(498a) Real-Time Modeling of Crystal Nucleation, Growth, and Breakage in an Agitated Bioreactor

We use GPU-based CFD/DEM simulations to model crystal nucleation, growth and break-up in an agitated tank in real-time. This approach, which pairs lattice-Boltzmann-based direct numerical simulations with fully resolved discrete element modeling (DEM), enables mechanistic and time-accurate modeling of crystal growth via solvent reactions and crystal growth via reactions and particle interactions. In addition to particle growth and agglomeration, particle break-up is modeled at the level of individual particles, providing insights into the competition between grown and break-up. Additionally, since the particle trajectories are modeled using Newtons second law, the effects of particle growth and break-up on settling on are also predicted. Since the particle field is solved in tandem with the fluid field, incorporate the effects of particle size and concentration into the local fluid viscosity when modeling fluid flow. Using this model, we can predict the spatiotemporal particle size distribution, and show how this distribution is informed by reactor operating conditions, solvent chemistry, particle interactions, particle settling, and particle break-up.

In fluid mechanical systems, momentum transport can be described by the Navier-Stokes equations. The Navier-Stokes equations link fluid acceleration and the applied body and surface forces, which typically include gravity, buoyancy, and shear stress gradients. Although only a few exact solutions to the Navier-Stokes equations exist, many numerical solution approaches are available. One of the most general and computationally efficient approaches for solving the transient Naiver-Stokes equation is Lattice-Boltzmann. The Lattice-Boltzmann method scales exceptionally well on GPU-based architecture, enabling high-resolution large eddy simulation of turbulent flows at industrial scale. Following this approach, CFD simulations running lattice points at lattice updates per second are routine on a multi-GPU workstation.

In solid granular systems, particle trajectories are governed by Newton’s second law. Newton’s second law links the acceleration of a particle to the sum of the forces acting on it, including gravity, buoyancy, fluid-interaction, and particle contact. Exact solutions are not available for generalized granular systems containing more the two particles. Computational approaches must be applied. One of the most general and computationally efficient approaches for solving this N-body problem is to use a velocity Verlet integration scheme for particle trajectories with a GPU-based BVH tree to account for neighbor-neighbor interactions. Following this approach, DEM simulations tracking interacting particles at particle updates per second are routine on a multi-GPU workstation.

From a modeling perspective, it is practical to combine fluid mechanical systems and solid granular systems into a unified multi-phase system, wherein both transport processes are solved simultaneously. In this approach, the local and instantaneous properties of the fluid inform the local and instantaneous forces on the particles. Likewise, the properties of the particles inform the local properties and forces applied to the fluid. Since these processes are solved in real time and directly on the GPU, it is straightforward to model time-varying physics, including reactions, phase change, and particle growth/breakage within this unified model.