Modeling of Biopharmaceutical Processes. Part 2: Process Chromatography Unit Operation - How to apply the latest thinking in process modeling to your process using a Quality by Design approach. - BioP
CONSIDERATIONS FOR MODELING PROCESS CHROMATOGRAPHY
Figure 2. Comparison of pool purity measured by reversed-phase high performance liquid chromatography with that predicted
by the statistical model
When modeling chromatographic separation processes, the model used to describe mass transport within the column must first
be selected. Models used to describe the separation process are well established in the literature and are based on fundamental
thermodynamic and mass-transfer relationships.8 A schematic of the separation process that occurs within the chromatography column during protein adsorption is shown in
Figure 3. During the adsorption process, protein is first transported from the bulk-liquid phase to the surface of the porous
adsorbent, at which point it diffuses into the porous structure and is adsorbed to the surface by electrostatic or hydrophobic
interactions. The mode of adsorption is dependent on the type of chromatography ligand chosen for the adsorption process,
such as affinity, ion exchange, or hydrophobic interaction. Model input parameters include the process operating conditions
(feed concentration and operating velocity), properties of the packed bed (bed porosity, bed height, and HETP) and the protein-adsorbent
equilibrium isotherm relationship. A material balance is used to relate the protein present in the liquid phase of the column
to that adsorbed inside the porous adsorbent and predict the protein concentration in the column outlet.
Figure 3. Schematic showing the mass transfer and adsorption processes within a chromatography column, and the equations used
to model the process
The adsorption and separation processes in a column are complex, and vary with both column position and time. Protein mass
transport in the column is governed by two resistances: transport of protein from the bulk fluid to the surface of the adsorbent
(called film mass transfer) and transport of protein within the porous adsorbent (called intraparticle mass transfer). Intraparticle
mass transfer is composed of: protein diffusion into the adsorbent and protein binding to the adsorbent surface (surface reaction).
Several assumptions are routinely made to simplify the models used to describe mass transport in the column. First, columns
are assumed to be radially homogenous, and therefore, properties vary only with the column bed height but not with the column
radius. Second, for porous adsorbents, intraparticle mass transfer is governed by protein diffusion, as protein adsorption
to the stationary phase (surface reaction) occurs much more rapidly and does not contribute significantly to mass transport.
The adsorption process is assumed to occur instantaneously, with equilibrium between the protein adsorbed to the stationary
phase and that present in the liquid solution.
Table 1. Models used to describe intraparticle mass transfer (governed by diffusion) and adsorption equilibrium used to model
chromatography separations
The adsorption equilibrium data, also known as the adsorption isotherm, are used to relate the protein concentration in the
liquid phase inside the column to that adsorbed to the surface of the adsorbent over a range of concentrations. Data for
the adsorption isotherm are usually generated in separate experiments under equilibrium conditions. A variety of models can
be used to describe the equilibrium adsorption isotherm, with the two most common being the Langmuir and Steric-Mass Action
(SMA) models.9–10 Correlations for several of the other column model parameters, including the film mass-transfer coefficient and axial dispersion,
are used to estimate values under the process operating conditions evaluated in the separation.
Table 2. Experimental and model predictions for the step yield and aggregate levels using a Phenyl Sepharose Fast Flow column.
The feed used in the studies consisted of 87% monomer and 13% aggregate.1
Models are also required to describe intraparticle protein diffusion and are shown in Table 1. Two of the most commonly used
models include the homogenous (surface) diffusion and the pore diffusion model. These two models assume different physical
mechanisms for the diffusion of proteins into the porous stationary adsorbents. The homogeneous diffusion model assumes that
the protein adsorbed to the stationary phase is free to migrate, or diffuse, along the solid surface. The driving force for
the homogeneous diffusion model is the protein concentration gradient in the adsorbed phase. On the other hand in the pore
diffusion model, it is assumed that intraparticle mass transfer occurs by diffusion in liquid-filled pores with a driving
force expressed in terms of the radial pore fluid concentration gradient. The adsorbed protein is assumed to be in equilibrium
with that in the pore fluid at each radial position in the particle.
Anurag S. Rathore, PhD, is a consultant, Biotech CMC Issues, and a member of the faculty in the department of chemical engineering at the Indian Institute of Technology. Rathore is also a member of BioPharm International's Editorial Advisory Board.
Articles by Anurag S. Rathore, PhD
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