Performance of the Equilibrium Stage

This section examines the effect of temperature, pressure, and, in certain situa- 

Although the obvious purpose of separation processes is to raise or lower the concentration of certain components to certain levels, another factor must be considered and that is the recovery of those components. Thus, the amount of a product as well as its purity is of concern to the process engineer. The concentration, commonly expressed as mole fraction of the components of interest, X or T , is a measure of quality, while the total product rate or component recovery is a measure of quantity. The recovery of a component or group of components is defined as the fraction or percentage of these components in the feed that are recovered in a given product. If, for instance, the mole fraction of component i in the feed to a flash drum is Z and its mole fraction in the vapor product is T , the amount of i in the feed is FZ and in the vapor product is where F is the molar feed rate and t / is the vapor mole fraction. The recovery of component i in the vapor product is, therefore. 

The performance of an equilibrium stage may be examined in terms of components concentration and recovery in a given product and the dependence of these quantities on the independent variables and the phase equilibrium characteristics of the system. 

In certain systems, phase separation is enhanced by introducing an additional feed to the separation device such as in absorption or stripping and in azeotropic and extractive distillation. Although these processes are usually multistage, their characteristics are discussed in this section using the single-stage model. 

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In order to define the quantitative relationships among the various parameters in a nnit operation, a mathematical model is employed, in which the physical relationships are expressed as mathematical equations. Thus, the equilibrium stage may be simulated by a model for which the mathematical solution represents physical performance. When physical relations are translated into analytical expressions, certain assumptions mnst be made and the accuracy of the simulation model depends on the validity of these assumptions. For an equilibrium stage model, it is assumed that the stage is essentially at equilibrium. Additionally, it is assumed that the models used for predicting the thermodynamic properties, namely the distribution coefficients and enthalpy, are accurate. To the extent that these assumptions are met, the performance of the equilibrium stage can be accurately predicted. 

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