(32b) Packed Column Faq: Is There a Relationship between HETP and the Depth of Packing to Use in a Rate-Based Column Simulation?

The use of non-equilibrium (NEQ) models (also widely known as Rate-Based models) for distillation has become increasingly common as such models can provide a more realistic model of real-world columns. We should note that two of the authors of this paper – RT and HK – are the creators of ChemSep, one of the more well-known rate-based column simulation tools; why we state this here will become evident in the next paragraph.

For tray-columns there is a one-to-one correspondence between the number of trays in a column and the number of stages used in a rate-based model of said column. For packed columns the situation is much less clear. For packed columns a single rate-based stage represents a slice of packing covering the entire column cross section (or, that part of the packing enclosed between the column shell and any internal dividing walls in a parallel column model of a DWC). The question most frequently asked of us (our FAQ) is a version of this one: “What depth of packing should we assign to a single rate-based stage?”

For a long time the standard suggestion has been to use three rate-based stages for each equilibrium stage with a depth of packing in each one equal to one-third of the expected HETP. We refer to this number as the Height Equivalence of a Rate-Based Stage (HERBS).

There is an immediate issue with this answer to this FAQ: Does stating that HERBS = HETP/3 not detract from the entire raison d’etre of a rate-based model? The answer to that is “undoubtedly yes.” For many packings the expected HETP is known, but typically only for one or, at best, a small number of well-studied test systems. Does that expected HETP apply to all other cases? What about packings for which the HETP is not known? We acknowledge that the point of many rate-based simulations is to predict the expected HETP. Indeed, one should not have to know the expected HETP before conducting a rate-based simulation.

Given the uncertainty over the most appropriate value for the depth of packing to assign to a rate-based stage, we conducted an in-depth study to see if we can say something definitive about the value of HERBS to use in non-equilibrium column simulations of packed columns. What parameters affect the value of HERBS? How does packing size, packing type, column operational considerations (pressure and stripping factor) or simulation choices (mass transfer coefficient model, flow models) affect the answer. We also discuss the relationship between HETP and HERBS.