Evaluation of a Fractional Theis Equation

ABSTRACTThe Theis solution is the most widely used solution for determination of confined aquifer parameters. Because each aquifer is a unique system, sometimes an aquifer cannot accurately be described with the assumptions of the Theis solution. To offer a more general solution for aquifers where piezometric head at a given position is governed in a non- local manner, a generalized groundwater flow equation was developed by Cloot and Botha (2006). This thesis analyzes the flow equation, based on non- integer order derivatives and its numerical implementation developed by Cloot and Botha. However, their equation was found faulty and a new robust derivation of a fractional Theis solution developed by Baeumer et al. (2009) is presented. The new fractional Theis equation solution type curves (drawdown and radius of influence) are evaluated for relationships between aquifer properties and a fractional Theis solution. The fractional Theis solution is then used to reanalyze the aquifer test data used by Cloot and Botha (2006) in their analysis. Conclusions are made on the necessity of using a fractional Theis equation for the given data and suggestions are made for future work with a fractional Theis solution