CHE 4151                                                                                                                                 Fall, 2016 Chemical Reactor Design                                                                                                      Jennings           HOMEWORK  # 10  ?  Nonisothermal  Gas-Phase  MFRs ( due  Friday,  11 / 4 )           1

CHE 4151                                                                                                                                 Fall, 2016

Chemical Reactor Design                                                                                                      Jennings

HOMEWORK  # 10  ?  Nonisothermal  Gas-Phase  MFRs

( due  Friday,  11 / 4 )

1.   [Problem 5-29, pp.245-246 in Schmidt.]  A catalyst has been developed for the oxidative dehydrogenation of ethane to ethylene:

2 C₂H₆   +   O₂    →    2 C₂H₄   +   2 H₂O

The heat of reaction is −25 kcal/mol.A.  The process produces only ethylene when carried out in an adiabatic mixed-flow reactor at 2 atm pressure.  The feed contains 5% ethane, 19% oxygen, and 76% nitrogen at 300 K.  The heat of reaction is –25 kcal/mol.ethane.  Assume that the heat capacity of all components is 7 cal/mol-K.  If the reaction goes to completion:  (a) calculate the moles of gas produced for each mole fed to the reactor, (b) calculate a value of the effluent temperature, and (c) calculate a value of the ratio of space time to residence time.

2.   [Problem 4-2, p.209  in Hayes.]  A mixed-flow reactor is to be designed to produce butadiene from butene by dehydrogenation (gas-phase reaction), C₄H₈   →   C₄H₆  +  H₂.  The

first-order reaction rate expression is written in terms of the partial pressure of butene as:

r_C4H8   =   k p_C4H8mol/L-hr

The rate constant (k) may be expressed as

k  =  (1.666 x 10¹⁵) e^{−30,109 / T}atm^–1-L^–1-hr^–1

The reaction is endothermic with a heat of reaction of110 kJ/mol.butene.  The reactor is often operated adiabatically, therefore steam is often added to the feed to provide thermal energy for the reaction.  For this reactor, the feed is a mixture of 10 mol of steam for each mol of butene.  The reactor pressure is 2 atm and the feed temperature is 650^oC.  The heat capacity of the

feed stream may be considered constant at 2.1 kJ/kg-K.

a)   Calculate the reactor volume for a 20% conversion of butene if the reactor is operated isothermally at 650^oC with a total inlet molar flow rate of 11,000 mol/hr.

b)   Determine the reactor volume for 20% conversion of butene for a total inlet molar feed rate of 11,000 mol/hr in an adiabatic reactor.

3.  [Problem 8-6, p.298  in Roberts.]  Methyl cyclohexane (M) is being dehydrogenated to toluene (T) [ M → T + 3 H₂ ] in a catalytic,  mixed-flow reactor.  The feed to the reactor is a 2:1 (molar) mixture of hydrogen and methyl cyclohexane at a temperature of 500^oC and atmospheric pressure.  The feed rate of methyl cyclohexane is 1.2 mol/s.  The reactor contains 10.0 kg of catalyst and operates adiabatically.  At what temperature and fractional conversion of methyl cyclohexane does the reactor operate?

Additional data:

Δ?_R⁰  =  54.3 kcal/mol.M

?_P,M = 32.3 cal/mol-K    ,    ?_P,T = 24.3 cal/mol-K    ,    ?_P,H2 = 6.89 cal/mol-K

 k = (4.31x10³³) e^{–35,000 / T} L/kg.cat-s

4.  [Problem 8-7, pp.298-299  in Roberts.]  Methyl cyclohexane (M) is being dehydrogenated to toluene (T) [ M → T + 3 H₂ ] in a catalytic,  mixed-flow reactor.  The feed to the reactor is a 2:1 (molar) mixture of hydrogen and methyl cyclohexane at a temperature of 500^oC and atmospheric pressure.  The feed rate of methyl cyclohexane is 1.2 mol/s.  The reactor contains 10.0 kg of catalyst and operates adiabatically.  There is a heating coil in the reactor with hot flue gases flowing through the coil at a temperature of 600^oC.  The overall heat transfer coefficient between the coil and the reactor contents is 20.0 cal/m²-K-s.  If the desired fractional conversion is 0.50, at what temperature should the reactor operate?  What area of heating coil is necessary to maintain that temperature?

Additional data:

Δ?_R⁰  =  54.3 kcal/mol.M

?_P,M = 32.3 cal/mol-K    ,    ?_P,T = 24.3 cal/mol-K    ,    ?_P,H2 = 6.89 cal/mol-K

 k = (4.31x10³³) e^{–35,000 / T} L/kg.cat-s

Example Problems

( no solution needed )

[Problem 8-2, p.296  in Roberts.]  The elementary gas-phase isomerization reaction,  A  ↔  B ,  is being carried out in a fluidized-bed reactor (which may be modeled as an ideal mixed-flow reactor) containing 10 kg of catalyst.  The adiabatic operating conditions are: temperature = 300^oC and pressure = 1 atm.  The feed is 40% A and 60% inert carrier gas (C) at a total volumetric flow rate of 50 m³/hr (at STP).

a)   Under these conditions, what will be the fractional conversion of A?

b)   What feed temperature is required to operate at steady-state at these conditions?

         Additional information:

k_f   =   14.9 L/g.cat-hr  at  300^oC

K_EQ  =  4.19 at 300^oC

Δ?_R,A =  + 3.50 kcal/mol.A

?_P,A  =  ?_P,B  =  17.5 cal/mol-K   ,   ?_P,C  =  7.0 cal/mol-K

[Problem 8-E. (original)]The elementary, irreversible, gas-phase reaction, A + B → D, is to be carried out in a 10-liter mixed-flow reactor.  The feed contains only A and B in stoichiometric proportions at 580 kPa and 77^oC.  The molar feed rate of A is 20 mol/s.  Calculate the amount of heat that must be added to or removed from the reactor to maintain an operating temperature of 500 K.

Additional  Data:

            Rate law parameters:

                        k    =  0.065  L/mol-min  at  25^oC

                        E*  =  70  kJ/mol

            Thermodynamic parameters at 25^oC:

                        ?_F,A  =  –40 kJ/mol     ,     ?_P,A  =  25 J/mol-K

                        ?_F,B  =  –30 kJ/mol     ,     ?_P,B  =  15 J/mol-K

                        ?_F,D  =  –45 kJ/mol     ,     ?_P,D  =  35 J/mol-K