Report No 565/1/01


The assessment of recharge to fractured Karoo aquifers, especially below a substantial cover of Kalahari deposits, has occupied the minds of many researchers. This project follows several approaches to the problem: isotope data obtained from pumping tests are used to assess ground water mean residence times, from which integrated recharge rates can be deduced. The method of cumulative rainfall departures is applied to long-term rest level, pump rate and rainfall observations.

The study originated as an attempt to use long-term, well-documented abstraction of ground water at the Orapa mine, Botswana to evaluate critically borehole pumping tests of fractured Karoo aquifers, which are of necessity limited in their duration. As a more comprehensive investigation was being carried out by Anglo American, the present study was redirected, focussing specifically on the refinement of recharge estimation in the area. An original objective, the characterisation of the Karoo aquifers in the Orapa/Lethlakane area as compared to similar aquifers in South Africa using a new method of interpreting pumping tests, was retained in the revised project. The aims of the present Water Research Commission Project, having, been redefined were:

  1. Assessing the recharge to the aquifer using different methods. Appropriate techniques to be considered were:
  2. To reach a better understanding of the effective mechanism of recharge and to assess the reliability and value of isotopic measurements in ground water studies, especially in Karoo aquifers, in a semi-arid environment.
  3. To characterise the aquifer in terms of its hydraulic response by re-examining data on pumping tests conducted previously.
  4. To collate the findings of the investigation in a report.

Ground water at Orapa mines has been investigated by different consultants since the latter sixties. In the early seventies, recharge to aquifers in the Kalahari was regarded as negligible. This was challenged by environmental isotope studies, initially conducted at Orapa and subsequently extended to the Kalahari in general.

The area, of featureless topography, lies in the central Kalahari, with average annual rainfall 350 mm.

The main stratigraphical units of the geology are: the archaean metamorphic and granitic basement rocks; the Karoo sequence consisting of the upper Ecca, Mosolotsane and Ntane sandstone formations; Stormberg lavas and a cover of Kalahari Beds. There are intrusions of Kimberlite and extensive dolerite dykes.

Tectonic activity produced a system of larger and smaller intersecting fractures, only some of which are intruded by dykes, and horst and graben structures, all of which play an important role in the occurrence of exploitable ground water.

The Kalahari Beds hold ground water which sustains shallow boreholes and hand-dug wells. The Stormberg basalt acts as a confining layer over the underlying Ntane and Mosolotsane, has fracture zones, but is not regarded as suitable for exploitation. The Ntane sandstone is the main aquifer of the area, with relatively high intrinsic porosity and secondary permeability, sustaining yields from deep boreholes of up to 110 m3/hr. The Mosolotsane is a poor aquifer, containing poor quality water. The dykes act partially as barriers to ground water flow, and partially as permeable zones.

Exploitation from the five well fields established at the mines rose from 225 megalitres per month in 1984 to 528 megalitres per month in 1992.

The earliest indications that recharge was occurring came from isotope observations. Water balance studies confirmed these conclusions, and showed that recharge can be quantified in spite of it being small. These conclusions have a significant impact on the water household at the mines.

Various methods for assessing, recharge in this environment are reviewed. In the unsaturated zone, chloride and environmental tritium profiles can be employed in moisture in cores of sand or soil. The chloride method relies on the increase in concentration of chloride in soil moisture due to evapotranspiration. Tritium profiles trace the increase of tritium in rain following the thermonuclear test period of the early sixties. Although these methods can be used to assess the downward movement of moisture in the soil matrix, the spatial and temporal variability of soil moisture conditions and the existence of preferential or bypass flow, complicate the interpretation of such profiles in terms of ground water recharge. Typical recharge values calculated lie in the range of a few mm of water column per annum.

Sporadic recharge events would constitute a regionally averaged long-term diffusive recharge. Environmental radiocarbon labels rainwater entering the saturated zone. Its concentration as measured in water pumped from a borehole can be interpreted in terms of a ground water mean residence time. If the depth of water column being exploited and the porosity of the aquifer can be ascertained, a recharge rate can be calculated. The assumption when assessing the mean residence time is that around water flow lines develop, obeying the so-called exponential model. Although ground water in the area is not subject to significant regional flow, it is shown that successive layering due to recharge produces a degree of "age" stratification.

The resulting age stratification is assumed to be approximated by the exponential model, as the boreholes would tap and mix the stratified zone. As radiocarbon with a mean life of 8270 years will be able to label all the water in the aquifer through diffusion, the total porosity rather than the storativity, which is orders of magnitude smaller for a confined aquifer, is appropriate in this regard. Although isotope data was obtained for Orapa since 1969, only the data gathered since 1987 is considered. With only one exception, first strike water obtained at the basalt/sandstone interface is found to have low radiocarbon values, indicating residence times of many thousands of years. This is taken to indicate that (lateral) flow in the Ntane is very slow. This, and the absence of any visible discharge from the ground water system, indicates that only evapotranspirative losses are important. As good porosity values are available for the Ntane, mean recharge values based on radiocarbon-derived mean residence times were calculated, which lie in the range of 1-3.7 mm a-1. The higher value was obtained including data on a borehole which happened to be drilled in a section of the basalt with high vertical permeability. Very consistent stable isotope values, independent of residence times, show no great variability in climate over the time span indicated by radiocarbon measurements of the ground water.

Three water balance techniques are discussed in terms of the long-term exploitation of the aquifers. i) Saturated volume fluctuation using a finite-element grid over the entire aquifer, but applied only to well fields 4, 5 and 6. Average storativities of some 0.00075 and recharge of some 1.4 % of mean annual rainfall were obtained. ii) Recharge derived from periods of equal volume showed for the first time a 4 month lag of water level response to an anomalous rainfall event in wellfield 6. An apparent lateral recharge component may result from insufficient coverage of the area with observation boreholes. The adapted Hill method assumes a linear relationship between abstraction and change in saturated volume.

The cumulative rainfall departure (CRD) method calculates the departure of rainfall in individual months from the long-term mean. Only positive values are considered. Recharge is then taken to be proportional to these departures, with a constant of proportionality depending on the short-term response of the system. A linear correspondence is also assumed between water level response and the CRD series. The uncertain storativity of the aquifer precludes the calculation of recharge using this method. The modified CRD relationship relates the average rainfall over a few months to the average over several years - so-called short-term and long-term memory - which reflect changes in rainfall and variable loss mechanisms respectively.

Various correlations are attempted. For n (long-term memory) of 36 months, the best correspondence is obtained and the correlation increases for m (short-term memory) from 1 to 12 months. For n = 60 the correspondence is poorer and declines for m increasing from 1 to 12 months. Correlations decrease to n = 120 months; decrease for m = 1 to 3 months but improve slightly for m up to 12 months.

It is concluded that ground water levels conform more closely to average rainfall over 12 months than averages over shorter intervals. This is taken to reflect the integrating effect of the soil overburden. For the CRD relationship with m<n, the losses from the system are most closely related to the average rainfall over the preceding 36 months.

The effect of abstraction is accounted for by including this factor in the constant of proportionality, linking CRD with recharge. For well field 6, the best fit regression is obtained for a value of the constant somewhat greater than one, assuming constant abstraction. Using this constant in the CRD series for Orapa/Lethlakane the rest level correlation coefficient improves from 0.86 to 0.92. Various factors, such as the nature of the aquifer and the presence of dykes will determine the area of influence. The correlation increases until the area is reduced to less than 1 km2. This shows that pumping dominates the water level response.

The correlation is found to improve even further when the short and long-term memory of the system are reversed. The implication is that the effective recharge which controls the response of the ground water levels is lower when the average rainfall over the preceding months is higher than the long-term average. Although difficult to conceptualise in hydrological terms, this phenomenon can be understood in terms of enhanced vegetation activity in response to higher soil moisture which in turn inhibits recharge. Such a mechanism was proposed to explain isotopic values in ground water in Gordonia. Alternatively, the best fit between the normal cumulative rainfall departures and around water levels is attained Incorporating a lag of 14 months.

Further modifications to the recharge-CRI) relationship take account of the equivalent ineffective rainfall, and pumpage, as well as the lag in response. These increase the correlation coefficient to 0.99 and produce a CRD series which best predicts the aquifer behaviour at Orapa. Its applicability to other areas needs to be investigated.

Aquifer storativity is assessed using integrated fluctuation of saturated volume. It has been established that values of the storativity decline with increasing distance of the observation borehole from the pumped borehole using normal interpretations of pumping tests. As experience had shown that all pumping tests at Orapa showed similar behaviour, a limited number was re-examined. The data was obtained from drawdown graphs, and analysed according to the methods of Theis, Walton and Moench. The results conform reasonably with those obtained for the Karoo formations in the Free State, and a storativity value of 0.0035 is inferred for Orapa.

The phenomenon of declining S values with increasing distance to the observation well elicited comment by Professor Neuman of Tucson, Arizona. He points out that in fractured aquifers world-wide there is a nesting of parameters. With a continuous local range of S and T values, the early log-log behaviour would resemble a Theis curve, and only longer pumping tests would reveal deviations. These remarks are in agreement with the analysis of the isotope data and the similarity in behaviour caused by the fractal feature of different southern African aquifers.

Revised interpretations of all suitable pumping tests would require a comparison of the storativity values obtained with those based on water balance, in order to arrive at realistic figures. This study has led to a better understanding of the behaviour of fractured aquifers.

The study has shown further that the quality of the pumping test data was not as good as initially assumed. Water balance methods gave consistent values of recharge, but not of storativity, the best value of which at 0.0035, gives a recharge rate of a few mm/a. Flooding of the ephemeral Lethlakane river could locally contribute significantly to this recharge.

Recharge rates based on radiocarbon observations in the saturated zone confirm the value obtained from water balance considerations. Both as qualitative indicators of aquifer behaviour and in quantitative interpretation of recharge, isotope methods have the advantage of not having to rely on long-term observations. In view of the largely confined aquifer conditions, values in the range of 1 - 3.7 mm/a from isotopes compare reasonably with values of 1.75 - 4.8 mm/a from CRD, using values of porosity and storativity of 0.2 and 0.0035 respectively.

The modified CRD method with reversed lone, term and short term responses, incorporating a pumping factor and a rainfall response lag of four months, simulates water level responses to both recharge and abstraction.

The objectives of the study were realised, in that reasonably consistent values of recharge were obtained from both water balance and radiocarbon methods which in turn agree in general terms with estimates by other workers based on chloride and tritium profiles in the unsaturated zone.