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.     

VS2DRTI: Simulating Heat and Reactive Solute Transport in Variably Saturated Porous Media

Variably saturated groundwater flow, heat transport, and solute transport are important processes in environmental phenomena, such as the natural evolution of water chemistry of aquifers and streams, the storage of radioactive waste in a geologic repository, the contamination of water resources from acid‐rock drainage, and the geologic sequestration of carbon dioxide. Up to now, our ability to simulate these processes simultaneously with fully coupled reactive transport models has been limited to complex and often difficult‐to‐use models. To address the need for a simple and easy‐to‐use model, the VS2DRTI software package has been developed for simulating water flow, heat transport, and reactive solute transport through variably saturated porous media. The underlying numerical model, VS2DRT, was created by coupling the flow and transport capabilities of the VS2DT and VS2DH models with the equilibrium and kinetic reaction capabilities of PhreeqcRM. Flow capabilities include two‐dimensional, constant‐density, variably saturated flow; transport capabilities include both heat and multicomponent solute transport; and the reaction capabilities are a complete implementation of geochemical reactions of PHREEQC. The graphical user interface includes a preprocessor for building simulations and a postprocessor for visual display of simulation results. To demonstrate the simulation of multiple processes, the model is applied to a hypothetical example of injection of heated waste water to an aquifer with temperature‐dependent cation exchange. VS2DRTI is freely available public domain software.     

Analytic Element Modeling of Steady Interface Flow in Multilayer Aquifers Using AnAqSim

This paper presents the analytic element modeling approach implemented in the software AnAqSim for simulating steady groundwater flow with a sharp fresh‐salt interface in multilayer (three‐dimensional) aquifer systems. Compared with numerical methods for variable‐density interface modeling, this approach allows quick model construction and can yield useful guidance about the three‐dimensional configuration of an interface even at a large scale. The approach employs subdomains and multiple layers as outlined by Fitts (2010) with the addition of discharge potentials for shallow interface flow (Strack 1989). The following simplifying assumptions are made: steady flow, a sharp interface between fresh‐ and salt water, static salt water, and no resistance to vertical flow and hydrostatic heads within each fresh water layer. A key component of this approach is a transition to a thin fixed minimum fresh water thickness mode when the fresh water thickness approaches zero. This allows the solution to converge and determine the steady interface position without a long transient simulation. The approach is checked against the widely used numerical codes SEAWAT and SWI/MODFLOW and a hypothetical application of the method to a coastal wellfield is presented.     

Discussion about the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers

Analytical models have been exhaustively used to study simple seawater intrusion problems and the sustainable management of groundwater resources in coastal aquifers because of its simplicity, easy implementation, and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, and their governing equations are expressed in terms of a single potential theory to calculate critical pumping rates in a coastal pumping scenario. The Ghyben–Herzberg approach neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. Therefore, the results of the analytical solutions may be inaccurate and unacceptable for some real‐complex case studies. This paper provides insight into the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers, i.e. when they can be applied to obtain accurate enough results. For that purpose, this work compares sharp‐interface solutions, based on the Ghyben–Herzberg approach, with numerical three‐dimensional variable‐density flow simulations for a set of heterogeneous groundwater flow and mass transport parameters, and different scenarios of spatially distributed recharge values and spatial wells placement. The numerical experiment has been carried out in a 3D unconfined synthetic aquifer using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. This paper finds under which situations the sharp‐interface solution gives good predictions in terms of seawater penetration, transition zone width and critical pumping rates. Additionally, the simulation runs indicate to which parameters and scenarios the results are more sensitive. Copyright © 2013 John Wiley & Sons, Ltd.     

Laboratory and numerical investigation of flow and transport near a seepage-face boundary

Laboratory and numerical modeling investigations were completed to study the unconfined ground water flow and transport processes near a seepage-face boundary. The laboratory observations were made in a radial sand tank and included measurements of the height of the seepage face, flow velocity near the seepage face, travel time distribution of multiple tracer slugs, and streamlines. All the observations were reliably reproduced with a three-dimensional, axi-symmetric, variably saturated ground water flow model. Physical data presented in this work demonstrate and quantify the importance of three-dimensional transport patterns within a seepage-face zone. The results imply that vertically averaged flow models that employ Dupuit approximations might introduce error in the analysis of localized solute transport near a seepage-face boundary. The experimental dataset reported in this work will also be of interest for those who are attempting to validate a numerical algorithm for solving ground water and contaminant discharge patterns near a surface-water boundary.     

A Coupled Groundwater–Surface Water Modeling Framework for Simulating Transition Zone Processes

There is an identified need for fully representing groundwater–surface water transition zone (i.e., the sediment zone that connects groundwater and surface water) processes in modeling fate and transport of contaminants to assist with management of contaminated sediments. Most existing groundwater and surface water fate and transport models are not dynamically linked and do not consider transition zone processes such as bioturbation and deposition and erosion of sediments. An interface module is developed herein to holistically simulate the fate and transport by coupling two commonly used models, Environmental Fluid Dynamics Code (EFDC) and SEAWAT, to simulate surface water and groundwater hydrodynamics, while providing an enhanced representation of the processes in the transition zone. Transition zone and surface water contaminant processes were represented through an enhanced version of the EFDC model, AQFATE. AQFATE also includes SEDZLJ, a state‐of‐the‐science surface water sediment transport model. The modeling framework was tested on a published test problem and applied to evaluate field‐scale two‐ and three‐dimensional contaminant transport. The model accurately simulated concentrations of salinity from a published test case. For the field‐scale applications, the model showed excellent mass balance closure for the transition zone and provided accurate simulations of all transition zone processes represented in the modeling framework. The model predictions for the two‐dimensional field case were consistent with site‐specific observations of contaminant migration. This modeling framework represents advancement in the simulation of transition zone processes and can help inform risk assessment at sites where contaminant sources from upland areas have the potential to impact sediments and surface water.     

Multi-functional heat pulse probe measurements of coupled vadose zone flow and transport

Simultaneous measurement of coupled water, heat, and solute transport in unsaturated porous media is made possible with the multi-functional heat pulse probe (MFHPP). The probe combines a heat pulse technique for estimating soil heat properties, water flux, and water content with a Wenner array measurement of bulk soil electrical conductivity (EC_bulk). To evaluate the MFHPP, we conducted controlled steady-state flow experiments in a sand column for a wide range of water saturations, flow velocities, and solute concentrations. Flow and transport processes were monitored continuously using the MFHPP. Experimental data were analyzed by inverse modeling of simultaneous water, heat, and solute transport using an adapted HYDRUS-2D model. Various optimization scenarios yielded simultaneous estimation of thermal, solute, and hydraulic parameters and variables, including thermal conductivity, volumetric water content, water flux, and thermal and solute dispersivities. We conclude that the MFHPP holds great promise as an excellent instrument for the continuous monitoring and characterization of the vadose zone.     

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.     

Changes in water table level influence solute transport in uniform porous media

Changes in the water table level result in variable water saturation and variable hydrological fluxes at the interface between the unsaturated and saturated zone. This may influence the transport and fate of contaminants in the subsurface. The objective of this study was to examine the impact of a decreasing and an increasing water table on solute transport. We conducted tracer experiments at downward flow conditions in laboratory columns filled with two different uniform porous media under static and transient flow conditions either increasing or decreasing the water table. Tracer breakthrough curves were simulated using a mobile–immobile transport model. The resulting transport parameters were compared to identify dominant transport processes. Changes in the water table level affected dispersivities and mobile water fractions depending on the direction of water table movement and the grain size of the porous media. In fine glass beads, the water flow velocity was similar to the decline rate of the water table, and the mobile water fraction was decreased compared with steady‐state saturated conditions. However, immobile water was negligible. In coarse glass beads, water flow was faster because of fingered flow in the unsaturated part, and the mobile water fraction was smaller than in the fine material. Here, a rising water table led to an even smaller mobile water fraction and increased solute spreading because of diffusive interaction with immobile water. We conclude that changes of the water table need to be considered to correctly simulate transport in the subsurface at the transition of the unsaturated–saturated zone. Copyright © 2014 John Wiley & Sons, Ltd.     

Simulation of submarine ground water discharge to a marine estuary: Biscayne Bay, Florida

Variable density ground water flow models are rarely used to estimate submarine ground water discharge because of limitations in computer speed, data availability, and availability of a simulation tool that can minimize numerical dispersion. This paper presents an application of the SEAWAT code, which is a combined version of MODFLOW and MT3D, to estimate rates of submarine ground water discharge to a coastal marine estuary. Discharge rates were estimated for Biscayne Bay, Florida, for the period from January 1989 to September 1998 using a three-dimensional, variable density ground water flow and transport model. Hydrologic stresses in the 10-layer model include recharge, evapotranspiration, ground water withdrawals from municipal wellfields, interactions with surface water (canals in urban areas and wetlands in the Everglades), boundary fluxes, and submarine ground water discharge to Biscayne Bay. The model was calibrated by matching ground water levels in monitoring wells, baseflow to canals, and the position of the 1995 salt water intrusion line. Results suggest that fresh submarine ground water discharge to Biscayne Bay may have exceeded surface water discharge during the 1989, 1990, and 1991 dry seasons, but the average discharge for the entire simulation period was only approximately 10% of the surface water discharge to the bay. Results from the model also suggest that tidal canals intercept fresh ground water that might otherwise have discharged directly to Biscayne Bay. This application demonstrates that regional scale variable density models are potentially useful tools for estimating rates of submarine ground water discharge.     

Estimation of Salt Water Upconing Using a Steady‐State Solution for Partial Completion of a Pumped Well

A new steady‐state analytical solution to the two‐dimensional radial‐flow equation was developed for drawdown (head) conditions in an aquifer with constant transmissivity, no‐flow conditions at the top and bottom, constant head conditions at a known radial distance, and a partially completed pumping well. The solution was evaluated for accuracy by comparison to numerical simulations using MODFLOW. The solution was then used to estimate the rise of the salt water‐fresh water interface (upconing) that occurs under a pumping well, and to calculate the critical pumping rate at which the interface becomes unstable, allowing salt water to enter the pumping well. The analysis of salt water‐fresh water interface rise assumed no significant effect on upconing by recharge; this assumption was tested and supported using results from a new steady‐state analytical solution developed for recharge under two‐dimensional radial‐flow conditions. The upconing analysis results were evaluated for accuracy by comparison to those from numerical simulations using SEAWAT for salt water‐fresh water interface positions under mild pumping conditions. The results from the equation were also compared with those of a published numerical sharp‐interface model applied to a case on Cape Cod, Massachusetts. This comparison indicates that estimating the interface rise and maximum allowable pumping rate using the analytical method will likely be less conservative than the maximum allowable pumping rate and maximum stable interface rise from a numerical sharp‐interface model.     

Analytical models of contaminant transport in coastal aquifers

The Henry formulation, which couples subsurface flow and salt transport via a variable-density flow formulation, can be used to evaluate the extent of sea water intrusion into coastal aquifers. The coupling gives rise to nontrivial flow patterns that are very different from those observed in inland aquifers. We investigate the influence of these flow patterns on the transport of conservative contaminants in a coastal aquifer. The flow is characterized by two dimensionless parameters: the Péclet number, which compares the relative effects of advective and dispersive transport mechanisms, and a coupling parameter, which describes the importance of the salt water boundary on the flow. We focus our attention on two regimes – low and intermediate Péclet number flows. Two transport scenarios are solved analytically by means of a perturbation analysis. The first, a natural attenuation scenario, describes the flushing of a contaminant from a coastal aquifer by clean fresh water, while the second, a contaminant spill scenario, considers an isolated point source.     

Small‐Scale ASR Between Flow Barriers in a Saline Aquifer

Regular aquifer storage recovery, ASR, is often not feasible for small‐scale storage in brackish or saline aquifers because fresh water floats to the top of the aquifer where it is unrecoverable. Flow barriers that partially penetrate a brackish or saline aquifer prevent a stored volume of fresh water from expanding sideways, thus increasing the recovery efficiency. In this paper, the groundwater flow and mixing is studied during injection, storage, and recovery of fresh water in a brackish or saline aquifer in a flow‐tank experiment and by numerical modeling to investigate the effect of density difference, hydraulic conductivity, pumping rate, cyclic operation, and flow barrier settings. Two injection and recovery methods are investigated: constant flux and constant head. Fresh water recovery rates on the order of 65% in the first cycle climbing to as much as 90% in the following cycles were achievable for the studied configurations with constant flux whereas the recovery efficiency was somewhat lower for constant head. The spatial variation in flow velocity over the width of the storage zone influences the recovery efficiency, because it induces leakage of fresh water underneath the barriers during injection and upconing of salt water during recovery.     

On the application of the boundary layer approximation for the simulation of density stratified flows in aquifers

Stratification of the density in groundwater flow stems from the contact between water which contains minerals in low concentration with water containing a high concentration of minerals. The flow in such a flow field should be simulated by solving simultaneously the equations of continuity, motion and solute transport, because solute concentration affects the dynamics of the flow. Such an approach is generally associated with complicated calculations and numerical schemes subject to problems of convergence and stability, as the basic equations are highly nonlinear.This study applies the phenomenological boundary layer approximation, and suggests a reference to three different zones in the flow field: (a) fresh water zone, (b) transition zone, and (c) mineralized water zone. In zones (a) and (c) it is assumed that the potential flow theory can be applied. In zone (b) the flow is nonpotential but the basic similarity conditions typical to boundary layers exist.The approach suggested in this study simplifies the mathematical models that should be used for the flow field simulation. This approach is especially attractive in cases where the Dupuit approximation is applicable. In such cases very often analytical solutions can be obtained for unidirectional flows. In cases that are too complicated for representation by analytical solutions, the method can be used for the creation of simplified numerical schemes.Various examples in this study demonstrate the application of the method for various field problems associated with steady state as well as unsteady state conditions.The simplicity of the method makes it useful for variety of problems. It can be used even by small institutions and small consulting firms, who have usually access to minicomputers and microprocessors.     

Relative Recovery of Thermal Energy and Fresh Water in Aquifer Storage and Recovery Systems

This paper explores the relationship between thermal energy and fresh water recoveries from an aquifer storage recovery (ASR) well in a brackish confined aquifer. It reveals the spatial and temporal distributions of temperature and conservative solutes between injected and recovered water. The evaluation is based on a review of processes affecting heat and solute transport in a homogeneous aquifer. In this simplified analysis, it is assumed that the aquifer is sufficiently anisotropic to inhibit density‐affected flow, flow is axisymmetric, and the analysis is limited to a single ASR cycle. Results show that the radial extent of fresh water at the end of injection is greater than that of the temperature change due to the heating or cooling of the geological matrix as well as the interstitial water. While solutes progress only marginally into low permeability aquitards by diffusion, conduction of heat into aquitards above and below is more substantial. Consequently, the heat recovery is less than the solute recovery when the volume of the recovered water is lower than the injection volume. When the full volume of injected water is recovered the temperature mixing ratio divided by the solute mixing ratio for recovered water ranges from 0.95 to 0.6 for ratios of maximum plume radius to aquifer thickness of 0.6 to 4.6. This work is intended to assist conceptual design for dual use of ASR for conjunctive storage of water and thermal energy to maximize the potential benefits.     

Analytical Solutions for Water Flow and Solute Transport in the Unsaturated Zone

Analytical solutions for the water flow and solute transport equations in the unsaturated zone are presented. We use the Broadbridge and White nonlinear model to solve the Richards’ equation for vertical flow under a constant infiltration rate. Then we extend the water flow solution and develop an exact parametric solution for the advection-dispersion equation. The method of characteristics is adopted to determine the location of a solute front in the unsaturated zone. The dispersion component is incorporated into the final solution using a singular perturbation method. The formulation of the analytical solutions is simple, and a complete solution is generated without resorting to computationally demanding numerical schemes. Indeed, the simple analytical solutions can be used as tools to verify the accuracy of numerical models of water flow and solute transport. Comparison with a finite-element numerical solution indicates that a good match for the predicted water content is achieved when the mesh grid is one-fourth the capillary length scale of the porous medium. However, when numerically solving the solute transport equation at this level of discretization, numerical dispersion and spatial oscillations were significant.     

Transience of seawater intrusion and retreat in response to incremental water‐level variations

This paper provides for the first time an experimental study where the impact of sea‐level fluctuations and inland boundary head‐level variations on freshwater–saltwater interface toe motion and transition zone dynamics was quantitatively analysed under transient conditions. The experiments were conducted in a laboratory flow tank where various (inland and coastal) head changes were imposed to the system and the response of the key seawater intrusion parameters was analysed with high spatial and temporal resolution. Two homogeneous aquifer systems of different grain size were tested. The numerical code SEAWAT was used for the validation. The results show that in cases of sea‐level variations, the intruding wedge required up to twice longer time to reach a new steady‐state condition than the receding wedge, which thereby extend the theory of timescale asymmetry between saltwater intrusion and retreat processes in scenarios involving sea‐level fluctuations. The intruding and receding rates of the saltwater wedge were respectively similar in the scenario involving sea‐level and the freshwater‐level changes, despite change in transmissivity. The results show that, during the intrusion phase, the transition zone remains relatively insensitive, regardless of where the boundary head change occurs (i.e., freshwater drop or sea‐level rise) or its magnitude. By contrast, a substantial widening of the transition zone was observed during the receding phase, with almost similar amplitude in the scenario involving a rise of the freshwater level compared with that caused by a drop of the saltwater level, provided that an equivalent absolute head change magnitude was used. This transition zone widening (occurring during saltwater retreat) was greater and extended over longer period in the low hydraulic conductivity aquifer, for both freshwater‐level rise and sea‐level drop scenarios. The concentration maps revealed that the widening mechanism was also enhanced by the presence of some freshwater sliding and into the wedge during saltwater retreat, which was thereafter sucked upward towards the interface because of density difference effects.     

Fluid dispersion effects on density-driven thermohaline flow and transport in porous media

This study introduces the dispersive fluid flux of total fluid mass to the density-driven flow equation to improve thermohaline modeling of salt and heat transports in porous media. The dispersive fluid flux in the flow equation is derived to account for an additional fluid flux driven by the density gradient and mechanical dispersion. The coupled flow, salt transport and heat transport governing equations are numerically solved by a fully implicit finite difference method to investigate solution changes due to the dispersive fluid flux. The numerical solutions are verified by the Henry problem and the thermal Elder problem under a moderate density effect and by the brine Elder problem under a strong density effect. It is found that increment of the maximum ratio of the dispersive fluid flux to the advective fluid flux results in increasing dispersivity for the Henry problem and the brine Elder problem. The effects of the dispersive fluid flux on salt and heat transports under high density differences and high dispersivities are more noticeable than under low density differences and low dispersivities. Values of quantitative indicators such as the Nusselt number, mass flux, salt mass stored and maximum penetration depth in the brine Elder problem show noticeable changes by the dispersive fluid flux. In the thermohaline Elder problem, the dispersive fluid flux shows a considerable effect on the shape and the number of developed fingers and makes either an upwelling or a downwelling flow in the center of the domain. In conclusion, for the general case that involves strong density-driven flow and transport modeling in porous media, the dispersive fluid flux should be considered in the flow equation.     

Anisotropic dispersive Henry problem

The Henry problem has played a key role in our understanding of seawater intrusion into coastal aquifers and in benchmarking density dependent flow codes. This paper seeks to modify Henry’s problem to ensure sensitivity to density variations and vertical salinity profiles that resemble field observations. In the proposed problem, the “dispersive Henry problem”, mixing is represented by means of the traditional Scheidegger dispersion tensor (dispersivity times water flux). Anisotropy in the hydraulic conductivity is acknowledged and Henry’s seaside boundary condition of prescribed salt concentration is replaced by a flux dependent boundary condition, which represents more realistically salt transport across the seaside boundary. This problem turns out to be very sensitive to density variations and its solution gets closer to reality. However, an improvement in the traditional Henry problem (gain in sensitivity and realism) can be also achieved if the value of the Peclet number is significantly reduced.Although the dispersive problem lacks an analytical solution, it can shed light on flow in coastal aquifers. It provides significant information about the factors controlling seawater penetration, width of the mixing zone and influx of seawater. The width of the mixing zone depends basically on dispersion with longitudinal and transverse dispersion controlling different parts of the mixing zone but displaying similar overall effects. Toe penetration is mainly controlled by the horizontal permeability and by the geometric mean of the dispersivities. Finally, transverse dispersivity and the geometric mean of the hydraulic conductivity are the leading parameters controlling the amount of saltwater that enters the aquifer.     

SEAWAT‐Based Simulation of Axisymmetric Heat Transport

Simulation of heat transport has its applications in geothermal exploitation of aquifers and the analysis of temperature dependent chemical reactions. Under homogeneous conditions and in the absence of a regional hydraulic gradient, groundwater flow and heat transport from or to a well exhibit radial symmetry, and governing equations are reduced by one dimension (1D) which increases computational efficiency importantly. Solute transport codes can simulate heat transport and input parameters may be modified such that the Cartesian geometry can handle radial flow. In this article, SEAWAT is evaluated as simulator for heat transport under radial flow conditions. The 1971, 1D analytical solution of Gelhar and Collins is used to compare axisymmetric transport with retardation (i.e., as a result of thermal equilibrium between fluid and solid) and a large diffusion (conduction). It is shown that an axisymmetric simulation compares well with a fully three dimensional (3D) simulation of an aquifer thermal energy storage systems. The influence of grid discretization, solver parameters, and advection solution is illustrated. Because of the high diffusion to simulate conduction, convergence criterion for heat transport must be set much smaller (10^?10) than for solute transport (10^?6). Grid discretization should be considered carefully, in particular the subdivision of the screen interval. On the other hand, different methods to calculate the pumping or injection rate distribution over different nodes of a multilayer well lead to small differences only.