Review Of Basic Hydrogeology Principles

transcript

ReviewOf

Basic Hydrogeology

Principles

Types of Terrestrial WaterTypes of Terrestrial Water

GroundwaterGroundwater

SoilSoilMoistureMoisture

SurfaceWater

Unsaturated Zone – Zone of Aeration

Pores Full of Combination of Air and Water

Zone of Saturation

Pores Full Completely with Water

PorosityPorosity

Primary PorosityPrimary Porosity Secondary PorositySecondary Porosity

SedimentsSedimentsSedimentary RocksSedimentary Rocks

Igneous RocksIgneous RocksMetamorphic RocksMetamorphic Rocks

PorosityPorosity

n = 100 (Vv / V)n = 100 (Vv / V)

n = porosity (expressed as a percentage)n = porosity (expressed as a percentage)Vv = volume of the void spaceVv = volume of the void spaceV = total volume of the material (void + rock)V = total volume of the material (void + rock)

PorosityPorosityPermeabilityPermeability

Ability to hold water Ability to transmit water

Size, Shape, Interconnectedness

PorosityPorosity PermeabilityPermeability

Some rocks have high porosity, but low permeability!!Some rocks have high porosity, but low permeability!!

Vesicular BasaltVesicular Basalt

PorousPorous

But Not PermeableBut Not Permeable

ClayClay

PorousPorous

But Not PermeableBut Not Permeable

High Porosity,High Porosity, but Low Permeability but Low Permeability

InterconnectednessInterconnectedness Small PoresSmall Pores

SandSand

Porous andPorous and PermeablePermeable

The Smaller the Pore SizeThe Smaller the Pore Size

The Larger the Surface AreaThe Larger the Surface Area

The Higher the Frictional ResistanceThe Higher the Frictional Resistance

The Lower the PermeabilityThe Lower the Permeability

HighHigh

LowLow

Darcy’s ExperimentDarcy’s Experiment

He investigated the flow of water in a column of sandHe investigated the flow of water in a column of sand

He varied:He varied: Length and diameter of the columnLength and diameter of the column

Porous material in the columnPorous material in the column

Water levels in inlet and outlet reservoirsWater levels in inlet and outlet reservoirs

Measured the rate of flow (Q): volume / timeMeasured the rate of flow (Q): volume / time

K = constant of proportionality

Q = -KA (Q = -KA (h / L)h / L)

Darcy’s LawDarcy’s Law

Empirical Law – Derived from Observation, not from TheoryEmpirical Law – Derived from Observation, not from Theory

Q = flow rate; volume per time (L3/T)A = cross sectional area (L2)

h = change in head (L)L = length of column (L)

LL33 x L x L T x LT x L22 x L x L

What is K?What is K?K = Hydraulic Conductivity = coefficient of permeabilityK = Hydraulic Conductivity = coefficient of permeability

K = QL / A (-K = QL / A (-h)h) //// //

What are the units of K?What are the units of K?

The larger the K, the greater the flow rate (Q)The larger the K, the greater the flow rate (Q)

KK is a function of both: is a function of both:

Porous mediumPorous medium

The FluidThe Fluid

ClayClay 1010-9-9 – 10 – 10-6-6

SiltSilt 1010-6-6 – 10 – 10-4-4

Silty SandSilty Sand 1010-5-5 – 10 – 10-3-3

SandsSands1010-3-3 – 10 – 10-1-1

GravelGravel 1010-2-2 – 1 – 1

Sediments have wide range of values for K (cm/s)Sediments have wide range of values for K (cm/s)

ClayClay SiltSilt

SandSand GravelGravel

Not a true velocity as part of the column is filled with sedimentNot a true velocity as part of the column is filled with sediment

Q = -KA (Q = -KA (h / L)h / L)

RearrangeRearrange

q =q = = -K = -K ((h / L)h / L)

q = specific discharge (Darcian velocity)q = specific discharge (Darcian velocity)

““apparent velocity” –velocity water would move through an aquifer apparent velocity” –velocity water would move through an aquifer if it were an open conduitif it were an open conduit

Average linear velocity = v =Average linear velocity = v =

True Velocity – Average Mean Linear Velocity?True Velocity – Average Mean Linear Velocity?

q =q = = -K = -K ((h / L)h / L)

Only account for area through which flow is occurringOnly account for area through which flow is occurring

Flow area = porosity x areaFlow area = porosity x area

Water can only flow through the poresWater can only flow through the pores

QQnAnA

Aquifers

Aquifer – geologic unit that can store and transmit water at rates fast enough to supply reasonable amounts to wells

Confining Layer – geologic unit of little to no permeability

Aquitard, Aquiclude

Gravels

Clays / Silts

Water table aquifer

Confined aquifer

Types of AquifersUnconfined Aquifer

high permeability layers to the surface

overlain by confining layer

Homogeneity – same properties in all locations

Homogeneous vs Heterogenous

Variation as a function of Space

Heterogeneityhydraulic properties

change spatially

Anisotropicchanges with direction

Isotropy vs Anisotropy

Variation as a function of direction

Isotropicsame in direction

In Arid Areas: Water table flatter

In Humid Areas: Water Table Subdued Replica of Topography

Regional Flow

Subdued replica of topography

Discharge occurs in topographically low spots

Water Table Mimics the Topography

Need gradient for flowIf water table flat – no flow occurring

Sloping Water Table – Flowing Water

Flow typically flows from high to low areas

Q = -KA (Q = -KA (h / Lh / L))

Discharge vs Recharge Areas

RechargeDownward

Vertical Gradient

DischargeUpward

Vertical Gradient

Discharge

Topographically High Areas

Deeper Unsaturated Zone

Flow Lines Diverge

Recharge

Topographically Low Areas

Shallow Unsaturated Zone

Flow Lines Converge

Equations of Groundwater Flow

Fluid flow is governed by laws of physics

Any change in mass flowing into the small volume of the aquifer must be balanced by the corresponding change in mass flux out of the volume or a change in the mass

stored in the volume or both

Law of Mass ConservationContinuity Equation

Matter is Neither Created or Destroyed

Darcy’s Law

Balancing your checkbook

My Account

Let’s consider a control volume

Area of a face: dxdz

Confined, Fully Saturated Aquifer

q = specific discharge = Q / A

w = fluid density (mass per unit volume)

Apply the conservation of mass equation

Change in Mass in Control Volume = Mass Flux In – Mass Flux Out

Conservation of Mass

The conservation of mass requires that the change in mass stored in a control volume over time (t) equal the difference between the mass that enters the control volume and that which exits the control volume over this same time increment.

- (wqx) dxdydz

wqx + y

wqy + z

wqz ) dxdydz

- (wqy) dxdydzy

- (wqz) dxdydzz

(wqx) dydz

Volume of control volume = (dx)(dy)(dz)

Volume of water in control volume = (n)(dx)(dy)(dz)

Mass of Water in Control Volume = (w)(n)(dx)(dy)(dz)

[(w)(n)(dx)(dy)(dz)]Mt

[(w)(n)(dx)(dy)(dz)]t =

wqx + y

wqy + z

wqz ) dxdydz

Divide both sides by the volume

[(w)(n)]t = - (

xwqx +

ywqy +

zwqz )

If the fluid density does not vary spatially

[(w)(n)]t = - (

qz )1w

qx = - Kx(h/x)

qy = - Ky(h/y)

qz = - Kz(h/z)

Remember Darcy’s Law

hz )+ +

hz )+ +[(w)(n)]

[(w)(n)]t

After Differentiation and Many Substitutions

(wg + nwg) ht

= aquifer compressibility

= compressibility of water

hz )+ +=(wg + nwg) h

Ss = wg ( + n)

But remember specific storage

hz )+ + = Ss

3D groundwater flow equation for a confined aquifer

If we assume a homogeneous system

K Ssht

+ +2hy2

transientanisotropicheterogeneous

hz )+ + = Ss

If we assume a homogeneous, isotropic system

Transient – head changes with time

Steady State – head doesn’t change with time

Homogeneous – K doesn’t vary with space

Isotropic – K doesn’t vary with direction: Kx = Ky = Kz = K

Let’s Assume Steady State System

Laplace Equation

Conservation of mass for steady flow in an IsotropicHomogenous aquifer

+ +2hy2

If we assume there are no vertical flow components (2D)

Kb Ssbht

+ 2hy2

K Ssht

+ +2hy2

hz )+ + = 0

Heterogeneous Anisotropic Steady State

K Ssht

+ +2hy2

Homogeneous Isotropic Transient

+ +2hy2

Homogeneous Isotropic Steady State

Unconfined Systems

Water is derived from storage by vertical drainage

Pumping causes a decline in the water table

In a confined system, although potentiometric surfacedeclines, saturated thickness (b) remains constant

In an unconfined system, saturated thickness (h) changes

And thus the transmissivity changes

Water Table

hz )+ + = Ss

Remember the Confined System

hy )+ = Sy

Let’s look at Unconfined Equivalent

Assume Isotropic and Homogeneous

(hhx )

y )+ =Sy

Boussinesq Equation

Nonlinear Equation

Let v = h2

For the case of Island Recharge and steady State

Review Of Basic Hydrogeology Principles

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