Tracer travel and residence time distributions in highly heterogeneous aquifers: Coupled effect of flow variability and mass 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 k1 and k2 where k1 is a forward rate and k2 a reverse rate, plus an exponent as an additional parameter. For the Fickian diffusion model, k1 and k2 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 k1 which depends on the active specific surface area and is the most difficult parameter to characterize in the field.

1 / k_{2}

g (t) = A k_{0} ν {normalE}_{ν} (k_{0} t)

where

{normalE}_{ν} ()

is the exponential integral.…”

Section: Retention Modelsmentioning

confidence: 99%

Statistical Formulation of Generalized Tracer Retention in Fractured Rock

Cvetković

2017

“…This time quantifies how long a tracer particle will be immobilized along a trajectory with water travel time

τ

over a distance

L

. The RTD is the probability density function (PDF) of

T

(Cvetkovic, ; Cvetkovic et al, ).…”

Section: Theorymentioning

confidence: 99%

“…If the advection scale of interest is denoted by L (e.g., length scale of a tracer test, or the extent of a discrete fracture), the total time a tracer molecule will spend over the distance L is 𝜏 + T, where T is a retention time. This time quantifies how long a tracer particle will be immobilized along a trajectory with water travel time 𝜏 over a distance L. The RTD (4) is the probability density function (PDF) of T (Cvetkovic, 2017;Cvetkovic et al, 2016).…”

Section: Single Advection Trajectorymentioning

confidence: 99%

Inference of Retention Time From Tracer Tests in Crystalline Rock

Cvetković

Poteri

Selroos

et al. 2020

A statistical parametrization of transport combined with a new, general partition function for diffusive mass transfer (Cvetkovic, 2017, https://doi.org/10.1002/2017WR021187) is here developed into a practical tool for evaluating tracer tests in crystalline rock. The research question of this study is how to separate the characteristic times of retention and advection, using tracer test information alone; this decoupling is critical for upscaling of transport. Three regimes are identified based on the unconditional mean number of trapping events. Analytical expressions are derived for inferring transport‐retention parameters; these are first tested on a series of generic examples and then using two sets of tracer test data. Our results indicate that the key transport‐retention parameters can be inferred separately with reasonable accuracy by a few simple steps, provided that the macrodispersion is not too large and retention not too strong. Of particular interest is inference of the retention time from the breakthrough curve peak that avoids costly asymptotic monitoring. Finally, we summarize the retention times as inferred from a series of nonsorbing tracer tests in the Swedish granite, demonstrating the uncertainties when estimating retention based on material and structural properties from samples. Possible strategies for reducing these uncertainties that combine improved understanding of crystalline rock evolution with numerical simulations are noted as topics for future research.

“…For transport in heterogeneous porous media, Hansen and Berkowitz (2014) introduced a cognate CTRW approach, capturing transport as a series of transitions among parallel planes orthogonal to mean flow (leading to a quasi‐1‐D upscaled transport model). Subsequently, another quasi‐1‐D approach that approximates flow in heterogeneous media with an effective medium and also incorporates MIMT was discussed by Cvetkovic et al (2016). TDRW solutions based on classical (ADE) ideas and that include transverse dispersion were also presented by Bodin (2015).…”

Section: Introductionmentioning

confidence: 99%

Modeling Non‐Fickian Solute Transport Due to Mass Transfer and Physical Heterogeneity on Arbitrary Groundwater Velocity Fields

Hansen

Berkowitz

2020

We present a hybrid approach to groundwater transport modeling, "CTRW-on-a-streamline," that allows continuous-time random walk (CTRW) particle tracking on large-scale, explicitly delineated heterogeneous groundwater velocity fields. The combination of a non-Fickian transport model (in this case, the CTRW) with general heterogeneous velocity fields represents an advance of the current state of the art, in which non-Fickian transport models or heterogeneous velocity fields are employed but generally not both. We present a general method for doing this particle tracking that fully separates the model parameters characterizing macroscopic flow, subscale advective heterogeneity, and mobile-immobile mass transfer, such that each can be directly specified a priori from available data. The method is formalized and connections to classic CTRW and subordination approaches are made. Numerical corroboration is presented.