Aquifer - a geologic unit that stores and transmits water
1.72, Groundwat er Hydrology Prof. Charles Harvey
Le ct u r e Pa ck e t # 2 : Aqu ife r s, Por osit y , a n d D a r cy’s La w
River Lake
( Exposed Wat er Precipit at ion
I nfilt rat ion Table) Unsat urat ed
Sat urat ed zone Wat er t able zone - Aquifer
Unsat urat ed Zone, Vadose Zone, Soil Moist ure Zone, Zone of Aerat ion – rock, wat er and air
Ca pilla r y Fr in ge – region above wat er t able where wat er rises due t o capillary forces in t he porous m edium .
Sat urat ed Zone, Phreat ic Zone – rock and w at er Wat er Table
- Top of saturated zone
- Depressed version of topography
- Surface waters are m anifestations of the water table – exposed water table
Aqu ife r - a geologic unit t hat st ores and t ransm it s w at er
Recharge Area Wat er Table
Unconfined Aquifer
Confined or Art esian Aquifer
Un con fin e d Aqu ife r – w at er is in cont act w it h at m ospheric pressure – drill and w ell
hit t he w at er t able
Con fin e d Aqu ife r – recharge upgradient forces w at er t o flow dow n and get t rapped
under an aquiclude. Wat er is under pressure due t o t he weight of t he upgradient w at er and t he confinem ent of t he w at er bet ween “ im perm eable” lay ers. Wat er flows t o surface under art esian pressure in an Art esian Well.
Aquifer cont am inat ion Cont am inant Source
Wat er Table Unconfined Aquifer
Confined or Art esian Aquifer
I n confined vs. unconfined aquifers
- Although unconfined aquifers are used for water supply, they are often cont am inat ed by w ast es and chem icals at t he surface.
- Confined aquifers are less likely to be contam inated and thereby provide supplies of good qualit y.
- Mechanism s of transport are advection and dispersion.
- There can be chem ical interactions in aqueous phase or between the water and solid m edia
- Covered in Contam inant Hydrology course (1.72 is a prerequisite)
Unconfined Aquifer
Confined or Art esian Aquifer
Wat er Table Unconfined Aquifer
Confined or Art esian Aquifer
Key Aquifer Propert ies
Por osit y – Percent age volum e occupied by voids. Porosit y is independent of scale.
For exam ple, a pile of m arbles and a pile of beach balls have spherical shape and differing sizes; t he porosit ies are ident ical due t o t he sim ilar shaping.Pe r m e a bilit y – Measures t he t ransm ission propert y of t he m edia and t he int erconnect ion of t he pores. Relat ed t o hydraulic conduct ivit y and t ransm issivit y.
( m ore lat er) Good aquifer – High porosit y + High perm eabilit y
- Sand and gravel, sandstone, lim estone, fractured rock, basalt Aqiuiclude, Confining bed, Aquit ard – “ im per m eable” unit form ing a barrier t o groundw at er flow .
- Granite, shale, clay
Por osit y
Well Sort ed I nt ragranular Dissolut ion Poorly Sort ed Decreased Porosit y
Fract ure by Diogenesis
D ioge ne sis – The form at ion of rock; pores fill up w it h precipit at ions of m ineral and
reduce porosit y
- A function of grain size distribution, also packing
- Decreases with depth – com paction and pressure solution
D e p th ( k il o m e te rs )
Se con da r y
50 Porosit y Porosit y increases as dept h decreases. This is on account of t he weight on t op of t he deeper m at erials. Porosit y also t ends t o increase w it h grainsize. Why?
40
30
20
10
( At hy, 1930) Sandst ones ( Blat t , 1979)
1 Shales Porosit y vs. Dept h Curves
7
6
5
4
3
2
Pr im a r y
Tw o Origins of Porosit y
- Dissolution • Fracture Lit hology
Q C a lc it e F ra c tu re N u m b e r u a r tz S S C e m e n te d S S L im e s to n e Tw o t ypes of Porosit y
- I ntergranular o
Bet w een grains, m ost ly part of t he effect of porosit y, but also dead- end pores
- I ntragranular o o
Wit hin grains o Usually not considered part of t he effect ive porosit y I ncredible w ide range of w idt hs and lengt h scales
- Sim ple dichotom ous m odel - dual porosity Darcy’s Law I n 1856 in Dij on, France, Henry Darcy conduct ed his now fam ous experim ent of pouring w at er t hrough sedim ent - packed pipes t o see how m uch w ould flow t hrough t hem in a given am ount of t im e [ volum e of flow per unit t im e] . 3 Flow t hrough colum n is Q in L / T m ost im port ant quant it y The flow per unit area is spe cific disch a r ge
- K is the intrinsic perm eability (L 3 ρ is the m ass density (M/ L •
- shearing t hat is necessary for flow
- Com pacted clays and low gradients
- Threshold gradient to get flow
- Below a certain gradient – nonlinear High Gradient s 2
- Term 1 is loss – viscous friction against wall of solids and
- Term 2 is loss – dissipation of kinetic energy in pores – flow converges and diverges.
- Com m only cm / s, m / d, ft/ d 2<
- Older unit, gpd/ ft , or m einzer 2 Measures of perm eabilit y, ( L ) Oft en t he D a r cy Un it is used, recall
- - 8 2
- I t equals about 10 cm o
- About 0.831 m / d at 20
- Very com m on quantity for site and regional studies
- Much m ore on this when we get to groundwater flow equation and well tests
Q
called D a r cia n ve locit y or
q = w it h unit s of velocit y L/ T – D a r cia n flu x , but not act ual
A
velocit y of t he fluid Q h 1
∆h h 2 Area, A ∆l
Flow , Q Darcy showed t hat : Q is in direct ion of decreasing head q is proport ional t o h 2 – h 1 = ∆h, given ∆l fixed, q α ( -∆h) q is inversely proport ional t o ∆l, given ∆h fixed, q α (1/ ∆l)
The proport ionalit y const ant is K, and flow is from higher t o low er hydraulic head.
∆ h dh
Hydraulic gradient
q = K − = K − ∆ l dl
K is hydraulic conduct ivit y and has unit s of velocit y ( L/ T) . I t is a funct ion of bot h m edia and fluid.
Q is a flow per unit cross sect ion and is n ot the actual velocity of groundwater flow. ∆ h represents the frictional energy loss due to flow through m edia.
Darcy’s law is a m acroscopic law . I t doesn’t t ell you about t he flow t hrough individual pores. 3 The discharge is Q in L / T
∆ h q = K − = KiA −
∆ l i is com m only used for gradient .
Not e t he difference bet w een Q and q! What is hydraulic conduct ivit y? K is a propert y of bot h m edia and fluid.
k ρ g
Experim ent s show :
K = µ 2
) , a propert y of m edia only
) µ is the dynam ic viscosity (M/ LT) and m easures the resistance of fluid to
Range of Applicabilit y of Darcy’s Law At ext rem e gradient s som e have quest ioned t he applicabilit y of Darcy’s Law ( cont roversial) Low Gradient s
dh = q c + q c 1 2 dl
Must have lam inar flow w it hin pores.
v d Inertial forces ρ
R = ≡ e µ Viscous forces
Lam inar in pipes < 2,000 in rocks < 10 U
D a r cy ’s La w Re a l La w
L L 2 L 1 Measures of hydraulic conduct ivit y ( L/ T)
k g dh k g dh ρ ρ q = − Q = 1 cm/s = −
µ dl cp dl
1 da r cy is t he perm eabilit y t hat gives a specific discharge of 1 cm / s for a fluid w it h a
viscosit y of 1 cp under a h ydr a u lic gr a die n t t im e s de n sit y t im e s g of 1 a t m / cm .
I m por t a n t – A t ypical aquifer m easure of t he t ransm ission propert y of m edia for t he
flow of w at er is given over a t hickness, b 2 Tr a n sm issivit y – T = Kb [ L / T]
2D
C
Re la t ion s Be t w e e n Gr a in Siz e a n d H ydr a u lic Con du ct ivit y
2 10( ) 2 3 T sa S T C g
σ g = geom et ric m ean st andard deviat ion [ L]
ρ = densit y [ M/ L 3 ]
µ = dynam ic viscosit y [ M/ LT]
φ = t ot al porosit y, account ing for com pact ion [ - ]
K = hydraulic conduct ivit y [ L/ T]
]
d 1 0 = grain diam et er for w hich 10% of part icles are sm aller [ L] d g = geom et ric m ean grain diam et er [ L] d = represent at ive grain diam et er [ L] g = gravit at ional accelerat ion [ L/ T 2
= fact or reflect ing pore shape and packing in Kozeny eqn, m od. By Collins [ - ] = fact or in t he Hazen equat ion [ T/ L]
C = fact or reflect ing pore shape and packing in t he Kozeny- Carm en eqn. [ - ] C T
Kozeny Equat ion, m odified by Collins ( 1961)
⎜⎜ ⎝ ⎛ =
ρ ⎟⎟ ⎠ ⎞
K φ µ
Kozeny- Carm an ( in de Marsily, 1986)
) (d C K =
S C g K
⎝ ⎛ = sa
ρ − ⎟⎟ ⎠ ⎞ ⎜⎜
( ) 2 2 3 1 φ φ µ
Kozeny- Carm an ( in Bear, 1972)
⎜⎜ ⎝ ⎛ = d g K
− ⎟⎟ ⎠ ⎞
φ µ ρ
( ) 2 3 2 1 180 φ
Krum bein and Monk ( 1942)
EXP d E K σ − − =
04 66 . 9 ( 2 g g
) 31 . ) 1 ( 760 )(
Equat ion Hazen ( 1911) Reference
S sa = surface area exposed t o fluid per unit volum e of solid m edium [ 1/ L] T = t ort uosit y [ - ]
Rem em ber Darcian Velocit y is not an act ual velocit y; it is discharge per unit area ( area is TOTAL cross sect ion)
D a r cia n Ve locit y
Tot al Area Q
Area of Pore Space Act s like t his
Average Linear Velocit y
Pr im a r y por osit y – t he original int erst ices Se con da r y por osit y – secondary dissolut ion or st ruct ural openings ( fract ures,
fault s, and openings along bedding planes) .
ρ
Com pu t e d por osit y - n = 100[ 1- ρ b / p ] 3
ρ b – bulk densit y, M/ L - > m ass of dry sam ple/ original volum e 3 ρ p – part icle densit y, M/ L - > m ass of dry sam ple/ volum e of m ineral m at t er from w at er- displacem ent t est ( 2.65 g/ cc)
Effe ct ive por osit y – porosit y available for flow , n e
Can have isolat ed w at er as dead- end pores or t rapped gas. I MPORTANT t o t ransport !
− K ∆h − K dh
V = =
n n dl e e ∆lV is t he average linear pore w at er velocit y. Measure of t he rat e of advect ion of a slug of wat er. V is larger t han t he Darcian Velocit y. - > q = n e
V