Predicting the performance of immobilized enzyme reactors using reversible Michaelis–Menten kinetics

A general mathematical model is developed in the present work for predicting the steady state performance of immobilized enzyme reactor performing reversible Michaelis - Menten kinetics. The model takes into account the effect of external diffusional limitations, the axial dispersion and the equilibrium constant on reactor performance quantified as relative substrate conversion and yield. The performance of reactor is characterized using the dimensionless parameters of Damkohler number, Stanton number, Peclet number, the equilibrium constant and the dimensionless input substrate concentration. The reactor performance is described for the two extreme cases of plug flow reactor (PFR) and continuous stirred tank reactor (CSTR) in addition to the intermediate case of dispersed plug flow reactor (DPFR). The performance of reactor is compared for the two cases of zero order and reversible first order kinetics.     

Xylanase mass transfer studies in aqueous two-phase systems using spray and sieve plate columns

Aqueous two-phase systems (ATPSs) have long been used for biomolecule partitioning; these systems offer the possibility of using continuous or semicontinuous extraction processes. They require relatively simple equipment like spray or sieve plate columns that can be adapted for use in ATPSs. The aim of this work was to study the semicontinuous extraction of a model enzyme, xylanase, in spray and sieve plate columns, since, unlike centrifugal contactors, the cost of construction and maintenance of this equipment is low and it is easy to operate. For the spray column, the dispersed phase hold-up and overall mass transfer coefficients K(D) a were evaluated for different column heights and for different superficial velocities of the dispersed phase (light phase). Results indicated that an increase in superficial velocity in the range of 0-0.18 mm/s of the dispersed phase had a positive effect on K(D) a and on hold-up in all column heights studied, 75, 161 and 246 mm. For the same superficial velocity of the dispersed phase, the larger the hold-up was, the shorter the column. For the sieve plate column, the effects of the superficial velocity of the dispersed phase and the number of plates were also studied. Results showed that the K(D) a and hold-up increased with an increase in both parameters. The selectivity of separation of xylanase and BSA (model contaminant) was very high, since 60% of the enzyme was extracted in the light phase, whereas no significant amount of BSA was extracted. The possibility of using the sieve plate column in continuous operation for enzyme extraction was studied because previous work had only addressed the semicontinuous extraction of enzyme. The residence time distribution of the PEG phase using different superficial velocities of the salt phase was studied in continuous operation. The time required to reach the steady state was 40 min, and 70% of the xylanase was recovered. It was found that the Modified Power Spline software was well adjusted to the experimental results.     

Caffeine Extraction with a Karr Reciprocating Plate Column

A Karr reciprocating plate column was used in extracting caffeine from the methylation mother solution of a caffeine synthesis plant with chloroform as the extractant. Pilot tests were carried out in a 38 mm diameter column to determine holdup, flooding and mass transfer at various reciprocation velocities. Results show that the holdup in the presence of mass transfer is higher than that in the absence of mass transfer, and the height of the equivalent theoretical stage (HETS) was 0.57 m for a 99.9 % recovery at the optimum reciprocation velocity. The Karr empirical correlation for scale‐up was used to predict the column height in the design of the industrial process. A 0.4 m and a 0.6 m diameter column were used to treat 2.5 m³/h and 6.0 m³/h methylation mother solution, and the corresponding HETSs were 1.42 m and 1.53 m for a 99.9 % recovery, respectively. The axial dispersion coefficients of the dispersed phase were estimated for the 0.4 m and the 0.6 m diameter columns. For a better recovery the ratio of the axial dispersion coefficient of the dispersed phase to that of the continuous phase was about 2.7–3.0.     

Apparent and true longitudinal concentration profiles in reciprocating plate column

Mass transfer for kerosene-water system with benzoic acid and n-butyric acid as solutes has been studied in a reciprocating plate column at different operating conditions including the agitation rate of the plate stack, the plate geometry, the flow rates of the phases and the direction of mass transfer. Apparent and true concentration profiles for the dispersed and the continuous phase along the length of the column were generated, taking axial mixing of the phase into consideration. It is noticed that high agitation rate for the plate stack and low free area for the plate give rise to large difference between the apparent and true values. These observations also agree with the data obtained for carbon dioxide — water system studied in a reciprocating plate column.     

Continuous countercurrent salting-out extraction of 1,3-propanediol from fermentation broth in a packed column

The possibility of continuous extraction of 1,3-propanediol in a experimental packed column was investigated using a salting-out extraction system of dipotassium phosphate/ethanol. Mass transfer of 1,3-propanediol takes place from the dispersed phase (salt-rich solution) to the continuous phase (ethanol). The influences of flow rate of dispersed phase and size of packing material on partition coefficient and recovery of 1,3-propanediol were investigated and the results were compared with those obtained in spray column and test tube. Furthermore, the influences of various system compositions on hold up of dispersed phase, mass transfer coefficient, and system stability were also studied in the column packed by stainless steel Dixon 3 × 3 mm. It was found that the packed column showed a good extraction efficiency and stability. Besides, 1,3-propanediol recovery of 90.30% was obtained during a 11 h continuous operation when the real fermentation broth was used. At the same time, 94.4% of phosphate could be recovered when 0.2 volume of anhydrous ethanol was added into the raffinate phase at pH 4.0.     

Oxygen mass transfer into aerated CMC solutions in a bubble column

Differing findings on the volumetric mass transfer coefficients k(L)a in CMC solutions in bubble column bioreactors have been reported in the literature. Therefore, oxygen mass transfer was studied again in CMC solutions in a 14-cm-i.d. x 270-cm-height bubble column using different spargers. The k(L)a values were determined along with the dispersion coefficients by fitting the prediction of the axial dispersed plug model with the experimental oxygen concentration profiles in the liquid phase. Surprisingly, the obtained liquid phase dispersion coefficients for CMC solution are higher than one would expect from correlations. The k(L)a data depend largely on the flow regime. In general, they are lower than those reported in the literature. The data for developing slug and established slug flow are dependent on the gas velocity and the effective viscosity of the solution and can br correlated by a simple correlation. This correlation describes k(L)a values measured on fermentation broth of Penicillium chrysogenum with striking agreement.     

Protein mass transfer studies on a spray column using the PEG-Reppal PES 100 aqueous two-phase system

The characterization of Bovine Serum Albumin mass transfer mechanisms in a spray column using an aqueous two-phase system composed of poly(ethylene glycol) and a modified starch-Reppal PES 100-is done. The poly(ethylene glycol) rich phase is used as the dispersed phase and protein transfer takes place from the dispersed phase to the continuous phase. The effect of dispersed phase superficial velocity, system composition, continuous phase height and distribution system design on either overall protein mass transfer coefficient or column hold-up is described. It is shown that continuous phase superficial velocity and phase composition are the main controlling factors for protein transfer. It is also observed that, with the tested system, only at very low dispersed phase superficial velocities is it possible to operate the spray column as an extraction column. In this system the upper operating limit of the dispersed phase velocity is ten times smaller than in other aqueous two-phase systems.List of Symbols ATPS Aqueous Two-Phase System - BSA Bovine Serum Albumin - C _i kg m^–3 inlet dispersed phase protein concentration - C ₀ kg m^–3 outlet dispersed phase protein concentration - C _d kg m^–3 dispersed phase protein concentration - C _c kg m^–3 continuous phase protein concentration - D m column internal diameter - H hold-up - h, h _d m dispersion height - h ₀ m initial dispersion height (initial continuous phase height) - k _da s^–1 overall mass transfer coefficient - m protein partition coefficient - n number of holes of distribution system - PEG Poly(ethylene glycol) - Q m³ s^–1 dispersed phase volumetric flow rate - S m² column internal area - V m³ dispersion volume A. Venâncio was supported by a JNICT (Junta Nacional de Investigaçäo Científica e Tecnológica) grant.     

Growth models of cultures with two lipid phases. I. Substrate dissolved in dispersed phase

Mathematical models which can be used to describe batch growth in fermentations with two liquid phases are developed for systems in which the growth limiting substrate is dissolved the dispersed liquid phase. In the models, the possibilities of growth occurring at the surface of the dispersed phase and in the continuous phase are considered. It is assumed that the composition of the dispersed phase is such that substrate utilization from it causes little of no change, in interfacial area. Three special cases are examined. In the first, it is assumed that all growth occurs at the surface of the dispersed phase. In the second and third, it is assumed that growth occurs both at the interface and in the continuous phase. The second case assumes that substrate equilibrium is continuously established between the two phases while the third assumes substrate consumption in the continuous phase is limited by rate of transport of substrate to that phase. Comparison of the first model with available experimental data shows good agreement between model and data.     

Continuous aqueous two-phase extraction of human antibodies using a packed column

The performance of a pilot scale packed differential contactor was evaluated for the continuous counter-current aqueous two-phase extraction (ATPE) of human immunoglobulin G (IgG) from a Chinese hamster ovary (CHO) cells supernatant (CS) enriched with pure protein. Preliminary studies have been firstly performed in order to select the dispersed phase (phosphate-rich or polyethylene glycol 3350 Da (PEG)-rich phase) and the column packing material. The PEG-rich phase has been selected as the dispersed phase and the stainless steel as the preferred material for the column packing bed since it was not wetted preferentially by the selected dispersed phase. Hydrodynamic studies have been also performed, and the experimental results were successfully adjusted to the Richardson-Zaki and Mísek equations, typically used for the conventional organic-aqueous two-phase systems. An experimental set-up combining the packed column with a pump mixer-settler stage showed to have the best performance and to be advantageous when compared to the IgG batch extraction. An IgG recovery yield of 85% could be obtained with about 50% of total contaminants and more than 85% of contaminant proteins removal. Mass transfer studies have revealed that the mass transfer was controlled by the PEG-rich phase. A higher efficiency could be obtained when using an extra pump mixer-settler stage and higher flow rates.     

Hydrodynamics and mass transfer in aqueous two-phase protein extraction using a continuous perforated rotating disc contactor

A continuous perforated rotating disc contactor was used to extract bovine serum albumin (BSA) with aqueous two-phase systems based on polyethylene glycol (PEG) and phosphate salts. The dispersed phase holdup and mass transfer coefficient were determined. It was found that the dispersed phase holdup increased with increasing PEG phase velocity. The overall mass transfer coefficient for BSA was independent of the PEG phase velocity.     

Breakthrough performance of plasmid DNA on ion-exchange membrane columns

Breakthrough performance of plasmid DNA adsorption on ion-exchange membrane columns was theoretically and experimentally investigated using batch and fixed-bed systems. System dispersion curves showed the absence of flow non-idealities in the experimental arrangement. Breakthrough curves (BTC) were significantly affected by inlet flow rate and solute concentration. In the theoretical analysis, a model was integrated by the serial coupling of the membrane transport model and the system dispersion model. A transport model that considers finite kinetic rate and column dispersed flow was used in the study. A simplex optimization routine, coupled to the solution of the partial differential model equations, was employed to estimate the maximum adsorption capacity constant, the equilibrium desorption constant, and the forward interaction rate constant, which are the parameters of the membrane transport model. The analysis shows that as inlet concentration or flow rate increases, the deviation of the model from the experimental behavior decreases. The BTCs displacement as inlet concentration increases was explained in terms of a greater degree of column saturation reached and more efficient operation accomplished. The degree of column saturation was not influenced by inlet flow rate. It was necessary to consider in the column model the slight variation in the BTC produced by the axial dispersion, in order to accomplish the experimental curve dispersion. Consequently, the design criteria that for Pe > 40 the column axial dispersion can be neglected should be taken with precaution.     

Design and physical characteristics of a multistage,continuous tower fermentor

A multistage tower laboratory fermentor has been constructed consisting of eight compartments separated by sieve plates. Flow of substrate and air is concurrent from the bottom to the top of the column. It, was hoped that this system could be used to reproduce, simultaneously on a continuous basis, eight distinct phases of a batch growth curve. It was believed that the extent of batch curve simulation would depend upon the character of hydraulic mean residence time of broth in the column and in the individual compartments. The expected relationship did not occur. Rather it was found that growth in the column involved residence time characteristics not only for the fluid but also for the microorganisms, and for the growth limiting substrate. Depending upon the column operation, these could be distinct and different. The purpose of this investigation was to study the residence time distribution (RTD) of the continous (fluid) and dispersed (microorganisms) phases for model systems as well as for a yeast fermentation. Various degrees of flow nonideality, i.e., fluid blackflow and dispersed phase sedimentation, were noticed. The former seems to be due to interaction of the concurrent gas and liquid flow; it is particularly dependent upon void area of the sieve plate holes. Sedimentation is probably a function of plate design as well as cell size and density. It wa concluded that for a particular plate design the gas hold-up wass controlled by superficial air velocity and was the main parameter governing the differences between dispersed and continous phase(Rt1). This conclusion was supported by a computeraided styudy utilizing a mathematical model of fluid flow to fit the growth kinetics and cell distribution observed experimentally throughout the fermentor. Some advantages of foam control in the tower fermentor by surface active compounds are mentioned. Also, suggestions are made for carrying out fermentations that have two liquid phases, such as a hydrocarbon fermentation. The possibility of closely approximating plug-flow conditions in the multistage tower fermentor, a necessary condition for batch growth simulation, is discussed from a practical point of view.     

Morphological analysis of tumor cell/endothelial cell interactions under shear flow

In the process of hematogenous cancer metastasis, tumor cells (TCs) must shed into the blood stream, survive in the blood circulation, migrate through the vascular endothelium (extravasation) and proliferate in the target organs. However, the precise mechanisms by which TCs penetrate the endothelial cell (EC) junctions remain one of the least understood aspects of TC extravasation. This question has generally been addressed under static conditions, despite the important role of flow induced mechanical stress on the circulating cell-endothelium interactions. Moreover, flow studies were generally focused on transient or firm adhesion steps of TC-EC interactions and did not consider TCs spreading or extravasation. In this paper, we used a parallel-plate flow chamber to investigate TC-EC interactions under flow conditions. An EC monolayer was cultured on the lower plate of the flow chamber to model the endothelial barrier. Circulating TCs were introduced into the flow channel under a well-defined flow field and TC cell shape changes on the EC monolayer were followed in vitro with live phase contrast and fluorescence microscopy. Two spreading patterns were observed: radial spreading which corresponds to TC extravasation, and axial spreading where TCs formed a mosaic TC-EC monolayer. By investigating the changes in area and minor/major aspect ratio, we have established a simple quantitative basis for comparing spreading modes under various shear stresses. Contrary to radial spreading, the extent of axial spreading was increased by shear stress.     

Influence of reactor geometry on mixing characteristics in a down flow jet loop bioreactor: newtonian and non-newtonian fluids

Mixing characteristics in the downcomer and the riser of a continuous down-flow jet loop bioreactor was studied with Newtonian and non-Newtonian fluids. The mixing parameters were determined through the curve fitting of the experimental impulse response data with the solution of one dimensional axial dispersion model. It was found that circulation number and axial dispersion coefficient increased with an increase in liquid flow rate and draft tube to column diameter ratio and the axial dispersion coefficient was comparatively higher in the riser. The circulation number increased with decrease in nozzle diameter. The model predicted the experimental data well within 8% deviation for both the systems (water and CMC). Correlations were obtained to predict axial dispersion coefficients in the riser and downcomer of the reactor.     

Probing the impact of axial diffusion on nitric oxide exchange dynamics with heliox.

Exhaled nitric oxide (NO) is a potential noninvasive index of lung inflammation and is thought to arise from the alveolar and airway regions of the lungs. A two-compartment model has been used to describe NO exchange; however, the model neglects axial diffusion of NO in the gas phase, and recent theoretical studies suggest that this may introduce significant error. We used heliox (80% helium, 20% oxygen) as the insufflating gas to probe the impact of axial diffusion (molecular diffusivity of NO is increased 2.3-fold relative to air) in healthy adults (21-38 yr old, n = 9). Heliox decreased the plateau concentration of exhaled NO by 45% (exhalation flow rate of 50 ml/s). In addition, the total mass of NO exhaled in phase I and II after a 20-s breath hold was reduced by 36%. A single-path trumpet model that considers axial diffusion predicts a 50% increase in the maximum airway flux of NO and a near-zero alveolar concentration (Ca(NO)) and source. Furthermore, when NO elimination is plotted vs. constant exhalation flow rate (range 50-500 ml/s), the slope has been previously interpreted as a nonzero Ca(NO) (range 1-5 ppb); however, the trumpet model predicts a positive slope of 0.4-2.1 ppb despite a zero Ca(NO) because of a diminishing impact of axial diffusion as flow rate increases. We conclude that axial diffusion leads to a significant backdiffusion of NO from the airways to the alveolar region that significantly impacts the partitioning of airway and alveolar contributions to exhaled NO.     

Augmentation of axial dispersion by intermittent oscillatory flow.

The efficiency of axial gas dispersion during ventilation with high-frequency oscillation (HFO) is improved by manipulating the oscillatory flow waveform such that intermittent oscillatory flow occurs. We therefore measured the velocity profiles and effective axial gas diffusivity during intermittent oscillatory flow in a straight tube to verify the intermittency augmentation effect on axial gas transfer. The effective diffusivity was dependent on the flow patterns and significantly increased with an increase in the duration of the stationary phase. It was also found that the ratio of effective diffusivity to molecular diffusivity is two times greater than that in sinusoidal oscillatory flow. Moreover, turbulence during deceleration or at the beginning of the stationary phase further augments axial dispersion, with the effective diffusivity being over three times as large, thereby proving that the use of intermittent oscillatory flow effectively augments axial dispersion for ventilation with HFO.     

Residence time distributions of gas flowing through rotating drum bioreactors

Residence time distribution studies of gas through a rotating drum bioreactor for solid-state fermentation were performed using carbon monoxide as a tracer gas. The exit concentration as a function of time differed considerably from profiles expected for plug flow, plug flow with axial dispersion, and continuous stirred tank reactor (CSTR) models. The data were then fitted by least-squares analysis to mathematical models describing a central plug flow region surrounded by either one dead region (a three-parameter model) or two dead regions (a five-parameter model). Model parameters were the dispersion coefficient in the central plug flow region, the volumes of the dead regions, and the exchange rates between the different regions. The superficial velocity of the gas through the reactor has a large effect on parameter values. Increased superficial velocity tends to decrease dead region volumes, interregion transfer rates, and axial dispersion. The significant deviation from CSTR, plug flow, and plug flow with axial dispersion of the residence time distribution of gas within small-scale reactors can lead to underestimation of the calculation of mass and heat transfer coefficients and hence has implications for reactor design and scale-up.     

Contribution of upper airway geometry to convective mixing

We investigated the axial dispersive effect of the upper airway structure (comprising mouth cavity, oropharynx, and trachea) on a traversing aerosol bolus. This was done by means of aerosol bolus experiments on a hollow cast of a realistic upper airway model (UAM) and three-dimensional computational fluid dynamics (CFD) simulations in the same UAM geometry. The experiments showed that 50-ml boluses injected into the UAM dispersed to boluses with a half-width ranging from 80 to 90 ml at the UAM exit, across both flow rates (250, 500 ml/s) and both flow directions (inspiration, expiration). These experimental results imply that the net half-width induced by the UAM typically was 69 ml. Comparison of experimental bolus traces with a one-dimensional Gaussian-derived analytical solution resulted in an axial dispersion coefficient of 200-250 cm(2)/s, depending on whether the bolus peak and its half-width or the bolus tail needed to be fully accounted for. CFD simulations agreed well with experimental results for inspiratory boluses and were compatible with an axial dispersion of 200 cm(2)/s. However, for expiratory boluses the CFD simulations showed a very tight bolus peak followed by an elongated tail, in sharp contrast to the expiratory bolus experiments. This indicates that CFD methods that are widely used to predict the fate of aerosols in the human upper airway, where flow is transitional, need to be critically assessed, possibly via aerosol bolus simulations. We conclude that, with all its geometric complexity, the upper airway introduces a relatively mild dispersion on a traversing aerosol bolus for normal breathing flow rates in inspiratory and expiratory flow directions.     

The hydrodynamics of a Graesser ("raining bucket") contactor with a reverse micellar phase

A variety of contactor types have been assessed for the liquid-liquid extraction of proteins using reversed micelles; however, many of these contactors suffer from drawbacks such as emulsion formation and poor mass transfer performance. In this study, a small (1.25 L) Graesser "raining bucket" contactor was assessed for use with this system since it has the potential to ameliorate many of these problems. The aim of the work was to evaluate the hydrodynamics of the contactor in order to use this information for future work on mass transfer performance. Hydrodynamic characteristics such as the axial mixing coefficient were determined by residence time distribution studies using a tracer injection method. The effect of rotor speed and flow rate of each phase on axial mixing was investigated, and as a result of its unusual structure, i.e., falling/rising sheet, the interfacial mass transfer area in the Graesser was determined by image analysis. It was found that rotor speed had more influence on the axial mixing coefficient in the aqueous phase than in the reverse micellar phase. The axial mixing coefficient in each phase increased by increasing the flow rate of the same phase. The images obtained in a dropping cell showed that under the conditions of this study (3 rpm, 22 degrees C), the bucket pours one phase through the other in the form of a curtain or sheet. A new image technique was developed to determine the interfacial area of both phases, and it was found that the specific area was 8.6 m(2)/m(3), which was higher than in a spray column but considerably lower than in a RDC or a Graesser run at high rotational speed (50 rpm) without the addition of a surfactant.