Physical Properties of Aquifers

Groundwater Hydraulics

Daene C. McKinney

Outline• Porous Medium

– Porosity– Moisture Content– Particle Size– Distribution of water in subsurface– Capillary Pressure– Soil Moisture Characteristic Curves– Specific Yield and Retention

• Piezometric head in aquifers• Aquifer Types

– Aquifer Storage

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.

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

8

Material Porosity (%)Peat Soil 60-80Soils 50-60Clay 45-55Silt 40-50Med. to Coarse Sand 35-40Uniform Sand 30-40Fine to Med Sand 30-35Gravel 30-40Gravel and Sand 30-35Sandstone 10-20Shale 1-10Limestone 1-10

Volumetric Water Content

Soil volume V(Unsaturated)

SaturationSoil volume V(Unsaturated)

Particle Size of Some Soils

11

Particle Size Distribution

12

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

13

Sand 49%

Clay 40%

Soil Characteristics of Cyprus Soil Sample

Occurrence of Groundwater

14

• 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

Saturation

• Saturation

• Water Content

• Water Saturation

Soil volume V(Unsaturated)

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

zph g

zph g

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 g

1d

Water table

z

0p0<p 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

b

CritacalHead

(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

Aquifer Storage• Storativity (S) - ability of

an aquifer to store water• Change in volume of

stored water due to change in piezometric head.

• Volume of water released (taken up) from aquifer per unit decline (rise) in piezometric head.

Unit area

Unit decline in head

Released water

Aquifer Storage• Fluid Compressibility (b)• Aquifer Compressibility (a)• Confined Aquifer

– Water produced by 2 mechanisms

1. Aquifer compaction due to increasing effective stress

2. Water expansion due to decreasing pressure

• Unconfined aquifer– Water produced by draining

pores

gV ar

Unconfined Aquifer Storage

• Storativity of an unconfined aquifer (Sy, specific yield) depends on pore space drainage.

• Some water will remain in the pores - specific retention, Sr

• Sy = f – Sr

Unit area

Unit decline in head

Released water

Porosity, Specific Yield, & Specific Retentionyr SS f

Confined Aquifer Storage

• Storativity of a confined aquifer (Ss) depends on both the compressibility of the water (b) and the compressibility of the porous medium itself (a).

Unit area

Unit decline in head

Released water

Example• Storage in a sandstone aqufier• f = 0.1, a = 4x10-7 ft2/lb, b = 2.8x10-8 ft2/lb, g = 62.4 lb/ft3

• ga 2.5x10-5 ft-1 and gbf 1.4x10-7 ft-1

• Solid Fluid• 2 orders of magnitude more storage in solid• b = 100 ft, A = 10 mi2 = 279,000,000 ft2

S = Ss*b = 2.51x10-3

• If head in the aquifer is lowered 3 ft, what volume is released?V = SAh = 2.1x10-6 ft3

Summary• Porous Medium

– Porosity– Moisture Content– Particle Size– Distribution of water in subsurface– Capillary Pressure– Soil Moisture Characteristic Curves– Specific Yield and Retention

• Piezometric head in aquifers• Aquifer Types

– Aquifer Storage