Residence time distributions of gas flowing through rotating drum bioreactors

Residence time distribution studies of gas through a rotating drum bioreactor for solid-state fermentation were performed using carbon monoxide as a tracer gas. The exit concentration as a function of time differed considerably from profiles expected for plug flow, plug flow with axial dispersion, and continuous stirred tank reactor (CSTR) models. The data were then fitted by least-squares analysis to mathematical models describing a central plug flow region surrounded by either one dead region (a three-parameter model) or two dead regions (a five-parameter model). Model parameters were the dispersion coefficient in the central plug flow region, the volumes of the dead regions, and the exchange rates between the different regions. The superficial velocity of the gas through the reactor has a large effect on parameter values. Increased superficial velocity tends to decrease dead region volumes, interregion transfer rates, and axial dispersion. The significant deviation from CSTR, plug flow, and plug flow with axial dispersion of the residence time distribution of gas within small-scale reactors can lead to underestimation of the calculation of mass and heat transfer coefficients and hence has implications for reactor design and scale-up.     

Oxygen transfer and axial dispersion in an aeration tower containing static mixers

Oxygen transfer from gas to liquid under steady-state cocurrent flow conditions was modeled using the dispersion model, and the oxygen transfer coefficients were estimated from available data for a column with Koch motionless mixers. The dispersion in the column was estimated for several different gas and liquid flow rates using steady-state tracer experiments. The estimated oxygen transfer coefficients were compared with those estimated using complete mixing and plug flow models. The results indicate that the dispersion model is the most appropriate model for estimating the mass transfer coefficient from the available data.     

Characterisation of the gas-liquid mass transfer in shaking bioreactors

The maximum gas-liquid mass transfer capacity of 250ml shaking flasks on orbital shaking machines has been experimentally investigated using the sulphite oxidation method under variation of the shaking frequency, shaking diameter, filling volume and viscosity of the medium. The distribution of the liquid within the flask has been modelled by the intersection between the rotational hyperboloid of the liquid and the inner wall of the shaking flask. This model allows for the calculation of the specific exchange area (a), the mass transfer coefficient (k(L)) and the maximum oxygen transfer capacity (OTR(max)) for given operating conditions and requires no fitting parameters. The model agrees well with the experimental results. It was furthermore shown that the liquid film on the flask wall contributes significantly to the specific mass transfer area (a) and to the oxygen transfer rate (OTR).     

Oxygen transfer phenomena in 48-well microtiter plates: determination by optical monitoring of sulfite oxidation and verification by real-time measurement during microbial growth

Oxygen limitation is one of the most frequent problems associated with the application of shaking bioreactors. The gas-liquid oxygen transfer properties of shaken 48-well microtiter plates (MTPs) were analyzed at different filling volumes, shaking diameters, and shaking frequencies. On the one hand, an optical method based on sulfite oxidation was used as a chemical model system to determine the maximum oxygen transfer capacity (OTR(max)). On the other hand, the Respiration Activity Monitoring System (RAMOS) was applied for online measurement of the oxygen transfer rate (OTR) during growth of the methylotropic yeast Hansenula polymorpha. A proportionality constant between the OTR(max) of the biological system and the OTR(max) of the chemical system were indicated from these data, offering the possibility to transform the whole set of chemical data to biologically relevant conditions. The results exposed "out of phase" shaking conditions at a shaking diameter of 1 mm, which were confirmed by theoretical consideration with the phase number (Ph). At larger shaking diameters (2-50 mm) the oxygen transfer rate in MTPs shaken at high frequencies reached values of up to 0.28 mol/L/h, corresponding to a volumetric mass transfer coefficient (k(L)a) of 1,600 1/h. The specific mass transfer area (a) increases exponentially with the shaking frequency up to values of 2,400 1/m. On the contrary, the mass transfer coefficient (k(L)) is constant at a level of about 0.15 m/h over a wide range of shaking frequencies and shaking diameters. However, at high shaking frequencies, when the complete liquid volume forms a thin film on the cylindric wall of the well, the mass transfer coefficient (k(L)) increases linearly to values of up to 0.76 m/h. Essentially, the present investigation demonstrates that the 48-well plate outperforms the 96-well MTP and shake flasks at widely used operating conditions with respect to oxygen supply. The 48-well plates emerge, therefore, as an excellent alternative for microbial cultivation and expression studies combining the advantages of both the high-throughput 96-well MTP and the classical shaken Erlenmeyer flask.     

Characterization of gas-liquid mass transfer phenomena in microtiter plates

Gas-liquid mass transfer properties of shaken 96-well microtiter plates were characterized using a recently described method. The maximum oxygen transfer capacity (OTR(max)), the specific mass transfer area (a), and the mass transfer coefficient (k(L)) in a single well were determined at different shaking intensities (different shaking frequencies and shaking diameters at constant filling volume) and different filling volumes by means of sulfite oxidation as a chemical model system. The shape (round and square cross-sections) and the size (up to 2 mL maximum filling volume) of a microtiter plate well were also considered as influencing parameters. To get an indication of the hydrodynamic behavior of the liquid phase in a well, images were taken during shaking and the liquid height derived as a characteristic parameter. The investigations revealed that the OTR(max) is predominantly dependent on the specific mass transfer area (a) for the considered conditions in round-shaped wells. The mass transfer coefficient (k(L)) in round-shaped wells remains at a nearly constant value of about 0.2 m/h for all shaking intensities, thus within the range reported in the literature for surface-aerated bioreactors. The OTR(max) in round-shaped wells is strongly influenced by the interfacial tension, determined by the surface tension of the medium used and the surface properties of the well material. Up to a specific shaking intensity the liquid surface in the wells remains horizontal and no liquid movement can be observed. This critical shaking intensity must be exceeded to overcome the surface tension and, thus, to increase the liquid height and enlarge the specific mass transfer area. This behavior is solely specific to microtiter plates and has not yet been observed for larger shaking bioreactors such as shaking flasks. In square-shaped microtiter plate wells the corners act as baffles and cause a significant increase of OTR(max), a, and k(L). An OTR(max) of up to 0.15 mol/L/h can be reached in square-shaped wells.     

Mass transfer correlations for rotating drum bioreactors

Evaporative cooling is extremely important for large-scale operation of rotating drum bioreactors (RDBs). Outlet water vapour concentrations were measured for a RDB containing wet wheat bran with the aim of determining the mass transfer coefficient for evaporation from the bran bed to the headspace. Mass transfer was expressed as the mass transfer coefficient times the area for transfer per unit volume of void space in the drum. Values of ka' were determined under combinations of aeration superficial velocities ranging from 0.006 to 0.017 ms(-1) and rotation rates ranging from 0 to 9 rpm. Mass transfer coefficients were evaluated using a variety of residence time distributions (RTDs) for flow in the gas phase including plug flow and well-mixed and a Central Jet RTD based on RTD studies. If plug flow is assumed, the degree of holdup at low effective Peclet (Pe(eff)) numbers gives an apparent under-estimate of ka' compared with empirical correlations. Values of ka' calculated using the Central Jet RTD agree well with values of ka' from literature correlations. There was a linear relationship between ka' and effective Peclet number: ka' = 2.32 x 10(-3)Pe(eff).     

Implications of non-uniform stomatal closure on gas exchange calculations

Abstract. This paper discusses the consequences of non-uniform (= patchwise) stomatal closure on the estimation of gas exchange parameters. The estimation of the partial pressure of internal CO₂ (c_i) appears to be little sensitive to complete non-uniform stomatal closure. During the process of closure of these patches, however, a lower c_i will be calculated. For gas exchange measurements done at low wind speeds, it can be shown that an error is made in the partitioning of the total vapour transfer resistance into boundary layer and stomatal resistance. This error influences the calculated total transfer resistance of gases other than water vapour (e.g. CO₂). The apparent negative internal gas concentrations that have sometimes been found in fumigation experiments with SO₂ can possibly be explained by this error.     

The effect of changing the gaseous diffusion coefficient on the mass loss pattern of Hyalophora cecropia pupae

The importance of gas phase diffusion in insect gas exchange remains unclear. The role of diffusion in gas exchange of developing Hyalophora cecropia pupae was examined by altering the gaseous diffusion coefficient in the breathing mixture. Gaseous diffusion coefficients were manipulated by substituting helium or sulfur hexafluoride for the nitrogen usually present in air. Sensitive mass loss recordings were employed to monitor gas exchange activity. Mass loss recordings showed a two-phase cycle, open and closed-flutter. Mass loss rates during the open and closed-flutter periods were not altered in proportion to the changes induced in the rate of diffusion. Open-phase duration was inversely and proportionally related to the diffusion coefficient. These results are consistent with changes in spiracle resistance or convective flow during the open period in response to a change in the diffusion coefficient. In addition, they indicate a significant gas phase diffusive resistance within the pupal tracheal system. This previously unreported gas phase resistance appears to be a major determinant of the duration of the open period and thus of overall water loss rates in these pupae.     

Improvement of mass transfer characteristics and productivities of inclined tubular photobioreactors by installation of internal static mixers

The feasibility of improving mass transfer characteristics of inclined tubular photobioreactors by installation of static mixers was investigated. The mass transfer characteristics of the tubular photobioreactor varied depending on the type (shape) and the number of static mixers. The volumetric oxygen transfer coefficient ( k(L)a) and gas hold up of the photobioreactor with internal static mixers were significantly higher than those of the photobioreactor without static mixers. The k(L)a and gas hold up increased with the number of static mixers but the mixing time became longer due to restricted liquid flow through the static mixers. By installing the static mixers, the liquid flow changed from plug flow to turbulent mixing so that cells were moved between the surface and bottom of the photobioreactor. In outdoor culture of Chlorella sorokiniana, the photobioreactor with static mixers gave higher biomass productivities irrespective of the standing biomass concentration and solar radiation. The effectiveness of the static mixers (average percentage increase in the productivities of the photobioreactor with static mixers over the productivities obtained without static mixers) was higher at higher standing biomass concentrations and on cloudy days (solar radiation below 6 MJ m(-2) day(-1)).     

The Diffusion of Oxygen, Carbon Dioxide, and Inert Gas in Flowing Blood

Measurements were made of exchange rates of oxygen, carbon dioxide, and krypton-85 with blood at 37.5°C. Gas transfer took place across a 1 mil silicone rubber membrane. The blood was in a rotating disk boundary layer flow, and the controlling resistance to transfer was the concentration boundary layer. Measured rates were compared with rates predicted from the equation of convective diffusion using velocities derived from the Navier-Stokes equations and diffusivities calculated from the theory for conduction in a heterogeneous medium. The measured absorption rate of krypton-85 was closely predicted by this model. Significant deposition of material onto the membrane surface, resulting in an increased transfer resistance, occurred in one experiment with blood previously used in a nonmembrane type artificial lung. The desorption rate of oxygen from blood at low P_o2¹ was up to four times the corresponding transfer rate of inert gas. This effect is described somewhat conservatively by a local equilibrium form of the convective diffusion equation. The carbon dioxide transfer rate in blood near venous conditions was about twice that of inert gas, a rate significantly greater than predicted by the local equilibrium theory. It should be possible to apply these theoretical methods to predict exchange rates with blood flowing in systems of other geometries.     

Performance of a shaking vessel with current pole

To improve solid particle suspensions in liquids in a shaking vessel, a pole was installed at the axis of the shaking vessel, which was referred to as the "current pole". The performance of a shaking vessel with current pole at its central axis was examined experimentally with respect to particle dispersion, power consumption, mixing time and solid-liquid mass transfer coefficient. The current pole improved the particle suspension without an increase in power consumption and reduced the critical circulating frequency for complete suspension. The current pole was very effective in eliminating the stagnation point on the vessel bottom and to decrease the mixing time. The mass transfer coefficient with a current pole had the same value as that without a current pole above the critical circulating frequency for complete suspension. As the diameter of the current pole increased, the mixing time decreased. A pole diameter of 5% of the vessel diameter was effective for suspension.     

Hydrodynamics and mass transfer of CO2 in water in a tubular photobioreactor

Microalgae cultivation has received growing importance because of its potential applications in CO₂ bio‐fixation, wastewater treatment and biofuel production. In this regard, proper design of photobioreactors is crucial for large‐scale commercial applications. The hydrodynamics of a photobioreactor has great influence on the transfer of CO₂ from gas phase to liquid phase. Considering the facts, the present research focused on studying the gas holdups and mass transfer from the gas to liquid phase in a tubular photobioreactor at various superficial liquid velocities ranging from 8.4 to 22.4 cm/s and superficial gas velocities ranging from 3.66 to 8.1 cm/s. It was found that the gas holdups were radially distributed. The highest gas holdups were observed at the center zone while the lowest holdups are found near the reactor wall. CO₂ mass transfer coefficient in the photobioreactor was also estimated under different superficial liquid velocities (0.206, 0.355 and 0.485 cm/s) and gas velocities (0.67, 1.16 and 1.37 cm/s). The overall mass transfer coefficient was estimated by fitting the experimental data and comparing results with an unsteady state differential mole balance equation solved by Runge‐Kutta‐Gill method. Model predictions were comparable to experimental results.     

CFD analysis of the turbulent flow in baffled shake flasks

In this work, computational fluid dynamics (CFD) technique is used to simulate the complicated unsteady-state turbulent flow field formed in baffled flask. The baffled flask shows advantages both in mass transfer capacity and in shear formation in comparison with unbaffled flasks. Detailed investigations of power consumption, mass transfer and shear rate are carried out in baffled flasks under shaking frequencies ranging from 100 rpm to 250 rpm, and filling volumes from 50 mL to 150 mL. The results show that the specific power input and specific interface area are both greatly influenced by shaking frequency and filling volume. For the positive effect of shaking frequency on both mass transfer coefficient (k_L) and specific interface area (a), the volumetric mass transfer coefficient (k_La) increases greatly with shaking frequency. Results also show that filling volume has no significant effect on k_L but negative effect on specific interface area. Shear force formed in baffled flask shows great dependent on shaking frequency, but it is insensitive to the filling volume. Based on these investigations, correlations linking these parameters are proposed. Finally, cultivations of filamentous fungus conducted in unbaffled and baffled flasks validated the simulating results.     

Region-dependent oxygen transfer rate in the rectangular airlift reactor

Gas hold-up and the oxygen transfer in the zones of the internal loop airlift reactor with rectangular cross-section was studied. It was found, that the downcomer to the riser gas hold-up ratio depends on the gas flow rate, the physicochemical properties of the system and on the reactor height. The ratio of the downcomer mass transfer coefficient to the global mass transfer coefficient was less than 6%. The ratio of the downcomer to the global mass transfer coefficient slightly increased with increase of the gas flow rate and decreased with increase of the liquid viscosity. The proposed correlation for the global overall mass transfer coefficient predicts the experimental data well within 16.6% deviation. It was confirmed that the reactor height is the important parameter for a design and a scale-up of the airlift reactors.     

Diffusion and reaction within porous packing media: a phenomenological model

A phenomenological model has been developed to describe biomass distribution and substrate depletion in porous diatomaceous earth (DE) pellets colonized by Pseudomonas aeruginosa. The essential features of the model are diffusion, attachment and detachment to/from pore walls of the biomass, diffusion of substrate within the pellet, and external mass transfer of both substrate and biomass in the bulk fluid of a packed bed containing the pellets. A bench-scale reactor filled with DE pellets was inoculated with P. aeruginosa and operated in plug flow without recycle using a feed containing glucose as the limiting nutrient. Steady-state effluent glucose concentrations were measured at various residence times, and biomass distribution within the pellet was measured at the lowest residence time. In the model, microorganism/substrate kinetics and mass transfer characteristics were predicted from the literature. Only the attachment and detachment parameters were treated as unknowns, and were determined by fitting biomass distribution data within the pellets to the mathematical model. The rate-limiting step in substrate conversion was determined to be internal mass transfer resistance; external mass transfer resistance and microbial kinetic limitations were found to be nearly negligible. Only the outer 5% of the pellets contributed to substrate conversion. (c) 1993 Wiley & Sons, Inc.     

Gas-liquid mass transfer in bioreactor with three-phase inverse fluidized bed

In the present study the oxygen mass transfer from the gas to the aqueous phase in a Three-Phase Inverse Fluidized Bed (TPIFB) has been studied. A pilot scale TPIFB has been designed and constructed. For determination of the volumetric oxygen mass transfer coefficient the elegant dynamic method, described by Dang et al. (1977) was used. The influence of hydrodynamic parameters, e.g., superficial velocities of the gas and liquid phases on the mass transfer rate was studied. In the range of variables covered, it was found that the superficial liquid velocity had a weak effect on the mass transfer whereas the gas flowrate affects the mass transfer positively. The results for the volumetric oxygen transfer coefficient in the TPIFB were compared to reported values of that coefficient, measured in a classic three-phase fluidised bed under similar hydrodynamic conditions and solid phase properties. The comparison demonstrated a two-fold increase of the oxygen transfer rate in the inverse bed over that in the classic one.     

Development of a strategy to control the dissolved concentrations of oxygen and carbon dioxide at constant shear in a plant cell bioreactor

To examine the effects of volatile components on plant cell growth, a bioreactor control system was developed to simultaneously control the dissolved concentrations of both oxygen and carbon dioxide. The first step in this work was to develop a mathematical model to account for gas-liquid mass transfer; biological utilization and production of O(2) and CO(2); and the series of chemical reactions of CO(2) in water. Using this model and dynamic measurements for dissolved O(2) and CO(2), it was observed that (1) both absorption and desorption of a volatile component could be described by a single mass transfer coefficient, K(l)a, and (2) K(l)a values for oxygen and carbon dioxide transfer were directly proportional. The second step of this work was to employ the mathematical model in an adaptive feed-forward strategy to control the dissolved O(2) and CO(2) concentrations by manipulating the inlet gas composition to the bioreactor. This strategy allowed dissolved concentrations to be controlled without the need for changing either the total gas flow rate or agitator speed. Adaptive control was required because the volumetric rates of O(2) and CO(2) consumption and production vary with time during long term operation and therefore these rates must be continually updated. As the final step, we demonstrated that this control strategy was capable of controlling the dissolved gas concentrations in both short- and long-term studies involving the cultivation of Catharanthus roseus plant cells.     

Heat and water rate transfer processes in the human respiratory tract at various altitudes

The process of the respiratory air conditioning as a process of heat and mass exchange at the interface inspired air-airways surface was studied. Using a model of airways (Olson et al., 1970) where the segments of the respiratory tract are like cylinders with a fixed length and diameter, the corresponding heat transfer equations, in the paper are founded basic rate exchange parameters-convective heat transfer coefficient h(c)(W m(-2) degrees C(-1)) and evaporative heat transfer coefficient h(e)(W m(-2)hPa(-1)). The rate transfer parameters assumed as sources with known heat power are connected to airflow rate in different airways segments. Relationships expressing warming rate of inspired air due to convection, warming rate of inspired air due to evaporation, water diffused in the inspired air from the airways wall, i.e. a system of air conditioning parameters, was composed. The altitude dynamics of the relations is studied. Every rate conditioning parameter is an increasing function of altitude. The process of diffusion in the peripheral bronchial generations as a basic transfer process is analysed. The following phenomenon is in effect: the diffusion coefficient increases with altitude and causes a compensation of simultaneous decreasing of O(2)and CO(2)densities in atmospheric air. Due to this compensation, the diffusion in the peripheral generations with altitude is approximately constant. The elements of the human anatomy optimality as well as the established dynamics are discussed and assumed. The square form of the airways after the trachea expressed in terms of transfer supposes (in view of maximum contact surface), that a maximum heat and water exchange is achieved, i.e. high degree of air condition at fixed environmental parameters and respiration regime.     

Study of gaseous substrate fermentations: carbon monoxide conversion to acetate. 2. Continuous culture

The fermentation of gaseous substrates such as CO, H(2), and CO(2) may be performed in a continuous stirred tank reactor, as well as the traditional batch reactor. In this article, the conversion of carbon monoxide by Peptostreptococcus productus is demonstrated in a stirred tank reactor under both mass transfer-controlled and nonmass transfer-controlled conditions. Utilizing a non-steady-state procedure, intrinsic rates are evaluated under non-mass transfer-controlled conditions in a time period of only 5-6 hours. A steady-state procedure was used to evaluate CSTR performance under mass transfer-controlled conditions. The mass transfer coefficient was calculated, followed by the development of a model to predict CSTR behavior for this gas phase substrate.