Theoretical Modelling

A number of approaches have been adopted for the modelling of adsorption and chromatography operations in computer-aided process engineering. Some of these describe the features of the separation in gross, overall terms and essentially describe the mass balance over the process. Alternatively, other attempts have involved a detailed consideration of the details of such processes. One approach towards understanding the features that dictate the success and characteristics of an affinity separation has involved a detailed study of the nature and characteristics of the equilibrium and mass transfer processes for the adsorption/desorption of the adsorbate, and in some cases other key components in the separation. The nature of adsorbents adopted for use in practical affinity separations results in a totally thorough approach to modelling being complicated and impractical. Accurate analysis is frustrated by the presence of a distribution of particle diameters and pore characteristics, in addition to a non-homogeneous distribution of immobilized ligand throughout the interstices of the adsorbent. It has often been necessary to use approximate methods that overlook the latter complications. In general, the modelling of preparative chromatography is also difficult as a result of the need to consider the simultaneous adsorption of multiple species. However, the fact that affinity separations often involve the adsorption of only one or a few components can simplify the task. It must be remembered that although the selection and subsequent solution of a set of algebraic equations which describe the characteristics of an adsorption system can often be undertaken, it is also essential to obtain values for the parameters used in such equations which apply to the actual separation under

Table 2 Strategies for optimizing the stages of affinity separations

Stage

Criteria ofeffciency

Achievedby

Adsorption

Washing

Elution (gradient)

Elution (step)

Sharp breakthrough curves

Selectivity

Maximum removal of contaminants, minimum removal of adsorbate

Maximum concentration of product

Minimum denaturation of product

Adsorbents with good kinetic properties (small particles, adsorption to outer surfaces) Low flow rates

High inlet concentrations of adsorbate Appropriate choice of ligand Appropriate choice of buffers

Reversed flow direction Strong eluents Low flow rates Weak eluents High flow rates consideration. Commercial packages are now available which are reported to be effective for scale-up and optimization of affinity separations, although substantial improvements to a process can also be made on the basis of a qualitative understanding of the basic features of an affnity separation (Table 2).

It has already been pointed out that resolution in affinity separations is almost always achieved during the adsorption process and is less likely to be necessary during elution unless the specificity of the affinity ligand is low and multiple species have been adsorbed. Hence the majority of effort has been expended towards understanding the events that occur during the adsorption stage of the separation and is thus directed towards optimizing the duration of the adsorption stage to ensure that the potential adsorption capacity of the bed is utilized as far as possible, i.e. full use has been made of the costly immobilized ligand. Of particular importance is the correct assessment of the amount of adsorbate that can be removed from the feedstock during a cycle of operation. This requires knowledge of not only the maximum capacity of the adsorbent (qm) but also the dissociation constant (Kd) of the adsorbed species. It is important to remember that the capacity of the adsorbent is governed by the nature of the adsorption isotherm, even when kinetic limitations allow the adsorbent to become loaded to equilibrium with the feedstock. In many cases, the equilibrium characteristics have been shown to be adequately described by a simple Langmuir isotherm, although the situation is certainly more complicated where more than one component can bind to the adsorbent. The shape of the adsorption isotherm is in most cases hyperbolic, with characteristics described by:

Only in situations where the concentration of adsorbate in the feedstock, cA, is of greater magnitude than the value of the dissociation constant of the adsorbed species (Kd) will the affinity adsorbent show equilibrium binding capacities as great as the maximum adsorption capacity (qm). Indeed for values of cA smaller than Kd, the equilibrium capacity of the adsorbent (q) decreases linearly with decreasing cA and is given by q =

qmCA

This simple consequence of the law of mass action often accounts for the apparently low adsorption capacities that are observed during the development of affinity separations which are frequently mistakenly identified as a malfunction of the adsorbent. This point shows the importance of knowing the value of Kd of the selected ligand, but also the need to select an affinity ligand where the dissociation constant of the adsorbed complex with adsorbate is sufficiently low to ensure satisfactory capture of adsorbate from feedstock, particularly if attempts are being made to capture an adsorbate present at low concentrations.

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