1. FLOW THROUGH GRANULAR BEDS AND PACKED COLUMN
By: Dr Akmal Hadi Bin Ma’ Radzi

2. Introduction
Most of technical process, liquid or gases flow through beds of solid particles.
Example:
i) A single fluid flow through a bed of granular solid
ii) Two phase countercurrent flow of liquid and gas through packed columns.

3. Flow of single fluid through a granular bed
Single fluid flow through a granular bed or
porous medium involves in;
fixed bed reactor
filtration
adsorption
seepage of underground water or petroleum

4. Darcy Law and Permeability
Permeability measurement is conducted to determine the surface powder
Where ;
–ΔP = the pressure drop across the bed
l = the thickness of the bed
uc =the average velocity of flow of the fluid, defined as (1/A) (dV/dt)
A = the total cross sectional area of the bed
V = the volume of fluid flowing in time t
K = a constant depending on the physical properties of the bed and fluid
Darcy’s Law: the flow is proportional to the pressure drop and inversely proportional to the
fluid viscosity

5. Specific surface and Voidage
The general structure of a bed of particles can often be characterized by the specific surface area of the bed and the fractional voidage of the bed .
Voidage/porosity (ε) -The fraction of the volume of the bed not occupied by solid material. It is dimensionless and given by;

6. Specific surface area of the particles (a)
The surface area of a particle divided by its volume. Its units are (length)^-1
Sp : surface area of a particle in m2
vp: volume of particle in m3
For a spherical particle,
Dp : diameter in m
For a packed bed of nonspherical particle, the effective
particle diameter Dp is defined as

8. Example

9. Solution

10. Then,

11. General expressions for fluid flow through beds in terms of Carman-Kozeny equations.
1.Physical model for granular bed
The pore space in the bed is assumed to be a tube with equivalent diameter
which satisfies the following assumptions:
• The internal surface area is equal to the surface area of particles
• The free space is equal to that in granular bed.
- The hydraulic radius rH for flow can be calculated as follows: rH

12. For packed bed, Reynolds number for a packed be can be defined as follows:

13. 2.Pressure drop At a steady state, and negligible gravity effect,
The pressure drop is given by;
However, the experimental show that the constant should be 150, which gives the Kozeny-Carman equation for laminar flow, void fraction less than 0.5, effective particle diameter Dp and NRe < 10

14. For Re > 1000,
Ergun proposed the following general equation for low, intermediate, and high Reynolds numbers which has been tested experimentally

15. Then, this equation can be rewriting in term of dimensionless group,
This equation can be used for gases by taking the density  of the gas as the arithmetic average of the inlet and outlet pressures

16. Factors affecting pressure drop:
operation parameters: e.g., VO
• physical properties of fluid: μ , ρ
• characteristics of the bed: ε , s

17. Example 2
12.7
0.61 m
0.358

18. Solution 2

19. To calculate Δp

20. Dispersion in packed beds
Axial dispersion is nonideal flow phenomenon occurred in packed beds when flow rate of fluid and pressure are high
The importance of axial dispersion in liquid flow through porous beds is well known for numerous engineering applications.
Many studies concerned with diffusion and dispersion in porous media have been undertaken to understand their effects on mass and heat transfer and on chemical reactions taking place within packed beds.

21. The axial dispersion maybe describes by a diffusion-like equations
Where,
C = fluid concentration
D= Axial dispersion coefficient
Z =Axial coordinate in packed bed
v= fluid velocity