H14C-01 INVITED
Multiscale Hydrogeophysical Data Integration for Parameterization of Transport Model at Savannah River Site
We developed a multiscale characterization approach that integrates various data types, collected at differing measurement scales, to improve transport predictions at the Savannah River Site. The approach uses surface- based and cross-borehole-based geophysical data, and wellbore data to provide input for a site-wide dual- domain transport model. The transport model, also being developed in the characterization effort, incorporates the key interactions between mobile and immobile regions that are expected to play a role in long-term plume evolution. Analysis of existing characterization data suggests that the study site can be described by two hydrofacies, with one that is on average more mobile than the other, and that these hydrofacies are related to two lithofacies (L=0 and L=1, respectively). A statistical model is used to estimate the unknown proportion of lithofacies (FI) in each pixel I and the unknown lithofacies type (Li) in each pixel i, given the following data sets: (1) large-scale surface- based geophysical data; (2) small-scale cross-borehole geophysical data; and (3) small-scale wellbore data, such as from geophysical logs, flowmeter logs, or core samples. Using a Bayesian framework, we derive a conditional probability distribution of the unknown variables (FI and Li) for all of their respective pixel locations. The resulting distribution depends on the probability distribution of the large-scale geophysical data given the unknown values of FI; the probability distribution of FI given the unknown values of Li; and the probability distribution of unknown Li given the small-scale cross-borehole and wellbore data. The MCMC sampling method is used to efficiently draw samples from the conditional probability distribution, so that the probability distributions of the unknowns can be inferred. We are currently applying the approach to synthetic data and petrophysical relationships that are representative of site conditions. The approach is being modified, as needed, based on ongoing collection and reduction of multi- scale hydrological and geophysical data, and on the evolving characterization objectives that are identified during development of the site-wide transport model. Once refined, the multiscale approach will be used to characterize the relevant field-scale properties at the study site and to parameterize the transport model. This approach expands the scale of hydrogeophysical investigations, traditionally restricted to local-scale regions between closely spaced boreholes (~10m), to site-wide scales that are relevant for modeling plume fate and transport.
H14C-02
Impact of Sampling Volume on the Probability Density Function of Steady-State Concentration
In recent years, statistical theory has been used to compute the ensemble mean and variance of concentration in formations with second-order stationary log-conductivity fields. The merit of accurately estimating the mean and variance of concentration, however, remains unclear without knowing the shape of the probability density function (pdf). In a set-up where a conservative solute is continuously injected into a domain, the concentration can never exceed the range between zero and the concentration value in the injected solution. At small travel distances close to the fringe of the plume, an observation point may fall into the plume or outside, so that the statistical concentration distribution clusters at the two limiting values. Obviously, this results in non-Gaussian pdf's of concentration. With increasing travel distance, the lateral plume boundaries are smoothed, resulting in increased probability of intermediate concentrations. Likewise, averaging the concentration in a larger sampling volume, as typically done in field measurements, leads to intermediate concentrations. We present analytical results of concentration pdf's for point-like and spatially averaged measurements based on stochastic theory applied to stationary media. The approach is based on backtracking of the sampling volume to the injection plane. While effective dispersion describes the increase of the volume of influence with increasing time of backtracking, the difference between ensemble and effective dispersion quantifies the uncertainty of identifying the center of mass. We assume Gaussian pdf's for lateral displacements and the shape of the volume of influence. The resulting concentration pdf can be fitted by beta distributions. The results are compared to Monte Carlo simulations of flow and steady-state transport in 3-D heterogeneous domains. In both methods the shape of the pdf changes with distance to the contaminant source: Near the source, the distribution is bimodal, whereas it becomes an unimodal beta distribution far away from the contaminant source. The pdf of concentrations in the Monte Carlo simulations approaches a Gaussian-like shape with increasing distance to the contaminant source. Increasing the measurement volume decreases the distance over which the bimodal shape is a predominant feature of the concentration pdf. The analytical and empirical pdf's differ slightly, which we contribute to numerical artifacts in the Monte Carlo simulations but also to the hard assumptions made in the analytical approach. Our results imply that geostatistical techniques for interpolation and other statistical inferences based on Gaussian distributions, such as kriging and cokriging, maybe feasible only far away from the contaminant source. For calculations near the source, the beta-like distribution of concentration must not be neglected.
H14C-03
Identification of Reliability Limits in the Transfer Function Approach for the Solution of Inverse Problems in Groundwater Transport
In recent time a great attention is devoted to the solution of inverse problems in groundwater and, more specifically, in pollution transport. One of the main problems occurring in literature is the identification of the location of the pollutant source of the release history of the pollutant injection. Such information is deduced by the analysis of the pollutant concentration measured in monitoring points located in the aquifer. The reliability of the results of the different numerical procedures depends on several factors linked up with the presence of errors in the main data as important measurement errors, uncertainty in the knowledge of the aquifer parameters, etc. Nevertheless, the transport process itself, because of the effect of the dispersion, can be the reason for unreliable results of such procedures: in fact the role of the dispersion can hide the original characteristics of the release history smoothing peak values and broadening the duration of impulsive release. Moreover, the identification of the source can lead to a low confidence location since a too-wide area can be suspected to contain the font of pollution. As an example if the monitoring point is too far from the source or a long time is elapsed from the release the detected concentrations can be useless for the inversion procedure. In this work we identify threshold criteria that can, a priori, define if the inversion procedure can lead to reliable or unreliable results in order to distinguish the uncertainty due to the dispersion process itself from the measurement and hydraulic parameter errors. We have experience in the geostatistic approach for the restoring of the release history that is based on the use of the transfer function: starting from the analysis of the transfer function in a monitoring point we define the criteria which allow the forecast of unreliable solution of the inverse problem.
H14C-04
Numerical simulation of saltwater intrusion experiment
We have modeled laboratory experiments of saltwater intrusion, similar to the so-called Henry Problem, using TOUGH2/EOS7. In general, the simulation showed good agreement to the experiment including the transient advancement and the final profile of the saltwater wedge that showed little dispersion in a homogeneous case. In a two-layer heterogeneous case, however, the simulation could not reproduce the experiment in one aspect. In the experiment, the fast-moving colored saltwater traveling in the higher permeability layer was observed encroaching into the lower permeability layer below. However, at this writing, we have not been able to reproduce this phenomenon, which could be caused by some instability or heterogeneity within the layers.
H14C-05
Coupling Seepage and Radionuclide Transport in and Around Emplacement Drifts at Yucca Mountain
The proposed nuclear waste repository of the United States is located at Yucca Mountain, Nevada. Waste packages will be placed in deep (~350 m) underground drifts in volcanic tuff. Seepage may potentially occur at the repository drifts when the drifts get rewetted after a dryout period. The potential seepage water will be quickly evaporated or boiled to near dryness as long as it falls on the top of the hot waste package leading to formation of brine, precipitation of salts and volatilization of gases. These processes may potentially impact the long-term safety of waste packages in the drift. The objectives of this study are to: (1) develop a quantitative model of coupled thermal, hydrological, and chemical (THC) processes potentially leading to brine formation, salt precipitation and gas volatilization on top of waste packages and/or a drip shield and (2) dynamically integrate such a model into the larger-scale models of processes within and around waste emplacement drifts, as well as into the smaller-scale waste-package corrosion models. Process models were implemented into an existing reactive transport numerical simulator, TOUGHREACT, to allow modeling of (1) evaporative concentration to very high ionic strength (up to 40 molal), (2) boiling point elevation due to dissolved salts, (3) boiling/evaporation to dryness, and (4) salt deliquescence. An integrated near-field and in-drift THC simulation was run using a vertical 2-D grid extending from near the ground surface to the groundwater table, and covering a width equal to half the design drift spacing of 81 m. The integrated model was then used to simulate a discrete dripping event within the drift. The model considered the release of radionuclides into seepage water as this water contacts the waste package and flows through the invert. The precipitation of uranophane and Np-uranophane was also considered. These minerals form in the invert from the neutralization of mildly acidic seepage water by clay minerals. The main findings from this modeling effort are as follows: (1) the near-field and in-drift brine chemical evolution is dominated by the precipitation of NaCl, CaSO4, and CaCO3; (2) the generation of acid gases at high evaporative concentration yields PHCl ~10-7 bar at boiling temperatures, with pH staying > 5 in condensation areas; (3) the clay minerals in the invert neutralize the pH of seepage water, although this result is sensitive to assumptions regarding the kinetics of reactions with clays; (4) the drift invert may act as a pH buffer that promotes the precipitation of uranophane and impedes further downward migration of radionuclides at elevated concentrations, however, the pH buffer effect is subject to the content and composition of the clay minerals in the invert. The model captures some of the processes involved in salt formation and radionuclide transport, and can be further applied to capturing the details of radionuclide transport between the waste form and the rock through the invert.
H14C-06
An Inverse Model of Three-Dimensional Flow and Transport in Heterogeneous Porous Media
A three-dimensional flow and transport model was developed to simulate the results of a laboratory-scale experiment in which snapshots of concentration were obtained using magnetic resonance imaging (MRI) during the displacement of tracer through a 14 by 8 by 8 cm flow cell. The medium was deliberately constructed to be heterogeneous with a known spatial correlation structure using sand of five different grain-size distributions. The extremely well characterized flow cell and large, high-precision data set of concentrations during displacement make this a unique experiment for examining the validity of flow and transport models, and for exploring new methods for interpreting large data sets using advanced optimization algorithms. A transport model was constructed by solving the steady state flow equations using the Finite Element Heat and Mass (FEHM) code, using FEHM's particle tracking transport model for simulating tracer migration. The particle tracking model was selected so that precise estimates of the transport parameters could be obtained that are not corrupted by numerical dispersion; a large number of particles (typically one million) were required to provide accuracy. The inverse model included nine uncertain parameters, the five permeability values of the individual sand units, and four dispersion/diffusion parameters. The inverse problem was solved with AMALGAM and DREAM, two recently developed self-adaptive multimethod optimization algorithms. The computations were enabled by performing both the transport model and the optimization loop on a high-performance computing cluster. Computational results indicate that parameter estimates and increased understanding of the behavior of the system can be obtained, and significant improvements in the fit to the data over hand calibration can be achieved, using this inverse modeling approach. The study also illustrates that numerical methods that make effective use of high- performance computing resources and advanced optimization algorithms are crucial in enabling the interpretation of very large data sets using large-scale, distributed parameter models.
H14C-07
Solute transport in a synthetic fracture with one porous wall: fracture-matrix interaction
Contaminant transport in heterogeneous fractured aquifers occurs mostly through the networks of intersecting fractures. The physical mechanisms of solute transport in a single fracture with impermeable walls are well identified (Dronfield and Silliman 1993; Roux, Plouraboué et al. 1998; Keller, Roberts et al. 1999; Detwiler and Rajaram 2000): advection, Taylor-Aris dispersion, roughness dispersion, aperture-variation dispersion and molecular diffusion. However, when the permeability of the surrounding rock matrix cannot be neglected, there is, to our knowledge, no fundamental description of the mass transfert coefficient between the region of high permeability (the fracture) and that of low permeability (the surrounding matrix). We address here solute transport through a synthetic fracture with a porous wall. We present an analog experimental model setup in which we can focus on specific dispersion mechanisms, neglecting molecular diffusion, in order to extract descriptive laws that will be integrated in future numerical models. The planar horizontal fracture is 1 m long, 5 cm wide and its mean aperture is 5 mm. It is bounded by either two smooth parallel Plexiglass plates (impermeable walls configuration), or by one such plate and a porous medium consisting of 1 mm glass beads ("semi-permeable" configuration). A permanent laminar water flow is forced through the fracture at controlled mean velocity (~ 1mm/s), and a dye (patent blue) injection system simulates a point source of contaminant along the center plane of the fracture. The tracer plume is tracked using a visualization system based on (i) lasers illuminating a series of vertical linear optical sensor arrays, and (ii) 4 cameras positioned side by side and providing a composite image of the fracture viewed from the side. The two measurement systems yield consistent quantitative temporal descriptions of the tracer concentration, integrated over the fracture width and at several positions along the fracture length. The setup was validated by checking the conservation of the total dye quantity in the impermeable walls configuration, with comparison to classical advection-dispersion models (for different injection modes). The semi-permeable configuration was then investigated. Mass transfer between the fracture and the bounding porous matrix was measured, for various concentrations of the injected dye and with different geometries (roughness) of the fracture-matrix interface. Changing the overall flow rate allowed investigation of gravity effects, which are generally disregarded in theoretical studies. As recently suggested by Polak, Grader et al. (2003), they were observed to be significant. References: Detwiler, R. L. and H. Rajaram (2000), Water Resour.Res. 36(7):1611-1625 -- Dronfield, D. G. and S. E. Silliman (1993), Water Resour.Res. 29(10):3477-3483 -- Keller, A. A., P. V. Roberts, et al. (1999), Water Resour.Res. 35(1):55-63 -- Polak, A., A. S. Grader, et al. (2003), Hydrology 67:95-112 -- Roux, S., F. Plouraboué, et al. (1998), Transport in Porous Media 32: 97-116.