17 research outputs found
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Theory and Simulation of Diffusion Processes in Porous Media
Get PDFThe subsurface is spatially heterogeneous in geologic material composition leading to non-uniform groundwater flow fields. Preferential flow in highly conductive materials and diffusion into less conductive materials such as silts and clays, commonly present in alluvial aquifer systems in substantial volume fractions as high as 20 to 80 percent, enhance the dispersion, sequestration, and dilution of contaminants. This dissertation elucidates processes affecting groundwater solute migration in highly heterogeneous porous media, concentrating on ( 1) the role of diffusion in the dilution and sequestration of contaminants in the subsurface, (2) the modeling methods needed to address this phenomenon, and (3) the implications for natural attenuation of contaminant plumes.Simulations of contaminant migration and remediation in the alluvial-fan system of Lawrence Livermore National Laboratory confirm the importance of molecular diffusion in sequestering contaminants due to its role in promoting mass transfer in local- and field-scale low-permeability zones. Overall transport behavior and efficacy of pump-and-treat remediation show acute sensitivity to magnitude of effective diffusion coefficient, particularly within the range of uncertainty as inferred through laboratory studies of solute diffusion in clays. Simulations reveal an increase in the holdback of mass near source locations and a decrease in pump-and-treat efficiency with increase in effective diffusion coefficient. Results help to explain observations of scale-dependent-dispersion phenomena and confirm the well-founded limitations of pump and treat. Further, they emphasize the importance of characterizing the geologic structure of low-permeability lithologic units in assessing the viability of remedial technologies. In light of the need for scientific justification of natural attenuation phenomena recently endorsed as remedial technologies by the EPA, this research is particularly relevant to groundwater remediation problems confronting hydrologists and engineers.Transport simulations are facilitated by new theory and numerical methods to simulate diffusion processes by random walks in composite porous media, i.e., porous media in which effective subsurface transport parameters may be discontinuous (step functions). Discontinuities in effective subsurface transport properties commonly arise (1) at abrupt contacts between geologic materials (i.e., composite porous media) and (2) in discrete velocity fields of numerical groundwater-flow solutions. However, standard random-walk methods for simulating transport and the theory on which they are based only apply when effective transport properties are sufficiently smooth. Limitations of standard theory have precluded development of random-walk methods that obey advection dispersion equations in composite porous media. This problem is solved by generalizing stochastic differential equations (SDEs) to the case of discontinuous coefficients and developing random-walk methods to numerically integrate these equations. The new random-walk methods obey advection-dispersion equations, even in composite media. The techniques retain many of the computational advantages of standard random-walk methods, including the ability to efficiently simulate solute-mass distributions and arrival times while suppressing errors, such as numerical dispersion. The results apply to problems found in many scientific disciplines and offer a unique contribution to diffusion theory and the theory of SDEs
Role of Molecular Diffusion in Contaminant Migration and Recovery in an Alluvial Aquifer System
No full textDevelopment of RWHet to Simulate Contaminant Transport in Fractured Porous Media
Get PDFAccurate simulation of matrix diffusion in regional-scale dual-porosity and dual-permeability media is a critical issue for the DOE Underground Test Area (UGTA) program, given the prevalence of fractured geologic media on the Nevada National Security Site (NNSS). Contaminant transport through regional-scale fractured media is typically quantified by particle-tracking based Lagrangian solvers through the inclusion of dual-domain mass transfer algorithms that probabilistically determine particle transfer between fractures and unfractured matrix blocks. UGTA applications include a wide variety of fracture aperture and spacing, effective diffusion coefficients ranging four orders of magnitude, and extreme end member retardation values. This report incorporates the current dual-domain mass transfer algorithms into the well-known particle tracking code RWHet [LaBolle, 2006], and then tests and evaluates the updated code. We also develop and test a direct numerical simulation (DNS) approach to replace the classical transfer probability method in characterizing particle dynamics across the fracture/matrix interface. The final goal of this work is to implement the algorithm identified as most efficient and effective into RWHet, so that an accurate and computationally efficient software suite can be built for dual-porosity/dual-permeability applications. RWHet is a mature Lagrangian transport simulator with a substantial user-base that has undergone significant development and model validation. In this report, we also substantially tested the capability of RWHet in simulating passive and reactive tracer transport through regional-scale, heterogeneous media. Four dual-domain mass transfer methodologies were considered in this work. We first developed the empirical transfer probability approach proposed by Liu et al. [2000], and coded it into RWHet. The particle transfer probability from one continuum to the other is proportional to the ratio of the mass entering the other continuum to the mass in the current continuum. Numerical examples show that this method is limited to certain ranges of parameters, due to an intrinsic assumption of an equilibrium concentration profile in the matrix blocks in building the transfer probability. Subsequently, this method fails in describing mass transfer for parameter combinations that violate this assumption, including small diffusion coefficients (i.e., the free-water molecular diffusion coefficient 1×10-11 meter2/second), relatively large fracture spacings (such as meter), and/or relatively large matrix retardation coefficients (i.e., ). These “outliers” in parameter range are common in UGTA applications. To address the above limitations, we then developed a Direct Numerical Simulation (DNS)-Reflective method. The novel DNS-Reflective method can directly track the particle dynamics across the fracture/matrix interface using a random walk, without any empirical assumptions. This advantage should make the DNS-Reflective method feasible for a wide range of parameters. Numerical tests of the DNS-Reflective, however, show that the method is computationally very demanding, since the time step must be very small to resolve particle transfer between fractures and matrix blocks. To improve the computational efficiency of the DNS approach, we then adopted Roubinet et al.’s method [2009], which uses first passage time distributions to simulate dual-domain mass transfer. The DNS-Roubinet method was found to be computationally more efficient than the DNS-Reflective method. It matches the analytical solution for the whole range of major parameters (including diffusion coefficient and fracture aperture values that are considered “outliers” for Liu et al.’s transfer probability method [2000]) for a single fracture system. The DNS-Roubinet method, however, has its own disadvantage: for a parallel fracture system, the truncation of the first passage time distribution creates apparent errors when the fracture spacing is small, and thus it tends to erroneously predict breakthrough curves (BTCs) for the parallel fracture system. Finally, we adopted the transient range approach proposed by Pan and Bodvarsson [2002] in RWHet. In this method, particle transfer between fractures and matrix blocks can be resolved without using very small time steps. It does not use any truncation of the first passage time distribution for particles. Hence it does not have the limitation identified above for the DNS-Reflective method and the DNS-Roubinet method. Numerical results were checked against analytical solutions, and also compared to DCPTV2.0 [Pan, 2002]. This version of RWHet (called RWHet-Pan&Bodvarsson in this report) can accurately capture contaminant transport in fractured porous media for a full range of parameters without any practical or theoretical limitations
Direct numerical simulation of matrix diffusion across fracture/matrix interface
No full textAccurate descriptions of matrix diffusion across the fracture/matrix interface are critical to assessing contaminant migration in fractured media. The classical transfer probability method is only applicable for relatively large diffusion coefficients and small fracture spacings, due to an intrinsic assumption of an equilibrium concentration profile in the matrix blocks. Motivated and required by practical applications, we propose a direct numerical simulation (DNS) approach without any empirical assumptions. A three-step Lagrangian algorithm was developed and validated to directly track the particle dynamics across the fracture/matrix interface, where particle's diffusive displacement across the discontinuity is controlled by an analytical, one-side reflection probability. Numerical experiments show that the DNS approach is especially efficient for small diffusion coefficients and large fracture spacings, alleviating limitations of the classical modeling approach
Monte Carlo simulation of superdiffusion and subdiffusion in macroscopically heterogeneous media
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Space‐fractional advection‐dispersion equations with variable parameters: Diverse formulas, numerical solutions, and application to the Macrodispersion Experiment site data
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Modeling groundwater contaminant transport in the presence of large heterogeneity: A case study comparing MT3D and RWhet.
Get PDFA case study is presented that implements two numerical models for simulating a 30-year PAT operation conducted at a large contaminated site for which high-resolution data sets are available. A Markov chain based stochastic method is used to conditionally generate the realizations with random distribution of heterogeneity for the Tucson International Airport Area (TIAA) federal Superfund site. The fields were conditioned to data collected for 245 boreholes drilled at the site. Both MT3DMS and the advanced random walk particle method (RWhet) were used to simulate the PAT-based mass removal process. The results show that both MT3DMS and RWhet represent the measured data reasonably, with Root Mean Square Error (RMSE) less than 0.03. The use of fine grids and the total-variation-diminishing method (TVD) limited the effects of numerical dispersion for MT3DMS. However, the effects of numerical dispersion were observed when compared to the simulations produced with RWhet using a larger number of particles, which provided more accurate results with RMSE diminishing from 0.027 to 0.024 to 0.020 for simulations with 1, 20, and 50 particles. The computational time increased with more particles used in the model, but was still much less than the time required for MT3DMS, which is an advantage of RWhet. By showing the results using both methods, this study provides guidance for simulating long-term PAT systems. This work will lead to improve understanding of contaminant transport and plume persistence, and in turn will enhance site characterization and site management for contaminated sites with large plumes
The Effects of Dual-Domain Mass Transfer on the Tritium−Helium-3 Dating Method
No full textDiffusion of tritiated water (referred to as tritium) and helium-3 between mobile and immobile regions in aquifers (mass transfer) can affect tritium and helium-3 concentrations and hence tritium−helium-3 (3H/3He) ages that are used to estimate aquifer recharge and groundwater residence times. Tritium and helium-3 chromatographically separate during transport because their molecular diffusion coefficients differ. Simulations of tritium and helium-3 transport and diffusive mass transfer along stream tubes show that mass transfer can shift the 3H/3He age of the tritium and helium-3 concentration ([3H + 3He]) peak to dates much younger than the 1963 peak in atmospheric tritium. Furthermore, diffusive mass-transfer can cause the 3H/3He age to become younger downstream along a stream tube, even as the mean water-age must increase. Simulated patterns of [3H + 3He] versus 3H/3He age using a mass transfer model appear consistent with a variety of field data. These results suggest that diffusive mass transfer should be considered, especially when the [3H + 3He] peak is not well defined or appears younger than the atmospheric peak. 3H/3He data provide information about upstream mass-transfer processes that could be used to constrain mass-transfer models; however, uncritical acceptance of 3H/3He dates from aquifers with immobile regions could be misleading
