hydro lecture 2

7/21/2019 Hydro Lecture 2

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93-482Hydrogeological Engineering

Properties of AquifersSummer 2012


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What do Hydrogeologists do? Prepares plans for development of a groundwater supply

Locates and develops a source of groundwater Determines if there is enough water of acceptable quality available

Groundwater Control To lower water levels, prepares dewater plan (where, how much etc) Evaluates impact of a mine dewatering plan on overlying surface-

water bodies

Aquifer protection and water conservation Significant groundwater recharge area delineation to prohibit

activities that pose threat to groundwater quality Determines capture zones for a well field to protect it from

contamination Delineates plume of contaminated groundwater


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Hydrogeologists . Need training in geology, hydrology, chemistry,

mathematics, physics, fluid mechanics and flow throughporous media

For a typical project.. Gather all available information about the areas hydrogeology,

such as well logs, published geological and water supply reports Map or obtain geological maps and examine air photos Develops an idea of where to locate a test well, which will be used

to conduct aquifer tests to determine the hydraulic properties Determine if there is enough water of acceptable quality available Identify if one well or well field is needed to develop the

groundwater either for supply or dewatering.


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Learning OutcomesIf completed correctly, you will be able to Identify various properties that affect the groundwater flow apply Darcys law estimate hydraulic conductivity

draw water table and potentiometric surfaces, anddetermine flow gradients Associate/identify various aquifer properties (such as

specific storage, specific yield, storativity, transmissivity)corresponding to confined or unconfined aquifers


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Basic Properties of Media and Fluid Media Porosity (n), permeability (k) and

compressibility ( )

Fluid Density ( ), dynamic viscosity ( ) andCompressibility (

w)

Others are derived. Hydraulic Conductivity (K), Specific Storage (S s);

Transmissivity (T) and Storativity (S) in confinedaquifers; Hydraulic Conductivity (K) and specific yield(S y) in unconfined aquifers etc.


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Physical Properties and Principles Porosity void volume/total volume Effective porosity amount of interconnected

pore space available for fluid flow Permeability Ease with which fluid can move

through a porous rock

Todd and Mays (2005)

Types of PoreSpaces


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Specific Yield Storativity in case of unconfined

aquifer is Specific Yield

Specific Yield (S y) : Ratio of thevolume of water that drains by

gravity to the total volume of rock

Specific Retention (S r ): Ratio ofthe volume of water the rockretains against force of gravity tothe total volume of rock

Total porosity = S y+ S r + ratio of volume of water contained inthe unconnected pore space to the total volume


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Fluid Potential Groundwater moves in the direction of decreasing potential

Candidate potentials Gravitational (or potential energy) Pressure Kinetic Energy Others (Thermal, Electrical, Osmotic -chemical)

Hydraulic Head (h) is a potential the driving force forgroundwater flow

Potential is the energy (or work) expended against aforce field to move a unit mass of material from areference point, or condition, to the point of interest


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Total Potential

Gravitational potentialWork Energy = (work/mass)

potential for unit mass

Pressure Potential ( p)

Kinetic Potential

2

21T L

gz dz mg m

z

z g

o

cetandis F dz mg Work z

z o

.

o p

p

p

p

p

p p

p pdpV dp

mV

Vdpm

ooo

1

221 22 vmvmm

W k k


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Total Potential

2

2v p p gz ok p g

Bernoullis Equation Flow along a stream lineSimplify for groundwater, v is very small so the kinetic potentialterm will be negligible

Total head or Hydraulic Head = Datum head + pressure head

h = z +

Z = elevation of point of measurement or elevation or datum head = pressure head or height of column of water abovemeasurement point

o p p gz


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Concept of Head and Pressure


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Fluid Motion and Darcys Law Henri Darcy (1856) beginningof science of groundwater

Described an experimentiIlustrating the controls on watermovement through a column of

sand

L

hh KA

l

h KAQ

LQand hhQ

B A L

B A )/1(

dl dh

KAQ

A

B

h AhB

HydraulicGradient


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Darcys Law Ki

l

h K

A

Qq

By convention Darcys Law is stated asq = specific discharge (Darcys flux); units : (L 3/T)/L2 = L/T

Do Not Confuse with Velocity

q is the volume of water flowing through a unit time

is the volume of averaged flux. Hence, historically referred

to as Darcy Flux

It makes an attempt to describe microscopic behaviour withmacroscopic parameters

L

hh KA

l

h KAQ B A L


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Validity of Darcys Law

Limits: Macroscopic representation of flow Upper and lower limits of flow rates

Macroscopic Behaviour It is assumed that a porous mediumcan be sampled to obtain measurementson a Representative Elementary Volume (REV) Three conditions apply

A representative CONTINUUM can be selected to characterizethe ensemble of individual grains

The Continuum is MACROSCOPIC

There is a lower limit to the size of the element for which Darcyslaw is valid. The lower limit of the volume is the REV.


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Validity of Darcys Law

Upper and lower limits of Flowq

h/ l

q

h/ l

LaminarLinear

TurbulentNon-linear

Low permeability materialsmay have a thresholdhydraulic gradient belowwhich flow does not occur.


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Validity of Darcys Law Darcys law is valid only for laminar flow in porous media

Reynolds number is defined asR e = (VD)/ where = fluid density,

v = average linear velocity (q/n)D= effective grain size (d 10 ) = fluid viscosity

R e < 1 (sometimes the range of 1 to 10 is given)

Ratio of inertial forces to viscous forces

Where do you think Darcys law is not valid?


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Hydraulic ConductivityT L

L L

T L

l h

q K /

/

/

a measure of the ease with which a specific fluid (H 2O) willpass through a particular porous medium

Depends on both (i) fluid and (ii) medium An empirical factor which is the average of the microscopic

effects to describe macroscopic behaviour Assumes that there is a representative continuum for the

porous mediumNote: Darcys law is EMPIRICAL. This assumption may not

always hold. But most real world situations it holds good.


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Physical interpretation of K Darcys proportionality coefficient or hydraulic

conductivity isK w K 1/ K d 2

g k gd N K ww

2

2* d K K w

h grad d K

q w

2*

h grad gR N

q w

2

k = intrinsic permeability(Darcy)


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Hydraulic Conductivity vs. Permeability

K = upper case Hydraulic conductivity (groundwaterterminology)

k = lower case Permeability (from petroleumterminology) or intrinsic permeability

T L L LT L

l hq

K ///

T L LT M

T L L M L g k K //

/*/ 23

2


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Estimation/Determination of K Grain size techniques

Simple, good for sands and silts and not for clays Based on standard grain size analysis

Permeameter tests Laboratory

Constant head and Falling head methods

In-situ Single well tests (field) Slug/Bail tests

constant head Packer/pressure-pulse tests

Pumping tests (field)


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Estimation/Determination of KPermeameter tests Laboratory

Constant head and Falling head methodsConstant Head

Falling Head

Lhh KAt

Qt B A )(

AthVL

hh At QtL

K B A )(

hh

t d Ld K oc

t ln22

ho

h

d t=diameter of tube = 2r td c=diameter of soil chamber = 2r c


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SLUG TEST


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Heterogeneity and Anisotropy of K In field situations, K varies through space and

with the direction of measurement in porousmedium

Homogeneity vs Heterogeneity Isotropic vs Anisotropic

Layering, Discontinuities (i.e.,faults, folds, etc.) Spatial trends Depositional trends joint and fracture spacing (ie., distance from igneous

intrusion

Causes of Heterogeneity


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Causes of Anisotropy Layering, Discontinuities (i.e.,faults, folds, etc.) Local grain orientation Fracture orientation (rocks +clays) (local and

regional)


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Heterogeneity and Anisotropy of K

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Equivalent Hydraulic Conductivity Assume Layered system K1

K3

K2

K4

d1

d2

d3

d4

i

ii x d

K d K

i

i

i z

K d d

K


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Flow gradients and directions


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Water Table and Potentiometric Maps These are 2D representation of 3D surfaces Unconfined aquifers Water table surface Confined aquifers Potentiometric surface

Need water level readings made in a number of wells,each of which is open only in the aquifer of interest


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Piezometers Water levels in piezometers give

mean pressure head atsampling (usually slotted zone ofpipe/porous interval)

When tied to a datum (e.g.,

mean sea level) gives total headh

Need more than onepiezometers to determine

gradients (i.e., h/L)


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Types of Piezometer

Simplest Open type/slotted screen(Big Straw!!!)

Can physically measure water levels

Can obtain water samples for chemistry) Simple to install, cheap, reliable and durable Other types

Closed hydraulic, pneumatic, vibrating wire,strain gauge (pressure transducer), etc.


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Specific Storage (S s) - Also called elastic storage coefficient

proportionality constant relating the volumetric changes in fluid volume per unit volume to the time rate of change in hydraulic head

S s = wg ( + n ) Expansion of water

compression of porous medium

and are compressibility of pore structure and water

Unconfined Aquifer: The amount of water obtained per unit volumedrained is substantial and is equal to the volume of pore space actuallydrained.

Confined Aquifer: a drop in head is not accompanied by drainage fromstorage as the aquifer remains fully saturated at all times

Amount of water obtained in response to unit head drop is small fractionof that obtained in case of unconfined aquifer

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Aquifer Characteristics


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Concept of storativity in unconfined and confinedaquifers (Heath, 1982)

Aquifer Characteristics


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Storage Properties How confined aquifers take

additional water in response toincrease in head? Water and porous structure

are elastically compressible.Changes in head leads tochanges in both water andpore volume

The interstitial pore space ofthe sandstone was reduced

to the extent of theunaccountable volumetricwithdrawals from storage.


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Storativity or Storage Coefficient

For confined aquifers only Volume of water that an aquifer releases

from or takes into storage per unit surface

area of aquifer per unit change in thecomponent of head normal to that surface0.00005 < S < 0.005


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Transmissivity Rate at which water is transmitted through a unit width of

aquifer under a unit hydraulic gradient T = K b where b= saturated thickness of the aquifer

The concept is applicable only in case of Confinedaquifer

where as in unconfined aquifers, b changes as thepumping starts. Hence, the working parameter is K


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Stress

P eT P

Total stress due to the weightof solids and water ( T) issupported by solidframework ( e) and porewater (P p).

Relation between e to h and e = - P where P = g e = - g

When the reference point is fixed, ie., doesnt change, e = - g h because z = 0

Change in head h causes changes in e and deformation of porous medium.


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A material property relating the change in volume (per

unit volume to applied stress)

compressibility of porous medium; db change inaquifer thickness; b original aquifer thickness, d e change in effective stress

Inverse of modulus of elasticity Volume change can occur with change in hydraulic head

in three ways Expansion of water ( P) db by compression of grains db by compression of medium (consolidation)

dP

bdbd

bdbe

//

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Compressibility


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Topics Covered Today Basic Material Properties of Media and Fluid

Fluid Potential and Hydraulic Head Darcys Law Hydraulic Conductivity and Estimation methods Concept of Heterogeneity and Anistropy Equivalent K in case of layered soils Water Table and Potentiometric surfaces, flow gradients Aquifer Properties

Specific Storage, Specific Yield, Storativity,Transmissivity and Stress

hydro lecture 2

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