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Experiment C2

PERMEABILITY

I. Introduction/Summary

Permeability or hydraulic conductivity refers to the ease with which water can flow in

soil. This property is necessary for the calculation of seepage through earth dams or under

sheet pile walls, the calculation of the seepage rate from waste storage facilities (landfills,

ponds, etc.) and the calculation of the rate of settlement of clay soil deposits [1].

Darcy's Law is a generalized relationship for flow in porous media. It shows the

volumetric flow rate is a function of the flow area, elevation, fluid pressure and proportionality

constant. It may be stated in several different forms depending on the flow conditions. Since its

discovery, it has been found valid for any Newtonian fluid. Likewise, while it was established

under saturated flow conditions, it may be adjusted to account for unsaturated and multiphase

flow [2].

The saturated hydraulic conductivity of a soil can be predicted using empirical

relationships, capillary models, statistical models, and hydraulic radius theories. A well-known

relationship between permeability and the properties of pores was proposed by Kozeny and

later modified by Carman. The resulting equation is largely known as the Kozeny-Carman

equation, although the two authors never published together. In the geotechnical literature,

there is a large consensus that the Kozeny-Carman equation applies to sands but not to clays [3].

II. Objectives

The experiment aimed to determine the permeability and the filtration grain diameter of a

porous granular media (sand).

III. References

[1] Retrieved fromhttp://www2.ggl.ulaval.ca/personnel/paglover/CD%20Contents

/GGL66565%20Petrophysics%20English/Chapter%203.PDF on February 16, 2013

[2] Retrieved from www. legacy.library.ucsf.edu on February 16, 2013

[3] Retrieved from http://infohost.nmt.edu/~petro/faculty/Engler524/PET524-perm-2-ppt.pdf

on February 16, 2013

Figure 1 Armfield Permeability and Fluidization apparatus

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[4] Retrieved from www. onlinelibrary.wiley.com on February20, 2013

[5] Retrieved from www. http://www.discoverarmfield.co.uk/data/w3/?js=enabled on February

20, 2013

[6] Retrieved from [5] Retrieved from http://www.discoverarmfield.co.uk/data/w3/?js=enabled

on February 21, 2013

IV. Equipment/Materials

The apparatus used in the experimentation is shown in Figure 1. The pre-sieve sand, with

diameter greater than 0.5mm and weighs 501.9g, was used and dehumidified. Additional

equipment includes analytical balance, 50-mL beaker and thermometer (0.1 0C calibration).

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V. Theory

VI. Operating Conditions and Procedure

The pre-sieve sand was placed in the machine dryer to remove the moisture content.

Then it was weighed in an analytical balance to obtain 501.9 grams. Valves 1, 2, 3 and 4 of the

permeability apparatus were securely closed while valves 5, 6, 7 and 8 were opened. After the

sand was put in the Perspex column and filled with water. The valves were adjusted to let the

water flow through the sand eliminating the air trapped in the voids of the sand. The water was

permitted in the column by opening valves 1 and 4 and its manometer levels were noted for

each setting of the flow rate. The valves 5 and 6 were closed once the manometer approached

its limits. Then another set of readings of the decreasing flow rate was done.

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VII. Data and Results

Q (cm3/min

)

Va (mm/s)

dh (mm)

dh/dL (mm/mm)

0 0 22 0.04

25 0.367394

42 0.076363636

50 0.734787

87 0.158181818

75 1.102181

129 0.234545455

100 1.469575

197 0.358181818

125 1.836968

252 0.458181818

150 2.204362

312 0.567272727

175 2.571756

353 0.641818182

Q (cm3/min)

Va (mm/s)

dh (mm)

dh/dL (mm/mm)

0 0 8 0.01454545525 0.367394 69 0.12545454550 0.734787 131 0.23818181875 1.102181 181 0.329090909

100 1.469575 244 0.443636364125 1.836968 302 0.549090909150 2.204362 375 0.681818182175 2.571756 423 0.769090909150 2.204362 377 0.685454545125 1.836968 311 0.565454545100 1.469575 246 0.44727272775 1.102181 181 0.32909090950 0.734787 136 0.24727272725 0.367394 82 0.1490909090 0 3 0.005454545

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200 2.939149

422 0.767272727

175 2.571756

383 0.696363636

150 2.204362

353 0.641818182

125 1.836968

299 0.543636364

100 1.469575

254 0.461818182

75 1.102181

193 0.350909091

50 0.734787

143 0.26

25 0.367394

92 0.167272727

0 0 28 0.050909091

Table 1: Data obtained in Trial 1 Table 2: Data obtained in Trial 2

VIII. Treatment of Results

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

f(x) = 0.29606679250571 x + 0.0166746411483255R² = 0.997620900336109

Va

dh/dL

Figure 2: Head Loss versus Fluid Velocity Graph of Trial 1

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0 0.5 1 1.5 2 2.5 30

50100150200250300350400450

f(x) = 162.83673587814 x + 9.17105263157887R² = 0.997620900336109

Va

dh

Figure 3: Head Loss versus Fluid Velocity Graph of Trial 2

0 0.5 1 1.5 2 2.5 3 3.50

0.10.20.30.40.50.60.70.80.9

f(x) = 0.251185981965776 x + 0.0334329597343294R² = 0.96529971415591

Va

dh/dL

Figure 4: Hydraulic Gradient versus Fluid Velocity Graph of Trial 1

0 0.5 1 1.5 2 2.5 3 3.50

0.10.20.30.40.50.60.70.80.9

f(x) = 0.251185981965776 x + 0.0334329597343295R² = 0.96529971415591

Va

dh

Figure 5: Hydraulic Gradient versus Fluid Velocity Graph of Trial 2

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IX. Analysis/Interpretation of Results

Plotting the obtained data from trials 1 and 2, the relationship of the head loss and fluid

flow rate or velocity can be correlated wherein the head loss also increases as the fluid velocity

increases thus demonstrating a direct proportionality as shown in figures 2 and 3. The

parameter, R2, is 0.997 for both trials by using the linear regression of the graphs. Averaging

the inverse of the slopes will result to 3.378mm/s per mm H2O as their permeability constant.

The diameter was also computed obtaining the value of 0.46mm which was close enough in the

given diameter in the literature.

X. 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.

Evaluation of the permeability of a given medium is important in quantifying flow rate of

the fluid which is essential in most of the chemical processing industries. Porous media

have many applications in chemical engineering area such as calculation of seepage

through earth dams or under sheet pile walls, the calculation of the seepage rate from

waste storage facilities (like landfills and ponds) and the calculation of the rate of

settlement of clay soil deposits, etc.

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?

The factors that affect the degree of permeability, considering the pressure differential

is constant, are grain size and shape, moisture content used in tempering the grain,

temperature and lastly, fluid density and viscosity. Also the choice of the liquid affects the

result of the experimentation because of its physical properties, the more viscous and

denser the fluid is, the more it will inhibit the fluid flow thus it decreases.

XI. Findings, Conclusion, and Recommendation

The experimentation proved that the hydraulic gradient and head loss with volumetric

flow per area has linear relationship which is in accordance to Darcy’s Law. The calculated

permeability and diameter of the sand are 3.378mm/s and 0.46mm, respectively and still

acceptable though there were discrepancies comparing the calculated results from the given

values in the literature.

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Furthermore, it is recommendable to tap continuously the Perspex column in the

experimentation proper in order to minimize the source error because this ensures that less air

will be trapped in the voids of the sand. Squeeze in the bubbles or the air gaps in the pipes

wherein this reduces the discrepancies of the results from the theoretical values as well as for

an easier determination of the data. The use of other type of porous media is also

recommendable in this experiment, except of using clay, which is a limitation to the use of

Kozeny-Carman equation because it only applies to materials with uniform pore size

distribution.