(355a) Modeling Mixing Processes Using Computational Fluid Dynamics and z-Transform

Computer simulations of mixing processes are typically performed at two levels: Computational fluid dynamics (CFD) can be employed to analyze the internal details of a mixing unit operation with high spatial and temporal fidelity, and flowsheet simulations can be used to study the overall performance of a mixing process as it interacts with other unit operations and responds to disturbances and control strategies.

Each of these simulation approaches has its own utilities as described above, but also its own limitations. The boundaries of a CFD model do not usually extended beyond the walls of the mixing process vessel, thus to a lesser or greater extent decoupling the process from the universe. In a flowsheet model the available transfer function description of a mixing process is often limited to prescribed black-boxes that are derived based on idealized assumptions, which may not be applicable to modeling complex processes or troubleshooting defective operations.

That said, CFD and flowsheet analysis are not mutually exclusive tools, and in fact they should complement each other quite well. In this presentation we will illustrate the fundamental aspects of using these two methods together by examining a linear system and its open-loop response, such as the residence time distribution (RTD) function of a continuous-flow stirred-tank reactor that might not necessarily exhibit classical first-order characteristics. We will show how to obtain a z-transform transfer function—the discrete equivalent of the Laplace transform transfer function—for the process from CFD simulation results. Then we will use the z-transform transfer function to generate additional RTDs corresponding to various conditions at the inlet to the mixing process, and compare these results with those obtained from the corresponding CFD simulations. To conclude our presentation, we will discuss issues related to the truncation error that is introduced when obtaining the z-transform transfer function from CFD simulation results.