Equilibrium-stage concept

This equilibrium-stage concept based on a transfer unit has been proposed for such continuous-contacting devices as, for example, packed towers. 

Nonequilibrium methods attempt to get around the difficulty of predicting efficiencies by doing away with the equilibrium-stage concept. Instead, they apply a transport phenomena approach for predicting mass transfer rates. The mass transfer rates are calculated continuously along the column length and not in discrete equilibrium stages. This process is similar to the transfer unit concept (Sec. 10.3.1). 

The separation processes we are studying in Chapters 1 to 14 are based on the equilibrium stage concept, which states that streams leaving a stage are in equilibrium What do we mean by equilibrium ... 

Any design procedure requires a calculation of the number of mass transfer stages required and then a determination of the packed depth required to achieve such a stage. The use of the equilibrium stage concept in liquid-liquid extraction is similar to its use in distillation operations. A theoretical stage of mass transfer is one from which the extract and the raffinate leave in equilibrium. Stated in a different manner, the ratio of the concentration of solute in the extract to the concentration of solute in the raffinate equals the distribution coefficient. 

Design of columns based on equilibrium-stage concept involves 3 Major steps ... 

As an example of the use of lumped versus distributed mathematical models, consider the equilibrium stage concept of distillation, extraction, and similar processes. As shown in Fignre 2.1, we usually assume that the entire stage acts as a whole, and we do not consider variations in temperature, composition, or pressure in various parts of the stage. All of these variables are lumped together into some overall average. The errors introduced are compensated for by the stage efficiency factor. 

Modeling in multifunctional operations can also be categorized as steady-state, dynamic and data-driven modeling. The steady-state models based on equilibrium stage concept are employed by commercial software such as ASPEN PLUS for process design purposes. The CFD modeling is useful in evaluating the intrinsic mechanisms of mass, momentum, heat transfer and reaction kinetics with the help of rate based models. Very few studies have been reported on the development of dynamic models for reactive and hybrid separations, with the exception of reactive distillation [30] and reactive... 

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