Your boss thinks it will be just as good to combine the two feeds in Problem 14.D4 than to keep them separate. Calculate the number of equilibrium stages required to achieve the same outlet concentrations with the same flow rates if two feeds are combined before being fed to the washing cascade. Compare with your answer to Problem 14.D4.

Problem 14.D4

Wash alumina solids to remove \(\mathrm{NaOH}\) from the entrained liquid. Underflow from the settler tank is \(20.0 \mathrm{vol} \%\) solid and \(80.0 \mathrm{vol} \%\) liquid. Two feeds to the system are also \(20.0 \mathrm{vol} \%\) solids. In one of these feeds, the \(\mathrm{NaOH}\) concentration in the liquid is \(5.0 \mathrm{wt} \%\). This feed's solid flow rate (on a dry basis) is \(1000.0 \mathrm{~kg} / \mathrm{h}\). The second feed has a \(\mathrm{NaOH}\) concentration in the liquid of \(2.0 \mathrm{wt} \%\), and its solids flow rate (on a dry basis) is 2000.0 \(\mathrm{kg} / \mathrm{h}\). We desire the final \(\mathrm{NaOH}\) concentration in underflow liquid to be 0.6 \(\mathrm{wt} \% \mathrm{NaOH}\). A countercurrent operation is used. Inlet washing water is pure and flows at \(4000.0 \mathrm{~kg} / \mathrm{h}\). Find the optimum feed location for the intermediate feed and the number of equilibrium stages required.

D4. ata: \(ho_{\mathrm{w}}=1.0 \mathrm{~kg} /\) liter (constant), \(ho_{\text {alumina }}=2.5 \mathrm{~kg} /\) liter (dry crushed).