Citation
The interdependence of economic and hydrologic criteria in planning water resources development

Material Information

Title:
The interdependence of economic and hydrologic criteria in planning water resources development
Uniform Title:
Transactions (Society of Mining Engineers of AIME)
Creator:
Mao, S. W
Hildebrand, Peter E
Crain, C. N
Place of Publication:
New York?
Publisher:
Society of Mining Engineers, AIME
Publication Date:
Language:
English
Physical Description:
p. 15-24 : ill. ; 29 cm.

Subjects

Subjects / Keywords:
Water-supply -- Management -- Pakistan ( lcsh )
Water resources development -- Planning -- Pakistan ( lcsh )
Water-supply -- Economic aspects -- Pakistan ( lcsh )
Spatial Coverage:
Pakistan

Notes

General Note:
Originally published in Transactions, Vol. 244, March 1969.
Statement of Responsibility:
by S.W. Mao, P. E. Hildebrand, and C.N. Crain.

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University of Florida
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Full Text





THE INTERDEPENDENCE OF ECONOMIC AND HYDROLOGIC CRITERIA IN PLANNING WATER RESOURCES DEVELOPMENT




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


Hydrologic and economic criteria figure in many obvious ways in water resources development, but they are rarely linked quantitatively, and most of the applications 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 concept of safe yield. The analysis demonstrated that mining of groundwater is clearly indicated for areas where alternative supplies are unavailable. The second 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 specifications on site during construction. The nomograph can be modified for use in any alluvial terrain.

I n the Northern Zone of the Indus Plains the region known as the Punjab Pakistan is proceeding 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 irrigation supplies and to provide drainage relief to the irrigated lands. By the close of 1966 about 2500 highcapacity 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 Hydrologist 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 Transactions, 1969, Vol. 244.


wells with an aggregate capacity of 120,000 cfs by 1980. This is part of an integrated program eventually affecting over 20 million acres of irrigated lands. [This development program is administered by the West Pakistan Water and Power Development Authority (WAPDA) for which the firm of Tipton and Kalmbach, 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 development plan for the Northern Zone.] Pakistan is proceeding with this large-scale development of land and water resources at a time when she is at the threshold of an almost calamitous population 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 development of the agricultural resources can other sectors grow and contribute to a viable economy. Because 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 development must come from the outside. But the overriding restraint to development of the land and labor resources is the availability of water.

ECONOMICS OF DEVELOPMENT
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 dominates the economy and its development can be considered 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-


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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 alternatives.
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 controlled by concepts of "safe yield," and (2) how hydrologic data could be integrated into an economic model to provide the necessary parameters for determining optimum well design. The logic used in providing answers to these two questions involves very basic concepts of regional planning and development.
In this case, analysis of the area indicated the following conditions which provided the framework for decision-making in the development of the regional plan:
(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 excess 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 assumed 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 obvious that only a radical, massive and rapid expansion of agriculture would be effective.* The ultimate purpose of such development is less the establishment of long range agricultural capability than the promotion of capital formation and the generation of a longrange balance of development among the economic sectors.
Thus the demand for resources in agriculture is immediate and urgent. Later, the results of this development 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 demand and DH a higher probable estimate of demand. P, 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 safeyield 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 imports and thus upon foreign aid. Furthermore, the widening gap between demand and supply will adversely affect any future development program.
In contrast, if the utilization of water resources is developed at the highest rate possible, the production curve exceeds the demand curve by about 1970. Then dependence on food imports ceases. Subsequently, 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 product, 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 population increase. Per capital demand for goods will probably continue to increase. Dr. Kingsley Davis, who is Director of International 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 projections. See also, for example, Harold F. Dorn, "World Population 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.


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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.


FEASIBILITY OF GROUNDWATER DEVELOPMENT

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 demonstrate 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 development 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 development 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 government 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.




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


o
Si lI i | I I i


To establish that a low level of groundwater development is economic is a simple matter. Various estimates 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 increase. 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 required 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 approximately 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 De 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 areaNorthern Zone, 19602000 (excluding livestock products).


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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,

t Wd.

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(Hn) (3)

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

C =
pw =
0.12Vp, Il [dt140+n(3.12 Vp-2.16Dc-0.8)1] (4)
t=l

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 moderately 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(V, + Dc)] (6)

where d is the discount factor for a uniform series specified by V, 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 Cpw as Vp is changed or:
d Cp,
MCp = p (7)
d Vp
The optimum pumping rate with (1) present water value, (2) a planning span of 50 years, and (3) discounting 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 projected level of ground water development for the development plan falls well within the bounds of economic feasibility.
It should be noted that the optimum pumping rate increases 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 estimate.
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 criterion which specifies a maximum present worth of net return. However, the higher future costs when discounted, are offset by the higher return from pumping early in the period of analysis. Moreover, it is estimated that by 1990 the marginal value of irrigation 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 pumping plant capable of pumping from any depth. Obviously, if future depth to water and annual pumping volume are known at the time of tubewell construction, the capacity and depth of the tubewell will be affected. A tubewell designed to pump greater volumes will be more expensive because both its capacity 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 different 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


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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 present values, an additional 15 rupees per GA is generated by the additional pumping in Case B, and an additional 24 rupees per GA is forthcoming annually from groundwater development in Case C. For the 16.7 million acres underlain by nonsaline groundwater, 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 paramount importance, is the creation of additional water generated by pumping from greater depths. Inflow to the aquifer in one area (recharge) cannot be withdrawn from another area (pumpage) unless a gradient or differential in elevation exists between the two areas. In the Northern Zone the tubewells will be arranged 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 uniform, the other major component of recharge consisting 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 evaporation 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
@HWC @HWC @HWC @HWC

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 recharge by a like amount. In Case B, pumpage equals recharge.
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 safeyield levels but can proceed as required by the de-


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


OPTIMUM TUBEWELL DESIGN
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 precipitation, and irrigation requirements for the projected level of agricultural development. This procedure generally results in a large number of tubewells of varying capacities with various utilization factors. Many physical, technical and economic factors affect the design of these tubewells. Engineering considerations and construction techniques restrict the range of choice of components and physical conditions affect performance. Still, within the restrictions imposed by these factors, a wide range of design 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 components. 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 consumption 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 increase 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 diameter, 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 design.
The construction components that vary with screen length or diameter are:
(1) Depth of tubewell
(2) Borehole diameter and amount of gravel shrouding
(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 variable construction cost and energy consumption cost. Operation and maintenance cost is treated as constant for all the tubewells. Total initial construction cost, CI, is computed by:

CI = Pdl(D,,) + P,(L,) + P,(B) +

Phg(Hg) + 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 Pb = cost of blank pipe per linear ft Pg = cost of housing pipe per linear ft Pg = cost of gravel shrouding per linear ft D,, = 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: CI. = 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.


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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 tubewell drawdown, aquifer and screen losses, pipe friction head and velocity head. The annual energy consumption cost, CE, can be reduced to:


CE = FQUH


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-


(10)


In this equation F is a derived factor consisting of wire to water efficiency and the unit cost of electricity, Q is tubewell capacity, U is the annual utilization 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


(11)


This equation is a continuous, concave function of screen length. Its minimum can be found by differentiation 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 conditions 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


-Gravel pack








C---entralizer





-:Blank pipe as required
for clay formation

--lotted casing

--Centralizer


NOTATIONS: a0 Pump discharge Dw Depth of drilling Hq = Length of housing pipe Ls Length of screen a Length of blank pipe G Length of gravel shrouding Os Diameter of screen
Do Diameter of bore hole w, Static head s, = Total tubewell drowdown S' Aaquifer loss s;- Screen loss NOTE
This sketch is not to scale


Fig. 2 Typical tubewell arrangement.


I I I I I

TUBEWELL CAPACITY = 4 CUSECS
SCREEN DIAMETER = 8 INCHES
DEPTH TO STATIC WATER LEVEL. 20 FEET LIFE OF TUBEWELL = IS YEARS
UTILIZATION FACTOR = 60%
INTEREST RATE = 4%


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


I I I I I I I I o
oann 0 400


TUEWELL SCREEN LENGTH,FT


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i -0


a

DEPTH TO STATIC WATER LEVEL'20 FT.
LIFE OF TUBEWELL =IS YEARS ,
INTEREST RATE = 44%



UTILIZATION FACTOR, PERCENT

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 optimum 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 designing 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 permeability on cost per acre-foot of water. The heavy dots represent the optimum design for each of three permeability values. The deviation of the curves from these points shows the effect on water cost when actual permeability conditions differ from the assumed design 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 permeability value can be established. In the case of Fig. 5, the minimum cost design permeability value appears to be near, but less than, the mean permeability value.
A nomograph such as that in Fig. 6 can be developed 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 optimum 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 because the lenticular clay beds are randomly distributed. However, as drilling proceeds, the inspector can log the length of blank pipe required as shown by


TUBEWELL CAPACITY = 4 CUSECS
SSCREEN DIAMETER = B INCHES
DEPTH TO STATIC WATER LEVEL 20 FEET
- \ UTILIZATION FACTOR 60 o


] ASSUMED AQUIFER PERMEABILITY
-*

-- Optimum screen length designed
on the basis of aquifer permeobliy -.
i< .7O, IO3 ft./sec.
- --Optimum screen length designed
on the boasis of aquifer permeability
U o 2iH 1, ft. eRs.
oH tie boen of OeUIIRY ferd ability
.0. .1.0 2.
AQUIFER PERMEABILITY, 10 FT./SEC.

os to is io as
CHAJ DOAB AREA
TOTAL NUMBER OF SAMPLES'470 R 1n = 1.065 1 ft./sec.











AOUI FER PERMEA ILITY, 10- FT /SEC

Fig. 5 Graphs showing (a) the influence of aquifer 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


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22 MARCH 1969


TRANSACTIONS VOL. 244

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the dash line in the nomograph. When the log intercepts the curve in the upper right-hand quadrant corresponding to the capacity of the well being drilled, approximate well depth has been reached. A horizontal line drawn to the left from the point of intersection to the appropriate curve in the upper left quadrant 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 depth.
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 geological, engineering, and economic factors, can be constructed throughout the entire project area.

SUMMARY
Well-planned water resource development hinges on a series of joint decisions involving many disciplines. 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 optimum planning of water resources development.


FIBERGLASS PLASTIC CASING OVERCOMES CORROSION


PROBLEM IN WATER WELLS IN WEST PAKISTAN



by Don K. Smith


The Reclamation Program for the Northern Zone of the Indus Plains in West Pakistan involves the construction of 30,000 irrigation wells to serve 20 million acres with an annual pumpage of nearly 40 million acre-ft. Detailed hydrologic studies indicated that mild steel would be satisfactory for casing; however, 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 noncorrosive 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.

T he northern zone of the Indus Basin comprises a
vast area of essentially level land in West Pakistan 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 requirements 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 irrigation is practiced, and many thousands of acres of valuable crop land have been removed from production or seriously affected by salinity and waterlogging.
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 Development 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 waterlogged 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


TRANSACTIONS VOL. 244

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