Estimation of the sustainable yields of boreholes in fractured rock formations

The simplest way to derive an estimate for the sustainable yield of a boreh ole is to study the behaviour of drawdowns observed during a hydraulic (als o known as a pumping test) of the borehole, through an appropriate conceptu al model. The choice of this model is probably the most difficult choice th at the analyst of such a hydraulic test has to make, since a wrong model ca n only lead to the wrong conclusions and failure of the borehole. This paper discusses a semi-analytical and two numerical methods that can b e used to simplify the analyses of hydraulic tests in fractured rock format ions. The first method, called the Method of Derivative Fitting (MDF), uses a new approach to identify the conceptual model needed in such analyses. T his is achieved by characterizing the various flow periods in fractured roc k aquifers with numerical approximations of the first logarithmic derivativ e of the observed drawdown (the derivative of the drawdown with respect to the logarithm of the time). Semi-analytical expressions are used to estimat e the influence that boundaries may have on the observed drawdown and the s ustainable yield of a borehole - the rate at which a borehole can be pumped without lowering the water level below a prescribed limit. An effort has a lso been made to quantify errors in the estimates introduced by uncertainti es in the parameters, such as the transmissivity and storativity, through a Gaussian error propagation analysis. These approximations and the MDF, cal led the Flow Characteristics Method (FCM) have been implemented in a user-f riendly EXCEL notebook, and used to estimate the sustainable yield of a bor ehole on the Campus Test Site at the University of the Orange Free State. The first numerical method, a two-dimensional radial flow model, is include d here because it allows the user more freedom than the FCM, although it re quires more information. One particular advantage of the method is that it allows one to obtain realistic estimates of the storativity and transmissiv ity of Karoo aquifers in particular, which is required in the estimation of the sustainable yield of a borehole. There is no doubt that a three-dimensional numerical model, the second nume rical method discussed here, is the best method with which to analyse a hyd raulic test in a fractured aquifer. The method was consequently used to eva luate the accuracy of the implementation of the MDF in the Excel notebook a nd its application to the borehole on the Campus Test Site. The good agreem ent between the sustainable yield estimated with the three-dimensional nume rical model and the FCM indicates that the FCM can be used with confidence to estimate the sustainable yields of boreholes in fractured media. (C) 200 1 Elsevier Science B.V. All rights reserved.