university of arizona department of hydrology and water...

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University of Arizona

Department of Hydrology and Water Resources

Dr. Marek Zreda

HWR431/531 - Hydrogeology

Midterm exam - 18 October 2000

Open books and notes

The test contains 5 problems on 3 pages. Read the entire test before you start.

Problem 1. (15 points, 5 point each)

(a) Describe two geological processes that increase the porosity, pore size and permeability of aquifers. Use one short paragraph for each process.

(b) Karstic aquifers, with large solution channels and caverns are usually regarded in subsurface hydrology as ordinary porous media. Under what conditions is this approach justified?

(c) Design (conceptually only) a laboratory experiment to determine the hydraulic conductivity tensor of a sample. Make your design efficient (i.e., use the smallest possible number of sepa-rate experiments/steps/tasks). Describe these experiments/steps/tasks. In the end, your results should be sufficient to define the components of the hydraulic conductivity tensor.

Problem 2. (20 points, 10 points each)

Water enters the L-shaped confined aquifer (figure) at point A and leaves at point C in the form of a spring. Assume steady state flow. Do the following (in symbolic form only; we don’t have any numbers):

(a) Determine the piezometric head at an observation well located at B.

(b) Under what conditions will the well at B be an artesian well?

h1

h2

L2 L1

a

d

spring

b1 b2

B

K1K2

A

C

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Problem 3. (20 points)

Given is a specific discharge vector q

and a gradient vector J

in two-dimensional flow in the x-y space. Do the following:

(a) Determine the hydraulic conductivity tensor K (this double underbar is the same as double overbars before) if x and y are principal directions. (10 points)

(b) Determine the hydraulic conductivity Kq in the direction of specific discharge q. (5 points)

(c) Determine the hydraulic conductivity KJ in the direction of the gradient J. (5 points)


In a confined aquifer (figure) the thickness varies linearly between points A (thickness bA) and B (thickness bB (<bA). Points A and B are on the same flow line. The pie-zometric heads are hA and hB, respec-tively, and the distance between them is L. Assume constant flow Q. Do the follow-ing:

(a) Derive a symbolic expression for the discharge Q in the aquifer assuming that the flow is in the direction of aqui-fer axis. (10 points)

(b) Draw (qualitatively) the piezometric line between A and B for two cases: (1) hA>hB and (2) hA<hB. (5 points)

qqx

qy

0.010

0.005 m/d==

JJx

Jy

0.01

0.02==

��yyyyyyyyyy

impermeable

��

yyyyyyyyyyyy

B AbB bA

L

impermeable

impermeable

hB

hA

flow direction

can be either way

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Equipotentials in the figure are for steady-state flow between an injection well and a pumping well (this is called a closed-cell flow system). The aquifer thickness is 10 m. Do the following:

(a) Complete the flow net; use arrows to indicate the direction(s) of flow. (5 points)

(b) If the pumping rate and injection rates are the same and are 1000 m3 d-1, calculate the aquifer transmissivity and the hydraulic conductivity. (10 points)

(c) A chemical tracer injected in the injection well was detected in the pumping well after 1 day. (assume that water leaves injection well at contour 26 m, and enters the pumping well at con-tour 14 m). Determine the porosity of the aquifer. What kind of porosity is this? (10 points)

(d) If the tracer injection continues for 2 days and then injection of clean water resumes, how late would you expect the tracer to be detected in the pumping well? Why? (5 points)

X (m)

0 10 20 30 40 50 60

Y (

m)

0

10

20

30

40

50

60

14

15

26

25

24

23

22

21

16

17

20

18

19

Contours in meters

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Dr. Marek Zreda













h1

h2

L2 L1

a

d

spring

b1 b2

B

K1K2

A

C