically. The kinetic parameters were evaluated by fitting a model to experimental data using nonlinear regression analysis. Simulation profiles of the effects of reactor geometry, substrate concentration, membrane thickness, and enzyme leading on the hydrolysis rate are presented. From the profiles generated by the mathematical model, the best operational reactor strategy is recommended.     

On the optimal control of fed-batch reactors with substrate-inhibited kinetics

The optimal feed rate profiles, for fed-batch fermentation that maximizes the biomass production and accounts for time, are analyzed. The solution can be found only if the final arc of the optimal control is a batch arc, since in this case the final concentrations of substrate and biomass can be determined by ulterior conditions on the mass balance and on the final growth rate of biomass and thus it is possible to solve the resulting time optimal problem by using Green's theorem. This evidences the "turnpike property" of the solution, which tries to spend the maximum time on or at least near the singular arc along which the substrate concentration is maintained constant. The optimality of the final batch arc is related to the time operational cost in the performance index. The sequence of the control depends on the initial conditions for which six different regions, with the respective patterns, have been identified, in case the performance index allows the control sequence to have a final batch.     

A nonsingular optimization approach to the feed rate profile optimization of fedbatch cultures

A new method to calculate the optimal feed rate profile for fedbatch culture is proposed. Instead of the usual singular control approach of taking the feed rate as the control variable, the substrate concentration profile is used as the transformed control variable to avoid the computational difficulty associated with the singular control. Thus, the problem is converted into a nonsingular optimization problem of determining the optimal substrate concentration profile subject to a constraint. The equivalent feed rate profile to match the optimal substrate concentration profile is then generated. With this method the computational difficulty associated with singular controls for high-order systems is circumvented. The proposed method is illustrated by a number of examples.     

Preparation of an immobilized two-enzyme system, Beta-amylase--pullulanase, to an acrylic copolymer for the conversion of starch to maltose. III. Process kinetic studies on continuous reactors

Kinetic studies on the parameters influencing the potential industrial application of an immobilized two-enzyme system of β-amylase and pullulanase for conversion of starch to a product with high maltose content, have been performed. The apparent Michaelis constant, the apparent product inhibitor constant, and the activation energy have been determined for the immobilized preparation and compared to the values for the corresponding soluble enzyme system. The catalytic activity of the immobilized enzymes was studied in a plug-flow reactor and a continuous feed stirred tank reactor. Mathematical models for these reactors have been formulated and adapted to fit the experimental data. Comparisons of the reactor efficiencies were made and the conditions were found to be such as to favor the plug-flow reactor. Results on operational stability tests at different temperatures and substrate concentrations are given.     

Economic improvement of continuous pharmaceutical production via the optimal control of a multifeed bioreactor

Projections on the profitability of the pharmaceutical industry predict a large amount of growth in the coming years. Stagnation over the last 20 years in product development has led to the search for new processing methods to improve profitability by reducing operating costs or improving process productivity. This work proposes a novel multifeed bioreactor system composed of independently controlled feeds for substrate(s) and media used that allows for the free manipulation of the bioreactor supply rate and substrate concentrations to maximize bioreactor productivity and substrate utilization while reducing operating costs. The optimal operation of the multiple feeds is determined a priori as the solution of a dynamic optimization problem using the kinetic models describing the time‐variant bioreactor concentrations as constraints. This new bioreactor paradigm is exemplified through the intracellular production of beta‐carotene using a three feed bioreactor consisting of separate glucose, ethanol and media feeds. The performance of a traditional bioreator with a single substrate feed is compared to that of a bioreactor with multiple feeds using glucose and/or ethanol as substrate options. Results show up to a 30% reduction in the productivity with the addition of multiple feeds, though all three systems show an improvement in productivity when compared to batch production. Additionally, the breakeven selling price of beta‐carotene is shown to decrease by at least 30% for the multifeed bioreactor when compared to the single feed counterpart, demonstrating the ability of the multifeed reactor to reduce operating costs in bioreactor systems. © 2017 American Institute of Chemical Engineers Biotechnol. Prog., 33:902–912, 2017     

Optimization of biphasic growth of Saccharomyces carlsbergensis in fed-batch culture

The optimal glucose feeding policy for the fed-batch culture of Saccharomyces carlsbergensis is presented. The biphasic nature of growth results in a singular feed rate policy that is unique to this organism. When the operating cost is high, the reduction in operating time forces the cells to utilize both glucose and ethanol toward the end of fermentation time and results in a decreasing rate of glucose addition, unlike the normally observed in creasing feed rate. The optimal feeding policy depends heavily on the initial conditions and is highly sensitive to changes in kinetic parameters. A semiempirical scheme for feedback optimization is suggested for the fed-batch yeast culture.     

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.