I. Packed bed reactors are commonly used for catalytic reactions and consist of solid catalyst particles packed into tubes with fluids entering and leaving through headers. Heat is transferred between the reaction occurring within the catalyst particles and a cooling or heating fluid on the shell side. II. Effective heat transfer requires a high ratio of heat transfer surface area to reactor volume. Boiling fluids are often used as they have high heat transfer coefficients and can maintain a constant temperature over the cooling jacket. III. Heat transfer coefficients in packed beds are calculated based on temperature profiles and effective thermal conductivity, accounting for resistance near the tube wall and in the packed bed region. Coefficients depend on particle size, tube diameter, and fluid properties and flow

1. HEAT
TRANSFER IN
PACKED BEDS
PREETI BIRWAL
PH.D
NDRI
PH.D (DE)
14-P-DE-02

2. I. Many catalytic reactions are carried out in multi-tubular
reactors that are similar to shell-and-tube exchangers.
II. The solid catalyst particles are packed in the tubes, and the
reactant gases enter and leave through headers at the ends of
the reactor.
III. For an exothermic reaction, the heat of reaction is removed by
a circulating coolant or a boiling fluid on the shell side.
IV. For an endothermic reaction, the energy needed for the
reaction is transferred from hot fluid in the shell to the catalyst
particles in the tube.
V. Outside of the tubes is the heating or cooling medium, which
can be water, steam, oil or a molten salt. Boiling water or steam
is often preferred as heat transfer medium for exothermic and
endothermic reactions respectively
VI. Reactor models vary from pseudo-homogeneous to
heterogeneous, from one dimensional to three dimensional,
from assumed flow pattern to computed flow and transport
fields. The needed sophistication depends on the reaction
system.

3.  Advantage of these media is the high heat
transfer coefficient, which is caused by the phase
transitions that occur at the outer surface of the
tubes, and the fact that it is relatively easy to
have a constant temperature over the entire
cooling jacket.
 Compared to other types of packed bed
reactors, the diameter of the individual reactor
tubes of a tubular reactor is small, which allows
for effective heat transfer because of the high
ratio of the heat transfer surface and the reactor
volume.

5. TEMPERATURE AND VELOCITY PROFILES:
The radial temperature profile for an exothermic
reaction in a packed tube has the shape shown in fig.
There is a steep gradient near the inside wall and a
nearly parabolic temperature profile over the rest of
the catalyst bed. The velocity profile has a peak near
the wall, since the particles are packed more loosely in
this region than in the rest of the tube.
Temperature and velocity
profile of packed- bed
tube reactor.

6. HEAT-TRANSFER COEFFICIENTS
For a simple one-dimensional treatment of packed
tubes, the heat-transfer coefficient is based on a
radial average temperature of the gas, where T is
the temperature that would result from mixing all the
gas flowing through the tube at a given distance
along the tube. Thus where
( )jdq UdA T T 
idA DdL
0
1 1 1 1
i O i m i OU h h D D k D D
  
Temperature and velocity
profile of packed- bed
tube reactor.
………….1

8. In this simple treatment, the gas and solid temperatures are
assumed to be the same, even though, with an exothermic
reaction, the catalyst particle must be hotter than the
surrounding gas.
. The difference between gas and solid temperatures is
generally only a few degrees compared to a typical driving
force (T — Tj) of 20 to 30°C.
I. The presence of solid particles makes the inside coefficient
much greater than for an empty tube at the same flow rate,
since the actual gas velocity between the particles is up to
several times the superficial velocity.
V. For air in tubes packed with spheres, the coefficients are 5 to
10 times those for an empty pipe.
V. The coefficients increase with about the 0.6 power of the
flow rate and decrease more with increasing tube size than
for an empty tube.

9. The coefficients for a packed tube are highest when the
ratio Dp/Di is about 0.15 to 0.2.
For very small particles, the turbulent mixing in the bed is
depressed, and there is a large resistance to heat transfer in
the central region, which leads to a temperature profile
similar to that for laminar flow.
For very large particles, there is rapid mixing and almost no
gradient in the center of the tube. The dip in the curves at
Dp/Di ~͌ 0.3 was attributed to an increase in the void
fraction.”
. To predict the rate of heat transfer for different particle and
tube sizes, gas flow rates, and gas properties, the Coefficient
hi, is split into two parts to account for the resistance in the
region very near the wall and for the resistance in the rest of
the packed bed: 1 1 1
i bedh hw h
  ……………………..2

10.  The bed coefficient is obtained from an effective thermal
conductivity ke.
 The following equation applies if the temperature profile in the
bed is parabolic:
 The effective bed conductivity is usually about 5kg when the
particles are a porous inorganic material such as alumina, silica
gel, or an impregnated catalyst, and kg is the thermal
conductivity of the gas.
 The turbulent flow contribution to the conductivity is proportional
to the mass flow rate and particle diameter, and the factor 0.1 in
the following equation agrees with the theory for turbulent
diffusion in packed beds
 Note that the particle diameter is used in calculating the
Reynolds number for Eq. (4), but only the gas properties are used
in calculating the Prandtl number. The bed coefficient is obtained
by using Eq. (4) and the gas conductivity to get ke and then Eq.
(3) gives the value of hbed.
4 e
bed
k
h
r
 ………..3
………..4Re, Pr5 0.1e
p
g
k
N N
k
 

11.  The coefficient hw, can be estimated from the following empirical
equation, which was determined by subtracting the calculated bed
resistance from the measured overall resistance”:
 Equation (5) in combination with the equations for hw explains why the
combined coefficient hbed, goes through a maximum when Dp/Di is
between 0.1 and 0.2. When Dp/Di is small, the bed resistance is the more
important, and increasing Dp, increases NRe,p , and hbed.
 With large Dp/Di the wall film controls, and increasing Dp, leads to a lower
hw and a lower hi since, as shown by Eq. (5), hw varies with
Dp
-0.5
 Equation (5) was based on results for spheres, but it gives a fairly good fit
to the data for cylinders and ring-shaped packings.
 For packed tubes operating at 200°C or higher, radiation between
particles and from the particles to the wall becomes significant, and
predicted overall coefficients should be corrected for this effect.
0.5 0.33
, Re, Pr1.94( ) ( )
w p
Nu w p
g
h D
N N N
k
  ……………5