Estimation of the sustainable yields of boreholes in fractured rock formations

Abstract

The simplest way to derive an estimate for the sustainable yield of a borehole is to study the behaviour of drawdowns observed during a hydraulic (also known as a pumping test) of the borehole, through an appropriate conceptual model. The choice of this model is probably the most difficult choice that the analyst of such a hydraulic test has to make, since a wrong model can only lead to the wrong conclusions and failure of the borehole. This paper discusses a semi-analytical and two numerical methods that can be used to simplify the analyses of hydraulic tests in fractured rock formations. The first method, called the Method of Derivative Fitting (MDF), uses a new approach to identify the conceptual model needed in such analyses. This is achieved by characterizing the various flow periods in fractured rock aquifers with numerical approximations of the first logarithmic derivative of the observed drawdown (the derivative of the drawdown with respect to the logarithm of the time). Semi-analytical expressions are used to estimate the influence that boundaries may have on the observed drawdown and the sustainable 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 also been made to quantify errors in the estimates introduced by uncertainties in the parameters, such as the transmissivity and storativity, through a Gaussian error propagation analysis. These approximations and the MDF, called the Flow Characteristics Method (FCM) have been implemented in a user-friendly EXCEL notebook, and used to estimate the sustainable yield of a borehole on the Campus Test Site at the University of the Orange Free State. The first numerical method, a two-dimensional radial flow model, is included here because it allows the user more freedom than the FCM, although it requires more information. One particular advantage of the method is that it allows one to obtain realistic estimates of the storativity and transmissivity 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 numerical method discussed here, is the best method with which to analyse a hydraulic test in a fractured aquifer. The method was consequently used to evaluate the accuracy of the implementation of the MDF in the Excel notebook and its application to the borehole on the Campus Test Site. The good agreement between the sustainable yield estimated with the three-dimensional numerical model and the FCM indicates that the FCM can be used with confidence to estimate the sustainable yields of boreholes in fractured media.