Hydrology Academic Paper January 2015

EXPLOITATION OF AQUIFERS

Itzel Almache Joseph Hernández Carol Pacheco Alexandra Terán

Escuela Superior Politécnica Del Litoral (ESPOL) Facultad Ciencias De La Tierra (Science Of The Earth Faculty) Ingeniería Civil (Civil Engineering) Guayaquil, Ecuador

ABSTRACT

The exploitation of natural sources

such as fresh water for human

beings consumption and for

production processes, is an

important matter. Having that

purpose in mind, this research

examines the exploitation of an

aquifer at its main calculations. And

it is done by examining the basic

parameters that have to be

determined and analyzed prior an

aquifer exploitation. Those

parameters are flow (Q), Hydraulic

conductivity (K) and Transmissivity

(T). Knowing that is essential to

have the right knowledge of this

factors. This research will provide

valuable information regarding

aquifer exploitation analysis.

Key Words: Aquifer, Exploitation,

Hydraulic conductivity, Transmissivity

INTRODUCTION

The Earth is composed by seventy

percent of salt water and just a thirty

percent of freshwater. In similar way

it is the human body; that is why

water is vital for development of life.

Real problems about current society

are human activities. Those cause

the planet experience environmental

damages as a consequence of

pollution, deforestation, co2

emissions, imbalance of ecosystems

and other factors that include the

controversial issue of global

warming. Because of population

growth, the access to water sources

become on increasing pressure.

Nowadays, it is not surprising to find

dry riverbeds on polluted streams.

One of the basics needs of mankind

is to satisfy the growing demand for

water used for human consumption

and for production processes.

Therefore the efficient usage of

hydric resources both surface

storage and groundwater, is crucial.

The feasibility of exploiting a specific

water resource is based on its

hydrological cycle expressed in

terms of inputs, outputs and

throughputs, the quality and the

quantity of the water that could be

obtained and its availability. These

conditions, have to fulfill not only

population demands protection, but

also the need to preserve the water

quality and ensure environment.

The exploitation of groundwater is a

viable choice. It has several

advantages such as the process of

filtration and consequently cleaning

of the unsaturated zone and the fair

returning of investment on the

groundwater supply engineering.

However, it has to be considered the

depth of the aquifer and the

biological and infiltration of chemical

components, such as arsenic,

fluoride nitrate and others.

In Ecuador, according to the

International Groundwater

Resources Assessment Centre

(IGRAC) the groundwater

abstraction is only the 0.09% of the

total water consumption.

Nevertheless, the extent of highly

productive intergranular aquifers and

fissure aquifers are over 20% of the

total area. These numbers confirm

that there are sufficient supply of

fresh groundwater across most of the

country, which could be exploited.

(IGRAC,2000)

This is the main objective of this

study.

LITERATURE REVIEW

Groundwater constitutes one part of

the hydrologic cycle. Saturated

formations below the surface act as

mediums for the transmission of

groundwater, and as reservoirs for

the storage of water. Water infiltrates

to these formations from the ground

surface or from bodies of surface

water and is transmitted slowly for

varying distances until it returns to

the surface by action of natural flow,

vegetation, or man (Todd 1964).

Groundwater occurs in the

subsurface in two zones: the

unsaturated zone and the saturated

zone. The unsaturated zone (vadose

zone), consists of soil pores which

are filled to a varying degree with air

and water. The zone of saturation

consists of water-filled pores that are

assumed to be at hydrostatic

pressure. For an aquifer, the zone of

saturation is overlain by an

unsaturated zone that goes from the

water table to the ground surface.

(Fetter, 2001).

The occurrence and movement of

groundwater are related to physical

forces that include gravity, pressure

from the atmosphere and overlying

water, and molecular attraction

between solids and water, acting in

the subsurface and the geologic

environment in which they occur.

(Freeze, 1979)

In the subsurface, water can occur in

the following: as water vapor which

moves from regions of higher

pressure to lower pressure, as

condensed water which is absorbed

by dry soil particles, as water which

is retained on particles under the

molecular force of adhesion, and as

water which is not subject to

attractive forces towards the surface

of solid particles and is under the

influence of gravitational forces. In

the saturated zone, groundwater

flows through interconnected voids in

response to the difference in fluid

pressure and elevation. (USACE

1999)

An aquifer is a water bearing

geological formation that can store

and yield usable amounts of water

and are identified by characteristics

such as type, areal extent, depth

form the land surface, thickness,

yield, and direction of groundwater

movement.

FORMATION OF AQUIFERS

According to the lithological

characteristics of the rocks aquifers

are classified as consolidated or

unconsolidated rock

Consolidated rock includes

sandstone; limestone, granite or

other rock, since the material is

almost impervious groundwater

cannot move easily therefore they

are low water yielding formation.

Unconsolidated rock consists of

granular material such as sand and

gravel, more permeable materials,

hence generally yields larger amount

of water

A perched aquifer is found in

formations of glacial outwash where

clay layers form impermeable layers

above a primary aquifer.

A fractured aquifer is found in

rocks, such as granite and basalt,

which contain usable amounts of

groundwater in cracks, fissures, or

joints.

An aquiclude is a formation that

contains groundwater but cannot

transmit it at significant rate to supply

a well. (Cech, 2009 )

TYPES OF AQUIFERS

Depending upon the absence or

presence of a water table affecting

the hydrostatic pressure summited in

the water contained in the interstices

or rock fractures there are the

following types of aquifers

A confined aquifer or pressure

aquifer is the one delimited form

above and below by impermeable

formations. (Bear, 2007)

Water pressure caused by gravity will

cause confined groundwater to find

exit points anywhere in the geologic

system, occasionally, the path of

least resistance is upward to the land

surface, therefore if enough pressure

exists in the aquifer, a spring may

form. (Cech, 2009 )

A subtype of the unconfined aquifer

is the artesian aquifer, where the

water occupies the total amount of

the pores or voids of the geological

formations maintaining it saturated.

The upper confining impermeable

layer gives it a higher atmospheric

pressure resulting that a well in this

type of aquifer will flow freely without

pumping. (INAMHI, 2011)

When water table function as its

upper boundary, the aquifer is an

unconfined aquifer or phreatic

aquifer. Although there is a capillary

fringe above the phreatic surface,

which is often, neglected in

groundwater studies. (Bear, 2007)

The water table rises and falls in

undulating form depending on the

permeability of the soil and the areas

of recharge and discharge

corresponding to the changes in the

volume of the storage of water within

an aquifer. (Todd D, 2005 )

Alluvial aquifers are excellent

examples of unconfined aquifers.

Recharge can occur from the

downward seepage of surface water

trough the unsaturated zone or from

lateral movement or upward seepage

of groundwater from underlying

geologic strata. (Cech, 2009 )

Aquifers that can lose or gain water

through the upper or below bounding

formations are called leaky aquifers.

These are common feature in alluvial

valleys, plans or former lake basins

(Todd D, 2005 )

All of the types of aquifers mentioned

before are shown in Figure 1. For a

better comprehension.

Figure 1. Types of aquifers

A: Unconfined aquifer B: Confined aquifer C: Confined aquifer

Portions of aquifers A,B, and C, are leaky, with the direction and rate of leakage determined by the elevations of the piezometric surface of each of these aquifers

(Bear, 2007)

PIEZOMETRIC SURFACE

The saturated thickness of an aquifer

is the total water-bearing thickness of

a geological formation, which affects

significantly it potential water yield.

The piezometric surface is the areal

variation of the hydraulic head of an

aquifer represented by the level

which water will rise if a well pierced

completely a confined aquifer (Figure

2). The shape of this imaginary plane

defines the directions of the

groundwater movements. In

unconfined aquifers the hydraulic

heads coincide with the actual

groundwater surface and therefore it

is called groundwater table (Sen,

1995)

Homogeneous aquifer

HeteErogeneous aquifer

Figure 2. Hydraulic gradient: Piezometric Level (Sen, 1995 )

GROUNDWATER MOVEMENT

The direction and rate of movement

are determined by the lithology

stratigraphy and structure of

geological deposits, within there are

the following hydraulic properties to

determine them

Porosity (p) is defined as the

volume of the pores of a rock or soil

sample (Vv) divided by the total

volume of both pores and solid

material (Vt). (Delleur, 2006)

Obtaining the following equation:

p=Vv/Vt

For permeable soil, the effective

porosity is the rate between the

volume of the drainable by gravity of

the soil and the total volume of it.

Where the total amount of water in a

permeable soil is the volume of it

multiply by its porosity. (INAMHI,

2011)

Permeability is the ability of porous

materials to allow fluids to move

through it and it depends on various

aspects such as grain size, shape

and arrangement of the formations.

For example, groundwater may only

move a few centimeters per year in

clay, but several meters per day in

gravel.

Hydraulic conductivity also known

as permeability coefficient is the

measurement of the rate of flow of a

fluid through porous material. Is

expressed as a rate of discharge en

meters per day.

Hydraulic head (h) is the driving

force that moves groundwater. It

combines fluid pressure and

gradient, and is represented by the

height that groundwater will rise

inside a well (Cech, 2009 )

Is expressed as:

h= Z+P/ ρg

Where Z is the elevation head or the

distance of the reference point above

a datum plan (mean sea level) and P

is the fluid pressure at the point

exerted by the column of water

above the point. (Delleur, 2006)

Flow and Transmissivity.-

Transmissivity is a measure of the

volume of water they can travel

horizontally through the net width of

an aquifer saturated thickness under

a hydraulic gradient equal to 1.

(USACE 1999)

Transmissivity (T) is the rate that

water is transmitted trough a unit

width of an aquifer uneder a unit

hydraulic gradient. It represents the

ability of an aquifer to transmit

groundwater. It is expressed in

square meters per day:

T=Kb

Where K is the hydraulic conductivity

(m/day), and b is saturated thickness

of an aquifer (m). (Cech, 2009 )

Specific yield (Sy) represents the

amount of water that can be available

for supply or consumption, is the

volume of water that will drain from

soil or rock under the influence of an

unconfined aquifer, expressed by the

following ratio.

𝑺𝒚 =𝑽𝒈

𝑽𝒕

Where, Vg is the volume if water

drained by gravity, and Vt the total

volume. (Kasenow, 2001).

The values for unconfined aquifers

usually are between 0.05 and 0.3.

(Kresic, 2007)

Darcy's Law.- Rate is laminar flow of

a constant temperature and fluid

density between two points in a

porous medium, which is

proportional the hydraulic gradient

(dh / dl) between the two points. The

equation that defines the flow rate is

known through a porous medium as

Darcy's law. (USACE 1999)

Q=-KA (dh/dl)

Where:

Q: Volumetric Flow rate K: Hydraulic conductivity A: Cross-sectional area of flow

The hydraulic conductivity is

defined as an average conductivity,

which is a function of the properties

of the contour and the fluid

properties. (Thomas Harter, 2008)

Homogeneity and Isotropy, a

homogeneous unity is one that has

similar global properties. Therefore

the porosity, hydraulic conductivity

and other parameters are similar in

formation geological and defined

isotropic when empty geometry is

similar in any direction.(USACE

1999)

AQUIFER STORAGE

Storage coefficient or storativity

(s) is the volume of water released

from storage with respect to water

level and surface area of the aquifer,

as shown in Figure 3.

Also is expressed for most

unconsolidated and many loosely

consolidated aquifers as the sum of

the specific yield and the specific

storage multiplied by the thickness of

the aquifer. (Kasenow, 2001)

The value of the storage coefficient is

dependent upon whether the aquifer

is unconfined or confined.

𝜕(∅𝜌)

𝜕𝑡= 𝜌

𝜕∅

𝜕𝑡+ ∅

𝜕𝜌

𝜕𝑡= 𝜌

𝑑∅

𝑑𝑝

𝜕𝑝

𝜕𝑡+ ∅

𝑑𝜌

𝑑𝑝

𝜕𝑝

𝜕𝑡

𝛽 =1

𝜌

𝑑𝜌

𝑑𝑝 →

𝑑𝜌

𝑑𝑝= 𝛽𝜌 𝑎𝑛𝑑

𝑑∅

𝑑𝑝= 𝛼

𝜕(∅𝜌)

𝜕𝑡 = 𝜌(∝ +𝛽∅)

𝜕𝜌

𝜕𝑡

= 𝜌(∝ +𝛽∅) (𝜌𝑔𝜕ℎ

𝜕𝑡)

𝜕(∅𝜌)

𝜕𝑡= 𝜌2𝑔(∝ +𝛽∅)

𝜕ℎ

𝜕𝑡

Figure 3. Water released from storage

(Heath, Ralph C.,1983)

Storage of unconfined aquifers

The principal source of water is from

gravity drainage as the aquifer

materials are dewatered during

pumping.

The storage coefficient tends to be

equal to the percentage of pore

space in the aquifer

The storage coefficient for an

unconfined aquifer ranges from 0.01

to 0.30.

Unconfined aquifers can get more

water for a smaller change in head

than to confined aquifers (Fletcher

G.,1995)

Storage of confined aquifers

Water released from storage in a

confined aquifer is from compression

of the aquifer and expansion of the

water when pumped.

During pumping, the pressure is

reduced in a confined aquifer, but the

aquifer is not dewatered.

The storage coefficient in confined

aquifers ranges from 1 x 10-5 to 1 x

10-3 (Fletcher G.,1995)

METHODOLOGY

One of the most important analyses

is water balance, which includes

recovering the total inputs and

outputs during a period of time.

The inputs depend on: lateral

subsurface inflow (QLS), rainfall

recharge (QRR), recharge from

nearby rivers (QRN), recharge due to

irrigation (QIR), and sewage return

(QSR).

The outputs are quantified on natural

discharges such as springs (QSQ),

lateral subsurface outflow (QLA) and

evaporation from groundwater table

(QEGT) But also on the usage

groundwater has or will be given

through wells; such as domestic and

industrial (QDI) water uses, and

irrigation water uses (QIW). (Sen,

1995)

For example, it has been determined

that the inputs and outputs of an

unconfined aquifer during one month

were (Table 1):

Inputs Quantity

(x10^6 m3)

Outputs Quantity

(x10^6 m3

)

QLS 0,06 QSQ 0,003 QRR 0,7 QLA 0,15 QRN 0,1 QEGT 0,012 QIR 0,2 QDI 0,13 QSR 0,07 QIW 1,1 SUM

Inputs (IT)

1,13 SUM Outputs

(OT)

1,395

Table 1. Inputs and Outputs

(Harter, 2008)

Since the total of outputs is grader

than the inputs, the aquifer is not

sustainable during the month of

analysis, because if this additional

support must be brought from other

sources for instance, nearby

aquifers, surface reservoirs, etc. The

deficit is about 0,265 x10^6 m3

CONFINED AQUIFERS

The condition of ''Dupuit-

Forchheimer'' provides that for some

systems the flow, can be considered

as horizontal, and distributed

uniformly with depth. The flow in

these systems is vertical and

horizontal, but may be simplified

when the water mostly moves in one

direction.

The flow of a well in a confined

aquifer, may be analyzed with

Dupuit-Forchheimer hypothesis,

assuming an infinite aquifer and

horizontal flow. The water is pumped

through a cylinder of radius (r) at a

rate Q. The cylinder area is 2πrD

then the flow rate Q can be

expressed by Darcy as: (Bouwer,

1978)

𝑸 = 𝑲. 𝟐𝝅𝒓𝑫. (𝒅𝒉/𝒅𝒓)

Where:

Q: Flow of the well K: Hydraulic conductivity r: Radial distance from the center of the well D: Height of the aquifer dh/dr: Hydraulic gradient Separating and integrating between h2 and h1

𝑸(𝒅𝒓/𝒓) = 𝟐𝝅𝑲𝑫. 𝒅𝒉 obtaining:

𝑸 = (𝟐𝝅𝑲𝑫(𝒉𝟐 − 𝒉𝟏))/(𝒍𝒏(𝒓𝟐/𝒓𝟏))

UNCONFINED AQUIFERS

For unconfined aquifers, D is

replaced with the height h, of the

water table in edge conditions.

then:

𝑸 = 𝑲. 𝟐𝝅𝒓𝒉. (𝒅𝒉/𝒅𝒓)

Separating and integrating is

obtained:

𝑸 = (𝝅𝑲(𝒉𝟐𝟐 − 𝒉𝟏𝟐))/(𝒍𝒏(𝒓𝟐/𝒓𝟏))

Also:

𝑲 = 𝑸. (𝒍𝒏(𝒓𝟐/𝒓𝟏))/(𝝅(𝒉𝟐𝟐 − 𝒉𝟏𝟐))

This equation allows calculating the

value of hydraulic conductivity as a

function of height (h), distances (r)

and the rate of extraction (Q).

UNSTEADY RADIAL FLOW IN A

CONFINED AQUIFER.

The drawdown for an infinitesimal

diameter well in a confined aquifer

obtained by Theis is represented with

the following equation:

𝑺 =𝑸

𝟒𝝅𝑻∫ (

𝒆−𝒖

𝒖

−∞

𝒖

) 𝒅𝒖

Where:

S: Drawdown Q: constant well discharge

𝒖 =𝒓𝟐𝑺

𝟒𝑻𝒕

Obtaninig:

𝒔 =𝑸

𝟒𝝅𝑻[−𝟎. 𝟓𝟕𝟕𝟐𝟏𝟔 − 𝐥𝐧 𝒖 + 𝒖 −

𝒖𝟐

𝟐.𝟐!+

𝒖𝟑

𝟑.𝟑!− ⋯ . .]

𝒔 =𝑸𝑾(𝒖)

𝟒𝝅𝑻

EXAMPLE 1

A well with a radius of 0.5 meters

completely penetrates an unconfined

aquifer gravel with a hydraulic

conductivity K = 30 m/day and a

height H = 50 meters. The well is

pumped until the water level inside

the object is 40 meters from the

background. Assume that the pump

does not affect the pressure head

greater and equal to 500 meters

radius, and the loss in the well are

negligible.

Determine which the pumping flow

rate is.

𝑸 =𝝅𝒌(𝒉𝟐𝟐 − 𝒉𝟏𝟐)

𝐥𝐧 (𝒓𝟐𝒓𝟏)

𝑸 = (𝝅.

𝟑𝟎𝒎𝒅

((𝟓𝟎𝒎)𝟐 − (𝟒𝟎𝒎)𝟐)

𝐥𝐧 (𝟓𝟎𝟎𝒎𝟎, 𝟓𝒎 )

𝑸 = 𝟏𝟐𝟐𝟖𝟎𝒎𝟑

𝒅= 𝟏𝟒𝟐

𝒍

𝒔

EXAMPLE 2

A 1m diameter well penetrates

vertically through a confined aquifer

30 m thick. When the well is pumped

at 113 m3/h, the drawdown in a well

15 m away is 1.8 m. In another well

50 m away is 0.5 m. What is the

approximate head in the pumped

well for steady-state conditions and

what is the approximate drawdown in

the well? Also compute the

transmissivity of the aquifer and the

radius of influence of the pumping

well. Take the initial piezometric level

as 40 m above the datum.

First determine the hydraulic

conductivity using equation.

Q=113𝑚3

ℎ𝑟= 2712

𝑚3

𝑑𝑎𝑦

𝑲 =𝑸

𝟐𝝅𝒃(𝒔𝟏 − 𝒔𝟐)𝐥𝐧 (

𝒓𝟐

𝒓𝟏)

𝐾 =2712

𝑚3

𝑑𝑎𝑦

2𝜋(30𝑚)(1.8𝑚 − 0.5𝑚)ln (

50

15)

𝑲 = 𝟏𝟑. 𝟑𝒎

𝒅𝒂𝒚

The transmissivity (T) is

T=Kb

T=13.3m/day * 30

𝑻 = 𝟏𝟏𝟑𝒎𝟐

𝒅𝒂𝒚

To compute approximate head

(𝒉𝒘) in the pumped well

ℎ2 = ℎ0 − 𝑠2 = 40 − 0.5 = 39.5𝑚

ℎ𝑤 = ℎ2 −𝑄

2𝜋𝐾𝑏ln (

𝑟2

𝑟𝑊)

ℎ𝑤 = 39.5𝑚 −

2712𝑚3

𝑑𝑎𝑦

2𝜋 (13.3𝑚

𝑑𝑎𝑦) (30𝑚)

ln (50𝑚

0.5𝑚)

𝒉𝒘 = 𝟑𝟒. 𝟓 𝒎

Drawdown is then:

𝑠𝑤 = ℎ0 − ℎ𝑤 = 40 − 34.5

𝒔𝒘 = 𝟓. 𝟓 𝒎

The radius of influence (R) of

pumping well can be found by

rearranging (solving for)

r which is R

𝑹 = (𝒓𝒊). 𝒆𝒙𝒑 [𝟐𝝅𝑲𝒃(𝒉𝒐 − 𝒉𝟏)

𝑸]

𝑅 = (15𝑚) exp (2𝜋 (

13.3𝑚𝑑𝑎𝑦

) (30𝑚)(40𝑚 − 38.2𝑚)

2712𝑚3

𝑑𝑎𝑦

)

𝑹 = 𝟕𝟗𝒎

EXAMPLE 3

A well fully penetrates a 25 m thick

confined aquifer. After a long period

of pumping at a constant rate of 0.05

𝑚3/𝑠 the drawdowns at distances of

50 and 150 m the well were observed

to be 3 and 1.2 m, respectively.

Determine the hydraulic conductivity

and transmissivity. What hope of

unconsolidated deposit would you

expect this to be?

𝑄 = 0,05𝑚

𝑠 = 4320

𝑚3

𝑑𝑎𝑦

𝑟1 = 50 𝑚 , 𝑟2 = 150 𝑚

𝑠1=ℎ0 − ℎ1 and 𝑠2=ℎ0 − ℎ2, so 𝑠1 −

𝑠2=ℎ2 − ℎ1=3-1.2=1.8 m

𝑲 =𝑸

𝟐𝝅𝒃(𝒉𝟐 − 𝒉𝒕)𝐥𝐧 (

𝒓𝟐

𝒓𝟏)

𝐾 =

4320𝑚3

𝑑𝑎𝑦

2𝜋 (25𝑚

𝑑𝑎𝑦) (1.8𝑚)

ln (150𝑚

50𝑚)

𝑲 = 𝟏𝟔. 𝟖𝒎

𝒅𝒂𝒚 , showing it is a

medium clean sand (Figure 4).

The transmissivity (T) is

T=Kb

T=16.8m/day * 25 m

𝑻 = 𝟒𝟐𝟎𝒎𝟐

𝒅𝒂𝒚

Figure 4. Hydraulic Conductivity

(Heath, 1983)

CONCLUSION

Aquifers have been and are one of

the most important hydric resources

to supply the society.

Men exploit aquifers because it is a

good source to take advantage of it.

Even though technological

advances, aquifers have been

drought and polluted.

There are many alternatives to avoid

any kind of aquifer damages, the only

thing is to implement them.

Permeability is analyzed for many

different reasons such as: letting us

know about the water flow inside the

aquifer, and to get information about

the exploitation flow.

Transmissibility depends on the

permeability coefficient and the

aquifer thickness, which let us know

about the water flow.

The calculated flow rate indicates

you how much water was taken out

from the aquifer, and when

comparing this flow with other flows,

will help to analyze this amounts

avoiding aquifer droughts.

Aquifers take thousands years to

mold, it depends on physical and

hydrological conditions.

The exploitation of aquifers has

turned one of the most important

topics in the world with a lot research

work.

REFERENCES

Bear, J. (2007). Hydraulics of

Groundwater. New York , NY, USA:

Courier Corporation .

Cech, T. V. (2009 ). Principles of

Water Resources: History,

Development, Management, and

Policy. Hoboken , New Jersey, US:

John Wiley & Sons.

Delleur, J. W. (2006). The Handbook

of Groundwater Engineering,

Second Edition (Second edition ed.).

Boca Raton, Florida, US: CRC

Press.

USACE, Genetti, Albert J., U.S. Army

Corps of Engineers (1999)

Engineering and Design:

Groundwater Hydrology. EM 1110-2-

1421

INAMHI. (2011). Introducción a la

hidrogeología del Ecuador. Quito-

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