Parameter Estimation in a Model for Tracer Transport in One-Dimensional Fractals
The problem of parameter estimation in a model for one-dimensional fractals is analysed and solved. The model describes advection and dispersion of a tracer pulse in a one-dimensional fractal continuum with uniform flow. It involves three parameters: fractal dimension of length, connectivity index associated to dispersion and dispersion coefficient. By using synthetic tracer breakthrough data the effect of data noise level, amount of data points and number of fitting parameters on the results have been analysed. It has been found that the developed estimation methodology is in general robust to the standard data noise level, and to the amount of data points between the typical cases of around 10 and 40. It has been also found that the curve fitting procedure is consistently more sensitive to the fractal dimension of length than to the other two parameters: the connectivity and the dispersion coefficient.
KeywordsSynthetic Data Dispersion Coefficient Fractal Continuum Connectivity Index Tracer Breakthrough
This work has been suported by Sener-Conacyt-Hidrocarburos Fund through the project No. 143935. ECHH acknowledges financial support from Conacyt for the postdoctoral fellowship at the Instituto Mexicano del Petróleo and the Cátedra Conacyt at CIDESI.
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