Improvements and Corrections to AT123D Code

Burnell, Daniel K.; Lester, Barry H.; Mercer, James W.

doi:10.1111/j.1745-6584.2011.00905.x

Cited by 8 publications

(4 citation statements)

References 13 publications

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“…Additional multispecies analytical solutions may be developed using CTRW spatial and temporal Green's functions for various initial and boundary conditions in a similar manner as presented in Burnell et al (2017) for a single species. Spatial Green's functions can be convolved spatially against an initial solute distribution for various source geometries (e.g., Burnell et al 2012b) in order to determine the resident or flux concentration at any desired location. For arbitrary concentration history boundary conditions, temporal-pulse semi-infinite solutions can be used with the Laguerre expansion method (e.g., Hansen and Kueper 2009).…”

Section: Mim Mass Exchangementioning

confidence: 99%

A Practical Modeling Framework for Non‐Fickian Transport and Multi‐Species Sequential First‐Order Reaction

Burnell¹,

Hansen

et al. 2018

Groundwater

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Many studies indicate that small-scale heterogeneity and/or mobile-immobile mass exchange produce transient non-Fickian plume behavior that is not well captured by the use of the standard, deterministic advection-dispersion equation (ADE). An extended ADE modeling framework is presented here that is based on continuous time random walk theory. It can be used to characterize non-Fickian transport coupled with simultaneous sequential first-order reactions (e.g., biodegradation or radioactive decay) for multiple degrading contaminants such as chlorinated solvents, royal demolition explosive, pesticides, and radionuclides. To demonstrate this modeling framework, new transient analytical solutions are derived and are inverted in Laplace space. Closed-form, steady-state, multi-species analytical solutions are also derived for non-Fickian transport in highly heterogeneous aquifers with linear sorption-desorption and matrix diffusion for use in spreadsheets. The solutions are general enough to allow different degradation rates for the mobile and immobile zones. The transient solutions for multi-species transport are applied to examine the effects of source remediation on the natural attenuation of downgradient plumes of both parent and degradation products in highly heterogeneous aquifers. Results for representative settings show that the use of the standard, deterministic ADE can over-estimate cleanup rates and under-predict the cleanup timeframe in comparison to the extended ADE analytical model. The modeling framework and calculations introduced here are also applied for a 30 year groundwater cleanup program at a site in Palm Bay, Florida. The simulated plume concentrations using the extended ADE exhibited agreement with observed long concentration tails of trichloroethene, cis 1,2 DCE, and VC that remained above cleanup goals.

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Section: Mim Mass Exchangementioning

confidence: 99%

A Practical Modeling Framework for Non‐Fickian Transport and Multi‐Species Sequential First‐Order Reaction

Burnell¹,

Hansen

et al. 2018

Groundwater

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“…The modified AT123D code, AT123D‐AT [ Burnell et al . ] was used to evaluate the model subject to the appropriate initial and boundary conditions, as well as source function. Using parameter values given in Tables and while setting

D_{f}

α

λ_{w}

λ_{s}

to zero, and using the values for

q_{0}

and

t_{p}

given in Table (assuming the source function takes the form of slug mass loading as described by equation (5)), the model solution would be simplified to represent transport in a three‐dimensional aquifer with finite thickness and uniform groundwater velocity.…”

Section: Evaluation Of Model Solutionsmentioning

confidence: 99%

Semianalytical solutions for transport in aquifer and fractured clay matrix system

Huang

Goltz

2015

Water Resour. Res.

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A three-dimensional mathematical model that describes transport of contaminant in a horizontal aquifer with simultaneous diffusion into a fractured clay formation is proposed. A group of semianalytical solutions is derived based on specific initial and boundary conditions as well as various source functions. The analytical model solutions are evaluated by numerical Laplace inverse transformation and analytical Fourier inverse transformation. The model solutions can be used to study the fate and transport in a three-dimensional spatial domain in which a nonaqueous phase liquid exists as a pool atop a fractured low-permeability clay layer. The nonaqueous phase liquid gradually dissolves into the groundwater flowing past the pool, while simultaneously diffusing into the fractured clay formation below the aquifer. Mass transfer of the contaminant into the clay formation is demonstrated to be significantly enhanced by the existence of the fractures, even though the volume of fractures is relatively small compared to the volume of the clay matrix. The model solution is a useful tool in assessing contaminant attenuation processes in a confined aquifer underlain by a fractured clay formation.

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“…As expected, the semiinfinite first‐type parent solution concentration values are slightly higher. The infinite domain ADRE analytical solution for a continuous source was developed by integrating a one‐dimensional Green's function [e.g., Bear , ; Yeh , ; Burnell et al ., ] in order to examine particles that disperse and degrade upgradient of the source. The volume‐averaged concentration of this analytical solution (Table ) was transformed to flux‐averaged concentration using

C_{1 f} = C_{1 v} - \frac{D_{x}}{v} \frac{\partial C_{1 v}}{\partial x}

[ Kreft and Zuber , ], and is presented in Figure a.…”

Section: Application Of 1‐d Stochastic Monte Carlo Ctrw Models Of Tramentioning

confidence: 99%

Stochastic modeling analysis of sequential first-order degradation reactions and non-Fickian transport in steady state plumes

2014

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Stochastic analyses were performed to examine sequential first-order monomolecular reactions at the microscopic scale and both Fickian and non-Fickian plume reactive transport at the macroscopic scale. An analytical solution was derived for the chemical master equation (CME) for a closed system of irreversible first-order monomolecular reactions. Taking a Lagrangian reference frame of particles migrating from a source, analyses show that the relative concentration of each species in the deterministic analytical solution for 1-D steady state plug flow with first-order sequential degradation is mathematically equivalent to the mean of a multinomial distribution of plume particles moving at constant velocity with sequential transformations described by transition probabilities of a discrete state, continuous-time Markov chain. In order to examine the coupling of reaction and transport terms in subdiffusive-reactive transport equations, a closed-form multispecies analytical solution also was derived for steady state advection, dispersion, and sequential first-order reaction. Using a 1-D continuous-time random walk (CTRW) embedded in Markov chains, computationally efficient Monte Carlo simulations of particle movement were performed to more fully examine effects of subdiffusive-reactive transport with an application to steady state, sequentially degrading multispecies plumes at a site in Palm, Bay, FL. The simulation results indicated that non-Fickian steady state plumes can resemble Fickian plumes because linear reactions truncate the waiting time between particle jumps, which removes lower velocity particles from the broad spectrum of velocities in highly heterogeneous media. Results show that fitting of Fickian models to plume concentration data can lead to inaccurate estimates of rate constants because of the wide distribution of travel times in highly heterogeneous media.

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Improvements and Corrections to AT123D Code

Cited by 8 publications

References 13 publications

A Practical Modeling Framework for Non‐Fickian Transport and Multi‐Species Sequential First‐Order Reaction

A Practical Modeling Framework for Non‐Fickian Transport and Multi‐Species Sequential First‐Order Reaction

Semianalytical solutions for transport in aquifer and fractured clay matrix system

Stochastic modeling analysis of sequential first-order degradation reactions and non-Fickian transport in steady state plumes

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