Department of Chemical & Biomolecular Engineering
THE NATIONAL UNIVERSITY
of SINGAPORE
Chemical Engineering Laboratory
Experiment F3
Fluid Flow in Packed Bed
Name
:
Metric No.
:
Group
:
Date of Expt. :
Demonstrator’s :
signature
GRADE :
Objectives:

To determine the pressure drop and friction factor for fluid flowing through columns
packed with different sizes of glass beads.

To study the relationship between friction factor and Reynolds number for flow through
packed bed.
Apparatus :
A set of three horizontal glass columns packed with spherical glass beads of different sizes.
Theory :
Fluid flow through packed beds has many important engineering applications. Filtration,
drying columns, fixed bed catalytic reactors and absorbers are some of the examples of
packed beds. It is often required to estimate parameters such as pressure drop through
packing and friction factor to optimally design the equipment. Analytical solutions for these
parameters are difficult to obtain hence experimental correlation’s are needed.
Fluid flow through a pipe is characterised by a dimensionless group, the Reynolds number
(NRe), defined by
N Re 
d U 

Where
d
U


Diameter of the pipe [m]
Average linear velocity of fluid [m s-1]
Absolute viscosity of fluid [N s m-2]
Density of fluid [kg m-3]
NRe has been the basis for the calculation of pressure gradient in a pipe through which a fluid
is flowing and it can be used to determine the stable form of flow in a pipe in given
conditions is streamline or turbulent. NRe is proportional to the ratio of non-viscous force to
the viscous forces and is often used when we are concerned with a moving fluid. At low
Reynolds numbers (less then about 2100) laminar flow persists with a uniform parabolic
velocity profile across the tube. At high Reynolds numbers (greater than about 4000) the
nature of the flow changes to a more random eddying flow called turbulent flow. At
intermediate values of the Reynolds number, flow may be either laminar or turbulent. This
flow regime (2100 < Re < 4000) is called the transition region. The change from transition to
turbulent flow is not well defined. Different authors quote Reynolds numbers from 4000 to
10,000 for the onset of turbulent flow.
When a fluid flows through a bed of particulate solids then
Average Velocity  Driving Pressure 
1
Bed Thickness
If the flow in the bed is laminar then due to viscous drag , superficial velocity (u) which is
nothing but the velocity through empty column is inversely proportional to the fluid viscosity
and can be represented as
u=K
Flowrate of liquid
1 dv
P
P

= B
=
Cross  sec tional area of the column
L
 L A dt
where
K
P
L
B
A
dv
dt
= Proportionality constant
= Pressure drop
= Length of the Bed
= Permeability coefficient of the bed
= Cross-sectional area of the bed
= Differential Volume
= Differential Time
By determining Bed Characteristics such as void fraction () , specific surface area (S), etc.
NRe and the friction factor  can be estimated.
From the basic definition, Reynolds Number for flow through packed bed filled with
6
spherical particles (S=
) can be written as
dp
NRe =
 u dp
6  (1   )
The resistance to the flow of a fluid through the bed of solids is the net result of the total drag
of all the particles in the bed. Depending on the NRe, friction factor, laminar /turbulent flow,
form drag and wake formation will occur. Hence, friction factor () for the above system can
be obtained by equating total drag force to the total pressure force.
i.e.
R’ S L (1-) =   P
Where R’ is the drag force per unit area of particle surface. Therefore friction factor can be
obtained as
dp 3
P
[
]
Exptl 
L 6 (1   )  u 2
Ergun equation was developed attributing viscous drag force and inertial force to the total
pressure drop in the bed and can be written as
Ergun = 4.17 NRe-1 + 0.29
in the above equation for higher values of NRe viscous force becomes negligible and inertial
forces control.
According to Carman the co-relation for friction factor and Reynolds Number can be written
as
Carman = 5 NRe-1 + 0.4 NRe-0.1
for laminar flow, when NRe  2, the second term of the Ergun and Carman equations
becomes negligible.
Experimental Procedure
This experiment investigates the relationship between the friction factor and Reynolds
number of a single fluid flowing through a packed bed. Three packed beds of similar
dimensions each filled with different sized beads were used. The flow rate of water through
these beds were varied and the corresponding pressure drop were recorded.







Measure the bulk density of three different sizes of glass beads
Select the column for the experiment
Calculate void fraction  for the column.
Adjust the control valves appropriately and commence the experiment with a water flow
rate of 1 l/min.
Ensure steady state is achieved before recording any readings.
Note down the pressure drop across the bed from the manometer.
For the given flow rate calculate Superficial Velocity (u), Reynolds Number (NRe) and
Friction factor () from.
a. Experimental data
b. Ergun’s Correlation
c. Carman’s Correlation





Adjust the control valves to the next higher flow rate and carry out the experiments to
cover as wide a pressure drop difference as possible. (conduct experiments at least at 2025 different flow rates in steps of approximately 0.5 L/min.)
Tabulate the results.
Plot Exptl vs NRe, Ergun vs and Carman vs NRe
1
1
1
Plot Exptl vs
, Ergun vs
and Carman vs
NR e
NR e
NR e
Carryout similar experiments, calculations and generate similar plots for other columns.
Tabulation and Calculations:
Density of beads
Void fraction of columns
Reynolds Number
Friction factor
Plots:
For each column
1. Plot Exptl, Ergun and Carman vs NRe
2. Plot Exptl and Ergun vs 1/NRe and record the slope and intercept of these lines.
Results and Discussions:
Conclusions:
Questions:
1. Three identical columns packed with solid spheres of same size but of different materials
(glass ceramics and plastic). If the liquid flows through the columns at the same velocity
in highly turbulent condition, what would you expect for pressure drops in the three
columns?
2. A column has to be packed by spherical catalyst particles to use as a catalytic reactor.
What are the factors you would consider in selection of optimum catalyst size?
3. A column packed with a certain material gives a void fraction of 0.45. If the packing
material is changed to another size, the void fraction is decreased by 10 % and the
specific surface area of the bed is increased by 50%. How much change in pressure drop
per unit packing height is expected if the flow is in laminar condition. (Specific surface
area of the bed, SB= S(1-), where S is the specific surface area of the particle)
REFERENCES :
1. McCabe, W.L., J.C. Smith, and P. Harriott, “Unit Operations of Chemical Engineering”,
5th Edition, McGraw-Hill, Chapter 7 (1993).
2. Coulson, J.M., J.F. Richardson, J.R., Backhurst and J.H. Harkaer, “Chemical
Engineering” Vol. II, 3rd Edition, Pergamon Press, Chapter 4 (1978).