On the kinetics of dextransucrase and dextran synthesis in batch reactors

Summary Basic dextransucrase kinetics are described by the substrate inhibition model and the parameters are evaluated; the model describes fairly well the behaviour in a batch stirred reactor. Optimum conditions for maximum productivity are experimentally and theoretically determined.     

Kinetic model of elemental sulfur oxidation by Thiobacillus thiooxidans in batch slurry reactors

The kinetics of sulfur oxidation by T. thiooxidans has been studied in a batch well-mixed reactor and in shaker flasks. A mathematical model is proposed, which considers the attachment of the cells onto the sulfur particles' surface following Freundlich isotherm, growth of the attached bacteria, and growth inhibition by sulfates accumulation. Best-fit values of the model parameters have been calculated from the experimental data. Results show that the addition of dimethyl-dichloro-silane in the aerated reactor to prevent the formation of foam reduces the maximum specific growth rate of attached bacteria, probably because of the resulting changes in surface properties of the sulfur particles. The other model parameters are not significantly affected. The formation of clusters of sulfur particles has been observed at an initial sulfur concentration of 5% . This phenomenon reduces the rate of sulfur conversion due to the reduction of the total surface area of the particles, and the model therefore over-estimates the formation of sulfates. At lower initial sulfur concentration, the phenomenon has not been observed and the model simulations are then satisfactory.     

Continuous production of L-tert-leucine in series of two enzyme membrane reactors

The L-tert-leucine synthesis was performed continuously in series of two enzyme-membrane reactors by reductive amination of trimethylpyruvate with leucine dehydrogenase. The necessary “native” cofactor NADH is regenerated with the aid of a second enzyme, formate dehydrogenase. Considering detailed kinetic studies of initial reaction rates under conditions relevant to the process a kinetic model was developed. The model shows that the overall reaction rate is strongly inhibited by the reaction product. The reactor's models combine the mass balances and proposed kinetic equations. The model adequacy was verified by using it to simulate the experiments and by comparing experimental and computed conversion, space-time yield and enzyme consumption. The calculations for the three reactor's types (batch, single CSTR and a cascade of two CSTRs in series) were compared. The results showed that a single CSTR is no favourable reactor configuration due to the very strong product inhibition. Space-time yield drops from 560 g litre^?1 day^?1 in a batch reactor to 110 g litre^?1 day^?1 in a single CSTR at the highest conversion of 98%. At the conversion of 95% the difference in biocatalyst costs between batch and two CSTR in series is negligible. Therefore the use of two enzyme membrane reactors in series was proposed. The modelling in this work shows that the optimisation of the quantity of the enzyme used results in a minimisation of the biocatalyst costs.     

Mathematical modeling of non-ideal mixing continuous flow reactors for anaerobic digestion of cattle manure

Most conventional digesters used for animal wastewater treatment include continuously stirred-tank reactors. While imperfect mixing patterns are more common than ideal ones in real reactors, anaerobic digestion models often assume complete mixing conditions. Therefore, their applicability appears to be limited. In this study, a mathematical model for anaerobic digestion of cattle manure was developed to describe the dynamic behavior of non-ideal mixing continuous flow reactors. The microbial kinetic model includes an enzymatic hydrolysis step and four microbial growth steps, together with the effects of substrate inhibition, pH and thermodynamic considerations. The biokinetic expressions were linked to a simple two-region liquid mixing model, which considered the reactor volume in two separate sections, the flow-through and the retention regions. Deviations from an ideal completely mixed regime were represented by changing the relative volume of the flow-through region (a) and the ratio of the internal exchange flow rate to the feed flow rate (b). The effects of the hydraulic retention time, the composition of feed, the initial conditions of the reactor and the degree of mixing on process performance can be evaluated by the dynamic model. The simulation results under different conditions showed that deviations from the ideal mixing regime decreased the methane yield and resulted in a reduced performance of the anaerobic reactors. The evaluation of the impact of the characteristic mixing parameters (a) and (b) on the anaerobic digestion of cattle manure showed that both liquid mixing parameters had significant effects on reactor performance.     

Effect of repeated addition of nitrite to semi-continuous activated sludge reactors

To a semi-continuous lab-scale activated sludge system (SCAS), nitrite was dosed discontinuously, i.e. together with the feed. The nitrite was added at a concentration (50 mg N/l) which had been found earlier not to cause acute inhibition of the general running of the reactors. Repeated nitrite addition, however, exerted an inhibitory effect which was reflected in decreased removal efficiencies and was also expressed in decreases in total respiratory and nitrifying activity of 20% and 40%, respectively. The inhibition by nitrite was reversible as removal efficiencies improved after ceasing nitrite addition. The two consecutive test runs revealed that addition of nitrite gave rise to high amounts of dispersed cells and free-swimming protozoa. Moreover, DGGE patterns confirmed a shift in microbial community structure upon application of nitrite.     

Enzymatic saccharification of cellulose in membrane reactors

The kinetics of enzymatic saccharification of ball-milled sugar-cane bagasse, sorghum stubble and peanut shells was studied and their conversions compared. Particle size analyses were performed on the bagasse sample and pure cellulose (Solka-Floc). It was revealed that most of the size reduction of cellulose particle took place between 0 5% conversion. Means of using commercially available ultrafiltration units as continuous-flow membrane reactors to reduce glucose inhibition were tested and compared using Solka-Floc as substrate. It was pointed out that a low conversion CSTR placed between a ball-mill and a hollow-fibre cartridge could reduce the cost of pretreatment and prevent possible blockage of hollow fibres.     

Dynamic mathematical modeling of sulfate reducing gas-lift reactors

This paper presents a mathematical model able to simulate under dynamic conditions the physical, chemical and biological processes prevailing in a biological sulfate reducing gas-lift reactor. The proposed model is based on differential mass balance equations for substrates, products and bacterial groups involved in a sulfate reduction process. Heterotrophic sulfate reducing bacteria (HSRB), autotrophic sulfate reducing bacteria (ASRB), homoacetogenic bacteria (HB), methanogenic archaea (MA) and acetate degraders (AD) are the microbial groups taken into account in the model. The model is also used to validate a steady-state design model previously proposed by Esposito et al. [1].The proposed model is able to simulate the competition between the biological bacteria growing in the reactor, and predict the performance of a gas-lift reactor. The model includes two main parts: (1) a kinetic part including growth, metabolism and competition of SRB, HB, MA and AD in the system and (2) a mass-transfer part describing the thermodynamic concentration equilibria of gaseous components in the liquid and gas phase. The model has been validated using experimental data obtained by operating a laboratory-scale gas-lift reactor as described in Esposito et al. [2].The model can be applied to simulate the sulfate reduction process in a gas-lift reactor for several purposes, such as the evaluation of the optimal process conditions in terms of COD:SO₄^2? ratio, hydraulic retention time and gas input flow. In particular, model simulations reported in this paper show the model capability to predict the prevailing bacterial species and concentrations in the reactor as a function of the hydraulic retention time.     

Continuous production of protein hydrolysates in immobilized enzyme reactors

The digestion of several proteins, casein, α-lactalbumin, human serum albumin and a mixture of whey proteins by immobilized pronase, thermitase and leucine aminopeptidase was studied on various conditions in five types of enzyme reactors. Reactors and operating conditions were designed to maximize the extent of hydrolysis and to minimize the adverse effects of the macromolecular nature of the substrates. A simple analytical method was developed to follow routinely the extent of hydrolysis. Substrate proteins were subjected to various pretreatments intended to disturb their native structure. The maximum feasible extent of hydrolysis in the reactor effluent, which is an average quantity, clustered around the magic figure of 33% in all systems studied. Protein digestion in bubbled column reactors charged with the polyaminomethylstyrene-fixed thermostable proteinase “thermitase” and operated at 50 to 60°C turned out to be the most efficient setup to produce continuously amino acid/peptide mixtures.     

Simplified models for packed-bed biofilm reactors

For a packed-bed biofilm reactor two reactor models are proposed. One model is for the limiting case of a biofilm with a constant biofilm thickness in which diffusion within the biofilm is shown to be negligible. The second model assumes that the thickness of the biofilm is limited by the concentration of substrate within the biofilm. The analytical solutions for these reactor models are shown to agree very well with the numerical solutions to the exact differential equations.     

Inhibition of propionate degradation by acetate in methanogenic fluidized bed reactors

Summary The degradation of acetate, propionate and butyrate was monitored during start-up of five lab-scale methanogenic fluidized bed reactors on an artificially prepared waste water. The acetate concentration in the reactor content was found to influence the degradation of propionate but not of butyrate. In general, at acetate levels over 200 mg/l the degradation of propionate was below 60%, whereas the degradation was complete at acetate levels under 100 mg/l. The rationale of the inhibition of propionate degradation by acetate is discussed.     

On-line measurement of dissolved and gaseous hydrogen sulphide in anaerobic biogas reactors

The paper presented demonstrates the calibration of a silicone membrane probe for measurement of hydrogen sulphide in liquid and gas phase. The probe is connected to a quadrupole mass spectrometer as detector. The calibration of the probe results in linear calibration functions for different liquids and the gas phase. An example of the application of the measuring device for on-line measurement is reported for an experiment where sulphide is precipitated as iron sulphide by the addition of ferrous chloride. As a consequence of the addition of ferrous chloride, the concentration of H₂S in the biogas rapidly decreases from 4.2% to 1.0% (by volume). The inhibition of the anaerobic treatment process is calculated on the basis of the reduction of dissolved total organic carbon before and during the experiment. The reduction of dissolved total organic carbon before the experiment starts is constant at 60%, rising to a maximum of 70% during the addition of FeCl₂. The difference in the conversion rate corresponds to an inhibition of about 14%. The gas production increases from 7.51 l^–1 day^–1 to 8.51 l^–1 day^–1. This inhibition observed before the addition of FeCl₂ is caused by 65 mg/l undissociated hydrogen sulphide in the liquid phase as calculated from the data obtained after precipitation of sulphide as zinc sulphide. The data show clearly that the conversion of acetic acid to methane is inhibited by dissolved H₂S. The concentration of acetic acid drops sharply from about 25 mM to 15 mM after the FeCl₂ dosage has been started. The concentration of propionic acid decreases slightly from 12 mM to 9 mM. Most of the iron introduced during the experiment is immediately precipitated. The maximum concentration of dissolved iron measured in the effluent is 93 mg/l.     

Biofilm reactors: an experimental and modeling study of wastewater denitrification in fluidized-bed reactors of activated carbon particles

A fluidized-bed biofilm reactor using activated carbon particles of 1.69 mm diameter as the support for biomass growth and molasses as the carbon source is used for wastewater denitrification.The start-up of the reactor was successfully achieved in 1 week by using a liquor from garden soil leaching as the inoculum and a superficial velocity u(0) = 5u(mf). Typical biofilm thickness is 800 mum; therefore covered activated carbon particles have 3.3 mm in diameter.Reactor hydrodynamics was studied by tracer (KCl solution) experiments. The analysis based on residence time distribution theory involved a model with axial dispersion flow and tracer diffusion with linear adsorption inside the biofilm. Peclet numbers higher than 100 were found, allowing the plug flow assumption for the reactor model.Experimental profiles of nitrate and nitrite species were explained by a kinetic model of two consecutive zero-order reactions coupled with substrate diffusion inside the biofilm. Under the operating conditons used thick biofilms were obtained working in a diffusion-controlled regime.Comparison is made with results obtained in the same reactor with sand particles as the support for biomass growth. Activated carbon as the support has the following advantages: good adsorptive characteristics, homogeneous biofilm thickness along the reactor, and easy restart-up of the reactor. (c) 1992 John Wiley & Sons, Inc.     

Advantages of continuous over batch reactors for the kinetic analysis of enzymes inhibited by an unknown substrate impurity

A new experimental technique, employing a continuous stirred-tank reactor, for studying enzyme kinetics in the presence of inhibitor-contaminated substrate is described. The proposed method is simulated mathematically for competitive, uncompetitive, and mixed-type noncompetitive inhibition. The step-by-step experimental procedure is described, as is the necessary data analysis for determining the kinetic parameters. Differences in system response for enzyme inhibition by excess substrate and by an impurity are illustrated, and a stability analysis of the system is performed.     

Modeling continuous bioleach reactors

The results of recent research have shown that the bioleaching of sulfide minerals occurs via a two‐step mechanism. In this mechanism, the sulfide mineral is chemically oxidized by the ferric‐iron in the bioleaching liquor. The ferrous‐iron produced is subsequently oxidized to ferric‐iron by the microorganism. Further research has shown that the rates of both the ferric leaching and ferrous‐iron oxidation are governed by the ferric/ferrous‐iron ratio (i.e., the redox potential). During the steady‐state operation of a bioleach reactor, the rate of iron turnover between the chemical ferric leaching of the mineral and the bacterial oxidation of the ferrous‐iron will define the rate and the redox potential at which the system will operate. The balance between the two rates will in turn depend on the species used, the microbial concentration, the residence time employed, the nature of the sulfide mineral being leached, and its active surface area. The model described proposes that the residence time and microbial species present determine the microbial growth rate, which in turn determines the redox potential in the bioleach liquor. The redox potential of the solution, in turn, determines the degree of leaching of the mineral; that is, conversion in the bioleach reactor. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 64: 671–677, 1999.     

Heterogeneous one-dimensional model for fixed bed enzyme reactors

A one-dimensional model, taking into account the diffusion of substrate between the liquid phase and the solid support, has been used to describe fixed bed enzyme reactors. The equations were solved numerically, and the values of the different parameters were calculated by a nonlinear regression method. The model was applied to different systems. The results are presented and discussed.     

Examination of substrate and product inhibition kinetics on the production of ethanol by suspended and immobilized cell reactors

Kinetic expressions for the fermentative production of relatively high concentrations [12% (w/v)] of ethanol have been examined. Several expressions which account for both substrate and product inhibition have been formulated, and have been applied to suspended cell and immobilized cell reactors. Experimental data have been used to validate the kinetic expressions used, and the impact of combined inhibition on optimal reactor configuration has been assessed. The process implications of combined substrate and product inhibition for suspended and immobilized cell systems have been discussed.     

Modeling of biofilm reactors with consecutive reactions

Modeling of biofilm reactors has been carried out by several authors. Most of the models use first-order or zero-order kinetics, because of the simplicity of the solution of the mathematical problem. However, the reaction kinetics for many practical situations is a non-linear Monod kinetics, which requires numerical solutions. This paper deals with the modeling of biofilm reactors and effectiveness factor calculations for a biofilm particle with Monod kinetics and two consecutive reactions. The model is applied to biological denitrification in a fluidized bed bioreactor, in which the liquid phase is assumed to be in plug flow. Effectiveness factors of biofilm are numerically calculated by solving the system of ODES by orthogonal collocation. Axial concentration profiles of nitrate and nitrite species are calculated and compared with experimental results.