
PROBABILITY
DISTRIBUTION OF YIELD FROM BOREHOLES IN CRYSTALLINE ROCK
William M. Turner, Ph.D.
INTRODUCTION
Banks (1998) points out that the decision to drill a groundwater supply well into a
bedrock aquifer is a difficult financial decision. The investment in a bedrock well
is significant and the outcome is problematical.
The use of statistical and probabilistic methods (Sander, 1997) or hydrotectonic models
(Larsson, 1972) is of questionable value in most areas of crystalline bedrock.
Though we may have a gross understanding of favorable areas for groundwater exploration,
these methods are not able to site a well.
In our continuing examination of the statistical distribution of transmissivity based
on our own data and the data of others, we report here on the work of Banks (1998).
STATISTICAL DISTRIBUTION OF YIELD
Many of AGW library reports conclude that transmissivity of aquifers is lognormally
distributed in space. This seems to hold true for basinfill alluvium, karst and
fluviomarine aquifers. It also seems to hole true for fractured sedimentary
rock.
Banks (1998) investigated the statistical distribution of well yield. Because
well yield is directly proportional to aquifer transmissivity, conclusions reached in our
examination of the statistical distribution of transmissivity will also apply to well
yield.
Banks (1998) states that many authors have pointed out that the distribution of yield
from bedrock wells is nearly lognormally distributed (Persson et al., 1985; Banks et
al, 1994). He relates this to the lognormal distribution of fracture
aperture.
Banks (1998) points out that based on the KolmogorovSmirnov test (Cheeney, 1983) the
yield of 317 wells in Precambrian Iddefjord Granite of southern Norway, and 76 wells in
the Hvaler Islands area is lognormally distributed.
CONCLUSIONS
Banks concludes that in the Hvaler area, there is only a 30 percent chance of finding a
well site with a yield of 1,000 l/hr. The chance of obtaining this total yield from
two boreholes is only 58 percent.
There is less than 5 percent chance of finding a well site having a yield of about
6,000 l/hr. Yet, one site yielding 6,000 l/hr would take the place of many lower capacity
wells.
Though we can say that the transmissivity or yield distribution is lognormally
distributed, we can say nothing about the spatial distribution of high aquifer
transmissivity or high well yield. That is, there is no correlation between well
yields. They are independently or very nearly independently distributed in
space. Banks (1998) states that two wells drilled close to one another can have
significantly different yield. The degree of yield correlation between pairs of
nearby wells is low.
COST SIGNIFICANCE
Wells producing as little as 200 l/hr are sufficient for residential use and about 25
percent of wells randomly located in the Hvaler or Iddefjord Granite should produce this
quantity.
But, if the wells are being drilled for a municipal supply where higher capacities are
needed, the probability of locating a high capacity well site is remote without
appropriate groundwater exploration methods. Too many, low capacity wells
substantially increase piping cost and operation and maintenance costs.
REFERENCES
Banks, D., RohrTorp, E., and Skarphagen, H., 1994, Groundwater resources in
hard rock, Experienced from the Hvaler study, southeastern
Norway, Applied
Hydrogeology, v. 2, n. 2, pp. 3342.
Banks, D., 1998, Predicting the probability distribution of yield from multiple
boreholes in crystalline bedrock, Ground Water, v. 36, n. 2, pp.
269274.
Cheeney, R.F., 1983, Statistical Methods in Geology, London: George Allen &
Unwin.
Larsson, I., 1972, Groundwater in granite rocks and tectonic models, Nordic
Hydrology, v. 3, pp. 111129.
Persson. G.J., de Geer, Egorov, S.V., Kirkhusmo, L.A., Olsson, T., Panova, Z.P.,
Taka, M., and Wikner, T., 1985, Explanatory notes for the
hydrogeological map
of Europe, scale 1:1,500,000, Sheet D2 Haparanda, IAH Commission
of the
Geological Map of the World, Publ. Bundesanstalt fur
Geowissenschaften und
Rohstoff, Hannover and UNESCO, Paris.
Sander, P., 1997, Waterwell siting in hard rock areas, identifying promising
targets
using a probabilistic approach, Hydrogeology Journal, v. 5, n. 3,
pp. 3243.
