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Showing papers in "Bioprocess Engineering in 1993"


Journal ArticleDOI
TL;DR: There has been an increasing number of biotechnical processes for use or treatment of olive mill wastewaters over the last twenty years, both at laboratory size and on pilot scale.
Abstract: There has been an increasing number of biotechnical processes for use or treatment of olive mill wastewaters (OMW) over the last twenty years, both at laboratory size and on pilot scale. This paper reviews the methods described in the literature emphasizing the most important features and constraints of each of these processes.

127 citations


Journal ArticleDOI
TL;DR: Comparison of the results from the three scales showed that impeller tip speed is a poor scale up parameter whereas a term based on mycelial circulation through the zone of high energy dissipation fitted the data well.
Abstract: The influence of mechanical forces resulting from the rotation of (multiple) turbine impellers on the morphology and penicillin production of Penicillium chrysogenum Panlabs P-1 was investigated in batch fermentations using semi-defined media. Experiments were carried out at three different scales of fermentation, 5 dm3,100 dm3 and 1000 dm3 working volume, with the impeller tip speed ranging from 2.5 to 6.3 m/s. Throughout all fermentations, the dissolved oxygen concentration never fell below the critical value for maximum penicillin production. Morphological measurements using image analysis showed that the mean main hyphal length and mean hyphal growth unit increased during the rapid growth period and then decreased to a relatively constant value dependent on the agitation intensity. The specific rate of penicillin production (q pen)and the average main hyphal length during the linear penicillin production phase were lower at high agitation speed, which promoted more rapid mycelial fragmentation and a higher branching frequency. Comparison of the results from the three scales showed that impeller tip speed is a poor scale up parameter whereas a term based on mycelial circulation through the zone of high energy dissipation fitted the data well.

106 citations


Journal ArticleDOI
TL;DR: Up to 6% less biomass was produced and a larger amount of ethanol was formed in the two-compartment reactor system, due to the uneven sugar concentration distribution, which emphasizes the importance of the location of, and the mixing conditions at, the feeding point in a bioreactor.
Abstract: Substrate concentration gradients are likely to appear during large scale fermentations. To study effects of such gradients on microorganisms, an aerated scale-down reactor system was constructed. It consists of a plug flow reactor (PFR) and a stirred tank reactor (STR), between which the medium is circulated. The PFR, which is an aerated static mixer reactor, was characterized with respect to plug flow behaviour and oxygen transfer. A Bodenstein number of 15–220, depending on residence time and aeration rate, and a kLa of 500–1130 h−1, depending mainly on aeration rate, were obtained. The biological test system used, was aerobic ethanol production by Saccharomyces cerevisiae, due to sugar excess. The ethanol concentration profile and the yield of biomass were compared in two fed-batch fermentations. In the first case, the feeding point of molasses was located at the inlet of the PFR. This simulates location of the feeding point in the segregated part of a heterogeneous reactor, with local high sugar concentrations. In the second mode of operation, as a control with good mixing conditions, the PFR was disconnected from the STR, into which the substrate was fed. Differences were found: Up to 6% less biomass was produced and a larger amount of ethanol was formed in the two-compartment reactor system, due to the uneven sugar concentration distribution. This emphasizes the importance of the location of, and the mixing conditions at, the feeding point in a bioreactor.

100 citations


Journal ArticleDOI
TL;DR: In this paper, the removal of mixtures of two ketones, methyl ethyl ketone (MEK) and methyl isobutyl (MIBK), from effluent air streams in downward flow biofilters operating at relative humidities in excess of 95 percent was reported.
Abstract: The work reported concerns the removal of mixtures of two ketones, methyl ethyl ketone (MEK) and methyl isobutyl ketone (MIBK), which find wide application as industrial solvents, from effluent air streams in downward flow biofilters operating at relative humidities in excess of 95 percent. The inlet concentrations of the two pollutants were 300 mg m−3MEK and 330 mg m−3MIBK. Maximum elimination capacities achieved were 50 g m−3h−1 for MEK and 20 g m−3h−1 for MIBK. Marked interaction between the elimination of the two ketones was observed and established biophysical models for the kinetic analysis of biofilter operation proved inadequate as far as the complex processes involved in multi-component biodegradable vapour elimination were concerned. The complexity of such systems requires further definition and the development of appropriate models for process evaluation and design.

78 citations


Journal ArticleDOI
H. J. Henzler1, D. J. Kauling1
TL;DR: Design principles for surface aeration, bubble columns, loop reactors, and stirred tanks, as well as oxygenation with Accurel or silicone membranes, are presented and discussed specifically for the low oxygen inputs desired in cell cultures.
Abstract: Submersed cultures are increasingly being used for fermentation with animal cells. Reactor design is particularly important in these operations, because of the sensitivity of the cells to shear. In addition to the usual aeration methods, open-pore membranes or pure diffusion membranes are used for oxygenation in order to avoid gas bubbles. The various oxygenation methods are described in the present article [1]. Design principles for surface aeration, bubble columns, loop reactors, and stirred tanks, as well as oxygenation with Accurel or silicone membranes, are presented and discussed specifically for the low oxygen inputs desired in cell cultures. The scale laws are formulated, and special reference is made to problems of scale up. The various oxygenation methods are finally compared on the basis of the design principles presented, with particular attention to mechanical stress on the cells and to the laws of scale translation.

74 citations


Journal ArticleDOI
TL;DR: Control of fed-batch culture of hybridoma cells was investigated based on two approaches optimal control theory and feedback control, finding that there was a delay in the assimilation of the glutamine that should be included in the model to explain the lower MAb production in feedback mode.
Abstract: Control of fed-batch culture of hybridoma cells was investigated based on two approaches optimal control theory and feedback control. Experiments were conducted for both approaches-with a feed enriched in glutamine. The optimal feed trajectory, a decreasing one, yielded a final monoclonal antibody (MAb) concentration of 170 mg/l, a three-fold increase compared to a typical batch operation.

56 citations


Journal ArticleDOI
TL;DR: Scale-up of stirred tank bioreactors from 0.02 m3 to 0.3 m3 commercial plant is discussed for hybridoma suspension culture and hybridomas are shown to withstand significant impeller tip speed and fluid turbulence.
Abstract: Scale-up of stirred tank bioreactors from 0.02 m3 to 0.3 m3 commercial plant is discussed for hybridoma suspension culture. Schemes for dissolved oxygen control with sparged air in serum containing media are described as well as mechanical breakage of foam in small and large bioreactors. Porous metal spargers (180−200×10−6 m) are found to produce foams which are hard to control. Aeration with larger (> 0.001 m) multihole spargers is recommended. Combined cell damage due to foam formation and control, and possible damage at mechanical seals or submerged bearings, are found to have no measurable effect on cell growth relative to roller bottle production. Hybridomas are shown to withstand significant impeller tip speed (> 1 ms−1) and fluid turbulence as evidenced by impeller Reynolds numbers in excess of 105. The size of the energy dissipating terminal eddies is calculated to be > 10-fold that of the hybridoma cells. Specific fluid turnover rate is employed as the scale-up criterion.

48 citations


Journal ArticleDOI
TL;DR: A simple mathematical model for the interaction of mass transport with biochemical reaction in solid state fermentations in static tray type bioreactors under isothermal conditions has been developed and will be most useful in the prediction of the concentration gradients.
Abstract: A simple mathematical model for the interaction of mass transport with biochemical reaction in solid state fermentations (SSF) in static tray type bioreactors under isothermal conditions has been developed. The analysis has enabled scientific explanations to a number of practical observations, through the concept of critical substrate bed thickness. The model will be most useful in the prediction of the concentration gradients as also in efficient design of these bioreactors.

35 citations


Journal ArticleDOI
TL;DR: In this paper, the use of neural networks to achieve non-linear control of a continuous stirred tank fermenter has been investigated, where the influent dilution rate and the substrate concentration have been selected as control variables.
Abstract: This paper describes an experimental investigation concerning the use of neural networks to achieve the non-linear control of a continuous stirred tank fermenter. The influent dilution rate and the substrate concentration have been selected as control variables. The backpropagation learning algorithm has been used for both off-line and on-line identification of the inverse model which provides the control action. Experimental results show the performance and the implementation simplicity of this control approach.

34 citations


Journal ArticleDOI
TL;DR: The results obtained were found quite encouraging at pH 10 with 1 LPM of air flow rate at low initial liquid height, and the effects of different parameters studied on the purification efficiency by foam fractionation were pH of the broth,Air flow rate, initial liquid Height.
Abstract: Studies on the cost effective purification method is very much essential for the industrially important enzyme like protease. As foam fractionation is an important technique in downstream processing of the biologicals, purification of the crude proteolytic enzyme produced by Rhizopus oryzae has been attempted using converging-diverging foam fractionator. The effects of different parameters studied on the purification efficiency by foam fractionation were pH of the broth, air flow rate, initial liquid height. The results obtained were found quite encouraging at pH 10 with 1 LPM of air flow rate at low initial liquid height.

34 citations


Journal ArticleDOI
TL;DR: In this paper, four systems comprising of an ethanol fermentation integrated with microfiltration and/or pervaporation, and a conventional continuous culture, were compared with respect to the performance of the fermentation and economics.
Abstract: Four systems comprising of an ethanol fermentation integrated with microfiltration and/or pervaporation, and a conventional continuous culture, were compared with respect to the performance of the fermentation and economics. The processes are compared on the basis of the same kinetic model. It is found that cell retention by microfiltration leads to lower production costs, compared to a conventional continuous culture. Pervaporation becomes profitable at a high selectivity of ethanol/water separation and low membrane prices.

Journal ArticleDOI
TL;DR: Mixing models for bioreactors on the basis of the tanks-in-series concept are presented and a suitable parameter-estimation method is introduced and results of the parameter optimization procedure are given.
Abstract: Mixing models for bioreactors on the basis of the tanks-in-series concept are presented and a suitable parameter-estimation method is introduced. The Monte-Carlo-optimization procedure with the inhomogeneity-curve included in the objective function is used. Results of the parameter optimization procedure are given for stirred-tank-bioreactors equipped with one and three Rushton turbines under aerated conditions. The model designed for the stirredtank with three Rushton turbines is capable to describe the mixing properties, while in case of the stirred-tank with one Rushton turbine the simulated radial circulation time does not correlate with the measured one.

Journal ArticleDOI
TL;DR: In this article, a self-generated oscillation-based operation strategy for bioreactors is proposed and applied to a model system consisting of two continuous stirredtank bioreators connected in series.
Abstract: A novel operation strategy employing self-generated oscillation to imrpove the performances of bioreactors is proposed and applied to a model system consisting of two continuous stirredtank bioreators (CSTBs) connected in series. It is demonstrated via computation that the performance of the system (in terms of timeaveraged cell concentration) can be greatly enhanced by adopting the proposed strategy. The process concept presented and the results obtained in this paper are expected to have significant implications beyond the bioprocessing industry.

Journal ArticleDOI
TL;DR: A rule-based fuzzy logic control is developed for control of penicillin concentration in a fed-batch bioreactor and a fuzzy rule base is constructed relating error to the control output based on operators' knowledge.
Abstract: A rule-based fuzzy logic control is developed for control of penicillin concentration in a fed-batch bioreactor. The membership functions, fuzzy ranges for the error and for the controller output are defined. A fuzzy rule base is constructed relating error to the control output based on operators' knowledge. The performance of the fuzzy-logic controller is evaluated by simulating a mathematical model of the fed-batch bioreactor.

Journal ArticleDOI
TL;DR: Bioreactors are compared based on oxygen transfer rate and efficiency, mixing performance, cell mass productivity as well as with respect to enzyme and metabolite productivity.
Abstract: Bioreactors are compared based on oxygen transfer rate and efficiency, mixing performance, cell mass productivity as well as with respect to enzyme and metabolite productivity.

Journal ArticleDOI
TL;DR: It is shown, that oscillating oxygen concentrations, give effects on E.coli metabolism, and the relevance of this model system for studies on the bioreactor performance, are discussed.
Abstract: A coupled reactor system, consisting of one aerated stirred reactor and one anaerobic plug flow reactor was constructed. Circulation of microbial cells in this system, is chosen to represent the insufficient mixing conditions, present in a large scale vessel. Hereby it is shown, that oscillating oxygen concentrations, give effects on E.coli metabolism. The hydrogen production, resulting from mixed acid fermentation of anaerobically grown cells, is used to indicate the metabolic changes. These changes are measured as hydrogen concentration in the gas outlet of the aerated fermenter, with a Pd-MOS sensor. The dependency of the hydrogen evolution on the anaerobic residence time is shown, and the relevance of this model system for studies on the bioreactor performance, are discussed.

Journal ArticleDOI
TL;DR: The model was applied to optimize the feeding rate of a fedbatch process with consideration of final product quality and suggested that the cell cycling process indeed is essentially in a pseudo-steady state during fed-batch cultivation, as was assumed in the model.
Abstract: The cell cycling model (CCM) for S. cerevisiae proposed earlier is modified and tested with our own experimental data. Although the original CCM was well verified in steady states and exponential growth with data available in literature, some discrepancies between model predictions and experiments were found for the dynamics of fed-batch culture. The redistribution pattern of the age distribution of daughter cells is suggested as cause of the model error. With an exponential type of redistribution, instead of the original linear one, the model behaviour in transients is improved. The modified model was verified with data of fraction of budding cells and cell number for five fed-batch cultivations. The model agreed well with the experimental data. The simulation results suggest that the cell cycling process indeed is essentially in a pseudo-steady state during fed-batch cultivation, as was assumed in the model. Due to the strong correlation between the quality of baker's yeast and the state of the population in the cell cycling process, the model was applied to optimize the feeding rate of a fedbatch process with consideration of final product quality. The optimal feeding was used succesfully in a laboratory experiment, which demonstrates the validity of the model.

Journal ArticleDOI
TL;DR: The direct gas sparging into the culture broth in porous microcarrier cultures improved the cell density without mechanical damage to animal cells and also found that not all the cells grown on the interior surface of the porousmicrocarrier were protected against mechanical damage due to agitation.
Abstract: CHO-K1 cells were cultured by using a porous microcarrier. The effects of microcarrier concentration and agitation rate on cell growth in porous microcarrier cultures were investigated. The specific growth rate of 0.041 h−1 in porous microcarrier cultures was independent of both microcarrier concentration and agitation rate. By estimating the total surface area occupied by cells from the maximum cell number, it was found that not all the surface area of the porous microcarrier was utilizable for cell growth.

Journal ArticleDOI
TL;DR: A bioreactor which uses enzyme immobilized within a ceramic membrane support (1 mm thickness) and forced-flow membrane enzyme reactor, FFMER, applicable to processes using substrates present in “impure” feeds.
Abstract: We have developed a bioreactor which uses enzyme immobilized within a ceramic membrane support (1 mm thickness). Substrate is forced through the membrane by cross-flow filtration with the reaction taking place during the process of crossing the membrane. The bioreactor is termed forced-flow membrane enzyme reactor, FFMER. Invertase, which uses sucrose to form glucose and fructose, was tested in this system. The immobilized invertase membrane converted 100% of the sucrose in a feed stream made up of a 50% molasses solution. Because molasses contains many substances besides sucrose, this method is applicable to processes using substrates present in “impure” feeds.

Journal ArticleDOI
TL;DR: The immobilization of lipase from Candida lipolytica on alumina by adsorption for the hydrolysis of ricebran oil is described and the stability of the immobilized enzyme to different pH and temperature conditions has been studied.
Abstract: The immobilization of lipase from Candida lipolytica on alumina by adsorption for the hydrolysis of ricebran oil is described. Some of the factors which influence the activity of immobilizate and the stability of immobilizate are discussed. About 69% of the initially added enzyme activity is found in the biocatalyst when immobilized at pH 7.2. The stability of the immobilized enzyme to different pH and temperature conditions has also been studied.

Journal ArticleDOI
TL;DR: Sodium gluconate method is promising with respect to lesser time for slant age and lesser time of fermentation compared to the calcium glu Conate method.
Abstract: Sodium gluconate and calcium gluconate methods are important techniques available for gluconic acid fermentation. The comparative analysis of these fermentations has been addressed using Aspergillus niger. The techniques are equally influenced by the spores age in slant growth, inoculum level in germination and production media, different levels of Fe, Cu, Zn and Mn. Sodium gluconate method is promising with respect to lesser time for slant age (3 d) and lesser time of fermentation (6 d) compared to the calcium gluconate method (slant age — 6 d, and time of fermentation — 7 d).

Journal ArticleDOI
TL;DR: In this article, a model was proposed to predict variations in D-xylose consumed, and biomass and g biomass ethanol produced, in which parameters for the specific Yx/s growth rate, for the consumption of D xyloses and production of g xylose ethanol either related or not to growth.
Abstract: We have studied the ethanolic fermentation of D-xylose g ethanol with Pachysolen tannophilus in batch cultures. We propose a model Y~/s g xylose to predict variations in D-xylose consumed, and biomass and g biomass ethanol produced, in which we include parameters for the specific Yx/s growth rate, for the consumption of D-xylose and production of g xylose ethanol either related or not to growth, g xylitol The ideal initial pH for ethanol production turned out to be 4.5.. fxi/$ At this pH value the net specific growth rate was 0.26 h 1, biomass g xylose yield was 0.16 g.g- 1, the cell-maintenance coefficient was 0.073 g.g-1.h-1, the parameter for ethanol production non-related to growth was 0.064 g.g- 1.h 1 and the maximum ethanol yield was 0.32 g.g-1 Greek letters

Journal ArticleDOI
TL;DR: In this paper, it was shown that the first normal stress difference measured in fermentation broths is highly dependent on shear rate, and this viscoelastic level is modified by the heat treatment to which the broths are subjected as a postfermentative procedure.
Abstract: Viscoelasticity has important implications in mass transfer and mixing processes Previous studies regarding to the viscoelastic behaviour of xanthan solutions have been carried out with diluted solutions or they have not covered a wide range of polymer concentrations In this study, it was shown that the first normal stress difference measured in fermentation broths is highly dependent on shear rate, and this viscoelastic level is modified by the heat treatment to which the broths are subjected as a postfermentative procedure The viscoelasticity level is different for xanthan solutions prepared with products arising from different sources and for fermentation broths before the heat treatment, if compared with that measured in end-products In general, the higher the polymer concentration, the higher the viscoelasticity (expressed as first normal stress difference or Weissenberg number) The addition of a biocide, the change in ionic strength and the addition of sucrose to the xanthan solutions, lead to significant changes in the first normal stress difference

Journal ArticleDOI
TL;DR: Computer application for fed-batch culture of Brevibacterium flavum for L-lysine production has been developed and the cultivation strategy results in high productivity and high conversion yield.
Abstract: Computer application for fed-batch culture of Brevibacterium flavum for L-lysine production has been developed. The organisms are auxotrophic mutants for L-homoserine and are resistant to S-(2-aminoethyl)-L-cysteine. Adaptive control is applied for substrate addition. The sugar concentration is estimated using online respiratory measurement. During the period of fed-batch culture, the total sugar concentration is maintained at a given value. The cultivation strategy results in high productivity and high conversion yield.

Journal ArticleDOI
TL;DR: In this paper, a support medium for an anaerobic biofilm fluidized bed reactor (AFBR) for waste water treatment was selected, and the authors evaluated the performance of different carriers under various loading rates, stability against toxic shock loadings, recovery capacity after intoxication and starvation, and adsorption/desorption behavior of the carriers.
Abstract: The aim of this study was to select a support medium for an anaerobic biofilm fluidized bed reactor (AFBR) for waste water treatment. Six materials, shale, pumice, porous glass, quartz sand, activated carbon and anthracite were used as carriers for the biofilm. The reactors were operated in parallel for several months with vapour condensate from a sulfite cellulose process as feed. The criteria used for the evaluation were: a) Reproducibility of the reactor performance, b) performance of the different carriers under various loading rates, c) stability against toxic shock loadings using 2,4,6-trichlorophenol (TCP) as toxicant, d) recovery capacity after intoxication and starvation, e) adsorption/desorption behavior of the carriers.

Journal ArticleDOI
TL;DR: An approach to modify external loop air-lift bioreactor that examines its performance with respect to mass transfer was presented in this article, where the riser was replaced by a tube of irregular geometry, in the form of converging-diverging sections (CDT-ALF), so that better mass transfer may be obtained due to better liquid mixing caused by the bubble flow, pulsation effect and early transition to turbulence.
Abstract: An approach to modify external loop airlift bioreactor is presented that examines its performance with respect to mass transfer. There are various designs of airlift fermenter [1]. In the proposed system [2] the riser has been replaced by a tube of irregular geometry, in the form of converging-diverging sections (CDT-ALF), so that better mass transfer may be obtained due to better liquid mixing caused by the bubble flow, pulsation effect and early transition to turbulence. Mass transfer characteristics of the modified airlift fermenter CDT-ALF were studied and compared with those of a conventional one, UT-ALF. Overall volumetric mass transfer coefficient,KLa, was determined by sulfite oxidation method.KLa was determined with respect toUG for differenthi. HigherKLa was always observed in CDT-ALF compared to that in UT-ALF under any operating condition ofhi andUG. If theKLa values are compared in both the systems under their optimum conditions ofhi andUG, CDT-ALF showed 122.5% higher values ofKLa compared to UT-ALF. However, when both the systems were operated at the lowest experimental conditions ofUG, thekLa in CDT-ALF was found to be 170% higher. In UT-ALF while with the decrease ofUG,kLa decreased, in CDT-ALF the reverse was observed i.e. at lowUG,KLa was higher. However with the increase ofhi,KLa decreased in both the systems. To predict volumetric mass transfer coefficientKLa, empirical correlations were developed by dimensional analysis for both the reactors. The correlations were experimentally verified to determine their reliability to predict mass transfer coefficient and the deviation was found within reasonable limit.

Journal ArticleDOI
TL;DR: In this paper, Rice straw, micro-crystalline cellulose powder (MCCP) and bagasse were used as the lignocellulosic residues used as adsorbents.
Abstract: Preferential adsorption of water in the vapor phase by lignocellulosic residues for the production of anhydrous ethanol has been reported in this work. Rice straw, microcrystalline cellulose powder (MCCP) and bagasse were the lignocellulosic residues used as adsorbents. Starting with an ethanol concentration of 80–90% a final concentration above the azeotropic concentration was obtained. An energy analysis of the process was made and a possible explanation of phenomena suggested.

Journal ArticleDOI
TL;DR: In this article, a necessary condition is found for the intermediate temperatures and substrate concentrations in a series of CSTR's performing an enzyme-catalyzed reaction, which leads to the minimum overall volume of the cascade for given initial and final temperatures.
Abstract: A necessary condition is found for the intermediate temperatures and substrate concentrations in a series of CSTR's performing an enzyme-catalyzed reaction which leads to the minimum overall volume of the cascade for given initial and final temperatures and substrate concentrations. The reaction is assumed to occur in a single phase under steady state conditions. The common case of Michaelis-Menten kinetics coupled with first order deactivation of the enzyme is considered. This analysis shows that intermediate stream temperatures play as important a role as intermediate substrate concentrations when optimizing in the presence of nonisothermal conditions. The general procedure is applied to a practical example involving a series of two reactors with reasonable values for the relevant five operating parameters. These parameters are defined as dimensionless ratios involving activation energies (or enthalpy changes of reaction), preexponential factors, and initial temperature and substrate concentration. For negligible rate of deactivation, the qptimality condition corresponds to having the ratio of any two consecutive concentrations as a single-parameter increasing function of the previous ratio of consecutive concentrations.

Journal ArticleDOI
TL;DR: The influence of the acetate addeed to the M9 minimal medium and to the Luria-Bertani medium without and with glucose supplement on the growth of recombinant Escherichia coli J103 with three different types of multicopy plasmids and on the production of the fusion protein SpA :: EcoRI was investigated.
Abstract: The influence of the acetate addeed to the M9 minimal medium and to the Luria-Bertani medium without and with glucose supplement on the growth of recombinant Escherichia coli J103 with three different types of multicopy plasmids and on the production of the fusion protein SpA :: EcoRI were investigated in shake flasks without and with induction of the gene expression by a temperature shift from 30 °C to 42 °C. At the beginning of the induction of gene expression concentrated LB-medium was added to the shake flask. Without this supplement of M9 medium no gene expression occurred.

Journal ArticleDOI
TL;DR: In this paper, a necessary condition is found for the optimum temperature policy which leads to the minimum reaction time for a given final conversion of substrate in a well stirred, enzymatic batch reactor performing an enzyme-catalyzed reaction following Michaelis-Menten kinetics in the presence of first order enzyme decay.
Abstract: A necessary condition is found for the optimum temperature policy which leads to the minimum reaction time for a given final conversion of substrate in a well stirred, enzymatic batch reactor performing an enzyme-catalyzed reaction following Michaelis-Menten kinetics in the presence of first order enzyme decay. The reasoning, which is based on Euler's classical approach to variational calculus, is relevant for the predesign steps because it indicates in a simple fashion which temperature program should be followed in order to obtain the maximum advantage of existing enzyme using the type of reactor usually elected by technologists in the fine biochemistry field. In order to highlight the relevance and applicability of the work reported here, the case of optimality under isothermal operating conditions is considered and a practical example is worked out.