Ethanol from hydrolyzed whey permeate using Saccharomyces cerevisiae in a membrane recycle bioreactor

A diauxic fermentation was observed during batch fermentation of enzyme-hydrolyzed whey permeate to ethanol by Saccharomyces cerevisiae. Glucose was consumed before and much faster than galactose. In the continuous membrane recycle bioreactor (MRB), sugar utilization was a function of dilution rate and concentration of sugars. At a cell concentration of 160 kg/m³, optimum productivity was 31 kg/(m³ · h) at ethanol concentration of 65 kg/m³. Low levels of acetate (0.05–0.1 M) reduced cell growth during continuous fermentation, but also reduced galactose utilization.     

Integration of continuous production and recovery of solvents from whey permeate: use of immobilized cells of Clostridium acetobutylicum in a flutilized bed reactor coupled with gas stripping

An investigation was performed into the operation of an integrated system for continuous production and product recovery of solvents (acetone-butanol-ethanol) from the ABE fermentation process. Cells of Clostridium acetobutylicum were immobilized by adsorption onto bonechar, and used in a fluidized bed reactor for continuous solvent production from whey permeate. The reactor effluent was stripped of the solvents using nitrogen gas, and was recycled to the reactor. This relieved product inhibition and allowed further sugar utilization. At a dilution rate of 1.37 h^–1 a reactor productivity of 5.1 kg/(m³ · h) was achieved. The solvents in the stripping gas were condensed to give a solution of 53.7 kg/m³. This system has the advantages of relieving product inhibition, and providing a more concentrated solution for recovery by distillation. Residual sugar and non-volatile reaction intermediates are not removed by gas stripping and this contributes to high solvent yields.List of Symbols C kg/m³ Lactose concentration in reactor effluent - C _b kg/m³ Lactose concentration in bleed stream - C _c kg/m³ Lactose concentration in whey permeate feed - C _i kg/m³ Lactose concentration at reactor inlet - C _p kg/m³ Lactose concentration in condensed solvent stream (=0) - C _r kg/m³ Lactose concentration in recycle line (C _b=C _r) - C kg/h Amount of lactose utilized during certain time period - D h¹ Dilution rate of reactor, F _i/D=F/D - F dm³/h, m3/h F _i = Rate of feed flow to the reactor - F _b dm ³/h, m³/h Rate of bleed - F _c dm³/h, m³/h Rate of feed of whey permeate solution - F _p dm³/h, m³/h Rate of concentrated product removal - F _r dm³/h, m³/h Rate of recycle of stripped effluent to the reactor - P _l % Percent lactose utilization - R _l kg/(m³ · h) Overall lactose utilization rate - R _p kg/(m³ · h) Overall reactor (solvent) productivity - R _sl kg/h Rate of solvent loss - S kg/m³ Solvent concentration in reactor effluent - S _b kg/m³ Solvent concentration in bleed - S _c kg/m³ 0; Solvent concentration in concentrated whey permeate solution - S _i kg/m³ Solvent concentration at inlet of reactor - S _p kg/m³ Solvent concentration in concentrated product stream - S _r kg/m³ Solvent concentration in stripped effluent, S _r=S_b - S kg/h Amount of solvent produced from C amount of lactose in a particular time - ds/dt kg/(m³ · h) Rate of accumulation of solvents in the stripper - t h Time - V dm³, m³ Total reactor volume - V ¹ dm³, m³ Liquid volume in stripper - Y _P/S Solvent yield     

Modelling of alcohol fermentation in a tubular reactor with high biomass recycle

Fermentation in tubular recycle reactors with high biomass concentrations is a way to boost productivity in alcohol production. A computer model has been developed to investigate the potential as well as to establish the limits of this process from a chemical engineering point of view. The model takes into account the kinetics of the reaction, the nonideality of flow and the segregation in the bioreactor. In accordance with literature, it is shown that tubular reactors with biomass recycle can improve productivity of alcohol fermentation substantially.With the help of the computer based reactor model it was also possible to estimate the detrimental effects of cell damage due to pumping. These effects are shown to play a major role, if the biomass separation is performed by filtration units which need high flow rates, e.g. tangential flow filters.List of Symbols Bo d Bodenstein number - c kg/m³ concentration of any component - CPFR continuous plug flow reactor - CSTR continuous stirred tank reactor - d _h m hydraulic diameter - D _eff m²/s dispersion coefficient - f residence time distribution function - K _s kg/m³ monod constant for biomass production - K _s kg/m³ monod constant for alcohol production - p kg/m³ product concentration - P _i kg/m³ lower inhibition limit concentration for biomass production - p _i kg/m³ lower inhibition limit concentration for alcohol production - p _m kg/m³ maximum inhibition limit concentration for biomass production - p _m kg/m³ maximum inhibition limit concentration for alcohol production - q _p h^–1 specific production rate - q _p,max h^–1 maximum specific production rate for alcohol production - q _s h^–1 specific substrate consumption rate - Q _L m _gas ³ /m³h specific gas rate - r _p , r _s , r _x kg/(m³ · h) reaction rate for ethanol production substrate consumption and cell growth, respectively - S _F kg/m³ substrate concentration in feed stream - s kg/m³ substrate concentration - t h time - x kg/m³ biomass concentration - x _max kg/m³ maximum biomass concentration for biomass production - Y _p/s yield coefficient - h^–1 specific growth rate - _max h^–1 maximum specific growth rate - dimensionless time (t/) - h mean residence time - _s glucose conversion     

Investigations of cephalosporin C production in an airlift tower loop reactor

Summary Cephalosporin C was produced by Cephalosporium acremonium in a 60 l airlift loop reactor on complex medium (with 30 kg/m³ peanut flour) in fed-batch operation. A final product concentration of 5 kg/m³ and a maximum productivity of 45 g/m³ h were attained. On-line analysis was used to determine ammonia, methionine, phosphate, reducing sugar and cephalosporin C by an autoanalyser, glucose by a flow injection analyser and cephalosporin C, penicillin N, deacetoxycephalosporin C, deacetylce-phalosporin C and methionine by HPLC. The volumetric productivity of the stirred tank reactor was higher than that of the airlift reactor because of differences in cell concentration. Specific productivities in relative to cell mass were similar in the two reactors. The substrate yield coefficient in the airlift reactor was twice that in the stirred tank reactor.Nomenclature E _o2 efficiency of oxygen transfer with regard to the specific power input - K _La volumetric mass transfer coefficient - OTR oxygen transfer rate - P power input - PR volumetric productivity of CPC - q _a volumetric aeration rate/broth volume (vvm) - SPR specific productivity with regard to RNA - V _L broth volume in reactor - z relative height of the aerated reactor     

In-situ recovery of butanol during fermentation

End-product inhibition in the acetone-butanol fermentation was reduced by using extractive fermentation to continuously remove acetone and butanol from the fermentation broth. In situ removal of inhibitory products from Clostridium acetobutylicum resulted in increased reactor productivity; volumetric butanol productivity increased from 0.58 kg/(m³h) in batch fermentation to 1.5 kg/(m³h) in fed-batch extractive fermentation using oleyl alcohol as the extraction solvent. The use of fed-batch operation allowed glucose solutions of up to 500 kg/m³ to be fermented, resulting in a 3.5- to 5-fold decrease in waste water volume. Butanol reached a concentration of 30–35 kg/m³ in the oleyl alcohol extractant at the end of fermentation, a concentration that is 2–3 times higher than is possible in regular batch or fed-batch fermentation. Butanol productivities and glucose conversions in fed-batch extractive fermentation compare favorable with continuous fermentation and in situ product removal fermentations.List of Symbols C _g kg/m³ concentration of glucose in the feed - C _w dm³/m³ concentration of water in the feed - F(t) cm³/h flowrate of feed to the fermentor at time t - V(t) dm³ broth volume at time t - V _i dm³ initial broth volume - V _si dm³ volume of the i-th aqueous phase sample - effective fraction of water in the feed Part 1. Bioprocess Engineering 2 (1987) 1–12     

Continuous ethanol production by Zymomonas mobilis in a fluidized bed reactor. Part II: Process development for the fermentation of hydrolysed B-starch without sterilization

A continuous fluidized bed reactor operation system has been developed for ethanol production by Zymomonas mobilis using hydrolysed B-starch without sterilization. The operation system consists of two phases. In the first phase macroporous glass carriers in a totally mixed fluidized bed reactor were filled up totally with a monoculture of Z. mobilis by fast computer-controlled colonization, so that in the subsequent production phase no contaminants, especially lactic-acid bacteria, could penetrate into the carrier beads. In the production phase the high concentration of immobilized Z. mobilis cells in the fluidized bed reactor permits unsterile fermentation of hydrolysed B-starch to ethanol at short residence times. This results in wash-out conditions for contaminants from the substrate. Long-term experimental studies (more than 120 days) of unsterile fermentation of hydrolysed B-starch in the laboratory fluidized bed reactor (2.2 l) demonstrated stable operation up to residence times of 5 h. A semi-technical fluidized bed reactor plant (cascade of two fluidized bed reactors, each 55 l) was operated stably at a mean residence time of 4.25 h. Glucose conversion of 99% of the unsterile hydrolysed B-starch was achieved at 120 g glucose/l^–1 in the substrate, resulting in an ethanol concentration of 50 g·l^–1 and an ethanol space-time yield of 13 g·l^–1·h^–1. This is a factor of three compared to ethanol fermentation of hydrolysed B-starch with Z. mobilis in a continuous stirred tank reactor, which can only be operated stably under sterile conditions. Correspondence to: D. Weuster-Botz     

Propionic acid fermentation: improvement of performances by coupling continuous fermentation and ultrafiltration

The present paper presents a study of propionic acid production from whey by using Propionibacterium acidipropionici in batch and continuous fermentation with cell recycle. The experimental investigation is carried through with a biomass concentration (DW) of 112kg/m³. The highest propionic acid productivity is 2.14 kg/(m³ h). Biomass concentration is 9 times as high, propionic acid productivity 6 times as high as compared to batch results.     

Application of an airlift bioreactor to the nystatin biosynthesis

Pilot plant studies were performed using a concentric-tube airlift bioreactor of 2.5 m³ fermentation volume. The results have proven the relative merits of such a system in the biosynthesis of nystatin, produced by Streptomyces noursei, in submerged aerobic cultivation and batch operation mode. The results were compared to those obtained in a pilot-scale stirred tank bioreactor of 3.5 m³ fermentation volume. The fermentation processes in the two fermentation devices were similar with respect to substrate utilization, biomass production and nystatin biosynthesis. In the riser section, the dissolved oxygen concentration was higher than that in the downcomer. The volumetric oxygen mass transfer coefficient was dependent on the rheological behaviour of the biosynthesis liquids, which was not constant during the fermentation process. The total energy consumption for nystatin production in the airlift bioreactor was 56% of that in the stirred tank, while the operating costs represented 78% of those in the stirred tank bioreactor.     

Growth of E. coli in a stirred tank and in an air lift tower reactor with an outer loop

E. coli ATCC 11105 was cultivated in a 10-1 stirred tank reactor and in a 60-1 tower loop reactor in batch and continuous operation. By on-line measurements of O₂ and CO₂ concentrations in the outlet gas, pH, temperature, cell mass concentration X as well as dissolved O₂ concentration along the tower in the broth, gas holdup, broth recirculation rate through the loop and by offline measurements of substrate concentration DOC and cell mass concentration along the tower, the maximum specific growth rate _m , yield coefficients Y _X/S. Y _X/DOC and were evaluated in stirred tank and tower loop in batch and continuous cultures with and without motionless mixers in the tower and at different broth circulation rates through the loop. To control the accuracy of the measurements the C balance was calculated and 95% of the C content was covered.The biological parameters determined depend on the mode of operation as well as on the reactor used. Furthermore, they depend on the recirculation rate of the broth and built-ins in the tower. The unstructured cell and reactor models are unable to explain these differences. Obviously, structured cell and reactor models are needed. The cell mass concentration can be determined on line by NADH fluorescence in balanced growth, if the model parameters are determined under the same operational conditions in the same reactor.List of Symbols a, b empirical parameters in Eq. (1) - CPR kg/(m³ h) CO₂ production rate - C kg/m³ concentration - D l/h dilution rate - DOC kg/m³ dissolved organic carbon - I net. fluorescence intensity - K _S kg/m³ Monod constant - k _L a l/h volumetric mass transfer coefficient - OTR kg/(m³ h) oxygen transfer rate - OUR kg/(m³ h) oxygen utilization rate - RQ = CPR/OUR respiratory quotient - S kg/m³ substrate concentration - t h,min, s time - t _u min recirculation time - t _M min mixing time - v m³/h volumetric flow rate through the loop - X kg/m³ (dry) cell mass concentration - Y _X/S yield coefficient of cell mass with regard to the consumed substrate - Y _X/DOC yield coefficient of the cell mass with regard to the consumed DOC - Y _X/O yield coefficient of the cell mass with regard to the consumed oxygen - Z relative distance in the tower from the aerator with regard to the height of the aerated broth - l/h specific growth rate - _m l/h maximum specific growth rate Indices f feed - e outlet     

Jet aeration as alternative to overcome mass transfer limitation of stirred bioreactors

In industrial biotechnology increasing reactor volumes have the potential to reduce production costs. Whenever the achievable space time yield is determined by the mass transfer performance of the reactor, energy efficiency plays an important role to meet the requirements regarding low investment and operating costs. Based on theoretical calculations, compared to bubble column, airlift reactor, and aerated stirred tank, the jet loop reactor shows the potential for an enhanced energetic efficiency at high mass transfer rates. Interestingly, its technical application in standard biotechnological production processes has not yet been realized. Compared to a stirred tank reactor powered by Rushton turbines, maximum oxygen transfer rates about 200% higher were achieved in a jet loop reactor at identical power input in a fed batch fermentation process. Moreover, a model‐based analysis of yield coefficients and growth kinetics showed that E. coli can be cultivated in jet loop reactors without significant differences in biomass growth. Based on an aerobic fermentation process, the assessment of energetic oxygen transfer efficiency [kgO₂ kW^?1 h^?1] for a jet loop reactor yielded an improvement of almost 100%. The jet loop reactor could be operated at mass transfer rates 67% higher compared to a stirred tank. Thus, an increase of 40% in maximum space time yield [kg m^?3 h^?1] could be observed.     

Optimization of the microbial synthesis of dihydroxyacetone from glycerol with <Emphasis Type="Italic">Gluconobacter oxydans</Emphasis>

An optimized repeated-fed-batch fermentation process for the synthesis of dihydroxyacetone (DHA) from glycerol utilizing Gluconobacter oxydans is presented. Cleaning, sterilization, and inoculation procedures could be reduced significantly compared to the conventional fed-batch process. A stringent requirement was that the product concentration was kept below a critical threshold level at all times in order to avoid irreversible product inhibition of the cells. On the basis of experimentally validated model calculations, a threshold value of about 60 kg m^-3 DHA was obtained. The innovative bioreactor system consisted of a stirred tank reactor combined with a packed trickle-bed column. In the packed column, active cells could be retained by in situ immobilization on a hydrophilized Ralu-ring carrier material. Within 17 days, the productivity of the process could be increased by 75% to about 2.8 kg m^-3 h^-1. However, it was observed that the maximum achievable productivity had not been reached yet.Abbreviations K _O Monod half saturation constant of dissolved oxygen (kg m^-3) - K _S Monod half saturation constant of substrate glycerol (kg m^-3) - O Dissolved oxygen concentration (kg m^-3) - P Product concentration (kg m^-3) - P _crit Critical product concentration constant (kg m^-3) - S Substrate concentration (kg m^-3) - t Time (s) - X Biomass concentration (dry weight) (kg m^-3) - Y _P/S Yield coefficient of product from substrate - Y _X/S Yield coefficient of biomass from substrate - Growth dependent specific production rate constant (kg m^-3) - Growth independent specific production rate constant (s^-1) - Specific growth rate (s^-1) - _max Maximum specific growth rate constant (s^-1)     

Bioprocess engineering characteristics of the horizontal stirred tank

Bioreactor performance studies of the recently developed horizontal stirred tank with a volume of 421 have been carried out for fermentation with Trichosporon cutaneum. Quantification on the basis of measured oxygen transfer capacity and power consumption is presented and compared with data for a conventional vertical tank bioreactor.During the experiments it has been observed that two different forms of morphology of Trichosporon, i.e. the normal yeast-form (Y) with single cells and a mycelium-form (M) with filamentous cells, are present in the horizontal stirred tank when working with the original strain (DSM 70698). After separation both forms were characterized and later on used for bioreactor performance studies in the horizontal and vertical stirred tank. Results of oxygen efficiency show the drastic effect of the morphology change on bioreactor performance. Finally different bioreactors are quantitatively compared on the basis of oxygen transfer, power consumption and productivity using the reference fermentation system Trichosporon cutaneum.List of Symbols F m³/h flow rate (volumetric) - k _La1/h volumetric transfer coefficient of OTR - M Nm torque - n 1/s rotational speed - P Nm/s power - V m³ volume - V _G1/min gas flow rate - x kg/m³ biomass concentration - ^* morphology index - ^* engineering (specific) viscosity - _app Ns/m² apparent viscosity - ₀ N/m² yield stress (Casson law) - t _1/e h measured time acc. to momentum method [17] - tEh characteristic time of electrode response - t _Gh mean residence time of gas phase Abbreviations CFR completely filled reactor - CRR cyclic ring reactor (torus) - JLR jet loop reactor - HSTR horizontal stirred tank reactor - M mycelium-form of Trichosporon cutaneum - O₂-eff O₂-efficiency - OUR O₂-uptake rate - OTR O₂-transfer rate - STR stirred tank reactor - ThLR thin layer reactor - VSTR vertical stirred tank reactor - Y yeast-form of Trichosporon cutaneum The work presented in this paper was supported by an Austrian Research Grant (FFWF, Project no. 4496)     

Denitrification Performance of Pseudomonas denitrificans in a Fluidized‐Bed Biofilm Reactor and in a Stirred Tank Reactor

Denitrification of a synthetic wastewater containing nitrates and methanol as carbon source was carried out in two systems – a fluidized‐bed biofilm reactor (FBBR) and a stirred tank reactor (STR) – using Pseudomonas denitrificans over a period of five months. Nitrogen loading was varied during operation of both reactors to assess differences in the response to transient conditions. Experimental data were analyzed to obtain a comparison of denitrification kinetics in biofilm and suspended growth reactors. The comparison showed that the volumetric degradation capacity in the FBBR (5.36 kg _N · m^–3 · d^–1) was higher than in the STR, due to higher biomass concentration (10 kg _BM · m^–3 vs 1.2 kg _BM m^–3).     

Cephalosporin C production in a stirred tank reactor

Summary Cephalosporin C was produced with the moldCephalosporium acremonium in a 20 1 stirred tank reactor with 100 kg/m³ peanut flour in fed-batch operation. The growth and product formation was followed by on-line analysis of the broth composition. The cell concentration was estimated from the RNA-content of the cells. By optimization of the fed-batch operation and by increasing the phosphate content in the broth, a final cephalosporin C concentration of 12 kg/m³ was attained.Nomenclature CPC cephalosphorin C - DAC deacetylcephalosporin C - DAOC deacetoxycephalosporin C - k _L a volumetric mass transfer coefficient - MMBS 2-Hydroxy-4-methylmercaptobutyric acid - PABAH p-Hydroxybenzoicacidhydrazid - RNA ribonucleic acid - RQ respiratory quotient - oxygen transfer rate - CO₂-production rate - t fermentation time     

Kinetics of inhibition in propionic acid fermentation

The inhibitory effect of propionic acid P and biomass concentration X is studied in batch and continuous fermentations with cell recycle.In batch fermentations, the specific growth rate decreases and cancels out at a critical propionic acid concentration Pc ₁; the formerly decreasing specific production rate becomes constant after Pc ₁ and cancels out when a second critical propionic acid concentration Pc ₂ is reached.In continuous fermentation with cell recycle, a similar inhibition is observed with biomass. The specific rates decrease and become constant at a critical biomass concentration Xc. They cancel out at different high biomass concentrations.In both cases, the specific production rate can be related to the specific growth rate by the Luedeking and Piret expression: =+, [1], where the constants and are determined by the fermentation parameters.List of Symbols t h time - X kg/m³ biomass concentration - P kg/m³ propionic acid concentration - A kg/m³ acetic acid concentration - S kg/m³ lactose concentration - dX/dt kg/(m³h) instantaneous rate of cell growth - dP/dt kg/(m³h) instantaneous rate of propionic acid production - h^–1 specific growth rate - h^–1 specific propionic acid production rate - D h^–1 dilution rate     

Penicillin acylase production by E. coli

Enzyme production with E. coli ATCC 11105, in a complex medium using phenylacetic acid as inducer is carried out in a stirred-tank reactor of 10 dm³ and an airlift tower-loop reactor of 60 dm³ with outer loop at a temperature of 27 °C. The optimum inducer concentration was 0.8 kg/m³, which was kept constant by fed-batch operation. The optimum of the relative dissolved O₂-concentration with regard to saturation is below 10% in a stirred-tank reactor and at 35% in a tower-loop reactor. It was kept constant by parameter-adaptive control of the aeration rate. In a stirred-tank enzyme productivity is slightly higher than in a tower-loop reactor, and much higher than in a bubble column reactor.List of Symbols CPR kg/(m³ h) CO₂-production rate - OTR kg/(m³ h) O₂-transfer rate - OUR kg/(m³ h) O₂-utilization rate - PAA phenylacetic acid (inducer) - RQ = CPR/OUR respiratory quotient - X kg/m³ cell mass concentration - _m h^–1 maximum specific growth rate     

Fermentation analysis by clustering

To supervise, stabilize and optimize antibiotic fermentations in the industrial scale expert systems are presently worked out. For the knowledge acquisition various classifiers are tested using a set of 27 nourseothricin fermentation runs. Two methods are applied: optimal clustering by help of minimum variance criterion and hierarchical clustering by help of dendrograms. The fermentations are classified with respect to the specific material costs as well as the product formation kinetics.List of Symbols a kg/m³ initial value of linearized product kinetics - b kg/(m³ · h) slope of linearized product kinetics - B binary variable (value 0 or 1) - C DM/kg specific costs - d distance - m number of samples - p kg/m³ product concentration - pO₂ % dissolved oxygen concentration - t h fermentation time - T h initial time of linearized product kinetics - n number of fermentation runs     

Development of an immobilized cell reactor for the production of 1,3-propanediol by Citrobacter freundii

Citrobacter freundii DSM 30040 immobilized on modified polyurethane carrier particles PUR 90/16 was used for continuous glycerol fermentation in an anaerobic fixed bed reactor with effluent recycle and pH control (fixed bed loop reactor). The fermentor was run with buffered mineral medium under growth conditions resulting in the permanent renewal of active biomass. The effects of glycerol concentration in the feed, dilution rate (D), pH and temperature (T) were investigated to optimize the process. With 400 mm glycerol in the feed, pH 6.9, T = 36°C and D = 0.5 h^–1 the maximum productivity could be determined as 8.2 g/l per hour of 1,3-propanediol.     

Continuous fermentation of sweet whey permeate for propionic acid production in a CSTR with UF recycle

Summary Propionic acid was produced byPropionibacterium acidi-propionici from sweet-whey permeate in a stirred tank reactor (CSTR) with cell recycle by ultrafiltration. The highest volumetric productivity achieved was 14.3 g.l^–1. h^–1, with a biomass of 100 g.l^–1 (dry weight). More concentrated product can be obtained by electrodialysis of the cell free fermentation medium.     

Production of glutamine by micro-gel bead-immobilized Corynebacterium glutamicum 9703-T cells in a stirred tank reactor

The effectiveness of using micro-gel bead-immobilized cells for aerobic processes was investigated. Glutamine production by Corynebacterium glutamicum, 9703-T, cells was used as an example. The cells were immobilized in Sr-alginate micro-gel beads 500 m in diameter and used for fermentation processes in a stirred tank reactor with a modified impeller at 400 min^–1. Continuous production of glutamine was carried out for more than 220 h in this reactor and no gel breakage was observed. As a result of the high oxygen transfer capacity of this system, the glutamine yield from glucose was more than three times higher, while the organic acid accumulation was more than 24 times lower than those obtained with 3.0 mm-gel bead-immobilized cells in an airlift fermentor under similar experimental conditions. During the continuous fermentations there was evolution and proliferation of non-glutamine producing strains which led to a gradual decrease in the productivity of the systems. Although a modified production medium which suppresses cell growth during the production phase was effective in maintaining the productivity, the stability of the whole system was shortened due to high cell deactivation rate in such a medium.List of Symbols C kg/m³ glutamine concentration - C _A mol/m ³ local oxygen concentration inside the gel beads - C _AS mol/m ³ oxygen concentration at the surface of the gel beads - De m²/h effective diffusion coefficient of oxygen in the gel bead - DO mol/m³ dissolved oxygen concentration - F dm³/h medium flow rate - K h^–1 glutamine decomposition rate constant - Km mol/m³ Michaelis Menten constant - QO _2max mol/(kg · h) maximum specific respiration rate - R m radius of the gel beads - r m radial distance - t h time - V _C dm ³ volume of the gel beads - V _L dm ³ liquid volume in the reactor - Vm mol/(m³ · h) maximum respiration rate - X kg/m³ cell concentration - x r/R - y C _A /C_AS - h^–1 cell deactivation rate constant - Thiele modulus defined by R(Vm/De Km) ^1/2 - C _AS /Km - _C kg/(m³-gel · h) specific glutamine formation rate - _c dm³-gel/dm³ V _C /V _L