Question $1$

Remarks: Parts a$),$ b$)$ and c$)$ can be treated independently. The

overbar is used for denoting steady$-$state quantities.

Consider the continuous stirred tank reactor $($CSTR$)$ of Figure Q$1,$

whereby the two following chemical reactions take place:

$2A+B{k}_{1}C$

$2B{k}_{2}D$

The goal is to produce $C,$ thus the second reaction is a side reaction.

the rate of production of $C$ is $r_1=k_1{C}_A(t)C_B(t)$

the rate of production of $D$ is $r_2=k_2{C}_B^2(t)$

the kinetic rate constants are functions of the temperature, that is:

$k_1=k_1(T(t))$ and $k_2=k_2(T(t))$

$\frac{?}{\text{b}\text{a}\text{r}}(C{)}_{A,in}=6$mol.$L^{-1}\frac{,}{b}ar(C{)}_{B,in}=4\mathrm{.}5$mol.$L^{-1}$ and $\frac{?}{\text{b}\text{a}\text{r}}(q{)}_{A,in}=100L*mi{n}^{-1}$

Note that $"$L$"$ in the units of process variables stands for litres.

$x_c$I,$VI$ and $TI$ of Figure Q$1$ denote sensors that measure the

concentration of $C,$ the liquid volume and the temperature in the

reactor tank, respectively.

riguie wi

a$)$

$($i$)$ Classify all process variables as Manipulated Variables $($MVs$),$

Disturbances $($Ds$),$ State Variables $($SVs$)$ and$/$or Controlled

Variables $($CVs$).$

$($ii$)$ Explain and justify the structure of the three control loops

depicted in Figure Q$1.$

b$)$ Consider the process of Figure Q$1.$ Assume that the volume and

temperature are perfectly controlled and are thus constant at their

steady$-$state values, i$.$e$.V(t)\frac{?}{b}=ar(V)$ and $T(t)\frac{?}{b}=ar(T)$ for all $t,$ with:

$\frac{?}{\text{b}\text{a}\text{r}}(D)=100L,k_1(T)=2L*mo{l}^{-1}*mi{n}^{-1},$ and $k_2(T)=0\mathrm{.}25L*mo{l}^{-1}*mi{n}^{-1}.$

$($i$)$ Write the dynamic overall mass balance and dynamic molar

balances for species $A,B$ and $C.$