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Statistical Formulation of Generalized Tracer Retention in Fractured Rock
Author(s) -
Cvetkovic Vladimir
Publication year - 2017
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2017wr021187
Subject(s) - tracer , continuous time random walk , parametrization (atmospheric modeling) , advection , random walk , fick's laws of diffusion , diffusion , mass transfer , statistical physics , mathematics , physics , mechanics , thermodynamics , statistics , quantum mechanics , nuclear physics , radiative transfer
We study tracer retention in fractured rock by combing Lagrangian and time domain random walk frameworks, as well as a statistical representation of the retention process. Mass transfer is quantified by the retention time distribution that follows from a Lagrangian coupling between advective transport and mass exchange processes, applicable for advection‐dominated transport. A unifying parametrization is presented for generalized diffusion using two rates denoted by k 1 and k 2 where k 1 is a forward rate and k 2 a reverse rate, plus an exponent as an additional parameter. For the Fickian diffusion model, k 1 and k 2 are related to measurable retention properties of the fracture‐matrix by the method of moments, whereas for the non‐Fickian case dimensional analysis is used. The derived retention time distributions are exemplified for interpreting tracer tests as well as for predictive modeling of expected tracer breakthrough. We show that non‐Fickian effects can be notable when transport is upscaled based on a non‐Fickian interpretation of a tracer test for which deviations from Fickianity are relatively small. The statistical representation of retention clearly shows the significance of the forward rate k 1 which depends on the active specific surface area and is the most difficult parameter to characterize in the field.