Stagewise

Although the stagewise model is not physically reaUstic for differential contactors, it is sometimes used. The number of equivalent theoretical stages N can be determined graphically usiag the stepwise constmction illustrated ia Figure 7. For the case where both the equihbrium and operating lines are linear, it can be shown that ... 

Fig. 1. The analogy between the separation stage and the transfer unit or equivalent theoretical plate (a) ia a stagewise process (b) ia a...

NTU (Number of Transfer Units) The NTU required for a given separation is closely related to the number of theoretical stages or plates required to cariy out the same separation in a stagewise or plate-type apparatus. For equimolal counterdiffusion, such as in a binary distillatiou, the number of overall gas-phase transfer units Nqg required for changing the composition of the vapor stream from yi to yo is... 

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)]. 

Liquid-hquid contacting equipment may be generally classified into two categories stagewise and continuous (oifferential) contact. 

The design techniques used include both stagewise and continuous-contac ting methods and can be applied to batch, continuous, and semi-continuous operations. 

Henley, E. J. and H. K. Staffm, Stagewise Process Design, John Wiley Sons Inc, New York (1963). 

A flue gas is to be desulfurized using water scrubbing in a stagewise column. It is desired to remove 95% of SO2 from the flue gas containing 100 ppm SO2. The flowrate of the gas is 0.03 kg mol/s (approximately 2 MMscfd). The water entering the absorber is free of SO2. The equilibrium data for transferring SO2 from the gas to the water may be described by ... 

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. 

Stagewise mass transfer processes 622 Standard orifice meter 249... 

Fig. 1.25 shows a countercurrent stagewise mass transfer cascade and the resulting staged profile of the two streams, owing to the mass transfer between the streams. 

Figure 1.25. Concentration profiles for countercurrent, stagewise contactor.

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. 

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