03-presentation_basic groundwater hydraulics

7/28/2019 03-Presentation_Basic Groundwater Hydraulics

1/46

1

11


2/46

2

3-2

this topic we will study the concepts of groundwater flow in aermeable or semi-permeable medium.

What is an aquiferWhat are aquicludes and aquitards?Definition of hydraulic head.Hydraulic parameters that control saturated groundwater flowSteady state flow and non-steady state (transient) flow.

The assumptions that are made in (use of) the governingequations.Flownets, equipotentials and groundwater flowlines.


3/46

3

3-3

Basic hydraulic parameters and termsBasic hydraulic parameters and terms

Aquifers, aquicludes and aquitards. Hydraulic head Hydraulic gradient Hydraulic conductivity Permeability

Transmissivity Porosity Confined and unconfined aquifers Specific yield Sy for Unconfined Aquifers Specific storage Ss and Storativity for Confined Aquifers

Water table Phreatic surface Confined aquifer - Potentiometric surface Steady and Non-steady State Flow


4/46

4

3-4

What is an Aquifer?What is an Aquifer?

An aquifer is a geological unit that carries water and can be

exploited economically for water supply or can be drained usingpumping wells. Typically aquifers are areally extensive butpermeable fractured rock systems that we see in somemining environments are normally limited in area and depth.

There is no clear definition of an aquifer in terms of its hydraulicconductivity it is somewhat arbitrary. However it is clear thatin most cases in mining we are not dealing with aquifers.

A more formal definition is provided in Freeze and Cherry.

There an aquifer is defined as a saturated permeable geologicunit that can transmit significant quantities of water underordinary hydraulic gradients.


5/46

5

3-5

What is an Aquifer? (2)What is an Aquifer? (2)

In most (but certainly not all) mining cases we are notdealing with true aquifers but with low permeability media,typically fractured rock which does not act as a true porousmedium for which most groundwater flow theory is developed.

Some exceptions that can be encountered in a mining contextare alluvium overlying the mine, limestones, highly fractured andextensive hard rock systems, coal beds, gravels (in gravel pits),

etc.


6/46

6

3-6

AquicludesAquicludes andand AquitardsAquitards

An aquiclude is a saturated geological unit that is incapableof transmitting significant quantities of water under ordinaryhydraulic gradients.

An aquitard is defined as a low permeability unit within ageologic sequence that may be significant in a regionalsense but does not transmit water on a local scale.

VERY VAGUE DEFINITIONS!!


7/46

7

3-7

Components of Hydraulic HeadComponents of Hydraulic Head

Hydraulic HeadHydraulic Head

FigurefromFreeze&Cherry.Groundwater


8/46

8

3-8

Illustration of Hydraulic HeadIllustration of Hydraulic Head

Ground surface

Water Table elevation = 1800 msnm hydraulic head = 1800m

elevation head = 1800m

pressure head = 0

hydraulic head = 1800m

Elevation = 1200 msnm elevation head = 1200m

pressure head = 600m

Datum = sea level = 0 msnm

1 kPa = 0.102 m of water

1m of water = 9.804 kPa

1psi = 2.3 ft of water = 0.704m of water

Conversion factors


9/46

9

3-9

Hydraulic GradientHydraulic Gradient

The head difference between two points over a horizontal

distance. Groundwater flows as a result of this hydraulicgradient.

Hydraulic gradient = (h1-h2)

L

h1 h2

L

Confined aquifer

Note: Definition the same for unconfined aquifer


10/46

10

3-10

Permeability & Hydraulic ConductivityPermeability & Hydraulic Conductivity

(Related to water) a permeable medium is one through which water will

flow under the influence of a hydraulic gradient. There are two definedparameters - Hydraulic Conductivity and Intrinsic Permeability.

Intrinsic permeability can be referred to as permeability but HydraulicConductivity should not be referred to a permeability although it often is.

Intrinsic permeability k is a property of the medium, independent of thefluid.

Hydraulic conductivity relates k to density and dynamic viscosity ofthe fluid and gravitational constant g.

K (hydraulic conductivity) = kg/

Hydraulic conductivity is an integral parameter in Darcys Law andother groundwater flow equations.


11/46

11

3-11

Derivation of Hydraulic ConductivityDerivation of Hydraulic Conductivity

DARCY'S LAW for steady-state flow

For flow Q in a cross-section of Area = A

With hydraulic gradient i= Dh/Dx

Q = KiA

Where K = Hydraulic Conductivity

Units SI units

Q m3/d

i

A m2

so k m/d

L2

L3/L

2T = L/T

x

Dimensions

L3/T

dimensionless

This relationship is analagous to those governing heattransfer and flow of electricity. Also note that Hydraulic

Conductivity K has units of L/T but it IS NOT a velocity.

Groundwater flow velocity depends upon the porosity ofthe medium in which it flows.

(v = Ki/where is porosity)

Qin

Qout

h

Cross-sectional Area = A


12/46

12

3-12

Hydraulic Conductivity Values for Different Materials


13/46

13

3-13

Controls on Fracturing and Permeability ofControls on Fracturing and Permeability of

Rock MassRock Mass

Structure Depth Lithology Alteration Mineralization Secondary effects from Blasting and Unloading


14/46

14

3-14

TransmissivityTransmissivity

AND:Alternate form of Darcy's Law Q = KiA is Q = Tiw

where i = (h1-h2)/L

Aquifer with Hydraulic Conductivity K, Width w,

and thickness b

TRANSMISSIVITY T = Kb (the product of hydraulicconductivity x aquifer thickness per unit width of

aquifer.)

b

w

h1 h2

h

L

Groundwater flow

through element


15/46

15

3-15

PorosityPorosity

Porosity is the percentage of void space within a soil or rock,typically denoted as or n.

However not all voids are connected and so we talk ofInterconnected Porosity. Of this the majority of the void spacecan be drained under gravity, and this term is called SpecificYield Sy. The part that cannot be drained is called SpecificRetention Sr


16/46

16

3-16

Unconfined & Confined AquifersUnconfined & Confined Aquifers

Flowingwell

Piezometric surface

FigurefromJohnsonScreensGroundwater&Wells


17/46

17

3-17

Specific Yield (from unconfined aquifer)Specific Yield (from unconfined aquifer)

Specific Yield Sy of an unconfined aquifer is the volume ofwater released from storage per unit area per unit decline inhead. It is dimensionless.


18/46

18

3-18

StorativityStorativity of Confined Aquiferof Confined Aquifer

The storativity S of a confined aquifer is the volume of waterreleased from storage per unit area per unit decline inpressure head. It is dimensionless.


19/46

19

3-19

Specific Storage (Elastic Storage)Specific Storage (Elastic Storage)

The volume of water released from storage in a unit volume ofconfined aquifer for a unit decline in head. Specific Storage,Ss is related to porosity and compressibility of the systemmatrix and of water by the equation

Ss= g(+)

where is the density of water, gis acceleration due to gravity, is the porosity of the rock, is the compressibility of the

matrix framework and is the compressibility of water.

Dimensions of Specific Storage are 1/L, typical range is from1 x 10-4 to 5 x 10-7 m-1


20/46

20

3-20

Storage andStorage and StorativityStorativity

FigurefromFreeze&CherryGroundwater


21/46

21

3-21

PhreaticPhreatic Surface andSurface and PotentiometricPotentiometric SurfaceSurface

Direction of groundwater flow

(piezometric)



22/46

22

3-22

Groundwater Flow VelocityGroundwater Flow Velocity

Dimensions of Hydraulic conductivity are L/T (e.g m/d).

However it is NOT a velocity.

Darcys Law is stated as Q = KiA

Dimensions for Hydraulic Conductivity should correctly beshown as L3/T/L2 (e.g) m3/d/m2 .

In reality A is a unit area (e.g. m2) through which water flows

only within the pore space . It can be deduced thereforethat flow velocity should be estimated by

v = Ki////


23/46

23

3-23

Groundwater Flow VelocityGroundwater Flow Velocity


Think of Darcys Law, Q moving uniformly, obviously actual velocity is faster toproportion of porosity AND, higher K pathways flow faster.


24/46

24

3-24

Hydraulic Conductivity and Groundwater FlowHydraulic Conductivity and Groundwater Flow

We see how Hydraulic Conductivity is a controlling factor in groundwaterflow, along with hydraulic gradient and flow area. Clearly the flow in asystem is limited by the lowest overall K, i and A.

Plan view

EdgeSection

K1 K2 K3

Possible pressure surface


25/46

25

3-25

Steady and Non SteadySteady and Non Steady--State Groundwater FlowState Groundwater Flow

Steady-state flow occurs when the magnitude and directionof the flow velocity is constant with time at any point in theflow field.

Non-Steady State (transient) flow occurs when the magnitudeand direction of the flow velocity changes with time at any pointin the flow field.


26/46

26

3-26

Steady and Non SteadySteady and Non Steady--State Groundwater FlowState Groundwater Flow

Qzout

Qyout

Qxin Qxout

y

Qyin

Qzin

z

x

For Steady State Flow:

/x(Kx

h/x) + /y(Ky

h/y) + /z(Kz

h/z) = 0

For Transient (non-steady state) Flow

((((/x(Kxh/x) + /y(Kyh/y) + /z(Kzh/z) = Ssh/t + Q


27/46

27

3-27

r2

h2 h1

Then, Q 2T(h2-h1)

ln(r2/r1)

r1

If there are two observation wells at radii R1 and R2, and where

piezometric heads are h1 and h2 respectively

THEIM Equation for Steady State Flow to a well

Usual constraints re aquifer continuity, etc.

Then by applying Darcy's Law, Q = kiA which is the same as Q

= k x dh/dr x 2rm

=2Ts

ln(r2/r1)


28/46

28

3-28

Note that as the volume of water thatis drawn towards a pumping wellremainsconstant it is logical that the cross-section area through which it passesis reduced.

It therefore follows from Darcys Lawthat the hydraulic gradient must

increase as the water nears the well.(see following slide).

Figurefro

mJohnsonScreensGroundwater&Wells


29/46

29

3-29

Methods for Solving NonMethods for Solving Non--Steady FlowSteady Flow

Equation to find Hydraulic Conductivity andEquation to find Hydraulic Conductivity and

Confined Storage (Confined Storage (StorativityStorativity))

There are a number of solutions to solving the non-steadystate equation to determine the aquifer hydraulic parametershydraulic conductivity and storativity.

Note that there are many assumptions made in using all ofthese types of solutions, such as: (For most methods) that the aquifer is fully confined,

The aquifer has uniform thickness and is of infinite arealextent, The aquifer is homogeneous (conductivity and storativity

does not vary with depth or direction).


30/46

30

3-30

TheisTheis Equation for Solving NonEquation for Solving Non--Steady FlowSteady Flow

EquationEquation

Q r2S

4T 4Tts = W(u) where u =

W(u) is an exponential integralW(u) = -.5772 ln u + u + u2/2.2! + u3/3.3! + u4/4.4!

and T = Kd Transmissivity(hydraulic conductivity x aquifer thickness).Q = flowrate,s = drawdown.t = elapsed time


31/46

31

3-31

TheisTheis Equation for NonEquation for Non--Steady Groundwater FlowSteady Groundwater Flow


32/46

32

3-32

FunctioningFunctioning TheisTheis SpreadsheetSpreadsheet

Spreadsheet with THEIS solution to find s (drawdown) for combinations of Q, kD, t, r and S

Q

(m3/d)

kD

(m2/d)

Time

t

(day)

Radius

r (m)S u W(u) s (m)

200 1000 100 500 0.0001 6.25E-05 9.1025 0.1449

ONLY CHANGE VALUES IN YELLOW CELLS MAX u!

9


33/46

33

3-33

CooperCooper--Jacob Approximation ofJacob Approximation of TheisTheis EquationEquation

for Solving Nonfor Solving Non--Steady Flow EquationSteady Flow Equation

We have seen that the Theis solution is

or s = Q/4T(-.5772 ln u + u + u2/2.2! + u3/3.3! + u4/4.4! )

for large values of t or small values of r the value of u becomes negligible

so that the series can be rewritten as s = Q/4T x (-.5772 ln r2S/4Tt)

In decimal logarithms this becomes s = (2.3Q/4T)log(2.25Tt/r2S),Then T = 2.3Q/4s

Plot graph of drawdown against log time (see next slide), determine sand estimate T

For data from an observation well it is possible to derive storativity S

S = 2.25 Tt0/r2

Qr2S

4T 4Tts = W(u) where u =


34/46

34

3-34

Jacob PlotJacob Plot Drawdown per Log CycleDrawdown per Log Cycle

Decenso in Pozo de Bombeo Z1

15

16

17

18

19

20

100 1000 10000

Tiempo (minutos)

Decenso(m)

s = drawdown per log cycle = 2.3m

Time (minutes)


35/46

35

3-35

The Effect of Varying Hydraulic Parameters onThe Effect of Varying Hydraulic Parameters on

Depressurization EffectsDepressurization Effects



36/46

36

3-36

EquipotentialEquipotential SurfacesSurfaces

Surface joining points of equal hydraulic head


37/46

37

3-37

EquipotentialsEquipotentials and Flow in Uniformand Flow in Uniform

MediumMedium


equipotential


38/46

38

3-38

Groundwater Flow Patterns Close toGroundwater Flow Patterns Close to

BoundariesBoundaries



39/46

39

3-39

Steady State andSteady State andTransient FlowTransient Flow



40/46

40

3-40

SimpleSimple FlownetFlownet ExampleExample



41/46

41

3-41

Variations in Hydraulic ConductivityVariations in Hydraulic Conductivity



42/46

42

3-42

Effects of Anisotropy on Hydraulic HeadEffects of Anisotropy on Hydraulic Head

DistributionDistribution



43/46

43

3-43

Flow System from Recharge Area toFlow System from Recharge Area to

Discharge AreaDischarge Area



44/46

44

3-44

Unconfined AquiferUnconfined Aquifer Flow to a WellFlow to a Well



45/46

45

3-45

Flow to Well in aFlow to Well in aConfined AquiferConfined Aquifer



46/46

3-46

Flow Towards an Open PitFlow Towards an Open Pit


03-presentation_basic groundwater hydraulics

Documents