Q6.1. You are operating a batch reactor in which the first order liquid phase reaction A => Products is
taking place. An inert coolant is added to the reaction mixture to control the temperature.
(a) Calculate the flow rate program needed.
(b) What is the flow 2 hours after start?
Reactor temperature = 38°C

k = 1.02 * 10^{- 4} /sec ; Coolant temperature = 26°C ;Heat capacity = 0.5 kcal/kg °C
Density = 800 kg/m^{3} ; ΔHR = -14000 kcal/kmol ; C_{Ai} = 8 kmol/ m^{3} ; V_{i} = 1.5 m^{3}

285 exp(-kt), 135 kg/sec

Q6.2. Hexamethylene tetramine is to be produced in a well stirred semi batch reactor by adding aqueous ammonia solution at a constant rate to an initial charge of formalin solutions.
4NH_{3} (A) + 6HCHO (B) = N_{4} (CH_{2})6 + 6 H_{2} O
The reaction is instantaneous, irreversible and exothermic. A cooling coil is immersed for head removal
Data:
Vi = 2000 L
C_{Bi} = 15 gmol/L C_{A0} = 15 gmol/L
T_{A0} and T_{i} = 0°C
Cp = 1000 cal/L °C
v_{A0} = 10 L/min
ΔH = -74 kcal/gmol HMT

Q6.2.1. Calculate the time required for complete consumption of formaldehyde

133.3 min

Q6.2.2. Calculate time required to reach 60°C under adiabatic operation.

54.6 min

Q6.2.3. Estimate heat to be added or removed if reaction mixture in is to be maintained at 60°C

-2200 kcal / min

Q6.3. A CSTR is used to carry out an exothermic liquid phase reaction

A = B; r_{B} = kC_{A}

A= C; r_{C} = kC_{A}

The reactor has a coil through which suitable heating/cooling medium is circulated.
Other data are given below:

Q6.3.1 Obtain a relationship between tT and residence time for maximizing the production rate of B Q6.3.2 Determine the conversion, reactor temperature for B.

= 82 deg C, X_{1} = 0.545,
X_{2} = 0.273

Q6.3.3. What is the area of cooling coil required?

= 2.8 sqm

Q6.4 A liquid phase reaction carried out in a CSTR. The reactor has a coil through which large quantity of fluid is circulated. Other data are

Feed C_{A0} (kmol/cum)

= 1.66

Feed temperature, T_{0} (°C)

= 21

Volumetric flow V_{0} (cum/hr)

= 0.6

Volumetric specific heat, cp (kcal/cum °C)

= 1000

Activation energy E_{1} (kcal /kmol)

= 25000

Heat of reaction (kcal /kmol A)

= -20000

Coolant temperature (°C)

= 10

Heat transfer coefficient, kcal/sqm. hr.°C

= 1000

The variation of rate and equilibrium constant is given below. This data may be used to estimate needed parameters quickly.

T(K)

293

303

315

323

k_{1} (1/hr)

1.06

4.37

21.3

57.2

Ke

21.6

6.96

1.97

0.89

Q6.4.1. Derive the equation for the locus of maximum reaction rates at constant X.

Q6.4.2. Specify best conditions required to get a conversion of x = 0.52

T = 315 K, V = 67.8 lit

Q6.4.3. Show steady state attained by plotting heat generation and heat dissipation curves.

Q6.4.4. Derive conditions for stability of steady state.

Q6.4.5. Examine nature of stability of steady states in (Q6.4.3.)

Q6.4.6. A two tank sequences are to be used to get a final conversion of 0.8. Specify the best operating conditions to be used (T = 303 C)

Q6.4.7. Examine the nature of steady states in (6.4.6.)

Q6.4.8. Plot RB versus T for constant X Q6.4.9. Plot Xe versus T Q6.4.10. Plot Xm versus T Q6.4.11. Derive equation to locus of X/ T at constant RB . Plot X’m versus T Q6.4.12. Plot locus of RB /T) X and plot Xm versus T

Q6.5Design of a utility
Nitrogen dioxide - nitrogen tetraoxide system is proposed as a thermal utility. The fluid picks up energy from an environment A at 80 °C and delivers to an environment B at 20 °C. It is desired to specify a process design for a space heating application. The relevant data are as below:

Component ΔH_{f} @ 25 C ΔG_{f} 25 C cP
kcal / mol kcal/mol cal/mol.k

0.45 @ 20 C

NO_{2} 7.96 12.26 12.5
N2O_{4} 2.23 23.41 25

5.8 @ 80 C

Q6.5.1.Specify the composition and molar flow of gases in reactors A and B if 1.0 mol/s of nitrogen is flowing in system. Estimate the heat load the system can deliver

Q6.5.2. How would the system adjust if heat supply or demand changes ? Can you set out the equations that govern the transient processes due to changes in flow or heat loads?

Q6.5.3.Review the thermodynamics of the process and comment on the possible application of this system for heat to work conversion.

Q6.6. Fed Batch Operation: A first order irreversible reaction A <=> B produces a volatile product B. The reaction is highly exothermic. Therefore it is fed batch reactor .in order to ensure that temperature of the reaction mixture dose not rise above 38°C an inert coolant is continuously added at the rate just sufficient to maintain the reactor temperature.

Other Data:
Reaction temperature desired =38°C
Coolant feed temperature =26°C
First order rate coolant at 38°C =1.4*10^{-4} /sec
Density of the reaction mixture = 800 g/L
ΔHR = -20 kcal/ mol
Initial concentration of A = 8 gmol/lit
Initial volume =1500 lit
Volumetric specific heat, Cp = 0.5 Kcal/lit. °C

Q6.6.1. Determine the time course of variation of volume flow required to achieve the result desired.

Q6.6.2. Estimate the reactor volume, conversion coolant flow rate at a time when 95 percent conversion is attained.

Q6.6.3. Fermentation processes such as penicillin employ fed batch operation? Why?

Q6.7.Process design for storage of reactive intermediates
A reactive/volatile liquid intermediate A is a commercial product. It undergoes during age an undesirable change due to an elementary instantaneous endothermic reversible reaction A <=> B. Consequently the product A is stored at low temperature. In this exercise we estimate the extent of loss of this product A during storage.

The storage tank is typically (50 m^{3} or more) with a typical external surface area of 100 m^{2}. The tank has recirculating pumps to keep the contents well mixed. The tank is insulated. In addition external cooling coil is also available to augments the cooling leads.

Data:
Gas constant ® =0.001987 Kcal/mol.K
Equilibrium constant (K) =exp [15.3+5000/T(K)]
Specific heat of Rxn-mixture (Cp) =1230 Kcal/m3.K
Ambient temperature (T) =-50 C
heat transfer coefficient (coolant reaction mixture ) (hc) =300 Kcal/m^{2}.hr.C
Heat Transfer Coefficient (Ambient Reaction mixture) (ha) =30 Kcal/m^{2}.hr.C
External cooling coil area (AC) =5 m^{2}
Volume of storage tank =50 m^{3}
External surface area of tank (AT) =100 m^{2}
Initial Temperature of Product A =
Heat of Reaction (H) =10 Kcal/mol
Initial Concentration of A (CAO) =50 Kmol/m^{3}
Initial charge of A in tank (NAO) =2500 Kmol

Q6.7.1. Show that the variation of the tank contents can be given as

Q6.7.2. What is the steady state temperature and composition of the tank contents?
What is the extent of product A lost during storage? What can be done to prevent the loss?

Q6.7.3. Estimate the time required to reach 95 percent of the steady state temperature.

Q6.7.4. Can you recognize the hazardous physical situations due to storage of material prone to exothermic decompositions. Use your result of 3.1 and comment.

Q6.7.5. Many aerobic biological reactions generate heat to the extent of 122 kcal/mol oxygen consumed and take place over 2 to 8 hours. How serious is the heat transfer in this situation and how to control these heat loads.

Q6.8. It is proposed to produce 60 mol/min of product B from pure A. The reaction A<=>B is reversible and exothermic and is to be carried out in a CSTR. The reactor effluents pass to a separator in which B is fully recovered and A is recycled.

Assume that the energy for separation is externally provided and that the streams A and B emerge from separator at the same temperature as that of reactor exit. Other data are as below

Feed Pure A ; Desired Production of A 60 mol.min ; Feed temperature 40°C

Molar density reaction mixture 20 mol / lit ; Specific heat of reaction mixture 1.0 kcal/lit C

Heat Transfer coefficient 5 kcal/m^{2}. min C ;Coolant temperature 5°C large quantity Quantity Available

Heat of Reaction 20 kcal/mol T independent ; Activation energy E_{1} 20 kcal/mol
Rate Constant k_{1} 0.4/min at 20C ; Rate constant k_{2} 0.1/min at 20C ; Gas Constant R 1.987 cal/mol

Q6.8.1. Specify a suitable reaction temperature. Justify the rationale for your choice.

Q6.8.2. What are the molar flow rates of A and B in different positions inside and outside the recycle loop. What are the recycle ratio, reactor volume and residence employed?

Q6.8.3. What is the heat load, heat transfer area, temperature required at different positions to achieve the productions desired? How would you provide this heat transfer surface?

Q6.8.4. If it is desired that the heat transfer area must be provided as a jacket only. What changes in process design if any would you carry out? Show one set of calculation to illustrate your procedure.

Q6.8.5. List one commercially important reaction where the chemical reaction and product separation are both carried out in the same equipment. Explain the rationale for such a design.

Q6.9. Organic oxidations in fluidized beds
Pthalic anhydride is an important intermediate in the manmade fiber industry. It can be produced by controlled oxidation of naphthalene over vanadium pentoxide catalyst. Many reactions occur during the oxidation and all are exothermic. A fluid bed is preferred because of ease of heal removal. The reactions are represented as
A =>P [k_{1}] (desired)
And
P => X [k_{2}] (undesired)
We plan to express the behavior of the system in terms of the following
α = (C_{AO} - CA) /C_{AO}; β = CP / (C_{AO} –C_{AO}); η = Cp/ C_{AO}

The bed behaves like a CSTR and our aim here is to choose conditions that will maximize η.

Q6.9.1 Set up the balance equations and express α, β and η in terms of rate constant and residence time (τ). Keeping τ fixed it is desired to choose the optimum operating temperature such that η is maximized. Show that the temperature that maximizes η is given as
E_{1}/E_{2} = k_{2}τ (1+k_{1}τ) / (1+k_{2}τ)

Q6.9.2 A thermic fluid at 275°C is available for cooling purpose. The temperature of the cooling fluid does not change much as it passes through the coil. Estimate the heat transfer surface area unit volume required for an optimum choice of reactor temperature = 331°C. Tabulate residence time, Rate constants for this choice of reactor temperature, Heat transfer area per unit reactor volume.

Q6.9.3 Tubular reactor could be an alternative reactor choice for such catalytic reactions. Comment on the effect of tube and packing sires on the profile of temperature and hence reactor performance.
Data:
∆H_{1} = -449 kcal/gmol
∆H_{2} = -784 kcal/gmol
k_{10} = (5.3 )1015 s^{-1}
k_{20} = (2.65 )1015s^{-1}
Cp = 0.12 cal/lit °C
T0 = 150°C (feed temp.)
U = 300 kcal/m2h°C
E_{1} = 43900cal/gmol
C_{AO} = (4.46) 10 -4 gmol/lit
E_{2} = 20414 cal/gmol