PERMEABILITY/FLUIDIZATION STUDIES

Date: 13th March 2025.

Name: Hillary Acheampong Cecil Wiredu Collins Aduko
Department of Chemical Engineering, Kwame Nkrumah University of Sci. and Tech.

REPORT INFO ABSTRACT

Keywords: The focus of this experiment is to conduct a constant head

Fluidization permeability test on a given soil sample and calculate the

Permeability permeability coefficient using darcy’s law for saturated
Coefficient
homogeneous soils. The hydraulic height difference of the
Darcy’s law
Constant head water in the permeameter was measured at different
permeability test volumetric flowrates after the valves were properly
Porosity
configured. The coefficient of permeability, k, was

calculated from the slope of the plot of pressure against

flow as 4.6811 cm/s. From the coefficient, the degree and

type of soil sample was deduced from the standard table as

medium to high sand gravel or clean or fine sand.

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 1. INTRODUCTION

The flow of fluids through porous media is a topic of immense practical interest in a great

diversity of technical field such as groundwater recovery and management, contaminant

transport analysis, subsurface disposal of nuclear wastes, enhanced geothermal energy

system, oil and gas production, thermal/chemical/biological enhanced oil recovery, hydraulic

fracturing, CO2 sequestration and so on (Govindarajan, 2019). In 1856, Darcy put forward a

law to describe the flow of fluid through a porous media in a one-dimensional phase under

steady state conditions. It states that, ‘the flow of fluid (flux density) through a porous media

is directly proportional to the area A and hydraulic slope (( H2 -H1 )/L) of the media (Zand et

al., 2007). This enables scientists and researchers calculate the permeability coefficient

(hydraulic conductivity) of a media sample, say soil, which in turn provides an accurate

estimate of the degree of permeability.

Objective

To determine the permeability coefficient using a given soil sample

Theory

Darcy’s law is the fundamental equation that is used to describe the flow of fluids within a

classical porous medium with a definite hydraulic conductivity and with a porosity varying

between 0 and 100 % (Govindarajan, 2019). It is expressed by the mathematical equation

below;

∆h
Q=kA ( )
L

Where k is the permeability coefficient of the sample,

A is the cross-sectional area of medium

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h = H2 -H1, Hydraulic heads

L is the height of the medium filled with the sample

For this experiment, the permeability coefficient of a given soil sample will be determined in

the laboratory (ex-situ) using the constant head test and applying the darcy equation for

homogenous saturated soils. The coefficient of permeability is an important design parameter

used in designing earth fill or rock fill dams, and determining the stability of underground

excavation and sand filters in wastewater treatment plants (Munenori Hatanaka, n.d.).

Darcy’s equation is only valid for homogeneous saturated mediums only. For unsaturated or

layered mediums, the Buckingham equation is applied. It is given by;

∆P ∆P
q=−k ( ϑ ) ∨q=−k (h)
∆H ∆H

Where k (h) or k (v) is the unsaturated hydraulic conductivity function (permeability

coefficient)

P is the total energy and

H is the height

To develop a relationship between permeability and texture of a sample (porosity), the

Carman-Kozeny equation is employed. The equation defines important characteristics of the

sample such as porosity and void ratio. Porosity refers to the ratio of the volume of sample

particles to that of the entire vessel with the sample while void ratio refers to the ratio of the

volume of the spaces occupied by air and water to that occupied by the sample particles

(Valdes-parada et al., 2009).

The EDIBON permeability/fluidization equipment will be used to conduct the experiment on

a homogeneous soil sample. There are two types of ex-situ permeability test that can be done

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with the EDIBON equipment known as falling head and constant head test.

Figure 1: The EDIBON equipment used

The falling and constant head test are carried out on fine and coarse-grained soils

respectively. The constant head test used in this experiment is ideal for soils for soils with

high degree of permeability. In this test, water is allowed to flow continuously through the

soil sample under constant hydraulic head (difference in water levels). The volume of water

passing through the soil in a given time is measured and the permeability coefficient is

calculated using darcy’s law (Nagy & Varga, 1977). Below is a standard table of soil types

and their coefficient of permeability with their degree of permeability;

SOIL PERMEABILITY DEGREE OF PERMEABIITY

COEFFICIENT, K

Gravel >0.1 Very high

Sandy gravel, clean sand, 0.1>k>10-3 High to medium

fine sand

Sand, dirty sand, muddy 10-3>k>10-5 Low

sand

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 Silt, muddy clay 10-5>k>10-7 Very low

Clay <10-7 Virtually impermeable

The degree of permeability of soils is dependent on several factors including soil type,

particle size, grain size distribution and soil history (location, organic matter content etc.)

2.0 METHODOLOGY
The mass of the dry soil sample was measured with a balance and filled into the permeameter

to a desired height where the flow of water through the transparent cylindrical vessel of the

permeameter could be observed. The apparatus was not bumped into since coarse-grained

soils are densified easily with vibrations. The cross-sectional area of the cylinder and the

height of the soil sample in the permeameter was noted.

The permeameter was screwed tightly down and clamped as the upper tank or reservoir was

filled with water to the overflow by opening the main pipe valve. Valve V2 was opened

slowly until water was seen at the bottom inlet and it was closed. The water level L1 was

recorded while the purge valve located at the top of the cylinder was opened. Valve V2 was

then opened until water flowed out of the purge valve as the new water level L2 was

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recorded. The corresponding manometer readings of water level L1 and L2 were recorded as

280m and 208m respectively at a volumetric flowrate of 0.25L/min.

The open and close valve units were configured as V1 and V3 were closed with V2 and V4

opened. The difference in manometer reading at the two water levels was recorded at

different time intervals as the experiment was repeated for flowrates of 0.5, 0.75, 1.0, 1.25,

1.50, 1.75 and 2.0.

3.0 TABLE OF RESULTS

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 Q(L/min) Q(cm3/s) H1(dm) H2(dm) H2 – H1(dm)

0.25 4.16667 28.00 20.80 -7.2

0.50 8.33333 29.20 20.80 -8.4

0.75 12.5 29.00 20.80 -8.2

1.00 16.66667 28.40 21.20 -7.2

1.25 20.83333 28.00 21.20 -6.8

1.50 25 27.60 20.80 -6.8

1.75 29.16667 27.00 20.60 -6.4

2.00 33.33333 27.00 20.80 -6.2

A GRAPH OF PRESSURE HEAD AGAINST

FLOW RATE
0
0 5 10 15 20 25 30 35
-1

-2
PRESSURE HEAD(dm)

-3

-4

-5

-6
f(x) = 0.0617142857142857 x − 8.30714285714286
-7
R² = 0.634050880626223
-8

-9

FLOW RATE(cm3/s)

Figure 2: A graph of pressure head against flowrate

CALCULATIONS
Diameter of the cylinder containing the soil = 4.6cm

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Height of sand in cylinder= 48cm
2
πd
Area of the permeameter =
4
2
π × 4.6
= = 16.619 cm2
4

Conversion from l/min to cm3/s for the flow rate, Q

−3
0.25 ×10
0.25 l/min = = 4.1667 cm3/s
60
−3
1× 10
1 l/min = = 8.3333 cm3/s
60
−3
1.25× 10
1.25 l/min = = 12.5 cm3/s
60

L
∆ H= Q
KA

From the graph,

L
=slope=0.0617 dm . s /cm3
KA

¿ 0.0617 ×10=0.617 s /cm2

Where;

L=48 cm
2
A=16.619 cm

48
K= =4.6811cm/ s
16.619 ×0.617

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The K- value signifies the rate at which water passes through the sand. The permeability

coefficient value implies that the sand used is a gravel.

5.0 DISCUSSION
The calculated permeability coefficient was 4.6811cm/s using Darcy’s equation. According

to the experimental data in the lab manual, since this k value is between 0.1 and 10-3, the

sample can be classified as having a medium to high degree of permeability. This also

suggests that the soil sample may be mainly composed of sand gravel or clean or fine sand. The

permeability coefficient tells how easily water or fluid flows through a medium or material.

The higher the coefficient, the easier it is for the fluid to flow through the material. This is

because of the high amount of voids present in the material. The voids in the material are the

pathways that water follows, so a greater amount of voids means the material is highly

porous. A highly porous material will also lead to a high permeability coefficient, as it

indicates how easily water can flow through the material.

The line of best fit y = 0.0617x - 8.3071 from the graph above, shows a negative slope, which

means that as the flow rate increases, pressure head decreases. This happens because lower

pressure decreases resistance, allowing water to move more freely. According to Darcy's

Law, flow rate is proportional to the hydraulic gradient, so as pressure decreases, the fluid

can flow faster, especially in soils with higher permeability. This happens because the water

encounters resistance from the particles in the material; as more water flows, it creates a

greater hydraulic gradient, which can lower the pressure head. Essentially, the faster the

water flows, the less pressure is exerted at a given point, as the energy is being used to

maintain that flow.

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6.0 CONCLUSION
From the experimental results, materials with higher permeability coefficients show greater

ease of fluid flow through their porous structure. The permeability coefficient directly reflects

a material's ability to transmit fluids. A higher value indicates greater permeability compared

to materials with lower coefficients. The sample is likely composed primarily of sand gravel or

clean or fine sand indicating high permeability.

7.0 REFERENCES

Govindarajan, S. K. (2019). An Overview on Extension and Limitations of Macroscopic

Darcy’s Law for a Single and Multi -Phase Fluid Flow through a Porous Medium. 5(4), 1–

21.

Munenori Hatanaka, A. U. (n.d.). Permeability Characteristics of high quality undisturbed

gravelly soils measured in laboratory tests. 41, 45–55.

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Nagy, L., & Varga, G. (1977). Comparison of permeability testing methods. 399–402.

Valdes-parada, F. J., Ochoa-tapia, J. A., & Alvarez-ramirez, J. (2009). Validity of the

permeability Carman – Kozeny equation : A volume averaging approach. 388, 789–798.

Zand, A., Sanders, M. S., & Navaz, H. K. (2007). A Simple Laboratory Experiment for the

Measurement of Single Phase Permeability. January.

8.0 APPENDIX
2. The permeability of a soil sample refers to how easily fluids can flow through it.
There are different methods for measuring a sample's permeability using a device
called a permeameter, which can utilize both liquid and gas flow systems.
Understanding permeability is crucial in several applications, including:

I. Assessing the stability of slopes and retaining structures.

II. Treating water and wastewater.

III. Conducting oil exploration and studying petroleum geology.

3. Porosity of soil indicates its capacity to retain fluid. It is defined mathematically as

the volume of open spaces in the soil divided by the total volume of the soil, which

includes both solid material and voids. On the other hand, permeability measures how

easily a fluid can flow through a porous material. A soil can have high porosity, but if

the pores are not interconnected, it will not exhibit permeability.

4. a. Particle Size: Generally, larger soil particles tend to have higher permeability

because they create larger pore spaces between them, allowing fluids to flow more

easily.

b. Void Ratio: The void ratio is the ratio of the volume of voids to the volume of

solids. A higher void ratio typically indicates more interconnected voids, which can

enhance fluid movement and increase permeability.

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 c. Mass of Soil Sample: While the overall mass of the soil sample does not directly

affect permeability, the distribution of this mass—through factors like particle size

distribution and compaction—can influence the void ratio and structural arrangement,

thereby impacting permeability.

d. Structural Arrangement of Soil Particles: The way soil particles are arranged

influences the size and connectivity of pore spaces. A well-graded soil, which has a

variety of particle sizes that are evenly packed, may exhibit lower permeability

compared to poorly graded soil with uniform particle sizes and high porosity.

e. Pore Fluid Properties: The characteristics of the pore fluid, such as temperature and

viscosity, can affect permeability. Fluids that flow more easily, like water, generally

increase permeability, while more viscous fluids, like oil, reduce it. Increasing

temperature can enhance permeability by lowering fluid viscosity.

f. Degree of Saturation: Fully saturated soil typically has more air gaps due to trapped

air released by percolating fluids, making it more permeable than partially saturated

soil. Air pockets can hinder fluid flow, reducing permeability.

g. Soil Stratification: Soil stratification occurs when there are abrupt changes in

porosity at different depths within the active root zones, which can increase the overall

permeability on the soil.

5. The falling head method: This test is utilized to determine the permeability of fine-

grained soils with intermediate to low permeability, such as silts and clays, which

typically range from 1x10^-5 to 1x10^-9. In the falling head permeability test, water

flows through a relatively short soil sample that is connected to a standpipe, which

provides the water head and allows for measuring the volume of water passing

through the sample. The diameter of the standpipe is determined by the permeability

of the soil being tested. This test can be conducted in a Falling Head permeability cell.

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 Before measurements begin, the soil sample is saturated, and the standpipes are filled

with de-aired water to a specified level. The test commences by allowing water to

flow through the sample until the water in the standpipe reaches a designated lower

level. The time taken for the water to drop from the upper to the lower level is

recorded. Often, the standpipe is refilled, and the test is repeated several times.

PRELAB

HILLARY ACHEAMPONG 7226921: 2/5

CECIL WIREDU 7242421: 4/5

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COLLINS ADUKO 3174420: 2/5

12. DECLARATION

I declare that:

 This report is my unaided work and is a true reflection of the lab I participated in.

 Large portions of it have not been submitted by another student for assessment.

 A significant portion of it was not copied from an internet source or a book (Daboo).

 A significant portion of it was not written using ChatGPT or any other AI tool.

 If any of the above statements turn out to be false, I forfeit the marks awarded to this

report.

CECIL WIREDU 13/03/25 …………………

NAME DATE SIGNATURE

COLLINS ADUKO 13/03/25 …………………

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NAME DATE SIGNATURE

HILLARY ACHEAMPONG 13/03/25 …………………

NAME DATE SIGNATURE

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