Fractional flow in fractured chalk; a flow and tracer test revisited

Abstract

A multi-borehole pumping and tracer test in fractured chalk is revisited and reinterpreted in the light of fractional flow. Pumping test data analyzed using a fractional flow model gives sub-spherical flow dimensions of 2.2-2.4 which are interpreted as due to the partially penetrating nature of the pumped borehole. The fractional flow model offers greater versatility than classical methods for interpreting pumping tests in fractured aquifers but its use has been hampered because the hydraulic parameters derived are hard to interpret. A method is developed to convert apparent transmissivity and storativity (L(4-n)/T and S(2-n)) to conventional transmissivity and storativity (L2/T and dimensionless) for the case where flow dimension, 2<n<3. These parameters may then be used in further applications, facilitating application of the fractional flow model. In the case illustrated, improved fits to drawdown data are obtained and the resultant transmissivities and storativities are found to be lower by 30% and an order of magnitude respectively, than estimates from classical methods. The revised hydraulic parameters are used in a reinterpretation of a tracer test using an analytical dual porosity model of solute transport incorporating matrix diffusion and modified for fractional flow. Model results show smaller fracture apertures, spacings and dispersivities than those when 2D flow is assumed. The pumping and tracer test results and modeling presented illustrate the importance of recognizing the potential fractional nature of flow generated by partially penetrating boreholes in fractured aquifers in estimating aquifer properties and interpreting tracer breakthrough curves.