Lin S.D. Water and Wastewater Calculations Manual

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3. Draw a best-fit straight line.

4. Extend the line to the zero-drawdown and read the value of the

intercept, r

Example: A water supply well is pumping at a constant discharge rate of

1000 m

/d (11,000 gpm). It happens that there are five observation wells

available. After pumping for 3 h, the drawdown at each observation well is

recorded as below. Estimate transmissivity and storativity of the aquifer

using the distance-drawdown method.

solution:

Step 1. Plot the distance-drawdown data on semilog paper as shown in

Fig. 3.7

Step 2. Draw a best-fit straight line over the observed data and extend the

line to the x-axis

Step 3. Read the drawdown value for one log cycle

From Fig. 3.7, for the distance for a cycle from 4 to 40 m, the value of the draw-

down, then ⌬(h

– h) is read as 2.0 m (2.8 m – 0.8 m).

Step 4. Read the intercept on the X axis for r

⫽ 93 m

Step 5. Determine T and S by Eqs. (3.41) and (3.43)

⫽ 183 m

Time of pumping: t ⫽ 3 h/24 h/d

⫽ 0.125 days

⫽ 0.006

S 5

2.25Tt

2.25 3 183 m

/d 3 0.125 days

s93 md

T 5

0.366Q

⌬sh

2 hd

0.366 3 1000 m

2.0 m

Distance

m ft Drawdown, m

3 10 3.22

7.6 25 2.21

20 66 1.42

50 164 0.63

70 230 0.28

Groundwater 205

5.4 Slug tests

In the preceding sections, the transmissivity T and storativity S of the

aquifer and permeability K of the soil are determined by boring one or

two more observation wells. Slug tests use only a single well for the

determination of those values by careful evaluation of the drawdown

curve and information of screen geometry. The tests involve either rais-

ing or lowering the water level in the well and measuring the return to

a static water level as a function of time.

206 Chapter 3

Figure 3.7 Plot of observed distance-drawdown data.

A typical test procedure requires introducing an object to record the

volume (the slug) of the well. The Hvorslev (1951) method using a

piezometer in an confined aquifer is widely used in practice due to it

being quick and inexpensive. The procedures of conducting and ana-

lyzing the Hvorslev test (Fig. 3.8) are as follows:

1. Record the instantaneously raised (or lowered) water level to the

static water level as H

2. Read subsequently changing water levels with time as h. Thus h ⫽

at t ⫽ 0.

3. Measure the final raised head as H at infinite time.

4. There is a relationship as

(3.45)

where

(3.46)

⫽ Hvorslev-defined basic time lag

F ⫽ shape factor

H 2 h

H 2 H

5 e

2t/T

Groundwater 207

Figure 3.8 Hvorslev slug test.

5. Calculate ratios (H – h)/(H – H

) as recovery.

6. Plot on semilogarithmic paper (H – h)/(H – H

) on the logarithmic

scale versus time on the arithmetic scale.

7. Find T

at recovery equals 0.37 (37% of the initial change caused by

the slug).

8. For piezometer intake length divided by radius (L/R) greater than 8,

Hvorslev evaluated the shape factor F and proposed an equation for

hydraulic conductivity K as

(3.47)

where K ⫽ hydraulic conductivity, m/d or ft/d

r ⫽ radius of the well casing, cm or in

R ⫽ radius of the well screen, cm or in

L ⫽ length of the well screen, cm or in

⫽ time required for water level to reach 37% of the initial

change, s

Other slug test methods have been developed for confined aquifers

(Cooper et al., 1967; Papadopoulous et al., 1973; Bouwer and Rice, 1976).

These methods are similar to Theis’s type curves in that a curve-matching

method is used to determine T and S for a given aquifer. Afamily of type

curves H

versus Tr/r

were published for five values of the variable,

(defined as (r

) S, to estimate transmissivity, storativity, and hydraulic

conductivity.

The Bouwer and Rice (1976) slug test method is most commonly used

for estimating hydraulic conductivity in groundwater. Although the

method was originally developed for unconfined aquifers, it can also be

applied for confined or stratified aquifers if the top of the screen is some

distance below the upper confined layer. The following formula is used

to compute hydraulic conductivity:

(3.48)

where K ⫽ hydraulic conductivity, cm/s

r ⫽ radius of casing, cm

, y

⫽ vertical difference in water levels between inside and

outside the well at time t ⫽ 0, and t ⫽ t, m

R ⫽ effective radius distance over which y is dissipated, cm

K 5

ln sR/r

K 5

lnsL/Rd

2LT

208 Chapter 3

⫽ radius distance of undisturbed portion of aquifer from well

centerline (usually r plus thickness of gravel).

L ⫽ length of screen, m

t ⫽ time, s

Example 1: The internal diameters of the well casing and well screen are

10 cm (4 in) and 15 cm (6 in), respectively. The length of the well screen is 2

m (6.6 ft). The static water level measured from the top of the casing is 2.50

m (8.2 ft). A slug test is conducted and pumped to lower the water level to 3.05

m (10 ft). The time-drawdown h in the unconfined aquifer is recorded every

3 s as shown in the following table. Determine the hydraulic conductivity of

the aquifer by the Hvorslev method.

solution:

Step 1. Calculate (h – H

)/(H – H

)

Given: H

⫽ 2.50 m, H ⫽ 3.05 m

Then H – H

⫽ 3.05 m – 2.50 m ⫽ 0.55 m.

Step 2. Plot t versus (h – H

)/(H – H

) on semilog paper as shown in Fig. 3.9,

and draw a best-fit straight line

Step 3. Find T

From Fig. 3.9, read 0.37 on the (h – H

)/(H – H

) scale and note the time for

the water level to reach 37% of the initial change T

caused by the slug. This

is expressed as T

. In this case T

⫽ 16.2 s

Step 4. Determine the L/R ratio

R ⫽ 15 cm/2 ⫽ 7.5 cm

L/R ⫽ 200 cm/7.5 cm ⫽ 26.7 ⬎ 8

Thus Eq. (3.47) can be applied

Time t, s h, m h – H

, m (h – H

)/0.55

0 3.05 0.55 1.00

3 2.96 0.46 0.84

6 2.89 0.39 0.71

9 2.82 0.32 0.58

12 2.78 0.28 0.51

15 2.73 0.23 0.42

18 2.69 0.19 0.34

21 2.65 0.15 0.27

24 2.62 0.12 0.22

27 2.61 0.10 0.18

30 2.59 0.09 0.16

Groundwater 209

Step 5. Find K by Eq. (3.47)

r ⫽ 10 cm/2 ⫽ 5 cm

⫽ (5 cm)

ln 26.7/(2 ⫻ 200 cm ⫻ 16.2 s)

⫽ 0.0127 cm/s

⫽ 0.0127 cm/s ⫻ (1 m/100 cm) ⫻ 86,400 s/d

⫽ 11.0 m/d

⫽ 36 ft/d

Example 2: A screened, cased well penetrates a confined aquifer with gravel

pack 3.0-cm thickness around the well. The radius of casing is 5.0 cm and the

screen is 1.2 m long. A slug of water is injected and water level raised by m. The

effective radial distance over which y is dissipated is 12 cm. Estimate hydraulic

conductivity for the aquifer. The change of water level with time is as follows:

t, s y

, cm t,s y

, cm

1 30 10 4.0

2 24 13 2.0

3 17 16 1.1

4 14 20 0.6

5 12 30 0.2

6 9.6 40 0.1

8 5.5

K 5

ln sL/Rd

2LT

210 Chapter 3

Figure 3.9 Plot of Hvorslev slug test results.

solution:

Step 1. Plot values of y versus t on semilog paper as shown in Fig. 3.10

Draw a best-fit straight line. The line from y

⫽ 36 cm to y

⫽ 0.1 cm covers

2.5 log cycles. The time increment between the two points is 26 s.

Step 2. Determine K by Eq. (3.48), the Bouwer and Rice equation

r ⫽ 5 cm

R ⫽ 12 cm

⫽ 5 cm ⫹ 3 cm ⫽ 8 cm

⫽ 9.56 ⫻ 10

–3

cm/s

6 Groundwater Contamination

6.1 Sources of contamination

There are various sources of groundwater contamination and various

types of contaminants. Underground storage tanks, agricultural activity,

municipal landfills, abandoned hazardous waste sites, and septic tanks

s5 cmd

lns12 cm/8 cmd

2s120 cmd

26 s

36 cm

0.1 cm

K 5

ln sR/r

Groundwater 211

Figure 3.10 Plot of y

versus t.

are the major threats to groundwater. Other sources may be from indus-

trial spill, injection wells, land application, illegal dumps (big problem

in many countries), road salt, saltwater intrusion, oil and gas wells,

mining and mine drainage, municipal wastewater effluents, surface

impounded waste material stockpiles, pipelines, radioactive waste dis-

posal, and transportation accidents.

Large quantities of organic compounds are manufactured and used by

industries, agriculture, and municipalities. These man-made organic

compounds are of most concern. The inorganic compounds occur in

nature and may come from natural sources as well as human activities.

Metals from mining, industries, agriculture, and fossil fuels also may

cause groundwater contamination.

Types of contaminants are classified by chemical group. They are

metals (arsenic, lead, mercury, etc.), volatile organic compounds

(VOCs) (gasoline, oil, paint thinner), pesticides and herbicides, and

radionuclides (radium, radon). The most frequently reported ground-

water contaminants are the VOCs (Voelker, 1984; Rehfeldt et al.,

1992).

Volatile organic compounds are made of carbon, hydrogen, and oxygen

and have a vapor pressure less than one atmosphere. Compounds such

as gasoline or dry cleaning fluid evaporate when left open to the air.

They are easily dissolved in water. There are numerous incidences of

VOCs contamination caused by leaking underground storage tanks.

Groundwater contaminated by VOCs poses cancer risks to humans either

by ingestion of drinking water or inhalation.

6.2 Contaminant transport pathways

The major contaminant transport mechanisms in groundwater are

advection, diffusion, dispersion, adsorption, chemical reaction, and

biodegradation. Advection is the movement of contaminant(s) with the

flowing groundwater at the seepage velocity in the pore space and is

expressed as Darcy’s law:

(3.49)

where v

⫽ seepage velocity, m/s or pps

K ⫽ hydraulic conductivity, m/s or fps

n ⫽ porosity

dh ⫽ pressure head, m or ft

L ⫽ distance, m or ft

Equation (3.49) is similar to Eq. (3.10b).

212 Chapter 3

Diffusion is a molecular-scale mass transport process that moves

solutes from an area of higher concentration to an area of lower con-

centration. Diffusion is expressed by Fick’s law:

(3.50)

where F

⫽ mass flux, mg/m

⭈ s or lb/ft

⭈ s

⫽ diffusion coefficient, m

/s or ft

dc/dx ⫽ concentration gradient, mg/(m

⭈ m)

or lb/(ft

⭈ ft)

Diffusive transport can occur at low or zero flow velocities. In a tight soil

or clay, typical values of D

range from 1 to 2 ⫻ 10

/s at 25⬚C (Bedient

et al. 1994). However, typical dispersion coefficients in groundwater are

several orders of magnitude greater than that in clay.

Dispersion is a mixing process caused by velocity variations in porous

media. Mass transport due to dispersion can occur parallel and normal

to the direction of flow with two-dimensional spreading.

Sorption is the interaction of a contaminant with a solid. It can be

divided into adsorption and absorption. An excess concentration of con-

taminants at the surfaces of solids is called adsorption. Absorption refers

to the penetration of the contaminants into the solids.

Biodegradation is a biochemical process that transforms contami-

nants (certain organics) into simple carbon dioxide and water by microor-

ganisms. It can occur in aerobic and anaerobic conditions. Anaerobic

biodegradation may include fermentation, denitrification, iron reduction,

sulfate reduction, and methane production.

Excellent and complete coverage of contaminant transport mecha-

nisms is presented by Bedient et al. (1994). Theories and examples are

covered for mass transport, transport in groundwater by advection, dif-

fusion, dispersion, sorption, chemical reaction, and bio-degradation.

Some example problems of contaminant transport are also given by

Tchobanoglous and Schroeder (1985). Mathematical models that analyze

complex contaminant pathways in groundwater are also discussed else-

where (Canter and Knox, 1986; Willis and Yeh, 1987; Canter et al., 1988;

Mackay and Riley, 1993; Smith and Wheatcraft, 1993; Watson and

Burnett, 1993; James, 1993; Gupta, 1997).

The transport of contaminants in groundwater involves adsorption,

advection, diffusion, dispersion, interface mass transfer, biochemical

transformations, and chemical reactions. On the basis of mass balance,

the general equation describing the transport of a dissolved contaminant

through an isotropic aquifer under steady-state flow conditions can be

mathematically expressed as (Gupta, 1997).

52D

Groundwater 213

(3.51)

where c ⫽ solute (contaminant in liquid phase)

concentration, g/m

S ⫽ concentration in solid phase as mass of

contaminant per unit mass of dry soil, g/g

t ⫽ time, day

␳

⫽ bulk density of soil, kg/m

␸ ⫽ effective porosity

, k

⫽ first-order decay rate in the liquid and soil phases,

respectively, day

–1

x, y, z ⫽ Cartesian coordinates, m

, D

⫽ directional hydrodynamic dispersion coefficients, m

, V

⫽ directional seepage velocity components, m/d

There are two unknowns (c and S) in Eq. (3.51). Assuming a linear

adsorption isotherm of the form

S ⫽ K

c (3.52)

where K

⫽ distribution coefficient due to chemical reactions and bio-

logical degradation, and substituting Eq. (3.52) into Eq. (3.51), we obtain

(3.53)

where R ⫽ 1 ⫹ k

(␳

/␸)

⫽ retardation factor which slows the movement of

solute due to adsorption

k ⫽ k

⫹ k

(␳

/␸)

⫽ overall first-order decay rate, day

–1

The general equation under steady-state flow conditions in the x direc-

tion, we modify from Eq. (3.53).

6.3 Underground storage tank

There are 3 to 5 million underground storage tanks (USTs) in the United

States. It is estimated that 3% to 10% of these tanks and their associ-

ated piping systems may be leaking (US EPA 1987). The majority of

1 kc 5 D

1 D

2 V

5 D

1 D

2 V

1 ck

1 Sk

214 Chapter 3