Journal of Chromatography A, 1218 (2011) 9121–9127 Contents lists available at SciVerse ScienceDirect Journal of Chromatography A jou rn al h om epage: www.elsevier.com/locat e/chroma Mathematical model using non-uniform flow distribution for dynamic protein breakthrough with membrane adsorption media Steven Schneiderman a , Hemanthram Varadaraju a , Lifeng Zhang b , Hao Fong b , Todd J. Menkhaus a,∗ a Department of Chemical and Biological Engineering, South Dakota School of Mines and Technology, 501 East St. Joseph Street, Rapid City, SD 57701, USA b Department of Chemistry, South Dakota School of Mines and Technology, Rapid City, SD 57701, USA a r t i c l e i n f o Article history: Received 22 August 2011 Received in revised form 7 October 2011 Accepted 10 October 2011 Available online 28 October 2011 Keywords: Protein adsorption breakthrough model Convection/diffusion equation Navier–Stokes equation Breakthrough prediction Membrane chromatography a b s t r a c t A mathematical model has been investigated to predict protein breakthrough during membrane adsorp- tion/chromatography operations. The new model incorporates a non-uniform boundary condition at the column inlet to help describe the deviation from plug flow within real membrane adsorption devices. The model provides estimated breakthrough profiles of a binding protein while explicitly accounting for non- uniform flow at the inlet of the separation operation by modeling the flow distribution by a polynomial. We have explored experimental breakthrough curves produced using commercial membrane adsorption devices, as well as novel adsorption media of nanolayered nanofiber membranes, and compare them to model predictions. Further, the impact of using various simplifying assumptions is considered, which can have a dramatic effect on the accuracy and predictive ability of the proposed models. The new model, using only simple batch equilibrium and kinetic uptake rate data, along with membrane properties, is able to accurately predict the non-uniform and unsymmetrical shape for protein breakthrough during operation of membrane adsorption/chromatography devices. © 2011 Elsevier B.V. All rights reserved. 1. Introduction Membrane adsorption/chromatography has shown great promise as an alternative to packed bed separation due to the relatively low pressure drop associated with elevated flow rate (leading to reduced processing time) and faster adsorption kinetics allowing for rapid adsorption without internal diffusion limitations [1–5]. These advantages are especially prominent when purifying large biopharmaceutical products such as proteins, nucleic acids, and viruses. Unfortunately, while the processing times were generally much faster than comparable packed bed operations, the binding capacities have been shown to be lower [6,7]. In addition, the high aspect ratio (low bed height to diameter) has complicated flow distribution and led to unexpectedly rapid breakthrough and exacerbated the limited capacity issue [8,9]. As a result, the large amount of membrane adsorption media required for a purification process may be economically challenging. Recent progress in membrane adsorption technology has improved adsorption capacity by using advanced materials such as nano-scale solid supports, more efficient functionalization of the media to allow for grafted active layers, and new module designs to facilitate better hydrodynamics and flow distribution ∗ Corresponding author. Tel.: +1 605 394 2422; fax: +1 605 394 1232. E-mail address: Todd.Menkhaus@sdsmt.edu (T.J. Menkhaus). [10–14]. These technological advances, along with a shifting emphasis toward more single-use/disposable operations for bio- pharmaceutical processes, have led to the adoption of membrane adsorption systems within large-scale production of therapeu- tic products [15,16]. However, there are still concerns that with uneven flow distribution the devices may prove difficult to imple- ment with strict regulations imposed by the Food and Drug Administration requiring tightly controlled and reproducible oper- ations [17]. Along with the improved membrane adsorption devices, there has also been an increasing awareness and effort toward developing more sophisticated models to predict the performance (dynamic breakthrough) for these adsorption systems. Initial models applied correlative equations that had been designed for packed bed systems [6]. Although these were able to adequately represent experimental data to a rough approximation, there were a few key discrepancies (relatively early breakthrough and an uncharacter- istically broad, tailing breakthrough profile) that pointed to the need for models specifically developed for membrane adsorbers, and especially for cases when axial dispersion was not negligible [18–20]. More recently, models have been developed that account for the early breakthrough and strong tailing in membrane adsorp- tion systems by incorporating a zonal flow description [8,9]. This method quantitatively characterizes the different flow paths and void volumes within the membrane, and uses fit parameters to trace experimental breakthrough curves for non-binding solutes. 0021-9673/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2011.10.063