Groundwater Flow Continued Lecture notes

7/30/2019 Groundwater Flow Continued Lecture notes

1/16

Groundwater Flow and Contamination 1

Introduction to Groundwater Flow

Hydraulic rock properties

hydraulic conductivity

effective porosity specific storage

Hydraulic parameter measurement

water pressure measurement

hydraulic conductivity measurement

typical hydraulic conductivity values

Groundwater resources

confined and unconfined aquifers

aquitards and aquicludes

complex aquifer systems

storativity and specific yield

modelling aquifer flow


Hydraulic and Piezometric Head

In hydraulics, the hydraulic (or energy) head in an incompressible

fluid is given by:

where u is the fluid velocity.

In porous media velocities are always very slow so the term u2/2gis

omitted and the piezometric head is given by:

Hydraulic (or piezometric ) heads are generally expressed in relation to

the mean sea level as with topography.

Pressure headH, is defined by

hu

g

p

gz= + +

2

2

hp

gz= +

H h zp

g= =


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Measurement of Water Pressure

Saturated Medium

(1) Piezometer

Hole drilled in ground fitted with perforated tube. The water levelgives the elevation of the water table (the point where the pressure is

equal to atmospheric)

Beneath the free surface pressure generally increases with depth

(2) Pressure Gauge - Required for low permeability formations

Electric pressure transducers

Hand operated pressure gauge: A tube with a porous point is

hammered into the ground. Air is injected by a foot pump. A rubber

membrane is held in place at the base of the air tube by the water

pressure. When the air pressure exceeds the water pressure, air comesout of the tube outlet (which can be placed in water to make it

visible!)


Darcys Law for Saturated Flow - Reminder

water

sandstone

cross-sectionalarea of pipe,

h

A

Q

constant water level

L

h

LhKQ

dxdhKq

=

==

Kq

:dimensionsin threeor

Aor


3/16


Hydraulic conductivity - depends not only on the rock type, but also on

fluid viscosity and density.

A requirement to separate the hydraulic conductivity into that p art derived

from the rock and that from the fluid, has lead to the introduction of intrinsic

permeability, k, which is entirely dependent on the rock properties

where is the fluid viscosity, is the fluid density andgis the acceleration

due to gravity.

Intrinsic permeability is essentially a function of the diameter of the pore

throats that provide interconnected flow pathways through the rock; the largerthe square of the mean pore diameter, the higher the intrinsic permeability.

gkK

=

Intrinsic Permeability


Anisotropic Permeability in a

Sedimentary Formation


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Laboratory Measurement of Permeability

Medium to high permeability

constant head permeameter (Darcys Experiment)

falling-head permeameter

Low permeability medium

Apply large pressure differences with the help of pumps and measure

pressures up and down flow for different values ofQ.

Q

h


Typical Hydraulic Conductivity Values for Different

Rock Types (m/s)

UNCONSOLIDATED SEDIMENTS

coarse gravels 10-1-10-2

sands and gravels 10-2-10-5

fine sands silts loess 10-5-10-9

clay, shale, glacial till 10-9-10-13

HARD ROCKS

dolomitic limestones 10-3-10-5

weathered chalk 10-3-10-5

unweathered chalk 10-6-10-9

limestone 10-5-10-9

sandstone 10-4-10-10

granite, gneiss, compact basalt 10-9-10-13


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Specific Storage

Specific storage, SS, represents the volume of water that a fully

saturated porous rock will absorb or expel per unit volume per unit

change in head.

It is usually expressed in units m-1.

Specific storage depends on:

the elasticity of the water

the elasticity of the rock matrix structure

the elasticity of the rock


Groundwater Flow Equation

z

x

y

qx(x) qx(x+x)

qy(y)

qy(y+y)

q z(z)

qz(z+z)


6/16


Groundwater Resources

Groundwater resources are described in terms of:

aquifers

unconfined (or phreatic)

confined

aquitards

aquicludes

Groundwater resources tend to have a much greater lateral extent than

vertical extent

aquifer modelling is generally two dimensional with groundwater

flow assumed to be horizontal


Aquifers

Aquifer A layer, formation or group of formations of permeable rocks,

saturated with water and with a degree of permeability that allows

economically profitable amounts of water to be withdrawn.

Typical Unconfined or Phreatic

Valley Aquiferground surface

lakes

water table

vertical exaggeration approximately 100


7/16


Confined Aquifers

flowing artesian well

confined aquifer

aquiclude

aquiclude

water table

upland recharge area

The water table or phreatic surface, is the level to which the water

rises in a well

in an unconfined aquifer, this is the depth at which you reach water

in a confined aquifer the aquifer is under pressure, so this may even

be above the ground surface ...


Low Permeability Media

aquitard

a less permeable saturated geological formation

aquiclude

an almost zero permeability saturated geological formation

aquifuge

a saturated geological formation that neither contains nor transmits

significant quantities of water


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Aquitards & Aquicludes

An Unconfined Aquifer

System

saturated

unsaturated

unsaturated

saturated

AQUICLUDE

perchedwater table

mainwater table

AQUIFER

AQUIFER


Aquifers

AquiferA layer, formation or group of formations of permeable

rocks, saturated with water and with a degree of permeability that

allows economically profitable amounts of water to be withdrawn.

Unconfi ned (or Phreatic) Aquif ers: Aquifer where the piezometric

surface coincides with the free surface of the aquifer which is overlainby unsaturated zone

Valley aquifers in humid zones: Recharge occurs across the whole

surface, outlets are the low points in the topography such as sp rings and

rivers. The aquifers behave like underground watersheds.

Valley aquifers in arid zones: Recharge happens in short heavy

bursts. Water infiltrates through the river/waddy beds. The water table

is higher beneath the river than elsewhere contrary to what happens in

humid zones.


9/16


Alluvial aquifers: Unconfined aquifers situated in alluvial deposits

along the course of a stream. The water is in equilibrium with the

stream which continually drains and recharges it. At the entrance of an

alluvial plain, the water level in the stream is higher than that in the

aquifer, as the plain narrows at the downstream end this causes the

water table in the aquifer to rise often causing marshy areas.

Perched aquifers: These lie on an impermeable layer and are not

connected to a stream which feeds or drains them They often result in

spring lines and provide what is termed a perched water table

Confi ned Aqui fers:An aquifer is said to be confined if it is overlain

by a formation with low permeability and if the hydraulic head of the

water it contains is higher than the elevation of the upper limit of the

aquifer.


Combined Aquifer System


10/16


Modelling Aquifer Flow

Groundwater flow in large aquifers is generally assumed to be two-

dimensional and horizontal

In phreatic aquifers, the movement of the water table must be

accounted for

dewatering and resaturation of porous media

hence redevelopment of the storage term in the groundwater flow

equation

the concepts of storativity and specific yield are introduced


Storativity

The storativityorstorage coeff icient, S, represents the volume of

water that a porous rock will absorb or expel per unit surface area per

unit change in head.

It is a dimensionless quantity and is expressed as either a percentage

or fraction.

There are two basic components of storativity: specif ic storage, which refers to the compressibility of the water and

rock

specif ic yieldwhich describes the quantity of water drained from the

aquifer as the water table drops.

The specific storage of a porous medium is small in comparison to the

specific yield and only becomes significant in the case of confined

aquifers, where the rock matrix remains fully saturated.


11/16


Specific Storage - Confined Aquifers

Q

clay layer

clay layer

sandstone aquifer

b

Where the aquifer is fully saturated,storativity is the amount of water

released due to specific storage, SSb

where b is the depth of the aquifer.

Specific storage (m-1) depends on:

the elasticity of the water

the elasticity of the rock matrixstructure

The elasticity of the rock


At the free water surface, the water table can move in response to

pressure changes and either falls, releasing water from pore space,

or rises, saturating new pores within the rock.

this is termed specific yield, Sy and represents the volume of water

that can be drained under gravity per unit surface area, per unit drop

in head.

In a phreatic aquifer, storativity, S, describes the release of water due

to both compressibility and desaturation of the rock matrix:

where h is the head in the phreatic aquifer

S S hS y S= +

Specific Yield


12/16


Groundwater Flow Equation

h

x

y

qx(x) qx(x+x)

qy(y)

qy(y+y)


Recharge and Discharge Areas

In unconfined aquifers, some characteristics are common to most

recharge areas and some to most discharge areas.

Recharge areas:

topographical high places

deep unsaturated zone between the water table and the land surface

Flow lines tend to diverge from recharge areasDischarge areas:

topographical lows

water table is found either close to, or at, the ground surface

flow lines tend to converge, unless the discharge area is large, such as

the sea

physical manifestations of the groundwater take the form of a spring,

seep, lake, stream or presence of vegetation common in wet areas


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Springs


Groundwater Interaction with Lakes and Wetlands


14/16


Naturally Varying Flow Regimes


Groundwater Flow Patterns in Homogeneous Aquifers


15/16


A One-Lake System with a Homogeneous Anisotropic

Aquifer


A One-Lake System with a High Conductivity Layer


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Summary

Three important hydrogeological rock properties:

Hydraulic conductivity (or permeability), porosity and storativity

Groundwater flow governed by:

Darcys Law

Conservation of water mass groundwater flow equation

Groundwater resources

aquifers are economically viable groundwater resources that are either under

pressure, confined, or with a free surface, unconfined.

aquitards, aquicludes and aquifuges are all low permeability formations

aquifer systems are complex and may comprise several layers of aquifers

separated by low permeability formations

groundwater flow in large aquifers is generally assumed to be horizontal

storativity and specific yield are used to model two dimensionaltransient flow

groundwater can both drain and feed surface water features

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Groundwater Flow Continued Lecture notes

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