The capabilities of computational fluid dynamics (CFD) as a tool for trouble-shooting and Quality by Design have been demonstrated through case studies in bioprocesses from upstream, to downstream, to fill–finish. The applications involve, for example, multiple physics, fluid dynamics, transport phenomenon, heat transfer, phase transition, and rheology. Flow types include laminar flow in emulsification, turbulent flow in bioreactor mixing, and porous media flow in chromatographic columns, filtration, and centrifuge machine. Part 1 of this article series is an overview of the technology, followed by a discussion of the model setup. Part 2 of this series will discuss how CFD is used to perform flow characterization, mixing, resuspension, fermentation, and cell culture.
Pharmaceutical and biopharmaceutical processes that can benefit from CFD analysis include turbulent flow in bioreactors; multiphase flow, heat, and mass transfer; chemical reactions; phase transitions; porous media flow; and granular particle material dynamics. These processes cover upstream, downstream, and fill–finish, and involve unit operations such as fermentation and cell culture, mixing, chromatography, filtration, centrifuge separation, product freezing and thawing, lyophilization, emulsification, spray drying, product packing, and transportation. With growing capabilities and flexibility, CFD has been the most widely applicable tool available to simulate the physical processes involved in process development, manufacturing, and drug delivery.
There have many reviews of the application of CFD to various industrial processes, only a few of which have covered the role of CFD in the pharmaceutical industry.3,5,6 The biotechnology industry has its own unique processes, in addition to shared common unit operation processes with the pharmaceutical industry. This review will focus on applying CFD to bioreactor (fementer) operations.
OVERVIEW OF CFD
The fundamental basis of any CFD problem is the Navier-Stokes equations that describe the motion of fluids. Additional physiochemical processes are coupled with fluid flow, such as multiphase (gas–liquid, or solid–liquid, or solid–liquid–gas) interaction, species transport, heat transfer, mass diffusion, and chemical reactions. Numerical algorithms are used to solve conservation equations for mass, momentum, and energy, and provide solutions on flow and physical variables such as velocity, pressure, temperature, density, concentration, and volume or mass fraction, from which other derived variables such as shear stress, pH, height equivalent to a theoretical plate (HETP), etc., are obtained.
CFD involves two procedures of discretization—domain discretization and equation discretization—followed by the application of a suitable algorithm to solve the resulting ordinary differential equations for unsteady problems and an algebraic equation for steady problems, subject to appropriate boundary conditions and initial conditions, to get solutions on the grid.7 Either an iterative solver or a direct solver can be used, depending on the size of the problem, available computer memory, and CPU speed. In the step of equation discretization, partial differential equations are discretized into a finite difference equation, whereas in domain discretization, the continuous spatial domain is discretized into small control volumes to form a volume mesh or grid. A postprocessor is used for the analysis and visualization of the resulting solution.
Mesh-based methods include the finite difference method (FDM), the finite volume method (FVM), the finite element method (FEM), the boundary element method (BEM), and some high-resolution schemes that treat shocks and discontinuities. Non-mesh–based methods include smoothed particle hydrodynamics (SPH)—a Lagrangian method of solving fluid problems, Spectral methods—a technique where the equations are projected onto basis functions like the spherical harmonics and Chebyshev polynomials, and Lattice Boltzmann methods (LBM), which simulate an equivalent mesoscopic on a Cartesian grid instead of solving the macroscopic system (or the real microscopic physics).