Countercurrent stage stripping is to be used to remove a tai

Countercurrent stage stripping is to be used to remove a taint from cream. The taint is present in the original cream to the stripper at a concentration of 20 parts per million (ppm). For every 100 kg of cream entering per unit time, 50 kg of steam will be used for stripping. It is desired to reduce the concentration of the taint in the cream to 1 ppm. The equilibrium relation between the taint in the steam vapor and the liquid cream is y_A = 10x_A, where y_A is ppm of taint in the steam and x_A ppm in the cream (E1). Determine the number of theoretical stages needed.

Solution

Inlet cream taint concentration    = 20 ppm
                                                = x_a

Assume a cream flow rate of 100 arbitrary units = L
so steam flow rate                          V = 100
If y₁ is the outlet steam taint concentration,
                  Total taint into equipment = total taint out of equipment.
                                            100(20) = 100y₁ + 100(0.3)
                                     100(20 - 0.3) = 100y₁

Therefore                                      y₁  = 19.7 ppm = y_a

                                       y_n+1 = x_nL/V + y_a - x_aL/V

                                         y_n+1 = x_a (100/100) + 19.7 - 20(100/100)
                                                = 1x_a - 0.3
Equilibrium condition:             y_n  = 7x_a

The operating and equilibrium lines have been plotted on and it can be seen that two contact stages are sufficient to effect the required separation. The construction assumes 100% efficiency so that, with a stage efficiency of 70%, the number of stages required would be 2(100/70) and this equals approximately three stages.

So the number of contact stages required assuming:
        (a) 100% efficiency = 1.9, and
        (b) 70% efficiency   = 1.8