Physical Properties of Aquifers

Groundwater Hydraulics

Daene C. McKinney

Summary

• Occurrence of Groundwater– Distribution of water in subsurface

• Porous Medium– Porosity– Moisture Content– Particle Size– Capillary Pressure– Soil Moisture Characteristic Curves– Specific Yield and Retention

• Aquifer Types– Aqufier Storage

• Piezometric head

Occurrence of Groundwater

3

• Ground water occurs when water recharges the subsurface through cracks and pores in soil and rock

• Shallow water level is called the water table

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

Porous Medium• Groundwater

– All waters found beneath the ground surface

– Occupies pores (void space space not occupied by solid matter)

• Porous media – Numerous pores of small size– Pores contain fluids (e.g., water

and air) – Pores act as conduits for flow of

fluids• Type of rocks and their

– Number, size, and arrangement of pores

– Affect the storage and flow through a formation.

• Pores shapes are irregular– Differences in the minerals

making up the rocks – Geologic processes experienced

by them.

Particle Size of Some Soils

6

Continuum Approach to Porous Media

• Pressure, density etc. apply to fluid elements that are large relative to molecular dimensions, but small relative to the size of the flow problem

• We adopt a Representative Elementary Volume (REV) approach

• REV must be large enough to contain enough pores to define the average value of the variable in the fluid phase and to ensure that the pore-to-pore fluctuations are smoothed out

• REV must be small enough that larger scale heterogeneities do not get averaged out (layering, etc.)

Porosity

solid

Pore with water

Soil volume V(Saturated)

Porosity• Property of the voids of

the porous medium• % of total volume

occupied by voids solid

Pore with water

Soil volume V(Saturated)

Cubic Packing

RhomboPacking

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

rm = particles density (grain density)rd = bulk density

Void Ratio:

Typical Values of Porosity

11

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

Flow of Immiscible Fluids

• Miscible displacement - fluids are completely soluble in each other, the interfacial tension between the fluids is zero, the fluids dissolve in each other, and a distinct fluid-fluid interface does not exist

• Immiscible displacement - simultaneous flow of immiscible fluids or phases in the porous medium. The interfacial tension between the fluids is not aero, distinct fluid-fluid interfaces exist and separate the phases in each pore.

• Unsaturated flow - flow of two immiscible fluids (water and air), except that the air is practically immobile.

Saturation

• Saturation

• Water Content

• Water Saturation

Soil volume V(Unsaturated)

Particle Size Distribution

14

Well sorted fine sand

Poorly sorted silty fine to

medium sand

• Particle size distribution curves– Relative % of grain sizes

• Soil classification standards• Soil texture

Particle Size Distribution

15

Sand 49%

Clay 40%

Soil Characteristics of Cyprus Soil Sample

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– s = 0.073 N/m (@ 20oC)

• Capillary pressure– Relates pressure on both sides of interface

water

air

No net force

Net forceinward

Interface

Surface Tension

gas

solid

ssg

sgl

ssl

bliquid

Hg

solid

air

bwater

solid

air

b

Mercury nonwetting solid Water wetting solid

b < 90o - liquid is wetting the solidb > 90o - liquid is non-wetting the solid

Capillary Pressure

• Two immiscible fluids in contact exhibit a discontinuity in pressure across the interface separating them.

• This pressure difference is capillary pressure pc • It depends on the curvature of the interface.

pnw is the pressure in the nonwetting fluid (air, say) pw is the pressure in the wetting fluid (water, say)

Solid

Solid

Water

Air

r

Capillary Pressure

Rise of water in a capillary tube. Capillary forces must balance the weight of water

Capillary pressure head

Solid Solid

Water

Air

r

Negativepressure

Positivepressure

Capillary Pressure

A

B

(A) Below the water level

(B) Above the water level

Difference in pressure across the interface is

Drainage• Drainage occurs when the water pressure in

the pores becomes less than the air pressure• Interfacial tension prevents displacement of

water in the left pore

r

solid

solid

Pore water press. = -p

Pore air press. = 0

If pc increases, radius must decrease, or water occupies smaller pores. Water recedes into pores small enough to support the interface with a radius required to balance the capillary force. Water drains from the large pores first.

Energy in Flow Systems

EGL

HGL

v2/(2g)

v2/(2g)

p/g

z

datumHydraulic grade line (HGL) – height of water in piezometer tube

Energy grade line (EGL) – Height of water in pitot tube

Velocity headPressure headElevation head

v2/(2g)

p/gz

Piezometric Head• Confined aquifer

• Unconfined aquifer

zp

h

zp

h

0p

zh

Pressure head = 0

Piezometric Head in Unsaturated Flow

Saturated Zone Water Table Unsaturated Zone = q f < q f < 0 = 0 > 0

pw > 0 pw = 0 pw < 0

Soil volume V(Unsaturated)

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

Pressure is negative above water table

Soil Water Characteristic Curves

• Capillary pressure head• Function of:

– Pore size distribution– Moisture content

PorosityVadose Zone

Capillary Zone

qo fIrreducible

Water contentPorosity

y

ybCritacalHead

(Bubbling Press.)

Capillary Rise in Soils

Aquifer Types

• Confined aquifer – Under pressure– Bounded by impervious layers

• Unconfined aquifer – Phreatic or water table– Bounded by a water table

• Aquifer – Store & transmit water– Unconsolidated deposits sand and gravel,

sandstones etc.• Aquitard

– Transmit don’t store water– Shales and clay

Summary

• Occurrence of Groundwater– Distribution of water in subsurface

• Porous Medium– Porosity– Moisture Content– Particle Size– Capillary Pressure– Soil Moisture Characteristic Curves– Specific Yield and Retention

• Aquifer Types– Aqufier Storage

• Piezometric head