Efficient random walk particle tracking algorithm for advective‐dispersive transport in media with discontinuous dispersion coefficients and water contents

Bechtold, Michel; Vanderborght, Jan; Ippisch, Olaf; Vereecken, Harry

doi:10.1029/2010wr010267

Cited by 65 publications

(72 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…As mentioned by Delay et al [32], Lagrangian schemes (particle tracking methods) are more accurate and less computationally intensive than Eulerian schemes. The main Lagrangian schemes include random-walk particle tracking (RWPT) method [33,34], convolution-based particle tracking (CBPT) method [35,36], and continuous-time random-walk (CTRW) method [37,38]. For very heterogeneous media such as fractured rock mass, flow velocities may span several orders of magnitude.…”

Section: Literature Review About Nuclide Transport Simulationmentioning

confidence: 99%

Implementation of a Time-Domain Random-Walk Method into a Discrete Element Method to Simulate Nuclide Transport in Fractured Rock Masses

Liu

Chan

et al. 2017

Geofluids

View full text Add to dashboard Cite

It is essential to study nuclide transport with underground water in fractured rock masses in order to evaluate potential radionuclide leakage in nuclear waste disposal. A time-domain random-walk (TDRW) method was firstly implemented into a discrete element method (DEM), that is, UDEC, in this paper to address the pressing challenges of modelling the nuclide transport in fractured rock masses such as massive fractures and coupled hydromechanical effect. The implementation was then validated against analytical solutions for nuclide transport in a single fracture and a simple fracture network. After that, the proposed implementation was applied to model the nuclide transport in a complex fracture network investigated in the DECOVALEX 2011 project to analyze the effect of matrix diffusion and stress on the nuclide transport in the fractured rock masses. It was concluded that the implementation of the TDRW method into UDEC provided a valuable tool to study the nuclide transport in the fractured rock masses. Moreover, it was found that the total travel time of the nuclide particles in the fractured rock masses with the matrix diffusion and external stress modelled was much longer than that without the matrix diffusion and external stress modelled.

show abstract

Section: Literature Review About Nuclide Transport Simulationmentioning

confidence: 99%

Implementation of a Time-Domain Random-Walk Method into a Discrete Element Method to Simulate Nuclide Transport in Fractured Rock Masses

Liu

Chan

et al. 2017

Geofluids

View full text Add to dashboard Cite

show abstract

“…When the two retardation coefficients m R and f R equal 1, (10) reduces to the formula proposed by Bechtold et al [2011]. A uniform [0 1] random number U is generated and compared to the above probabilities.…”

Section: The Direct Numerical Simulation (Dns) Of Contaminant Transpomentioning

confidence: 99%

“…These are the same types of conditions that exist across a fracture-matrix interface. Previously developed particle tracking algorithms (e.g., LaBolle et al [1996,2000], LaBolle and Zhang [2006], and Bechtold et al [2011]), several of which are already included in RWHet, can be applied to track particles across a fracture-matrix interface. Figure 10.…”

Section: The Direct Numerical Simulation (Dns) Of Contaminant Transpomentioning

confidence: 99%

See 1 more Smart Citation

Development of RWHet to Simulate Contaminant Transport in Fractured Porous Media

Zhang¹,

LaBolle²,

Reeves³

et al. 2012

View full text Add to dashboard Cite

EXECUTIVE SUMMARYAccurate simulation of matrix diffusion in regional-scale dual-porosity and dualpermeability 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 particletracking 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 wellknown 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 freewater molecular diffusion coefficient ). 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 res...

show abstract

“…The reader is referred to Delay et al [2005] and Salamon et al [2006] for comprehensive reviews of space-based particle-tracking methods, including theoretical, conceptual, and numerical developments in the field of subsurface hydrology since the early works of Ahlstrom et al [1977] and Prickett et al [1981]. Additional recent publications of relevance include Bechtold et al [2011] and Lejay and Pichot [2012].…”

Section: Introductionmentioning

confidence: 99%

From analytical solutions of solute transport equations to multidimensional time‐domain random walk (TDRW) algorithms

Bodin

2015

Water Resources Research

View full text Add to dashboard Cite

In this study, new multi-dimensional time-domain random walk (TDRW) algorithms are derived from approximate one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) analytical solutions of the advection-dispersion equation and from exact 1-D, 2-D, and 3-D analytical solutions of the pure-diffusion equation. These algorithms enable the calculation of both the time required for a particle to travel a specified distance in a homogeneous medium and the mass recovery at the observation point, which may be incomplete due to 2-D or 3-D transverse dispersion or diffusion. The method is extended to heterogeneous media, represented as a piecewise collection of homogeneous media. The particle motion is then decomposed along a series of intermediate checkpoints located on the medium interface boundaries. The accuracy of the multi-dimensional TDRW method is verified against (i) exact analytical solutions of solute transport in homogeneous media and (ii) finite-difference simulations in a synthetic 2-D heterogeneous medium of simple geometry. The results demonstrate that the method is ideally suited to purely diffusive transport and to advection-dispersion transport problems dominated by advection. Conversely, the method is not recommended for highly dispersive transport problems because the accuracy of the advectiondispersion TDRW algorithms degrades rapidly for a low P eclet number, consistent with the accuracy limit of the approximate analytical solutions. The proposed approach provides a unified methodology for deriving multi-dimensional time-domain particle equations and may be applicable to other mathematical transport models, provided that appropriate analytical solutions are available.

show abstract

Efficient random walk particle tracking algorithm for advective‐dispersive transport in media with discontinuous dispersion coefficients and water contents

Cited by 65 publications

References 40 publications

Implementation of a Time-Domain Random-Walk Method into a Discrete Element Method to Simulate Nuclide Transport in Fractured Rock Masses

Implementation of a Time-Domain Random-Walk Method into a Discrete Element Method to Simulate Nuclide Transport in Fractured Rock Masses

Development of RWHet to Simulate Contaminant Transport in Fractured Porous Media

From analytical solutions of solute transport equations to multidimensional time‐domain random walk (TDRW) algorithms

Contact Info

Product

Resources

About