Permeability and FluidizationProblem C2 and C3

Group Members: Castillo, ArlynDela Cruz, LiezylEscover, JhealuzPangilinan, Jerina

Objective• To determine the permeability

and the filtration grain diameter of a porous granular media (sand)

Theory

• Darcy’s Law – linear relationship between headloss (h) and the flow rate expressed as approach to velocity

Va = k𝑑ℎ

𝑑𝐿

Where: 𝑑ℎ

𝑑𝐿= hydraulic gradient

k = permeability

Va = volumetric flow rate per unit area

• Permeability – a property of porous media in which a fluid can flow through the media in response to pressure gradient.

k = 𝜑𝑔

5𝜇

𝜀3

1−𝜀 2 (𝑑

6) 2

Where:

𝜑 = density of fluid

g = acceleration due to gravity

μ = dynamic viscosity of the fluid

ε = porosity of the permeable media

d = diameter of grains constituting the porous media

• Kozeny – Carman – analogy that the bundle of tortuous capillary tubes could represent the porous media and that an equivalent hydraulic radius could be developed for granular porous media.

𝑑ℎ

𝑑𝐿=

5𝜇𝑉𝑎𝜑𝑔

(1 − 𝜀)2

𝜀3(6

𝑑)2

Equipment / Apparatus / Materials

• Permeability & Fluidization apparatus (with mercury manometer and Perspex column)

• Electronic balance

• Pre-sieved sand (0.540 kg)

• Thermometer

• Beaker

Procedure

• Start Up

• Preparation of Media and filling column

• Experimental Procedure

Turn on water supply

Open valve (2) and valve (3)

Close valve (3)Unscrew air-release screw at the top of

the column

Close valve (2) open valves (1) and (4)

Close valve (1) and open valves (5, 6, 7,

8)

Open valves (1, 2) and close valves (3,

4)

Close valves (1, 2) open valves (4, 5, 6)

Continue water thru empty apparatus in an upward direction

thru column

Pre-sieve sand into uniform size and weigh 0.54 kg

close all the valves and open air-release screw

Remove Perspex column and pour sand into column containing water

Insert column back to the apparatus and screw it to place

Open valve (2) then tighten air-release screw

Close valves (1, 2, 3, 4) and tap gently along Perspex column

Insert drain tube (4) to beaker with thermometerRead temperature of

water leaving experiment period Read media surface

level zero to both manometers

Open valves (1, 4) and do 7 settings of flow rate

Note manometer reading and temperature or exit water for

each setting

Sample Calculations

Por𝑜𝑠𝑖𝑡𝑦, 𝜀 =fraction of pore volume

total volume

𝜀 =167.5𝑐𝑚3

𝜋4

4 2(33.5)=

167.5𝑐𝑚3

402.9734156𝑐𝑚3= 0.3978877505

Sample Calculations

Velocity, V =𝑣𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒, 𝑞

𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐. 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑃𝑒𝑟𝑠𝑝𝑒𝑥 𝑐𝑜𝑙𝑢𝑚𝑛, 𝐴

𝐸𝑥: 𝑉 =100

𝑐𝑚3

𝑚𝑖𝑛𝑥1𝑚𝑖𝑛60𝑠𝑒𝑐

𝑥1𝑚3

1003𝑐𝑚3

𝜋4(4)2𝑐𝑚2𝑥

1𝑚2

1002𝑐𝑚2

= 0.001326291192𝑚

𝑠

Sample Calculations

𝑑ℎ

𝑑𝐿=

ℎ𝑒𝑎𝑑𝑙𝑜𝑠𝑠

ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑠𝑎𝑛 𝑖𝑛 𝑝𝑒𝑟𝑝𝑒𝑥 𝑐𝑜𝑙𝑢𝑚

𝑑ℎ

𝑑𝐿=

2399.802632𝑃𝑎

0.335𝑚= 7163.59

𝑃𝑎

𝑚

Sample Calculations

From Handbook at 26°C of water:

Density = 993.4847572𝑘𝑔

𝑚3

𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 = 8.9276943𝑥10−4𝑃𝑎. 𝑠

Sample Calculations

For filtration grain diameter, d𝑑ℎ

𝑑𝑙=5𝜇𝑉𝑎𝜌𝑔

(1 − 𝜀)2

𝜀3(6

𝑑)2

𝑑ℎ

𝑑𝑙

1

𝑉𝑎=5𝜇

𝜌𝑔

(1 − 𝜀)2

𝜀3(6

𝑑)2 =

1

𝑘= 6𝑥106

Sample Calculations

5(0.00089276943𝑃𝑎 − 𝑠)

(993.4847572𝑘𝑔𝑚3)(9.81

𝑚𝑠2)

(1 − 0.39788736)2

0.397887363= (

6

𝑑)2 = 6𝑥106

𝑑 = 3.9790021𝑥10−6𝑚 = 0.003979𝑚𝑚

%𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =0.5𝑚𝑚 − 0.003979𝑚𝑚

0.5𝑚𝑚𝑥100 = 99.999%

DataTable 1 Summary of Results

Flow Rate

(cm3/min)

Velocity, Vs

(mm/s)

TRIAL 1 TRIAL 2

Head loss, h (Pa)Manometer Difference

(mmHg)

0 0 0 0 0

100 1.3263 18 18 2399.802632

200 2.6526 26 38 4266.315789

300 3.9789 44 46 5999.506579

400 5.3052 48 76 8265.986842

500 6.6315 100 94 12932.26974

600 7.9577 108 112 14665.46053

500 6.6315 92 94 12398.98026

400 5.3052 74 76 9999.177632

300 3.9789 54 58 7466.052632

200 2.6526 36 40 5066.25

100 1.3263 18 20 2533.125

0 0 0 0 0

Head loss vs Velocity

0

2000

4000

6000

8000

10000

12000

14000

16000

0 2 4 6 8 10

h (

Pa)

Va (mm/s)

Increasing

Decreasing

Hydraulic Gradient vs Velocity

0, 0

y = 6E+06x + 269.95R² = 0.9997

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

0 0.005 0.01

dh

/dL

(Pa/

m)

Va (m/s)

Increasing

Decreasing

Linear(Decreasing)

Answers to Questions:

1. What is the importance of knowing the

permeability of a given porous medium? In

what particular areas in chemical

engineering is the concept of permeability

most relevant? Give examples.

Porosity and permeability are primary factors that

control the movement and storage of fluids in rocks and

sediments. Thus, the evaluation of the permeability of a

given porous medium is important in quantifying the

flow rate of the fluid through a packed bed or reservoir.

This concept of permeability is important in many fields

of chemical engineering such as in petrochemical and

oil mining industry. It is also applicable in water

purification, calculation of seepage rate from waste

water facilities, pharmaceutical industry at the same

time in packaging.

Answers to Questions:

2. What operating parameters must be

considered in determining the permeability

of a given porous media? Does the choice

of liquid affect the result of the

experiment? Explain your answers.

The factors that affect the permeability of a givenporous, considering that the pressure difference isconstant, are the grain size, diameter and shape andthe porosity of the granular media. The choice ofliquid affects the result of the experiment since thepermeability varies depending on property of fluidused. If the fluid used is more viscous, the fluid willhave a hard time passing through the pores thusdecreasing the permeability.

o During the flow of the fluid through the

porous medium, the flow rate is directly

proportional to its pressure drop.

o the hydraulic gradient and head loss has linear

relationship which is in accordance to Darcy’s

Law.

o The calculated porosity and filtration grain

diameter was 0.3979 and 0.003979mm

respectively.

o The experimental porosity is within the sand

range of porosity while the experimental

diameter of the sand has a 99.999% difference

• to check the apparatus before

starting the experiment in order

to avoid leaks and other

important factors that may

affect the readings.

• maintain the pressure inside the

column by releasing the air

accumulating in the column.

• gently tap the Perspex column to

ensure that less air will be

trapped in the voids of the sand.

THANK YOU