Title: Mining
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Permanent Link: http://ufdc.ufl.edu/UF00075688/00001
 Material Information
Title: Mining
Physical Description: 12 leaves : ; 22 cm.
Language: English
Creator: Hildebrand, Peter E
Publication Date: 1967
Copyright Date: 1967
 Subjects
Subject: Water resources development -- Pakistan   ( lcsh )
Groundwater -- Pollution -- Pakistan   ( lcsh )
Mines and mineral resources -- Economic aspects -- Pakistan   ( lcsh )
Mines and mineral resources -- Environmental aspects -- Pakistan   ( lcsh )
Genre: non-fiction   ( marcgt )
Spatial Coverage: Pakistan
 Notes
Statement of Responsibility: P.E.H..
General Note: "PEH; 1-5-67."
General Note: Typescript.
 Record Information
Bibliographic ID: UF00075688
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 82491263

Full Text
/(7, (O/ PEH
1-5-67


MINING


The issue of ground water mining is clouded by controversy and

complicated by various methods of analysis concerning its economic

feasibility. Even the definition of mining is not clearly established. In

aquifers with little or no recharge potential, mining can be considered the

withdrawal of any amount of water from the water table. In aquifers such

as that in the Northern Zone of West Pakistan, where there is a relatively

high recharge potential, mining can be considered either as that volume

of ground water withdrawals exceeding recharge potential or alternatively,

S withdrawals beyond the level required to control waterlogging.

There are two basic issues involved in water mining. One is

concerned with depletion of a resource for present or near future use

at the expense of the use of this resource in the more distant future.

Secondly is the question of the cost of pumping a given volume of water

from greater depths as a result of mining versus pumping from shallower

depths in the absence of mining. Analysis of the second question is

relatively straightforward, while issues involved in the depletion of a

resource are subject more to subjective considerations than the question

simply of cost and benefits. Only the objective considerations of cost

and value are discussed in this paper.
/

One Time Mining

One approach to the question of mining involves the one time with-

drawal of a quantity of water in excess of "usual" or "normal" pumpage.














COf
6W XIV-W
PB

1441/


After this additional withdrawal has been achieved, volume pumped returns

to the so-called "normal level. In this situation, the water table will be
1 S
lowered by an amount equal to, where is the specific yield of the
1
aquifer, minus p-times the recharge derived from the mined water times

the volume of mined water pumped. The costs associated with this

situation involve the cost of pumping the added volume of water plus the

cost of pumping the "normal" volume of water a greater height over the

period of time that the "normal" volume of water will be pumped.

At a cost of 0. 07 rupees per KWH, the power cost of lifting one

acre foot, one foot in height is approximately 0. 12 rupees. Consider a

"normal" withdrawal of two feet per acre, a storage coefficient of 0. 25,

and recharge of 22 percent of the volume pumped. The cost of the added
0. 78
lift for the normal pumpage is (2 x 0. 12 x % ) rupees per acre foot

mined or 0. 75 rupees annually. Capitalized at 6 percent in perpetuity,

this amounts to 12. 50 rupees. Adding to this the cost of the acre foot
1
of water mined 0. 12 (40 + x ) rupees, assuming an initial pumping

head of 40 feet, the total cost of mining one acre foot is 17. 50 rupees.

The cost if two acre feet were mined is 16. 67 x (2 x 0. 12 2 (078)) +
0. 25
0. 12 x 2 (40 + 1) or 17. 75 rupees per acre foot. In general, the cost
0.25
of one time mining in rupees per acre foot mined reduces to C = 17. 27 +

0. 24X using the above parameters where X is volume mined in acre feet.

The constant term in the above equation is sensitive to the rate of interest

but regardless of the rate used, the cost increases only 0.24 rupees per

acre foot with additional mining. Furthermore, the higher the rate of

interest used, the lower is the cost of mining.

2


f'







To determine the feasibility of mining, given the above costs for

the water, these costs must be compared with the value of the added water.

As shown elsewhere, the present marginal value of the "normal" delivery

of two feet per gross acre or 2. 26 feet per culturable acre is about 65

rupees per acre foot. The addition of one acre foot per gross acre or 1. 1

feet per CA reduces present marginal value to about 45 rupees per acre

foot and addition of two acre feet reduces marginal value to about 25

rupees per acre foot, assuming no surface supplies. If historic surface

supplies of 1. 6 acre feet per culturable acre are available the present

marginal value of the "normal" withdrawal is about 35 rupees per acre

foot; an additional acre foot drops the marginal value to approximately

20 rupees and the addition of two acre feet drops the marginal value to

zero.


Feasibility of One Time Mining

Canal
Commanded
Canal deliveries AF/CA 1. 60
Normal pumpage AF/CA 2. 26
Total normal deliveries AF/CA 3. 86
Present marginal value Rs/AF 35
Mining one acre foot
Total deliveries AF/CA 4.96
Present marginal value Rs/AF 20
Cost Rs/AF 17. 50
Mining two acre feet
Total deliveries AF/CA 6. 06
Present marginal value Rs/AF 0
Cost Rs/AF 17. 75


I





41


pi


Uncommanded
0
2. 26
2. 26
65

3. 36
45
17. 50

4.46
25
17. 75









Hence, the one time mining of one acre foot is feasible with the

present marginal value of water whether or not the land is canal commanded,

but the one time mining of two acre feet reduces the present value of water

sufficiently on canal commanded land so that this is not a feasible alternative.

But on uncommanded land even two feet of mining is feasible. However,

one time mining is not a realistic approach to the question of mining

feasibility. It is doubtful that the water would be used productively if it

were available only during one growing year. It would probably not pay

a farmer to develop the distribution system and prepare the additional

land required to effectively utilize large quantities of added water only

once. It is evident that cost of one time mining is not the primary factor

in feasibility. Rather, it is the decline in value of water associated with

large amounts and with present production conditions. Thus, it is more

appropriate to consider mining from the standpoint of continuous with-

drawals in excess of the normal amount. With continuous large supplies

of water, the farmers not only can adjust their irrigation system, but also

will be in a position to utilize added amounts of other inputs which will

increase the value of the water.


Continuous Mining

As opposed to one time mining, continuous mining is defined as

withdrawing a fixed annual volume of ground water. In this situation it

is unnecessary to define mining per se. The issue can be skirted by

determining directly the "optimum" annual withdrawal. In other words,









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 ground water 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 four feet minus recharge for every acre foot pumped.

If recharge from pumped water is 22 percent of the volume pumped (Vp),

the net decline in the water table is 3. 12 Vp per gross acre. In the

Punjab, recharge from surface deliveries is approximately 54 percent

of the volume delivered to the heads of the water courses where the well

water is discharged. Recharge from canal deliveries per gross acre

(Dc) is 0. 54 Dc and the rise of the water table is 0. 54 Dc/0. 25 or 1. 52 Dc.

Minimum annual recharge from other sources is estimated at 0. 2 feet

per gross acre (GA). The rise of the water table from these sources is

0. 8 feet per year 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 Vp 1. 52 Dc 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








n
water table, T> Wd. Dynamic head is considered to be 30 feet and
t= 1
initial depth to water, 10 feet. Hence, pumping head in year n when V
P
is an annual constant is: ,

Hn = 40 + n (3. 1Z Vp (- Dc 0.8) (2)

At a cost of 0. 07 rupees per KWH, the power cost per acre foot per foot

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:

Cp = 0. 12V pd 40+n (3.12 V 5 0. 8 ) (4)
pw 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 feet per gross acre, V, is:

MV = 104 19.6 V (5)

As V = V + D the present worth of the marginal value of water is:
P
MVpw = d 104- 19.6 (Vp + Dc (6)

where d is the discount factor for a uniform series specified by V and D .
p c

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 C as Vp is changed or:

MCpw = dC (7)
dV
p




Ag


The optimum pumping rate using (1) present water value, (2) a/

planning span of 50 years, and (3) discounting at 5 percent, is 2. 94 acre

feet per gross acre annually when annual canal deliveries are 1.42 acre

feet per gross acre, which is the estimated future depth of canal supplies

to the development areas. This optimum, or upper limit of ground water

development compares with an annual ground water requirement of about

2 acre feet per gross acre 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 pump-

ing early in the period of analysis. Moreover, by 1990, it is estimated

that the marginal value of irrigation water at the combined volume of 4. 36

acre feet per gross acre annually, will have risen to nearly double its

present marginal value. Even if the marginal value of irrigation water




' a


does not rise about 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 ground

water development produces a definitely conservative estimate.

The feasibility criterion of the preceding section omits some

important factors involved in lowering the ground water 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 both because the capacity will be greater and it will have

to be deeper. But the greater initial expense will be spread over a

larger volume of water. Generally, within the relevant range of develop-

ment, the greater volume more than offsets the higher fixed costs,

resulting in lower fixed costs per acre foot pumped. Estimated costs

for three different cases are shown in the following table.




5'*


Comparison of Cost of Tubewell Water
for Various Rates of Pumpage and
Depths to Ground Water Table

Item Unit Case A Case B Case C

Canal supplies @ HWC ft/yr/GA 1.42 1.42 1.42

Tubewell supplies @ HWC ft/yr/GA 0. 79 1.24 1.69

Total supplies @ HWC ft/yr/GA 2.21 2.66 3. 11

Tubewell capacity cusecs 3. 0 3. 5 4. 0

Depth to water table after 50 yrs. feet 15 50 90

Maximum pump lift feet 36 75 118

Annual pumpage acre feet 670 1,050 1,440

Annual utilization factor percent 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/AF 9. 30 6.85 6.05

Power costs Rs/AF 4. 30 9. 00 14. 15

Total cost Rs/AF 13.60 15.85 20.20

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 the following table.









Cost and Value of Water
Per Acre Foot After
50 Years of Pumping

Total
Water Average Present Future
Supplies Cost of Average Average
ft/yr/GA Tubewell Water Value of Water Value of Water
@ HWC Rs/AF @ HWC Rs/AF @ HWC Rs/AF @ 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

Of more significance is the total net value of the water in each case
as shown below:
Net Value of Water
Per Gross Acre
After 50'Years

Total Tubewell Total Total Total Net Total Net
Water Water Cost of Cost of Present Present Future Future
Supplies Supplies Ground Irrigation Value of Value of Value of Value of
ft/yr/GA ft/yr/GA Water Supplies Water Water Water. Water
@ HWC @ HWC Rs/GA Rs/GA* Rs/GA Rs/GA Rs/GA Rs/GA

2. 21 0.79 10. 70 16.40 170 154 445 429

2.66 1.24 19. 70 25.40 194 169 545 520

3.11 1.69 34.20 39,90 218 178 628 588
* Including charge of 4 rupees per acre foot for canal supplies

Hence, in Case B, an additional 15 rupees per gross acre is generated

annually with present values by the additional pumping and in Case C, an

additional 24 rupees per gross acre is forthcoming annually from ground

water development. For the 16. 7 million acres underlain by non-saline

ground water, this involves an annual gain to the economy of 250 million

rupees and 400 million rupees annually for Case B and Case C, respectively.


c- il


Case A

Case B

Case C









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, res-

pectively, 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 com-

ponent 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 percent 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 non-beneficially through evaporation near

the source of recharge. But by establishing a gradient between these

sources of recharge and the areas of pumping, non-beneficial losses are

reduced and the recharge, when used for irrigation, enhances the results

of development.

For the cases described above, total recharge has been conserva-

tively estimated as 1. 14 feet per year per gross acre for Case A, 1. 24

feet for Case B and 1. 34 feet for Case C. The additional 0. 10 acre foot,

in each case, is worth more than 5 rupees annually at present water values.







In Case A, recharge exceeds pumping by 0. 35 ft/yr/GA and in Case C,

pumpage exceeds recharge by a like amount. In Case B, pumpage equals

recharge.


Summary

It has been demonstrated that the level of ground water development

envisioned in the development plan for the Northern Zone is economically

feasible. The rate of withdrawals in the heaviest pumping areas fall well

within the upper economic limits of feasibility. Furthermore, the additional

water generated by lowering the water table to projected levels has a

significant impact on the economy of the region. If decline of the water

table is held to a minimum, the loss to the economy could be such as to

jeopardize the entire national program of economic development.




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