Stagewise and differential mass transfer

The increasing diversity in the applications of liquid extraction has led to a correspondingly diverse proliferation of extraction devices that continue to be developed. This chapter focuses on those fundamental principles of diiiusion, mass transfer, phase equilibrium, and solvent selection that provide a unifying basis for the entire operation. Design procedures for both stagewise and differential contactors alM receive considemtion, including packed and perforated plate columns and mixer-settlers. Some mechanically aided columns are discussed and an attempt is made to conqiare the performance of various equipment tteigns. 

Other procedures and calculation techniques have been developed for both stagewise and differential permeation, such as those presented S-T Hwang and K. Kammermeyer, but they are not pursued here, inasmuch as the analogy is to be made specific to vapor-liquid mass transfer unit operations. In this way, the conventions and techniques already developed for mass transfer operations can be more readily utilized. Also note that the symbols and terminology used for membrane permeation have evolved through the years and vary from one author to another. 

The concept of a mass-transfer unit was developed many years ago to represent more rigorously what happens in a differential contactor rather than a stagewise contactor. For a straight operating line and a straight equilibrium line with an intercept of zero, the equation for calculating the number of mass-transfer units based on the overall raffinate phase N r is identical to the Kremser equation except for the denominator when the extraction factor is not equal to 1.0 [Eq. (15-23)]. 

Mass transfer processes involving two fluid streams are frequently carried out in a column countercurrent flow is usually employed although co-current flow may be advantageous in some circumstances. There are two principal ways in which the two streams may be brought into contact in a continuous process so as to permit mass transfer to take place between them, and these are termed stagewise processes and continuous differential contact processes. 

The principle of the perfectly-mixed stirred tank has been discussed previously in Sec. 1.2.2, and this provides essential building block for modelling applications. In this section, the concept is applied to tank type reactor systems and stagewise mass transfer applications, such that the resulting model equations often appear in the form of linked sets of first-order difference differential equations. Solution by digital simulation works well for small problems, in which the number of equations are relatively small and where the problem is not compounded by stiffness or by the need for iterative procedures. For these reasons, the dynamic modelling of the continuous distillation columns in this section is intended only as a demonstration of method, rather than as a realistic attempt at solution. For the solution of complex distillation problems, the reader is referred to commercial dynamic simulation packages. 

Since mass transfer in packed or spray towers occurs differentially rather than stagewise, their performance should be expressed in terms of the number of transfer units (NTU) rather than the number of theoretical stages (NTS). For dilute systems, the number of transfer units is given in terms of the terminal concentrations and the equilibrium relation by... 

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