Nonequilibrium stage model rate equations

In writing down the equations that model the behavior of this nonequilibrium stage, the flow rates of vapor and liquid phases leaving the jth stage are denoted by Vj and Lj, respectively. The mole fractions in these streams are y j and x j. The yT-y are the rates of mass transfer of species i on stage j. The temperature of the vapor and liquid phases are not assumed to be equal and we must allow for heat transfer as well as mass transfer across the interface. The symbol represents the rate of energy transfer across the phase boundary. 

Most of the quantities normally specified in an equilibrium stage simulation (number of stages, feed stage location, feed flow rates and composition, reflux ratio, distillate or bottoms rate, and so on) must be specified for a comparable nonequilibrium simulation. By including the hydraulic or pressure drop equations in the model it is not necessary to specify the pressure of each stage for a nonequilibrium simulation only the pressure of the top stage and of the condenser need be specified. 

It should be stated that the number of equations in this approach is very large, and specialized computer programs have been developed far their solution. Our objective here is very limited, namely to provide an idea of the basis of these equations. The basic set of equations in such rate based or nonequilibrium models of a distillation plate/ stage is sometimes referred to as the MERSHQ equations (Taylor et id., 2003), with each letter representing equations for a particular aspect of the problem for any plate n of the n-component system. 

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