Mathematical model for a three-phase fluidized bed biofilm reactor in wastewater treatment

A mathematical model for a three phase fluidized bed bioreactor (TFBBR) was proposed to describe oxygen utilization rate, biomass concentration and the removal efficiency of Chemical Oxygen Demand (COD) in wastewater treatment. The model consisted of the biofilm model to describe the oxygen uptake rate and the hydraulic model to describe flow characteristics to cause the oxygen distribution in the reactor. The biofilm model represented the oxygen uptake rate by individual bioparticle and the hydrodynamics of fluids presented an axial dispersion flow with back mixing in the liquid phase and a plug flow in the gas phase. The difference of settling velocity along the column height due to the distributions of size and number of bioparticle was considered. The proposed model was able to predict the biomass concentration and the dissolved oxygen concentration along the column height. The removal efficiency of COD was calculated based on the oxygen consumption amounts that were obtained from the dissolved oxygen concentration. The predicted oxygen concentration by the proposed model agreed reasonably well with experimental measurement in a TFBBR. The effects of various operating parameters on the oxygen concentration were simulated based on the proposed model. The media size and media density affected the performance of a TFBBR. The dissolved oxygen concentration was significantly affected by the superficial liquid velocity but the removal efficiency of COD was significantly affected by the superficial gas velocity. An erratum to this article can be found online at .     

Optimising Cell Aggregate Expansion in a Perfused Hollow Fibre Bioreactor via Mathematical Modelling

The need for efficient and controlled expansion of cell populations is paramount in tissue engineering. Hollow fibre bioreactors (HFBs) have the potential to meet this need, but only with improved understanding of how operating conditions and cell seeding strategy affect cell proliferation in the bioreactor. This study is designed to assess the effects of two key operating parameters (the flow rate of culture medium into the fibre lumen and the fluid pressure imposed at the lumen outlet), together with the cell seeding distribution, on cell population growth in a single-fibre HFB. This is achieved using mathematical modelling and numerical methods to simulate the growth of cell aggregates along the outer surface of the fibre in response to the local oxygen concentration and fluid shear stress. The oxygen delivery to the cell aggregates and the fluid shear stress increase as the flow rate and pressure imposed at the lumen outlet are increased. Although the increased oxygen delivery promotes growth, the higher fluid shear stress can lead to cell death. For a given cell type and initial aggregate distribution, the operating parameters that give the most rapid overall growth can be identified from simulations. For example, when aggregates of rat cardiomyocytes that can tolerate shear stresses of up to are evenly distributed along the fibre, the inlet flow rate and outlet pressure that maximise the overall growth rate are predicted to be in the ranges to (equivalent to to ) and to (or 15.6 psi to 15.7 psi) respectively. The combined effects of the seeding distribution and flow on the growth are also investigated and the optimal conditions for growth found to depend on the shear tolerance and oxygen demands of the cells.     

Automatic control of isolated organ perfusion.

If provided with adequate physiological conditions explanted hearts may continue to operate in the regular beating mode. This property offers the opportunity to substitute extensive animal experiments by investigations on the isolated organs. At the same time it enables the development of an alternative method for the transport of donor hearts for transplantation. Experimental setups for both applications are described in this paper. The focus is laid on the optimisation of handling and effectiveness of these setups by means of automatic control. The method for investigating the controlled system ("plant") for blood gas exchange, and especially the determination of the transfer function for the partial pressure of oxygen are described. The plant was triggered with stepwise changes on the gas side at several operating points. A first order lag element with time delay was chosen as approximation of every transfer function. The parameter 'time delay', 'gain of the plant' and 'time constant' were analysed as to the dependency on blood flow rate, gas flow rate and partial pressure of oxygen at the blood outlet of the oxygenator. As a result an equation was found to calculate the time delay from gas flow rate and blood flow rate. Correlation of gain and time constant with parameters of the plant were obtained, too. The data is used for the design of a controller, adapting to the different operating points of the plant.     

Carbon dioxide uptake efficiency by outdoor microalgal cultures in tubular airlift photobioreactors

The influence of solar irradiance and carbon dioxide molar fraction of injected CO(2)-air mixtures on the behavior of outdoor continuous cultures of the microalga Phaeodactylum tricornutum in tubular airlift photobioreactors was analyzed. Instantaneous solar irradiance, pH, dissolved oxygen, temperature, biomass concentration, and the mass flow rates of both the inlet and outlet oxygen and carbon with both the liquid and gas phases were measured. In addition, elemental analysis of the biomass and the cell-free culture medium was performed. The oxygen production rate and carbon dioxide consumption rate increased hyperbolically with the incident solar irradiance on the reactor surface. Carbon losses showed a negative correlation with the daily variation of the carbon dioxide consumption rate. The maximum CO(2) uptake efficiency was 63% of the CO(2) supplied when the CO(2) concentration in the gas supplied was 60% v/v. Carbon losses were >100% during the night, due to CO(2) production by respiration, and hyperbolically decreased to values of 10% to 20% in the midday hours. An increase in the carbon fixed in the biomass with the solar cycle was observed. A slight daily decrease of carbon content of the cell-free culture medium indicated the existence of carbon accumulation in the culture. A decrease in CO(2) molar fraction in the injected gas had a double benefit: first, the biomass productivity of the system was enhanced from 2.05 to 2.47 g L(-1) day(-1) by reduction of CO(2) inhibition and/or pH gradients; and second, the carbon losses during the daylight period were reduced by 60%. The fluid dynamics in the reactor also influenced the carbon losses: the higher the liquid flow rate the higher the carbon losses. By using a previous mass transfer model the experimental results were simulated and the usefulness of this method in the evaluation and scale-up of tubular photobioreactors was established.     

A Fermentor System for Regulating Oxygen at Low Concentrations in Cultures of Saccharomyces cerevisiae

The growth of yeast cells to high densities at low, but constant, oxygen concentrations is difficult because the cells themselves respire oxygen; hence, as cell mass increases, so does oxygen consumption. To circumvent this problem, we have designed a system consisting of a computer-controlled gas flow train that adjusts oxygen concentration in the gas flow to match cellular demand. It does this by using a proportional-integral-differential algorithm in conjunction with a three-way valve to mix two gases, adjusting their proportions to maintain the desired oxygen concentration. By modeling yeast cell yields at intermediate to low oxygen concentrations, we have found that cellular respiration declines with oxygen concentration, most likely because of a decrease in the expression of genes for respiratory proteins. These lowered rates of oxygen consumption, together with the gas flow system described here, allow the growth of yeast cells to high densities at low oxygen concentrations. This system can also be used to grow cells at any desired oxygen concentration and for regulated shifts between oxygen concentrations.     

Gas Exchange of Algae: III. Relation between the Concentration of Carbon Dioxide in the Nutrient Medium and the Oxygen Production of Chlorella pyrenoidosa

The oxygen production of a photosynthetic gas exchanger containing Chlorella pyrenoidosa (1% packed cell volume) was measured when various concentrations of carbon dioxide were present within the culture unit. The internal carbon dioxide concentrations were obtained by manipulating the entrance gas concentration and the flow rate. Carbon dioxide percentages were monitored by means of electrodes placed directly in the nutrient medium. The concentration of carbon dioxide in the nutrient medium which produced maximal photosynthesis was in the range of 1.5 to 2.5% by volume. Results were unaffected by either the level of carbon dioxide in the entrance gas or the rate of gas flow. Entrance gases containing 2% carbon dioxide flowing at 320 ml/min, 3% carbon dioxide at 135 ml/min, and 4% carbon dioxide at 55 ml/min yielded optimal carbon dioxide concentrations in the particular unit studied. By using carbon dioxide electrodes implanted directly in the gas exchanger to optimize the carbon dioxide concentration throughout the culture medium, it should be possible to design more efficient large-scale units.     

Indirect estimation of cell mass and substrate concentration using a computer-coupled mass spectrometer

On-line estimation of cell mass and substrate concentration based on exhaust gas analysis was developed. The O₂, CO₂, H₂O, and N₂ contents at the inlet and outlet of fermentor, analyzed by a computer-coupled quadrupole mass spectrometer, were used to calculate the oxygen uptake rate and carbon dioxide evolution rate, and these rates were further used to evaluate cell mass and substrate concentration in a recombinant Escherichia coli fermentation. Cell mass, glucose concentration, specific growth rate, and specific consumption rate of glucose were well estimated by this method; the oxygen uptake rate gave more accurate estimates for these state variables than did the carbon dioxide evolution rate.     

Growth kinetics and cellulase biosynthesis in the continuous culture of Trichoderma viride.

Continuous culture studies have been carried out growing Trichoderma viride QM 9123 in a 10 liter stirred fermentor on a medium containing commercial glucose as the carbon source. Experiments were carried out at 30 degrees C and at three controlled pH values of 2.5, 3.0, and 4.0 over a range of dilution rates from 0.01 to 0.11 hr-1. Steady-state values of cell, glucose, and cellulase concentration oxygen tension, and outlet gas oxygen partial pressure were recorded. Values of maximum specific growth rate, endogenous metabolism coefficient, Michaelis-Menten coefficient, yield and maintenance coefficient for glucose were derived and correlated the effect of the hydrogen ion concentration. Specific oxygen uptake rates were correlated with specific growth rates and absorption coefficients were shown to be a function of dilution rate independent of pH. Some data on cellulase biosynthesis were examined and correlated in terms of a maturation time model.     

High cell density suspension culture of mammalian anchorage independent cells: Oxygen transfer by gas sparging and defoaming with a hydrophobic net

Gas sparging directly into the culture-broth is not done in cell culture, except when the gas flow rate is very small, because much foaming occurs.During screening of defoaming methods, foam was observed to be broken up effectively when it made contact with a net fabricated from hydrophobic materials. Providing a highly efficient oxygen supply to suspension culture was tried using the new defoaming method. In a 5 1 reactor equipped with the foam-eliminating net fabricated with polysiloxane, oxygen was transferred at 21 mmole/l·h equivalent to an about forty-fold higher rate than in conventional surface aeration. This was equivalent to a consumption rate of 1×10⁸ cells/ml, even at a low oxygen gas flow rate of 0.1 cm/s corresponding to a fourth of the gas flow rate when foam leaked through the net.Perfusion culture of rat ascites hepatoma cell JTC-1 was successfully carried out in the 51 scale culture system with the net and a hydrophobic membrane for cell filtration. The viable cell concentration reached 2.7×10⁷ cells/ml after twenty-seven days, in spite of the nutrient-deficient condition of the lower medium exchange rate, that is, a working volume a day, and viability was maintained at more than 90%. In a 1.21 scale culture of mouse-mouse hybridoma cell STK-1, viable cell concentration reached 4×10⁷ cells/ml. These results showed that oxygen transfer by gas sparging with defoaming was useful for high density suspension culture. A foam-breaking mechanism was proposed.Abbreviations Eagle's MEM Eagle's minimal essential medium - Dulbecco's modified Eagle MEM Dulbecco's modified Eagle minimal essential medium     

Simultaneous measurement of acetylene reduction and respiratory gas exchange of attached root nodules

A method was developed for the simultaneous measurement of acetylene reduction, carbon dioxide evolution and oxygen uptake by individual root nodules of intact nitrogen-fixing plants (Alnus rubra Bong.). The nodules were enclosed in a temperature-controlled leak-tight cuvette. Assay gas mixtures were passed through the cuvette at a constant, known flow rate and gas exchange was measured by the difference between inlet and outlet gas compositions. Gas concentrations were assayed by a combination of an automated gas chromatograph and a programmable electronic integrator. Carbon dioxide and ethylene evolution were determined with a coefficient of variation which was less than 2%, whereas the coefficient of variation for oxygen uptake measurements was less than 5%. Nodules subjected to repeated removal from and reinsertion into the cuvette and to long exposures of 10% v/v acetylene showed no irreversible decline in respiration or acetylene reduction. This system offers long-term stability and freedom from disturbance artifacts plus the ability to monitor continuously, rapidly and specifically the changes in root nodule activity caused by environmental perturbation.     

Aerobic oxidation of hydrogen sulfide by Thiobacillus denitrificans

It has been demonstrated that Thiobacillus denitrificans may be readily cultured aerobically in batch and continuous flow reactors on H(2)S(g) under sulfide limiting conditions. Under these conditions sulfide concentrations in the culture medium were less than 1muM resulting in very low concentrations of H(2)S in the reactor outlet gas. Biomass yield under aerobic conditions was much lower than previously reported for anaerobic conditions, presumably because of oxygen inhibition of growth. However, biomass yield was not affected by steady state oxygen concentration in the range of 45muM-150muM. Biomass yield was also observed to be essentially independent of specific growth rate in the range of 0.030-0.053 h(-1). Indicators of reactor upset were determined and recovery from upset conditions demonstrated. Maximum loading of the biomass for H(2)S oxidation under aerobic conditions was observed to be 15.1-20.9 mmol/h/g biomass which is much higher than previously reported for aerobic conditions. Other aspects of the stoichiometry of aerobic H(2)S oxidation are also reported.     

Continuous cultivation of Saccharomyces cerevisiae. II. Growth on ethanol under transient-state conditions

Growth of Saccharomyces cerevisiae LBG H 1022 on ethanol under transient-state conditions was studied. As a cultivation device, an aerated Chemap fermentor combined with continuously working gas analyzers for oxygen and carbon dioxide was used. Yeast cell dry matter, substrate concentration, specific oxygen uptake, specific carbon dioxide release, and respiration quotient were measured during the different transient states. Depending on which range of the dilution rate the initial steady state was found, we obtain different responses to the shift experiment. For the lower range, up to D = 0.07, we deal with damped oscillations ranging above and below the steady-state values. For the higher specific growth rates, the rate of damping is strongly enhanced and the shape of the curves becomes an asymptotic approach to the final steady states.     

Pressure drop,gas hold-up,and oxygen transfer in tower systems

Pressure drop, gas hold-up, and oxygen transfer were investigated in a sieve tray column, a column with Koch motionless mixers, and a bubble column. The oxygen transfer experiments were conducted using cocurrent flow of gas and liquid under steady-state conditions with oxygen transfer from the gas to the liquid phase. The oxygen transfer rates and efficiencies of the sieve tray column and the column with Koch mixers were found to be superior to those of the conventional bubble column. Gas hold-up was also greater when sieve trays or Koch mixers were inserted in the tower. The pressure drop was found to be primarily due to the liquid head in all three columns.     

Effect of serum concentration on hybridoma viable cell density and production of monoclonal antibodies in CSTRs and on shear sensitivity in air-lift loop reactors

The death rate of hybridoma cells, grown in a continuous culture, has been studied in a small air-lift loop reactor as a function of reactor height and injected gas flow rate. The first-order death-rate constant was found to be proportional to the reciprocal height and to the gas flow rate, in accordance with the hypothetical killing volume model for insect cells in bubble columns. Furthermore, the effect of the serum concentration on viable cell concentration and cell productivity has been investigated in a continuous culture. A serum component became growth limiting when the serum concentration was decreased from 2% to 1%. No effect of the serum concentration on specific cell productivity could be measured. Samples from this culture were also studied in the air-lift loop reactor to determine the effect of serum concentration on the shear sensitivity. The cells' shear sensitivity increased with decreasing serum concentration. The protective effect of serum was found to be physical as well as physiological.     

A molecular dynamics analysis of homogeneous bubble nucleation with a noncondensable gas in cryogenic cavitation inception

In this paper, homogeneous bubble nucleation in liquid oxygen (as one of the cryogenic fluids) with a noncondensable gas of nitrogen or that of helium was investigated using molecular dynamics method employing a fitted Lennard-Jones potential. We evaluated the influence of nitrogen gas and helium gas on the SATuration line (SAT) and the spinodal line as the thermodynamic limit of stability (TLS), and on the kinetic limit of stability (KLS) defined from a bubble nucleation rate. As a result, it was obtained that the influence of the noncondensable gases on the SAT and the TLS was negligible at molar fraction less than 1% although helium gas had several times stronger action to decrease the KLS compared with nitrogen gas. On the other hand, it was also indicated that the actual influence of both noncondensable gases on the cavitation inception in liquid oxygen might be negligible at least at standard conditions where the fluid starts to flow around or less than the atmospheric pressure.     

Oxygen and carbon monoxide kinetics of Glycera dibranchiata monomeric hemoglobin.

Oxygen and carbon monoxide kinetics of Glycera dibranchiata monomeric hemoglobin have been studied using laser photolysis, air flash, and stopped flow techniques. The reactions of this hemoglobin with both ligands were found to be more rapid than the corresponding reactions involving myoglobin and were also biphasic in nature, the rate constants being approximately an order of magnitude different for the fast and slow phases in each case. No pH or hemoglobin concentration dependence of the pseudo-first order rate constants was apparent between pH 6 and 9 and in the concentration range of 1.25 to 40 muM heme. Both fast and slow pseudo-first order oxygen combination rate constants varied linearly with oxygen concentration between 16 and 1300 muM. A first order slow relaxation was also noted which was linearly dependent on heme concentration and inversely dependent on oxygen concentration. This reaction has been shown to be due to a replacement of oxygen by carbon monoxide. The presence of this reaction is a result of the high affinity of Glycera monomer for carbon monoxide as shown by the partition coefficient Mr = approximately 20,000 ana an equilibrium dissociation constant of the order L = 1.1 X 10(-9) M.     

Two-tier vessel for photoautotrophic high-density cultures

Two-tier vessels, developed for culturing of microalgae and cyanobacteria at high cell density on a shaken platform, were assembled from a flat lower chamber to be filled with a CO₂ buffer and an upper flat sterile chamber for the culture that was separated from the lower chamber by a porous polypropylene membrane. Diffusive gas exchange with the atmosphere was controlled by the O₂ outlet channel. Referred to surface area, rates of CO₂ transfer to a shaken weakly alkaline buffer solution across the membrane were higher than those reached on the conventional pathway through the free upper liquid surface. Membrane-mediated CO₂ supply enabled rapid growth of Synechocystis sp. PCC 6803 and Synechococcus sp. PCC 7002 up to ultrahigh cell density. The biomass (dry weight) concentration of Synechococcus cultures reached more than 30 g L^?1 on a buffered medium with adequate concentrations of mineral nutrients. An increase of 15 to 20 g L^?1 was observed during repeated two-day cycles. Separate pathways for CO₂ supply and oxygen outlet prevented significant loss of CO₂. Convective gas flow through the oxygen outlet channel enabled the estimation of the O₂ generation rate. The permeability of the channel for diffusive O₂/N₂ exchange limited the O₂ concentration to a moderate value. It is concluded that shaken flat cultures using CO₂ supply through a porous hydrophobic membrane and diffusive release of O₂ through a separate pathway are promising for research on microalgae and cyanobacteria.     

Batch culture of Alcaligenes eutrophus ATCC 17697T using recycled gas closed circuit culture system

Batch culture of Alcaligenes eutrophus ATCC 17697^T using the recycled gas closed circuit culture system was done with the intention of developing a practical fermentation system for industrial culture of autotrophs. The gas phase of the culture system consisted of substrate gas so that gases in this culture system could be recycled forever as long as the amount of the gas consumed would be refilled. All gasses supplied into this system could be completely used without any loss as exhaust. Thus, this system assures high gas usage efficiency as well as operation safety. Studies on the effect of oxygen concentration showed the high oxygen concentration in substrate gas mixture suppressed the specific growth rate while a low oxygen concentration promoted the growth rate. This introduced the possibility of development of an explosion-free fermentation system with a high growth rate if appropriate system design and fermentation conditions were given. Since this system is closed, material balance and elementary analysis provide the ultimately accurate stoichiometry of the autotrophic culture of this bacterium.     

A new method for breath-to-breath determination of oxygen flux across the alveolar membrane

A new method for breath-to-breath determination of the oxygen flux across the alveolar membrane is described. The principle of the method is to integrate the product of oxygen concentration and flow in the respiratory gas over an interval, which covers a complete respiratory cycle. The result is corrected for the change in oxygen content of the lungs through a formula, which, in contrast to those used in other methods, is independent of the residual capacity of the lungs. The method was evaluated with respect to repeatability by repetitive measurement of oxygen flux in twenty volunteer subjects, and with respect to accuracy by comparing the measured oxygen fluxes with those obtained by the gas collection method. The coefficient of variation was found to be 8% and the breath to breath determinations were, on an average, 6% lower than those of the gas collection method.     

Computer simulation of damped oscillations during peroxidase-catalyzed oxidation of indole-3-acetic acid

Oscillation patterns in horseradish peroxidase (HRP)-catalyzed oxidation of indole-3-acetic acid (IAA) at neutral pH were studied using computer simulation. Under certain conditions, such as the presence of a reaction promoter and continuous intake of oxygen from the gaseous phase, the simulated system exhibits damped oscillations of the concentrations of oxygen in the aqueous phase, [O(2)](aq), and of all the reaction intermediates. The critical concentration of oxygen in aqueous phase, [O(2)](cr)(aq), was used to describe the nature of the oscillations. The critical concentration is the concentration at which the system abruptly changes its properties. If [O(2)](aq) is higher than [O(2)](cr)(aq) then the reaction develops as an avalanche, otherwise, the reaction stops. The nature of oscillations is accounted for by the interaction of two processes: the consumption/accumulation of oxygen and the accumulation/consumption of reaction intermediates. Oscillations are always damped. Neither HRP or umbelliferone (Umb) deactivation nor IAA consumption can account for the damping. The nature of the damping is determined by the termination reactions of free radical intermediates and ROOH. The three major parameters of oscillations: period of oscillations, initial amplitude of oscillations and the rate of damping were studied as functions of: (i) oxygen concentration in the gaseous phase, (ii) initial oxygen concentration in aqueous phase, (iii) the concentration of IAA and (iv) the initial concentration of HRP.