A simple dynamic method for on-line and off-line determination of kLa during cultivation of animal cells

Summary A new, fast method is described to determine k_La either off-line, or on-line during animal-cell cultivation. Since it does not need the equilibrium concentration of oxygen in the liquid phase (C*), it is not required to await a new steady state. Furthermore, the results do not depend on the calibration value of the dissolved-oxygen probe. The method yielded accurate values for k_La, both for an oxygen-consuming and a non-consuming system.Nomenclature C _L Dissolved-oxygen concentration [mol·m^-3] - C ^* C _L in equilibrium with the oxygen concentration in the gas phase [mol·m^-3] - C _L, Equilibrium oxygen concentration at stationary conditions [mol·m^-3] - k_La Volumetric oxygen transfer coefficient [s^-1] - r Specific oxygen consumption of biomass [mol·cell^-1·s^-1] - X Cell concentration [cells·m^-3] - t Time [s] - Noise of dissolved-oxygen probe [mol·m^-3] - Absolute error of k_La-measurement [s^-1]     

Equilibrium and dynamic investigations of organic acids adsorption onto ion-exchange resins

The aim of the study was to determine properties of selected ion-exchange resins for citric and lactic acids recovery, to define sorption isotherms for these acids at different temperatures (in the range of 20–60°C) and to determine diffusion coefficients inside sorbent particles. A mathematical model of the ion-exchange process in the chromatographic column and its experimental verification is also presented. During investigations 18 types of ion-exchange resins were tested. It was found that weakly basic resins were more suitable for the recovery process than strongly basic ones. The best resin for the separation of citric acid was Amberlite IRA-67 and for lactic acid Amberlite IRA-92. As a result of transient-state sorption experiments diffusion coefficients of the citric acid inside the sorbent particle at different temperatures were obtained. It was found that D_p increased with the temperature by two times in the range of 20–60°C, and its value at 60°C was 7.2×10^–10 m²/s. The proposed mathematical model was applied to identify bed operation parameters in the column for the needs of the simulated moving bed chromatography method.List of symbols b Equilibrium constant in Langmuir equation, [dm³/g] - c Acid concentration in the liquid phase inside the particle pores, [g/dm³] - C Acid concentration in the liquid, [g/dm³] - D_L Axial dispersion coefficient, [m²/s] - D_p Intraparticle diffusion coefficient, [m²/s] - k_f Liquid film mass transfer coefficient, [m/s] - L Ion-exchanger bed height, [m] - q Acid concentration in the adsorbent phase, [g/dm³] - R_p Particle radius, [m] - U Volumetric flow rate of the feeding solution, [dm³/s] - V Volume of the solution, [dm³] - W Weight of the wet resin particles, [g] - The ion-exchanger bed porosity, [-] - _p Particle porosity, [-] - Linear liquid velocity, [m/s] - Apparent density of the wet resin, [g/dm³]     

Optimization and control of a continuous stirred tank fermenter using learning system

A variable structure learning automaton is used as an optimization and control of a continuous stirred tank fermenter. The algorithm requires no modelling of the process. The use of appropriate learning rules enables to locate the optimum dilution rate in order to maximize an objective cost function. It is shown that a hierarchical structure of automata can adapt to environmental changes and can also modify efficiently the domain of variation of the control variable in order to encompass the optimum value.List of Symbols f Random number - F Dimensionless flow rate (F/V ₀) - F m³/h Flow rate - F ₀ m³/h Inlet flow rate - J Objective function - K _i Dimensionless constant in Eq. (3) (k _i/s₀) - k _i · kg/m³ Substrate inhibition constant in Haldane model - K _m Dimensionless constant in equation (3) (k _s/s₀) - k _m kg/m³ Substrate inhibition constant in Haldane model - L Number of levels of the hierarchical system of automata - N Number of possible control actions - p Probability - S Dimensionless substrate concentration (s/s ₀) - s kg/m³ Substrate concentration - T Dimensionless sampling period - t h Time - v Dimensionless volume (V/V ₀) - V m³ Liquid volume in fermenter - W Input to the stochastic automaton - X Dimensionless biomass concentration - x kg/m³ Biomass concentration - Y Biomass/substrate yield coefficient - Weighting factor in Eq. (4) - Dimensionless specific growth rate (/ ^*) - ^* h^–1 Maximum specific growth rate - h^–1 Specific growth rate - Dimensionless time ( t)     

Flow dynamics of immobilized enzyme reactors

Summary Enzymic conversion of glucose to fructose was carried out in a packed bed and in a fluidized bed reactor. The flow dynamics of these two flow systems, loaded with two different types of immobilized loaded with two different types of immobilized glucose isomerase particles, were studied. The theoretical RTD curve calculated from the axial dispersed plug flow model equation was matched to the experimental RTD curve by an optimization technique. The effect of fluid velocity on the extent of liquid dispersion was established. Theoretical predictions on the conversion of glucose to fructose were calculated using three mathematical models, namely, a plug flow model, a continuous stirred tank reactor (CSTR) model and an axial dispersed plug flow model. The experimental results showed that the axial dispersed plug flow model was superior in predicting the performance of both the packed bed and fluidized bed reactor.Abbreviations C Dimensionless concentration - D Dispersion coefficient [cm²/sec] - d _p Mean particle diameter [cm] - E Enzyme concentration [mol/gm] - F Fructose concentration [mol/cm³] - F _e Equilibrium fructose concentration [mol/cm³] - G Glucose concentration [mol/cm³] - G _e Equílibrium glucose concentration [mol/cm³] - G _o Initial glucose concentration [mol/cm³] - Reduced glucose concentration [mol/cm³] - K Equilibrium constant - K _mf Forward reaction rate constant [mol/cm³] - K _mr Reserve reaction rate constant [mol/cm³] - K _m Rate constant [mol/cm³] - L Total length of the reactor bed [cm] - l Length [cm] - Q Flow rate [cm³/s] - r Rate of reaction based on volume of substrate - u Superficial liquid velocity [cm/s] - v Interstitial liquid velocity [cm/s] - V Reactor bed volume [cm³] - V _mf Forward reaction rate constant [mol/s·g enzyme] - V _mr Reserve reaction rate constant [mol/s·g enzyme] - z Dimensionless distance along the reactor - Density [g/cm²]     

Optimizing control of a continuous stirred tank fermenter using a neural network

Feedforward neural networks are a general class of nonlinear models that can be used advantageously to model dynamic processes. In this investigation, a neural network was used to model the dynamic behaviour of a continuous stirred tank fermenter in view of using this model for predictive control. In this system, the control setpoint is not known explicitly but it is calculated in such a way to optimize an objective criterion. The results presented show that neural networks can model very accurately the dynamics of a continuous stirred tank fermenter and, the neural model, when used recursively, can predict the state variables over a long prediction horizon with sufficient accuracy. In addition, neural networks can adapt rapidly to changes in fermentation dynamics.List of Symbols F Dimensionless flow rate (F/ V₀) - F m³/h Flow rate - F ₀ m³/h Inlet flow rate - J Objective cost function - K _i Dimensionless constant in Eq. (3) (k _i /s₀) - k _i kg/m³ Substrate inhibition constant in Haldane model - k _m Dimensionless constant in Eq. (3) (k _s /s₀) - k _m kg/m³ Substrate inhibition constant in Haldane model - n prediction horizon - S Dimensionless substrate concentration (s/s₀) - s kg/m³ Substrate concentration - t h Time - v Dimensionless volume (V/V₀) - V m³ Liquid volume in fermenter - W _ij , W _jk Weight matrices in neural network - X Dimensionless biomass concentration - x kg/m³ Biomass concentration - Y Biomass/substrate yield coefficient - Weighting factor in Eq. (4) - Dimensionless specific growth rate (/ ) - 1/h Maximum specific growth rate - 1/h Specific growth rate - Dimensionless time ( t)     

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.     

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)     

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     

Hydrodynamics and mass transfer in an airlift loop fermentor

Summary The hydrodynamics and mass transfer behaviour of an airlift fermentor with an external loop (height 10m) has been investigated by measuring gas and liquid velocities, gas hold-up, liquid mixing and oxygen transfer coefficients. Liquid phase properties, i.e., ionic strength, viscosity and surface tension have been varied by altering the fermentation media. Results are compared with those from bubble column experiments performed in the same unit. It is shown, that more uniform two-phase flow in the airlift leads to advantages in scale-up and operation.Nomenclature a Specific interfacial area per volume of dispersion (m²/m³) - c Local concentration of tracer (kmol/m³) - c Concentration of tracer at infinite time (kmol/m³) - C_L Concentration of oxygen in the liquid bulk (kmol/m³) - C_L ^* Concentration of oxygen in the interface (kmol/m³) - D_ax Axial dispersion coefficient (cm²/s) - I Ionic strength (kmol/m³) - i Inhomogeneity [defined in Eq. (2)] - Rate of oxygen transfer (kmol/s) - t_c Circulation time (s) - t_M Mixing time (s) - V_R Volume of gas-liquid dispersion (m³) - V_SG Superficial gas velocity in up-flow column (m/s) Greek letter symbols _L Oxygen transfer coefficient (m/s) - Dynamic viscosity (m Pa s) - Surface tension (m N/m) Presented at the First European Congress on Biotechnology, Interlaken, September 25–29, 1978     

Viscous media in tower bioreactors: Hydrodynamic characteristics and mass transfer properties

Studies in tower reactors with viscous liquids on flow regime, effective shear rate, liquid mixing, gas holdup and gas/ liquid mass transfer (k _La) are reviewed. Additional new data are reported for solutions of glycerol, CMC, PAA, and xanthan in bubble columns with diameters of 0.06, 0.14 and 0.30 m diameter. The wide variation of the flow behaviour index (1 to 0.18) allows to evaluate the effective shear rate due to the gas flow. New dimensionless correlations are developed based on the own and literature data, applied to predict k _La in fermentation broths, and compared to other reactor types.List of Symbols a(a) m^–1 specific interfacial area referred to reactor (liquid) volume - Bo Bond number (g D _c ² _L/) - c _L(c _L ^* ) kmol m^–3 (equilibrium) liquid phase oxygen concentration - C coefficient characterising the velocity profile in liquid slugs - C _s m^–1 coefficient in Eq. (2) - d _B(d_vs) m bubble diameter (Sauter mean of d _B) - d ₀ m diameter of the openings in the gas distributor plate - D _c m column diameter - D _L m²s^–1 diffusivity - E _L(E_W) m² s^–1 dispersion coefficient (in water) - E ² square relative error - Fr Froude number (u _G/(g D_c)^0.5) - g m s^–2 gravity acceleration - Ga Gallilei number (g D _c ³ _L ² / _eff ² ) - h m height above the gas distributor the gas holdup is characteristic for - k Pasⁿ fluid consistency index (Eq. 1) - k _L m s^–1 liquid side mass transfer coefficient - k _La(k_La) s^–1 volumetric mass transfer coefficient referred to reactor (liquid) volume - L m dispersion height - n flow behaviour index (Eq. 1) - P W power input - Re liquid slug Reynolds number ( _L(u _G +u _L) D _c/_eff) - Sc Schmidt number ( _eff/( _L D _L )) - Sh Sherwood number (k _La D _c ² /D_L) - t s time - u _B(u_sw) m s^–1 bubble (swarm) rise velocity - u _G(u_L) m s^–1 superficial gas (liquid) velocity - V(V_L) m³ reactor (liquid) volume Greec Symbols W m^–2 K^–1 heat transfer coefficient - y(y _eff) s^–1 (effective) shear rate - _G relative gas holdup - s relaxation time of viscoelastic liquid - _L(_eff) Pa s (effective) liquid viscosity (Eq. 1) - _L kg m^–3 liquid density - N/m surface tension     

Verification studies of a simplified model for the removal of dichloromethane from waste gases using a biological trickling filter

The removal of dichloromethane from waste gases in a biological trickling filter was studied experimentally as well as theoretically within the concentration range of 0–10,000 ppm. A stable dichloromethane elimination performance was achieved during two years of operation, while the start-up of the system only amounted to several weeks at constant inlet concentrations. The trickling filter system was operated co-currently as well as counter-currently.However, experimental and theoretical results revealed that the relative flow direction of the mobile phases did not significantly affect the elimination performance. Moreover, it was found that the gas-liquid mass-transfer resistance in the trickling filter bed applied was negligible, which leaves the biological process inside the biofilm to be the rate limiting step.A simplified model was developed, the Uniform-Concentration-Model, which showed to predict the filter performance close to the numerical solutions of the model equations. This model gives an analytical expression for the degree of conversion and can thus be easily applied in practice.The dichloromethane eliminating performance of the trickling filter described in this paper, is reflected by a maximum dichloromethane elimination capacity EC _max=157 g/(m³ · h) and a critical liquid concentration C _lcr=45 g/m³ at a superficial liquid velocity of 3.6 m/h, inpendent of the gas velocity and temperature.List of Symbols a _s m²/m³ specific area - a _w m²/m³ specific wetted area - A m² cross-sectional area - C _g g/m³ gas phase concentration - C _go g/m³ inlet gas phase concentration - C _gocr g/m³ critical gas phase concentration - C _g ^* C_g/C_go dimensionless gas concentration - C _l g/m³ liquid concentration - C _lcr g/m³ critical liquid concentration - C _lcr ^* mC_lcr/C_go dimensionless critical concentration - c _li g/m³ substrate concentration at liquid-biofilm interface - C _l ^* mC_l/C_go dimensionless liquid concentration - C _o g/m³ oxygen concentration inside the biofilm - C _oi g/m³ oxygen concentration at liquid-biofilm interface - C_s g/m³ substrate concentration inside the biofilm - C _si g/m³ substrate concentration at liquid-biofilm interface - D _eff m²/h effective diffusion coefficient in the biofilm - D _o m²/h effective diffusion coefficient for oxygen in the biolayer - E mu_g/u_l extraction factor - E _act kJ/mol activation energy for the biological reaction - EC g/(m³· h) K _o a _w : elimination capacity, or the amount of substrate degraded per unit of reactor volume and time - EC _max g/(m³ · h) K _o a_w: maximum elimination capacity - f degree of conversion - h m coordinate in height - H m height of the packed bed - K ₀ g/(m³ · h) _maxX_b/Y zeroth order reaction defined per unit of biofilm volume - k _og m/h overall gas phase mass transfer coefficient - K ^* dimensionless constant given by Eq. (A.5) - K _l ^* dimensionless constant given by Eq. (A.6) - K ₂ ^* dimensionless constant given by Eq. (A.6) - m C _g /C_l gas liquid distribution coefficient - N g/(m² · h) liquid-biofilm interfacial flux of substrate - N _og k_oga_wH/u_g number of gas phase transfer units - N _r k_o a_w H/u_g C_go number of reaction units - OL g/(m³· h) u _g C _go /H organic load - r _s g/(m³ ·h) zeroth order substrate degradation rate given by Eq. (1) - R _s g/(g TSS ·h) specific activity - T K absolute temperature - u _g m/h superficial gas velocity - u _t m/h superficial liquid velocity - X _b g TSS/m₃ biomass concentration inside biofilm - X _s g TSS/m₃ liquid suspended biomass concentration - x m coordinate inside the biofilm - Y g TSS/(g_DCM) yield coefficient Greek Symbols dimensionless parameter given by Eq. (2) - m averaged biofilm thickness - biofilm effectiveness factor given by Eqs. (7a)–(7c) - m penetration depth of substrate into the biofilm - _max d^–1 microbiological maximum growth rate - v _o stoichiometric utilization coefficient for oxygen - v _s stoichiometric utilization coefficient for substrate - dimensionless height in the filter bed - h H/u _g superficial gas phase contact time - _o (K ₀ /DC _ii )^1/2 - _o C _o /C _oi dimensionless oxygen concentration inside the biofilm - _s C _s /C _si dimensionless substrate concentration inside the biofilm Experimental results, verifying the model presented will be discussed Part II (to be published in Vol. 6, No. 4)     

A mathematical model for solid state fermentation in tray bioreactors

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.List of Symbols C g/cm³ Oxygen concentration in the bed - C _g g/cm³ Atmospheric oxygen concentration - C ^* Dimensionless oxygen concentration, C/C _g - D _e cm²/h Effective diffusivity - H cm Bed thickness or height - H _c cm Critical bed thickness or height - H _m cm Maximum height of zone of zero oxygen concentration - p _i mg/(g · h) Productivity (Eq. 13) - R g/(cm³ · h) Biochemical reaction rate - t h Fermentation time - t ^* Dimensionless time, D _e t/H² - X mg/cm³ Biomass concentration - X _max mg/cm³ Maximum biomass concentration - y Dimensionless thickness or height, (y = z/H) - y cm Thickness of zone of zero oxygen concentration (Eq. 12) - Y Yield coefficient - z cm Bed thickness or height along tray axis - Bed void fraction - _max h^–1 Specific growth rate - Thiele modulus      

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     

Theoretical analysis of the baker's yeast production: An experimental verification at a laboratory scale

The scale-down procedure seems an adequate tool in the design, optimization and scale-up fermentation processes. The first step in this procedure is a theoretical analysis, called process analysis, which is based on characteristic times of the mechanisms which may influence the performance of the bioreactor. This analysis must give information about the behaviour of large and small scale fermentation processes. At a small scale a verification of the results of such an analysis of the fed-batch baker's yeast production is carried out.In this paper a comparison of calculated and measured characteristic times of liquid mixing and mass transfer is presented. It was concluded that the literature correlations give a rough estimation of the characteristic times and can be used in the process analysis. Depending on the kind of sparger, the medium and the scale of the reactor, more knowledge is needed about bubble coalescence in fermentation media.The volumetric oxygen transfer coefficient increased when the biomass concentration increased. Probably this is caused by the interaction between biomass and the anti-foaming agent used.List of Symbols C kg/m³ concentration - D m diameter - m²/s effective dispersion coefficient - d m holes of the sparger - g m/s² gravitational acceleration - H m height - k _L a s^–1 volumetric mass transfer coefficient based on the liquid volume - L m length - m kg/kg gas liquid distribution coefficient - OTR kg/(m³ · s) oxygen transfer rate - OUR kg/(m³ · s) oxygen uptake rate - t s time - ^s m/s superficial gas flow rate - m length - s time constant - _g m³/s gas flow rate Indices 0 value at t=0 - cal calculated - e value at t=t (end) - g gas phase - in flow going to the fermentor - l liquid phase - m mixing - mt mass transfer - O ₂ oxygen - out flow coming out the fermentor     

Theoretical analysis of the baker's yeast production: An experimental verification at a laboratory scale

The scale-down procedure can be used to optimize and scale up fermentation processes. The first step in this procedure, a theoretical analysis of the process at a large scale, must give information about the regime, or bottle necks, ruling the process. In order to verify the theoretical results the process analysis has been applied to the fed-batch baker's yeast production at a laboratory scale. The results of this analysis are compared with results from fed-batch experiments. It was concluded that if only one mechanism is ruling the process, for instance mass transfer, the results of the analysis are quite clear. If more than one mechanism is important, for example mass transfer and liquid mixing, additional knowledge is needed to predict the behaviour of the process.Concerning the baker's yeast production, it was concluded that if oxygen limitation occurs, liquid mixing is of little importance.List of Symbols C kg/m³ concentration - C ^* kg/m³ saturation concentration - D m diameter - D _E m²/s effective dispersion coefficient - d m holes of the sparger - F _sm³/s substrate flow to the fermentor - g m/s² gravitational acceleration - H m height - k _La s^–1 volumetric mass transfer coefficient based on the liquid volume - L m length - m _skg/(kg·s) maintenance coefficient - OTR kg/(m³·s) oxygen transfer rate - OUR kg/(m³·s) oxygen uptake rate - r kg/(m³·s) reaction rate - t s time - V m³ volume - v m/s velocity - v _sm/s superficial gas flow rate - y _ijkg/kg yield of componentj oni - s^–1 specific growth rate - s time constant - _gm³/s gas flow rate Indices 0 value att=0 - cir liquid circulation - e ethanol - f feed concentration - g gas phase - in flow going to the fermentor - l liquid phase - m mixing - mt mass transfer - o, O₂ oxygen - oc oxygen consumption - out flow coming out the fermentor - s substrate - sa substrate addition - sc substrate consumption - x biomass     

Enhancement of oxygen mass transfer in stirred bioreactors using oxygen-vectors. 1. Simulated fermentation broths

Oxygen mass transfer represents the most important parameter involved in the design and operation of mixing-sparging equipment for bioreactors. It can be described and analyzed by means of the mass transfer coefficient, k_La. The k_La values are affected by many factors such as geometrical and operational characteristics of the vessels, media composition, type, concentration and microorganism morphology, and biocatalysts properties. The efficiency of oxygen transfer could be enhanced by adding oxygen-vectors in broths, such as hydrocarbons or fluorocarbons, without increasing the energy consumption for mixing or aeration. The experimental results obtained for simulated broths indicated a considerable increase of k_La in the presence of n-dodecane, and the existence of a certain value of n-dodecane concentration that corresponds to a maximum mass transfer rate of oxygen. The magnitude of the positive effect of n-dodecane depends both on the broths characteristics and operational conditions of the bioreactor.Notation d stirrer diameter, mm - d oxygen electrode diameter, mm - D bioreactor diameter, mm - h distance from the inferior stirrer to the bioreactor bottom, mm - H bioreactor height, mm - k_La oxygen mass transfer coefficient, s^-1 - l impeller blade length, mm - I oxygen electrode immersed length, mm - P power consumption for mixing of non-aerated broths, W - P_a power consumption for mixing of aerated broths, W - (P_a/V) specific power input, W/m³ - s baffle width, mm - v_S superficial air velocity, m/s - V volume of medium, m³ - w impeller blade height, mm - volumetric fraction of oxygen-vector - _a apparent viscosity, Pa*s - density, kg/m³     

Packed-bed immobilized enzyme reactors for complex processes

Utilization of enzymic reactors for biotechnological-biomedical applications is currently developing at a sustained pace.Our present study concentrates on development of procedures for describing the performance of devices where enzyme-catalyzed reactions between two substrates take place, and for the rational design and optimization of the reactors considered. Within this context, an analytical model was developed for immobilized enzyme packed-bed reactors; it takes into account internal diffusion limitations for the cosubstrates, and hydrodynamic backmixing effects. In order to overcome the complex mathematical problems involved, the compartmental analysis approach was employed.Using this model, performance was simulated for various configurations of the enzymic unit, i.e. from a continuously operated stirred tank reactor (CSTR) to an essentially plug flow type. In addition, an experimental method is described for quantitatively assessing the backmixing effects prevailing in the reactor.The procedures established also provide the ground for further developments, particularly for systems where, in parallel to the enzymic reaction, additional processes (e. g. complexation) take place.List of Symbols C _j,i mM Concentration of substrate j in the pores of stage - iD _j cm²/s Internal (pore) diffusion coefficient of substrate j; defined in Eq. (7) - D _e cm²/s Axial dispersion diffusion coefficient - D _j, cm²/s cm²/s Bulk diffusion coefficient for substrate j - E mM Enzyme concentration inside the catalytic pores - J _j,immol/s/cm² Net flux of substrate j taking place from the bulk of stage i into the corresponding pores; defined in Eq. (6) - K _m,1, K _m,2 mM Michaelis-Menten constants for cosubstrates 1 and 2, respectively - k s ^–1 Catalytic constant - k _s cm/s Catalytic constant - n Total number of elementary stages in the reactor - Q cm³/s Volumetric flow rate throught the reactor - r cm Radius of the pore - R _j,i mM/s Reaction rate of substrate j in stage i, in terms of volumetric units - S cm² Internal surface of a pore - S _j,0 mM Concentration of substrate j in the reactor feed - S _j,i–1, S _j,i mM Concentration of substrate j in the bulk phase leaving stages i — 1 and i, respectivley - V _i cm³ Total volume of stage i (bulk phase + pore phase + inert solid carrier) - V cm³ Total volume of the reactor - V _m ^* mmol/s/cm² Maximal reaction rate in terms of surface units; defined in Eq. (8) - V _m mM/s Maximal reaction rate in terms of volumetric units; defined in Eq. (8) - V _p cm³ Volume of one pore - y cm Axial coordinate of the pores - y ₀ cm Depth of the pores - Z cm Axial coordinate of the reactor - Z ₀ cm Length of the reactor - ₁ Dimensionless parameter; defined in Eq. (27) - ₂ Dimensionless parameter; defined in Eq. (27) - ₁ Dimensionless parameter; defined in Eq. (27) - ₂ Dimensionless parameter; defined in Eq. (27) - Ratio between the radius of the enzyme molecule and the radius of the pore (dimensionless) - V₁ Dimensionless parameter; defined in Eq. (21) - v₂ Dimensionless parameter; defined in Eq. (21) - Q Volumetric packing density of catalytic particles (dimensionless) - Ø Porosity of the catalytic particles (dimensionless) - Ø Dimensionless concentration of substrate j in pores of stage i; defined in Eq. (16) - _j,i-1,_j,i Dimensionless concentration of substrate j in the bulk phase of stage i; defined in Eq. (18) - Dimensionless position; defined in Eq. (16) - ² s² Variance; defined in Eq. (33) - Mean residence time in the reactor; defined in Eq. (33)     

Rapid Ca2+ extrusion via the Na+/Ca2+ exchanger of the human platelet

Summary This communication reports the kinetics of the Na⁺/ Ca²⁺ exchanger and of the plasma membrane (PM) Ca²⁺ pump of the intact human platelet. The kinetic properties of these two systems were deduced by studying the rate of Ca²⁺ extrusion and its Na⁺ dependence for concentrations of cytoplasmic free Ca²⁺ ([Ca²⁺]_cyt) in the 1–10-m range. The PM Ca²⁺ATPase was previously characterized (Johansson, J.S. Haynes, D.H. 1988. J. Membrane Biol. 104:147–163) for [Ca²⁺]_cyt] 1.5 m with the fluorescent Ca²⁺ indicator quin2 (K _d= 115 nm). That study determined that the PM Ca²⁺ pump in the basal state has a V _max = 0.098 mm/min, a K _m= 80 nm and a Hill coefficient = 1.7. The present study extends the measurable range of [Ca²⁺]_cyt with the intracellular Ca²⁺ probe, rhod2 (K _d= 500 nm), which has almost a fivefold lower affinity for Ca²⁺. An Appendix also describes the Mg²⁺ and pH dependence of the K _dand fluorescence characteristics of the commercially available dye, which is a mixture of two molecules. Rates of active Ca²⁺ extrusion were determined by two independent methods which gave good agreement: (i) by measuring Ca²⁺ extrusion into a Ca²⁺-free medium (above citation) or (ii) by the newly developed ionomycin short-circuit method, which determines the ionomycin concentration necessary to short circuit the PM Ca²⁺ extrusion systems. Absolute rates of extrusion were determined by knowledge of how many Ca²⁺ ions are moved by ionomycin per minute. The major findings are as follows: (i) The exchanger is saturable with respect to Ca²⁺ with a K _m= 0.97 ± 0.31 m and V_max = 1.0 ± 0.6 mm/ min. (ii) At high [Ca²⁺]_cyt, the exchanger works at a rate 10 times as large as the basal V _max of the PM Ca²⁺ extrusion pump. (iii) The exchanger can work in reverse after Na⁺ loading of the cytoplasm by monensin. (iv) The PM Ca²⁺ extrusion pump is activated by exposure to [Ca²⁺]_cyt 1.5 m for 20–50 sec. Activation raises the pump V _max to 1.6 ± 0.6 mm/min and the K _mto 0.55 ± 0.24 m. (v) The Ca²⁺ buffering capacity of the cytoplasm is 3.6 mm in the 0.1 to 3 m range of [Ca²⁺]_cyt. In summary, the results show that the human platelet can extrude Ca²⁺ very rapidly at high [Ca²⁺]_cyt. Both the Na⁺/Ca²⁺ exchanger and Ca²⁺ pump activation may prevent inappropriate platelet activation by marginal stimuli.Abbreviations cAMP cyclic adenosine 3,5-monophosphate - cGMP cyclic guanosine 3,5,-monophosphate - Ca-CAM calcium calmodulin; - DT dense tubules - B intrinsic cytoplasmic Ca²⁺ binding sites - R rhod2 or 5-(3,6-bis(dimethylamino)xanth-9-yl)-1-(2-amino-4-hy droxy lphenoxy)-2-(2-amino-5-methylphen- oxy)ethane-N,N,NN-tetraacetic acid - [Ca²⁺]_cyt cytoplasmic Ca²⁺ activity - quin2 2-[[2-bis[(carboxymethyl)amino]-5-methyl-phenoxy]methyl]-6-methoxy-8-[bis(carboxymethyl)amino]quinoline - V or V_extrusion true rate of Ca²⁺ extrusion - fura-2 1-[2-(5-carboxyoxazol-2-yl)-6-aminobenzofuran-5-oxy]-2-(2-amino-5-methylphenoxy)-ethane-N,N,NN-tetraacetic acid - AM acetoxymethyl ester - DMSO dimethylsulfoxide - CTC chlortetracycline - EGTA ethyleneglycol-bis(-aminoethyl ether) N,N,N,N- tetraacetic acid - HEPES 4-(2-hydroxyethyl)-1-piperazine ethanesulfonic acid - NMDG N-methyl-d-glucamine - PIPES 1,4-piperazine-bis-(ethanesulfonic acid) - HPLC high performance liquid chromatography - _I fraction of high-affinity rhod2 complexed with Ca²⁺ - F the observed fluorescence - F_min the minimal fluorescence observed in the absence of Ca²⁺ - F_max the maximal fluorescence observed when the dye is saturated with Ca²⁺ - X₁ the fraction of high-affinity dye - K _d,1 dissociation constant of high-affinity dye - K _d,2 dissociation constant of the low-affinity dye - -d₁/dt rate of Ca²⁺ removal from the rhod2-Ca complex; - -dF/dt the slope representing the absolute rate of fluorescence decrease in a progress curve - F_max (F_max — F_min)_cyt difference between maximal and minimal fluorescence for cytoplasmic high affinity form of rhod2 - F₅₀ fluorescence of the high-affinity form ofrhod2for[Ca²⁺]_cyt=50 nM - [Ca²⁺]₀ external Ca²⁺concentration - K _p proportionality constant between the total number of Ca²⁺ ions moved and the change in high-affinity rhod2 complexation to Ca² - (d[Ca²⁺]_{cyt, T})/dt rate of Ca²⁺ influx obtained with maximal levels of ionomycin - k_leak rate constant for passive inward Ca²⁺ leakage - k_inno rate constant for ionomycin-mediated Ca²⁺ influx - T total - [rhod2]_cyt,T total intracellular rhod2 concentration - [quin2]_cyt,T total intracellular quin2 concentration - [B]_T total cytoplasmic buffering capacity - A[Ca²⁺]_cyt,T total number of Ca²⁺ ions moved into the cytoplasm - [rhod2-Ca]_{cyt, T} change in concentration of total intracellular high-affinity rhod2 complexed to Ca²⁺ - [B-Ca]_T change in concentration of total cytoplasmic binding sites complexed to Ca²⁺ - [quin2]_{cyt, T} change in concentration of total intracellular quinl complexed to Ca²⁺ - change in the degree of intracellular quin2 saturation - ₁ change in degree of saturation of cytoplasmic high-affinity rhod2 - ₁-/t rate of change in degree of saturation of cytoplasmic high affinityrhod2 - V_obs observed rate of Ca²⁺ removal from the rhod2-Ca complex - V_{8.3 m} the rate of Ca²⁺ removal from the high affinity rhod2-Ca complex at [Ca²⁺]_cyt = 8.3 m - /t rate of change in of the degree of quin2 saturation - [Ca²⁺]_cytT/_t initial linear rate of ionomycin-mediated Ca²⁺ influx - EC₅₀ effective concentration giving a half-maximal effect - [Na⁺]_cyt cytoplasmic Na⁺ activity - CAM calmodulin - ACN acetonitrile - TFA trifuloroacetic acid     

Bubble coalescence behaviour in biological media

Summary Volumetric mass transfer coefficients (k_La) were measured by a steady state method in a twin bubble column to characterize the coalescence behaviour of the medium. Employing Hansenula polymorpha cultivation broths, k_La values were compared with those measured in model media in the presence and absence of antifoam agents. The ratio of the volumetric mass transfer coefficient in the system investigated to that in water, , was employed to characterize the cultivation medium.Symbols a Specific gas/liquid interfacial area with regard to the liquid volume in reactor - d_e Dynamical equilibrium bubble diameter - d_H Perforated plate hole diameter - d_p Primary bubble diameter - d_S Sauter bubble diameter - F_v Liquid feed rate - H Bubbling layer height - k_L Gas/liquid mass transfer coefficient - k_La Volumetric mass transfer coefficient - m k_La/(k_La)_r coalescence index - m_corr Corrected coalescence index [Eq. (3)] - OTR Oxygen transfer rate - P_O Dissolved O₂-partial pressure in BS2 - P₁ Dissolved O₂-partial pressure in BS1 - P_O P_O/P_S relative oxygen saturation in BS2 - P₁ P₁/P_S relative oxygen saturation in BS1 - P_S Saturation dissolved oxygen partial pressure - R_c dn_B/dt coalescence rate - S Substrate concentration - t_F Time since the beginning of the cultivation - X Biomass concentration - V₁ Liquid volume in BS1 - w_SG Superficial gas velocity in BS1 - G Gas holdup in BS1 - ₁ V₁/F_v mean liquid residence time in BS1 - BS1 O₂ absorber column - BS2 O₂ desorber column - D Desmophen (antifoam agent) - NS Nutrient salt solution (Table 1)     

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)