Analytical modeling of large-scale bioreactors using diffusion equations: perspectives on bioprocess design

Abstract

BACKGROUND: Modeling is a widely employed tool in the study of bioreactor scale-up where mixing, reaction, mass transfer, and biological phenomena interact. Heterogeneous large-scale reactors have usually been modeled with numerical models that naturally employ an analysis workflow of determining an end result from operating conditions. Design perspective that uses the desired end result to infer the required operating conditions is usually not accounted for. RESULTS: One-dimensional axial diffusion equations have been proposed as a generalized model of high aspect ratio bioreactors to fill this gap. Using a previously published large-scale Escherichia coli fed-batch as a reference and a previously published kinetic model, the design perspective was demonstrated by using the analytically solved diffusion equation model to determine maximal mixing times and feed rates that avoid acetate overflow. Similarly, the minimum required oxygen transfer rate coefficients and oxygen gas partial pressures for the same scenario were determined. CONCLUSION: Analytical solutions to axial diffusion equations could be used for preliminary quick screening of process parameters required to fulfill a design objective. In future, the model could be used to initialize more involved numerical simulations or in the design of scale-down setups mimicking the environment found in large-scale reactors.