Development of RWHet to Simulate Contaminant Transport in Fractured Porous Media

Abstract

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...

Evaluating the Effects of Multiscale Heterogeneous Sediments on Solute Mixing and Effective Dispersion

“…RWHet is an accurate, computationally efficient particle‐tracking code that has been widely used in solute transport simulations in both heterogeneous porous and fractured media (Guo et al., 2019; Reeves et al., 2008a, 2008b; Yong et al., 2008; Zhang et al., 2013). RWHet can directly read cell‐by‐cell flux and hydraulic head outputs generated by MODFLOW (Zhang et al., 2012), and solves the Langevin equation which is equivalent to solving the governing equation for nonreactive solute transport in saturated porous media defined as: $$$\frac{\partial }{\partial t}\left[{\Theta}(\boldsymbol{x},t)c(\boldsymbol{x},t)\right]=-\sum\limits _{i=1}^{3}\frac{\partial }{\partial {x}_{i}}\left[{v}_{i}(\boldsymbol{x},t){\Theta}(\boldsymbol{x},t)c(\boldsymbol{x},t)\right]+\sum\limits _{i,j=1}^{3}\frac{\partial }{\partial {x}_{i}}[{D}_{ij}(\boldsymbol{x},t){\Theta}(\boldsymbol{x},t)\frac{\partial c(\boldsymbol{x},t)}{\partial {x}_{j}}]+\sum\limits _{k}{q}_{k}(\boldsymbol{x},t){c}_{k}(\boldsymbol{x},t){\delta }_{k}\left(\boldsymbol{x}-{\boldsymbol{x}}_{\boldsymbol{k}}\right)$$$ where c [M/L 3 ] is the dissolved resident concentration; v [L/T 1 ] is the velocity; Θ [L 3 /L 3 ] is the porosity; x i,j [L] is the distance along the respective Cartesian coordinate axis; c k [M/L 3 ] is the aqueous phase concentration in the flux q k [L 3 /T] of water at x k ; δ k is a Dirac function . D ij [L 2 /T] is the velocity‐dependent l...…”

“…RWHet is an accurate, computationally efficient particle-tracking code that has been widely used in solute transport simulations in both heterogeneous porous and fractured media (Guo et al, 2019;Reeves et al, 2008aReeves et al, , 2008bYong et al, 2008;Zhang et al, 2013). RWHet can directly read cell-by-cell flux and hydraulic head outputs generated by MODFLOW (Zhang et al, 2012), and solves the Langevin equation which is equivalent to solving the governing equation for nonreactive solute transport in saturated porous media defined as:…”

Incorporating Super‐Diffusion due to Sub‐Grid Heterogeneity to Capture Non‐Fickian Transport

“…The following particle‐tracking algorithms are coded into RWHet (LaBolle ), which is a mature Random Walk solver for simulating solute transport in heterogeneous porous media that has undergone significant model validation (Zhang et al ): Calculate the operational time for each particle during the k ‐th jump: …”