Environmental Engineering Reference
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Parameter Estimation in a Model for Tracer
Transport in One-Dimensional Fractals
E.C. Herrera-Hernández and M. Coronado
Abstract
The problemof parameter estimation in amodel for one-dimensional frac-
tals 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.
1 Introduction
Parameter estimation is a relevant stage in the dynamic characterization of aquifers,
oil fields and geothermal reservoirs. It is a process that looks for the determination of
reservoir properties like porosity, thickness of the production layer, fluids saturation,
dispersion coefficient, fault orientation, etc. It allows the understanding of the way
fluids move inside porous media, thus providing important elements in the design of
efficient oil recovering strategies inmature and partially depleted reservoirs (Illiassov
and Datta-Gupta
2002
; RamÃrez-Sabag et al.
2005
; Coronado et al.
2011
).
Of particular interest are models related to anomalous dispersion since they provide
new insights into the physics of the transport phenomenon. Anomalous behaviour in
heterogeneous systems is observed in field and laboratory scales (see for example,
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