Groundwater Processes and Concepts

S. Hughes, 2003

PorosityPorosity

solid

Pore with water

Soil volume V(Saturated)

Porosity: total volume of soil that can be filled with water

V = Total volume of elementVi = Volume of PoresVs = Volume of solids

ViV

V VsV

m dm

1 dm

m = particles density (grain density)d = bulk density

Void Ratio:

e ViVs

1

Porosity

solid

Pore with water

Soil volume V(Saturated)

Porosity: total volume of soil that can be filled with water

V = Total volume of elementVi = Volume of PoresVs = Volume of solids

ViV

V VsV

m dm

1 dm

m = particles density (grain density)d = bulk density

Void Ratio:

e ViVs

1

Typical Values of Porosity

Material Porosity (%)

Peat Soil 60-80

Soils 50-60

Clay 45-55

Silt 40-50

Med. to Coarse Sand

35-40

Uniform Sand 30-40

Fine to Med Sand 30-35

Gravel 30-40

Gravel and Sand 30-35

Sandstone 10-20

Shale 1-10

Limestone 1-10

Moisture Content

Pore with air

Soil volume V(Unsaturated)

Moisture Content (volumetric water content): volume of water in total volume

V = Total volume of elementVi = Volume of PoresVs = Volume of solids

Saturation (% water content):

VWV

S VWVi

The major source of all fresh water drinking supplies in some countries is groundwater.

Groundwater is stored underground in aquifers, and is highly vulnerable to pollution.

Understanding groundwater processes and aquifers is crucial to the management and protection of this precious resource.

Groundwater

Groundwater comes from precipitation. Precipitated water must filter down through the vadose zone to reach the zone of saturation, where groundwater flow occurs.

The vadose zone has an important environmental role in groundwater systems. Surface pollutants must filter through the vadose zone before entering the zone of saturation.

Subsurface monitoring of the vadose zone is used to locate plumes of contaminated water, tracking the direction and rate of plume movement.

Groundwater

The vadose zone includes all the material between the Earth’s surface and the zone of saturation. The upper boundary of the zone of saturation is called the water table. The capillary fringe is a layer of variable thickness that directly overlies the water table. Water is drawn up into this layer by capillary action.

Components of groundwater

The rate of infiltration is a function of soil type, rock type, antecedent water, and time.

Distribution of Water in Subsurface • Different zones

– depend on % of pore space filled with water

• Unsaturated Zone– Water held by

capillary forces, water content near field capacity except during infiltration

• Soil zone– Water moves down

(up) during infiltration (evaporation)

• Capillary fringe– Saturated ar base– Field capacity at top

• Saturated Zone– Fully saturated pores

Soil Profile DescriptionMoisture Profile

Field capacity - Water remaining after gravity drainageWilting point - Water remaining after gravity drainage & evapotranspiration

Field Capacity

• After infiltration - saturated• Drainage

– Coarse soils: a few hours– Fine soils: a 2-3 days

• After drainage – Large pores: air and water – Smaller pores: water only

• Soil is at field capacity– Water and air are ideal for plant

growth

SaturatedAfter

drainageAfter

drying

Wilting Point

• After drainage – Root suction & evaporation

• Soil dries out – More difficult for roots

• After drying – Root suction not sufficient for

plants – plant wilts

• Wilting Point = soil water content when plant dies

SaturatedAfter

drainageAfter

drying

Surface Tension• Below interface

– Forces act equally in all directions• At interface

– Some forces are missing– Pulls molecules down and together– Like membrane exerting tension on

the surface• Curved interface

– Higher pressure on concave side • Pressure increase is balanced by

surface tension– = 0.073 N/m (@ 20oC)

• Capillary pressure– Relates pressure on both sides of

interface

water

air

No net force

Net forceinward

Interface

Solid Solid

Water

Air

r

pair

pwNegativepressure

Positivepressure

pc

p

pair

z

pair 0

pw

pc pair pw

Capillary Pressure

pc 2r

2r

Liquid rises due to attractive force of pore, until gravity force stops it.

cos(2r) r2

2r

Solid

Solid

Water

Air

r

pair

pw

pc

p

pair

z

Capillary Pressure

pc 2r

2r

Subsurface Pressure Distribution

Capillary pressure head in zone above water table

Hydrostatic pressure distribution exists below the water table (p = 0).

01 dP

1d

Water table

z

0p0p 0p

0;0 pzPressure is positive below water table

Ground surface

Unsaturated zone

Saturated zone

pz

( )

Pressure is negative above water table

Soil Water Characteristic Curves

• Capillary pressure head• Function of:

– Pore size distribution– Moisture content

( )

( )

PorosityVadose

Zone

Capillary Zone

Capillary Rise in Soils

SPECIFIC YIELD (Sy) is the ratio of the volume of water drained from a rock (due to gravity) to the total rock volume. Grain size has a definite effect on specific yield. Smaller grains have larger surface area/volume ratio, which means more surface tension. Fine-grained sediment will have a lower Sy than coarse-grained sediment.

SPECIFIC RETENTION (Sr) is the ratio of the volume of water a rock can retain (in spite of gravity) to the total volume of rock.

Specific yield plus specific retention equals porosity

Groundwater Movement

Porosity, Specific Yield, & Specific Retention

An aquifer is a formation that allows water to be accessible at a usable rate. Aquifers are permeable layers such as sand, gravel, and fractured rock.

Confined aquifers have non-permeable layers, above and below the aquifer zone, referred to as aquitards or aquicludes. These layers restrict water movement. Clay soils, shales, and non-fractured, weakly porous igneous and metamorphic rocks are examples of aquitards.

Aquifers

Sometimes a lens of non-permeable material will be found within more permeable material. Water percolating through the unsaturated zone will be intercepted by this layer and will accumulate on top of the lens. This water is a perched aquifer.

An unconfined aquifer has no confining layers that retard vertical water movement.

Artesian aquifers are confined under hydraulic pressure, resulting in free-flowing water, either from a spring or from a well.

Aquifers

Aquifer Types

Aquifer Types

Aquifer Storage Coefficient• Fluid Compressibility ()• Porous Medium Compressibility ()• Confined Aquifer

– Water produced by 2 mechanisms

1. Aquifer compaction due to increasing effective stress, V = g2. Water expansion due to decreasing pressure, V = g

S = g()• Unconfined aquifer

– Water produced by draining pores, S = Sy

Water is continually recycled through aquifer systems. Groundwater recharge is any water added to the aquifer zone.

Processes that contribute to groundwater recharge include precipitation, streamflow, leakage (reservoirs, lakes, aqueducts), and artificial means (injection wells).

Groundwater discharge is any process that removes water from an aquifer system. Natural springs and artificial wells are examples of discharge processes.

Recharge and Discharge

S. Hughes, 2003

Groundwater supplies 30% of the water present in our streams. Effluent streams act as discharge zones for groundwater during dry seasons.

This phenomenon is known as base flow. Groundwater overdraft reduces the base flow, which results in the reduction of water supplied to our streams.

Recharge and Discharge

S. Hughes, 2003

Perennial Stream(effluent)

• Humid climate• Flows all year -- fed by groundwater base flow (1)• Discharges groundwater S. Hughes, 2003

Ephemeral Stream(influent)

• Semiarid or arid climate• Flows only during wet periods (flashy runoff)• Recharges groundwater

S. Hughes, 2003

Discharge of groundwaterfrom a spring.

Springs generally emerge atthe base of a hillslope.

Some springs produce waterthat has traveled for manykilometers; while others emitwater that has traveled onlya few meters.

Springs represent placeswhere the saturated zone(below the water table)comes in contact with theland surface.

Springs

S. Hughes, 2003

Summary of Groundwater Systems

(from Keller, 2000, Figure 10.9)

S. Hughes, 2003

The water table is actually a sloping surface.

Slope (gradient) is determined by the difference in water table elevation (h) over a specified distance (L).

Direction of flow is downslope.

Flow rate depends on the gradient and the properties of the aquifer.

Groundwater Movement -- General Concepts

Darcy’s Law

Q = KIA -- Henry Darcy, 1856, studied water flowing through porous material. His equation describes groundwater flow.

Darcy’s experiment:

• Water is applied under pressure through end A, flows through the pipe, and discharges at end B.

• Water pressure is measured using piezometer tubes

Hydraulic head = dh (change in height between A and B)Flow length = dL (distance between the two tubes)Hydraulic gradient (I) = dh / dL

The velocity of groundwater is based on hydraulic conductivity (K), as well as the hydraulic head (I).

The equation to describe the relations between subsurface materials and the movement of water through them is

Q = KIAQ = Discharge = volumetric flow rate, volume of water flowing through an aquifer per unit time (m3/day)

A = Area through which the groundwater is flowing, cross-sectional area of flow (aquifer width x thickness, in m2)

Rearrange the equation to Q/A = KI, known as the flux (v), which is an apparent velocity

Actual groundwater velocity is higher than that determined by Darcy’s Law.

Darcy’s Law

FLUX given by v = Q/A = KI is the IDEAL velocity of groundwater; it assumes that water molecules can flow in a straight line through the subsurface.

NOTE: Flux doesn't account for the water molecules actually following a tortuous path in and out of the pore spaces. They travel quite a bit farther and faster in reality than the flux would indicate.

DARCY FLUX given by vx = Q/An = KI/n (m/sec) is the ACTUAL velocity of groundwater, which DOES account for tortuosity of flow paths by including porosity (n) in the calculation. Darcy velocity is higher than ideal velocity.

Darcy’s Law is used extensively in groundwater studies. It can help answer important questions such as the direction a pollution plume is moving in an aquifer, and how fast it is traveling.

Darcy’s Law

S. Hughes, 2003

Groundwater Movement

The tortuous path of groundwater molecules through an aquifer affects the hydraulic conductivity. How do the following properties contribute to the rate of water movement?

• Clay content and adsorptive properties• Packing density• Friction• Surface tension• Preferred orientation of grains• Shape (angularity or roundness) of grains• Grain size• Hydraulic gradient

Hydraulic Conductivity• A combined property of the medium and the fluid• Ease with which fluid moves through the medium

k = intrinsic permeability ρ = densityµ = dynamic viscosityg = gravitational constant

g

kK

Porous medium property

Fluid properties

Hydraulic Conductivity• Specific discharge (q) per unit hydraulic gradient• Ease with which fluid it transorted through porous medium• Depends on both matrix and fluid properties

– Fluid properties:• Density and • Viscosity

– Matrix properties• Pore size distribution• Pore shape• Tortuosity• Specific surface area• Porosity

g

kK

k = intrinsic permeability [L2]

Estimating ConductivityKozeny – Carman Equation

• A combined property of the medium and the fluid• Ease with which fluid moves through the medium

k = intrinsic permeability ρ = densityg = gravitational constantµ = dynamic viscosityd = mean particle size = porosity

g

kK

22

32

)1(180dcdk

Kozeny – Carman eq.

Lab Measurement of ConductivityPermeameters

• Darcy’s Law is useless unless we can measure the parameters

• Set up a flow pattern such that– We can derive a solution – We can produce the flow pattern experimentally

• Hydraulic Conductivity is measured in the lab with a permeameter– Steady or unsteady 1-D flow– Small cylindrical sample of medium

Lab Measurement of ConductivityConstant Head Permeameter

• Flow is steady• Sample: Right circular cylinder

– Length, L– Area, A

• Constant head difference (b) is applied across the sample producing a flow rate Q

• Darcy’s Law

Continuous Flow

OutflowQ

Overflow

A

Q KAbL

K QLAb

Lab Measurement of ConductivityFalling Head Permeameter

• Flow rate in the tube must equal that in the column

OutflowQ

Qcolumn rcolumn2 K

hL

Qtube rtube2 dh

dt

rtube

rcolumn

2LK

dhh

dt

K rtube

rcolumn

2Lt

ln

b0

b1

h b0 @t 0; h b1@t t

WELL SORTEDCoarse (sand-gravel)

POORLY SORTEDCoarse - Fine

WELL SORTEDFine (silt-clay)

Permeability and Hydraulic ConductivityHigh Low

Sorting of material affects groundwater movement. Poorly sorted (well graded) material is less porous than well-sorted material.

Groundwater Movement

Porosity and hydraulic conductivity of selected earth materials

Hydraulic Porosity Conductivity

Material (%) (m/day)

UnconsolidatedClay 45 0.041Sand 35 32.8Gravel 25 205.0Gravel and sand 20 82.0

RockSandstone 15 28.7Dense limestone or shale 5 0.041Granite 1 0.0041

Aquifer Transmissivity

• Transmissivity (T) – Discharge through thickness of

aquifer per unit width per unit head gradient

– Product of conductivity and thickness

T =K b

Hydraulic gradient = 1 m/m

Potentiometric

Surfa

ce

Confining Bed

Confined Aquiferb

1 m

1 m

1 m

Transmissivity, T, volume of water flowing an area 1 m x b under hydraulic gradient of 1 m/m

Conductivity, K, volume of water flowing an area 1 m x 1 m under hydraulic gradient of 1 m/m

K(x,y)= 1b

K(x,y,z)dz0

b

Heterogeneity and Anisotropy • Homogeneous aquifer

– Properties are the same at every point

• Heterogeneous aquifer – Properties are different at

every point • Isotropic aquifer

– Properties are same in every direction

• Anisotropic aquifer– Properties are different in

different directions• Often results from stratification

during sedimentation

verticalhorizontal KK

www.usgs.gov

Layered Porous Media(Flow Parallel to Layers)

Q Qii1

3

( biKihx

)i1

3

h2 h1

W(biKi )

i1

3

biKii1

3 bK

K Parallel 1b

biKi i1

3

3K

2K

1K

W

b Q

1b

2b

3b

1Q

2Q

3Q

Q h2 h1

WbK

Layered Porous Media(Flow Perpendicular to Layers)

Q KiWhi

bi

hi biQKiW

QW

bi

Ki

i1

3

bK

bi

Ki

i1

3

K Perpendicular b

bi

Ki

i1

3

Q

3K

2K

1K

W

b

1b

2b

3b

1h

2h

3h

Q

Q K Whb

h QW

bK

Water table contour lines are similar to topographic lines on a map. They essentially represent "elevations" in the subsurface. These elevations are the hydraulic head mentioned above.

Water table contour lines can be used to determine the direction groundwater will flow in a given region. Many wells are drilled and hydraulic head is measured in each one. Water table contours (called equipotential lines) are constructed to join areas of equal head. Groundwater flow lines, which represent the paths of groundwater downslope, are drawn perpendicular to the contour lines.

A map of groundwater contour lines with groundwater flow lines is called a flow net.

Groundwater Flow Nets

Groundwater MovementDetermine flow direction from well data:

N

Well #2 4315’ elevdepth to WT = 78’(WT elev = 4237’)

Well #3 4397’ elevdepth to WT = 95’(WT elev = 4302’)

Well #1 4252’ elevdepth to WT = 120’(WT elev = 4132’) 4240

4260

4280

4300

41404160

4180

42004220

42404260

4280

41804200

4220

1. Calculate WT elevations.

2. Interpolate contour intervals.

3. Connect contours of equal elevation.

4. Draw flow lines perpendicular to contours.

Groundwater Flow Nets

Aquitard (granite)

Qal100 50

QalWT

A simple flow netCross-profile view

well

Aquitard

Qal

• Effect of a producing well

• Notice the approximate diameter of the cone of depression

Groundwater Flow Nets

Distorted contours may occur due to anisotropic conditions (changes in aquifer properties).

Area of high permeability (high conductivity)

DRAINAGEBASIN

NWTcontours

Flow lines

Groundwater Flow NetsWater table contours in drainage basins roughly follow the surface topography, but depend greatly on the properties of rock and soil that compose the aquifer:

• Variations in mineralogy and texture

• Fractures and cavities

• Impervious layers

• Climate

Drainage basins are often used to collect clean, unpolluted water for domestic consumption.

Pumping water from a well causes a cone of depression to form in the water table at the well site.

Groundwater Movement -- Cone of Depression

Water table

Cone of depressionflowflow

(from Keller, 2000, Figure 10.10)

Groundwater Flow Net

400

402

404

406

408

410

412414

N

Water Table Contours

Water Flow Lines

Well

Overpumping will have two effects:

1. Changes the groundwater flow direction.

2. Lowers the water table, making it necessary to dig a deeper well.

• This is a leading cause for desertification in some areas.

• Original land users and land owners often spend lots of money to drill new, deeper wells.

• Streams become permanently dry.

Groundwater Overdraft