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     

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     

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.     

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     

Gas-phase influence on the mixing in a fluidized bed bio-reactor

Summary The liquid and solids mixing in fluidized bed bio-reactors containing particles with a density only slightly higher than water (1100 kg/m³) is generally consistent with the results found in previous studies for reactors with particles of higher density. The liquid mixing can be described by an axial dispersion model for a large variety of conditions while the solids follow the streamlines of the liquid. In the presence of a gas phase the degree of mixing of both the liquid and the solid phase increased. This effect became larger with increasing reactor diameter. In the extrapolation of laboratory data of three phase fluidized bed bio-reactors to pilot plant systems this effect should be taken into account. The liquid and solids mixing may have a substantial effect on overall conversion rates and on possible microbial stratification in the reactor.Nomenclature Bo Bodenstein number v L/D (-) - D _r diameter of the fluidized bed reactor (m) - D ₁ Dispersion coefficient of the liquid phase (m²/s) - D _g dispersion coefficient of the solid phase (m²/s) - E(in) normalized dye concentration function entering the ideally mixed tank reactor (-) - E(t) normalized dye concentration function as measured (-) - L length of the axial dispersed reactor (m) - t time after dye injection (s) - t _m time constant for microbial selection (s) - t _s solid mixing time constant (s) - t time interval in which a particle migrates within the bed (s) - v _t superficial gas velocity (m/s) - v _g superficial liquid velocity (m/s) - z migration distance of a particle in the bed (m) - ₁ in situ growth rate of a dominant organism (s^-1) - ₂ in situ growth rate of a recessive organism (s^-1) - average residence time in the axial dispersed reactor (s) - _t average residence time in the ideally mixed tank reactor (s)     

Mixing time in a down-flow jet loop bioreactor

Mixing time was determined in a down-flow jet loop bioreactor with Newtonian and non-Newtonian fluids. It was observed that the mixing time decreased with an increase in linear liquid velocity, superficial gas velocity, draft tube to column diameter ratio, nozzle diameter and shear thinning of media. The optimum draft tube to column diameter ratio was found to be about 0.44. Correlations were presented for prediction of mixing time.List of Symbols A m² cross sectional area of the column - C kmol/m³ local tracer concentration - A _D m² flow area,A _D =/4 (D _Z ² -D _TO ² ) - D m column diameter - D _E m draft tube diameter - D _TO m outside diameter of the air tube - D _TFL m equivalent flow diameter,D _TFL =(D _Z ² -D _TO ² )^0.5 - D _z m nozzle diameter - g m/s² gravitational acceleration - h % inhomogeneity - H m height of the column - H _B m distance between the lower edge of the draft tube and the impact plate - H _T m distance between the upper edge of the draft tube and the liquid nozzle - K Pa.sⁿ consistency index in power-law model - L _E m length of the draft tube - n flow index in the power-law model - Re _j jet Reynolds number,Re _j =(D _TFL×w₁×_L)/ _eff - t _M s mixing time - t _sg m/s superficial gas velocity based onA - W _l m/s linear liquid velocity based onD _D Greek Letters N/m² shear stress - s shear rate - kg/m³ density of liquid - N/m surface tension of the liquid - Pa.sⁿ viscosity of liquid Indices X concentration at infinite time maximum value of tracer concentration - eff effective - L Liquid - obs observed - pred Predicted     

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     

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.     

Interpretation of gas residence time distributions in large airlift tower loop reactors

Gas-residence time distribution (RTD) response curves measured in a 23 m high pilot plant airlift tower loop reactor, which consisted of a riser, a special downcomer construction and at the top of the riser a large head. The measurements were evaluated by means of a deterministic dispersion model, which yielded the following particular parameters for the riser, downcomer and the head: Gas-Bo numbers, gas-mean residence times, gas holdups, liquid velocities, gas and liquid circulation times as well as a fraction of the large and small bubbles in a model medium (water) and during cultivation of baker's yeast.List of Symbols A cross section - Bo Bodenstein number - Bo _d (= l _d w _G,d /D _d ) - Bo _h (= l _h w _G,h /D _h ) - Bo _r (= l _r w _G,r /D _r ) - D longitudinal dispersion coefficient - E gas holdup - E(t) RTD-density function - L, l length parameter - q fraction of the gas throughput which is not recirculated (approximately equal to fraction of the large bubbles) - r fraction of the throughput which is recirculated (approximately equal to the fraction of the small bubbles) - t _c circulation time - t _cL liquid circulation time - t _c,L ^* liquid circulation time calculated from the measured w _Ld in the downcomer - V ^h hydrodynamical calculated gas-liquid volume - V _d ^h (=V _d+0.75/2 V _k ) - V _k ^h =(0.25V _k ) - V _r ^h = (V _r+0.75/2 V _k ) - V _L liquid volume - V _G dispersed gas volume - V _G ^* gas throughput at the gas distributor (given in m³/h) under standard conditions, 1 bar and 25°C) - V _G,d ^* gas throughput in downcomer (=V _G ^* ) - V _G,h ^* gas throughput in head (=V _G ^* ) - V _G,r ^* gas throughput in riser (V _G ^* (1+) - w _g gas velocity - w _G,rel relative gas velocity with respect to the liquid velocity w _L - w _G,d gas velocity in the downcomer (=w _G,rel –w _Ld ) - w _G,h gas velocity in the head (=w _G,rel ) (since wLh = o) - w _G,r gas velocity in the riser (=w _G,rel +w _Lr ) - w _L liquid velocity - w _L,d liquid velocity in the downcomer measured with mass flow meter - w _sg ·w _SL superficial gas and liquid velocities - first moment of the response curve - mean residence time Indices d downcomer - G gas phase - h head - L liquid phase - r riser - h hydrodynamic (upper position) Dedicated to the 65th birthday of Proffessor Fritz Wagner.The authors gratefully acknowledge the financial support by the Krupp Industrietechnik, Grevenbroich and the support of Pleser Co, Darmstadt. H. M. Rüffer thanks the Verband der Chemischen Industrie for a Fond der Chemie scholarship, and W. Liwei thanks the government of Lower Saxony for a graduate scholarship.     

Flow rate dependent kinetics of urease immobilized onto diverse matrices

Gas holdup and liquid circulation velocity meassurements were made for a range of liquid viscosities in a 22 l external loop airlift column and 250 l pilot-scale concentric cylinder airlift bioreactor. The results showed that for a fixed superficial gas velocity, liquid circulation velocity decreased monotonically with increasing liquid viscosity. The gas holdup for a fixed gas flow rate showed an initial increase with liquid viscosity followed by a decrease when liquid viscosity increased beyond a critical value. These observations could not be described satisfactorily using the available models of gas holdup and liquid circulation.List of Symbols U _sg m/s Superficial gas velocity - U _sl m/s Superficial liquid velocity in the riser Greek Letters Pas Liquid viscosity - _g Gas holdup in the riser     

The effect of antifoam agents on mass transfer in bioreactors

The influence of antifoam agents on the liquid-phase mass transfer coefficient in stirred tank and bubble column bioreactors is studied. A physical model based on a surface-renewal concept and additional data in 40-dm³ bubble column bioreactor are presented. Comparisons between the physical model and the data indicate that the model predicts the maximum influence of antifoam agents on the liquid-phase mass transfer coefficient.List of Symbols a 1/m specific surface area - D m²/s diffusivity - D _c m bubble column diameter - d _vs m bubble diameter - g m/s² gravitational acceleration - k _L m/s liquid-phase mass transfer coefficient - k _LO m/s liquid-phase mass transfer coefficient for clean surface - N 1/s impeller speed - Sc Schmidt number (v/D) - U _sg m/s superficial gas velocity Greek Letters W/kg energy dissipation rate per unit mass - _g gas hold-up - Pa s viscosity - v m²/s kinematic viscosity - kg/m³ density - N/m surface tension     

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

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.     

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     

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.     

Hydrodynamics of non-Newtonian liquids in external-loop airlift bioreactors

In order to obtain further information on the behaviour and optimal design of external-circulation-loop airlift bioreactors, the liquid circulating velocity was studied using highly viscous pseudoplastic solutions of starch and antibiotic biosynthesis liquids of Penicillium chrysogenum, Streptomyces griseus, Streptomyces erythreus, Bacillus licheniformis and Cephalosporium acremonium. Measurements of liquid circulation velocity were made in laboratory and pilot plant external-loop airlift bioreactors, under various conditions concerning gas flow rate, riser liquid height at constant downcomer height, A _D /A _R ratio, using the impulse-response technique. It has been found that these parameters had a significant effect on liquid circulation velocity together with the apparent viscosity and dry weight of the solid phase in the biosynthesis liquids. For the tested liquids, the superficial liquid velocity in the riser section of an external-loop airlift bioreactor may be described by the following equation: where the exponents and the constant c take different values depending on the liquid phase properties and flow regime.     

The behaviour of yeast flocs in hindered settling and fluidized bed regimes

Summary Sedimentation and fluidization of yeast flocs were found to be non-synonymous processes. The analysis of Richardson and Zaki (1954) was found not to hold when applied to yeast flocs in both regimes. Partial support and channelling were implicated in the deviations from idela behaviour. Other factors responsible for the behaviour of yeast flocs in these regimes are discussed.Symbols D bed height (cm) - g gravitational constant (981 cm·s^-1) - n constant (-) - R retardation factor (s) - S constant (-) - v liquid/particle velocity (cm·s^-1) - V _o particle terminal velocity (cm·s^-1) - bed voidage (-)     

Comparison of different bioreactor performances

Bioreactors are compared based on oxygen transfer rate and efficiency, mixing performance, cell mass productivity as well as with respect to enzyme and metabolite productivity.List of Symbols AC acetate concentration - AL airlift tower loop reactor - CFU colony-forming units - CP coalescence-promoting medium - CS coalescence-suppressing medium - D _D impeller clearance - D _M molecular diffusivity - D _S diameter of the column - DT flat-bladed disc turbine - D _v vessel diameter - E. act enzyme activity - EDR energy dissipation rate - EcoRI restriction endonuclease - EcoR4 protection plasmid - E _{O 2} efficiency of oxygen transfer rate - E _X efficiency of cell mass production with respect to the specific power input - g acceleration of gravity - H height of column - H _v vessel height - HV highly viscous medium - IPTG isopropyl thiogalactoside (inducer of Lacpromoter) - k fluid consistency factor - k _L mass transfer coefficient - k _La volumetric mass transfer coefficient - m exponent - N impeller speed - n exponent - n flow behaviour index - P power input - P/V_L specific power input - PR marine propeller - P _LacUV5 Lac-promoter-induced by IPTG - P _R promoter-induced with temperature shift - _{O 2} oxygen transfer rate - q _g,q _{O 2} aeration rate, specific aeration rate with respect to liquid volume - R density of cultivation medium - R _p product formation rate - R _X growth rate - SpA protein A - ST stirred tank reactor - TCC total cell count - t _Lc liquid circulation time - U enzyme activity unit - u _B bubble rise velocity - u _G superficial gas velocity - V _L volume of the liquid phase - v kinematic viscosity of the cultivation medium - W _SG superficial gas velocity - X cell mass concentration - Y _E/S yield coefficient of ethanol formation with respect to substrate consumption - Y _P/X specific product formation with respect to cell concentration - Y _X/E yield coefficient of cell growth with respect to ethanol consumption - Y _{X/O 2} yield coefficient of cell growth with respect to oxygen consumption rate - Y _X/S yield coefficient of growth with respect to substrate consumption - _L liquid mixing time - _eff effective dynamic viscosity of the cultivation medium - _W dynamic viscosity of water - _max maximum specific growth rate - surface tension of the cultivation medium     

Mathematical modeling of mixing in a horizontal rotating tubular bioreactor: “Simple flow” model

The construction of the horizontal rotating tubular bioreactor (HRTB) represents a combination of a thin-layer bioreactor and a biodisc reactor. The bioreactor was made of a plastic tube whose interior was divided by the O-ring shaped partition walls. For the investigation of mixing properties in HRTB the temperature step method was applied. The temperature change in the bioreactor as a response to a temperature step in the inlet flow was monitored by six Pt-100 sensors (t ₉₀ response time 0.08 s and resolution 0.002 °C) which were connected with an interface unit and personal computer. Mixing properties of the bioreactor were modeled using the modified tank in series concept which divided the bioreactor into ideally mixed compartments. A mathematical mixing model with simple flow was developed according to the physical model of the compartments network and corresponding heat balances. Numerical integration of an established set of differential equations was done by the Runge-Kutt-Fehlberg method. The final mathematical model with simple flow contained four adjustable parameters (N1,Ni, F _cr andF _p ) and five fixed parameters.List of Symbols A _u m² inner surface of bioreactor's wall - A _ui m² i-th part of inner surface of bioreactor's wall - A _v m² outlet surface of bioreactor's wall - A _vi m² i-th part of outlet surface of bioreactor's wall - C _p kJ kg^–1 K^–1 heat capacity of liquid - C _pr kJ kg^–1 K^–1 heat capacity of bioreactor's wall - D h^–1 dilution rate - E °C °C^–1 h^–1 error of mathematical model - F _cr dm³s^–1 circulation flow in the model - F _p dm³ s^–1 back flow in the model - F _t dm³s^–1 inlet flow in the bioreactor - I °C intensity of temperature step, the difference in temperature between the temperature of the inlet liquid flow and the temperature of liquid in the bioreactor before the temperature step - K1 Wm^–2K^–1 heat transfer coefficient between the liquid and bioreactor's wall - K2 Wm^–2K^–1 heat transfer coefficient between the bioreactor's wall and air - m _s kg mass of bioreactor's wall - L m length of bioreactor - L _k m wetted perimeter of bioreactor - n min^–1 rotational speed of bioreactor - n _s number of temperature sensors - N1 number of cascades - Ni number of compartments inside the cascade - Nu Nusselt number - Pr Prandtl number - r _u m inner diameter of bioreactor - r _v m outside diameter of bioreactor - Re Reynolds number - s(t) step function - t s time - T °C temperature - T _c °C calculated temperature - T _m °C measured temperature - T _N1,Ni °C temperature of liquid in a defined compartment inside cascade - T _N1,S °C temperature of defined part of bioreactor's wall - T _S °C temperature of bioreactor's wall - T _v °C temperature of liquid in bioreactor - T _z °C temperature of surrounding air - V _t dm³ volume of liquid in the bioreactor Greek Symbols kJm^–1s^–1 K^–1 thermal conductivity of liquid in the bioreactor - kgm^–3 density of liquid in the bioreactor - m²s^–1 kinematic viscosity of liquid in the bioreactor Matrix Coefficient B - C - D - E B+C+D - G1 - G2 - G3 - A _ui - A _vi - Q ₁ - Q ₂ - Q ₃      

Comparison of three granular support materials for anaerobic fluidized bed systems

Summary Three different materials, kaolin, pozzolana and biolite (a material used in a commercial anaerobic fluidized bed treatment process) when tested as supports for an anaerobic fluidized bed system had similar physical and fluidization properties but behaved differently towards the biomass hold-up. However, all three systems attained similar removal efficiency rates.Nomenclature U Fluidization velocity (m/s) - U₁ Terminal fluidization velocity (m/s) - g Local acceleration due to gravity (m/s²) - _s Solid density (kg/m³) - _f Fluid density (kg/m³) - P Pressure drop (Pa) - HRT Hydraulic retention time (days) - H_mf Height of bed at minimum fluidization (m) - H Height of bed (m) - C_d Drag coefficient (dimensionless) - W Mass of solids in bed (kg) - dp Particle diameter (m) - A Cross-sectional area of column (m²) - h column height (m) - Rc_t Terminal Reynolds no. - Voidagc (fractional free volume, dimensionless) - _mf Voidage (fractional free volume) at minimum of fluidization (dimensionless)