Please answer parts c and d
4.2
Consider a constant-volume continuous stirred tank reactor (CSTR), as shown in Figure P4.2, where the following irreversible consecutive reactions take place isothermally, with reaction rates r = kCR, r2 = kCp. The intermediate product P is the desired product, whereas B is an undesirable by-product. The feed is a solution of the reactant R of concentration Cin,R, that contains no P or B, and has a constant volumetric flowrate F. The input of the system is the feed concentration Cin.R, the output is the concentration Cp of species P in the reactor.
a) Write down a state space model for this system, consisting of mole balances for species R and P.
b) Derive the transfer function of the CSTR.
c) Suppose that the CSTR is initially at steady state. At t=0, nR moles of species R are quickly added to the reactor. Calculate the response of Cp.
d) Repeat questions a) and b) in case the first reaction is reversible:
R
>B
k
and the rate of the reverse reaction (from P to R) is r_ = k_ Cp
'in,R
F
CR Cp
F
Figure P.4.2. Isothermal CSTR.
