Fixed bed Shell and tube reactor consist of tubes packed with catalyst particles and operated in a vertical position. The catalyst particles are of spherical shape. Feed is passed from the top of reactor in to the tubes; due to exothermic reaction the rate will be relatively large at the entrances to the reactor tube owing to the high concentrations of reactants existing there. It will become even higher as the reaction mixture moves a short distance into the tube, because the heat liberated by the high rate of reaction is greater than that which can be transferred to the cooling fluid as water at high pressure. Hence the temperature of the reaction mixture will rise, causing an increase in the rate of reaction. This continues as the mixture moves up the tubes, until the disappearance of reactant has a larger effect on the rate than the increase in the temperature. Farther along the tube the rate will decrease. The heat can now be removed through the wall with the result that the temperature decrease.
Cumene shell and tube reactor model diagram
Assume that all properties are constant in a volume element associated with a single catalyst pellet. In the simplest case the entire reactor operates isothermally and there is no variation of axial velocity in the radial direction. The global rate is a function only of concentration. Further, the concentrations will change only in the axial direction. Plug flow model was used as a basis for designing homogeneous tubular- flow reactor

ü  Isothermal process
ü  Assume complete propylene conversion.
ü  catalyst particle diameter dp = 3 mm
ü  catalyst particle density = 1600 kg/m3
ü  void fraction = 0.50
ü  heat transfer coefficient from packed bed to tube wall h = 60 W/m2°C
ü  The catalyst is packed in tubes ; tube I.D = 76.2mm, O.D =80.0mm
ü  Catalyst packed tubes be arranged on square pitch of 100mm
ü  Baffle spacing as 1/5th of the shell diameter.
ü  Let the BFW heated to 253.24°C
ü  Length of the tube be 6m

Volume of catalyst bed required for the reaction = 6.36 m3
Number of tubes required for the catalyst = Nt= 6.36/ (π/4(0.0762)2 X 6
                                                                          = 232.4 = say 232 tubes
Mass flow rate of reacting material ‘G’ = 17298.38+4704.29
                                                               = 22002.67/3600 = 6.11 kg/sec
Mass flow rate per unit area ‘G’= 6.11/ (π/4(0.0762)2 X 232= 5.77 kg/ m2s
Heat transfer coefficient for spherical particle,
h = 15.1 X G0.95/dt0.42
= 15.1 X 5.770.95/0.07620.42
= 267.84 W/m2K
Let the catalyst packed tubes be arranged on square pitch of 100 mm
Minimum area required = 0.12 X 232
                                       = 2.32 m2
Therefore shell diameter required:
= (2.32 X 0.2) + 2.32
= 2.784 m
= [2.784/ (π/4)]0.5
= 1.8826 m
Use baffle spacing as (1/5) of the shell diameter:
Baffle spacing = 0.376 m = 37.6 cm
Cross section area on shell side = As = 1.8826 X 0.376 X 0.01 / 0.1
                                                            =0.07 m2
Heat evolved in the reaction = 10360 MJ/h
                                                = 2.87 M Watts
                                                = 2877 kW
Heat generated per unit volume of catalyst = 2.87 X 103/6.36
                                                                     = 452.35 KW/m3
Water circulation rate = 2877/4.18 X 10
                                    = 68.82 kg / sec
Mass flow rate of water on shell side Gs = 68.82/0.07 = 983.25 Kg/m2s