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 ground-water 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 hydro-tectonic models (Larsson, 1972) is of questionable value in most areas of crystalline bedrock.  Though we may have a gross understanding of favorable areas for ground-water 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 log-normally distributed in space.  This seems to hold true for basin-fill alluvium, karst and fluvio-marine 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 log-normally 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 Kolmogorov-Smirnov test (Cheeney, 1983) the yield of 317 wells in Precambrian Iddefjord Granite of southern Norway, and 76 wells in the Hvaler Islands area is log-normally 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 log-normally 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 ground-water exploration methods.  Too many, low capacity wells substantially increase piping cost and operation and maintenance costs. 

REFERENCES 

Banks, D., Rohr-Torp, E., and Skarphagen, H., 1994, Groundwater resources in
     hard rock, Experienced from the Hvaler study, southeastern Norway, Applied 
     Hydrogeology, v. 2, n. 2, pp. 33-42. 

Banks, D., 1998, Predicting the probability distribution of yield from multiple 
     boreholes in crystalline bedrock, Ground Water, v. 36, n. 2, pp. 269-274. 

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. 111-129. 

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, Water-well siting in hard rock areas, identifying promising targets 
     using a probabilistic approach, Hydrogeology Journal, v. 5, n. 3, pp. 32-43. 

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