Binary mixtures material balances, column

A mathematical formulation of the column of Figure 3.3 follows for a binary mixture. Material balances for components 1 and 2 are written for stages 1 and 2, with the first subscript referring to the stage and the second subscript to the component. 

Operating Line and "Equilibrium" Curve. Both terms are of importance for the graphical solution of a separation problem, i.e., for the graphical determination of the number of stages of a cascade. This method has been developed for the design of distillation columns by MacCabe and Thiele and should be well known. For all cases, the operating line represents the mass and material balances. In distillation, the equilibrium curve represents the thermodynamical va-por/liquid equilibrium. For an ideal binary system, the equilibrium curve can be calculated from Raoult s law and the saturation-pressure curves of the pure components of the mixture. In all other cases, however, for example, for all membrane processes, the equilibrium curve does not represent a thermodynamical equilibrium at all but will represent the separation characteristics of the module or that of the stage. 

A rigorous column simulation requires, besides material balances, the implementation of enthalpy balances. In binary mixtures the enthalpies of gas and liquid streams can be taken from enthalpy/concentration diagrams. 

With a column distilling a binary mixture of cyclohexane and w-heptane near to total reflux with 10% cyclohexane in the bottoms and 49% cyclohexane in the distillate and 4.0 theoretical stages, which stage would have the most responsive temperature due to changes in D/F material balance split ... 

SorePs Method. Sorel (Ref. 17) developed and applied the mathematical theory of the rectifying column for binary mixtures. He calculated the enrichment, the change in. composition from plate to plate, by makin 3Sergy and material balances around each plate and assunie that equilibrium was attained between the vapor and liquid leaving the plate. He proceeded stepwise through the column T)y applying this rhethod successively from one plate to the next. 

Two common graphical procedures used to calculate the number of theoretical plates for a separation system involving binary mixtures are the McCabe-Thiele and the Ponchon-Savarit methods. The former method is based on the assumptions of constant vapor and liquid flow rates, or constant molal overflow, throughout the column and negligible heat losses, whereas the latter method does not assume constant molal overflow. Before developing the appropriate material balances for either procedure, some standard notation and definitions are necessary. 

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