Effects of solid-phase mass transfer on the performance of a stirred anaerobic sequencing batch reactor containing immobilized biomass

This work reports on experiments for an anaerobic sequencing batch reactor containing immobilized biomass which aimed at verifying the effects of solid-phase mass transfer on the reactor's overall performance. Four experiments were carried out at 30 degrees C with cubic polyurethane foam particles previously inoculated with anaerobic biomass. Different solid-phase mass transfer conditions were reached in each experiment by varying the size of the bioparticle from 0.5 to 3.0 cm. The reactor was fed with a low-strength synthetic wastewater containing protein, carbohydrates and lipid and the effects of mass transfer were evaluated through dynamic substrate concentration profiles during 8-hour batch cycles. A modified first-order kinetic model provided a good representation of the behavior of the dynamic concentration profiles. The solid-phase mass transfer was found to slightly affect the concentration of effluent organic matter expressed as chemical oxygen demand (COD). The concentration of residual effluent substrate increased as the size of the bioparticle was increased. The cycle time was not affected as the size of the bioparticle was increased from 0.5 to 2.0 cm. However, it was found that the cycle time in a reactor with 3.0-cm cubic particles should be higher than that required in systems with smaller particles. The apparent first-order kinetic parameter was estimated as 0.59+/-0.01 h(-1) for experiments with bioparticle sizes ranging from 0.5 to 2.0 cm, while a value of 0.48 h(-1) was obtained in the experiment with 3.0-cm bioparticles.     

Effect of mass transfer in a recirculation batch reactor system for immobilized penicillin amidase

The effect of external mass transfer resistance on the overall reaction rate of the immobilized whole cell penicillin amidase of E. coli in a recirculation batch reactor was investigated. The internal diffusional resistance was found negligible as indicated by the value of effectiveness factor, 0.95. The local environmental change in a column due to the pH drop was successfully overcome by employing buffer solution. The reaction rate was measured by pH-stat method and was found to follow the simple Michaelis-Menten law at the initial stage of the reaction. The values of the net reaction rate experimentally determined were used to calculate the substrate concentration at the external surface of the catalyst pellet and then to calculate the mass transfer coefficient, k(L), at various flow rates and substrate concentrations. The correlation proposed by Chilton and Colburn represented adequately the experimental data. The linear change of log j(D) at low log N(Re) with negative slope was ascribed to the fact that the external mass transfer approached the state of pure diffusion in the limit of zero superficial velocity.     

Enzyme immobilized in a packed-bed reactor: kinetic parameters and mass transfer effects.

To describe axial dispersion, particle film mass transfer, intraparticle diffusion, and the chemical reaction of the substrate for enzymes immobilized in porous particles in packed columns, we have developed mathematical models for first- and zero-order limits of Michaelis-Menten kinetics. Steady-state solutions were derived for both long and short column boundary conditions and for plug flow. Theory was compared to experiments by hydrolysis of sucrose catalyzed by invertase bound to porous glass particles. Steady-state conversions were measured for a range of flow rates. Pulse response experiments with inert packing were used to determine values of bed void fraction and particle porosity.     

Selective biosorption of thorium ions by an immobilized mycobacterial biomass

The biosorption of thorium and uranyl ions by cells of Mycobacterium smeamatis has been studied as a function of initial cation concentration. A similar sorption saturation level was observed for both ions. For immobilized cells, optimal conditions of metal ion retention were found for a bacterial mass/support concentration ratio of 1/6. However, selective uptake of thorium was manifest in solutions of the mixed cations. X-ray diffraction studies of the heat-dried biomasses loaded with cations showed that uranyl-loaded samples present a distinct pattern typical of ammonium uranyl phosphate, whereas thorium-loaded samples are amorphous. The microorganism used appears to have useful properties for applications in connection with separation and concentration of natural radioelements under conditions of high dilution.     

A two-dimensional mass transfer model for an annular bioreactor using immobilized photosynthetic bacteria for hydrogen production

A two-dimensional model for substrate transfer and biodegradation in a novel, annular fiber-illuminating bioreactor (AFIBR) is proposed in which photosynthetic bacteria are immobilized on the surface of a side-glowing optical fiber to form a stable biofilm. When excited by light, the desired intensity and uniform light distribution can be obtained within the biofilm zone in bioreactor and then realize continuous hydrogen production. Substrate transfer and biodegradation within the biofilm zone, as well as substrate diffusion and convection within bulk fluid regions are considered simultaneously in this model. The validity of the model is verified experimentally. Based on the model analysis, influences of flow rate and light intensity on the substrate consumption rate and substrate degradation efficiency were investigated. The simulation results show that the optimum operational conditions for the substrate degradation within the AFIBR are: flow rate 100 ml h^?1 and light intensity 14.6 μmol photons m^?2 s^?1.     

The kinetic and mass transfer behavior of immobilized invertase on ion-exchange resin beads

Immobilized invertase was prepared by binding native invertase to a polyamine type ion-exchange resin. Kinetic behavior of the immobilized invertase on these small pellets was investigated in a packed-bed reactor. For low flow rates, an effect of interparticle diffusion on the Machaelis constant was observed and a correlation was proposed to evaluate the effect. At high flow rates, Michaelis and inhibition constants were determined and compared with those for native invertase. With large pellets, intraparticle diffusion was found to be important and at high substrate concentrations, the effectiveness factor exceeded unity. Good agreement was found between the theoretical analyses and the experimental data.     

A mathematical model for the batch reactor kinetics of algae growth

A mathematical model based on the Einstein law of photochemical equivalence is proposed to describe the batch growth of unicellular algae. The model was applied in an integrated form to cell concentration versus growth time data taken over an extended range of cell concentrations which include both the regions of “exponential” and “linear” growth. It is shown that a certain function of cell concentration contained in the integrated form of the model is linearly dependent on the growth time over both the “exponential” and “linear” growth regions.     

Mechanistic and kinetic evaluation of biosorption of reactive azo dyes by free,immobilized and chemically treated Citrus sinensis waste biomass

Sorption potential of Citrus sinensis biomass for reactive yellow 42 and reactive red 45 was investigated with variation of pH, biosorbent dose and dye concentration. Biosorbent was treated by organic and inorganic reagents of which acetic acid and acetonitrile enhanced the sorption capacities for reactive yellow 42 and reactive red 45, respectively. Sorption equilibrium was established within 60 min using free and chemically treated biosorbent, while prolonged to 120 min using immobilized biosorbent. Freundlich isotherm and pseudo-second-order rate law described best the sorption mechanism. FT-IR analysis of biosorbent revealed the presence of CO, CO, NH and OH groups on the surface of biosorbent. Desorption experiments were performed to regenerate the sorbent, making the process more economical and environment friendly.     

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.     

Heavy metal removal in a biosorption column by immobilized M. rouxii biomass

Mucor rouxii biomass was immobilized in a polysulfone matrix. The spherical immobilized biomass beads were packed in a column. The biosorption column was able to remove metal ions such as Pb, Cd, Ni and Zn not only from single-component metal solutions but also from multi-component metal solutions. Column kinetics for metal removal were described by the Thomas model. For single-component metal solutions, the metal removal capacities of the beads for Pb, Cd, Ni and Zn were 4.06, 3.76, 0.36 and 1.36 mg/g, respectively. For a multi-component metal solution containing Cd, Ni and Zn, the capacities were 0.36, 0.31 and 0.40 mg/g for Cd, Ni and Zn, respectively. The adsorbed metal ions were easily desorbed from the beads with 0.05N HNO3 solution. After acid desorption and regeneration with deionized water, the beads could be reused to adsorb metal ions at a comparable capacity.     

A kinetic hairpin transfer model for parvoviral DNA replication

The DNAs encapsidated by parvoviruses show distinctly different patterns with respect to the ratio of plus-to-minus strands and sequence heterogeneity at the ends. A kinetic model, based on differential rates of hairpin transfer at 3' termini, is described and shown to account for all known parvoviral DNA distributions.     

Mass-transfer limitations for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor

A mathematical model has been developed for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor in which the enzyme-catalyzed reaction (the irreversible uni-uni competitive Michaelis-Menten kinetics is chosen as an example) was coupled with intraparticle diffusion, external mass transfer, and axial dispersion. The effects of mass-transfer limitations, competitive inhibition of substrates, deactivation on the enzyme effective enantioselectivity, and the optical purity and yield of the desired product are examined quantitatively over a wide range of parameters using the orthogonal collocation method. For a first-order reaction, an analytical solution is derived from the mathematical model for slab-, cylindrical-, and spherical-enzyme supports. Based on the analytical solution for the steady-state resolution process, a new concise formulation is presented to predict quantitatively the mass-transfer limitations on enzyme effective enantioselectivity and optical purity and yield of the desired product for a continuous steady-state kinetic resolution process in a fixed-bed reactor.     

Mathematical analysis of solid-liquid mass transfer in a batch reactor for the enzymatic transformation of testosterone to 4AD

A previous mathematical analysis of mass transfer in a two-phase (solid-liquid) batch reactor for enzymatic transformation of testosterone to 4AD (Pereira et al., 1987) is extended to incorporate the effect of convective mixing. The results of the analysis showed that for a given enzyme loading, the mass transfer resistance in the solid (a function of the bead size) and the intensity of convective mixing (as embodied in the mass transfer coefficient) are two parameters that can be varied such that the overall mass transfer rate from the solid to the liquid phase ensures optimal reactor performance.     

A graphical method of determining the Michaelis-Menten constant free of external mass transfer resistance for immobilized enzymes in a packed bed reactor

Summary A graphical method of determining the Michaelis-Menten constant free of the external mass transfer resistance for a packed bed immobilized enzyme system was illustrated with examples from 3 different enzyme reactions. The intercept at the ordinate obtained by the straight line extrapolation of data points in the plot of apparent K_m value vs. the reciprocal of superficial velocity in column allowed an easy calculation of K_m free of external mass transfer resistance. An asymptotic value of apparent K_m value at infinite zero superficial velocity was ascribed to the fact that the mass transfer coefficient k_L, approached a definite value at this condition.Nomenclature K_m Michaelis-Menten constant, M/L³ - K_m' K_m free of external mass transfer resistance in a given ionic strength, M/L³ - Km" apparent K_m with external mass transfer resistance, M/L³ - S substrate concentration, M/L³ - S_o initial substrate concentration, M/L³ - k₂ rate constant, t^-1 - E enzyme concentration in support, M/L³ - void volume per unit volume of reactor, dimensionless - u superficial velocity of substrate, L/t - K_L mass transfer coefficient in liquid film, L/t - a external surface area of support per unit volume of reactor, L^-1 - ratio of average channeling length to particle diameter, dimensionless - d_p diameter of support particle, L - X fractional conversion of substrate, dimensionless - H partition coefficient, dimensionless - k a constant, 3 k₂E(1-)d_p/4 - T space time, t - N molecular flux, M/L²t - r radius of immobilized enzyme particle, L     

Lactic acid fermentation in a recycle batch reactor using immobilized Lactobacillus casei

Lactic acid production by recycle batch fermentation using immobilized cells of Lactobacillus casei subsp. rhamnosus was studied. The culture medium was composed of whey treated with an endoprotease, and supplemented with 2.5 g/L of yeast extract and 0.18 mM Mn(2+) ions. The fermentation set-up comprised of a column packed with polyethyleneimine-coated foam glass particles, Pora-bact A, and connected with recirculation to a stirred tank reactor vessel for pH control. The immobilization of L. casei was performed simply by circulating the culture medium inoculated with the organism over the beads. At this stage, a long lag period preceded the cell growth and lactic acid production. Subsequently, for recycle batch fermentations using the immobilized cells, the reducing sugar concentration of the medium was increased to 100 g/L by addition of glucose. The lactic acid production started immediately after onset of fermentation and the average reactor productivity during repeated cycles was about 4.3 to 4.6 g/L . h, with complete substrate utilization and more than 90% product yield. Sugar consumption and lactate yield were maintained at the same level with increase in medium volume up to at least 10 times that of the immobilized biocatalyst. The liberation of significant amounts of cells into the medium limited the number of fermentation cycles possible in a recycle batch mode. Use of lower yeast extract concentration reduced the amount of suspended biomass without significant change in productivity, thereby also increasing the number of fermentation cycles, and even maintained the D-lactate amount at low levels. The product was recovered from the clarified and decolorized broth by ion-exchange adsorption. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55:841-853, 1997.     

Mathematical model for evaluation of mass transfer limitations in phenol biodegradation by immobilized Pseudomonas putida

A mathematical model is proposed to analyze the mass transfer limitations in phenol biodegradation using Pseudomonas putida immobilized in calcium alginate. The model takes into account internal and external mass transfer limitations, substrate inhibition kinetics and the dependence of the effective diffusivity of phenol in alginate gel on cell concentration. The model is validated with the experimental data from batch fermentation. The effect of various operating conditions such as initial phenol concentration, initial cell loading, alginate gel loading on the biodegradation of phenol is experimentally demonstrated. Phenol degradation time is found to decrease initially and reach stationary value with increase in cell loading as well as gel loading. The model predicts these trends reasonably well and shows the presence of external mass transfer limitations. A new concept of effectiveness factor is introduced to analyze the overall performance of batch fermentation.     

A model for enzymatic isomerization of D-glucose to D-fructose in a batch reactor.

Using whole cells containing glucose isomerase, mathematical models for the enzymatic conversion of D-glucose to D-fructose and for the inactivation of the enzyme catalyst have been postulated and verified experimentally. The heat of reaction, the equilibrium constant, and the individual rate constants and their activation energies have been estimated. The model can be used to predict the time course for the enzymatic production of fructose in a batch reactor within the tested experimental range of 40-80 degrees C.