QUESTION $1$

$($PO$3,$ CO$1,$ C$2,$ C$3,$ C$4)$

A feed slurry with a flowrate of $2000k\frac{g}{h}$ containing $18wt\%BaS{O}_4,36wt\%H_{2}S{O}_4$ and balanced water is washed with a $1000k\frac{g}{h}$ of dilute solution $)$ to extract the water from the slurry feed which is then removed in decanted solution stream. The washing takes place in a settler tank resulting in a washed $BaS{O}_4$ slurry with $28$ wt $\%BaS{O}_4,12$ wt$\%H_{2}S{O}_4$ and balanced water. The washed $BaS{O}_4$ is subsequently heated in an evaporator to remove $90\%$ of the mass of the water resulting in concentrated $BaS{O}_4.$ The decanted solution drawn from the settler tank and retains $2wt\%$ of $BaS{O}_4.$ The flowchart of this process is shown in figure $1.$

Figure $1$ The process of washing $BaS{O}_4$ with $H_{2}S{O}_4$ solution

a$)$ Draw and label each component in every stream of the process flowchart.

$(4$ marks$)$

b$)$ Express the degree of freedom $($DOF$)$ analysis for the settler tank and the overall system.

$(4$ marks$)$

c$)$ Calculate the mass fraction of decanted solution stream, concentrated $BaS{O}_4$ stream and water evaporated from the evaporator.

$(7$ marks$)$