1. Find the volume of reactor needed for 70% conversion of A to product. Aqueous feed of A and B (200lit/min, 20mmolA/lit, 50mmolB/lit) is fed to MFR. Reaction kinetics is as follows
A+B → P
-rA = 200CACB mol/lit-min
a) 12.5
b) 3.6
c) 6.4
d) 1.5
Explanation:
CA0*XA = CB0*XB
XB = \(\frac{20*0.7}{50}\) = 0.28
\(\frac{τ}{CA0} = \frac{XA}{-rA}\)
τ = \(\frac{0.7*20*10^{-3}}{200*10^{-6}[20(1-0.7)*50(1-0.28)])}\) = 0.032 = \(\frac{V}{v0} \)
V = 0.032*200 = 6.4 lit.
2. An existing MFR is to be replaced by the one 4 times larger than it. Find the new conversion if a homogeneous liquid phase reaction with reaction kinetics as follows.
A → R
-rA = kCA2 with 30% conversion.
a) 0.67
b) 0.45
c) 0.53
d) 0.92
Explanation:
\(\frac{τ}{CA0} = \frac{XA}{-rA} \)
\(\frac{V}{CA0 V0} = \frac{0.3}{k[ CA0(1-0.3)]^2} \)
\(\frac{V}{CA0 V0}\) = kτCA0 = 0.6122
When replaced by new reactor
\(\frac{4τ}{CA0} = \frac{XA}{-rA} \)
\(\frac{4Vk}{CA0 V0} = \frac{XA}{(1-XA)^2} \)
XA = 0.53.
3. Replace the existing MFR with a PFR and calculate the new conversion if a homogeneous liquid phase reaction with reaction kinetics as follows.
A → R
-rA = kCA2 with 30% conversion
a) 0.65
b) 0.43
c) 0.38
d) 0.92
Explanation:
\(\frac{τ}{CA0} = \frac{XA}{-rA} \)
\(\frac{V}{CA0 V0} = \frac{0.3}{k[ CA0(1-0.3)]^2} \)
\(\frac{Vk}{CA0 V0} \) = kτCA0 = 0.6122
When replaced with a new PFR
\(\frac{τ}{CA0} = \int_0^{XA} \frac{dXA}{-rA} \)
For 2nd order on Integration we get,
kτCA0 = \(\frac{XA}{1-XA}\) = 0.6122
XA = 0.38.
4. Find the conversion of a 25 litre PFR if a gaseous feed of pure A (2 mol/lit, 150 mol/min)
Is decomposed, kinetics are as follows.
A → 2.5R
-rA = (15min-1) CA
a) 0.89
b) 0.92
c) 0.45
d) 0.68
Explanation:
\(\frac{τ}{CA0} = \frac{V}{FA0}\)
τ = (25*2)/150 = 0.33 min
For a 1st order reaction with variable volume on integration we get
kτ = (1+εA)ln\((\frac{1}{1-XA})\) – εAXA
15*0.33 = (1+1.5) ln\((\frac{1}{1-XA})\) – 1.5XA
XA = 0.92.
5. For a constant volume system, the size of batch reactor is _______________ PFR.
a) smaller than
b) larger than
c) same as
d) cannot be compared
Explanation:
For PFR, \(\frac{τ}{CA0} = \int_0^{XA}\frac{dXA}{-rA} \)
For Batch reactor, \(\frac{t}{CA0} = \int_0^{XA}\frac{dXA}{-rA} \)
From the above equations it is clear that theoretically the element of fluid reacts for same length of time in PFR and Batch reactor. But shutdown time as to be considered for actual design.
6. Space time is defined as ____
a) Time required to process unit volume of feed
b) Time required for the reaction to occur
c) Time required to produce unit volume of product
d) Time to process the entire volume of feed entering
Explanation: Space time is the time spent by a unit volume of reactants inside the reactor. It is the performance measure for a flow reactor.
7. The unit of space velocity is ____
a) sec
b) sec-1
c) m3
d) m-3
Explanation: Space velocity has the dimensions of time-1. A space velocity of 2 hr-1 implies that 2 reactor volumes are fed per hour.
8. Space time as a function of molar feed rate and initial concentration is given as ____
a) \(\frac{VC_{A0}}{F_{A0}} \)
b) \(\frac{C_{A0}}{VF_{A0}} \)
c) \(\frac{VF_{A0}}{C_{A0}} \)
d) \(\frac{C_{A0}}{F_{A0}} \)
Explanation: Space time is the ratio of the product of reactor volume and initial concentration to the feed rate. \(\frac{VC_{A0}}{F_{A0}} \) has the same unit as that of space time.
9. If V represents volume and Q represents volumetric flow rate, then which of the following is a valid expression for space velocity?
a) \(\frac{V}{Q} \)
b) \(\frac{Q}{V} \)
c) Q × V
d) \(\frac{V}{C_{A0}} \)
Explanation: Space velocity is the ratio of volumetric flow rate to volume. It has the unit hr-1.
10. State true or false.
Space velocity is the number of unit volumes of feed that can be treated per unit time.
a) true
b) false
Explanation: Space velocity is the inverse of space time. It gives a measure of what volume of feed can be processed in a unit time.