H12C-01 INVITED
Development of a "smart" tracer: The resazurin-resorufin assay of biological activity
A smart tracer is a tracer that provides, directly or through measurement of its concentration or in combination with another compound, at least 1 bit more information than a conservative tracer. In other words, the tracer provides information about conditions in the hydrologic system in addition to arrival time such as chemical conditions or biological activity. We have developed a smart tracer for quantifying biological activity along a flow path. We identified and characterized a suitable compound, resazurin (Raz), along with its reduction product resorufin (Rru). Resazurin is a weakly fluorescent redox-sensitive phenoxazin dye that undergoes an irreversible reduction to strongly fluorescent resorufin under mildly reducing conditions – most commonly in the presence of living bacteria. The Raz-Rru system has been widely used to test for the presence and viability of bacteria and other living cells. We characterized the decay, reaction, sorption and transport behavior of Raz and Rru in various waters and sediments. The compounds are stable (decay and reaction timescales of 100s-1000s of h) in natural water, except in the presence of strong light. Raz rapidly reacts to Rru in sediment (timescale of 1 h). The compounds are affected by significant sorption, with a Kd of 6.63 mL/g in sediment with 2.19% organic carbon. A set of mathematical models of the tracer concentrations were developed. Lastly, we conducted a successful field test of the tracer in the Riera de Santa Fe at Montseny, Catalonia, Spain. Results of these tests will be reported.
H12C-02
Geoelectrical Evidence of Bicontinuum Transport in Ground Water
The fate and transport of chemicals in ground water is commonly described by advection and dispersion processes. In many settings, however, observed transport behavior appears inconsistent with the standard advective-dispersive model; instead, concentration histories show long tailing behavior, non-Gaussian breakthrough, and/or rebound after pumping for mass removal has ceased. These phenomena have prompted the consideration of dual-domain, rate-limited mass transfer (RLMT) as a controlling process. Determination of parameters describing mass-transfer between mobile and immobile domains - or even verifying the occurrence of RLMT - is problematic because geochemical data-collection methods preferentially sample the mobile component of the pore space. We present direct evidence of RLMT at the field scale during an aquifer storage and recovery experiment. We observe a hysteretic relation between measurements of pore-fluid conductivity (from borehole fluid samples) and bulk earth conductivity (from borehole electrical-resistivity). This hysteresis contradicts advective-dispersive transport and the standard petrophysical model relating pore-fluid and bulk conductivity, but can be explained by bicontinuum transport models that include first-order RLMT. Using a simple model, we demonstrate that geoelectrical methods can be used to bound estimates of mass transfer-rates and immobile porosity that are otherwise difficult to estimate in situ. These findings suggest that RLMT is one of the fundamental processes controlling solute transport and the efficiency of aquifer remediation, and suggest that similar analyses in other geologic settings may help evaluate the prevalence of RLMT.
H12C-03
Mechanisms of Non-Fickian Transport
Non-Fickian transport behavior is due to a broad spectrum of rates limiting the solute movement. There are two generic mechanisms that can generate such a spectrum: the complex flow field of a disordered medium and the mass exchange between a mobile phase and a distribution of immobile states. We derive the basis of incorporating both of these mechanisms into the continuous time random walk (CTRW) framework and systematically study their interaction dynamics as a function of the spectra of advective- diffusive transition times and exchange times, and the relative separation of their respective time domains. Delineating the mechanisms is often subtle and the emphasis in the present study is on explicit physical situations in which these two different types of spectra are distinguishable, so that a more complete characterization of the transport can be obtained (i.e., rather than lumping all the rates together). Experimental data are analyzed from two such systems: (1) tracer transport in a fractured shear zone, and (2) sorbing species transported through a heterogeneous porous domain. In both systems, the data are analyzed within the CTRW framework, and compared also to the standard approach (use of the advection-dispersion equation and first order transfer). The latter does not account for the data while the CTRW framework is found to produce excellent fits and predictions, using a single set of parameters. New numerical techniques are also shown that enhance the stable solution of the nonlocal-in-time transport equation.
H12C-04
Some Comments on Nonlocal Transport Models
Nonlocal models have been developed in a variety of contexts for applications to transport in heterogeneous porous media, and can often represent more complex phenomena than can local models. However, this additional capability comes with some cost. Nonlocal models also demand more information, and thus require more effort to use both from the theoretical or applied perspective. In this work, a fully nonlocal development of the macroscale (nonreactive) transport equation for a heterogeneous porous media is presented in the context of volume averaging by upscaling from the microscale. In the most general case, the nonlocal model has nearly as much information content as the original microscale representation. It is not until certain simplifying assumptions are made that the nonlocal model shows a reduction in the number of degrees of freedom over that seen for the microscale model. Implications for nonlocal models, and models that are derivable from the nonlocal formulation, will be discussed.
H12C-05
Laboratory Observations of Non-Fickian Transport: The Effects of a Cutoff Time
The transport process in the framework of a continuous time random walk (CTRW) is portrayed as a sequence of transitions with displacements s and times t. A central focus of the CTRW approach is an accurate physical model of the entire spectrum ψ ( s, t) (or in the uncoupled case p( s)ψ(t)). Observations of non-Fickian transport in sandbox experiments1 have been analyzed using a power-law tail ψ(t)~ t-1- β with 0<β<2. For each sandbox medium a choice of β results in an excellent fit to the breakthrough curve (BTC) data. However, the value of β slowly increases with decreasing flow velocity. This is consistent with the shape of the full spectrum of ψ(t) gleaned from analytic calculations2, numerical simulations3 and permeability fields4. We represent the main features of this complete form with a truncated power-law (TPL), ψ(t)~ (t1 + t)-1-β \exp(-t/t2), where t1 and t2 are the limits of the power-law spectrum. An excellent fit to the entire BTC data set (including the changes in flow velocity) for each sandbox medium is accomplished with a single set of values of t1,β,t2. The use of the full spectrum of ψ(t) is not only necessary for the transition to Fickian behavior2 but to account for the dynamics of these laboratory observations of non-Fickian transport, especially the important role of the cutoff time t2. 1Levy, M. & B. Berkowitz, J.Cont.Hydrol. 64, 2003. 2Cortis, A., Y. Chen, H. Scher & B. Berkowitz, Phys. Rev. E 70, 2004. 3Bijeljic, B. & M. J. Blunt, Water Resour. Res. 42, 2006. 4Di Donato, G., E.O. Obi & M.J. Blunt, Geophys. Res. Lett. 30, 2003.
H12C-06
What is Wrong with the Boundary Conditions in Column Tracer Tests
Solute transport in a column is probably one of the most fundamental problems investigated in contaminant hydrology and soil physics because it serves as a benchmark for testing transport theories, for measuring dispersivities, etc. Despite its importance, there are still dispute and inconsistency on how to deal with the boundary conditions involved in such problems. The boundary condition could impose great influence upon transport in a column, particularly when the length of the column is relatively short, or the so-called Peclet number is not large. There are three types of boundary conditions to choose for transport in a column. Among these three types of boundary conditions, only the third-type boundary satisfies the mass balance requirement rigorously. The first type boundary, despite its frequent use in previous studies, could lead to serious mass balance problems. The most serious problem is on how to deal with the outlet boundary. Some studies have used a zero concentration gradient at the outlet (the so-called Danckwerts' boundary condition). This is named the model A. Another idea is to treat the finite length column as a part of an infinitely long column and to calculate the concentration at the outlet based on a formula developed for an infinitely long column. This is named the model B. The model A satisfies the mass balance requirement but was found to fit with the experimental data poorly. The model B does not satisfy the mass balance requirement, but usually agree well with the experimental data. So, the dilemma is: which model to choose? At present, most investigators prefer to choose the model B because of its close agreement with the experimental data, despite of its violation of the mass balance requirement. But the question is: why the model A, which satisfies the mass balance requirement, does not fit with the experimental data? It turns out that the advection-dispersion equation (ADE) that uses the Fick's first law to describe the hydrodynamic dispersion has some problems, particularly in the regions near the two boundaries. Taylor (1921) has pointed out that the dispersion coefficient varies linearly with time at the beginning and tends to its asymptotic, Fickian value after a travel time of a few correlation scales. Dagan and Bresler (1985) have further pointed out that the constant dispersivity is attained after the solute body has traveled tens of conductivity integral scales. For transport in a homogeneous column, the integral scale of the conductivity is probably around the pore scale or equivalent to the dispersivity value. Therefore, for a finite column whose length is not much greater than the dispersivity value, the transition zones in which solute transport is non-Fickian could consist of a significant portion of the column length. It is such non-Fickian transport in the column that is responsible for the failure of the model A. But still, why does the model B yield the right solution? There is no answer to this question based on a rigorous quantitative analysis yet. To resolve the dilemma, one must carry out a non-Fickian transport study to deal with the transition zones. It is my hypothesis that if the non-Fickian transport analysis succeeds, one will find that the mass balance requirement is indeed satisfied in the model B. Dagan and Bresler (1985) have pointed to the right direction, but a rigorous analysis has not followed. This is something interesting and worthwhile to investigate. REFERENCES CITED Dagan, G., and Bresler, E., 1985. Comment on ¡°Flux-averaged and volume-averaged concentration in continuum approaches to solute transport" by J.C. Parker and M.Th. van Genuchten. Water Resources Research, 21: 1299- 1300. Taylor, G.I., 1921. Diffusion by continuous movements. Proc. London Math Soc. 2: 196-212.
H12C-07
Nonlocal transport captured by spatiotemporal fractional derivative models: Modeling approach and field-scale applications
We investigate the spatiotemporal nonlocality underlying fractional derivative models as a possible explanation for regional-scale anomalous dispersion with heavy tails. Properties of four fractional advection-dispersion equation (fADE) models are analyzed systematically, including the space fADEs with either maximum or minimum skewness, the time fADE with a temporal fractional derivative 0<γ<1, and the novel extension of time fADE with 1<γ<2. Space fADEs describe the dependence of local concentration change on a wide range of spatial zones (i.e., the space nonlocality), while time fADEs describe dynamic mass exchange between mobile and immobile phases and therefore record the temporal history of concentration "loading" locally (i.e., the time nonlocality). We then apply the fADEs as models of anomalous dispersion to several extensively-studied, regional-scale, natural systems. Results suggest that large ranges of motion sizes require the space nonlocality, and long waiting times require time nonlocality. The unknown quantitative relationship between nonlocal parameters and subsurface heterogeneity, and the similarity in concentration profiles captured by different nonlocal models, all imply the importance of distinguishing the dominant nonlocality for the regional- scale anomalous dispersion process.