4-1

4. Groundwater ResourcesMajority (97 %) of unfrozen fresh water on earth exists as groundwater. In comparison to surface water,- groundwater is available all year around - groundwater is mostly invisible- groundwater flows very slowlyIt is also important to recognize that groundwater interacts with rivers and lakes.

Introductory definitions (D&L, p. 194-197)water table: water level in an open holecapillary fringe: the soil is saturated, but water is held by

capillary force and does not flow into an open hole

recharge: addition of water to the water tabledischarge: removal of water from the storage; seepage

into lakes/streams, evapotranspiration, etc.

D&L, Fig. 7-1

4-2

aquifer: geological formation having high permeability and significant storage capacity

aquiclude: formation unsuitable as an aquifer, mostly due to low permeability

confined aquifer: confined by aquicludes

unconfined aquifer: upper surface is the water table

perched aquifer: isolated zone of saturated material above a shallow aquiclude

D&L, Fig. 7-3

4-3

Hydraulic head and Darcy’s law

h = z + ψh : hydraulic head [m]z : elevation [m]ψ : pressure head [m]

zhK

zzhhK

AQq

∆∆

−=−−

−==12

12

A : cross sectional area [m2]K : hydraulic conductivity [m s-1]q: specific discharge [m s-1]

The flow is driven by gravity and pressure. Water flows from high h to low h.

Darcy’s law in the field setting

Hydraulic head is measured by a piezometer, which is a well having a short screen.

If the flow is vertical, we can calculate the flow rate using two piezometers;

q = -K ∆h/∆z =-K(h2 - h1)/(z2 - z1)Suppose we measured;

h1 = 985 m, h2 = 987 m, z1 = 970 m, z2 = 975 mIf K = 10-9 m/s, what is q?The negative sign of q indicates that the flow is downward.

ψ1

h1

z1

Q

Q

h2z2

ψ2

h2

h1

z2

z1

z

4-4

WT well

piezometer

Water table and hydraulic head

A water table (WT) well has a long screen that intersects the water table. In contrast, a piezometer has a short screen that measures the the hydraulic head at a point.

A water table map is constructed from the WT data in many wells.

Recall that h = ψ + z and that ψ = 0 at the WT. ∴ h = z at the WT

987

985

975z

=dzdh

The WT usually follows the topography. Groundwater tends to flow from uplands (recharge area) to lakes and streams (discharge area).

For example, Nose Hill is a recharge area and Bow Valley is a discharge area.

WT = 1075 m

WT = 1080 m82

81

77

78

74

73

0 1 km

N

4-5

Withdrawal of water from unconfined aquifers

Water comes from the partial drainage of pore space near the water table (WT), which causes the WT to go down. We express the amount of water pumped per unit area of aquifer as a depth of water.

e.g. 1,000 m3 over 10,000 m2 is 0.1 m.Specific yield (Sy) is defined by;

WT

pumping

Sy = [water pumped (m)] / [WT drop (m)]

If a material is completely drained, Sy is equal to the porosity of the material. Usually Sy is less than the porosity.

See D&L (Fig. 7-7) for the range of Sy.

The WT map can be used to estimate the horizontal direction of groundwater flow. If the material is reasonably homogeneous, groundwater flows in the direction of the steepest slope; i.e. normal to the WT contour.

What is the flow direction in the map on the last page?

Suppose K = 10-5 m/s. What is the horizontal q?

4-6

Storage mechanism in confined aquifers

A confined aquifer is conceptually similar to a pressurized rubber balloon. A small amount of water removal may cause a large pressure drop within a confined aquifer.We define the storativity (S) of an aquifer by;

S = [specific storage (m-1)] × [thickness of aquifer (m)]Specific storage (no confusion with Sy) is related to the compressibility of the material, and generally is in the range of 10-4 - 10-5 m-1 for sands.The water level drop in an aquifer and the amount of water pumped are related by;

[water pumped (m)] / [water level drop (m)] = S

Example

In many prairie farms, water supply comes from an isolated sand lens (aquifer) confined within clay-rich glacial till (aquiclude). Suppose the aquifer has a thickness of 5 m and a spatial extent of 1 km2.

pumping

Assuming that specific storage is 10-4 m-1,S = 10-4 m-1 × 5 m = 0.0005

The farmer pumps 1500 m3 in one year, which is 0.0015 m per unit area of the aquifer. This would cause the water level in the well to drop by 3 m, if the aquifer was not recharged by the flow from the aquiclude.

4-7

Transmissibility

The water-transmission property of aquifers (not aquifer materials) is given by transmissibility (T, m2 s-1), defined as:

T = Kywhere y is the aquifer thickness.

Transmissibility is usually determined for large volumes of aquifer in situ by a pumping test.

Measurement of hydraulic conductivity

(1) Laboratory permeameter

Pack a column, measure flow rate,and use Darcy’s law to calculatehydraulic conductivity.

(2) Piezometer response test

Raise the water level in a piezometer andmonitor the decay of water level to theequilibrium position.

(3) Pumping test

Pump water from an aquifer and observe how fast and howdeep the hydraulic head goes down in the aquifer.

Scale of the measurement?

heq

h

4-8

Application of Darcy’s law (D&L, p.211-215)

Specific discharge in a confined aquifer:

ql

y

w

h2

xhKq

∆∆

−=

Total flow rate:

lhhwT

lhhwyK

qwyQ

21

12

−=

−−=

=

D&L uses q [m2/s] to denote the flow per unit width of the aquifer. In this note, we follow the standard notation;

q : specific discharge [m/s] = flow rate per unit area.

T: transmissibility [m2/s]

D&L, Fig. 7-15

In unconfined aquifers, we may use Dupuit-Forcheimer equation when the slope of the water table is reasonably small:

)(2

21

20 hh

xwKQ −=

x

h1

4-9

Example:

Hydraulic conductivity of fluvial sand is 10-4 m/s.

Groundwater flow rate per unit length of stream section?

clay-rich till

fluvial sand

elev

atio

n (m

)

960

970

980

distance (m)0 200

977975

100

w

4-10

Groundwater “outcrops” at lakes, streams, and springs.The direction of flow is most conveniently indicated by the water table map.

Interaction of groundwater with surface water

What is the elevation of stream water surface at A?

gaining stream

A

1084

1082

1080

water table contours

1084

1082

1080

loosing stream

Groundwater has several important ecological functions:(1) It maintains the baseflow during dry periods.(2) It regulates the temperature of water around springs.(3) It brings nutrients (carbon, nitrogen, etc.) into the stream.(4) support stream-side (riparian) vegetationIn arid and semi-arid regions intermittent streams and ponds contribute significantly to recharging shallow groundwater.Reading assignment: Ground water and surface water: A single resource.

(http://water.usgs.gov/pubs/circ/circ1139)

Read the section “Hydrologic cycle and interactions of groundwater and surface water” from the beginning of the section up to Figure 18.

4-11

Groundwater budget (D&L, p.219-223)

Input - Output = Change of StorageQpump Qevt

QrchQsout

Qsin

Input = recharge (Qrch) + seepage from streams (Qsin)Output = evapotranspiration (Qevt) + pumpage (Qpump)

+ seepage to streams (Qsout)Storage change = change in water table (unconfined)

hydraulic head (confined)

Qrch + Qsin - Qevt - Qpump - Qsout = Storage change

Pumping will cause:(1) decline of water table and hydraulic head.

This stage is called ‘aquifer storage depletion’.

Prolonged pumping will also cause:

(2) increased recharge and seepage from streams.(3) decreased evapotranspiration and seepage to streams.This stage is called ‘surface water depletion’ or ‘capture’.

4-12

0

20

40

60

80

100

0.01 0.1 1 10 100time (year)

Gro

undw

ater

with

draw

al

(%)

aquifer storage depletion

surface water capture

In the early stage, almost all of the pumped water comes from aquifer storage. More surface water is captured in the later stage. The system will eventually reach the new equilibrium, where all of the pumped water comes from the capture.

Sustainable yield refers to the pumping rate that keeps the negative effects of aquifer storage depletion and capture within a tolerable limit.

What are the potential negative effects?

How do we predict the sustainable yield?

4-13

Case study: Dalmeny Aquifer, SaskatchewanRef: G. Fortin et al., 1991. Journal of Hydrology, 126: 265-292.

Fig. 1. Regional setting of the Dalmeny aquifer study area.

Fig. 3 Regional cross-section of the study area. Data obtained from boreholes.

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This is one of rare cases, where the rates of recharge and discharge are characterized for a regional aquifer to a reasonable accuracy.Discharge from springs = 1.2 × 106 m3/yr.Area of northern half of the aquifer = 300 km2

∴ 4 mm/yr averaged over the aquiferPumping from municipal/farm wells = 0.4 × 106 m3/yr

= 1 mm/yr∴ average recharge rate = 1 + 4 = 5 mm/yr.

1-10 mm/yr represents a common range of the recharge rates of prairie aquifers.

What is the sustainable yield?

Fig. 6. Potentiometric surface, springs, and regional flow.

4-15

Pumping and the cone of depression (D&L, p.223-225)

When water is pumped from a new well, initial withdrawal exceeds the rate at which groundwater flows into the vicinity of the well, which leads to the formation of the cone of depression or drawdown cone.

The cone of depression keeps deepening and expanding until a new equilibrium is reached, at which the pumping rate is balanced by increased recharge rate.

D&L, Fig. 7-21

Analysis of drawdown

Common methods of analysis assume that the aquifer is ideal referring to the following conditions:

h = h0

r →∞

Q1. Horizontal and infinitely large.2. Perfectly confined by

impermeable top and bottom.3. Constant transmissibility and

storativity.

4-16

4. Pumping at a constant rate Q.5. No other pumping wells in the neighborhood.6. The pumping well penetrates the entire aquifer thickness.

When all these conditions are satisfied, the drawdown is given by the Jacob formula.

SrTt

TQh 2

25.2log4

3.2π

=∆

∆h : drawdown [m]Q : pumping rate [m3/s]T ( = Ky) : transmissibility [m2/s]S : storativityt : time since the start of pumping [s]r : distance from well center [m]

Q

∆h

T, S

r

y

Suppose we want to drill a well in a sand aquifer and pump it at 500 m3/day. The aquifer has T = 10-2 m2/s, S = 10-3. There is another well owned by a farmer, located 3 km away. After 20 years of pumping, will the drawdown cone reach the farmer’s well?

This method only considers aquifer storage depletion. What will happen in reality?

4-17

“Leaky” aquiclude and land subsidence

When an aquifer is recharged by over and underlying aquicludes, water is squeezed out of the aquicludes that are usually clay layers. Withdrawal of water from the clay layers causes them to consolidate, which may result in land subsidence.

Examples: Mexico City, Tokyo, Venice, etc.

D&L, Fig. 1-5

Schematic geologic cross section beneath the Venetian lagoon. The dotted area represents aquifers

D&L, Fig. 1-6

Calculated subsidence of the land surface.Curve 1: Present pumping rateCurve 4: Closure of all wells

4-18

Specific capacity and well loss

well loss

Q

The Jacob formula suggests that ∆h is proportional to Q, at a given time (t) and location (r).

SrTt

TQh

ww 2

25.2log4

3.2π

=∆

where rw is the radius of the well casing.

We may attempt to use the Jacob formula to predict the drawdown (∆hw) within the pumping well.

The drawdown within the pumping well is larger than the cone of depression itself due to well loss, which is the extra drawdown due to the flow resistance through the screen.

Specific capacity accounts for the effects of the cone of depression and well loss, which is defined by;

specific capacity [m2/s] = Q / ∆h

It is a common practice to run a step pumping test to determine the specific capacity, when a new well is drilled.

0

5

10

150 5000 10000t (sec)

h 0 -

h (m

)

∆h1

∆h2

Specific capacity may not be constant, because well loss tends to increase with Q. It may change with time, too, due to chemical/biological precipitation on the well screen.

4-19

Estimating T from pumping test data

Accurate estimation of transmissibility requires a carefully designed pumping test with multiple observation wells. Such a test is very expensive and may not be feasible for practical studies with limited budget.

We can make a rough estimate of T using the specific capacity data, even though the validity of this approach is somewhat questionable.

Assumptions:- All assumptions for the ideal aquifer are satisfied.- Well loss has a relatively minor effect.- Pumping test has a long enough duration to reach

equilibrium.

Under these assumptions, an approximate T is give by:

T ≅ 1.22 Q / ∆h (Misstear, 2001. Hydrogeology Journal, 9: 125-126)

Example:

A 24-hr pumping test was conducted at Q = 60 L/min. The water level before the test was 20-m below the ground surface, and was 47-m below the surface at the end of the test.

T =

4-20

http://www3.gov.ab.ca/env/water/groundwater/index.html

The information of groundwater wells in Alberta is listed in Alberta Environment web page.

It should be noted that the data are based on the well drilling reports submitted by private contractors with essentially no quality control – use it carefully!