Group Title: Transactions (Society of Mining Engineers of AIME)
Title: The interdependence of economic and hydrologic criteria in planning water resources development
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 Material Information
Title: The interdependence of economic and hydrologic criteria in planning water resources development
Uniform Title: Transactions (Society of Mining Engineers of AIME)
Physical Description: p. 15-24 : ill. ; 29 cm.
Language: English
Creator: Mao, S. W
Hildebrand, Peter E
Crain, C. N
Publisher: Society of Mining Engineers, AIME
Place of Publication: New York?
Publication Date: 1969
Subject: Water-supply -- Management -- Pakistan   ( lcsh )
Water resources development -- Planning -- Pakistan   ( lcsh )
Water-supply -- Economic aspects -- Pakistan   ( lcsh )
Spatial Coverage: Pakistan
Statement of Responsibility: by S.W. Mao, P. E. Hildebrand, and C.N. Crain.
General Note: Originally published in Transactions, Vol. 244, March 1969.
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Bibliographic ID: UF00080639
Volume ID: VID00001
Source Institution: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 154301746

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by S. W. Mao, P. E. Hildebrand and C. N. Crain

Hydrologic and economic criteria figure in many ob-
vious ways in water resources development, but they
are rarely linked quantitatively, and most of the ap-
plications are pertinent only to the case in point. In
the preparation of a regional plan for the massive
program of groundwater development in the Punjab,
situations have arisen where the choice among two or
more alternatives was made by analyzing the economic
implications of critical hydrologic parameters. Two
of these situations which are of more or less general
interest are described herein. The first involves
basic development policy, i.e., the question of
whether groundwater development should be based on
the demand of the economy, or the conservation con-
cept of safe yield. The analysis demonstrated that
mining of groundwater is clearly indicated for areas
where alternative supplies are unavailable. The sec-
ond problem involves integrating hydrologic data into
an economic model to determine optimum well design.
From an analysis of all pertinent factors, a simple
nomograph was derived for determining well specifi-
cations on site during construction. The nomograph
can be modified for use in any alluvial terrain.

In the Northern Zone of the Indus Plains the
region known as the Punjab Pakistan is proceed-
ing with integrated development of water and land
resources on a scale never before contemplated. The
heart of the development plan is a massive program
of groundwater development to supplement canal irri-
gation supplies and to provide drainage relief to the
irrigated lands. By the close of 1966 about 2500 high-
capacity wells were in operation and furnishing the
water supply and drainage requirements for nearly
two million irrigated acres. The development plan
calls for the construction of a total of nearly 30,000

S. W. MAO and P. E. HILDEBRAND are respectively Hy-
drologist and Economist, Tipton and Kalmbach, Inc.,
Denver, Colo., and C. N. CRAIN is Professor of Geography
and Regional Planning, University of Denver, Denver,
Colo. TP 67190. Manuscript, January 10, 1967. This paper
was presented at the AIME Annual Meeting, Los Angeles,
Calif., February 19-23, 1967. Discussion of this paper,
submitted in duplicate prior to June 15, 1969, will appear
in SME Transactions, September, 1969, and AIME Trans-
actions, 1969, Vol. 244.

wells with an aggregate capacity of 120,000 cfs by
1980. This is part of an integrated program eventu-
ally affecting over 20 million acres of irrigated lands.
[This development program is administered by the
West Pakistan Water and Power Development Authori-
ty (WAPDA) for which the firm of Tipton and Kalm-
bach, Inc. serves as regional planning consultant for
the Northern Zone. The material presented herein is
derived from planning studies which have been made
in connection with the preparation of a regional de-
velopment plan for the Northern Zone.]
Pakistan is proceeding with this large-scale devel-
opment of land and water resources at a time when
she is at the threshold of an almost calamitous popu-
lation growth. Furthermore, she is attempting this
development at a time when most of her usable land
is already occupied and her food demands exceed
current production. Here in the Northern Zone is one
of the largest continuous areas of irrigated land in
the world, easily irrigated, with a warm, dry climate
and ample potential supplies of surface water and
groundwater. Except for an abundance of land and
labor, other primary resources are lacking or in very
limited supply. The agriculture sector so dominates
the economy that only by means of an effective de-
velopment of the agricultural resources can other
sectors grow and contribute to a viable economy. Be-
cause of inadequate irrigation, farming here has not
effectively participated in the twentieth century
revolution in agriculture, and only by means of
massive development of potential supplies can
Pakistan catch up. Capital for any kind of mass de-
velopment must come from the outside. But the over-
riding restraint to development of the land and labor
resources is the availability of water.

The decision-making process in planning regional
development becomes increasingly complex as the
various sectors of the economy become more highly
developed. Where, as in this case, one sector domi-
nates the economy and its development can be con-
sidered the key to development of other sectors, the
decision-making process is simplified and it is
easier to identify alternatives and to trace the prob-

Society of Mining Engineers, AIME


MARCH 1969 15

able consequences of each possible choice.
Since the development alternatives are dictated by
economic resource analysis on the one hand and by
the technical ability to provide tools on the other,
the engineer and the economist must work together to
enumerate the parameters which will provide both the
identification of alternative development choices and
the basis for scientific choice among these alterna-
A case in point is the regional planning of the
Northern Zone of West Pakistan, where engineers
and economists, working together, have evolved a
frame of reference which permits the design of water
development within optimum limits.
Two of the many questions which had to be resolved
in this planning project were: (1) whether groundwater
development could be regulated by the demands of
the economy or the economy would have to be con-
trolled by concepts of "safe yield," and (2) how
hydrologic data could be integrated into an economic
model to provide the necessary parameters for deter-
mining optimum well design. The logic used in pro-
viding answers to these two questions involves very
basic concepts of regional planning and development.
In this case, analysis of the area indicated the fol-
lowing conditions which provided the framework for
decision-making in the development of the regional
(1) High population density.
(2) Very high rate of population growth.
(3) Food deficits.
(4) Demand growing at a faster rate than production.
(5) Basic lack of primary nonagricultural resources.
(6) Lack of capital.
(7) Extensive areas of potentially very fertile land.
(8) Terrain which favors irrigation.
(9) Warm, dry climate which permits year-round
growth when water is available.
(10) Ample potential supplies of water.
(11) Population of competent, intelligent farmers.
(12) Adequate power for pumping.
(13) Sufficient technical skills available to achieve
potential water supplies.
(14) Population increases in Asia alone are in ex-
cess of 50 million per year, and resulting increases
in the demand for wheat would be about 8 million tons
per year or at least 80 million tons per year more
demand in the next decade.
(15) With U.S. grain surpluses fully committed and
Canada's contracted for by Russia for the next five
years, a market for surplus agricultural goods close
to home (India and China, for example) could be as-
sumed for the plan period.
The only means by which dependence upon imports
and foreign aid can be reduced or eliminated is the
development of agricultural resources to the point of
providing capital accumulation for use in developing
other sectors of the economy. In view of the magni-

tude of the area and population involved, it is obvi-
ous that only a radical, massive and rapid expansion
of agriculture would be effective.* The ultimate pur-
pose of such development is less the establishment
of long range agricultural capability than the promo-
tion of capital formation and the generation of a long-
range balance of development among the economic
Thus the demand for resources in agriculture is im-
mediate and urgent. Later, the results of this devel-
opment will initiate shifts in resource use to other
sectors of the economy.
In Fig. 1, two available alternatives are illustrated.
The horizontal axis is time and the vertical axis is
volume of production. Starting in 1960, the curve DL
projects the lowest probable estimate of internal de-
mand and DH a higher probable estimate of demand.
PL is a projection of production under the decision
not to develop reserves of water to the maximum
capability and PH illustrates the other alternative of
developing all available agricultural resources up to
their maximum utility in the shortest possible period
of time. In particular, it implies use of groundwater
resources in excess of that implied by the usual safe-
yield concept.
It can be seen that even with a low demand curve
the deficit continues to increase through the plan
period in the absence of intensive development. The
consequence is an increasing dependence upon im-
ports and thus upon foreign aid. Furthermore, the
widening gap between demand and supply will ad-
versely affect any future development program.
In contrast, if the utilization of water resources is
developed at the highest rate possible, the produc-
tion curve exceeds the demand curve by about 1970.
Then dependence on food imports ceases. Subse-
quently, exports replace imports and the capital
earned becomes available for decision-making without
the constraint of having to use it to supplement
deficit food supplies.
By the end of the plan period, gross national prod-
uct, and other values, will reflect a viable economy

*It is now generally understood that population control programs
in Asia cannot produce any immediate effect. In fact, in the
foreseeable future, even the most optimistic forecasts cannot
justify more than a hope for a slackening of the rate of popula-
tion increase. Per capital demand for goods will probably con-
tinue to increase. Dr. Kingsley Davis, who is Director of Inter-
national Population and Urban Research at the University of
California (Berkeley), for example, points out the futility of
birth control and family planning as an effective device
(Kingsley Davis, "Population Policy: Will Current Programs
Succeed?," Science, Vol. 158, No. 3802, 10 Nov. 1967, pp. 730,
ff.). Similarly, numerous other objective studies indicate the
same conclusions, Including some impressive statistical pro-
jections. See also, for example, Harold F. Dorn, "World Popula-
tion Growth: An International Dilemma," Science, Vol. 135,
No. 3500, 26 Jan. 1962, pp. 283, ff. These studies all tend to
confirm our observations in the field. Historically, the most
effective control has been physical well-being. For example, in
Asia, the only example of a significant change in the population
growth curve has been Japan, and this change was brought about
following the development of an effective productive system.
Scientific birth control devices appear to be effective only under
these conditions.

Society of Mining Engineers, AIME


16 MARCH 1969

and water values will reflect competing demands for
water. At this time, decisions can be made relative
to other alternatives available for further development
or uses of water resources.


Groundwater development beyond that implied by
the usual safe-yield concept is necessary if full
economic development of the Northern Zone of West
Pakistan is to be achieved. But in order to demon-
strate the feasibility of the development plan it is
necessary to establish the economic feasibility of
the high level of groundwater development which will
create a viable economy. If this level of development
is not economically feasible, agricultural develop-
ment would either have to be restricted or subsidized,
and full economic development would be jeopardized.
The history of the irrigated areas of the western
United States indicates that rapid and intensive de-
velopment of groundwater resources can provide the
impetus for over-all economic development. In these
areas, the value of water has always exceeded the
cost of development. It is tempting to conclude that
intensive groundwater development in any favorable
agricultural climate will always lead to the same
successful results. But in planning the development
of a large region, where coordinated, long-range gov-
ernment decisions are required and all segments of
the economy are directly affected, it is necessary to
demonstrate the feasibility of intensive development
for the particular case in point. Accordingly, for the
Northern Zone of West Pakistan, both economic and
technical considerations have been used to show the
feasibility of the plan evolved.

P. Production with Project (net)
PL -Production without Project (net)
o. High Demand
0L Low Demand
Food Surplus
0 Food Deficit

Sl l I i

To establish that a low level of groundwater devel-
opment is economic is a simple matter. Various esti-
mates of the value of water under present conditions
range from about 50 to over 100 rupees per acre-ft
annually at the heads of water courses. The cost of
pumping groundwater from present depths and with
present equipment range from about 15 to 30 rupees
per acre-ft. Obviously, the use of groundwater under
these conditions is a profitable venture.
But as the rate of pumping increases, the water
table will be lowered and the cost of water will in-
crease. Simultaneously, however, the impact of the
added water on agriculture will enhance the value of
water. The significant questions are: (1) at what rate
can the water table be lowered, and (2) how far can it
be lowered before the limit of economic feasibility is
reached. This is analogous to asking what is the
upper economic limit of groundwater development.
Consider first the case where the pumping equipment
is a fixed investment, adequate to pump from any re-
quired depth. The added cost of pumping from greater
depths is then primarily a function of the added
power cost.
If the storage coefficient of the aquifer is 0.25, the
water table will be lowered 4 ft minus recharge for
every acre-ft pumped. If recharge from pumped water
is 22% of the volume pumped (Vp), the net decline in
the water table is 3.12 V, per gross acre. In the
Punjab, recharge from surface deliveries is approxi-
mately 54% of the volume delivered to the heads of
the water courses where the well water is discharged.
Recharge from canal deliveries per gross acre (b0) is
0.54 Dc and the rise of the water table is 0.54,Dc/0.25
or 2.16 De. Minimum annual recharge from other
sources is estimated at 0.2 ft per gross acre (GA).

Fig. 1 Projection of
food supply and demand
in project area-
Northern Zone, 1960-
2000 (excluding live-
stock products).

Society of Mining Engineers, AIME

MARCH 1969 17


The rise of the water table from these sources is 0.8
ft per yr per GA and is considered constant. Hence,
the annual drop of the water table in a contiguous
pumping area in terms of acre-feet per GA is:

Wd = 3.12 V, 2.16 D, 0.8 (1)

Total pumping head, H, in any year, n, is the sum
of (1) initial depth to water, (2) dynamic head, and
(3) the accumulated drop of the water table,

Dynamic head is considered to be 30 ft and initial
depth to water, 10 ft. Hence, pumping head in year n
when V, is an annual constant is:

H, = 40 + n(3.12 Vp 2.16 Dc 0.8) (2)

At a cost of 0.07 rupees per kw-hr, the power cost per
acre-ft per ft of lift is 0.12 rupees, and the annual
cost of power for any year n is:

C = 0.12 Vp(H,) (3)

Using dt as the annual discount factor, the present
worth of power costs over a time span of n years is:

C =
Cpw =
0.12 Vp I [d,140+n(3.12Vp-2.16Dc-0.8)11 (4)

The annual marginal value of water, MV, measured at
the heads of the water courses has been estimated
elsewhere.* The present marginal value, in a moder-
ately productive area, in terms of total volume of
irrigation water in acre-ft per GA, V, is:

MV = 104 19.6 V (5)

As V = Vp + Dc, the present worth of the marginal
value of water is:

MVp, = d[104 19.6(Vp + Dc)] (6)

where d is the discount factor for a uniform series
specified by Vp and Dc.
For any selected volume of surface deliveries, an
optimum annual pumping volume which maximizes
present worth of net return can be found by equating
the present worth of marginal value with the present
worth of marginal costs. The latter is defined as the
change in present worth of costs Cp, as Vp is
changed or:
d Cp
MC d = W (7)
"w d V
The optimum pumping rate with (1) present water
value, (2) a planning span of 50 years, and (3) dis-
counting at 5%, is 2.48 acre-ft per GA annually when
annual canal deliveries are 1.42 acre-ft per GA, which
*Regional Development Plan for the Northern Zone of the Indus
Plain, Tipton and Kalmbach, Inc., In process.

is the estimated future depth of canal supplies to the
development areas. This optimum, or upper limit of
groundwater development compares with an annual
groundwater requirements of about 2 acre-ft per GA
projected in the development plan. Hence, the pro-
jected level of ground water development for the de-
velopment plan falls well within the bounds of eco-
nomic feasibility.
It should be noted that the optimum pumping rate in-
creases with a higher discount rate and with smaller
canal deliveries. The optimum pumping rate declines
with periods of analysis longer than 50 years, but the
decrease is not significant. Hence, the upper limit
found above can be considered a conservative esti-
It should also be noted that after pumping at the
optimum rate for about half the period of analysis,
the marginal cost will exceed the present marginal
value of the water. This results from the choice cri-
terion which specifies a maximum present worth of
net return. However, the higher future costs when
discounted, are offset by the higher return from pump-
ing early in the period of analysis. Moreover, it is
estimated that by 1990 the marginal value of irriga-
tion water at the combined volume of 4.36 acre-ft per
GA annually will have risen to nearly double its
present marginal value. Even if the marginal value of
irrigation water does not rise above its 1990 level,
the marginal cost will not exceed marginal value
during the 50-year period of analysis.
As it is certain that the marginal value of water will
increase through time, the above analysis of the
upper economic limit of groundwater development
produces a definitely conservative estimate. In the
area under consideration, water quality variations
fall within acceptable ranges for development and do
not provide a significant economic variable.
The feasibility criterion of the preceding section
omits some important factors involved in lowering the
groundwater table. The model assumed a fixed pump-
ing plant capable of pumping from any depth. Obvi-
ously, if future depth to water and annual pumping
volume are known at the time of tubewell construc-
tion, the capacity and depth of the tubewell will be
affected. A tubewell designed to pump greater vol-
umes will be more expensive because both its ca-
pacity and depth will have to be greater, but the
greater initial expense will be spread over a larger
volume of water. Generally, within the relevant range
of development, the greater volume more than offsets
the higher fixed costs, resulting in lower fixed costs
per acre-ft pumped. Estimated costs for three differ-
ent cases are shown in Table I.
Although the total cost of water does increase with
depth, the costs are well below the value of the
water even after 50 years of pumping. The costs are
compared with the value of water in Table II. Of more
significance, however, is the total net value of the

Society of Mining Engineers, AIME


18 MARCH 1969

Table I. Comparison of Cost of Tubewell Water for Various Rates of
Pumpage and Depths to Groundwater Table

Item Unit Case A Case B Case C

Canal supplies @ HWC ft per yr per GA 1.42 1.42 1.42
Tubewell supplies @ HWC ft per yr per GA 0.79 1.24 1.69
Total supplies @ HWC ft per yr per GA 2.21 2.66 3.11
Tubewell capacity cfs 3.0 3.5 4.0
Depth to water table after 50 yrs ft 15 50 90
Maximum pump lift ft 36 75 118
Annual pumpage acre-ft 670 1,050 1,440
Annual utilization factor % 31 41 49
Capital costs of tubewell rupees 44,000 54,100 69,400
Annual costs
Amortization @ 5% for 15 yrs rupees 4,240 5,210 6,690
O & M rupees 2,000 2,000 2,000
Power costs rupees 2,890 9,450 20,400
Total annual costs rupees 9,130 16,660 29,090
Cost of tubewell water
Fixed costs Rs per AF 9.30 6.85 6.05
Power costs Rs per AF 4.30 9.00 14.15
Total cost Rs per AF 13.60 15.85 20.20

water in each case, as shown in Table III. With pres-
ent values, an additional 15 rupees per GA is gener-
ated by the additional pumping in Case B, and an ad-
ditional 24 rupees per GA is forthcoming annually
from groundwater development in Case C. For the
16.7 million acres underlain by nonsaline ground-
water, this involves an annual gain to the economy
of 250 million and 400 million rupees for Case B and
Case C, respectively. Using future values of water,
the annual gain to the economy is 1520 million rupees
and nearly 2700 million rupees annually for Case B
and C, respectively, over Case A.
An additional factor, often overlooked, but of para-
mount importance, is the creation of additional water
generated by pumping from greater depths. Inflow to
the aquifer in one area (recharge) cannot be with-
drawn from another area (pumpage) unless a gradient
or differential in elevation exists between the two
areas. In the Northern Zone the tubewells will be ar-
ranged in a relatively uniform density pattern and
will withdraw water at an essentially uniform rate
over large areas. Although recharge originating from
water applied to the lands will also be relatively uni-
form, the other major component of recharge consist-
ing of leakage from canals, links, rivers and similar
line sources is not uniformly distributed. These latter
sources account for 40 to 60% of the total recharge.
If the water table is maintained at shallow depths
throughout the area, much of the recharge from these
line sources is lost nonbeneficially through evapora-
tion near the source of recharge. But by establishing
a gradient between these sources of recharge and the

Table II. Cost and Value of Water Per Acre-Foot
After 50 Years of Pumping

Total Average Present Future
Water Cost of Average Average
Supplies Tubewell Value of Value of
ft per yr Water Water Water
per GA Rs per AF Rs per AF Rs per AF

Case A 2.21 13.60 77 201
Case B 2.66 15.85 73 205
Case C 3.11 20.20 70 202

areas of pumping, nonbeneficial losses are reduced
and the recharge, when used for irrigation, enhances
the results of development.
For the cases described above, total recharge has
been conservatively estimated as 1.14 ft per yr per
GA for Case A, 1.24 ft for Case B and 1.34 ft for
Case C. The additional 0.10 acre-ft in each case is
worth more than 5 rupees annually at present water
values. In Case A, recharge exceeds pumping by 0.35
ft per yr per GA and in Case C, pumpage exceeds re-
charge by a like amount. In Case B, pumpage equals
Thus, groundwater development to the high levels
required to generate a viable economy in the Northern
Zone is economically feasible. That is, groundwater
development need not be restricted to so-called safe-
yield levels but can proceed as required by the de-

Society of Mining Engineers, AIME

MARCH 1969 19


velopment demand of the economy. It remains to de-
termine the technical design criteria for the tubewells
to provide the necessary quantities of groundwater.

In project planning, the magnitude of groundwater
development is determined in detail by coordinating
the availability of surface water supplies, existing
irrigation distribution systems, local effective pre-
cipitation, and irrigation requirements for the pro-
jected level of agricultural development. This pro-
cedure generally results in a large number of tube-
wells of varying capacities with various utilization
factors. Many physical, technical and economic fac-
tors affect the design of these tubewells. Engineering
considerations and construction techniques restrict
the range of choice of components and physical con-
ditions affect performance. Still, within the restric-
tions imposed by these factors, a wide range of de-
sign possibilities exists. The best or optimum design
is one which results in a minimum over-all cost for
the water pumped.
The cost of pumped water is derived from three cost
components: (1) initial construction cost, (2) energy
consumption cost, and (3) operation and maintenance
cost. Length and diameter of the screen are the most
important determinants of the first two cost compo-
nents. In the optimization of tubewell design, length
of screen is the most important factor.
For a tubewell of specified capacity at a particular
location, the length and diameter of the screen are
the primary factors governing electric energy con-
sumption owing to their effect on tubewell drawdown,
and thus, the dynamic head. In the absence of other
considerations, minimum drawdown would result in
minimum cost of water. But to reduce drawdown,
either the screen diameter or, more importantly, the
screen length must be increased. Both factors in-
crease the initial construction cost of the tubewells.
In order to determine optimum screen dimensions, a
balance between added construction cost and reduced
power cost must be achieved.

Regardless of changes in screen length and diam-
eter, many components of construction do not change
or are of minor influence. Only those components
whose cost change with screen dimensions need to
be considered in determining optimum tubewell
The construction components that vary with screen
length or diameter are:
(1) Depth of tubewell
(2) Borehole diameter and amount of gravel
(3) Length of housing as influenced by drawdown
(4) Length of blank pipe as influenced by amount of
impervious layers in the aquifer and total well depth
(5) Cost of screen
Fig. 2 shows the general arrangement of a tubewell
and the components which govern both initial vari-
able construction cost and energy consumption cost.
Operation and maintenance cost is treated as con-
stant for all the tubewells.
Total initial construction cost, C1, is computed by:

CI = Pdi(DW)i + P,(L,) + P,(B) +

Phg(H) + Pg(G) + FC (8)
Here the variables are:
Pdi = cost of drilling within interval i per linear ft
Ps = cost of screen per linear ft
P, = cost of blank pipe per linear ft
Phg = cost of housing pipe per linear ft
Pg = cost of gravel shrouding per linear ft
D,t = depth of drilling in feet within interval i
L, = length of screen in ft
B = length of blank pipe in ft
Hg = length of housing pipe in ft
G = linear feet of gravel shrouding
FC = fixed cost items
Using the life expectancy of the tubewells and the
interest rate on investment, the initial construction
cost can be converted to an annual basis:

CIa = ACt (9)

where A is the appropriate amortization factor.

Table III. Net Value of Water Per Gross Acre After 50 Years

Total Tubewell
Water Water Total Total Total Net Total Net
Supplies Supplies Cost of Cost of Present Present Future Future
ft per yr ft per yr Ground- Irrigation Value of Value of Value of Value of
per GA per GA water Supplies Water Water Water Water
@ HWC @ HWC Rs per GA Rs per GA* Rs per GA Rs per GA Rs per GA Rs per GA

Case A 2.21 0.79 10.70 16.40 170 154 445 429
Case B 2.66 1.24 19.70 25.40 194 169 545 520
Case C 3.11 1.69 34.20 39.90 218 178 628 588

*Including charge of 4 rupees per acre-ft for canal supplies.

Society of Mining Engineers, AIME

20 MARCH 1969


Electric energy consumption is a function of total
pumping head, H, which is the sum of static head,
Wt, and dynamic head, Hd. Static head is defined as
the design depth from discharge pipe to the static
groundwater level. It is assumed to be constant at a
future depth in optimum tubewell design analysis.
The dynamic head is a variable consisting of tube-
well drawdown, aquifer and screen losses, pipe
friction head and velocity head.
The annual energy consumption cost, CE, can be
reduced to:



In this equation F is a derived factor consisting of
wire to water efficiency and the unit cost of elec-
tricity, Q is tubewell capacity, U is the annual utili-
zation factor, and H is the total pumping head.
Annual variable cost of a volume of water specified
by U and Q is:

C, = CE + Cla


This equation is a continuous, concave function of
screen length. Its minimum can be found by differen-
tiation with respect to screen length and equating to
zero. Fig. 3 illustrates the shape of the cost curves
and the optimum design for a single well with current
unit costs, rate of interest, and other specified con-
ditions shown.
Fig. 4 is a composite of optimum design conditions
for several tubewell capacities. It demonstrates the
influence on pumped water cost as the utilization
factor varies. If annual volume is fixed and capacity

is variable, then smaller capacity wells pumping at a
higher annual utilization rate result in lower unit
water costs. If, on the other hand, capacity is speci-

-Grovel pack

----Centr lizer

-: Blank pipe as required
for clay formation

- -Slotted casing


0 Pump discharge
Dw Depth of drilling
Hg Length of housing pipe
Ls Length of screen
B Length of blank pipe
SLength of gravel shrouding
Os Diameter of screen
D Diameter of bore hole
wt Static head
s Total tubewell drowdown
s' Aquifer loss
s' Screen loss
This sketch is not to scale

Fig. 2 Typical tubewell arrangement.


Fig. 3 -Cost per
acre-foot of water vs.
tubewell screen length.

Society of Mining Engineers, AIME


I I I i I I I I
000 400






MARCH 1969 21

screen dimensions).


A I .

Fig. 4 Cost of water vs. tubewell capacity (optimum
screen dimensions).

fied, lower unit water costs result from higher annual
utilization of the tubewells. The influence on opti-
mum design and cost of water of other components,
such as static water level, length of blank pipe, cost
of screen and electric energy, rate of interest and
life of tubewell, can also be determined.
Fig. 5 demonstrates that economic decisions appear
even in selecting hydrologic parameters for tubewell
design purposes. In estimating tubewell dynamic
head (more specifically, the aquifer loss), a most
important, yet most uncertain, hydrologic parameter
is aquifer permeability. As site by site estimation to
determine the precise permeability for the design of
every tubewell is impractical, one value of aquifer
permeability normally has to be selected for design-
ing all the tubewells within one project area. From
an engineering point of view, there is a tendency to
select a low design value of aquifer permeability as
a conservative measure. However, from an economic
point of view, a design value of aquifer permeability
which would result in a minimum expected cost of
water within the area should be selected.
Fig. 5(a) shows the influence of aquifer perme-
ability on cost per acre-foot of water. The heavy dots
represent the optimum design for each of three perme-
ability values. The deviation of the curves from these
points shows the effect on water cost when actual
permeability conditions differ from the assumed de-
sign value. When an incorrect permeability value is
assumed, the cost of water is higher than when the
correct value is used. As can be seen in the figure,
the magnitude of deviation from optimum varies with
the choice of the assumed permeability.
Fig. 5(b) shows the typical variation of aquifer
permeability for the unconfined alluvial sediments of
unknown depth in the Punjab. Although the range of
variation is rather small from a geological point of
view, it is large enough to have a significant effect
on water costs. For use in design, a value which re-

sults in a minimum water cost over a broad area can
be selected if distribution of permeability for the
area is obtained in advance from exploration tests.
When the frequency distribution of permeability and
the effect of design permeabilities on water cost is
known, an average cost for any design permeability
value can be found and an optimum design perme-
ability value can be established. In the case of Fig.
5, the minimum cost design permeability value ap-
pears to be near, but less than, the mean permeability
A nomograph such as that in Fig. 6 can be devel-
oped from the optimum design concepts above. The
nomograph can be used in conjunction with the well
log on site at the time of drilling to determine opti-
mum screen length and concomitant lengths of
housing and blank pipe as well as the total depth of
a well.
In actual practice, the water-bearing formations
cannot be predetermined on site before drilling be-
cause the lenticular clay beds are randomly distrib-
uted. However, as drilling proceeds, the inspector
can log the length of blank pipe required as shown by

o -

o K-0 75o -0 ft/See o- s "

on the bosos Of 0quifer perreabiity

o s s io Tos

Fid. 5 Graphs showing (a) the influence of aquifer
K H 51-i35 O' ft /t/c.

permeability on cost per acre-foot of water, and (b) the
typical variation of aquifer permeability for the unconfined
l sd-- iment nn n death n the n
o* tIl boass of OqUIIRY trIHrbiIity
oft /se

1, 5 If Ir h 5i
X,_,n I NT R 1fH /sec

permeability on cost per acre-foot of water, and (b) the
typical variation of aquifer permeability for the unconfined
alluvial sediments of unknown depth in the Punjab.

Society of Mining Engineers, AIME

o" Po I 2.o "I

22 MARCH 1969






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Society of Mining Engineers, AIME

4I 2 1did ftwl IO .q.NI1


MARCH 1969 23

the dash line in the nomograph. When the log inter-
cepts the curve in the upper right-hand quadrant cor-
responding to the capacity of the well being drilled,
approximate well depth has been reached. A horizon-
tal line drawn to the left from the point of intersec-
tion to the appropriate curve in the upper left quad-
rant specifies the optimum length of the screen and a
vertical line from this point to the appropriate curve
in the lower left quadrant specifies the proper length
of the housing pipe. Rounded values of blank pipe,
screen and housing would be entered in the lower
right corner and their sum would give the actual well
Thus, all the components of tubewell design which
can be measured and specified at the time of tubewell

construction are embodied in Fig. 6. The use of such
a nomograph provides a simple process by which
tubewells of optimum dimensions, considering geo-
logical, engineering, and economic factors, can be
Constructed throughout the entire project area.

Well-planned water resource development hinges on
a series of joint decisions involving many disci-
plines. Selected examples have been used to show
that the disciplines of engineering and economics
lend themselves to joint analysis. Furthermore, it
has been demonstrated that engineering and economic
concepts are necessarily interdependent in the opti-
mum planning of water resources development.



by Don K. Smith

The Reclamation Program for the Northern Zone of
the Indus Plains in West Pakistan involves the con-
struction of 30,000 irrigation wells to serve 20 mil-
lion acres with an annual pumpage of nearly 40
million acre-ft. Detailed hydrologic studies indicated
that mild steel would be satisfactory for casing; how-
ever, within two years after construction, about 10%
of the wells began to fail due to encrustation and
corrosion of the casing. A search to find a noncor-
rosive substitute for the steel casing disclosed that
only fiberglass-reinforced plastic pipe satisfied all
requirements. The results of initial use of fiberglass
have been highly satisfactory and have resulted in a
lower over-all well cost. Advances in technology
promise further reduction in prices and improvement
in performance.

The northern zone of the Indus Basin comprises a
vast area of essentially level land in West Paki-
stan which is irrigated by means of a complex system

DON K. SMITH is with Tipton and Kalmbach, Inc.,
Denver, Colo. TP 67183. Manuscript, December 30, 1966.
This paper was presented at the AIME Annual Meeting,
Los Angeles, Calif., February 19-23, 1967. Discussion of
this paper, submitted in duplicate prior to June 15, 1969,
will appear in SME Transactions, September 1969, and
AIME Transactions, 1969, Vol. 244.

of canals that distribute more water to more land than
any other irrigation system in the world. In spite of
the development of this extensive irrigation system,
production of food and fiber has not met the require-
ments of the country. The major reasons that crop
production has not reached anticipated levels are the
lack of adequate irrigation supplies and effective
subsurface drainage. As a result, yields per acre are
among the lowest in the world for areas where irriga-
tion is practiced, and many thousands of acres of
valuable crop land have been removed from produc-
tion or seriously affected by salinity and water-
To rectify the problems of irrigation supply and
drainage the Government of Pakistan has undertaken
a program of Salinity Control and Reclamation which
is being administered by the Water and Power Devel-
opment Authority. The Authority retained Tipton and
Kalmbach, Inc., of Denver, Colo., as engineers for
the program in the northern zone of the Indus Basin.
This program consists of the construction of about
30,000 irrigation wells to provide drainage for water-
logged lands and full irrigation supplies, including
leaching requirements, for all cultivated lands. The
program will ultimately ensure the productivity of 20
million acres and involve an annual pumpage from
groundwater storage of nearly 40 million acre-ft of

Society of Mining Engineers, AIME

24 MARCH 1969


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