An Assessment of Flow through Porous Media to …...Dutse Journal of Pure and Applied Sciences...

Dutse Journal of Pure and Applied Sciences (DUJOPAS) Vol. 3 No. 1 June 2017

96

An Assessment of Flow through Porous Media to

Determine its Index Properties in Osun River Sand,

Osogbo, Osun State, Nigeria

A.O. Amoo Department of Environmental Sciences,

Federal University Dutse, Dutse, Nigeria

E.M. Ijanu Department of Environmental Sciences,


A.O Adeleye Department of Environmental Sciences,


C.S. Okoli Department of Civil and Environmental Engineering,

Federal University of Technology Akure, Nigeria

Abstract n experimental laboratory study of flow was conducted to determine the index properties of

the porous media. The porous media was dug from river bed of Osun River at eight different

locations and at five meters interval each during the month of November. Specific gravity,

moisture content and particle size distribution (PSD) of the porous media were determined in

accordance with the International Standard IS: 2720. Data from the above-mentioned tests were

analyzed using Statistical Package for Social Sciences (SPSS). The specific gravity of the sand at an

average of 2.66, Coefficient of curvature at an average of 0.79 and Uniformity coefficient at an

average of 2.01; which shows that all the sand samples are well graded and uniformly distributed.

The main aim of this study is to determine the index properties of Osun River sand of the porous

media in accordance with international standards of soil classification. It is recommended that

proper attention should be given to the specific gravity, moisture content and the particle size

distribution as these are the main parameters that result in flooding of embankment thereby

resulting in environmental hazard and seepage of water through dams.

Keywords: River Osun, Osun river sand, Porous media, Seepage and index properties.

A


97

1.0 Introduction

Flow through porous media is a subject of interest in many branches of science, i.e., environmental

science, water engineering, hydrogeology, chemical engineering, and in the field of petroleum

exploitation. The investigation of its features plays a major role in the comprehension of many

phenomena as the cause of seepage of pollutants, subsidence caused by water shortage, or the

process of crystallization of the ores in a well thermal exit, which makes them unusable for the

extraction of the heat. Moreover, it is important to investigate both the correlation between seismo-

genesis and the introduction of fluids in the subsoil, studied in the Rangeley Colorado experiment

(Raileigh et al., 1976), and the link between the increase in the seismic activity and the growth of the

water level in wells (Bell and Nur 1978).

The permeability is the most important physical property that determines the porosity of a medium,

which is the measure of the ability of a material to transmit fluid through it. Frequently, soil is

employed as a filter, and in preparing a good filter; knowledge of permeability of homogeneous

and heterogeneous media is very essential. A medium is homogeneous if the permeability is

constant from point to point over medium while it is heterogeneous if permeability changes from

point to point in the medium. The permeability can be determined or computed from hydraulic

conductivity (Domenico and Schwartz, 2008).

A porous medium is generally visualized as a continuum having properties of dimension and

porosity (Shih, 1990). The permeability of the porous medium is usually described in terms of

directly measurable quantities, most commonly the porosity and a large body of work has been

(and is still being) directed towards relating permeability and porosity. According to Scheidegger

(1960); Bear (1972); Le Mehaute, (1976); the permeability is however, obviously dependent upon

other properties including particle size, shape, orientation and surface roughness. Analytically, the

continuum approach requires averaging of the terms in the equations of motion and continuity, as

these quantities cannot be used directly owing to the complex boundary conditions of flow through

the pore spaces of the medium. Thus, the properties of velocity and pressure must be averaged over

a volume which is large enough for the averaging procedure to be valid and yet small enough so as

to be considered infinitesimal with respect to the total sample volume. This requires that the

magnitude of the flow be much greater than the pore volume. Therefore, flow through large pores

(or past large obstructions), such as waves passing through the armour layer of a breakwater,

cannot be validly described by this approach. Gray and O'Neill (1976) described such a technique of

"local averaging" to obtain generalized porous flow equations and Le Mehaute (1976) illustrated

how such an averaging of the terms in the Navier-Stokes equations can result in Darcy's law.

Fluid flow phenomena in porous heterogeneous materials can be found in many important

processes in nature and in society. In particular, fluid flow through a porous medium contribute to


98

several technological problems, e.g. exploiting of oil or gas from porous rocks, spreading of

contaminants in fluid-saturated soils and certain separation processes, such as filtration (Torquato,

2001).

The general laws describing creeping fluid flows are well known. However, a detailed study of

fluid flow in porous heterogeneous media is complicated. This is a direct consequence of the often

very complex, internal micro-scale structures of these materials. That is, the interplay between fluid

flow and complex internal structure at the micro-scale gives rise to the effective fluid flow

properties at the macro-scale. The details of the internal micro-scale structures of various materials

can be revealed by utilising computerised x-ray micro-tomography (Goetgeluk Hilferink et al.,

2001).

Darcy Law and Laminar Flow

Darcy's experiments yielded the results that over a limited range of flow rates (Q),

where;

= cross-sectional flow area, l = length of the sample, h1and h2 are the piezometric heads at

locations 1 and 2 at elevations ‘z’, i.e.

= the density of water, g = acceleration due to gravity and; k = constant of proportionality which

Darcy called the permeability of the material.

Expressing (2) in terms of pressure and noting that the average or "bulk" or "superficial" velocity is

Darcy's law can be written as:

Where;

= gradient operator, ἰ = slope of the energy grade line (i = dh/dx), commonly termed the

hydraulic gradient, fluid density, acceleration due to gravity and the permeability, k =

function of the fluid and the porous medium; these two aspects can be separated yielding.

where;

κ is defined as the intrinsic permeability of the material (because it depends only on properties of

the material) and has dimensions of (Length)2 and the dynamic viscosity of the fluid.

Hence, Darcy's law states that the energy loss across a porous medium due to friction is directly

proportional to the bulk velocity. However, this law applies only to a limited range of flowrates


99

where effects of inertia are negligible compared to those due to viscous forces (Wright, 1968;

Scheidegger, 1960; Philip, 1970; Dybbs and Edwards, 1982).

Moreover, it is important to investigate both the correlation between seismo-genesis and the

introduction of fluids in the subsoil, studied in the Rangeley Colorado experiment (Raileigh et al.,

1976), and the link between the increase in the seismic activity and the growth of the water level in

wells (Bell and Nur 1978). Control of the movement of water and prevention of the damaged caused

by the movement of water in soils are vital aspects of soil engineering (Leonard, 1962). The study of

seepage patterns in cross section with soils having more than one permeability’s is one of the most

worthwhile and rewarding applications, especially in selecting a protective filter or seepage control

in man-made constructions (Elsayed and Lindly, 1966). Excessive seepage is caused by high

permeability or short seepage path. Its permeability can be reduced by a proper selection of

materials, for example, mixing a small amount of clay with the sand (protective filter) used for

construction can reduce the permeability greatly (Sower and Sower, 1970). A filter or protective

filter is any porous material whose opening is small enough to prevent movement of the soil into

the drains and which is sufficiently pervious to offer little resistance to seepage (Jacob, 2001).

2.0 Description of the Study Area

Osogbo the capital city of Osun state, Nigeria became the state capital following the creation of the

new state out of Old Oyo state in 1991. It is located about 95 kilometres North East of Ibadan, which

lies on latitude 7°50' north of the equator and longitude 4°35' east of the Greenwich Meridian, and

lies within 7°00' - 8°02' Latitude and 4°02' - 5°01' Longitude (Duce and Ojo, 1982). It covers an area

of about 140 square kilometers and lies at height of 366metres above the sea level. It has a

population density of 350-500 persons/m2. Osogbo is characterized by Guinea Savannah climate

with annual rainfall range of 1100-1500mm. The population of Osogbo grew from 106,386 to 155,

507 between 1991- 2006 (NBS, 2010).


100

OSUN RIVER

ATAKUNMOSAWEST LGA

EDE NORTHLGA

OBOKUNLGA

EGB

EDO

RE

LGA

OLORUNDA L.G.A.

BORIPELGA

OSOGBO

4° 40'4° 35'7° 50'

7° 45'

................. STATE BOUNDARY

.................LOCAL GOVT. AREA BOUNDARY

.................STATE HEADQUARTER (OSOGBO)

.................River

4° 40'4° 35'

N

S

W E

Compass

Gbongan-Ibadan

Express road

Express road

Gbongan-

-Ibadan

OSUN

RIV

ER

upstream

downstream

A

B

C

D

E

FG

H

................. SAMPLE LOCATION

.................SAMPLE POINTS

.................Road

.................River Source:fieldwork, (2014)

OSU

N R

IVER

100 1000 200 300 400 500

Linear scale

Figure 1: Map of samples on Osun River in Osogbo L.G.A., Osun state.

Source: (Adopted from Google Maps, 2014)

3.0 Materials and Method

Soil samples were collected from eight (8) different locations randomly at five metres interval on the

river bed of Osun River in Osogbo. The materials for this test were sand, water, drying oven,

mechanical sieve shaker, sieve brush and a wire brush, glass jar, vacuum pump, weighing balance,


101

wash bottle, 50ml density bottle, spatula, and vacuum desiccators. The sand samples after collection

were labelled from A to H accordingly for easy identification. The water used for this study was

sourced from the dug well around the geotechnical laboratory of Federal University of Technology

Akure, as this is a good source of water around since it is clean. Immediately the samples are taken

to the laboratory and a few quantity was taken for moisture content test, in order to determine the

natural moisture content of the sand, after that the sand was then placed into the oven so as to

oven-dry the sand for proper analysis of the sand tests.

Laboratory Analysis

The laboratory tests performed were carried out in the Geotechnical laboratory of Civil and

Environmental Engineering Department, Federal University of Technology Akure. Basic

Information tests were carried out, which include Natural moisture content, particle size

distribution and specific gravity.

Natural Moisture Content is the amount of water within the pore space between the soil grains

which is removable by oven drying at a temperature not exceeding 110°C. The moisture content has

a profound effect on soil behavior.

The specific gravity of solid particles is the ratio of the mass density of solids to that of water.

Particle Size Distribution (Wet Sieving Method): This method encompasses the quantitative

determination of the particle size distribution in an essentially cohesion-less soil, down to the fine

sand size. The combined silt and clay fraction can be obtained by the difference (ASCE, 2002).

4.0 Results and Discussion

The results of the particle size analysis done on 200 grams of each of the sand samples were also

used to determine if the soil samples were uniformly graded or well graded. Figure 2 and 3 show

the particle size distribution curves for the sand samples A to H from the eight different locations in

the Osun River sand bed. The results reveal the uniformity coefficients of the samples got from the

locations are less than 4 and the coefficients of curvature ranges from (Cc < 1 3) hence they are all

of uniformly graded sand from different locations (Krishna, 2002).


102

Particle Size Distribution ChartBritish Standard Sieve Sizes

CLAY

FINE MEDIUM TO COARSE SAND WITH LITTLE SILT

DESCRIPTION

FINE MEDIUM TO COARSE SAND


FINE TO MEDIUM SAND

Legend

Fine

SAND

CoarseMedium

GRAVEL

MediumFine

Sample №& Depth

CoarseMediumFine

SILTBOULDERSCOBBLESCoarse

Clay (%)

Soil Composition

Gravel Sand (%) Silt (%)

1.04 8.90

84.11

91.21

99.41

0.52

0.40

0.16

B

C

D

90.06

0.00

0.00

0.00

15.37

8.39

0.43 0.00

A

0.0

53

0.0

75

0.1

5

0.2

5

0.3

0.4

25

0.6

1.1

8

1.7

2

2.3

6

4.7

5

6.7

9.5

13.2

20.0

26.5

37.5

53

600.0200.0

60.0

75

63

14

100.2

0.0

6

0.0

2

0.0

06

0.0

02

60

10

20

30

40

50

60

70

80

90

100

0.001 0.01 0.1 1 10 100 1000

Cu

mu

lati

ve %

Passin

g

Sieve Size (mm)

Sieve Size (mm)

Figure 2: Particle Size Distribution Curves for samples A, B, C & D


103

Particle Size Distribution ChartBritish Standard Sieve Sizes

0.00

E

H

84.27

0.00

0.00

0.00

6.33

14.28

15.06

0.44

92.95

85.44

84.70

0.72

0.28

0.24

F

G

BOULDERSCOBBLESCoarse

Clay (%)

Soil Composition

Gravel Sand (%) Silt (%)

15.29

Fine

Sample №& Depth

CoarseMediumFine

SILT

Fine CoarseMedium

GRAVEL

MediumCLAY


DESCRIPTION

FINE TO MEDIUM SAND



Legend

0.0

53

0.0

75

0.1

5

0.2

5

0.3

0.4

25

0.6

1.1

8

1.7

2

2.3

6

4.7

5

6.7

9.5

13.2

20.0

26.5

37.5

53

600.0200.0

60.0

75

63

14

100.2

0.0

6

0.0

2

0.0

06

0.0

02

6

0

10

20

30

40

50

60

70

80

90

100

0.001 0.01 0.1 1 10 100 1000

Cu

mu

lati

ve %

Passin

g

Sieve Size (mm)

Sieve Size (mm

Figure 3: Particle Size Distribution Curves for samples E, F, G & H


104

Summary of results from the basic identification tests conducted on the Osun River sand from the

eight different locations are shown in Table 1. Table 1: Classification tests on all samples

Sample Natural

Moisture

Content

Specific

Gravity

%

Passing

Sieve

200

D10

(mm)

D30

(mm)

D60

(mm)

Uniform

Coefficient

(Cu)

Coefficient

of

Curvature

(Cc)

Remarks

A 2.30 2.66 8.90 0.32 0.32 0.40 1.25 0.80 Uniformly

graded

sand

B 9.56 2.67 0.52 0.30 0.40 0.83 2.77 0.64 Uniformly

graded

sand

C 14.47 2.65 0.40 0.30 0.32 0.40 1.33 0.85 Uniformly

graded

sand

D 6.81 2.65 0.16 0.30 0.32 0.40 1.33 0.85 Uniformly

graded

sand

E 12.50 2.66 0.44 0.30 0.35 0.75 2.50 0.54 Uniformly

graded

sand

F 14.62 2.67 0.72 0.20 0.32 0.38 1.90 1.35 Uniformly

graded

sand

G 11.15 2.65 0.28 0.31 0.38 0.77 2.48 0.61 Uniformly

graded

sand

H 12.53 2.66 0.24 0.31 0.40 0.77 2.48 0.67 Uniformly

graded

sand

The index properties result for the specific gravity shows that all the samples from location A-H are

of good materials, i.e. there is passage of fluid through their pores and the standard also shows that

they are all inorganic soils. The particle size distribution also shows that, the sample location A has

much sand stone in its bed, i.e the flow of fluid is not ascertain for future purpose. The coefficient of

curvature results for all samples (A-H) are (< 1 ), and the uniformity coefficient are (< 4) less

than four which shows that all the location sample are well graded and uniformly sized particle; i.e.

there is a large space between the soil particles. Also, the flow of water can be determined to

develop models for design of hydraulic structures.


105

Table 2: Standard values of range for specific gravity of soil

Soils Range

Inorganic soil 2.60 – 2.80

Lateritic soil 2.75 – 3.00

Organic soil < 2.60

Sand particles 2.65 – 2.67

Inorganic clay 2.70 – 2.80

Source: ASTM (1999)

Table 3: Standard values of range for Uniformity coefficient and Coefficient of Curvature

Cu Cc Remark

> 4 – 6 Well graded

< 4 < 1 Uniformly graded

Cu ≈ 1 < 1 Poorly graded & Gap graded

Source: Krishna (2002); Murthy (2000)

CONCLUSION

The study was conducted to determine the flow of water through porous media and the porous

media used is River sand from Osun River, Osogbo, Osun State, Nigeria. Based on the laboratory

tests conducted on the index properties of river sand and the analysis, the natural moisture contents

range from 2.30% to 14.62% at an average of 10.49%, the specific gravity of the sand are of the range

2.65 to 2.67 at an average of 2.66, the uniformity coefficient and coefficient of curvature of the sand

samples are of the range 1.25 to 2.77 at an average of 2.01 and 0.54 to 1.35 at an average of 0.79

respectively. Since the uniformity coefficient of the samples is less than three (3) and coefficients of

curvature is less than one (1) and not greater than three (3), then the sand from the Osun River is of

uniformly sized particles. It is recommended that proper attention should be given to the specific

gravity, moisture content and the particle size distribution as these are the main parameters that

result in flooding of embankment thereby resulting in environmental hazard and seepage of water

through dams. Further research should be done on the hydraulic properties of Osun River sand in

order to know the Reynolds number, Friction factor, Hydraulic conductivity, Hydraulic gradient,

velocity of flow and flowrate of the the sand; so as to know the type of flow that is present, whether

is laminar or turbulent and if the medium of the Osun River bed sand is homogenous or

heterogeneous.


106

REFERENCE

American Society of Civil Engineer (ASCE). (2002). Task Force on Flow and Transport Over

Dunes. Journal of Hydrologic Engineering. 128(8), 726 – 728.

American Society for Testing and Materials (ASTM D 2488) (1999). Standard practice for

description and identification of soils. UIC

Bear, J. (1972). Dynamics of fluids in porous media. Elsevier Publishing Corporation, New

York.102(5), 432-541.

Bell, M.L. and Nur, A. (1978). Strength changes due to reservoir-induced pore pressure stresses and

application to Lake Oroville. Journal of Geophysics Resource (83), 4469-4483.

British S.B.S (1990). British Soil Classification System (BSCS) Methods of testing of soil for

Civil Engineering purposes. British standard Institution BS 1377–1990.

Domenico, P.A. and Schwartz, F.W. (2008). Physical and chemical hydrogeology. 16(2) 231, 342 John

Willey and Sons Inc. New York.

Duce & Ojo (1982). Senior Secondary School Atlas (Reviewed edition Macmillan pp13)

Dybbs, A. and Edwards, R.V. (1982). A New Look at Porous Media Fluid Mechanics-Darcy to

Turbulent, flow in Fundamentals of Transport Phenomenon in Porous Media. Bear J. and

Corapciogluch, M.Y. (Eds.), NATO ASI, Series E: Applied Sciences, (82) 199-256.

Elsayed, A.A. and Lindly, K.A. (1996). Measurement and estimating the permeability ofuntreated

roadway presented at 61st 23(7) 120-145. International conference meeting,

Washington. D.C.

Goetgeluk .H., Tzanakakis, M., Huang, S., Ramaswamy, S., Choi, D., and Ramarao, B.(2001).

Characterization of three-dimensional structure of paper using x-ray microtomography.

Tappi J., 84(5):72–80.

Google map (2014). www.google.com/Osogbo map, assessed on 21st June, 2014

Gray, J.K and O'Neill, A.S. (1976). Analysis of water resources and variation. Journal of Water

Resources Research, 12(2), 148-154.

Jacob, B. (2001). Modelling of groundwater flow and contaminant transport. (Israel: Technion

Israel Institute of Technology), (45) 654-789.

Krishna, R.V. (2002). Engineering properties of soil based on laboratory testing. ASTM D854 00, UIC

(47) 27-33.

Le Mehaute, B. (1976). An Introduction to Hydrodynamics and Water Waves. Springer Verlag,

New York. (76) 234-324.

Leonards, G.A. (1962). Foundation Engineering. (New York: McGraw-Hill) (23) 107-139.

Murthy, V.N.S. (2000). Principles and Practices of Soil Mechanics and Foundation Engineering.

Marcel Dekker Inc. 270, Madison avenue, New York.

National Bureau of Statistics (2010). Annual Abstract of Statistics, 2010. NBS, Federal Republic

of Nigeria.

Philip, J.R. (1970). Flow in Porous Media: Annual Review of Fluid Mechanics, van Dyke,Vincenti

and Wehausen (Eds.), Annual Reviews Inc.,California, (2), 177-205.

Raileigh, C.B., Healey, J.H. and Bredehoeft, J.D. (1976). An experiment in earthquake control at

Rangeley, Colorado. (191) 1230-1239.


107

Scheidegger, G.A. (1960). Analytical Physics of Flow in Porous Media. University of Toronto Press,

Toronto. 3(3) 46-76.

Shih, C.S. and Timco, G.W. (1990). Theoretical investigations of the motion of Ground water.

U.S, Geology, survey, 19th Annual Report, 295-384.

Sower, G.B. and Sower, G.F. (1970). Introductory to Oil mechanics and foundation. (New York:

Macmillan Publishing) 85-87.

Torquato S. & Hyun (2001). Random Heterogenous Materials: Microstructure and Macroscopic

properties, Dept. of Chemistry and Princeton materials Institute, Princeton University

Princeton, NJ 08544, USA.

Wright, D.E. (1968). Non-Linear How through Granular Media, journal of hydraulics Division,

ASCE, (4), 851-872.

An Assessment of Flow through Porous Media to …...Dutse Journal of Pure and Applied Sciences...

Documents

Transcript of An Assessment of Flow through Porous Media to …...Dutse Journal of Pure and Applied Sciences...