Modelling mixing parameters in concentric-tube airlift bioreactors

Axial dispersion of the liquid phase was investigated in a concentric-tube airlift bioreactor (RIMP: V _L=0.70?m³) as a whole and in the separate zones (riser, downcomer, gas-separator) using the axial dispersion model. The axial dispersion number Bo and the axial dispersion coefficient, D _ax were determined from the output curves to an initial Dirac pulse, using the tracer response technique. They were analyzed in relation to process and geometrical parameters, such as: gas superficial velocity, ν_SGR; top clearance, h _S; bottom clearance, h _B, and resistances at downcomer entrance expressed as A _d/A _R ratio. Correlations between Bodenstein numbers in the overall bioreactor and riser and downcomer sections (Bo_T,Bo_R,Bo_D) and the geometrical and process parameters were developed, which can allow to assess the complex influence of these parameters on liquid axial dispersion.     

Residence time distribution of liquid phase in an external-loop airlift bioreactor

The residence time distribution analysis was used to investigated the flow behaviour in an external-loop airlift bioreactor regarded as a single unit and discriminating its different sections. The experimental results were fitted according to plug flow with superimposed axial dispersion and tank-in-series models, which have proved that it is reasonable to assume plug flow with axial dispersion in the overall reactor, in riser and downcomer sections, as well, while the gas separator should be considered as a perfectly mixed zone. Also, the whole reactor could be replaced with 105-30 zones with perfect mixing in series, while its separate zones, that is the riser with 104-27, the downcomer with 115-35 and the gas separator with 25-5 perfectly mixed zones in series, respectively, depending on gas superficial velocity, A_D/A_R ratio and the liquid feed rate.List of Symbols A _D cross sectional area of downcomer (m²) - A _R cross sectional area of riser (m²) - A ₁ A ₂ length of connecting pipes (m) - Bo Bodenstein number (Bo=vL·L/D _ax (-) - C concentration (kg m^–3) - C residence time distribution function - C ₀ coefficientEquation (12) - C _r dimensionless concentration - D _D diameter of downcomer (m) - D _R diameter of riser column (m) - D _ax axial dispersion coefficient (m²s^–1) - H _d height of gas-liquid dispersion (m) - H _L height of clear liquid (m) - i number of complete circulations - L length of path (m) - m order of moments - N _eq number of perfectly mixed zones in series - n _c circulating number - Q _c recirculating liquid flow rate (m³ s^–1) - q _F liquid feed flow rate (m³s^–1) - Q _G gas flow rate (m³s^–1) - Q _T total liquid flow rate (m³s^–1) - r recycle factor - s exponent inEquation (12) regarded as logarithmic decrement of the oscillating part of RTD curve - t time (s) - t _C circulation time (s) - t _s mean residence time (s) - t ₉₉ time necessary to remove 99% of the tracer concentration (s) - V _A volume of connecting pipes (m³) - V _D volume of downcomer (m³) - V _L liquid volume in reactor (m³) - V _R volume of riser (m³) - V _LD linear liquid velocity in downcomer (m s^–1) - V _LR linear liquid velocity in riser (m s^–1) - V _SLD superficial liquid velocity in downcomer (m s^–1) - V _SLR superficial liquid velocity in riser (m s^–1) - x independent variable inEquation (1) - ¯x mean value of x - z axial coordinate - _GR gas holdup in riser - _m(x) central moment of m order - ² variance - dimensionless time     

Gas hold-up in converging-diverging tube airlift fermenter

Summary Fractional gas holdup study was carried out in two airlift fermenters: one having of conventional design, the other having an asymetric riser arm. Air flow rate was varied from 1.5 to 9.0 cm/sec and gas hold-up values compared. Fractional gas holdup, _G, was strongly dependent on superficial gas velocity and initial liquid height. The modified fermenter always showed a higher gas holdup than the conventionally designed one.Symbols ALF Airlift Fermenter - CDT Convergent-divergent Tube - UT Uniform Tube - U_G Superficial gas velocity, cm/s - h_i Initial liquid height in riser, cm - H_i Dispersed liquid height in riser, cm - H_O Dispersed liquid height in downcomer, cm - K,m,n Constant - a,a Constant - A_d Riser cross sectional area, cm^z - A_r Downcomer cross sectional area, cm^z - U_b Bubble rise velocity, cm/s - g Acceleration due to gravity, cm/s^z - d_B Bubble diameter, cm - R_ev Bubble's Reynolds number, dimensionless Greek Letters _G Fractional gas holdup, dimensionless - {ITG9}{INL} Liquid density, g/cc - {IT}{INL} Liquid viscosity, poise(g/cm.s) - {ITGS}{INL} Liquid surface tension, dyne/cm - porous plate pore diameter, cm     

Study of the liquid circulation velocity in external-loop airlift bioreactors

Liquid circulation velocity was studied in externalloop air-lift bioreactors of laboratory and pilot scale, respectively for different gas input rates, downcomer-to-riser cross-sectional area ratio, A _D/A_R and liquid phase apparent viscosities.It was found that, up to a gas superficial velocity in the riser v _SGR 0.04 m/s the dependency of v _SLR on v _SGR is in the following form: v _SLR = a v _SGR ^b , with the exponent b being 0.40. Over this value of v _SGR, only a small increase in liquid superficial velocity, v _SLR is produced by an increase in v _SGR. A _D/A_R ratio affects the liquid superficial velocity due to the resistance in flow and overall friction.For non-Newtonian viscous liquids, the circulation liquid velocity in the riser section of the pilot external-loop airlift bioreactor is shown to be dependent mainly on the downcomer-to-riser cross-sectional area ratio, A _D/A_R, the effective (apparent) liquid viscosity, _eff and the superficial gas velocity, v _SGR.The equation proposed by Popovic and Robinson [11] was fitted well, with an error of ± 20%.List of Symbols A _D m² downcomer cross-sectional area - A _Rm² riser cross-sectional area - a = coefficient in Eq. (7) - b = exponent in Eq. (7) - c _s m^–1 Coefficient in Eq. (3) - D _D m downcomer diameter - D _R m riser diameter - g m²/s gravitational acceleration - H _D m dispersion height - H _L m ungassed liquid height - K Pa s ⁿ consistency index - K _B = friction factor at the bioreactor bottom - K _F = friction factor - K _T = friction factor at the bioreactor top - V _L m³ liquid volume in the bioreactor - V _D m³ liquid volume in downcomer - V _R m³ liquid volume in riser - v _LDm/s downcomer linear liquid velocity - v _LR m/s riser linear liquid velocity - v _SGR m/s riser superficial liquid velocity - v _SLR m/s riser superficial liquid velocity - s^–1 shear rate - _GD = downcomer gas holdup - _GR = riser gas holdup - _eff Pa s effective (apparent) viscosity - Pa shear stress The authors wish to thank Mrs. Rodica Roman for the help in experimental data collection and to Dr. Stefanluca for the financial support.     

Fluiddynamic characterization of airlift tower loop bioreactors with and without motionless mixtures

In a 60 l airlift tower reactor with outer loop fluiddynamical measurements were carried out in presence of three motionless mixer modules (Type SMV, Sulzer) in water, 0.6%, 0.9% and 1.2% CMC solutions. The global mixing properties were determined in the liquid and gas phases by tracers. Detailed local measurements revealed differences of local flow patterns and mixing properties in the unhindered riser and in the immediate wake of the mixer module. The local liquid velocities were measured by the pseudorandom heat pulse technique. The local bubble velocities were determined by the ultrasound Doppler technique. The dependence of liquid velocity, gas velocity and gas holdup on the superficial gas velocity were determined. The radial profiles of the mean liquid velocities and their standard deviations were evaluated in water and CMC solutions upstream and downstream of the motionless mixer modules. The radial profiles of the mean large-bubble velocities and mean small-bubble velocities and their standard deviations were determined as well. The influence of the presence of the motionless mixers in the riser on these properties was evaluated.List of Symbols Bo _L w _L L/D _L liquid Bo number - Bo _G w _G L/D _G ,gas Bo number - c tracer concentration - CMC carboxymelthylcellulose - D _G gas dispersion coefficient - D ₁ local liquid dispersion coefficient - D _L liquid dispersion coefficient - D _r riser diameter - d distance between transmitter and detector of the heat pulse probe - E _G gas holdup - HBV horizontal bubble velocity - HLBV horizontal large-bubble velocity - HSBV horizontal small-bubble velocity - L length of the column - l relative distance of the detector position from the tracer injection with respect to L - LBV large-bubble velocity - n number of circulations - OHBV overall horizontal bubble velocity - OVBV overall vertical bubble velocity - P power input - Pe ₁ w ₁d/D₁, local liquid Peclet number - SBV small-bubble-velocity - V _L liquid volume - VBV vertical bubble velocity - VLBV vertical large-bubble velocity - VSBV vertical small-bubble velocity - w _G gas velocity - w ₁ local liquid velocity - w _L liquid velocity - w _SG superficial gas velocity - w _SL superficial liquid velocity - mean residence time of the liquid in the riser H.M.R. thank the Verband der Chemischen Industrie for a Fund der Chemie scholarship     

Effects of downcomer-to-riser cross sectional area ratio on operation behaviour of external-loop airlift bioreactors

Experiments performed in two external-loop airlift bioreactors of laboratory and pilot scale, (1.880–1.189) · 10^–3 m³ and (0.170-0.157)m³, respectively, are reported. The A _D /A _R ratio was varied between 0.111–1.000 and 0.040–0.1225 in the laboratory and pilot contractor respectively.Water and solutions of different coalescence (2-propanol 2% vol, 1 M Na (glucose 50% wt/vol) and rheological behaviour (non-Newtonian starch solutions with consistency index K=0.061–3.518 Pas ⁿ and flow behaviour index n=0.86-0.39), respectively, were used as liquid phase. Compressed air at superficial velocities v _SGR =0.016–0.178 ms^–1 in the laboratory contactor and v _SGR =0.010–0.120 ms^–1 in the pilot contactor, respectively was used as gaseous phase.The A _D /A _R ratio affect gas-holdup behaviour as a result of the influence of A _D /A _R on liquid circulation velocity.Experimental results show that A _D /A _R ratio affect circulation liquid velocity by modifying he resistence to flow and by varying the fraction of the total volume contained in downcomer and riser. A _D /A _R ratio has proven to be the main factor which determines the friction in the reactor. Mixing time increases with increasing of the reactor size and decreases with A _D /A _R decreasing.The volumetric gas-liquid mass transfer coefficient increases with A _D /A _R ratio decreasing, as a result of variations of the liquid velocity with A _D /A _R , which affect interfacial areas.Correlations applicable to the investigated contactors have been presented, together with the fit of some experimental data to existing correlation in literature.List of Symbols A _D downcomer cross sectional area (m²) - A _R riser cross sectional area (m²) - a coefficient in Eq. (9) (-) - a _L gas-liquid interfacial area per unit volume (m^–1) - b coefficient in Eq. (9) (-) - C tracer concentration (kg m^–3) - C tracer concentration at the state of complete mixing (kg m^–3) - c coefficient in Eq. (12) - c _S coefficient in Eq. (5) - D _D downcomer diameter (m) - D _R riser diameter (m) - d _B bubble size (m) - H _D downcomer height (m) - H _d dispersion height (m) - H _L gas-free liquid height (m) - H _R riser height (m) - I inhomogeneity (-) - K consistency index (Pa s ⁿ ) - k _L a volumetric gas-liquid oxygen mass transfer coefficient (s^–1) - m exponent in Eq. (12) (-) - n flow behaviour index (-) - P _G power input due to gassing (W) - t _M mixing time (s) - V _A connecting pipe volume (m³) - V _D downcomer volume (m³) - V _d volume of dispersion (m³) - V _R riser volume (m³) - V _T total reactor liquid volume (m³) - v _SGR riser gas superficial velocity (m s^–1) - _GR riser gas holdup (-) - shear rate (m s^–1) - _app apparent viscosity (Pa s) - shear stress     

Concentric-tube airlift bioreactors

Liquid circulation velocity was investigated in three concentric-tube airlift reactors of different scales (RIMP, V _L =0.07 m³; RIS-1, V _L =2.5 m³; RIS-2, V _L =5.20 m³). The effects of top and bottom clearance and resistance in flow pathway at downcomer entrance on the riser liquid superficial velocity, the circulation time, the friction coefficient and flow radial profiles of the gas holdup and the liquid superficial velocity in riser, using water-air as a biphasic system, were studied. It was found that the riser liquid superficial velocity is affected by the analyzed geometrical parameters in different ways, depending on their effects on the pressure loss. The riser liquid superficial velocity, the friction coefficient and the parameters of the drift-flux model were satisfactorily correlated with the bottom spatial ratio (B), gas separation ratio (Y) and downcomer flow resistance ratio (A _d /A _D ), resulting empirical models, with correlation coefficients greater than 0.85.     

Gas holdup and mass transfer characteristics of carboxymethyl cellulose solutions in a bubble column with a radial gas sparger

The gas phase holdup and mass transfer characteristics of carboxymethyl cellulose (CMC) solutions in a bubble column having a radial gas sparger have been determined and a new flow regime map has been proposed. The gas holdup increases with gas velocity in the bubbly flow regime, decreases in the churn-turbulent flow regime, and increases again in the slug flow regime. The volumetric mass transfer coefficient (k _La) significantly decreases with increasing liquid viscosity. The gas holdup and k _La values in the present bubble column of CMC solutions are found to be much higher than those in bubble columns or external-loop airlift columns with a plate-type sparger. The obtained gas phase holdup ( _g) and k _La data have been correlated with pertinent dimensionless groups in both the bubbly and the churn-turbulent flow regimes.List of Symbols a m^–1 specific gas-liquid interfacial area per total volume - A _d m² cross-sectional area of downcomer - A _r m² cross-sectional area of riser - d _b m individual bubble diameter - d _vs m Sauter mean bubble diameter - D _c m column diameter - D _L m²/s oxygen diffusivity in the liquid - Fr Froude number, U _g/(g D_c)^1/2 - g m/s² gravitational acceleration - G _a Galileo number, gD _c ^{3 2}/² _app - H _a m aerated liquid height - H _c m unaerated liquid height - K Pa · sⁿ fluid consistency index - k _L a s^–1 volumetric mass transfer coefficient - n flow behavior index - N _i number of bubbles having diameter d _bi - Sc Schmidt number, _app/( D _L) - Sh Sherwood number, k _L a D _c ² /D_L - U _sg m/s superficial gas velocity - U _gr m/s superficial riser gas velocity - V _a m³ aerated liquid volume - V _c m³ unaerated liquid volume - N/m surface tension of the liquid phase - _g gas holdup - _app Pa · s effective viscosity of non-Newtonian liquid - kg/m³ liquid density - ý s^–1 shear rate - Pa shear stress     

Dissolved carbon dioxide accumulation in a large scale and high density production of TGFβ receptor with baculovirus infected Sf-9 cells

Production of a TGF receptor with high density baculovirus infected Sf-9 cells (7×10⁶cells ml^-1) served as a test run for a retrofitted 150 L microbial fermentor. The entire 110 L batch run was performed in serum free medium, with an addition of a concentrated amino acid and yeastolate mixture at the time of infection. This addition strategy has been proven effective at a small scale by enabling cultures to maintain maximum product yield. In the bioreactor however, while cellular growth was comparable to that of the smaller scale control, TGF receptor production was three fold below the control. To minimize the mechanical stress, low flow rate of pure oxygen was used to control the dissolved oxygen at 40%. As a consequence, it seems that this aeration strategy involved an accumulation of dissolved carbon dioxide that in turn inhibited the protein production. A model has been developed that estimated the CO₂ partial pressure in the culture to be in the vicinity of 0.15 atm. The effect of dissolved CO₂ at this concentration has been assessed at smaller scale for TGF receptor and -gal expression, in controlled atmosphere incubators.Abbreviations CST cumulative sparging time (s) - dpi days post-infection (d) - CO₂/O₂ diffusivities ratio (=0.784 at 27 °C) - DO % saturation of dissolved oxygen (%) - hpi hours post-infection (h) - He Henry coefficient (He_{CO 2}=32.1×10^-3M atm^-1, He_{O 2}=1.23×10^-3 M atm^-1 at 27 °C) - k_La volumetric liquid-side mass transfer coefficient (h^-1) - LDH Lactate dehydrogenase - MOI multiplicity of infection (pfu cell^-1) - N agitation speed (rpm) - OTR oxygen transfer rate (mole O₂ ml^-1 h^-1) - OUR oxygen uptake rate (mole O₂ ml^-1 h^-1) - p partial pressure (atm) - P total pressure (atm) - pfu plaque forming units - q specific consumption or production rate (mole cell^-1 h^-1) - Q_{H, OUT} headspace outlet gas flow rate - Q_S,NOM nominal volumetric sparged gas flow rate (92 ml s^-1 at bioreactor conditions) - R ideal gas constant (82.05 ml atm mole^-1 K^-1) - SR_{V L} molar sparging rate per unit liquid volume (mole ml^-1 h^-1) - SSR specific sparging rate (mole cell^-1 h^-1) - T temperature (C or K) - V_L culture volume (ml) - VVD volume of feed per volume of culture per day (d^-1) - X cell concentration (cell ml^-1) - Y yield coefficient Indexes CO₂, O₂ related to CO₂ or O₂, respectively - glc glucose - H headspace gas phase or gas/liquid interface - L liquid phase - lact lactate - S sparged phase or gas/liquid interface - V viable     

Mixing performance of air-lift fermenters against working volume and draft tube dimensions

Mixing characteristics of a laboratory scale internal loop air-lift fermenter has been investigated. The effects of different draft tube dimensions and positions as well as varying levels of liquid height over the draft tube, on mixing time were determined. The results indicate the existance of an optimum liquid height and thus liquid volume with respect to mixing performance especially for the taller draft tubes.List of Symbols A mm distance between draft tube and reactor base - A _D mm² area of the downcomer region - A _R mm² area of the riser region - B mm width of annulus - D _d mm draft tube diameter - D _t mm fermenter diameter - H _d mm draft tube height - H _l mm liquid height in the fermenter - H _t mm fermenter height - V _d m³ draft tube volume - V _t m³ fermenter volume - D _d /D _l - _B H _d /H _l - _F H _l /D _t      

Concentric-tube airlift bioreactors

Gas holdup investigations were performed in three concentric-tube airlift reactors of different scales of operation (RIMP: 0.070 m³; RIS-1: 2.5 m³; RIS-2: 5.2 m³; nominal volumes). The influences of the top and bottom clearances and the flow resistances at the downcomer entrance were studied using tap water as liquid phase and air as gaseous phase, at atmospheric pressure. It was found that the gas holdup in the individual zone of the reactor: riser, downcomer and gas-separator, as well as that in the overall reactor is affected by the analyzed geometrical parameters in different ways, depending on their effects on liquid circulation velocity. Gas holdup was satisfactorily correlated with Fr, Ga, bottom spatial ratio (B), top spatial ratio (T), gas separation ratio (Y) and downcomer flow resistance ratio (A _d /A _R ). Correlations are presented for gas holdup in riser, downcomer, gas separator and for the total gas holdup in the reactor. All the above stressed the importance of the geometry in dynamic behaviour of airlift reactors.     

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     

Carbon dioxide desorption from fermentation broth by use of oxygen vectors

The ability of oxygen vector to extract produced carbon dioxide has been tested in an anaerobic fermentation. During the continuous culture of Clostridium acetobutylicum at pH 4.6 and at a dilution rate of 0.124 h^–1, a feed composed of an emulsion of 18.5% by volume of Forane F66E was able to extract about 9% of the total CO₂ produced under CO₂ partial pressure equal to 0.42 atm. A theoretical evaluation of the extracted amount, based on the hypothesis of total saturation of the vector by carbon dioxide, has lead to very good agreement.List of Symbols [AA] g/l acetic acid concentration - [BA] g/l butyric acid concentration - D 1/h Q _w /V dilution rate - [ETH] g/l ethanol concentration - H _w Henry constant of CO₂ for water at 37°C (=23.91 mmol/(l atm)) - H _F Henry constant of CO₂ for Forane at 37°C (=83.4 mmol/(l atm)) - H _i g/mol molar mass of componenti - P _i atm partial pressure of gasi - W _w l/h aqueous flow - Q_f 1/h Forane flow - mmol/(lh) dissolved CO₂ flow in aqueous effluent - mmol/(lh) CO₂ gas flow - mmol/(lh) CO₂ gas flow without Forane - mmol/(lh) CO₂ gas flow with Forane - mmol/(lh) total CO₂ production - r _X g/(lh) biomass production rate - r _G mmol/(lh) total gas flow - mmol/(lh) hydrogen production - mmol/(lh) nitrogen flow - r _S mmol/(lh) glucose input - V 1 fermentor volume     

One-dimensional model of the acid hydrolysis of cellulosic substrates in a solid-liquid cyclone reactor

The use of rotating flow in an annulus is investigated as a means of enhancing the yield of glucose and xylose in the acid hydrolysis of cellulosic slurries. A one-dimensional model of such a cyclone reactor is developed for flow cases, co-current and counter-current flow. For the case of 250°C, 1% w/w acid, the one-dimensional model indicates an increase in the maximum glucose yield from 48.1% in a plug flow reactor to 69.3% in a co-current cyclone reactor, and up to 81.0% in a countercurrent cyclone reactor. The corresponding xylose yields are 91.6% for co-current operation and 97.7% for countercurrent operation. In the co-current case the maximum glucose and xylose yields do not occur at the same location in the reactor; however, in the countercurrent case they do. Although product yields are dramatically improved over those obtained in a plug flow reactor, the product concentrations are lower than would typically be obtained in a plug flow reactor.List of Symbols A cm² cross sectional area perpendicular to radial flow - A _c cm² cross sectional area of slurry inlet - A _c cm² cross sectional area of steam inlet - A _w cm² cross sectional area of water inlet - C _c concentration of cellulose as potential glucose (grams of potential glucose/cm³ of total stream) - C _c ^* grams cellulose/cm³ of solids concentration of cellulose as potential glucose - C _ginitial ^* grams glulose/cm³ of solids concentration of cellulose entering reactor - C _g grams glucose/cm³ of total stream concentration of glucose - C _g ^* grams glucose/cm³ of liquid stream concentration of glucose - C _cinitial ^* grams cellulose/cm³ of liquid concentration of glucose entering reactor - C _xn concentration of xylan as potential xylose (grams of potential xylose/cm³ of total stream) - C _xs grams xyclose/cm³ of total stream concentration of nylose - d _f dilution factor - dr cm radial increment - g cm/s² gravitational acceleration - g ^* centrifugal acceleration proportionality constant - h cm height of cyclone reactor - j cm/s flux - K constant in general equation for vortex flow, Eq. (4.9) - k ₁ 1/s kinetic rate constant of cellulose hydrolysis - k _a 1/s kinetic rate constant of xylan hydrolysis - k ₂ 1/s kinetic rate constant of glucose decomposition - k _2a 1/s kinetic rate constant of xylose decomposition - m vortex exponent - M _steam g/s mass rate of steam addition at outer radius - M _water g/s mass rate of cold water addition at outer radius - n cm³/s empirically determined settling parameter - Q cm³/s net volumetric flow in outward radial direction - Q _tot cm³/s total volumetric flow through reactor - q _c cm³/s volumetric flow of slurry feed - q _s cm³/s volumetric flow of stream feed - q _water cm³/s volumetric flow of cold water feed - r cm radial position - r _c 1/s rate of cellulose hydrolysis - r _g 1/s rate of glucose decomposition - r _i cm inner radius - r _o cm outer radius - r _xn 1/s rate of xylan hydrolysis - r _xs 1/s rate of xylose decomposition - s _mom cm g/s² inlet steam momentum - T _bulk s bulk residence time in reactor - T °C reactor temperature - v _c cm³/g specific volume of slurry feed - v _s cm³/g specific volume of steam - v _w cm³/g specific volume of water - V _f cm/s velocity of liquid as a function of radius - V _i cm/s inlet velocity - V _s cm/s velocity of solids as a function of radius - V _steam cm/s inlet steam velocity to cyclone - V cm/s terminal settling velocity - V _q cm/s tangential velocity - w _mom cm g/s² water inlet momentum - Y grams product out/grams reactant in yield of product - solids volumetric fraction - _f solids volumetric fraction in slurry feed - _i initial solids volumetric fraction of slurry - Pi     

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     

Saccharomyces cerevisiae fermentations in a pilot scale airlift bioreactor: Comparison of air sparger configurations

Hydrodynamic and oxygen transfer comparisons were made between two ring sparger locations, draft tube and annulus, in a concentric pilot scale airlift reactor with a baker's yeast suspension. Sectional hydrodynamic measurements were made and a mobile DOT probe was used to characterise the oxygen transfer performance through the individual sections of the reactor. The hydrodynamic performance of the reactor was improved by using a draft tube ring sparger rather than the annulus ring sparger. This was due to the influence of the ratio of the cross sectional area of the downcomer and riser (A _D/A_R) in conjunction with the effect of liquid velocity and a parameter,C ₀, describing the distribution of the liquid velocity and gas holdup across the riser on the bubble coalescence rates. The mixing performance of the reactor was dominated by the frequency of the passage of the broth through the end sections of the reactor. An optimum liquid height above the draft tube, for liquid mixing was demonstrated, above which no further improvement in mixing occurred. The liquid velocity and degree of gas entrainment showed little dependency on top section size for both sparger configurations. Extreme dissolved oxygen heterogeneity was demonstrated around the vessel with both sparger configurations and was shown to be detrimental to the oxygen uptake rate of the baker's yeast. Dissolved oxygen tensions below 1% air saturation occurred along the length of the riser and then rose in the downcomer. The greater oxygen transfer rate in the downcomer than in the riser was caused by the combined effects of a larger slip velocity in the downcomer which enhancedk _La and gas residence time, high downcomer gas holdup, and the change in bubble size distribution between the riser and downcomer. The position of greatest oxygen transfer rate in the downcomer was shown to be affected by the reactor from the influence on downcomer liquid linear velocity. UCL is the Biotechnology and Biological Sciences Research Council sponsored Advanced Centre for Biochemical Engineering and the Council's support is greatly acknowledged.     

Apparent viscosity for non-Newtonian fermentation media in bioreactors

The apparent viscosity of non-Newtonian fermentation media is examined. The present state of this subject is discussed. The energy dissipation rate concept is used for a new evaluation of the apparent viscosity in bioreactors, i.e. stirred tank and bubble column bioreactors. The proposed definition of the apparent viscosity is compared with the definitions available in the literature.List of Symbols A _d m ² downcomer cross-sectional area - A _r m ² riser cross-sectional area - a m^–1 specific surface area - C constant in eq. (13) - D m column diameter - D _I m impeller diameter - g m s^–2 gravitational acceleration - h J m^–2 s^–1 K^–1 heat transfer coefficient - K Pa s ⁿ consistency index in a power-law model - k constant in eq. (3) - k _L m s ^–1 liquid-phase mass transfer coefficient - N s^–1 impeller speed - n flow index in a power-law model - P W power input - Re Reynolds number ND _I ^/2 /(/) - U _sg m s ^–1 superficial gas velocity - (U _sg ) _r m s^–1 superficial gas velocity based on riser - V-m³ liquid volume - v ₀ m s^–1 friction velocity Greek Symbols s^–1 shear rate - _c s^–1 characteristic shear rate - W kg^–1 energy dissipation rate per unit mass - W kg^–1 characteristic energy dissipation rate per unit mass - Pa s viscosity - _app Pa s apparent viscosity - kg m^–3 density - Pa shear stress     

Application of fuzzy multiobjective optimization for self-sucking impellers in a bioreactor

For three types of self-sucking impellers (fourand six-pipe and disk impellers) mixing power, initial point, amount of gas leaving the impeller and mass transfer coefficient were determined experimentally. Investigations were performed for two systems: water and biomass solution.From the point of view of a minimum mixing power and maximum mass transfer coefficient the best impeller has been chosen. Fuzzy multiobjective optimization for determination of optimum operating conditions is proposed.List of Symbols c concentration of oxygen - D tank diameter - d impeller diameter - g acceleration of gravity - H height of liquid in the tank - H height of liquid above impeller, H=H-y - k consistency coefficient - k _L a volumetric mass transfer coefficient - N rotational speed of impeller - n flow behaviour index - P mixing power for pure liquid - P _G mixing power for aerated liquid - V _G volumetric air flow rate - y distance of impeller from the tank bottom - v _a apparent kinematic viscosity of liquid - density of liquid - time - gas hold-up - Eu=P/N ³ d ⁵ or Eu_G=P _G /N ³ d ⁵ Euler Number for non-gassed or aerated liquid - Fr=N ² d/g Froude Number - Fr^*=N ² d ² /g(H -y) modified Froude Number - K_G=V _G /N d ³ gas flow number - Re=N d ² /v _a Reynolds Number - Sh=k _K a/(g ² /v _a )^1/3 Sherwood Number     

Estimation of oxygen penetration depth in immobilized cells

Summary A simple method is proposed for calculating oxygen pentration depth in immobilized cells by assuming zero order kinetics in the presence of several external oxygen transport resistances. Calculations indicate that typical penetration depths of oxygen for immobilized microbial cells are in the range of 50–200 and those for immobilized or encapsulated animal and plant tissue culture are about 500–1000 . Based on calculations, oxygen transport in microencapsulation and microcarriers for tissue cultures are not transport-limited, but a slight limitation is expected for those in a hollow fiber reactor.Nomenclature a_s specific area of a support (cm) - Bi Biot number - dimensionless - C_b oxygen concentration in the bulk liquid (mM) - C _b C _b ^* -C_cr (mM) - C _b ^* bulk oxygen concentration in equilibrium with air (mM) - C_cr critical oxygen concentration (mM) - C_s oxygen concentration in the solid phase (mM) - d_p diameter or thickness of a support (cm) - D_eff effective diffusivity of oxygen in the solid phase (cm²/s) - k_m membrane permeability of oxygen (cm/s) - k _m ^* D_eff/_m - k_La_L liquid phase mass transfer rate coefficient (1/s) - k_sa_s solid phase mass transfer rate coefficient (1/s) - (OUR)_v volumetric oxygen uptake rate (mmol O₂/l) - p geometry parameter, p=0 for slab, p=1 for cylinder, p=2 for sphere - P_d oxygen penetration depth (cm) - P _d oxygen penetration depth in the absence of external diffusion limitation (cm) - Q volumetric oxygen uptake rate, (mmol O₂/l·h) - specific oxygen uptake rate (mmol O₂gm biomass (dry)·h) - r length coordinate (cm) - r_c oxygen penetration depth for sphere (cm) - r _c r_c in the absence of external diffusion limitation (cm) - r _c ^* oxygen penetration depth for cylinder (cm) - r _c ^* r _c ^* in the absence of external diffusion limitation (cm) - r_com combined mass transfer rate resistance (s) - r_d location where C_s becomes zero or C_cr (cm) - r_i radius of cylinder or sphere, half thickness of slab (cm) - U_sg superficial gas velocity (cm/s) - X cell concentration (g/l) Greek letters Thiele modulus, dimensionless - _L, _s liquid and solid phase volume fraction, respectively, dimensionless - effectiveness factor On sabbatical leave from KAIST, Seoul, Korea     

Performance characteristics of yeast growth in a modified airlift fermenter

Two types of airlift fermenters, conventional (UT-ALF) and modified (CDT-ALF) were investigated to evaluate their performance with respect to baker's yeast growth. The riser tube of conventional external loop airlift fermenter is replaced by a converging-diverging tube, which is named as modified airlift fermenter having downcomer to riser cross-sectional area ratio A _d /A _r =1.8.The results were compared for the two types of airlift fermenter. A modified growth kinetics model for baker's yeast with oxygen as limiting substrate, has been proposed. The values of K _s and K _d of the growth model were determined from experimental data. The proposed model represented better for CDT-ALF system compared to UT-ALF. Compared to UT-ALF, CDT-ALF always showed higher cell mass concentration and low residual sugar concentration irrespective of the operating conditions. At optimum operating condition (initial glucose concentration 30 g/l, air flow rate 0.5 vvm and fermentation time 8 hrs.) 16.7% higher cell mass was observed in CDT-ALF compared to that in UT-ALF and yield (Y _x/s ) was found to be 0.51 which was theoretically very near to maximum achievable value.Symbols ALF Airlift fermenter - UT Uniform tube - CDT Converging-diverging tube - A _r Cross sectional area of riser - A _d Cross sectional area of downcomer - C _s Glucose cone, at any time, g/l - C _l Dissolved oxygen conc, at any time, g/l - _max Max. sp. growth rate, hr^–1 - Sp. growth rate, hr^–1 - X ₀ Initial cell mass cone. (dry wt.), g/l - X Cell mass conc. at any time t, g/l - C _s0 Initial glucose conc., g/l - C _s Glucose conc. at any time t, g/l - C _l Equilibrium conc. of oxygen, 0.0076 g/l - y _x/s Yield coefficient (dimensionless) - y _x/s gm cell mass produced/gm glucose consumed - Y _O2 gm cell produced/gm oxygen consumed - k _d maintenance coefficient, hr^–1 - K _L a volumetric mass transfer coefficient, hr^–1 - k _s saturation constant for the substrate, g/l - K _O2 saturation constant for the substrate of dissolved oxygen, g/l. This work was supported by a research grant from the Department of Biotechnology Govt. of India.