Breakthrough curve tailing in a dipole flow field

Abstract

Studying the tailing behavior of breakthrough curves (BTCs) is useful in the characterization of anomalous transport, matrix diffusion, and kinetic sorption. We analyze how BTCs of nonreactive and sorbing tracers behave at late time in well-to-well flow fields in homogeneous media. In the absence of regional flow, an asymptotic solution is derived for the traveltime distribution which follows a power law with exponent -4/3 at late times. With regional flow, the traveltime distribution exhibits a power law with exponent -4/3 over a certain period of time, followed by exponential decay. Dispersion influences the early time behavior but has little effect on the late-time tailing. We also consider the BTC tailing of tracers undergoing kinetic sorption and diffusive mass transfer into immobile regions. If the memory function characterizing sorption kinetics is exponential, the late-time behavior of the BTC is controlled by the traveltime distribution and thus follows a power law with exponent -4/3. In case of a matrix diffusion model, the memory function exhibits a power law with exponent -1/2, and the BTC in the dipole flow field follows a power law with exponent -7/6 in an intermediate time range, which differs from the exponent of -3/2 observed in uniform flow. Our analysis demonstrates that the flow configuration has to be considered when the tailing behavior of BTCs is used to characterize mass transfer kinetics. In particular, truncating a well-to-well tracer test at times where the traveltime distribution still follows the power law behavior may lead to the erroneous interpretation that the power law tailing of the BTC is caused by matrix diffusion. Copyright 2007 by the American Geophysical Union.