CHBE 345 Lecture Notes - Lecture 2: Countercurrent Exchange, Tridiagonal Matrix, Tridiagonal Matrix Algorithm
13 May 2016
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Multistage equilibrium operations: crossflow cascade with straight equilibrium line. Consider a steady-state cross-flow cascade having n equilibrium stages and using the same flow of extracting solvent at each stage. 0x is the raffinate concentration in equilibrium with the initial extracting solvent concentration. Substituting both equilibrium expressions into the material balance equation yields: or. S me s r s is known as the stripping factor . S slope of equilibriu linem slope of operating line. Ra s me s is called the absorption factor . Multiplying eq. (i) by eq. (ii) now gives: Similarly, a material balance around stage 3 eventually yields: S (iii) and multiplying eqs. (i), (ii), and (iii) together produces: In general, for n stages, it can be similarly proven that: or. Alternatively, if the desired outlet concentration, xn, is known, the above equation can be used to determine the number of stages required to achieve the separation, i. e. , ln.
