This set of Chemical Reaction Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Non Ideal Reactors – Dispersion Model”.

1. If D is the fluid dispersion coefficient, L is the length of spread of tracer and u is the fluid velocity, then which of the following represents Dispersion number?

a) \(\frac{L}{uD}\)

b) \(\frac{L}{D}\)

c) \(\frac{D}{uL}\)

d) \(\frac{Lu}{D}\)

View Answer

Explanation: Dispersion number is a dimensionless group characterizing spread in the entire reactor vessel. The value of D determines the spread.

2. The value of the Dispersion coefficient for plug flow is ____

a) 1

b) 0

c) ∞

d) 2

View Answer

Explanation: There is no axial mixing in a PFR. Hence, the dispersion of the fluid in the longitudinal direction is assumed to be zero.

3. Which of the following represents Peclet number?

a) \(\frac{Lu}{D} \)

b) \(\frac{u}{D} \)

c) \(\frac{u}{DL} \)

d) \(\frac{D}{uL} \)

View Answer

Explanation: Peclet number also defines the Dispersion model. It is the reciprocal of Dispersion number.

4. The value of the Peclet number for CSTR is ____

a) 1

b) 0

c) ∞

d) 2

View Answer

Explanation: CSTR is characterised by complete mixing and recycling between the reactants and products. Hence, there is high diffusion of molecules within the reactor. As peclet number is inversely proportional to dispersion coefficient, Pe

_{CSTR}= \(\frac{Lu}{∞}\) = 0.

5. The range of dispersion number for PFR is ____

a) \(\frac{D}{uL}\) < 0.1

b) \(\frac{D}{uL}\) < 0.01

c) \(\frac{D}{uL}\) > 1

d) \(\frac{D}{uL}\) > 10

View Answer

Explanation: For PFR, \(\frac{D}{uL}\) < 0.01. Due to negligible dispersion in PFR, \(\frac{D}{uL}\) nearly approaches 0.

6. The dispersion model accounts for ____

a) Deviation from ideal PFR

b) Modelling ideal CSTR

c) Combining batch and CSTR

d) CSTRs connected in parallel

View Answer

Explanation: Dispersion model involves a modification of the ideal PFR. It imposes axial dispersion on plug flow.

7. The the species continuity equation for the axial dispersion model is ____

a) u \(\frac{∂C_A}{∂z} = \frac{∂D_a}{∂z} \frac{∂C_A}{∂z}\) + (r_{A})C

b) u \(\frac{∂C_A}{∂z} = \frac{∂D_a}{∂z} \frac{∂C_A}{∂z}\) + C

c) \(\frac{∂C_A}{∂z} = \frac{∂D_a}{∂z} \frac{∂C_A}{∂z}\) + (r_{A})C

d) u \(\frac{∂C_A}{∂z} = \frac{∂D_a}{∂z} \frac{∂C_A}{∂z}\) + (r_{A})

View Answer

Explanation: For statistically stationary flow, the species continuity equation for the axial dispersion model is u\(\frac{∂C_A}{∂z} = \frac{∂D_a}{∂z} \frac{∂C_A}{∂z}\) + (r

_{A})C.

u is taken to be the mean (plug flow) velocity through the vessel, and D

_{a}is an axial dispersion coefficient to be obtained by means of experiments.

8. If D_{a} is diffusivity, C_{T} is tracer concentration and U_{T} is overall heat transfer coefficient, then the pulse tracer balance with dispersion is obtained as ____

a) \(\frac{∂^2 C_T}{∂z^2} – \frac{∂(UC_T)}{∂z} = \frac{∂C_T}{∂z} \)

b) D_{a}\(\frac{∂^2 C_T}{∂z^2} – \frac{∂(UC_T)}{∂z} = \frac{∂C_T}{∂z} \)

c) D_{a}\(\frac{∂^2 C_T}{∂z^2} + \frac{∂(UC_T)}{∂z} = \frac{∂C_T}{∂z} \)

d) D_{a}\(\frac{∂^2 C_T}{∂z^2} – \frac{∂(UC_T)}{∂z} = \frac{∂C_T}{∂z} \)

View Answer

Explanation: The equation D

_{a}\(\frac{∂^2 C_T}{∂z^2} – \frac{∂(UC_T)}{∂z} = \frac{∂C_T}{∂z} \) is obtained by a combination of mole balance on inert tracer and the molar flow rate of tracer by both convection and dispersion.

9. The range of reactor peclet number for open tubes is ____

a) 10^{6}

b) 10^{10}

c) 10^{2}

d) 10^{3}

View Answer

Explanation: Peclet number for open tubes is greater than that in packed beds. In open tubes, there is no restriction to flow velocity.

10. The dispersion model is a ____

a) Two parameter model

b) One parameter model

c) No parameter model

d) Three parameter model

View Answer

Explanation: Dispersion model is a one parameter model. The parameter modelling the non – ideal condition is the dispersion coefficient.

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