Optimization of Displacement and Gradient Chromatography (with Professor Bequette)

Significant progress was made in developing tools for the characterization of commercial ion-exchange resin materials and the optimization of ion-exchange displacement separation of proteins. A methodology for the characterization of commercial stationary phase materials was developed based on pulse analysis. For a given stationary phase material, pulse injections of proteins were made at various flow rates and under both unretained and retained conditions. The general rate model was employed in conjunction with the Steric Mass Action (SMA) isotherm under linear adsorption conditions to develop equations relating the HETP of the elution peaks to operational parameters such as the flow rate and salt concentration. These equations were then used to estimate the relevant transport parameters (axial dispersion parameter, film mass transfer coefficient, pore and surface diffusion coefficient and desorption rate constant). Subsequently, appropriate dimensionless groups were constructed to evaluate the relative importance of the various transport mechanisms. It was demonstrated that surface diffusion played a prominent role in stationary phase materials with high capacities.

We are currently extending this research on the characterization of  dominant non idealities to novel chromatographic resins including monolithic materials, monodisperse beads and diffusive matrices with long chains of dextran coupled to the agarose materials.  Preliminary results indicate that the monolithic materials are kinetically limited and the theoretical predictions have shed insight into the optimum performance of these materials.

A novel iterative scheme was also developed to optimize ion-exchange displacement separations of proteins. The results obtained using the iterative scheme were confirmed using a rigorous optimization algorithm. In addition, the utility of the iterative scheme in methods development was demonstrated using a very challenging model separation problem. The optimum operating conditions identified for this separation were contrary to conventional wisdom. Standard rules of thumb suggest the use of low salt concentration and high displacer concentration in developing displacement separations. However, if one were to use these conditions, one would end up with an extremely low-yield process. The optimum scheme identified the optimum conditions at relatively high salt and low displacer concentrations. The resultant separation was dramatically improved under these conditions and the experimental results were in excellent agreement with the theoretical predictions.
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In addition, the iterative scheme was employed to study the performance of various classes of separation problems on different resin materials. The studies have provided significant insights into the effect of various resin characteristics (e.g. capacity, efficiency) on the performance of displacement systems. In fact, the results suggest that a large particle system can perform better than a small particle system if it has a high protein binding capacity.

The general rate model was solved using orthogonal collocation on finite elements (OCFE) for the non-equilibrium Langmuir isotherm and non-equlibrium Steric Mass Action (SMA) Isotherm. The normalized space coordinates are divided into set of discrete elements of arbitrary length. Orthogonal collocation is performed on each normalized element. In the axial direction, Legendre polynomials are used to solve stiff problems. In the radial direction, Jacobi polynomials are used as they satisfy the boundary condition at the interior node of the element. Original model equations, partial differential equations, are converted to ordinary differential equations. The resulting temporal equations are solved using DDASSL (Differential/Algebraic System Solver).
Current work involves attempting to decrease the bandwidth of the equations solved in DDASSL. This is by employing Hermite polynomials in the axial direction. This eliminates the requirement of elemental continuity equations, thereby decreasing the bandwidth. To further decrease the computational cost adaptive finite elements for orthogonal collocation is being currently developed.

Preliminary work has been performed for run to run control of chromatographic separation processes. Run to run controllers are model-based controllers coupled with an observer. Run to run control uses information from previous batches to modify the parameters that are applied to subsequent batches, thus providing better target tracking. The final element of run to run controller is the control law, which specifies how the parameters for the process should be updated. The product qualities of interest are rarely measured in situ, so the process model (linear regressions, dynamic state space models etc.) is used to relate the measurable inputs and states to the desired product qualities. The process model is then used in the control law to determine which parameters, or process inputs, should be adjusted to give the desired output. The control law in the run to run controller specifies how the recipe must be modified in order to keep the process on target.
 
 
 

Representative Abstracts:

Natarajan V., Bequette B.W., and Cramer, S.M. “Optimization of ion exchange displacement separations. I. Validation of an iterative scheme and its use as a methods development tool”, in press, J. Chromatogr.

Displacement chromatography has been demonstrated to be a powerful, high-resolution preparative tool. The performance of displacement systems can be affected by a variety of factors such as the feed load, flow rate, initial salt concentration and the displacer partition ratio. Thus, the optimization of displacement separations is a uniquely challenging problem. In this manuscript, an iterative optimization scheme has been presented whereby one can identify the optimum operating conditions for displacement separations at a given level of loading on a given resin material. The solid film linear driving force model has been employed in concert with the Steric Mass Action formalism of ion-exchange chromatography to describe the chromatographic behavior in these systems. Simple pulse techniques have been employed to estimate the transport parameters. The iterative scheme has been validated using a rigorous Feasible Sequential Quadratic Programming algorithm. Finally, the utility of the iterative optimization scheme as a methods development tool for displacement separations has been demonstrated for a difficult separation. The results indicate that the use of the optimization scheme leads to significantly better performance than standard rules of thumb.
 

Natarajan, V., and Cramer, S. M., “A Methodology for the Characterization of Ion-Exchange Resins”, in press. Separation Science and Technology

Tremendous strides have been made in the field of stationary phase synthesis over the course of the last decade. Although important research has been carried out to elucidate the characteristics of various resins, there is currently a lack of understanding regarding the effect of the various resin materials on preparative modes of chromatography. To describe preparative chromatography, one needs to have appropriate isotherm and transport models. In this manuscript, a methodology is presented to enable the identification of appropriate transport models to describe the chromatographic behavior of solutes in preparative ion-exchange systems. The methodology involves simple pulse experiments to estimate the various transport parameters followed by the construction and analysis of various dimensionless groups to identify the dominant transport mechanisms in a given resin. Following this, one can identify an appropriate transport model to describe the chromatographic behavior of solutes on the resin material. This model is then employed in concert with the Steric Mass Action (SMA) isotherm and is validated using experimental data. The results presented in this manuscript provide significant insight into the identification of the dominant transport mechanisms on various ion-exchange resin systems.