Equilibrium Stages vs Mass Transfer Rates

The rigorous, mass transfer rate approach used for all column calculations by ProTreat modeling eliminates the need for empirical adjustments to simulate new applications correctly. The ProTreat mass transfer rate model is built on five key elements:

• Mass and energy balances around individual phases on a tray or in a packed segment
• Conventional thermodynamic phase equilibrium
• Equilibrium across interfaces
• Chemical kinetics effects on mass transfer rates, particularly in the liquid phase
• Mass and heat transfer rate models for transport across interfaces.

In contrast, even the most sophisticated equilibrium stage model uses only two of these elements, namely mass and energy balances around an entire ideal stage plus thermodynamic phase equilibrium. Often, an attempt is made to include reaction kinetics by empirical modeling via an adjustable parameter (H₂S and CO₂ tray efficiencies and/or liquid residence times) that forces the simulation to reproduce a conventionally-operated column’s treated gas composition. Some might call this a "rate" model but it is not a mass transfer rate model—it is an attempt to force a reaction parameter into a model that is inherently unrelated to rate processes in order to match some measure of plant performance. The fact is, regardless of any embellishments one might add, equilibrium stage models are nonpredictive. This makes them unable to deal with applications dependent on differences between mass transfer rates of CO₂ and H₂S for which operating experience is lacking. Furthermore, all equilibrium stage models deal exclusively with ideal stages, with no accurate way to translate into the real world of actual tray counts and packed bed depths, let alone to deal with such questions as the effect of packing type, size and material, or tray type and configuration.

In a mass transfer rate model, there are intricate interrelated effects between the five key elements already listed. They respond by a variety of chemical and physical, phase and component transport properties such as (i) chemical kinetics, (ii) diffusion coefficients, solvent viscosity, and other transport properties, (iii) salting-out effects on solubilities, and (iv) the mass transfer characteristics of the actual hardware being used. When a ProTreat column simulation is run, the tower is being modeled in full detail as a piece of real equipment, not as an idealization. From a separations standpoint, two-pass and single-pass trays perform differently. Metal packing gives different results from plastics and ceramics. In addition, all solvent properties, including the changes in these properties caused by acid gas loading, affect mass transfer coefficients and thereby influence the actual separation that a given column under a given set of operating conditions will achieve. A mass transfer rate model is rich in detail and is a faithful mirror of the real world. In the language of process control, a true mass transfer rate simulation uses a distributed parameter model that, consequently is mechanistic, detailed, and fully predictive. This is in contrast to the equilibrium stage approach which is a lumped parameter model (it assigns all the physical and chemical complexities to one or two parameters such as efficiency, or liquid residence time) and is accordingly nonpredictive.