/(7, (O/ PEH
1567
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.
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After this additional withdrawal has been achieved, volume pumped returns
to the socalled "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 ptimes 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 nonsaline
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 nonbeneficially through evaporation near
the source of recharge. But by establishing a gradient between these
sources of recharge and the 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 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.
