Operational stability of immobilized d-glucose isomerase in a continuous feed stirred tank reactor

d-Glucose isomerization has been studied using immobilized cells of Streptomyces phaeochromogenes in a continuous feed stirred tank reactor (CSTR) where the external film diffusion resistance was negligible. Experiments conducted with various sizes of enzyme particles indicated that a strong internal diffusion resistance improved the apparent stability of these particles. The performance equations of the CSTR were constructed by associating the material balances for the inside porous support matrix with the bulk liquid phase, and enzyme deactivation was also taken into consideration. An iterative method together with the orthogonal collocation method is proposed for the evaluation of effectiveness factor and the substrate concentration profile within the enzyme particles. The numerical results offer an alternative analytical proof for the observation that under strong internal diffusion control the apparent operational stability of immobilized enzyme is improved.     

The Role of the Liquid Phase in the Degradation of Toluene and m‐Cresol within a Biofilm Trickle‐Bed Reactor

The degradation of toluene and m‐cresol in a biofilm trickle‐bed reactor was experimentally and theoretically investigated. Degradation is the result of the cooperation between suspended and immobilized microorganisms in the trickling film and the biofilm. The role of the trickling film is that of a barrier for mass transfer to the biofilm or that of an additional reaction space. This is the result of physical availability of pollutants to the liquid phase as well as co‐substrate degradation of inherent biomass. An instationary reactor balance model is presented. In addition to this the change in wetting behavior of carrier surface due to biofilm formation is discussed. A partial wetting of biofilm surface by rivulets of the trickling film is proposed. The model was verified by experimental data. The different reactor operation modes denoted as biofilm regime versus trickling film regime for the chosen pollutant system were expressed in terms of dimensionless reactions and transfer numbers. It is shown that the volumetric reaction rates for toluene in a trickling film regime reaches values twice as high as that of a biofilm regime due to the presence of the second substrate m‐cresol. The limiting step in both cases is the mass transfer of oxygen to bacteria in the biofilm or trickling film.     

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.     

External and internal glucose mass transfers in succinic acid fermentation with stirred bed of immobilized Actinobacillus succinogenes under substrate and product inhibitions

This paper is dedicated to the study on the external and internal mass transfers of glucose for succinic acid fermentation under substrate and product inhibitions using a bioreactor with stirred bed of immobilized Actinobacillus succinogenes cells. By means of the substrate mass balance for a single particle of biocatalysts, considering the kinetic model adapted for both inhibitory effects, specific mathematical models were developed for describing the profiles of the substrate concentration in the outer and inner regions of biocatalysts and for estimating the substrate mass flows in the liquid boundary layer surrounding the particle and inside the particle. The values of the mass flows were significantly influenced by the internal diffusion velocity and rate of the biochemical reaction of substrate consumption. These cumulated influences led to the appearance of a biological inactive region near the particle center, its magnitude varying from 0 to 5.3% of the overall volume of particles.     

Determination of glucose diffusion coefficients in biofilms with micro-electrodes

A glucose micro-electrode was developed for direct measurements inside biofilms, and applied for the determination of effective diffusion coefficients in a model system of agar beads containing immobilized yeast cells. Two methods were used, one based on concentration gradients present at the liquid/solid interface of an active biofilm under steady-state conditions, the other based on the rate of glucose redistribution in an inactivated biofilm under transient-state conditions. Additional measurements with pH and oxygen micro-electrodes were performed and thus allowed for in-situ correction of the glucose electrode signal. From the micro-electrode measurements in the model system it was concluded that the glucose micro-sensor is a useful tool with which to obtain effective diffusion coefficients in biofilms.     

A multispecies biofilm model

Using a continuum approach and observing conservation principles, an analytical mathematical model of microbial interaction in biofilms was developed. The model predicts changes in biofilm thickness and describes the dynamics and spatial distribution of microbial species and substrates in the film. It allows for biomass detachment due to shear stress and sloughing, external mass transfer limitations, as well as variations in substrate concentrations in the bulk liquid. A computer implementation of the model is provided using an example of heterotrophicautotrophic competition to illustrate how the observed phenomena can be numerically reproduced and indicating how they might affect overall biofilm performance.     

Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study

A two-dimensional model for quantitative evaluation of the effect of convective and diffusive substrate transport on biofilm heterogeneity was developed. The model includes flow computation around the irregular biofilm surface, substrate mass transfer by convection and diffusion, biomass growth, and biomass spreading. It was found that in the absence of detachment, biofilm heterogeneity is mainly determined by internal mass transfer rate of substrates and by the initial percentage of carrier-surface colonization. Model predictions show that biofilm structures with highly irregular surface develop in the mass transfer-limited regime. As the nutrient availability increases, there is a gradual shift toward compact and smooth biofilms. A smaller fraction of colonized carrier surface leads to a patchy biofilm. Biofilm surface irregularity and deep vertical channels are, in this case, caused by the inability of the colonies to spread over the whole substratum surface. The maximum substrate flux to the biofilm was greatly influenced by both internal and external mass transfer rates, but not affected by the inoculation density. In general, results of the present model were similar to those obtained by a simple diffusion-reaction-growth model.     

Effectiveness factor for spherical biofilm catalysts

Immobilization is a method of avoiding wash-out of biocatalyst from a reactor system. For the modelling of these biocatalysts slab, cylinder, sphere and biofilm geometries are frequently used. A biofilm particle consists of an inert core which is used as a carrier for a layer that contains the enzymes or micro-organisms. This paper deals with the modelling and effectiveness factor calculations for such a biofilm particle and a general model for an immobilized, non-growing biocatalyst is presented. The model includes internal and external mass transfer resistance, the partitioning effect and inhibition or reversible reaction kinetics. Due to the non-linear reaction rate equations of the Michaelis Menten type, numerical techniques must be used for the solution of the combined diffusion reaction equation and calculation of the effectiveness factor. In this work we have used two different methods, orthogonal collocation and a method based on Runge-Kutta integration. Comparable use of CPU-time was found for these methods, but numerical stability and accuracy favour the Runge-Kutta method. In the case of Michaelis Menten kinetics (irreversible and without inhibition effects), an analytical expression for an approximate solution is presented. This method, which has an acceptable accuracy, takes far less CPU-time than the fore-mentioned numerical techniques.     

Theoretical and methodological studies of continuous microbial bioreactors

This article reviews most of the author's studies on process development and reactor design for continuous microbial reactions. (1) Enzyme reactions of growing and non-growing microbial cells immobilized in agar gel beads were analyzed pertaining to the effects of external and internal diffusion of substrate on reaction kinetics. (2) Experimental correlations of production rates of beta-fructosidase and acid phosphatase with dilution rate of continuous culture were simulated based on an operon model for enzyme regulation. (3) Population dynamics of an amylase-producing bacteria and their mutant were discussed in relation to enzyme productivity in a continuous culture of spore-forming bacteria. (4) Plasmid mobilization in a mixed population of donor, recipient, and helper cells was investigated in a continuous culture as a model study of accidental release of a genetically modified plasmid into a natural environment. (5) A production rate increase of up to 100-fold was achieved by cell-recycle culturing of continuous acetic acid fermentation using a filter module with a hollow fiber membrane. (6) The feasibility of a continuous surface culture for the biooxidation of organic substances was ascribed to an enhanced oxygen absorption rate in the presence of a microbial film on a liquid surface. (7) Simultaneous separation of inhibitory products using an electrodialysis module during some organic acid fermentations was effective for increasing production in a continuous culture.     

Dynamics of a biological fixed film for phenol degradation in a fluidized-bed bioreactor

Experimental and modeling studies were conducted to analyze the dynamic response behavior of a phenol-oxidizing fixed film using a differential, fluidized-bed bioreactor in a recycle loop with a well-mixed reservoir. With the bioreactor at steady state, a pulse of phenol was added to perturb the system, and the phenol concentration was monitored continuously until steady state was again achieved.The experimental dynamics were compared with a dynamic mathematical model based on diffusion and reaction within the biofilm, liquid mixing, and biofilm growth. Constant-pH experiments could be adequately described using an unstructured, double-Monod kinetic expression with substrate inhibition by phenol.However, in dynamic experiments without pH control, the pH of the liquid phase dropped, and damped oscillations were observed in the phenol concentration and reaction rate trajectories. Oscillatory solutions could not be induced in the model, even when product inhibition was included, and a linear stability analysis did not reveal tendencies toward instability. The cause of the experimental oscillations remains unknown.     

Succinic acid fermentation in a stationary-basket bioreactor with a packed bed of immobilized Actinobacillus succinogenes: 1. Influence of internal diffusion on substrate mass transfer and consumption rate

This paper is dedicated to the study on external and internal mass transfers of glucose for succinic fermentation under substrate and product inhibitions using a bioreactor with a stationary basket bed of immobilized Actinobacillus succinogenes cells. By means of the substrate mass balance for a single particle of biocatalysts, considering the Jerusalimsky kinetic model including both inhibitory effects, specific mathematical expressions have been developed for describing the profiles of the substrate concentrations and mass flows in the outer and inner regions of biocatalyst particles, as well as for estimating the influence of internal diffusion on glucose consumption rate. The results indicated that very low values of internal mass flow could be reached in the particles center. The corresponding region was considered biologically inactive, with its extent varying from 0.24% to 44% from the overall volume of each biocatalyst. By immobilization of bacterial cells and use of a basket bed, the rate of glucose consumption is reduced up to 200 times compared with the succinic fermentation system containing free cells.     

Modeling of an aerobic biofilm reactor with double-limiting substrate kinetics: bifurcational and dynamical analysis

A mathematical model of an aerobic biofilm reactor is presented to investigate the bifurcational patterns and the dynamical behavior of the reactor as a function of different key operating parameters. Suspended cells and biofilm are assumed to grow according to double limiting kinetics with phenol inhibition (carbon source) and oxygen limitation. The model presented by Russo et al. is extended to embody key features of the phenomenology of the granular‐supported biofilm: biofilm growth and detachment, gas–liquid oxygen transport, phenol, and oxygen uptake by both suspended and immobilized cells, and substrate diffusion into the biofilm. Steady‐state conditions and stability, and local dynamic behavior have been characterized. The multiplicity of steady states and their stability depend on key operating parameter values (dilution rate, gas–liquid mass transfer coefficient, biofilm detachment rate, and inlet substrate concentration). Small changes in the operating conditions may be coupled with a drastic change of the steady‐state scenario with transcritical and saddle‐node bifurcations. The relevance of concentration profiles establishing within the biofilm is also addressed. When the oxygen level in the liquid phase is <10% of the saturation level, the biofilm undergoes oxygen starvation and the active biofilm fraction becomes independent of the dilution rate. © 2011 American Institute of Chemical Engineers Biotechnol. Prog., 2011     

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.     

Studies on microbial glucose isomerase: 4. Characteristics of immobilized whole-cell glucose isomerase from Streptomyces spp.

Whole-cell glucose isomerase from a Streptomyces spp. was immobilized by entrapment in gelatin matrices crosslinked with glutaraldehyde. The resultant immobilized enzyme preparation had up to 40% recovery yield of the activity and showed relatively long stabilities during storage and the isomerizing reaction. The storage half-life of the preparation was 19 months at 5°C and the half-life of the enzyme during operation was 260 days in the presence of 1 mM Co²⁺ and 80 days in the absence of the metal ion. Optimum pH and temperature were 7.5 and 70–75°C, respectively. The K_m values for glucose and fructose were 0.29 and 0.46 m, respectively, with a maximum theoretical conversion yield of 56%. The simulation results based on the reversible one-substrate enzyme kinetic model agreed well with the experimental data obtained from a batch reactor. The continuous operation of packed bed reactors demonstrated that some effects of the external film diffusion resistance were apparent at low flow rates of the substrate feed solution, whereas the internal pore diffusion resistance was negligible up to the pellet size used in this work.     

Diffusion coefficients of metabolites in active biofilms

Diffusion coefficients of actual metabolites in completely active biofilms can be determined by applying a new concept that is based on a constant local activity in the entire biofilm. In that case, a concentration step will be transmitted unattenuated. Subsequently, the diffusion coefficient can be calculated from the response monitored with a microelectrode positioned in the biofilm without quantitative knowledge of the local microbial kinetics. The conditions required for such a constant microbial biofilm activity were formulated in terms of the Thiele modulus and the substrate concentration in the bulk liquid. This proposed method was successfully applied to determine diffusion coefficients of oxygen and glucose in agar gels containing various fractions of active immobilized microorganisms. The values obtained were compared to experimental results from well-defined inert systems. The transient response of oxygen was far more affected by the presence of the immobilized cells than glucose. This can be explained by partition of the diffusing solute between the microbial cells and the aqueous phase.     

Prediction of average biofilm density and performance of a spherical bioparticle under substrate inhibition

In this article, a model was proposed to predict the average performance and biofilm density of a spherical bioparticle under substrate inhibition in a fluidized bed system. The average biofilm density and substrate consumption rates were predicted for a definite biofilm thickness and limiting substrate concentrations. A diffusion and reaction model was developed over the bioparticle with biofilm-density dependent effective diffusion coefficients for maximum substrate consumption theory. This theory predicts the optimum density of a biofilm to yield a maximum substrate consumption rate within the biofilm, developed for the first time with this study and experimentally verified. A good correlation was observed between the model prediction and experimental results for biofilm density and substrate consumption rates. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 319-329, 1997.     

Immobilized enzymes: electrokinetic effects on reaction rates in a porous medium

The effect of the internal diffusion and electrical surface charge on the overall rate of a reaction catalyzed by an enzyme immobilized on a porous medium are examined. Effectiveness factors have been calculated which compare the global reaction rate to that existing in the absence of the internal diffusion and/or the electrical field. The surface charge, assumed to arise from the dissociation equilibria of the acidic and basic surface groups of the enzyme, generates an electrical double layer at the pore surface. The double-layer potential is governed by the Poisson-Boltzmann equation. It is shown that the diffusion potential can be characterized by a modulus which depends upon the surface reaction rate, the charges and diffusivities of the substrate and products, the ionic strength, and the pore dimensions. The flux of a charged species in the pore occurs under the influences of the concentration gradient and the electrical potential gradient. The governing equations are solved by an iterative numerical method. The effects of pH, enzyme concentration, and substrate concentration on the rates of two different hydrolysis reactions catalyzed by immobilized papain are examined. The release of H(+) in one of the reactions causes the lowering of internal pH, and also a constancy of the internal pH when the external pH in creases beyond a certain value. The latter reaction also shows a maximum in the reaction rate with respect to enzyme concentration. The reaction not involving H(+) as a product shows a maximum in the reaction rate with respect to external pH, but a monotonic increase in the reaction rate as the enzyme concentration increases.     

Bifurcational and dynamical analysis of a continuous biofilm reactor

A dynamical model of a continuous biofilm reactor is presented. The reactor consists of a three-phase internal loop airlift operated continuously with respect to the liquid and gaseous phases, and batchwise with respect to the immobilized cells. The model has been applied to the conversion of phenol by means of immobilized cells of Pseudomonas sp. OX1 whose metabolic activity was previously characterized (Viggiani, A., Olivieri, G., Siani, L., Di Donato, A., Marzocchella, A., Salatino, P., Barbieri, P., Galli, E., 2006. An airlift biofilm reactor for the biodegradation of phenol by Pseudomonas stutzeri OX1. Journal of Biotechnology 123, 464-477). The model embodies the key processes relevant to the reactor performance, with a particular emphasis on the role of biofilm detachment promoted by the fluidized state. Results indicate that a finite loading of free cells establishes even under operating conditions that would promote wash out of the suspended biophase. The co-operative/competitive effects of free cells and immobilized biofilm result in rich bifurcational patterns of the steady state solutions of the governing equations, which have been investigated in the phase plane of the process parameters. Direct simulation under selected operating conditions confirms the importance of the dynamical equilibrium establishing between the immobilized and the suspended biophase and highlights the effect of the initial value of the biofilm loading on the dynamical pattern.