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
Lake River
zone Sat urat ed
I nfilt rat ion
( Exposed Wat er Table) Precipit at ion
Unsat urat ed
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 w at er t able w here w at 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 sat urat ed zone
• Depressed version of t opography
• Surface w at ers are m anifest at ions of t he w at er t able – exposed w at er t able Aqu ife r - a geologic unit t hat st ores and t ransm it s w at er
Recharge Area
Unconfined Aquifer Confined or Art esian Aquifer Wat er Table
1.72, Groundw at er Hydrology Lect ure 2
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
Unconfined Aquifer Confined or Art esian Aquifer Wat er Table
I n confined vs. unconfined aquifers
• Alt hough unconfined aquifers are used for w at er supply, t hey are oft en cont am inat ed by w ast es and chem icals at t he surface.
• Confined aquifers are less likely t o be cont am inat ed and t hereby provide supplies of good qualit y.
• Mechanism s of t ransport are advect ion and dispersion.
• There can be chem ical int eract ions in aqueous phase or bet w een t he w at er and solid m edia
I n A.D. 1126, in t he province of Art ois:
Unconfined Aquifer
Unconfined Aquifer Wat er Table
Confined or Art esian Aquifer Wat er Table
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, sandst one, lim est one, fract ured rock, basalt
Aqiuiclude, Confining bed, Aquit ard – “ im per m eable” unit form ing a barrier t o groundw at er flow .
• Granit e, shale, clay
1.72, Groundw at er Hydrology Lect ure 2
Por osit y
Poorly Sort ed Fract ure
I nt ragranular Well Sort ed
Decreased Porosit y
Dissolut ion
by Diogenesis
Tw o Origins of Porosit y Pr im a r y
• A funct ion of grain size dist ribut ion, also packing
• Decreases w it h dept h – com pact ion and pressure solut ion
Porosit y vs. Dept h Curves
Tw o t ypes of Porosit y
• I nt ergranular
o Bet w een grains, m ost ly part of t he effect of porosit y, but also dead-end pores
• I nt ragranular
o Wit hin grains
o Usually not considered part of t he effect ive porosit y o I ncredible w ide range of w idt hs and lengt h scales
• Sim ple dichot om ous m odel - dual porosit y
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] .
Flow t hrough colum n is Q in L3/ T m ost im port ant quant it y The flow per unit area is spe cific disch a r ge
q
=
Q
A
w it h unit s of velocit y L/ T –called D a r cia n ve locit y or D a r cia n flu x, but not act ual velocit y of t he fluid
Q
∆h h1
h2
∆l Area, A
Flow , Q Darcy showed t hat :
Q is in direct ion of decreasing head
q is proport ional t o h2 – h1 = ∆h, given ∆l fixed, q α ( -∆h)
q is inversely proport ional t o ∆l, given ∆h fixed, q α ( 1/∆l)
∆
h
dh
What is hydraulic conduct ivit y?K is a propert y of bot h m edia and fluid. shearing t hat is necessary for flow
Range of Applicabilit y of Darcy’s Law
• Term 1 is loss – viscous frict ion against w all of solids and
• Term 2 is loss – dissipat ion of kinet ic energy in pores – flow converges and diverges.
Must have lam inar flow w it hin pores.
ρ
v
d
Inertial forces
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
L0 L2 L1
Measures of hydraulic conduct ivit y ( L/ T)
• Com m only cm / s, m / d, ft / d
• Older unit , gpd/ ft2, or m einzer Measures of perm eabilit y, ( L2)
Oft en t he D a r cy Un it is used, recall
q
=
−
k
ρ
g
dh
Q = 1 cm/s
=
−
k
ρ
g
dh
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 .
2 • I t equals about 10- 8 cm
• About 0.831 m / d at 20o
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
Tr a n sm issivit y – T = Kb [ L2/ T] 2D
• Very com m on quant it y for sit e and regional st udies
C
1.72, Groundw at er Hydrology Lect ure 2
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) .
Com pu t e d por osit y - n = 100[ 1-ρb/ρp]
ρb – bulk densit y, M/ L3 - > m ass of dry sam ple/ original volum e
ρp – part icle densit y, M/ L3 - > 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 , ne
Can have isolat ed w at er as dead- end pores or t rapped gas. I MPORTANT t o t ransport !
