One of the most critical steps in the production of pharmaceuticals is the separation of the desired compound from reaction byproducts and environmental contaminants. Among the most sensitive of these methods is High Pressure Liquid Chromatography (HPLC), in which an initial mixture of compounds is forced by high pressure fluid flow through a column packed with a porous solid medium. Size and charge interactions with the solid phase cause the compounds to elute at different times from the column.

The performance of an HPLC column is highly dependent on properties such as the length, ambient temperature, inlet pressure, and solid medium porosity. The ideal parameters are conventionally determined by purchasing and physically testing a series of columns, which can be prohibitive in cost, time, and materials. Thus there currently exists a pressing need for computer models to simulate the separation of two or more compounds in order to expedite the onerous process of physical optimization.

This study sought to simulate the physical phenomena that underlie the elution process in an HPLC column, and optimize the conditions such that species separation and purity are maximized. The computing software COMSOL was used to model the involved physics, which comprised the flow of a mobile phase through a porous matrix, modeled by the Navier-Stokes Brinkman equation; the diffusion and dispersion of two solutes in the matrix, modeled by the general mass transfer equation; and the effect of external heating on the materials’ behavior, modeled by the general heat equation. The geometry of the HPLC column consisted of an axisymmetric two-dimensional tube filled with a uniformly distributed porous matrix.

This model column was evaluated by simulating the separation of creatine and creatinine, two closely-related molecules involved in muscle tissue energetics. Once the model was tailored to a high degree of accuracy in comparison with experimental data, the column and species parameters were optimized. The optimal geometry for the separation of creatine and creatinine by HPLC, was a column of diameter 1.05 mm and length 78.4 mm, with a packed bed of spherical particles 5 µm in diameter. The optimal column temperature for this particular situation was found to be lower, at 15℃, as this slightly increases peak resolution but also elution time.

Though concentration plots derived from this model corroborated experimental elution absorbance plots with relatively high fidelity, lingering issues remain, including the unexpectedly small influence of temperature on elution characteristics. Future models may seek to correct this calculation error by including a less steep concentration gradient at the inlet at initial time points. Additionally, variations in column heating were found to have a very small effect on the diffusion of the solute bands, so the external temperature was excluded from the optimization process. The successful implementation of this model indicates that HPLC chromatography can be feasibly represented by computer modeling, and more specific models can reduce the time and material costs of extensive physical testing.