CHAPTER
9

Taking a mass balance over the first n stages as shown in Figure 9.2 (right hand side) we can write, for the total flow, mass entering must equal mass leaving, so:
and for the component being exchanged:
where V is the mass flow rate of the light stream, L is the flow rate of the heavy stream, y is the concentration of the component being exchanged in the light stream and x is the concentration of the component being exchanged in the heavy stream. In the case of the subscripts, n denotes conditions at equilibrium in the nth stage, n + 1 denotes conditions at equilibrium in the (n + 1)th stage and a denotes the conditions of the streams entering and leaving stage 1, one being raw material and one product from that stage Eliminating V_{n+1} between these equations, we have:
y_{n+1} = x_{n} [L_{n} / (L_{n}  L_{a}+ V_{a})] + [(V_{a}y_{a}  L_{a}x_{a})/ (L_{n}  L_{a} + V_{a})] (9.5) This is an important equation as it expresses the concentration in one stream in the (n + 1)th stage in terms of the concentration in the other streams in the nth stage. In many practical cases in which equal quantities, or equal molar quantities, of the carrying streams move from one stage to another, that is where the flow rates are the same in all contact stages, then for: A simplified equation can be written for such cases: y_{n+1} = x_{n}L / V + y_{a}  x_{a}L / V (9.6) ContactEquilibrium Processes  THEORY > CALCULATION OF SEPARATION IN CONTACTEQUILIBRIUM PROCESSES Back to the top 
