Analytical model for solute transport in discrete fracture networks: 2D spatiotemporal solution with matrix diffusion

Khafagy, Mohamed; El‐Dakhakhni, Wael; Dickson‐Anderson, Sarah

doi:10.1016/j.cageo.2021.104983

Cited by 10 publications

(4 citation statements)

References 33 publications

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“…Therefore, the application of the STRW approach in a DFN requires prior identification of the BTCs at the network's junctions. This can be achieved through the application of available techniques (e.g., the TDRW [62] or the convolution [56] methods). In addition, most of the fractures in a DFN are subjected to temporal contaminant release at their inlets.…”

Section: Methods Application In Discrete Fracture Networkmentioning

confidence: 99%

“…Several Lagrangian-based numerical methods have been developed to quantify the contaminant BTC at the junctions of a DFN, for which the Time Domain Random Walk (TDRW) approach has shown superiority in terms of accuracy and required computational resources [54,55]. Convolving the analytical solutions developed for single fractures using the temporal contaminant concentration at the fracture inlet has been recently suggested as an efficient alternative for estimating the BTCs at the network junctions [56]. On the other hand, the Random Walk Particle Tracking (RWPT) method has been extensively adopted to map the contaminant's concentration across DFNs as well as to estimate the BTCs at the network junctions [49,[57][58][59].…”

Section: Introductionmentioning

confidence: 99%

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Analytically Enhanced Random Walk Approach for Rapid Concentration Mapping in Fractured Aquifers

Yosri,

Ghaith,

Ahmed

et al. 2024

Water

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The efficient management and remediation of contaminated fractured aquifers necessitate an accurate prediction of the spatial distribution of contaminant concentration within the system. Related existing analytical solutions are only applicable to single fractures and have not yet been extrapolated to the aquifer scale where a network of connected fractures exists. The Random Walk Particle Tracking (RWPT) method has been extensively adopted for concentration mapping in Discrete Fracture Networks (DFNs), albeit at exorbitant computational costs and without efficiently accommodating complex physical processes (e.g., two-site kinetics). This study introduces an analytically enhanced Spatiotemporal Random Walk (STRW) approach that facilitates the efficient time-dependent mapping of contaminant concentration in DFNs. The STRW approach employs a distribution function to simultaneously estimate the displacement of particles released through the system either instantaneously or over time. The STRW approach efficiently reproduced the contaminant concentration, calculated using available analytical solutions under a range of fate and transport mechanisms. The efficacy of the STRW approach is also confirmed in a synthetic impermeable DFN through replicating the concentration maps produced using the RWPT method. The developed approach represents an accurate and computationally efficient dynamic concentration mapping technique that can support the effective operation, management, and remediation of fractured aquifers under contamination events.

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Section: Methods Application In Discrete Fracture Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytically Enhanced Random Walk Approach for Rapid Concentration Mapping in Fractured Aquifers

Yosri,

Ghaith,

Ahmed

et al. 2024

Water

Self Cite

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“…Processes 2023, 11, 3157 2 of 17 in two dimension or planar polygons in three dimensions, which can be denoted as 2D DFN and 3D DFN, respectively [21][22][23]. Previous investigations have demonstrated that 2D DFNs, which can be regarded as the cut planes from 3D DFNs, cannot capture the 3D structure of individual fractures, and thus underestimate the connectivity of fracture networks.…”

Section: Introductionmentioning

confidence: 99%

Effects of Topological Properties with Local Variable Apertures on Solute Transport through Three-Dimensional Discrete Fracture Networks

Huang,

Zhang,

Han

2023

Processes

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In this study, the effects of topological properties with local variable apertures on fluid flow and solute transport through three-dimensional (3D) discrete fracture networks (DFNs) were investigated. A series of 3D DFNs with different fracture density, length, and aperture distribution were generated. The fluid flow and solute transport through the models were simulated by combining the MATLAB code and COMSOL Multiphysics. The effects of network topology and aperture heterogeneity on fluid flow and transport process were analyzed. The results show that the fluid flow and solute transport exhibit a strong channeling effect even in the DFNs with identical aperture, in which the areas of fast and slow migration fit well with the high- and low-flow regions, respectively. More obvious preferential paths of flow and migration are observed in individual fractures for the DFN with heterogeneous aperture than the model with identical aperture. Increasing the fracture length exponent reduces the available flow and transport paths for sparse fracture networks but does not significantly change the flow and transport channels for dense fracture networks. The breakthrough curves (BTCs) shift towards the right and slightly lag behind as the fracture density decreases or the aperture heterogeneity increases. The advection–diffusion equation (ADE) model cannot properly capture the evolution of BTCs for 3D DFNs, especially the long tails of BTCs. Compared to the ADE model, the mobile-immobile model (MIM) model separating the liquid phase into flowing and stagnate regions is proven to better fit the BTCs of 3D DFNs with heterogeneous aperture.

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“…Darcy law is applied for each fracture segment and the mass balance must be achieved at each fracture intersection. The DFN approach was studied by Cacas et al (1990), Sahimi (1995), Adler and Thovert (1999), Liu and Bodvarsson (2001), Park et al (2001), Zhang and Sanderson (2002), de Dreuzy et al (2002Dreuzy et al ( , 2004, Hyman et al (2015), Maillot et al (2016), Ahmed et al (2019), Frampton et al (2019), Jarrahi et al 2019, Khafagy et al (2020, Sweeney and Hyman (2020), and Khafagy et al (2021). On the other hand, the SC modeling approach depends on the representative elementary volume (REV) concept which represents the rock mass as an equivalent porous medium.…”

Section: Introductionmentioning

confidence: 99%

Modeling radial groundwater flow in fractured media using fracture continuum approach

2022

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Two modeling approaches are commonly utilized for simulating flow in fractured formations: the discrete fracture network (DFN) approach and the stochastic continuum (SC) approach. Although the DFN approach is the most accurate, it has computational and memory constraints. The SC approach ensures fast processing but results in system over-homogenization. The fracture continuum (FC) approach arises as an integrated technique that incorporates the merits of both approaches. The main objective of this research is to develop a computationally efficient technique based on the FC approach to simulate the radial groundwater flow towards wells through two-dimensional fractured media under both steady and transient conditions. A stochastic generation of the DFN is performed in a Monte Carlo framework taking into account wells positioning. The DFN flow system is solved by applying the mass balance equation at fracture intersections. Fracture segments are mapped onto grids of 1 × 1 m and 5 × 5 m resolution as conductivity and specific storage cells. The grid flow problem is solved via MODFLOW. Flow and head discrepancies between the proposed technique and the DFN approach (reference solution) are assessed in steady and transient conditions. A grid-conductivity correction is needed to preserve the DFN flow in the presence of wells. A porosity estimation is proposed to identify the grid-pressure transient response. Promising flow and head results are observed for fine and coarse grid models. Some of the studied cases show large discrepancies in the maximum drawdown obtained on the coarse grid model. Accordingly, a new technique is proposed to handle such discrepancies and is found efficient in transient simulations (e.g., 11% and 26.12% discrepancies are minimized to − 0.93% and − 1.03% for two studied cases). The adopted mapping technique is found efficient when the interest is to estimate the average drawdown over an aquifer as correlation coefficients of 0.89 and 0.97 are found for the coarse and fine grid models, respectively when compared to the DFN model. However, the technique has limitations in estimating the drawdown at locations of wells.

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Analytical model for solute transport in discrete fracture networks: 2D spatiotemporal solution with matrix diffusion

Cited by 10 publications

References 33 publications

Analytically Enhanced Random Walk Approach for Rapid Concentration Mapping in Fractured Aquifers

Analytically Enhanced Random Walk Approach for Rapid Concentration Mapping in Fractured Aquifers

Effects of Topological Properties with Local Variable Apertures on Solute Transport through Three-Dimensional Discrete Fracture Networks

Modeling radial groundwater flow in fractured media using fracture continuum approach

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