Abstract
Groundwater velocity and hydrodynamic dispersion coefficients can be determined simultaneously from observed data of solute concentration at the center of a single borehole. Two types of asymptotic analytical solutions to the convection-dispersion equation were proved to be applicable to analyse single borehole dilution tests. In order to calculate the groundwater velocity, and the longitudinal and transverse dispersion coefficients as three unknown variables in the asymptotic solutions, Powell's optimization method was applied to several cases together with the optimization method of Fletcher and Powell. The results of the application of these two optimization methods to several assumed sets and one actual experimental set of tracer concentrations showed that Powell's method based upon a conjugate direction procedure without calculating derivatives is more reliable, more flexible and much faster in converging to the true values than the method of Fletcher-Powell, which is based on a conjugate gradient procedure utilizing both criterion functions and their first derivatives. Furthermore, when Powell's optimization method was applied together with the proposed asymptotic solution to single borehole dilution data measured in field, the obtained values of the groundwater velocity, and the longitudinal and transverse dispersion coefficients were quite reasonable.
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