Modeling of immobilized cell columns for bioconversion and wastewater treatment

Immobilized cells are widely used in bioconversions to produce biological products as well as in wastewater treatment such as solvent removal from wastewater streams. In this work, a rate model is proposed to simulate this kind of process in an axial-flow fixed-bed column packed with porous particles containing immobilized cells. The transient model considered various mass transfer mechanisms including axial dispersion, interfacial film mass transfer, and intraparticle diffusion. Cell death in the immobilized cell system was also considered. Effects of various parameters such as kinetic constants and mass transfer parameters were studied. Operational situations such as feed fluctuation flow rate increase and two columns in series were also investigated. The model can be used to study the behavior and characteristics of immobilized cell columns in order to perform scale-up predictions of effluent profiles and for the purpose of process optimization.     

Solute exclusion from cellulose in packed columns: experimental investigation and pore volume measurements

A packed column approach was used in this investigation to determine pore volume and surface area distributions of several celluloses. Specific surface areas for Avicel PH 102, Solka Floc BW 300, and two size fractions of corn cobs that have been pretreated to remove lignin and hemicellulose were measured using this technique. In addition to measuring pore volume and specific surface area, the molecular diameters of several PEGs (polyethylene glycol) were estimated using viscosity measurements. Also, the influence of cellulose particle size, molecular diameter of PEGs, and PEG solution velocity on dispersion and tailing were investigated. Molecular diameter estimates from this investigation were 30%-35% lower than those reported in the literature. This discrepancy is due to earlier investigators using an inappropriate relationship for estimating molecular diameter from viscosity measurements. The precision of the column approach to solute exclusion was higher than that obtained by investigators using a batch approach. Dispersion increased with increasing particle size. Tailing of the elution curve was increased with increasing solute molecular diameter and elution rate. For a cellulase with a molecular diameter of 5.1 nm, estimated specific surface area ranged from 7.2 to 10.5 m(2) g(-1).     

Hydraulic characteristics of aerobic granules using size exclusion chromatography

Elution of poly(ethylene glycol) of molecular weight 200-20,000 Da from a size exclusion chromatography column packed with phenol-fed aerobic granules of three different nominal sizes (types I-III) has been investigated. The pore sizes of the three types of granules were evaluated based on the mean hydraulic times of the elution curves that decreased directly proportional to the increased logarithm of the molecular mass of a standard tracer and increased as granule size decreased. The corresponding exclusion limits for types I-III granules were 139,000, 123,000, and 54,500 Da, respectively. A one-dimensional convection-dispersion model described the effective dispersion coefficients of the tracers through the granule column. The intra-granular permeabilities and convective and diffusional transit times through the granule interior were evaluated by a dual porosity model. For small molecules of molecular mass <5,000 Da, intra-granular convection dominated transport mechanisms at fast moving velocity. For comparatively larger molecules, diffusion barrier existed to limit nutrient supply to the granules. The size exclusion test provided intra granular transport characteristics using detailed analysis on the elution data.     

Pore network modelling of affinity chromatography: determination of the dynamic profiles of the pore diffusivity of beta-galactosidase and its effect on column performance as the loading of beta-galactosidase onto anti-beta-galactosidase varies with time.

A three-dimensional pore network model for diffusion in porous adsorbent particles was employed in a dynamic adsorption model that simulates the adsorption of a solute in porous particles packed in a chromatographic column. The solution of the combined model yielded the dynamic profiles of the pore diffusion coefficient of beta-galactosidase along the radius of porous adsorbent particles and along the length of the column as the loading of beta-galactosidase onto anti-beta-galactosidase immobilized on the surface of the pores of the particles occurred, and, the dynamic adsorptive capacity of the chromatographic column as a function of the design and operational parameters of the chromatographic system. It was found that for a given column length the dynamic profiles of the pore diffusion coefficient were influenced by (a) the superficial fluid velocity in the column, (b) the diameter of the adsorbent particles, and (c) the pore connectivity of the porous structure of the adsorbent particles. The effect of the magnitude of the pore connectivity on the dynamic profiles of the pore diffusion coefficient of beta-galactosidase increased as the diameter of the adsorbent particles and the superficial fluid velocity in the column increased. The dynamic adsorptive capacity of the column increased as (i) the particle diameter and the superficial fluid velocity in the column decreased, and (ii) the column length and the pore connectivity increased. In preparative affinity chromatography, it is desirable to obtain high throughputs within acceptable pressure gradients, and this may require the employment of larger diameter adsorbent particles. In such a case, longer column lengths satisfying acceptable pressure gradients with adsorbent particles having higher pore connectivity values could provide high dynamic adsorptive capacities. An alternative chromatographic system could be comprised of a long column packed with large particles which have fractal pores (fractal particles) that have high pore connectivities and which allow high intraparticle diffusional and convective flow mass transfer rates providing high throughputs and high dynamic adsorptive capacities. If large scale monoliths could be made to be reproducible and operationally stable, they could also offer an alternative mode of operation that could provide high throughputs and high dynamic adsorptive capacities.     

Mathematical Modeling of Size Exclusion Chromatography

A mathematical model of the size exclusion chromatography (SEC) process in chromatographic columns has been developed. It considers the following three mass transfer processes in the SEC column: axial dispersion in the bulk‐fluid phase, interfacial film mass‐transfer between the stationary and mobile phases, and diffusion of solutes within the macro pores of the packing particles. Differential equations of the process model were solved by the finite difference method. Characteristics of the column and the packing particles (bed void volume fraction, particle porosity, accessible particle porosity) were obtained experimentally, as well as retention times of different molecules with known molecular weights. Experiments were performed with two different columns containing two different packing materials, Superdex 75 HR 10/30 and BioSep SEC S2000, respectively. The model has been validated by comparing theoretical and experimental retention times for the different columns.     

Fractionation and characterization of a Polysaccharide from the sclerotia of Pleurotus tuber-regium by preparative size-exclusion chromatography

A kind of regenerated cellulose gel (RCG) particles were treated by toluene to obtain particles with smaller mean pore size, then was mixed with the cellulose gel with pore size of 370 and 525 nm. A preparative size-exclusion chromatography (SEC) column (700 x 20 mm) packed with three gel particles was used to fractionate water-soluble polysaccharide (WEP) extracted from the sclerotia of Pleurotus tuber-regium by aqueous solution. The exclusion limit and fractionation range of the stationary phase of the preparative SEC were molecular mass 8 x 10(5) and 5 x 10(3) to 8 x 10(5), respectively. The calibration curve of the preparative SEC was represented as: log M=13.96-0.53 Ve. The WEP sample (weight-average molecular mass M(w)=2.2 x 10(4), polydispersity=2.4) was divided into three fractions with M(w) ranging from 1.4 x 10(4) to 3.4 x 10(4) by the preparative SEC column, and the fractions were characterized by gas chromatography GC, SEC combined with laser light scattering (SEC-LLS) and viscometry. The unfractionated WEP exhibited triple peaks due to different molecular mass, but each fraction exhibited single peak with the polydispersity of 1.1-1.8 in the SEC patterns. The results indicated that the preparative SEC was efficient for fractionation of polysaccharides having low molecular weight and for determination of their molecular mass.     

Mass transfer kinetics in the chromatography of insulin variants under nonlinear conditions

Experimental data regarding the thermodynamics and kinetics of adsorption of lispro, an insulin variant, onto a YMC ODS-A column, from an aqueous solution of acetonitrile (31%) and TFA are reinterpreted, using a more complex model of the mass transfer kinetics. The adsorption behavior follows the Toth isotherm model, suggesting either a strongly heterogeneous surface or, rather, that when insulin molecules adsorb they contact the surface along different areas of the molecule. The lumped pore diffusion (POR) model of chromatography accounts well for the band profiles. The internal mass transfer resistances are higher than expected, which suggests that intraparticle diffusion is slower. Furthermore, the pore diffusion coefficient increases with decreasing sample size. That surface diffusion accounts for the mass transfer kinetics inside particles explains these results. Assuming that the gradient of the surface concentration is the driving force of surface diffusion, it is possible to account very well for the band profiles of samples of widely different sizes, using a single value of the surface diffusivity.     

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.     

Parameter estimation of perillyl alcohol in RP-HPLC by moment analysis

Parameter estimations were made for the reversed-phase adsorption of perillyl alcohol (POH), a potent anti-cancer agent, on octadecylsilyl-silica gel (ODS). The average particle diameter of ODS was about 15 μm, and the particles were packed in the column (3.9 × 300 mm). The mobile phase used was a mixture of acetonitrile and water, in which the acetonitrile ranged between 50 and 70 (v/v %). The first absolute moment and the second central moment were determined from the chromatographic elution curves by moment analysis. Experiments were carried out using POH solutions within the linear adsorption range. The fluid-to-particle mass transfer coefficient was estimated using the Wilson-Geankoplis equation. The axial dispersion coefficient and the intraparticle diffusivity were determined from the slope and intercept of a plot ofH vs 1/u ₀, respectively. The contributions of each mass-transfer step were axial dispersion, fluid-toparticle mass transfer, and intraparticle diffusion.     

Predicting the elution behavior of proteins in affinity chromatography on non-porous particles.

Affinity chromatography on non-porous particles of microsize is particularly useful for the rapid analysis and micropreparative separation of proteins. The elution behavior of proteins in an affinity column packed with non-porous copolymerized particles of styrene, methyl methacrylate and glycidyl methacrylate was investigated both theoretically and experimentally, using the lysozyme-Cibacron Blue 3G-A affinity system. Equations used to predict the elution profiles, resulting from the elution by increasing the ionic strength (NaCl concentration) in the mobile phase, were obtained. The maximum adsorbate concentration, desorption rate constant and equilibrium constant under elution conditions were determined by matching experimental data with predicted elution profiles. Based on the parameters determined at a flow-rate of 0.5 ml/min and with 1 M NaCl in the elution buffer, the model equations could predict the elution profiles for other experimental runs, where different flow-rates and sodium chloride concentrations were used. Both the experimental and predicted results revealed that the affinity interaction kinetics are not significantly influenced by the flow-rate and, hence, the film mass transfer. To elute bound lysozyme from immobilized dye ligand, a higher value of the ionic strength leads to a faster elution and a sharper elution peak. The influence of elution conditions on the kinetic and thermodynamic parameters and, consequently, on the elution peak profiles was evaluated. The model equations can also predict the behavior of protein elution from an affinity column by changing the pH of the mobile phase, according to a previous study.     

Comparative evaluation of the swelling and degrees of cross-linking in three organic gel packings for SEC through some geometric parameters

The size exclusion chromatographic (SEC) behavior of five solvent/polymer systems in three organic column packings based on polystyrene/divinylbenzene (PS/DVB) copolymer, TSK-Gel H(HR), mu-styragel and TSK-Gel H(XL), has been compared. All the packings offer similar characteristics (pore size, particle size and efficiency) but some differences have been found when eluting the same systems. The different elution behavior observed in both polymeric gels has been analyzed in terms of their swelling and cross-linking degrees and of the fractal parameters. From the Universal Calibration plots, values of the chromatographic partition coefficient, K(p), have been obtained and using some equations previously reported, values of the volume fraction of the network in the swollen state have been determined for the three sets of columns. Overall, for a given hydrodynamic volume and solvent-polymeric solute system the fraction of cross-linked polymer in the stationary phase was ordered according to: TSK-Gel H(XL)>mu-styragel>TSK-Gel H(HR). This means an enhanced swelling degree for TSK-Gel H(HR). In general, fractal calculations support the thermodynamic predictions since both the fractal dimension and the pore size can be ordered as TSK-Gel H(HR)>mu-styragel>TSK-Gel H(XL) (in 10 of the 15 situations studied). The exceptions can be explained in terms of strong preferential solvation.     

Zonal rate model for stacked membrane chromatography part II: characterizing ion-exchange membrane chromatography under protein retention conditions

The Zonal Rate Model (ZRM) has previously been shown to accurately account for contributions to elution band broadening, including external flow nonidealities and radial concentration gradients, in ion-exchange membrane (IEXM) chromatography systems operated under nonbinding conditions. Here, we extend the ZRM to analyze and model the behavior of retained proteins by introducing terms for intra-column mass transfer resistances and intrinsic binding kinetics. Breakthrough curve (BTC) data from a scaled-down anion-exchange membrane chromatography module using ovalbumin as a model protein were collected at flow rates ranging from 1.5 to 20 mL min(-1). Through its careful accounting of transport nonidealities within and external to the membrane stack, the ZRM is shown to provide a useful framework for characterizing putative protein binding mechanisms and models, for predicting BTCs and complex elution behavior, including the common observation that the dynamic binding capacity can increase with linear velocity in IEXM systems, and for simulating and scaling separations using IEXM chromatography. Global fitting of model parameters is used to evaluate the performance of the Langmuir, bi-Langmuir, steric mass action (SMA), and spreading-type protein binding models in either correlating or fundamentally describing BTC data. When combined with the ZRM, the bi-Langmuir, and SMA models match the chromatography data, but require physically unrealistic regressed model parameters to do so. In contrast, for this system a spreading-type model is shown to accurately predict column performance while also providing a realistic fundamental explanation for observed trends, including an observed increase in dynamic binding capacity with flow rate.     

Cadmium removal in a biosorption column

New biosorbent material derived from a ubiquitous brown marine alga Ascophyllum nodosum has been examined in packed-bed flow-through sorption columns. It effectively removed 10 mg/L of cadmium down to 1.5 ppb levels in the effluent, representing 99.985% removal. The experimental methodology used was based on the early Bohart and Adams sorption model, resulting in quantitative determination of the characteristic process parameters which can be used for performance comparison and process design. An average metal loading of the biosorbent (N(0)) determined was 30 mg Cd/g, corresponding closely to that observed for the batch equilibrium metal concentration of 10 mg Cd/L. The critical bed depth (D(min)) for the potable water effluent quality standard (0.005 mgg Cd/L) varied with the column feed flow rate (2.4 to 9.6 L/h . cm(2)) from 20 to 50 cm. The sorption column mass transfer and dispersion coefficients were determined, which are also required for solving the sorption model equations. (c) 1994 John Wiley & Sons, Inc.     

Modelling of the chromatographic separation of xylose-mannose in ion-exchange resin columns

A mathematical model was proposed for the chromatographic separation of xylose and mannose on an ion-exchange resin in the Pb form: dispersion in the mobile phase, external mass transfer around the particles and internal diffusion were taken into account. Small-scale experiments provided an evaluation of the different parameters. Dispersion in the mobile phase was found to be the predominant phenomenon. The Peclet numbers were calculated by identification in the Laplace domain of the elution profiles. Influence of temperature and initial concentration of the sample were studied.     

Systematic interpolation method predicts protein chromatographic elution with salt gradients,pH gradients and combined salt/pH gradients

A methodology is presented to predict protein elution behavior from an ion exchange column using both individual or combined pH and salt gradients based on high‐throughput batch isotherm data. The buffer compositions are first optimized to generate linear pH gradients from pH 5.5 to 7 with defined concentrations of sodium chloride. Next, high‐throughput batch isotherm data are collected for a monoclonal antibody on the cation exchange resin POROS XS over a range of protein concentrations, salt concentrations, and solution pH. Finally, a previously developed empirical interpolation (EI) method is extended to describe protein binding as a function of the protein and salt concentration and solution pH without using an explicit isotherm model. The interpolated isotherm data are then used with a lumped kinetic model to predict the protein elution behavior. Experimental results obtained for laboratory scale columns show excellent agreement with the predicted elution curves for both individual or combined pH and salt gradients at protein loads up to 45 mg/mL of column. Numerical studies show that the model predictions are robust as long as the isotherm data cover the range of mobile phase compositions where the protein actually elutes from the column.     

Recovery of biologically active enzymes after HPLC separation

The mass and activity recovery of eight different enzymes (two monomeric, six oligomeric) with molecular masses between 25,000 and 240,000 daltons were tested after HPLC separation on three different HPLC instruments (two with stainless steel and one with titanium flow paths). Most of the tested proteins are known to be sensitive to heavy metal ions. Eight wide pore, ion-exchange columns, two size-exclusion columns and two hydrophobic-interaction columns were used. Both stainless steel and glass column hardware were used in all three separation modes. The elution times were between 8 and 12 minutes. In almost all cases, the activity recovery was between 90% and 100% compared with a control sample incubated in the chromatographic elution buffer for the same time at the same temperature. A severe activity loss (about 30%) was observed with only one ion-exchange column and one enzyme. Neither the column hardware nor the material of the HPLC equipment had any negative effect on the activity recovery of the enzymes tested.     

Analysis of Dispersion Mechanism in Gel Chromatography

The mechanism of dispersion of solute in gel chromatography using various Sephadex gels was quantitatively studied. In order to simplify the mathematical treatment, non-ad- sorptive low-molecular weight substances such as NaCl and glucose were chosen as samples. A pulse response experiment was carried out in a column. The longitudinal dispersion coefficient and the diffusion coefficient in gel phase were determined separately by applying the moment method to the elution curve. Then, their contribution to the column efficiency characterized by HETP was studied. Particularly, the effect of gel phase diffusion was examined in detail. The gel phase diffusion coefficient was apparently much smaller than the molecular diffusion coefficient. Consequently, it was revealed that gel phase diffusion played a much more important role in gel chromatography than what was expected by other investigators.     

Entropic interaction chromatography: separating proteins on the basis of size using end-grafted polymer brushes

Partitioning of a macromolecule into the interfacial volume occupied by a grafted polymer brush decreases the configurational entropy (DeltaSbrush(c)) of the terminally attached linear polymer chains due to a loss of free volume. Self-consistent field theory (SCF) calculations are used to show that DeltaSbrush(c) is a strong function of both the size (MWp) of the partitioning macromolecule and the depth of penetration into the brush volume. We further demonstrate that the strong dependence of DeltaSbrush(c) on MWp provides a novel and powerful platform, which we call entropic interaction chromatography (EIC), for efficiently separating mixtures of proteins on the basis of size. Two EIC columns, differing primarily in polymer grafting density, were prepared by growing a brush of poly(methoxyethyl acrylamide) chains on the surface of a wide-pore (1,000-A pores, 64-microm diameter rigid beads) resin (Toyopearl AF-650M) bearing surface aldehyde groups. Semipreparative 0.1-L columns packed with either EIC resin provide reduced-plate heights of 2 or less for efficient separation of globular protein mixtures over at least three molecular-weight decades. Protein partitioning within these wide-pore EIC columns is shown to be effectively modeled as a thermodynamically controlled process, allowing partition coefficients (K(P)) and elution chromatograms to be accurately predicted using a column model that combines SCF calculation of K(P) values with an equilibrium-dispersion type model of solute transport through the column. This model is used to explore the dependence of column separation efficiency on brush properties, predicting that optimal separation of proteins over a broad MWp range is achieved at low to moderate grafting densities and intermediate chain lengths.     

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.     

Breakthrough performance of stacks of dye-cellulosic fabric in affinity chromatography of lysozyme

The breakthrough performance of stacks of dye-cellulosic fabric in affinity chromatography of lysozyme was investigated in batch and flow experiments. Breakthrough curves were significantly affected by flow rate and were not dependent on the feed solution concentration. System dispersion curves could not explain the flow-rate dependence. Breakthrough curves were analyzed by coupling the kinetic model for pore mass transfer as the only controlling resistance and a system dispersion model. From the analysis, pore film mass transfer resistance was found to be the leading rate-limiting factor when the residence time in the column is greater than 5 min. The model was used to predict the operating and design parameters needed to obtain sharp breakthrough curves. Selectivity studies using lysozyme and bovine serum albumin mixtures showed a high system selectivity for lysozyme.