Packed bed chromatography is an important unit operation for purification of product molecules in biopharmaceutical processes. Packed bed chromatographic processes are modeled as advection-diffusion-reaction partial differential equations. The advection term strongly dominates the diffusion term. Therefore, specialized numerical methods must be used for efficient simulation of packed bed chromatographic processes. In this paper, we use a discontinuous-Galerkin method on finite-elements for spatial discretization and low storage explicit Runge-Kutta (LSERK) methods for numerical solution of the resulting system of differential equations. We study the numerical solution of deterministic and stochastic models of packed bed chromatographic processes. The stochastic model and its corresponding numerical solution constitute the first step toward systematic monitoring, fault detection, and optimal predictive control of chromatographic processes. It is also an essential ingredient in uncertainty quantification for efficient and robust design and operation of chromatographic processes.
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