Modeling Variably Saturated Subsurface Solute Transport with MODFLOW‐UZF and MT3DMS

The MT3DMS groundwater solute transport model was modified to simulate solute transport in the unsaturated zone by incorporating the unsaturated‐zone flow (UZF1) package developed for MODFLOW. The modified MT3DMS code uses a volume‐averaged approach in which Lagrangian‐based UZF1 fluid fluxes and storage changes are mapped onto a fixed grid. Referred to as UZF‐MT3DMS, the linked model was tested against published benchmarks solved analytically as well as against other published codes, most frequently the U.S. Geological Survey's Variably‐Saturated Two‐Dimensional Flow and Transport Model. Results from a suite of test cases demonstrate that the modified code accurately simulates solute advection, dispersion, and reaction in the unsaturated zone. Two‐ and three‐dimensional simulations also were investigated to ensure unsaturated‐saturated zone interaction was simulated correctly. Because the UZF1 solution is analytical, large‐scale flow and transport investigations can be performed free from the computational and data burdens required by numerical solutions to Richards' equation. Results demonstrate that significant simulation runtime savings can be achieved with UZF‐MT3DMS, an important development when hundreds or thousands of model runs are required during parameter estimation and uncertainty analysis. Three‐dimensional variably saturated flow and transport simulations revealed UZF‐MT3DMS to have runtimes that are less than one tenth of the time required by models that rely on Richards' equation. Given its accuracy and efficiency, and the wide‐spread use of both MODFLOW and MT3DMS, the added capability of unsaturated‐zone transport in this familiar modeling framework stands to benefit a broad user‐ship.     

Can Contaminant Transport Models Predict Breakthrough?

A solute breakthrough curve measured during a two-well tracer test was successfully predicted in 1986 using specialized contaminant transport models. Water was injected into a confined, unconsolidated sand aquifer and pumped out 125 feet (38.3 m) away at the same steady rate. The injected water was spiked with bromide for over three days; the outflow concentration was monitored for a month. Based on previous tests, the horizontal hydraulic conductivity of the thick aquifer varied by a factor of seven among 12 layers. Assuming stratified flow with small dispersivities, two research groups accurately predicted breakthrough with three-dimensional (12-layer) models using curvilinear elements following the arc-shaped flowlines in this test.
Can contaminant transport models commonly used in industry, that use rectangular blocks, also reproduce this breakthrough curve? The two-well test was simulated with four MODFLOW-based models, MT3D (FD and HMOC options), MODFLOWT, MOC3D, and MODFLOW-SURFACT.
Using the same 12 layers and small dispersivity used in the successful 1986 simulations, these models fit almost as accurately as the models using curvilinear blocks. Subtle variations in the curves illustrate differences among the codes. Sensitivities of the results to number and size of grid blocks, number of layers, boundary conditions, and values of dispersivity and porosity are briefly presented. The fit between calculated and measured breakthrough curves degenerated as the number of layers and/or grid blocks decreased, reflecting a loss of model predictive power as the level of characterization lessened. Therefore, the breakthrough curve for most field sites can be predicted only qualitatively due to limited characterization of the hydrogeology and contaminant source strength.     

A Spatially Periodic Solute Boundary for MT3DMS and PHT3D

The assumption of spatial repetition is commonly made when producing bedform scale models of the hyporheic zone. Two popular solute transport codes, MT3DMS and PHT3D, do not currently provide the necessary boundary condition required to simulate spatial periodicity in hyporheic zone transport problems. In this study, we develop a spatially periodic boundary (SPB) for solutes that is compatible with a SPB that was previously developed for MODFLOW to simulate the flow component of spatially periodic problems. The approach is ideal for simulating groundwater flow and transport patterns under repeating surface features, such as ripples or dunes on the bottom of a lake or stream. The appropriate block‐centered finite‐difference approach to implement the boundary is presented and the necessary source code modifications are discussed. The performance of the solute SPB, operating in conjunction with the groundwater flow SPB, is explored through comparison of a multi‐bedform hyporheic‐zone model with a single bedform variant. The new boundary conditions perform well in situations where both dispersive effects and lateral seepage flux in the underflow regime beneath the hyporheic zone are minimal.     

Evaluating MT3DMS for Heat Transport Simulation of Closed Geothermal Systems

Owing to the mathematical similarities between heat and mass transport, the multi-species transport model MT3DMS should be able to simulate heat transport if the effects of buoyancy and changes in viscosity are small. Although in several studies solute models have been successfully applied to simulate heat transport, these studies failed to provide any rigorous test of this approach. In the current study, we carefully evaluate simulations of a single borehole ground source heat pump (GSHP) system in three scenarios: a pure conduction situation, an intermediate case, and a convection-dominated case. Two evaluation approaches are employed: first, MT3DMS heat transport results are compared with analytical solutions. Second, simulations by MT3DMS, which is finite difference, are compared with those by the finite element code FEFLOW and the finite difference code SEAWAT. Both FEFLOW and SEAWAT are designed to simulate heat flow. For each comparison, the computed results are examined based on residual errors. MT3DMS and the analytical solutions compare satisfactorily. MT3DMS and SEAWAT results show very good agreement for all cases. MT3DMS and FEFLOW two-dimensional (2D) and three-dimensional (3D) results show good to very good agreement, except that in 3D there is somewhat deteriorated agreement close to the heat source where the difference in numerical methods is thought to influence the solution. The results suggest that MT3DMS can be successfully applied to simulate GSHP systems, and likely other systems with similar temperature ranges and gradients in saturated porous media.     

PHT3D‐UZF: A Reactive Transport Model for Variably‐Saturated Porous Media

A modified version of the MODFLOW/MT3DMS‐based reactive transport model PHT3D was developed to extend current reactive transport capabilities to the variably‐saturated component of the subsurface system and incorporate diffusive reactive transport of gaseous species. Referred to as PHT3D‐UZF, this code incorporates flux terms calculated by MODFLOW's unsaturated‐zone flow (UZF1) package. A volume‐averaged approach similar to the method used in UZF‐MT3DMS was adopted. The PHREEQC‐based computation of chemical processes within PHT3D‐UZF in combination with the analytical solution method of UZF1 allows for comprehensive reactive transport investigations (i.e., biogeochemical transformations) that jointly involve saturated and unsaturated zone processes. Intended for regional‐scale applications, UZF1 simulates downward‐only flux within the unsaturated zone. The model was tested by comparing simulation results with those of existing numerical models. The comparison was performed for several benchmark problems that cover a range of important hydrological and reactive transport processes. A 2D simulation scenario was defined to illustrate the geochemical evolution following dewatering in a sandy acid sulfate soil environment. Other potential applications include the simulation of biogeochemical processes in variably‐saturated systems that track the transport and fate of agricultural pollutants, nutrients, natural and xenobiotic organic compounds and micropollutants such as pharmaceuticals, as well as the evolution of isotope patterns.     

A Straightforward Random Walk Model for Fast Push‐Pull Tracer Test Evaluation

In this article, we present a straightforward random walk model for fast evaluation of push‐pull tracer tests. By developing an adaptive algorithm, we overcome the problem of manually defining how many particles have to be used to simulate the transport problem. Beside this, we validate the random walk model by evaluating a push‐pull tracer test with drift phase and confirm the results with MT3DMS. The random walk model took less than 1% of computational time of MT3DMS, thus allowing a remarkable faster evaluation of push‐pull tracer tests.     

Assessing the Impact of a Heated Basement on Groundwater Temperatures in Bratislava,Slovakia

Groundwater temperature is a useful hydrogeological parameter that is easy to measure and can provide much insight into groundwater flow systems, but can be difficult to interpret. For measuring temperature directly in the ground, dedicated specifically designed monitoring wells are recommended since conventional groundwater wells are not optimal for temperature monitoring. Multilevel monitoring of groundwater temperature is required to identify contributions of different possible heat inputs (sources) on measured temperature signals. Interpreting temperature data as a cosine function, including period, average temperature, amplitude, and phase offset, is helpful. Amplitude dampening and increasing phase shift with distance from a boundary can be used for estimation of transport parameters. Temperature measurements at different depths can be used for evaluation of unknown parameters of analytical functions by optimization of regression fits in Python. These estimated parameters can be used to calculate temperatures at known water table depths which can be applied as a fixed transient boundary condition in MT3DMS to overcome the limitations of MT3DMS heat transport modeling in the unsaturated zone. In this study, temperature monitoring and modeling was used to evaluate the influence of a department store's heated basement foundation on groundwater temperature within a green space (city park), with the main outcome that 17 years after construction, the department store foundation has increased the mean groundwater temperature by 3.2 °C. Heat input evaluated by the MT3DMS model varied from 0.1 W/m² at a distance of 100 m up to 12 W/m² next to the building.     

Analytical solutions of the advection‐dispersion equation for transient groundwater flow. A numerical validation

An analytical transport‐model was developed to simulate the propagation of a contaminant in one‐ and two‐dimensional transient flow in groundwater. It is proved that the distribution of concentration at a given time and for a given discharge is identical to that obtained for a different discharge if the volumetric flux of water is the same in the two cases. The results of simulations have been compared with results obtained using the MT3DMS numerical model. There is good agreement when the calculated concentrations are flux‐weighted concentrations. On the other hand, there is a notable divergence when the resident mode is considered. Resident mode concentrations express the mass per unit volume whereas flux mode concentrations express the ratio of mass flux to fluid flux. The solutions presented in this paper can thus be a useful alternative to code MT3DMS when the objective is to simulate concentrations in transient flow according to a resident mode. Copyright © 2008 John Wiley & Sons, Ltd.     

Modeling Arsenic Sorption in the Subsurface with a Dual‐Site Model

Arsenic is a well‐known groundwater contaminant that causes toxicological and carcinogenic effects in humans. Predicting the transport of arsenic in the subsurface is often problematic because of its complex sorption characteristics. Numerous researchers have reported that arsenic sorption on soil material is initially fast and then subsequently slow. A dual‐site numerical sorption model was previously developed to describe arsenic desorption from arsenic‐contaminated soils in batch experiments in terms of two different release mechanisms. Experiments involving synthetic acid rain leaching of four arsenic‐contaminated soil columns were performed to verify the dual‐site numerical sorption model in the context of one‐dimensional vertical transport. The fitted models successfully simulated the signature long tailings and the two‐stage arsenic leaching patterns for all four soil columns. The dual‐site sorption model was incorporated within the general solute transport simulation code Modular Three‐Dimensional Multispecies (MT3DMS), version 5.10. The resulting version was named MT3DDS and is available for public access. This experimental study has shown that MT3DDS is capable of simulating phase redistribution during transport, and thus provides a new numerical tool for simulating arsenic transport in the subsurface.     

Positive solution of two-dimensional solute transport in heterogeneous aquifers

The transport of contaminants in aquifers is usually represented by a convection-dispersion equation. There are several well-known problems of oscillation and artificial dispersion that affect the numerical solution of this equation. For example, several studies have shown that standard treatment of the cross-dispersion terms always leads to a negative concentration. It is also well known that the numerical solution of the convective term is affected by spurious oscillations or substantial numerical dispersion. These difficulties are especially significant for solute transport in nonuniform flow in heterogeneous aquifers. For the case of coupled reactive-transport models, even small negative concentration values can become amplified through nonlinear reaction source/sink terms and thus result in physically erroneous and unstable results. This paper includes a brief discussion about how nonpositive concentrations arise from numerical solution of the convection and cross-dispersion terms. We demonstrate the effectiveness of directional splitting with one-dimensional flux limiters for the convection term. Also, a new numerical scheme for the dispersion term that preserves positivity is presented. The results of the proposed convection scheme and the solution given by the new method to compute dispersion are compared with standard numerical methods as used in MT3DMS.     

The influence of dimensionality on simulations of mass recovery from nonuniform dense non-aqueous phase liquid (DNAPL) source zones

The influence of model dimensionality on predictions of mass recovery from dense non-aqueous phase liquid (DNAPL) source zones in nonuniform permeability fields was investigated using a modified version of the modular three-dimensional transport simulator (MT3DMS). Thirty-two initial two- (2D) and three-dimensional (3D) tetrachloroethene–DNAPL source zone architectures, taken from a recent modeling study, were used as initial conditions for this analysis. Commonly employed source zone metrics were analyzed to determine differences between 2D and 3D predictions: (i) down-gradient flux-averaged contaminant concentration, (ii) reductions in contaminant mass flux through a down-gradient boundary, (iii) source zone ganglia-to-pool (GTP) ratio, and (iv) time required to achieve a remediation objective. 3D flux-averaged contaminant concentrations were approximately 3.5 times lower than concentrations simulated in 2D. This difference was attributed to dilution of the contaminant concentrations down gradient of the source zone. Contaminant flux reduction predictions for a given mass recovery were generally 5% higher in 3D simulations than in 2D simulations. The GTP ratio declined over time as mass was recovered in both 2D and 3D simulations. Although the source longevity (i.e., time required to achieve 99.99% mass recovery) differed between individual 2D and 3D realizations, the mean source longevity for the 2D and 3D simulation ensembles was within 2%. 2D simulations tended to over-predict the time required to achieve lower mass recovery levels (e.g. 50% mass recovery) due to a smaller contaminated area exposed to uncontaminated water. These findings suggest that ensemble averages of 2D numerical simulations of DNAPL migration, entrapment, dissolution, and mass recovery in statistically homogenous, nonuniform media may provide reasonable approximations to average behavior obtained using simulations conducted in fully three-dimensional domains.     

Spatial Periodic Boundary Condition for MODFLOW

Small‐scale hyporheic zone (HZ) models often use a spatial periodic boundary (SPB) pair to simulate an infinite repetition of bedforms. SPB's are common features of commercially available multiphysics modeling packages. MODFLOW's lack of this boundary type has precluded it from being effectively utilized in this area of HZ research. We present a method to implement the SPB in MODFLOW by development of the appropriate block‐centered finite‐difference expressions. The implementation is analogous to MODFLOW's general head boundary package. The difference is that the terms on the right hand side of the solution equations must be updated with each iteration. Consequently, models that implement the SPB converge best with solvers that perform both inner and outer iterations. The correct functioning of the SPB condition in MODFLOW is verified by two examples. This boundary condition allows users to build HZ‐bedform models in MODFLOW, facilitating further research using related codes such as MT3DMS and PHT3D.     

Flux-Corrected Transport with MT3DMS for Positive Solution of Transport with Full-Tensor Dispersion

Solute transport is usually modeled by the advection-dispersion-reaction equation. In the standard approach, mechanical dispersion is a tensor with principal directions parallel and perpendicular to the flow vector. Since realistic scenarios include nonuniform and unsteady flow fields, the governing equation has full tensor mechanical dispersion. When conventional grid-based numerical methods are used, approximation of the cross terms arising from the off-diagonal terms cause nonphysical solution with oscillations. As an example, for the common scenario of contaminant input into a domain with zero initial concentration, the cross-dispersion terms can result in negative concentrations that can wreak havoc in reactive transport applications. To address this issue, we use the well-known flux-corrected-transport (FCT) technique for a standard finite volume method. Although FCT has most often been used to eliminate oscillations resulting from discretization of the advection term for explicit time stepping, we show that it can be adapted for full-tensor dispersion and implicit time stepping. Unlike other approaches based on new discretization techniques (e.g., mimetic finite difference, nonlinear finite volume), FCT has the advantage of being flexible and widely applicable. Implementation of FCT requires solving an additional system of equations at each time step, using a modified “low order” matrix and a modified right-hand-side vector. To demonstrate the flexibility of FCT, we have modified the well-known and widely used groundwater solute transport simulator, MT3DMS. We apply the new simulator, MT3DMS-FCT, to several benchmark problems that suffer from negative concentrations when using MT3DMS. The new results are mass conservative and strictly nonnegative.     

MODFLOW/MT3DMS-based simulation of variable-density ground water flow and transport

This paper presents an approach for coupling MODFLOW and MT3DMS for the simulation of variable-density ground water flow. MODFLOW routines were modified to solve a variable-density form of the ground water flow equation in which the density terms are calculated using an equation of state and the simulated MT3DMS solute concentrations. Changes to the MODFLOW and MT3DMS input files were kept to a minimum, and thus existing data files and data files created with most pre- and postprocessors can be used directly with the SEAWAT code. The approach was tested by simulating the Henry problem and two of the saltpool laboratory experiments (low- and high-density cases). For the Henry problem, the simulated results compared well with the steady-state semianalytic solution and also the transient isochlor movement as simulated by a finite-element model. For the saltpool problem, the simulated breakthrough curves compared better with the laboratory measurements for the low-density case than for the high-density case but showed good agreement with the measured salinity isosurfaces for both cases. Results from the test cases presented here indicate that the MODFLOW/MT3DMS approach provides accurate solutions for problems involving variable-density ground water flow and solute transport.     

Analytical solutions for sequentially coupled one-dimensional reactive transport problems – Part I: Mathematical derivations

Multi-species reactive transport equations coupled through sorption and sequential first-order reactions are commonly used to model sites contaminated with radioactive wastes, chlorinated solvents and nitrogenous species. Although researchers have been attempting to solve various forms of these reactive transport equations for over 50 years, a general closed-form analytical solution to this problem is not available in the published literature. In Part I of this two-part article, we derive a closed-form analytical solution to this problem for spatially-varying initial conditions. The proposed solution procedure employs a combination of Laplace and linear transform methods to uncouple and solve the system of partial differential equations. Two distinct solutions are derived for Dirichlet and Cauchy boundary conditions each with Bateman-type source terms. We organize and present the final solutions in a common format that represents the solutions to both boundary conditions. In addition, we provide the mathematical concepts for deriving the solution within a generic framework that can be used for solving similar transport problems.     

MODFLOW/MT3DMS-based reactive multicomponent transport modeling

This paper presents a three-dimensional, MODFLOW/MT3DMS-based reactive multicomponent transport model for saturated porous media. Based on a split-operator technique, the model, referred to as PHT3D, couples the transport simulator MT3DMS and the geochemical modeling code PHREEQC-2. Through the flexible, generic nature of PHREEQC-2, PHT3D can handle a broad range of equilibrium and kinetically controlled reactive processes, including aqueous complexation, mineral precipitation/dissolution, and ion exchange. The diversity of potential applications is demonstrated through simulation of five existing literature benchmarks and a new three-dimensional sample problem. The model might be applied to simulate the geochemical evolution of pristine and contaminated aquifers as well as their cleanup. The latter problem class includes the natural and enhanced attenuation/remediation schemes of a wide range of organic and inorganic contaminants. Processes/reactions not included in the standard PHREEQC-2 database but typical for this type of application (e.g., NAPL dissolution, microbial growth/decay) can be defined and included via the extensible PHREEQC-2 database file.     

Numerical implementation of a backward probabilistic model of ground water contamination

Backward location and travel time probabilities can be used to characterize known and unknown sources or prior positions of ground water contamination. Backward location probability describes the position of the observed contamination at some time in the past; backward travel time probability describes the amount of time prior to observation that the contamination was released from its source or was at a particular upgradient location. The governing equation for backward probabilities is the adjoint of the governing equation for contaminant transport, but with new load terms. Numerical codes that have been written to solve the forward equations of contaminant transport, e.g., the advection-dispersion equation, can also be used to solve the adjoint equation for location and travel time probabilities; however, the interpretation of the results is different and some new approximations must be made for the load terms. We present the governing equations for backward location and travel time probabilities, and provide appropriate numerical approximations for these load terms using the cell-centered finite difference method, one of the most popular numerical methods in ground water hydrology. We discuss some additional numerical considerations for the backward model including boundary conditions, reversal of the flow field, and interpretation of the results. We illustrate the implementation of the backward probability model using hypothetical examples in one- and two-dimensional domains. We also present a three-dimensional application of a pump-and-treat remediation capture zone delineation at the Massachusetts Military Reservation. The illustrations are performed using MODFLOW-96 for flow simulations and MT3DMS for transport simulations.     

Implementation of Solute Transport in the Vadose Zone into the “HYDRUS Package for MODFLOW”

The “HYDRUS package for MODFLOW” is an existing MODFLOW package that allows MODFLOW to simultaneously evaluate transient water flow in both unsaturated and saturated zones. The package is based on incorporating parts of the HYDRUS-1D model (to simulate unsaturated water flow in the vadose zone) into MODFLOW (to simulate saturated groundwater flow). The coupled model is effective in addressing spatially variable saturated-unsaturated hydrological processes at the regional scale. However, one of the major limitations of this coupled model is that it does not have the capability to simulate solute transport along with water flow and therefore, the model cannot be employed for evaluating groundwater contamination. In this work, a modified unsaturated flow and transport package (modified HYDRUS package for MODFLOW and MT3DMS) has been developed and linked to the three-dimensional (3D) groundwater flow model MODFLOW and the 3D groundwater solute transport model MT3DMS. The new package can simulate, in addition to water flow in the vadose zone, also solute transport involving many biogeochemical processes and reactions, including first-order degradation, volatilization, linear or nonlinear sorption, one-site kinetic sorption, two-site sorption, and two-kinetic sites sorption. Due to complex interactions at the groundwater table, certain modifications of the pressure head (compared to the original coupling) and solute concentration profiles were incorporated into the modified HYDRUS package. The performance of the newly developed model is evaluated using HYDRUS (2D/3D), and the results indicate that the new model is effective in simulating the movement of water and contaminants in the saturated-unsaturated flow domains.     

An integrated approach for modeling solute transport in streams and canals with applications

A new modeling approach for solute transport in streams and canals was developed to simulate solute dissolution, transport, and decay with continuously migrating sources. The new approach can efficiently handle complicated solute source feeding schemes and initial conditions. Incorporating the finite volume method (FVM) and the ULTIMATE QUICKEST numerical scheme, the new approach is capable of predicting fate and transport of solute that is added to small streams or canals, typically in a continuous fashion. The approach was tested successfully using a hypothetical case, and then applied to an actual field experiment, where linear anionic polyacrylamide (LA-PAM) was applied to an earthen canal. The field experiment was simulated first as a fixed boundary problem using measured concentration data as the boundary condition to test model parameters and sensitivities. The approach was then applied to a moving boundary problem, which included subsequent LA-PAM dissolution, settling to the canal bottom and transport with the flowing canal water. Simulation results showed that the modeling approach developed in this study performed satisfactorily and can be used to simulate a variety of transport problems in streams and canals.     

Influence of Boundary Condition Types on Unstable Density‐Dependent Flow

Boundary conditions are required to close the mathematical formulation of unstable density‐dependent flow systems. Proper implementation of boundary conditions, for both flow and transport equations, in numerical simulation are critical. In this paper, numerical simulations using the FEFLOW model are employed to study the influence of the different boundary conditions for unstable density‐dependent flow systems. A similar set up to the Elder problem is studied. It is well known that the numerical simulation results of the standard Elder problem are strongly dependent on spatial discretization. This work shows that for the cases where a solute mass flux boundary condition is employed instead of a specified concentration boundary condition at the solute source, the numerical simulation results do not vary between different convective solution modes (i.e., plume configurations) due to the spatial discretization. Also, the influence of various boundary condition types for nonsource boundaries was studied. It is shown that in addition to other factors such as spatial and temporal discretization, the forms of the solute transport equation such as divergent and convective forms as well as the type of boundary condition employed in the nonsource boundary conditions influence the convective solution mode in coarser meshes. On basis of the numerical experiments performed here, higher sensitivities regarding the numerical solution stability are observed for the Adams‐Bashford/Backward Trapezoidal time integration approach in comparison to the Euler‐Backward/Euler‐Forward time marching approach. The results of this study emphasize the significant consequences of boundary condition choice in the numerical modeling of unstable density‐dependent flow.