Abstract
The classical Darcy law is generalised by regarding the water flow as a function of a non-integer order derivative of the piezometric head. This generalised law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Numerical solutions of this equation for various fractional orders of the derivatives are compared with experimental data and the Barker generalised radial flow model for which a fractal dimension for the flow is assumed. Water SA Vol.32 (1) 2005: pp.1-7
Highlights
A problem that arises naturally in groundwater investigations is to choose an appropriate geometry for the geological system in which the flow occurs
One can use a model based on percolation theory to simulate the flow in a fractured rock system with a very large fracture density (Berkowitz and Balberg, 1993) or the parallel plate model (De Marsily, 1986) to simulate flow through a single fracture
There are many fractured rock aquifers where the flow of groundwater does not fit conventional geometries (Black et al, 1986). This is in particular the case with the Karoo aquifers in South Africa, characterised by the presence of a very few bedding parallel fractures that serve as the main conduits of water in the aquifers (Botha et al, 1998)
Summary
A problem that arises naturally in groundwater investigations is to choose an appropriate geometry for the geological system in which the flow occurs. One way to circumvent this problem is to enlarge the spectrum of possible solutions supported by the differential operator This possibility was investigated by re-computing the drawdown using the same storativity and transmissivity value as obtained with the Theis model but assuming that Darcy law is represented by a complementary fractional order derivative, the order of the derivative, as well as the flow thickness, being considered free parameters. In that case it must be assumed that a dimension higher than 3 in Barker’s model is feasible
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