Consider a continuous stirred-tank reactor (CSTR), operated isothermally, with negligible volume
change due to reaction, in overflow mode with a constant fluid volume $V$, and with the two
chemical reactions.
$A + B \rightarrow C$
$C + B \rightarrow D$
$r_{R1} = k_1 C_A C_B$
$r_{R2} = k_2 C_C C_B^{1/2}$
where $k_1$, $k_2$ are the rate constants of each chemical reaction and $C_j$ is the concentration of
component $j$ in the reactor (kg/m³). With the assumption that the reactor is so perfectly mixed that
the concentration field of each species is spatially uniform. That is, every point in the reactor has
the same concentration of each species, governed by the components' mass balances
a) Develop the steady-state component mass balance that takes place in the reactor. The
general mass balance equation with reaction is as below:
$Accum = In - Out + Reaction \; term = 0$
$Reaction \; term = \sigma V r_{R_i}$
(2)
where $\sigma$ is the stoichiometric coefficient (+ for product and - for reactant), $V$ is the fixed
reactor volume, and $r_{R_i}$ is the rate of reaction for reaction $i$.
b) Determine the outlet concentration of each component at steady state condition for $q_{in} =$
$q_{out} = 1 \; m^3/hr$, $V = 100 \; m^3$, $k_1 = 1 \; m^3/(kg-hr)$, $k_2 = 1 \; (m^3/kg)^{1/2}/hr$, and inlet concentration
as $C_{A,in} = 1 \; kg/m^3$, $C_{B,in} = 2 \; kg/m^3$, $C_{C,in} = 0 \; kg/m^3$, and $C_{D,in} = 0 \; kg/m^3$. Tabulate all your
results.
c) Discuss on how to increase the concentration of component D (product) and reduce the
concentration of component C (bi-product). Do several calculations by varying volumetric
flowrate ($q_{in}$ and $q_{out}$), and the inlet concentration of component A and B ($C_{A,in}$ and $C_{B,in}$)
