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DISTRIBUTION OF FRACTURE TRANSMISSIVITY  IN THE CONGLOMERATE AND SANDSTONE   AQUIFERS OF THE SOUTHEASTERN VOLTAIAN  BASIN, EAST-CENTRAL GHANA, AFRICA 

William M. Turner, Ph.D. 
 

INTRODUCTION 

AGW scientists have long been interested in the statistical distribution of aquifer transmissivity because it is of significant importance in the exploration for ground-water resources.

Over the past three decade the Word Vision ground-water program in Ghana has produced mixed results (Acheampong and Hess, 1998).

The high failure rates in drilling successful wells and the high variability of well yield (World Vision, 1993; Prakla Seismos, 1984) show the need for precise ground-water exploration methods.  Many studies have focused on the hydrogeologic and tectonic processes.  Instead it must be recognized that regardless of the processes leading to fractures and fracture densities, an understanding of process will not describe the spatial distribution of aquifer transmissivity.  Nor, will it indicate which fracture contains water. 

This paper is based on transmissivity values presented by Acheampong and Hess (1998).  The work reported on by these workers is the outcome of rural water development program carried out by World Vision in Ghana.  Figure 1 shows the area of investigation carried out by Acheampong and Hess (1998).

Acheampong and Hess (1998) did not address either the statistical distribution of transmissivity or, more importantly, its spatial distribution.
 

HYDROGEOLOGIC SETTING 

Ground water in the southern Voltaian Sedimentary Basin occurs in fractures in highly consolidated siliciclastic aquifers overlain by a thin unsaturated zone.  The Conglomerate thickens eastward toward Lake Volta.  Near Lake Volta, erosion has removed the Conglomerate to expose underlying shale and grey sandstone.

Ground-water flow is through fracture zones to intermittent stream channels and ultimately to Lake Volta.

The hydrogeology of the area is primarily controlled by secondary porosity in the form of fractures developed in sedimentary rocks.  Primary porosity has been destroyed through compaction and slight metamorphism.

PROCEDURE 

Acheampong and Hess (1998) present 12 transmissivity values for the Conglomerate and 14 values for Sandstone.  Of these values, two values are indicated as both Sandstone and Conglomerate.  They are used to enrich both data sets for the purpose of statistical analysis.

The data set is heavily biased because only data from wells that produced more than 10 liters per minute (l/m) were used.

SANDSTONE 

Acheampong and Hess (1998) indicate that the success rate of wells with yields of at least 10 l/m drilled in the Sandstone ranges from 53 to 66 percent . If the average success rate is 59.5 percent, the average failure rate is 41.5 percent.

For the purpose of analysis, we assumed that the 14 transmissivity values for wells in the Sandstone represent the 59.5 percent of the wells that were successful.  Therefore, there were 24 wells in the Sandstone.  One of these wells must have had a transmissivity value such that 100 percent of the wells encountered the aquifer with higher transmissivities.  For purposes of computation, we assumed that there was one well with a transmissivity of "0" m2/d.  This well is ranked first in Table 1.  Table 1 shows the transmissivity values for the Voltaian Sandstone.

The first value in the table for Sandstone wells is ranked 11 because there were 10 unsuccessful wells in the population of values that had lower transmissivities. 
 

CONGLOMERATE 

Acheampong and Hess (1998), for wells drilled in the Conglomerate indicate the success rate ranges from 38 to 57 percent.  If the average success rate is 47.5 percent, the average failure rate is 52.5 percent.  Low capacity wells were not tested.  Table 2  contains the data for the wells used in our analysis of the transmissivity distribution in the Conglomerate.

The 12 transmissivity values for the Conglomerate represent 47.5 percent of the wells that were successful.  Therefore, 25 wells were drilled one of which, we assumed, encountered an aquifer with a transmissivity of "0" m2/d.  The first well in the table of Conglomerate wells is ranked 14 because there were 13 wells that had transmissivities less than the first recorded one. 
 

RESULTS 

We ranked the classed data and plotted it using the Weibull plotting position method where p = i/(n+1).

The data is heavily biased because only successful wells were tested.  Also, wells may not have completely penetrated the water-bearing zone and the aquifer performance tests did not consider wellbore storage effect.

The Weibull plotting position equals the average exceedance probability of the ranked observations.  They are unbiased plotting positions.  The data for the Sandstone and Conglomerate wells are plotted in Figures 2 and 3.

We used the Kolmogorov-Smirnov (Cheeney, 1983) to test whether the frequency distribution of the transmissivity values is lognormal.  The K-S method is an exact method and is useful when dealing with only a few data points.  We have only 14 transmissivity values for Sandstone wells and 12 transmissivity values for Conglomerate wells.

The maximum absolute deviations between the observed and calculated transmissivity values for Sandstone and Conglomerate wells were 0.0379 and 0.0627 respectively. These values are far less than the critical "a" values at the 0.05 significance level of 0.349 and 0.375 for sample sizes of 14 and 12 transmissivity values.  The null hypothesis is not rejected and the transmissivity data can be regarded as coming from a lognormally distributed population.

CONCLUSIONS 

The average transmissivity of fractures in Conglomerate wells is about 24.2 m2/d.  The average transmissivity of fractures in Sandstone wells is about 10.8 m2/d.  Fractures in the Conglomerate have greater transmissivity than those in the Sandstone.  Consequently, the Conglomerate terrane of southeastern Ghana is more prospective for ground water.

The average transmissivity of successful Conglomerate wells is about 24.2 m2/d. About 78 percent of wells drilled with the best exploration methods including satellite imagery and aerial photography failed to encounter a fracture with greater than the average transmissivity.  About 50 percent of the wells encountered fractures in the Conglomerate with less than 1.6 m2/d.

The average transmissivity of successful Sandstone wells is about 10.8 m2/d.  About 80 percent of wells drilled with the best exploration methods including satellite imagery and aerial photography failed to encountered a fracture with greater than the average transmissivity.  About 50 percent of the wells encountered fractures in the Sandstone with a transmissivity of less than 1.6 m2/d.

The lowest transmissivity associated with an acceptable well producing 13 l/min is 1.59 m2/d.  Using present exploration methods, about 80 percent of the wells will not meet minimum acceptable production of 10 l/m.

Unfortunately, our knowledge of the statistical properties of transmissivity distribution tells us nothing about the spatial distribution of transmissivity or the actual location of optimum well sites.

COST CONSEQUENCES 

Taylor et al. (1999) indicates that the cost of a single well in Ghana ranges from 2,000 to 4,000 USD.  Based on our knowledge of the statistical distribution of fracture transmissivity, if 100 wells are drilled at an average cost of 3,000 USD, at least 60,000 USD will be wasted because of poor well locations.  For these low cost wells, analysis of SPOT satellite imagery, TM infrared imagery and fracture trace analysis using aerial photography is a relatively inexpensive method of well-site location. 

Additional, inexpensive field methods, used by AGW scientists, costing about $500 per well site, can be used to further zero-in on optimum well sites in all areas including areas of dense vegetation.

The failure rate for wells in Ghana may be tolerable because the wells are of low capacity and the wells serve a broadly distributed population.  A high failure rate for wells needed to serve large communities and cities cannot be tolerated.

REFERENCES 

Acheampong, S.Y., and Hess, J.W., 1998, Hydrogeologic and hydrochemical 
     framework of the groundwater system in the southern Voltaian Sedimentary 
     Basin, Ghana, Hydrogeology Journal, v. 6, n. 4., pp. 527-537.

Cheeney, R.F., 1983, Statistical Methods in Geology, London: George Allen & 
     Unwin. 

Prakla Seismos GmbH, 1984, The 30 well drilling project, Internal Report, 
     Catholic Diocese of Accra, Ghana.

Taylor, K.C., Milnor, T.B., Chesley, M.M., and Matanawi, K., 1999, Cost 
     effectiveness of well site selection methods in a fractured aquifer, Ground Water, 
     v. 37, n. 2, pp. 271-286. 

Word Vision, 1993. Ghana rural water project: Fiscal Year 1992, Annual Report, 
     Report to the Hilton Foundation.

 

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