CEVE 518
Groundwater Flow and Contaminant Transport
Test 1 Review and Study Sheet
DEFINITIONS
Hydrologic Cycle
bulk density – mass of porous medium per volume of porous medium.
evapotranspiration – the combined processes of evaporation (process of water transfer from
soil to the atmosphere) and transpiration (loss of moisture from plants to the
atmosphere).
field capacity – soil moisture content after gravity drainage.
hydrogeology – study of the relationships of geologic materials and flowing water.
hydrologic cycle – circulation of water in the environment.
infiltration – the process of water entering from the ground surface into the vadose zone.
irreducible water content – the water content at which no amount of decrease in capillary
pressure will remove water.
pellicular water – the thin skin of water adsorbed to soil grains.
pendular water – water held by capillary forces at contact points in sand grains.
poorly graded soil – a soil consisting of particles of relatively uniform size (also called a well
sorted soil).
recharge – infiltrating water that reaches the water table.
solid density – mass of solid particles per volume of solid particles (particle density).
stream base flow – the quantity of stream flow attributed to groundwater inflow under “normal”
conditions.
well graded soil – a soil consisting of a wide range of particle sizes (also called a poorly sorted
soil).
wilting point – soil moisture content at which plants can no longer extract water.
Soil Texture and Moisture Distribution
aquiclude – saturated formation of relatively impermeable material (e.g., clay).
aquifer – formation that can store and transmit water at appreciable quantities.
aquitard – saturated formation of low permeability material that impedes water movement.
artesian well – a free-flowing well that taps an aquifer with a head greater than the ground
surface.
capillary fringe – saturated soil immediately overlying the water table in which the water
pressure is negative due to capillary forces.
confined aquifer – an aquifer bounded above and below by confining units. Water is under
pressure.
CEVE 518
Groundwater Flow and Contaminant Transport
Test 1 Review and Study Sheet
confining bed – relatively impermeable material located adjacent to one or more aquifers.
effective porosity – volume of voids that transmit water per volume of porous medium.
leaky aquifer – an aquifer that “leaks” water through an adjacent aquitard, usually below.
perched aquifer – an unconfined aquifer, usually limited in areal extent, that is vertically
separated from a larger aquifer below.
saturation – volume of water per volume of pore space.
semi-confined aquifer – aquifer that is confined in some areas and unconfined in other areas.
specific retention – volume retained after gravity drainage per bulk volume of soil.
specific yield – volume drained by gravity per bulk volume of soil.
total porosity – volume of voids per volume of porous medium.
unconfined aquifer – an aquifer that is not confined on top. Also called a water table aquifer or
phreatic aquifer. The top of an unconfined aquifer is at atmospheric pressure.
vadose zone – unsaturated soil extending from the ground surface to the water table.
void ratio – volume of voids per volume of solids.
water content – volume of water per unit bulk volume of porous medium.
water table – the locus of all points in a saturated aquifer that are at atmospheric pressure. In
less formal terminology, the surface of the groundwater in an unconfined aquifer.
Darcy’s Law and Groundwater Flow
anisotropic medium – parameter values vary with direction.
aquifer flux (U) – groundwater flow per unit width of aquifer.
elevation head – portion of hydraulic head due to the elevation of the measurement point
relative to some datum.
heterogeneous medium –parameter values are not the same everywhere within the medium.
homogeneous medium –parameter values are the same everywhere within the medium.
hydraulic conductivity – proportionality constant in Darcy’s Law that relates groundwater flux
to the hydraulic gradient. A measure of resistance to groundwater flow caused by the
combined effects of the fluid and the porous medium.
hydraulic head – energy per unit weight of water.
intrinsic permeability – resistance to flow caused by aquifer properties alone (not fluid
properties).
isotropic medium – parameter values do not vary with direction.
potential – a physical quantity, capable of measurement at every point in a flow system, whose
properties are such that flow always occurs from regions in which the quantity has a
higher values of those in which it has lower, regardless of the direction in space
(Hubbert, 1940).
CEVE 518
Groundwater Flow and Contaminant Transport
Test 1 Review and Study Sheet
potentiometric surface – the locus of points that define the hydraulic head which may (for an
unconfined aquifer) or may not (for an unconfined aquifer) correspond to the actual
groundwater surface.
pressure head – portion of hydraulic head due to the weight of water above the point of
measurement.
representative elementary volume (R.E.V.) – volume of porous media for which average
properties are well defined.
scalar – a quantity that is described by magnitude only.
seepage velocity (v) – the average groundwater velocity in an aquifer; equal to the specific
discharge divided by the effective porosity.
specific discharge (q) – groundwater flow per unit area of aquifer.
specific storage – the volume of water released from storage in a confined aquifer per unit
volume of the aquifer per unit decline in hydraulic head.
storage coefficient (or storativity) – the volume of water released from storage in a confined
aquifer per unit area of the aquifer per unit decline in hydraulic head.
tortuosity – square of the ratio of distance to path length.
transmissivity (T) – the product of hydraulic conductivity and saturated thickness in a confined
aquifer.
vector – a quantity described by both magnitude and direction.
CEVE 518
Groundwater Flow and Contaminant Transport
Test 1 Review and Study Sheet
REVIEW OUTLINE
Hydrologic Cycle
General water volume balance for an aquifer:
input  output  accumulation
Overall :
P  E  T  Ro 
S
t
Groundwate r :
P  E  T  Qo  Qi  Qp 
S
t
At Steady State (SS ) :
S
0
t
Soil Properties
 R.E.V. – definition.
 Porosity (total and effective)
 Density (bulk and solid)
MS
VT
b 
n  1-
S 
MS
VS
where M S  mass of solid particles.
b
S
VV
n
e
VS
1 n
 Saturation and water content:
 Void ratio: e 
w 
 i
VW
;
VT
SW 
 Si
0  w  n
 w   A   N  n
VW  w

;
VV
n
1
Soil Moisture Profile
 Vadose zone:
0  Sw  1
n
e
1 e
CEVE 518
Groundwater Flow and Contaminant Transport
Test 1 Review and Study Sheet
o Soil water
o Intermediate vadose zone
o Capillary fringe
 Saturated Zone
 Soil water characteristic curves
o Plots of water content vs. capillary pressure.
o Moisture content depends on the particle size distribution
o Well-sorted materials and coarse-gained materials, such as uniform sands,
exhibit relatively flat soil moisture curves because the relatively uniform pore
sizes retain water at about the same capillary pressures.
o Well-graded materials that contain many fine grains, such as mixtures of sands
and clays, exhibit more gradual soil moisture curves because they contain a
range of pore sizes that retain water at a wide range of capillary pressures.
 Soil water characteristic curves also represent water content as a function of height
above the water table.
Aquifers





Confined – water under pressure.
Unconfined – water at surface is at atmospheric pressure and is called the water table.
Semi-confined – both confined and unconfined portions.
Leaky – transmits water through adjacent (usually underlying) aquitards.
Perched – isolated unconfined aquifer.
Hydraulic Head





Head is energy per unit weight of water.
Based on Bernoulli equation, but we ignore velocity head in groundwater flow.
Total head consists of elevation head and pressure head.
Head is constant in a static water column.
“Potentiometric surface” is a map of hydraulic head which may (for an unconfined aquifer)
or may not (for an unconfined aquifer) correspond to the actual groundwater surface.
hz
P
w g
 z 
 Head is a scalar quantity.
Darcy’s Law
(h2  h1 )
h
A  K
A
L
L
Q
h
q   K
 Ki
A
L
 q = specific discharge – a flux (volume of water per unit area per unit time)
 Specific discharge has units of velocity (L/T), but is not the flow rate of water.
Q  K
CEVE 518
Groundwater Flow and Contaminant Transport
Test 1 Review and Study Sheet
 Flow rate of water is seepage velocity = v = q/ne.
 Specific discharge and seepage velocity are vector quantities.
 In differential form:
dh
dx
 Aquifer flux (U) is flow per unit width of aquifer and has same units as transmissivity
(L2/T):
q  K
Q
Q

A wb
Q
Q
U  qb 
b
wb
w
q
Hydraulic Conductivity
 Can be separated into the product of two multiples, one reflecting fluid properties and one
reflecting properties of the porous medium:
K k
g

 k is intrinsic permeability and has units L2. Intrinsic permeability can be related to
porosity and average particle diameter through the Kozeny-Carman equation:
k
n 3 d p2
180(1  n ) 2
 An effective hydraulic conductivity can be calculated for flow parallel or normal to
layering:
K i bi
o Effective K for flow in parallel layers: K e 
b

b
bi
Ki
 For mixtures of parallel and normal flow in layered media, use the geometric average.
o
Effective K for flow normal to layering: K e 
Streamline Refraction
 Angle taken between flow line and y-axis.

CEVE 518
Groundwater Flow and Contaminant Transport
Test 1 Review and Study Sheet
q1 K 1 sin 2

q 2 K 2 sin1
K1
tan 1

K 2 tan  2
 Implication – flow in aquifers is mostly horizontal; flow in aquitards is mostly vertical.
General Equations of Groundwater Flow
 Mass balance on R.E.V. gives:

h
   (  q )   Ss
t
Ss   g (  n )
 Meaning: the change is storage in the R.E.V. is the difference between water flowing into
and out of the R.E.V.
o
o
o
First term of Ss is water storage due to compression of porous medium.
Second term of Ss is water storage due to compression of water.
Storage medium compression is much larger than water compression.
 If water is incompressible (a good assumption for most groundwater problems):

h
   q  Ss
t
 Substituting Darcy’s Law for q:
  K  h  Ss
h
t
 For an isotropic medium oriented along principle axes of K:
 
h   
h   
h 
h
 K y
 
K x

Kz
  Ss
x 
x  y 
y  z 
z 
t
 For a homogenous, isotropic medium, K is constant and can be factored out and brought
to RHS of equation:
 2h
x
2

 2h
y
2

 2h
z
2
  2h 
Ss h
(transient diffusion equation)
K t
 For a confined aquifer, Ss = S/b, so:
2h 
S h
(where T = Kb; confined aquifer only)
T t
CEVE 518
Groundwater Flow and Contaminant Transport
Test 1 Review and Study Sheet
 At steady-state, the RHS =0 so we have:
 2 h  0 (Laplace’s equation)
Application of General Groundwater Flow Equation to 1-D Flow Problems
Confined Aquifer

h
   q  Ss
t
 Assume:
1. Steady-state.
2. Homogeneous and isotropic medium.
3. 1-D flow.
d 2h
dx
2

d dh
0
dx dx
 Integrate twice to get:
h  C1x  C 2
where C1 and C2 are constants of integration.
 Use boundary conditions to get values of C1 and C2:
o
at x=0, h=h1
o
at x=L, h=h2
 Then:
h
(h2  h1 )
x  h1 (head distribution in a confined aquifer).
L
 Flux in confined aquifer:
( h2  h1 )
L
U  qb
( h  h1 )
q  T 2
L
U  K
Unconfined Aquifer
 Must use Dupuit-Forchheimer assumptions because saturated thickness is not constant:
o All flow is horizontal;
o Discharge is proportional to slope of water table.
CEVE 518
Groundwater Flow and Contaminant Transport
Test 1 Review and Study Sheet


h
  U  Sy
; U  Kh
t
 In 1-D, SS, head distribution is:
h2 
(h2 2  h12 )
2
x  h1
L
 Flux in an unconfined aquifer:
U  Kh
dh
dh
K dh 2
1 dh 2
(applied trick to turn h
into
).

dx
dx
2 dx
2 dx
2
2
dh 2 (h2  h1 )
.

dx
L
2
2
K (h2  h1 )
2
L
U  qh
(note that, unlike a confined aquifer, q is a function of x).
U
q  Kh
(h2 2  h12 )
L
Unconfined Aquifer with Recharge
h2  h0
x div 
2
 hL 2  h0 2
W 2 W

x  L

K
L
 K


 x


L
K

(hL 2  h0 2 ) Point of maximum head (the dividing point for flow).
2 2WL
U  Wx 
WL K

(hL 2  h0 2 )
2
2L
Well Hydraulics and Principle of Superposition
 Working in radial coordinates.
 Application of mass balance to a cylinder results in:
 Q  U r  2T (Ur is radial aquifer flux (has negative sign when flow is directed toward
well.
 Darcy’s Law: U r  T
dh
dr
CEVE 518
Groundwater Flow and Contaminant Transport
Test 1 Review and Study Sheet
h2  h1 
r 
Q
ln 2  (Theim equation for steady-state flow in confined aquifer).
2 T  r1 
 In terms of drawdown: s1  s 2 
h2 2  h12 
Q  r2 
ln  (Note reversal of order on s).
2T  r1 
Q  r2 
ln  (Theim equation for steady-state flow in unconfined aquifer).
 K  r1 
 Principle of superposition – can add the drawdown from multiple wells to determine total
drawdown at any given location.
 Example – drawdown at some point (x,y) from wells located distances r1, r2 and r3 away
and pumping at rates Q1, Q2 and Q3, and aquifer has head h0 at distance R from wells:
h x,y  hR 
Q1  r1  Q2  r 2  Q3  r3 
ln  
ln  
ln 
2T  R  2T  R  2T  R 
 Principle can be applied in 1-D or 2-D.
CEVE 518
Groundwater Flow and Contaminant Transport
Test 1 Review and Study Sheet
WHAT TO EXPECT ON TEST 1
1. About 5 definitions.
2. Several short answer questions to test your conceptual understanding of the material.
3. A couple of short, simple problems.
4. Two more complex problems.
5. Bonus – problem or short answer question(s).
Potential subject areas for problems (simple and complex) include but are not limited to:
 Calculations using relationships between porosity, soil densities, water contents. and
other soil properties.
 Calculations of hydraulic head and piezometer elevations.
 Hydrologic cycle (water balance) calculations.
 Calculation of hydraulic conductivity using Kozeny-Carman theory.
 Hydraulic conductivity and flow in layered porous media.
 Streamline refraction.
 Aquifer storage.
 Calculation of head distribution and groundwater flow rates in 1-D confined and
unconfined aquifers.
 Groundwater flow and well hydraulics in 1-D and 2-D – Theim equation and application of
principle of superposition.
No derivations.
No calculus problems.
No deliberate trick questions.
Problems will be of a practical nature similar to those in homework problems, but may have a
unique aspect to test the depth of your understanding.