CHE 433 - Spring 2018 - Examination 2
This is an open book, open notes examination. Please read each problem carefully before
attempting its solution. Show details of your effort. Good luck.
1. [32 points] The transfer function for a chemical process is (tin min)
G(s) = 5(s−2)
(s+ 1)(s+ 2)(s+ 3), G(s) = Y(s)
U(s).
Obtain the response of the output, y′(t), subject to a step change in u′(t) of magnitude
2, i.e., u′(t) = 2S(t). What is the ultimate change in y′(t) (t→ ∞)? Equating dy′(t)/dt
to zero, calculate tat which y′(t) will be minimum/maximum. Use the substitution z=
exp(−t) to simplify the algebra for dy′(t)/dt = 0 [implies dy ′(z)/dz = 0] and identify zand
twhere dy′(t)/dt = 0. Comparing the signs of extremum y′(t) and y′(∞), deduce that this
extremum reflects an inverse response of the process.
2. [20 points] The dynamics of a process is described by
d2y′
dt2+ 2dy′
dt +ay′= 10u′(t), y′(0) = 0,dy′
dt (0) = 0,
with abeing an arbitrary constant.
(a). Obtain the transfer function for the process, G(s).
(b). Obtain expressions for the poles of G(s) - roots of the denominator of G(s). Show that
the process is unstable for a≤0.
(c). For a > 0, deduce that G(s) can be put in the standard form for a second-order process.
What are the values of K,τ, and ζ? At what value of ais the process critically damped?
What are the ranges of awhere the process is overdamped and underdamped?
3. [16 points] The homogeneous liquid phase reaction with kinetics
(−rA) = kCA
(1 + aCA)
occurs in an isothermal, steady state CSTR, with v=v0. For a= 5 L/mol, k= 0.5 min−1,
CA0= 2 mol/L and τ=V/v0= 20 min, obtain the fractional conversion of A,X.
4. [32 points] Consider two isothermal continuous flow well-mixed reactors (CSTRs) in
series with two-way interaction provided by a recycle stream (Fig. fig1fig1
1). A first order reaction
A→B, r =kC
occurs in both reactors. The volumes of reaction mixture in both reactors are constant and
equal (V), the densities of all streams and the reaction mixtures in the two reactors are
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