An experimental study of mass diffusion and reaction rate in an anaerobic biofilm

An experimental reactor consisting of two chambers, separated by a porous ceramic immobilization matrix, was constructed to measure the effective diffusivity of different compounds and the consumption rates of acetate in developing biofilms. In initial experiments, effective diffusivities for acetate, propionate, isopropanol, and lithium salt through the ceramic immobilization matrix in the absence of biofilm were determined to be 40% to 50% less than in water at infinite dilution. The effective diffusivity of the lithium salt was similar to that of acetate. The effective diffusivity of the lithium salt through biofilms of thickness in the range of 200 to 1200 mum was essentially constant with a value of approximately 7% of that in water at infinite dilution. Acetate consumption in the biofilm was linearly proportional to biofilm thickness up to a biofilm depth of 800 mum. Deviation from linearity appeared in biofilm thicknesses greater than 800 mum. Results of these experiments support previous reports that immobilized cell reactors have significantly higher bioconversion rates than suspended cell systems.     

Mathematical analysis of two-phase mass transfer in a batch reactor for the chemical transformation of a steroid

A reactor is described for the conversion of the slightly water-soluble steroid testosterone (T) to 4-androstene-3, 17-dione (4-AD) by enzyme in the presence of excess cofactor. Since the enzyme is subject to substrate inhibition, reaction rates are strong functions of aqueous substrate concentration. High concentrations of the substrate, testosterone, per unit reactor volume are maintained within poly(dimethylsiloxane) beads that are suspended in the aqueous enzyme solution. Mass transfer (controlled by bead size, polymer to water volume ratio, enzyme loading) is used to control the degree and rate of conversion. The reactor dynamics are predicted over a wide range of reaction conditions. The product steroid is recovered in the polymeric beads from the enzyme solution.     

Stoichiometry and kinetics of poly-beta-hydroxybutyrate metabolism in aerobic, slow growing, activated sludge cultures

This paper discusses the poly-beta-hydroxybutyrate (PHB) metabolism in aerobic, slow growing, activated sludge cultures, based on experimental data and on a metabolic model. The dynamic conditions which occur in activated sludge processes were simulated in a 2-L sequencing batch reactor (SBR) by subjecting a mixed microbial population to successive periods of external substrate availability (feast period) and no external substrate availability (famine period). Under these conditions intracellular storage and consumption of PHB was observed. It appeared that in the feast period, 66% to almost 100% of the substrate consumed is used for storage of PHB, the remainder is used for growth and maintenance processes. Furthermore, it appeared that at high sludge retention time (SRT) the growth rate in the feast and famine periods was the same. With decreasing SRT the growth rate in the feast period increased relative to the growth rate in the famine period. Acetate consumption and PHB production in the feast period both proceeded with a zero-order rate in acetate and PHB concentration respectively. PHB consumption in the famine period could best be described kinetically with a nth-order degradation equation in PHB concentration. The obtained results are discussed in the context of the general activated sludge models.     

Determination of diffusion coefficients and diffusion characteristics for chlorferon and diethylthiophosphate in Ca-alginate gel beads

Diffusion characteristics of chlorferon and diethylthiophosphate (DETP) in Ca-alginate gel beads were studied to assist in designing and operating bioreactor systems. Diffusion coefficients for chlorferon and DETP in Ca-alginate gel beads determined at conditions suitable for biodegradation studies were 2.70 x 10(-11) m(2)/s and 4.28 x 10(-11) m(2)/s, respectively. Diffusivities of chlorferon and DETP were influenced by several factors, including viscosity of the bulk solution, agitation speed, and the concentrations of diffusing substrate and immobilized cells. Diffusion coefficients increased with increasing agitation speed, probably due to poor mixing at low speed and some attrition of beads at high speeds. Diffusion coefficients also increased with decreasing substrate concentration. Increased cell concentration in the gel beads caused lower diffusivity. Theoretical models to predict diffusivities as a function of cell weight fraction overestimated the effective diffusivities for both chlorferon and DETP, but linear relations between effective diffusivity and cell weight fraction were derived from experimental data. Calcium-alginate gel beads with radii of 1.65-1.70 mm used in this study were not subject to diffusional limitations: external mass transfer resistances were negligible based on Biot number calculations and effectiveness factors indicated that internal mass transfer resistance was negligible. Therefore, the degradation rates of chlorferon and DETP inside Ca-alginate gel beads were reaction-limited.     

Determination of effective diffusion coefficient of substrate in gel particles with immobilized biocatalyst

A method of determining of the effective diffusion coefficient of substrate in a particle, where the diffusion and consumption of substrate by biocatalytic reaction are present simultaneously, was designed and experimentally verified. The method is based on measuring the overall rate of heterogeneous biocatalytic reaction in particles of varying diameter. The effective diffusion coefficient, D_e, was determined by fitting the measured reaction rates with the solution of the reaction-diffusion equation. The method is tailored for cases where the enzyme reaction is governed by the Michaelis-Menten kinetics. The value of K_m required for the solution of the mathematical model was adopted from the measurement of the kinetics of free cells, whereas the rate parameter, k₂, was optimized together with D_e. As an experimental model, the sucrose hydrolysis catalyzed by Ca-alginate-entrapped yeast cells was examined. The particle diameter varied in the range of 1.2–3.9 mm and the initial reaction rates were measured in a batch-stirred reactor at a sucrose concentration of 100 m . The D_e of sucrose at 30°C was found to be 2.9 · 10⁻¹⁰ m²s⁻¹.     

Some properties of a papain–agarose reactor provided with a pH monitor

A small reactor of immobilized papain was used to gain some knowledge about the effect of immobilization upon the reactivity of the enzyme towards one substrate and various types of inhibitors. A buffer solution containing benzoyl–arginine ethyl ester as substrate was run through a small column of papain immobilized by attachment to agarose beads. The pH of the effluent was measured continuously and provided the data used to calculate the substrate conversion during passage through the reactor. The operation of the system was checked by determining the substrate conversion as a function of flow rate. It proved to operate as theory demanded. The rate and extent of inhibition were measured after addition of various inhibitors to the buffer–substrate solution. The following quantities of immobilized papain were found to be equal within ±20% to those of the free enzyme in solution: the overall activity, the K_m of benzoyl–arginine ethyl ester, the K_i of the competitive inhibitor benzoylamino-acetonitrile, the rate of inactivation by chloroacetic acid and by chloroacetamide, the rate of activation by cysteine of the mixed disulfide of papain and cysteine, and the rate of spontaneous reactivation of the KCNO–papain adduct. The inactivation by KCNO proved to be strongly pH dependent. This may explain why the rate of the latter reaction is only 66% of the rate with free enzyme. It is concluded that the rates and equilibrium constants measured in the present reactor system are within ±20% of the values of the dissolved enzyme, provided that the reactions are not strongly pH dependent. Calculation showed there was no diffusion limitation.     

Dynamic modeling of immobilized cell reactor: application to ethanol fermentation

A mathematical model has been developed for the unsteady-state operation of an immobilized cell reactor. The substrate solution flows through a mixed-flow reactor in which cells immobilized in gel beads are retained. The substrate diffuses from the external surface of the gel beads to some internal location where reaction occurs. The product diffuses from the gel beads into liquid medium which flows out of the reactor. The model combines simultaneous diffusion and reaction, as well as cell growth, and it can predict how the rates of substrate consumption, product formation, and cell growth vary with time and with initial conditions. Ethanol fermentation was chosen as a representative reaction in the immobilized cell reactor, and numerical calculations were carried out. Excellent agreement was observed between model predictions and experimental data available in the literature.     

A silicone polymer as a Steroid Reservoir for enzyme-catalyzed Steroid reactions

Since steroids are only slightly soluble in the aqueous solutions in which enzymatic reactions take place, it is difficult to obtain high effective concentrations per unit reactor volume when enzymes are used to catalyze steroid reactions. In order to obtain high effective concentrations in the present work, we have used small particles of a hydrophobic polymer, poly (dimethyl siloxane), as a reservoir for the steroid substrate and product. The activity of a bacterial hydroxysteroid dehydrogenase in a buffer solution declines much more slowly in the presence of those polymer particles than in the presence of a comparable amount of butyl acetate or ethyl acetate, the organic solvents used as steroid reservoirs in previous work with steroid transforming enzymes. When another substrate of the hydroxysteroid dehydrogenase is loaded into the polymer particles and the particles are suspended in an aqueous solution containing the enzyme and its cofactor, more product is formed that when a similar solution is emulsified with butyl acetate.     

Mass transport in a microchannel bioreactor with a porous wall

A two-dimensional flow model has been developed to simulate mass transport in a microchannel bioreactor with a porous wall. A two-domain approach, based on the finite volume method, was implemented. For the fluid part, the governing equation used was the Navier-Stokes equation; for the porous medium region, the generalized Darcy-Brinkman-Forchheimer extended model was used. For the porous-fluid interface, a stress jump condition was enforced with a continuity of normal stress, and the mass interfacial conditions were continuities of mass and mass flux. Two parameters were defined to characterize the mass transports in the fluid and porous regions. The porous Damkohler number is the ratio of consumption to diffusion of the substrates in the porous medium. The fluid Damkohler number is the ratio of the substrate consumption in the porous medium to the substrate convection in the fluid region. The concentration results were found to be well correlated by the use of a reaction-convection distance parameter, which incorporated the effects of axial distance, substrate consumption, and convection. The reactor efficiency reduced with reaction-convection distance parameter because of reduced reaction (or flux), and smaller local effectiveness factor due to the lower concentration in Michaelis-Menten type reactions. The reactor was more effective, and hence, more efficient with the smaller porous Damkohler number. The generalized results could find applications for the design of bioreactors with a porous wall.     

Fed-batch culture of Bacillus thuringiensis for thuringiensin production in a tower type bioreactor

Fed-batch culture of Bacillus thuringiensis in a modified airlift reactor has been developed by using adaptive control of glucose concentration in the reactor. The glucose concentration was estimated via a correlation equation between carbon dioxide production rate and glucose consumption rate. The estimated glucose concentration as the output variable was fed back to computer for calculation of substrate addition. The modified reactor was an airlift reactor with a net draft tube. The airlift reactor had high oxygen transfer rate and low shear stress which were important factors for production of thuringiensin. Fed-batch culture of Bacillus thuringiensis in the modified airlift reactor provided significant improvement of thuringiensin production. (c) 1995 John Wiley & Sons, Inc.     

Fuzzy logic control of an unstable bioreactor

A rule based fuzzy controller (FLC) is developed for stabilization of an unstable continuous stirred tank bioreactor (CSTBR) from various start-up conditions. The output variable is the reactor substrate concentration and the manipulated variable is the dilution rate. The performance of the FLC is evaluated by simulating a mathematical model of an unstable CSTBR. FLC is robust to perturbations in the specific growth rate, specific consumption rate and also to a disturbance in the feed substrate concentration. The performance of the FLC is superior to that of a conventional proportional controller.     

Prediction of substrate consumption rate, average biofilm density and active thickness for a thin spherical biofilm at pseudo-steady state

In this work, a new approach is proposed to evaluate substrate consumption rate, average biofilm density and active thickness of a spherical bioparticle in a completely mixed fluidized bed system. The substrate consumption rate and average biofilm density are predicted for a given biofilm surface substrate concentration and operational biofilm thickness. A diffusion and reaction model is developed with an effective diffusion coefficient that depends on the average biofilm density. This approach, a first in the literature, predicts the optimum average density of a biofilm to yield the maximum substrate consumption rate within the biofilm. A reasonable correlation was observed between the model prediction and experimental results for substrate consumption rate and average biofilm density for thin and fully active biofilms.     

Acute impact of tetracycline and erythromycin on the storage mechanism of polyhydroxyalkanoates

The study investigated acute impact of tetracycline and erythromycin on substrate storage under aerobic conditions. A fill and draw reactor fed with peptone mixture was maintained at steady-state at a sludge age of 10 days; the acclimated biomass was used in a series of batch runs. The first run served as control reactor with organic substrate alone and the others were started with antibiotic doses of 50 mg/L and 200 mg/L for assessing intracellular storage. Parallel batch reactors were also conducted for recording oxygen uptake rate profiles. Both antibiotics enhanced substrate storage, leading to higher levels of polyhydroxyalkanoates incorporated into biomass, but they impaired its internal utilization for microbial growth. The observed decrease in oxygen consumption under the acute effect of antibiotics could partially be related to substrate storage – except for 50 mg/L of erythromycin dosing – suggesting an additional substrate binding mechanism by antibiotics, leading to residual biodegradable substrate.     

Rate-limiting mass transfer in immunosorbents: characterisation of the adsorption of paraquat-protein conjugates to anti-paraquat Sepharose 4B

A series of paraquat-protein conjugates of different molecular size has been prepared by the coupling of paraquat hexanoate to the proteins lysozyme, ovalbumin, bovine serum albumin. The characteristics of the adsorption of these conjugates to an immunosorbent consisting of monoclonal anti-paraquat antibodies covalently immobilised to Sepharose 4B have been determined. Equilibrium adsorption isotherms were found to obey the Langmuir equation and indicated that 80% or more of the antibody binding sites were accessible to the conjugates. The rates of mass transfer of the conjugates to their adsorption sites on the immobilised antibodies was well described by a model in which mass transfer is controlled by transfer across the external film and diffusion within the porous adsorbent bead. The effective diffusivities of the conjugates within the immunosorbent were measured and has allowed the effect of the size of the adsorbing molecule on the rate of adsorption to be considered. The amount of paraquat that could be adsorbed and the rates of adsorption decreased as the size of the protein to which it is conjugated increased. The diffusivity of the conjugates within the pores of the adsorbent is reduced between two and five times compared to their diffusivities in free solution. The reduction is greater for the larger proteins and the variations of the effective diffusivities and the pore diffusivities with the molecular weight of the conjugate can be well described with simple correlations.     

Detoxification of organophosphate pesticides using an immobilized phosphotriesterase from Pseudomonas diminuta

A purified phosphotriesterase was successfully immobilized onto trityl agarose in a fixed bed reactor. A total of up to 9200 units of enzyme activity was immobilized onto 2.0 mL of trityl agarose (65 mumol trityl groups/mL agarose), where one unit is the amount of enzyme required to catalyze the hydrolysis of one micromole of paraoxon in one min. The immobilized enzyme was shown to behave chemically and kinetically similar to the free enzyme when paraoxon was utilized as a substrate. Several organophosphate pesticides, methyl parathion, ethyl parathion, diazinon, and coumaphos were also hydrolyzed by the immobilized phosphotriesterase. However, all substrates exhibited an affinity for the trityl agarose matrix. For increased solubility and reduction in the affinity of these pesticides for the trityl agarose matrix, methanol/water mixtures were utilized. The effect of methanol was not deleterious when concentrations of less than 20% were present. However, higher concentrations resulted in elution of enzyme from the reactor. With a 10-unit reactor, a 1.0 mM paraoxon solution was hydrolyzed completely at a flow rate of 45 mL/h. Kinetic parameters were measured with a 0.1-unit reactor with paraoxon as a substrate at a flow rate of 22 mL/h. The apparent K(m) for the immobilized enzyme was 3-4 times greater than the K(m) (0.1 mM) for the soluble enzyme. Immobilization limited the maximum rate of substrate hydrolysis to 40% of the value observed for the soluble enzyme. The pH-rate profiles of the soluble and immobilized enzymes were very similar. The immobilization of phosphotriesterase onto trityl agarose provides an effective method esterase onto trityl agarose provides an effective method for hydrolyzing and thus detoxifyuing organophosphate pesticides and mammalian acetylcholinesterase inhinbitors.     

Transient response of encapsulated enzymes in hollow-fiber reactor

A mathematical model for the transient response of encapsulated enzymes is developed showing the effects of the outer boundary layer, the encapsulating membrane, the partition coefficient, and diffusion with reaction within the encapsulating medium. The model incorporates both first-order kinetics and Michaelis-Menten kinetics for the reaction rate. Using typical hollow-fiber or microcapsule parameters, the model shows that (a) the partition coefficient affects the overall rate only when the rate-limiting step is diffusion through the membrane, (b) the transient overall effectiveness factor rises sharply with time and approaches an asymptotic value for most situations, and (c) the first-order approximation to Michaelis-Menten kinetics is not valid when the initial outside bulk concentration is higher than the Michaelis constant and the overall rate is reaction limited. The model is compared with experimental data using uricase in a hollow-fiber enzyme reactor configuration. Batch assay and CSTUER (continuous-stirred ultrafiltration enzyme reactor) studies were conducted on the free enzyme to provide some of the parameters used in the model. The CSTUER data fit the case of substrate inhibition kinetics with the apparent Michaelis constant approaching zero. The hollow-fiber reactor was conducted with uricase dissolved in both a buffer solution and a concentrated hemoglobin solution. Diffusivities of the solute were measured in both solutions as was the osmotic pressure of the hemoglobin solution. While experimental data for uricase in buffer solution could easily be matched by the model, that in the concentrated hemoglobin solution could not.     

Kinetic study of a membrane enzyme reactor

A flat-membrane dialyzer was used as enzyme reactor by introducing enzyme solution into one of the membrane-separated chambers. The apparent Michaelis constant K_m(app) of urease was always larger (ten times at [urease] = 1 mg/ml) than that of free enzyme because the permeation of substrate through the membrane was rate determining. K_m(app) for urease decreased from 125 to 20mM with increasing flow rate of the substrate solution because of the turbulent flow near the membrane. In the case of glucose oxidase or creatine kinase, the reaction rate was limited by the permeation of less permeable substrates such as oxygen or ATP. Therefore, K_m(app) of more permeable substrates such as glucose or creatine became smaller than that of free enzyme. The reaction amount calculated from the permeation data agreed well with experimental results. By designing spacers for the reactor to give turbulence to the solution, the effectiveness of the reactor was improved fivefold.     

Recycle hollow fiber enzyme reactor with flow swing

The hollow fiber enzyme reactor with pulsation developed by Kim and Chang (1983) was operated in a differential mode by recycling a substrate solution, in order to assess the efficiency of ultrafiltration swing. The rates of lactose conversion by beta-galactosidase contained in the shell side of the reactor were measured to determine the effects of recirculation rate, pulsation period, and amplitude. The conversion increased with the increase of recirculation flow rate and the amplitude while variation in period affected the conversion relatively little. The maximum increase of 113% in the activity was observed in the reactor with pulsation as compared to that without pulsation. The two-compartment model well described the experimental data obtained in this study. Square-wave pulsation was theoretically more effective in increasing conversion than sine wave pulsation. However, in experimental operation the damping effect of the hollow fiber wall narrowed the difference between these two wave forms.     

Evaluation of kinetic parameters of biochemical reaction in three-phase fluidized bed biofilm reactor for wastewater treatment

This study evaluates the kinetic parameters of biochemical reaction in three-phase fluidized bed biofilm reactor from the steady state values of the response of the system to step changes in inlet concentration. It was observed from the outlet biological oxygen demand (BOD(5)) plot of the response of the system that as the inlet BOD(5) was increased, the outlet BOD(5) also increased, reached a peak value and then decreased until it leveled to a new steady state value corresponding to the new inlet concentration level. The increase in BOD(5) was attributed to the accumulation of substrate within the reactor as well as the decrease in biofilm substrate consumption rate as the microorganisms adjusted to the new environment. Using the substrate balance at steady state and assuming Monod kinetics, an equation relating the substrate consumption rate to substrate concentration (BOD(5)) and total biofilm surface area had been established. Monod kinetic parameters were found to be K=2.20g/m(2)/day, K(m)=17.41g/m(3) and K/K(m)=0.13m/day. The ratio K/K(m) can be taken as the indicator for biofilm substrate degradation effectiveness at low substrate concentrations.