Example $3.$ CSTR Example

$A+BP$

Two streams are feeding the reactor. One concentrated feed with flow rate $F_1(\frac{m^3}{s})$ and concentration $C_{B1}(\frac{\text{m}\text{o}\text{l}\text{e}}{m^3})$ and another dilute stream with flow rate $F_2(\frac{m^3}{s})$ and concentration $C_{B2}(\frac{\text{m}\text{o}\text{l}\text{e}}{m^3}).$ The effluent has flow rate $F_{\text{@}}(\frac{m^3}{s})$ and concentration $C_B($mole $\frac{?}{m^3}).$

The reactant $A$ is assumed to be in excess.

The reaction rate:

$r=\frac{k_1{C}_B}{(1+k_2{C}_B{)}^2},($ mole $\frac{?}{m^3}*s)$

Part $1-$ Model building

Example $3.$ CSTR Example

Assumptions: Isothermal, Constant density Total mass balance:

$A\frac{dL}{dt}=F_1+F_2-F_o$

Component $B$ balance:

$V\frac{d(C_B)}{dt}=F_1(C_{B1}-C_B)+F_2(C_{B2}-C_B)-\frac{k_1{C}_B}{(1+k_2{C}_B{)}^2}V$