## Nonequilibrium or Ratebased Methods

Stage efficiency prediction and scale-up from ideal or equilibrium stages to the actual design can be difficult and unreliable for many columns. For highly nonideal, polar and reactive systems, such as amine absorbers and strippers, prediction and use of efficiencies is particularly difficult. In such mixtures, mass transfer and not equilibrium often limits the separation.

Nonequilibrium methods attempt to get around the difficulty of predicting efficiencies by replacing the equilibrium stage concept. Instead, they apply a transport phenomena approach for predicting mass transfer rates. Here, the bulk vapour and liquid phases are not at equilibrium with each other, but there is equilibrium at the interface between phases with a movement from the bulk phase through the interface (Figure 3). The net loss or gain of material and energy at the interface is expressed as transfer rates. The mass and energy transfer rates are dependent on the mass and energy transfer coefficients for each phase which are in turn dependent on composition and conditions of each bulk phase and at the interface.

The correlations for the mass and heat transfer coefficients and interface also take into account packing or tray geometries for the actual column. The total mass and energy rates are calculated from integrating the mass and energy fluxes across the total interface surface.

Krishnamurthy and Taylor (1986) present and test a nonequilibrium model which includes rate equations among the traditional MESH equations. These include individual mass and energy balances in the vapour and the liquid and across the interface. An equilibrium equation exists for the interface only. The solution methods for these equations are the same as the global Newton methods.

The total mass transfer rates are added to an expanded set of the MESH equations called the MERQ equations. The new MERQ acronym stands for:

Material balances for each component - one for the bulk vapour, one for the bulk liquid and one across the interface.

Energy balance equations - one for the bulk vapour, one for the bulk liquid and one across the interface.

Rate equations for mass transfer for all but one component - one from the interface to the bulk vapour and one from the bulk liquid to the interface, plus one energy transfer rate equation from the liquid to the vapour. eQuilibrium equation at the interface only.

## Solar Panel Basics

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