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     

Process engineering aspects of the bioleaching of copper ores

The bioleaching of minerals is a complex process that is affected by a number of biological, mineralogical, electrochemical and engineering factors. This work presents and discusses the most significant process engineering aspects involved in the bacterial leaching of copper ores, i.e. bacterial population, type of mineral and particle size, nutrients and inhibitors, oxygen and carbon dioxide, temperature and pH, leaching kinetics and operation mode.It is concluded that more work is needed in this area in order to gain a deeper insight in the many factors that govern this process. This would allow to significantly improve its overall productivity.List of Symbols C _L kg/m³ dissolved oxygen concentration - C ^* kg/m³ equilibrium oxygen concentration - d, e, f, g % percentage of C, H, O and N in the cell - D m impeller diameter - K consistency index - K _S, K₁, K_c constants - k _La h^–1 volumetric oxygen transfer coefficient - M _b mol/kg biomass apparent molecular weight - N s^–1 rotation frequency - n behavior index - P kg/m³ ungassed agitation power, product concentration - P _g kW/m³ gassed agitation power - p % pulp density - Q m³/h air flow rate - S kg/m³ limiting substrate concentration - W kg/(m³ · h) mass transfer rate per unit volume - X cells/cm³ biomass concentration - Y _o g cells/g Fe oxygen cell yield - Y _x g cells/g Fe substrate cell yield - h^–1 specific growth rate - _m h^–1 maximum specific growth rate     

Kinetic behavior of penicillin acylase immobilized on acrylic carrier

The usefulness of Lilly's kinetic equation to describe penicillin G hydrolysis performed by immobilized penicillin acylase onto the acrylic carrier has been shown. Based on the experimental results characteristic kinetic constants have been estimated. The effect of noncompetitive inhibition of 6-amino penicillanic acid has not been found. Five components of reaction resistance have been defined. These components were also estimated for the reaction of the native enzyme as well as the Boehringer preparation.List of Symbols C _E g/m³ enzyme concentration - C _P,C _Q mol/m³ product concentrations - C _S mol/m³ substrate concentration - C _SO mol/m³ initial substrate concentration - K _A mol/m³ constant which defines the affinity of a substrate to the enzyme - K _iS mol/m³ substrate inhibitory constant - K _iP mol/m³ PhAA inhibitory constant - K _iQ mol/m³ 6-APA inhibitory constant - k ₃ mol/g/min constant rate of dissociation of the active complex - R(1) concentrational component of reaction resistance - R(2) resistance component derived from substrate affinity - R(3) resistance component due to the inhibition of the enzyme by substrate - R(4) resistance component due to the inhibition of the enzyme by PhAA - R(5) resistance component due to inhibition of the enzyme by 6-APA - r = dC_s/dt mol/m³ min rate of reaction - t min reaction time - (i) relative resistance of reaction     

Effects of dissolved oxygen concentration on lipase production by Rhizopus delemar

Summary The influence of the concentration of oxygen on lipase production by the fungus Rhizopus delemar was studied in different fermenters. The effect of oxygen limitation ( 47 mol/l) on lipase production by R. delemar is large as could be demonstrated in pellet and filamentous cultures. A model is proposed to describe the extent of oxygen limitation in pellet cultures. Model estimates indicate that oxygen is the limiting substrate in shake flask cultures and that an optimal inoculum size for oxygen-dependent processes can occur.Low oxygen concentrations greatly negatively affect the metabolism of R. delemar, which could be shown by cultivation in continuous cultures in filamentous growth form (D_optimal=0.086 h^-1). Continuous cultivations of R. delemar at constant, low-oxygen concentrations are a useful tool to scale down fermentation processes in cases where a transient or local oxygen limitation occurs.Symbols and Abbreviations CO Oxygen concentration in the gas phase at time = 0 (kg·m^-3) - C_{O 2i} Oxygen concentration at the pellet liquid interface (kg·m^-3) - C_{O 2i} Oxygen concentration in the bulk (kg·m^-3) - D Dilution rate (h^-1) - ID_{O 2} Diffusion coefficient for oxygen (m²·s^-1) - dw Dry weight of biomass (kg) - f Conversion factor (rs _{O 2} to oxygen consumption rate per m³) (-) - k Radial growth rate (m·s^-1) - K Constant - kla Volumetric mass transfer coefficient (s^-1) - klA Oxygen transfer rate (m^-3·s^-1) - kl Mass transfer coefficient (m·s^-1) - K _{O 2} Affinity constant for oxygen (mol·m^-3) - K _w Cotton plug resistance (m^-3·s^-1) - M Henry coefficient (-) - NV Number of pellets per volume (m^-3) - R Radius (m) - RO Radius of oxygen-deficient core (m) - RQ Respiration quotient (mol CO₂/mol O₂) - rs _{O 2} Specific oxygen consumption rate per dry weight biomass (kg O₂·s^-1[kg dw]^-1) - rX Biomass production rate (kg·m^-3·s^-1) - SG Soytone glucose medium (for shake flask experiments) - SG ₄ Soytone glucose medium (for tower fermenter and continuous culture experiments) - V Volume of medium (m^-3) - X Biomass (dry weight) concentration (kg·m^-3) - XR _o Biomass concentration within RO for a given X (kg·m^-3) - Y _{O 2} Biomass yield calculated on oxygen (kg dw/kg O₂) - Thiele modulus - Efficiency factor =1-(RO/R)³ (-) - Growth rate (m^-1·s^-1·kg^1/3) - Dry weight per volume of pellet (kg·m^-3)     

A dynamic cell cycling model for growth of baker's yeast and its application in profit optimization

A cell cycling model for unequal budding yeast Saccharomyces cerevisiae is proposed and verified by steady state data from experiments available in the literature. This model can be used to determine the relative fraction of the cells in any cycling phase or with any genealogical age during fermentation. As the quality of yeast is strongly influenced by the cycling process, the model could therefore be used to control the quality of the harvested yeast cells. The input of the cell cycling model is the specific growth rate , which is obtained from a metabolic model for S. cerevisiae proposed earlier. With this extended model system not only the quality control, but also the whole economical profit optimization can be carried out. Simulations were done to optimize the profit of a commercial scale baker's yeast production process by manipulating substrate feeding rate and substrate concentration under different aeration rates, fermentation periods and other conditions applied in industry.List of Symbols B h budding phase - C _d1, C _d2, C _p1' parameters in cycling phase equations - C _p2, C _b1, C _b2, d _s m Sauter-diameter - E kg/m³ ethanol concentration - E1, E2 state variables in the metabolic model - E _G mean relative gas hold-up - f parameter vector of the regulation model - F system matrix of the regulation model - F or F(t) m³/h substrate feeding rate - Fr Froude number - FBC, FDC, FPC % fraction of daughter cells, unbudded daughter cells and unbudded parent cells - g m/s² acceleration of gravity - K _B1–3, K _EG parameters in metabolic model - K ₃, K _Ad , L ₃ K ₃ E, K_O, K_S limitation constants for ethanol, oxygen and substrate - k _La h^–1 volumetric mas transfer coefficient - m _ATP mol(gh)^–1 maintenance coefficient - nb, nd, np number of cycling age intervals in budding cycling phase, unbudded daughter cycling phase and unbudded parent cycling phase - Nt number of total cells - OF mg/dm³ concentration of dissolved oxygen - P kg total yeast product in dry weight - P/O effectiveness of oxidative phosphorylation - q _O20 mol(gh)^–1 minimum specific oxygen uptake ability - q _O2 mol(gh)^–1 specific oxygen uptake rate - q _O2max mol(gh)^–1 maximum q _O2 given by metabolic regulation - q _s mol(gh)^–1 specific glucose uptake rate - q _Smax mol(gh)^–1 maximum q _S - R(·) switch function - r _Ac mol(gh)^–1 specific acetyl-CoA-consumption rate - r _Acmax saturation rate of r _Ac - r _E1 mol(gh)^–1 specific ethanol production rate - r _E2 mol(gh)^–1 specific ethanol uptake rate - r _SO mol(gh)^–1 minimum value of r _Smax - r _s mol(gh)^–1 specific rate of glycolysis - r _Smax mol(gh)^–1 maximum specific rate of gluconeogenesis given by metabolic regulation - S kg/m³ total reduced sugar concentration - S _R kg/m³ substrate concentration in feed - T h cell number doubling time - T _f h fermentation period - Ud h unbudded daughter phase - Up h unbudded parent phase - V _F m³ volume of liquid phase in fermentor - V _G m³/h aeration rate - w _sg m/s superficial gas velocity - X kg/m³ dried cell concentration - Y _ATP g(molATP)^–1 yield coefficient of ATP - z state vector in regulation model - the factor of fermentative activity decrease caused by budding cells - or(t) h^–1 specific growth rate - h discrete unit of cycling age     

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      

Malate degradation by Schizosaccharomyces yeasts included in alginate beads

Schizosaccharomyces yeasts can be used for deacidification of grape musts. To this aim, we studied malic acid degradation by yeasts included in double layer alginate beads in a bubble column reactor. Use of immobilized micro-organisms allowed a continuous process with high dilution rates giving a deacidification capacity of 0.032 g of malate/hour/dm³/g of beads. The pneumatic agitation was very convenient in this case.List of Symbols D h^–1 Dilution rate for continuous culture - h Residence time for continuous culture - dM/dt kg/(m³ · h) Rate of degradation of malic acid - dS/dt kg/(m³ · h) Rate of consumption of glucose - _max h^–1 Maximal specific rate of growth     

Mathematical modeling of production of microbial lipids

In the microbial lipid production system using the yeast Rhodotorula gracilis, CFR-1, kinetics of lipid accumulation and substrate utilisation at initial substrate concentrations in the range of 20–100 kg/m³ were investigated using shake flask experiments. A mathematical representation based on logistic model for biomass and Luedeking-Piret model for lipid accumulation gave reasonably good agreement between the theoretical and experimental values for substrate concentration less than 60 kg/m³. The kinetic expressions and parameters obtained through shake flask studies were directly applied to experiments in the laboratory fermentors also and the models were found to hold good for the prediction of the change of biomass, product as well as substrate with time. The attainment of a saturation in the intracellular lipid accumulation with time, however, was not predicted by the model which was shown to be an inherent feature of the Luedeking-Piret model.List of Symbols S ₀, P ₀ kg/m³ Initial concentrations of sugar and lipid respectively - S, S(t) kg/m³ Concentrations of sugar and lipid respeclively at any timet - p,p(t) L kg/m³ Maximum concentration of lipid produced - E % Maximum sugar utilised - dP/dt kg/(m³ · h) Rate of lipid production - -dS/dt kg/(m³ · h) Rate of sugar utilisation - _max h^–1 Maximum specific growth rate - X _max kg/m³ Maximum biomass reached in a run - P _max kg/m³ Maximum product concentration - m, n Constants used in Luedeking-Piret model in eq. (7) - , Constants used to predict residual sugar - k _e maintainance coefficient - Y _x g/g Biomass yield based on sugar consumed - Y _p g/g Lipid yield based on sugar consumed - (dP/d t)_stat kg/(m³ · h) Rate of lipid production at stationary phase - (dS/dt)_stat kg/(m³ · h) Rate of sugar utilisation at stationary phase     

Modelling continuous culture of Rhodospirillum rubrum in photobioreactor under light limited conditions

Rhodospirillum rubrum was grown continuously and photoheterotrophically under light limitation using a cylindrical photobioreactor in which the steady state biomass concentration was varied between 0.4 to 4 kg m^–3 at a constant radiant incident flux of 100 W m^–2. Kinetic and stoichiometric models for the growth are proposed. The biomass productivities, acetate consumption rate and the CO₂ production rate can be quantitatively predicted to a high level of accuracy by the proposed model calculations. Nomenclature: C _X, biomass concentration (kg m^–3) D, dilution rate (h^–1) Ea, mean mass absorption coefficient (m² kg^–1) I , total available radiant light energy (W m^–2) K, half saturation constant for light (W m^–2) R _W, boundary radius defining the working illuminated volume (m) r _X, local biomass volumetric rate (kg m^–3 h^–1) <r _X>, mean volumetric growth rate (kg m^–3 h^–1) V _W, illuminated working volume in the PBR (m^–3). Greek letters: , working illuminated fraction (–) _M, maximum quantum yield (–) bar, mean energetic yield (kg J^–1).     

The effect of body size on food consumption, absorption efficiency, respiration, and ammonia excretion by the inland silverside, Menidia beryllina (Cope) (Osteichthyes: Atherinidae)

The inland silverside, Menidia beryllina (Cope), is an annual zooplanktivore that occurs in estuarine and freshwater habitats along the Atlantic and Gulf of Mexico coasts and drainages of the United States. Experiments were conducted at 25 ± 1°C to quantify the relationship between mean dry weight (W_D) and rates of energy gain from food consumption (C), and energy losses as a result of respiration (R) and ammonia excretion (E) during routine activity and feeding by groups of fish. The absorption efficiency of ingested food energy (A) was also quantified. Rates of C, E, and R increased with W_D by factors (b in the equation y = aW_D^b) equal to 0.462, 0.667, and 0.784, respectively. Mean (±SE) rates of energy loss during feeding were 1.6 ± 0.1 (R) and 3.4 ± 0.6 (E) times greater than those for unfed fish. Absorption efficiency was independent of W_D and estimated to be 89% of C. From these measurements, the surplus energy available for growth and activity (G) and growth efficiency (K₁) were estimated. Over the range in sizes of juveniles and adults (5–500 mg W_D), predicted G and K₁ values decreased from 7.42 to 0.20 J mg fish^?1 day^?1 and 63 to 21%, respectively. Measured and predicted bioenergetic parameters are discussed within an ecological context for a northern population of this species.     

Modification and verification of the dynamic cell cycling model for baker's yeast

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.List of Symbols B h length of budding phase - C _b1, C _d1, C _p1 parameters in cycling phase equations - C _b2, C _d2, C _p2 h parameters in cycling phase equations - d(i) number of cells in ith cycling interval inU _d - E kg m^–3 ethanol concentration - F m³ h^–1 substrate feeding rate - F _max and F _min m³ h^–1 upper and lower limit of F - FBC, FDC, FPC % fraction of budding cells, unbudded daughter cells and unbudded parent cells - K _B1, K _B2, K _B3, K _EG, K _Ad parameters in the metabolic model - m _ATP mol(gh)^–1 maintenance coefficient for ATP - n _b, n _d, n _p number of age intervals in the budding phase, daughter phase and parent phase - PO _min, PO _max minimal and maximal effectiveness of oxidative phosphorylation - r _Acmax mol(gh)^–1 saturation value of the specific acetyl-CoA-reaction rate - S kg m^–3 concentration of total reduceable sugars - S _R kg m^–3 substrate concentration in the feed - T cell number doubling time - T _fh fermentation period - U _dh length of unbudded daughter cell cycling phase - U _ph length of unbudded parent cell cycling phase - V _cell m³ average volume of yeast cells - V _L m³ liquid volume of the reactor - X kg m^–3 cell mass concentration - X _N cm^–3 cell number concentration - Y _ATP g mol_ATP ^–1 yield coefficient of ATP - parameter in the exponential redistribution function - h^–1 specific growth rate - h length of the discrete age interval of cell cycle phases - suffix old and new denote the value before and after increasing of      

Mathematical modeling of production of microbial lipids

As a part of the investigations on the microbial lipid production using the yeast Rhodotorula gracilis, CFR-1, kinetics of the biomass synthesis has been studied using shake flask experiments. Using a medium containing a carbon to nitrogen ratio of 701, the rates of biomass production were followed at different initial substrate concentrations in the range of 20–100 kg/m³. A logistic model was found to be reasonably adequate to describe the kinetics of the growth of biomass; the maximum specific growth rate of 0.105 h^–1 was applicable for substrate concentrations less than 60 kg/m³, which gave reasonable agreement between predicted and actual biomass concentration values.List of Symbols S ₀, X ₀ kg/m³ Initial concentrations of sugar, non lipid biomass respectively - X, X(t) kg/m³ Concentrations of non lipid biomass at any time t - dX/dt kg/(m³ · h) Rate of biomass growth - h^–1 Specific growth rate - _max h^–1 Maximum specific growth rate - K _s mol/dm³ Monods constant - X _max kg/m³ Maximum biomass reached in a run     

Dependency of growth yield,maintenance and K s-values on the dissolved oxygen concentration in continuous cultures of Azotobacter vinelandii

Azotobacter vinelandii was grown diazotrophically in sucrose-limited chemostat cultures at either 12, 48, 108, 144 or 192 M dissolved oxygen. Steady state protein levels and growth yield coefficients (Y) on sucrose increased with increasing dilution rate (D). Specific rate of sucrose consumption (q) increased in direct proportion to D. Maintenance coefficients (m) extrapolated from plots of q versus D, as well as from plots of 1/Y versus 1/D exhibited a nonlinear relationship to the dissolved oxygen concentration. Constant maximal theoretical growth yield coefficients (Y ^G) of 77.7 g cells per mol of sucrose consumed were extrapolated irrespective of differences in ambient oxygen concentration. For comparison, glucose-, as well as acetate-limited cultures were grown at 108 M oxygen. Fairly identical m- and Y ^G-values, when based on mol of substrate-carbon with glucose and sucrose grown cells, indicated that both substrates were used with the same efficiency. However, acetate-limited cultures showed significantly lower m- and, at comparable, D, higher Y-values than cultures limited by either sucrose or glucose. Substrate concentrations (K _s) required for half-maximal growth rates on sucrose were not constant, they increased when the ambient oxygen concentration was raised and, at a given oxygen concentration, when D was decreased. Since biomass levels varied in linear proportion to K _s these results are interpreted in terms of variable substrate uptake activity of the culture.Abbreviations D dilution rate - K _s substrate concentration required for half maximal growth rate - m maintenance coefficient - q specific rate of substrate consumption - Y growth yield coefficient - Y ^G maximum theoretical growth yield coefficient     

Determination of the overall volumetric mass transfer coefficient kLa,by a temperature dependent change of gas solubility

Summary The solubility of oxygen in the liquid phase of a bioreactor was changed by a ramp change of temperature, and k_La was determined from the resulting return to equilibrium of dissolved oxygen activity. The maximum k_La that can be measured by this method in a standard laboratory scale bioreactor is 145 h^–1 corresponding to a temperature change rate of 320°C h^–1.Nomenclature p Difference between p_G and p_L (% saturation) - T Ramp change of temperature (°C) - E Temperature-compensated output from the oxygen electrode (A) - E_u Uncompensated output from the oxygen electrode (A) - k_La Overall volumetric mass transfer coefficient (h^–1) - k_La_Tm Overall volumetric mass transfer coefficient at temperature T_m (h^–1) - P_G Dissolved oxygen activity in equilibrium with the gas phase (% saturation) - p_L Dissolved oxygen activity (% saturation) - p_Lm Dissolved oxygen activity at time t_m (% saturation) - t Time (h) - t_m Time of maximum p (h) - T Temperature (°C) - T_cal Calibration temperature of the oxygen electrode (°C) - T_m Final temperature after a temperature shift (°C) - T_n Temperature at time t_n     

Enhanced oxygen transfer rates in fermentation using soybean oil-in-water dispersions

Summary The effect of soybean oil on the volumetric oxygen transfer coefficient during the cultivation ofAerobacter aerogenes cells is presented. For our aeration-agitation conditions (0.278 vvm and 500 rpm), it has been demonstrated that the use 19% (v/v) of soybean oil enabled a 1.85-fold increase of thek _l a coefficient (calculated on a per liter aqueous phase basis). For smaller volumetric oil fractions,k _L a increased linearly with the oil loading. Because of the oxygen-vector properties of soybean oil, this oil is able to significantly increase thek _L a of a bioreactor.Nomenclature C^*, C saturation and actual dissolved oxygen concentrations respectively (g/m³) - K_La volumetric oxygen transfer coefficient (h^–1) - K_La_initial k _La measured before the oil addition (h^–1) - M_O2 molar mass of oxygen (dalton) - N oxygen transfer rate (g/m³. h) - P_O2. P_N2 partial pressures ofO ₂ andN ₂ in the gas (atm) - P_H2OT partial pressure of water in air at the temperatureT (atm) - P_T total pressure (atm) - Q₀ volumetric flow rate of outlet air before seeding (m³/h) - Sp spreading coefficient (dynes/cm) - T absolute temperature of outlet gas (K) - V_i volume of the liquidi in the fermentor (m³) - V_M molar volume at 273 K and 1 atm (m³/mole) - _ij interfacial tension betweeni andj componants (dynes/cm) - _v volumetric fraction of the oil (v/v) - G gas - O oil - W water - i inlet - o outlet     

Modelling of enzyme hydrolysis of maltose in a single pellet of immobilized biocatalyst

The reversible hydrolysis of maltose to glucose by immobilized glucoamylase entrapped in spherical solid particles is studied theoretically. For this purpose a known kinetic model taking into account these reversible reactions and the competitive synthesis of iso-maltose was adopted. The mass transfer limitations in the bulk liquid and in the pores of the particles containing the enzyme are considered, using Fick's law. On the basis of mathematical modelling the optimum conditions for biocatalyst performance are established. An appropriate combination of particle size and initial substrate concentration may lead to reduction of undesirable mass transfer resistance and therefore product inhibition and to an improved selectivity of the biocatalyst with respect of glucose formation.List of Symbols C _i kmoles/m³ current concentration ofi-th component along the radius - C _oi kmoles/m³ bulk concentration ofi-th component - C _i ^* kmoles/m³ concentrations ofi-th component on the pellet surface - D _si ,D _i m²/s internal and molecular diffusion coefficient ofi-th component - W _M kmoles/m³·s reaction rate of maltose hydrolysis - W _IM kmoles/m³·s reaction rate of iso-maltose formation - W _G kmoles/m³·s reaction rate of glucose production - R ₀ m pellet radius - r m current radius of the pellet - t s time coordinate - r ₀ ratio of the time step to the square of the radial coordinate - Re Reynolds number =w·R/v - Sc Schmidt number =v/D - Bi Biot number = R/D - A _j ,B, C _j coefficients in the system of linear equations, Eq. (8) - X _i dimensionless degree of transformation - NR number of independent reactions - N number of division sections of the pellet radius - G kmoles/m³ concentration of glucose - M kmoles/m³ concentration of maltose - IM kmoles/m³ concentration of isomaltose - K _m kmoles/m³ Michaelis constant - V _max kmoles/m³·s maximum reaction rate in Eq. (6) - K _i kmoles/m³ inhibition constant - K _1eq ,K _2eq equilibrium constants in Eq. (6) - , h steps along the time and radial coordinate in the pellet - m/s mass transfer coefficient - dimensionless radius of the pellet - computation accuracy Indices i number of reaction component - j index along the radius of the pellet - k index along the time coordinate This work was accomplished with thanks to the financial support of the Bulgarian National Fund for Scientific Investigations —Grant No. MU-1-BE/93.     

Intraparticle mass-transfer resistance and apparent time stability of immobilized yeast alcohol dehydrogenase

The stability and, consequently, the lifetime of immobilized enzymes (IME) are important factors in practical applications of IME, especially so far as design and operation of the enzyme reactors are concerned. In this paper a model is presented which describes the effect of intraparticle diffusion on time stability behaviour of IME, and which has been verified experimentally by the two-substrate enzymic reaction. As a model reaction the ethanol oxidation catalysed by immobilized yeast alcohol dehydrogenase was chosen. The reaction was performed in the batch-recycle reactor at 303 K and pH-value 8.9, under the conditions of high ethanol concentration and low coenzyme (NAD⁺) concentration, so that NAD⁺ was the limiting substrate. The values of the apparent and intrinsic deactivation constant as well as the apparent relative lifetime of the enzyme were calculated.The results show that the diffusional resistance influences the time stability of the IME catalyst and that IME appears to be more stabilized under the larger diffusion resistance.List of Symbols C _A, C_B, C_E mol · m^–3 concentration of coenzyme NAD⁺, ethanol and enzyme, respectively - C _p mol · m³ concentration of reaction product NADH - d _p mm particle diameter - D _eff m² · s^–1 effective volume diffusivity of NAD⁺ within porous matrix - k _d s^–1 intrinsic deactivation constant - K _A, K_A, K_B mol · m^–3 kinetic constant defined by Eq. (1) - K _A ^x mol · m^–3 kinetic constant defined by Eq. (5) - r _A mol · m^–3 · s^–1 intrinsic reaction rate - R m particle radius - R _v mol · m^–3 · s^–1 observed reaction rate per unit volume of immobilized enzyme - t _E s enzyme deactivation time - t _r s reaction time - V mol · m^–3 · s^–1 maximum reaction rate in Eq. (1) - V ^x mol · m^–3 · s^–1 parameter defined by Eq. (4) - V _f m³ total volume of fluid in reactor - w _s kg mass of immobilized enzyme bed - factor defined by Eqs. (19) and (20) - kg · m^–3 density of immobilized enzyme bed - unstableness factor - effectiveness factor - Thiele modulus - relative half-lifetime of immobilized enzyme Index o values obtained with fresh immobilized enzyme     

New solution method for equations of reaction and mass transfer in biocatalyst particles

Summary For numerical solution of the reaction-mass transfer equations for immobilised biocatalysts it may be better to start integration at the particle surface and proceed inwards: calculations are targetted on the region to which practically interesting changes are often confined (because concentrations are effectively zero in the interior); and during iterative solution wrong initial estimates may be rejected after detecting anomalies early in the integration.Symbols C_b substrate concentration in bulk (mol m^–3) - c dimensionless substrate concentration (C/C_b) (-) - D_e effective diffusion coefficient (m²s^–1) - Da Damkohler number (V.r_o ²/D_e.K_s) (-) - K_s substrate concentration kinetic coefficient (mol m^–3) - k_e external mass transfer coefficient (ms^–1) - r_o bead radius (m) - Sh Sherwood number (k_e.r_o/D_e) (-) - V maximum rate per unit volume in beads (mol m^–3s^–1) - x dimensionless distance from bead centre (r/r_o) (-) - dimensionless kinetic coefficient (K_s/C_b) (-) - _o effectiveness factor (-)     

Strategy for the simulation of batch reactors when the enzyme-catalyzed reaction is accompanied by enzyme deactivation

The balance equations pertaining to the modelling of batch reactors performing an enzyme-catalyzed reaction in the presence of enzyme deactivation are developed. The functional form of the solution for the general situation where both the rate of the enzyme-catalyzed reaction and the rate of enzyme deactivation are dependent on the substrate concentration is obtained, as well as the condition that applies if a maximum conversion of substrate is sought. Finally, two examples of practical interest are explored to emphasize the usefulness of the analysis presented.List of Symbols C _E mol/m³ concentration of active enzyme - C _E,O mol/m³ initial concentration of active enzyme - C _S mol/m³ concentration of substrate - C _S,O mol/m³ initial concentration of substrate - C _S,min mol/m³ minimum value for the concentration of substrate - k 1/s first order rate constant associated with conversion of enzyme/substrate complex into product - k ₁ 1/s first order deactivation constant of enzyme (or free enzyme) - k ₂ 1/s first order deactivation constant of enzyme in enzyme/substrate complex form - K _m mol/m³ Michaelis-Menten constant - p mol/(m³s) time derivative of C _S - q mol/m³ auxiliary variable - t s time elapsed after reactor startup Greek Symbols 1/s univariate function expressing the dependence of the rate of enzyme deactivation on C _S - mol/m³ dummy variable of integration - mol/m³ dummy variable of integration - 1/s univariate function expressing the dependence of the rate of substrate depletion on C _S - m³/(mol s) derivative of with respect to C _S     

Reactor comparison and scale-up for the microaerobic production of 2,3-butanediol by Enterobacter aerogenes at constant oxygen transfer rate

Stirred tank (STR), bubble column (BCR) and airlift (ALR) bioreactors of 0.05 and 1.5 m³ total volume were compared for the production of 2,3-butanediol using Enterobacter aerogenes under microaerobic conditions. Batch fermentations were carried out at constant oxygen transfer rate (OTR=35 mmol/lh). At 0.05 m³ scale, the STR reactor achieved much higher biomass and product concentrations than the BCR and ALR reactors. At 1.5 m³ scale, however, exactly the same biomass and product concentrations could be obtained in both STR and ALR reactors. The 1.5 m³ ALR reactor performed also much better than its counterpart at small scale, achieving a productivity 2.4-fold as high as that of the 0.05 m³ BCL and ALR reactors. No differences in performances were observed between BCR and ALR. As compared to STR the tower reactors have a 12 time higher energetic efficiency (referred to product formation) and thus should be the choice for large scale production of 2,3-butanediol.The criterion of constant OTR or constant k _L a is not applicable for the scale-up of this oxygen-sensitive culture due to strong influence of reactor hydrodynamics under microaerobic conditions. The effects of mixing and circulation time on growth and metabolism of E. aerogenes were quantitatively studied in scaled-down experiments with continuous culture. For a successful scale-up of this microaerobic culture it is necessary to have an homogeneous oxygen supply over the entire reactor volume. Under conditions of inhomogeneous oxygen supply an optimum liquid circulation time exists which gives a maximum production of 2,3-butanediol.List of Symbols BD 2,3-butanediol - [mmol/l] saturation value of dissolved oxygen - D [h^–1] dilution rate - D [mm] reactor diameter - D _K [mm] top section diameter - D _R [mm] stirrer diameter - D _S [mm] draft tube diameter - EtOH ethanol - E _P [kg/kWh] energy efficiency refered to product formation - H [mm] height of reactor - HAc acetate - H _L [mm] height of liquid - k _L a [h^–1] volumetric oxygen transfer coefficient - N [rpm=min^–1] stirrer speed - OTR [mmol/lh] oxygen transfer rate - OUR [mmol/lh] oxygen uptake rate - p [Pa] pressure - P [kW] power input - P/V _L [kW/m³] specific power input - [mmHg] oxygen partial pressure (mmHg) or - [mmol/l] dissolved oxygen (mmol/l) - [mmol/gh] specific oxygen uptake rate - q _P [mmol/gh] specific productivity - R [Nm/kgK] gas constant, R = 287.06 - RQ respiration quotient - t _c [s] liquid circulation time - T [°C or K] temperature - TCA tricarboxylic acid - u _G [cm/s] mean superficial gas velocity - v _G [m/s] gas velocity at nozzels of gas distributor - V_G [l/h] aeration rate at inlet - V [m³ or l] total volume - V _L [m³ or l] liquid volume - V _N [l/mol] gas mole volume under normal conditions, V _N = 24.4116 - X [g/l] biomass concentration - CO₂ mole fraction in the effluent gas - O₂ mole fraction in the effluent gas - inlet (above the gas distributor) - ratio of oxygen consumed through TCA cycle to the total oxygen uptake rate - [g/l or kg/m³] density - [%] degree homogeneity - outlet of fermenter or top of the dispersion phase Dedicated to the 65th birthday of Professor Fritz Wagner.We thank Dr. C. Posten and T. Gabel for support with the computer control system UBICON. T.-G. Byun gratefully acknowledges financial support by DAAD.