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.     

Multivariate analyses of water chemistry: surface and ground water interactions

Multivariate statistical methods (MSMs) applied to ground water chemistry provide valuable insight into the main hydrochemical species, hydrochemical processes, and water flowpaths important to ground water evolution. The MSMs of principal component factor analysis (FA) and k-means cluster analysis (CA) were sequentially applied to major ion chemistry from 211 different ground water-sampling locations in the Amargosa Desert. The FA reduces the number of variables describing the system and finds relationships between major ions. The CA of the reduced system produced objective hydrochemical facies, which are independent of, but in good agreement with, lithological data. The derived factors and hydrochemical facies are innovatively presented on biplots, revealing composition of hydrochemical processes and facies, and overlaid on a digital elevation model, displaying flowpaths and interactions with geologic and topographic features in the region. In particular, a distinct ground water chemical signature is observed beneath and surrounding the extended flowpath of Fortymile Wash, presenting some contradiction to contemporary water levels along with potential interaction with a fault line. The signature surrounding the ephemeral Fortymile Wash is believed to represent the relic of water that infiltrated during past pluvial periods when the amount of runoff in the wash was significantly larger than during the current drier period. This hypothesis and aforementioned analyses are supported by the examination of available chloride, oxygen-18, hydrogen-2, and carbon-14 data from the region.     

Numerical method of moments for solute transport in a nonstationary flow field conditioned on hydraulic conductivity and head measurements

The unconditional stochastic studies on groundwater flow and solute transport in a nonstationary conductivity field show that the standard deviations of the hydraulic head and solute flux are very large in comparison with their mean values (Zhang et al. in Water Resour Res 36:2107–2120, 2000; Wu et al. in J Hydrol 275:208–228, 2003; Hu et al. in Adv Water Resour 26:513–531, 2003). In this study, we develop a numerical method of moments conditioning on measurements of hydraulic conductivity and head to reduce the variances of the head and the solute flux. A Lagrangian perturbation method is applied to develop the framework for solute transport in a nonstationary flow field. Since analytically derived moments equations are too complicated to solve analytically, a numerical finite difference method is implemented to obtain the solutions. Instead of using an unconditional conductivity field as an input to calculate groundwater velocity, we combine a geostatistical method and a method of moment for flow to conditionally simulate the distributions of head and velocity based on the measurements of hydraulic conductivity and head at some points. The developed theory is applied in several case studies to investigate the influences of the measurements of hydraulic conductivity and/or the hydraulic head on the variances of the predictive head and the solute flux in nonstationary flow fields. The study results show that the conditional calculation will significantly reduce the head variance. Since the hydraulic head measurement points are treated as the interior boundary (Dirichlet boundary) conditions, conditioning on both the hydraulic conductivity and the head measurements is much better than conditioning only on conductivity measurements for reduction of head variance. However, for solute flux, variance reduction by the conditional study is not so significant.     

Grid convergence of variable-density flow simulations in discretely-fractured porous media

Grid convergence in space and time of variable-density flow in fractured-porous rock is systematically assessed. Convergence of the flow simulation is attained using both uniform and adaptive time-stepping. This contrasts to variable-density flow in unfractured porous media where grid convergence variable-density flow problems is almost never achieved. At high discretization levels, the number of fingers in fractured-porous rock is no longer influenced by spatial-temporal grid discretization, which is not the case in unfractured porous media. However, similar to unfractured porous media, the number of fingers in fractured-porous media varies at low discretization levels. Simulated convective pattern and penetration depth of the dense plume in fractured rock depend more on spatial discretization than on temporal discretization. The appropriate spatial-temporal grid is then used to examine some aspects of mixed convection in fractured-porous rock, characterized by the mixed convection number M. The critical mixed convection number M_c = 46 represents the transition between forced and free convection in fractured porous media, which is much higher than M_c = 1 in unfractured porous media. Thus, for mixed convective flow problems, the value of M_c is not a sufficient indicator to predict the convective mode (free convection-forced convection), and the presence of vertical fractures must be included in the prediction of convective flow modes.     

The role of hand calculations in ground water flow modeling

Most ground water modeling courses focus on the use of computer models and pay little or no attention to traditional analytic solutions to ground water flow problems. This shift in education seems logical. Why waste time to learn about the method of images, or why study analytic solutions to one-dimensional or radial flow problems? Computer models solve much more realistic problems and offer sophisticated graphical output, such as contour plots of potentiometric levels and ground water path lines. However, analytic solutions to elementary ground water flow problems do have something to offer over computer models: insight. For instance, an analytic one-dimensional or radial flow solution, in terms of a mathematical expression, may reveal which parameters affect the success of calibrating a computer model and what to expect when changing parameter values. Similarly, solutions for periodic forcing of one-dimensional or radial flow systems have resulted in a simple decision criterion to assess whether or not transient flow modeling is needed. Basic water balance calculations may offer a useful check on computer-generated capture zones for wellhead protection or aquifer remediation. An easily calculated "characteristic leakage length" provides critical insight into surface water and ground water interactions and flow in multi-aquifer systems. The list goes on. Familiarity with elementary analytic solutions and the capability of performing some simple hand calculations can promote appropriate (computer) modeling techniques, avoids unnecessary complexity, improves reliability, and is likely to save time and money. Training in basic hand calculations should be an important part of the curriculum of ground water modeling courses.     

Fracture control of ground water flow and water chemistry in a rock aquitard

There are few studies on the hydrogeology of sedimentary rock aquitards although they are important controls in regional ground water flow systems. We formulate and test a three-dimensional (3D) conceptual model of ground water flow and hydrochemistry in a fractured sedimentary rock aquitard to show that flow dynamics within the aquitard are more complex than previously believed. Similar conceptual models, based on regional observations and recently emerging principles of mechanical stratigraphy in heterogeneous sedimentary rocks, have previously been applied only to aquifers, but we show that they are potentially applicable to aquitards. The major elements of this conceptual model, which is based on detailed information from two sites in the Maquoketa Formation in southeastern Wisconsin, include orders of magnitude contrast between hydraulic diffusivity (K/S(s)) of fractured zones and relatively intact aquitard rock matrix, laterally extensive bedding-plane fracture zones extending over distances of over 10 km, very low vertical hydraulic conductivity of thick shale-rich intervals of the aquitard, and a vertical hydraulic head profile controlled by a lateral boundary at the aquitard subcrop, where numerous surface water bodies dominate the shallow aquifer system. Results from a 3D numerical flow model based on this conceptual model are consistent with field observations, which did not fit the typical conceptual model of strictly vertical flow through an aquitard. The 3D flow through an aquitard has implications for predicting ground water flow and for planning and protecting water supplies.     

Quantification of the hydraulic diffusivity of a bentonite-sand mixture using the water head decrease measured upon sudden flow interruption

This paper presents a new modelling approach to quantify the hydraulic diffusivity of low-permeability unconsolidated porous media under confined saturated-flow conditions in the laboratory. The derived analytical solution for the transient variation of the hydraulic head after flow interruption was applied to experimental data obtained from continuous measurements of the water pressure at two locations in the soil column. Three soil samples made of a mixture of natural bentonite (at different mass fractions) and medium sand were studied during a series of stepwise constant flow rates of water. The numerical results well fit the experimentally measured decrease of the dimensionless hydraulic head. The study shows that the increase of the mass fraction of bentonite in the soil sample from 10 to 30% is accompanied by a strong decrease of the hydraulic diffusivity from 2.4 × 10⁻² to 1.1 × 10⁻³ m² s⁻¹, which is clearly due to the decrease of the hydraulic conductivity of the soil sample. The specific storages obtained for each of the three samples are in the same order of magnitude and seem to decrease with the increase of mass fraction of bentonite. However, they clearly reflect the predominant portion of the compressibility of the porous medium compared with that of water. Compared with reported literature values for clayey soils, the specific storage values in this study are slightly higher, varying within the range of 2 × 10⁻³ to 8.1 × 10⁻³ m⁻¹._. The experimental results also give insight into the limitations of the modelling approach. In the case of low-permeability soils (K < 2 × 10⁻⁶ ms⁻¹) and steady-flow conditions with low Reynolds numbers, for example, Re < 0.003, it is recommended to choose a time duration for flow interruption between subsequent flow rate steps of longer than 5 s. For high-permeability porous media, to increase the precision of the quantified hydraulic diffusivity, it might be useful to select a measuring frequency significantly higher than 1 Hz.     

International borders, ground water flow, and hydroschizophrenia

A substantial body of research has been conducted on transboundary water, transboundary water law, and the mitigation of transboundary water conflict. However, most of this work has focused primarily on surface water supplies. While it is well understood that aquifers cross international boundaries and that the base flow of international river systems is often derived in part from ground water, transboundary ground water and surface water systems are usually managed under different regimes, resulting in what has been described as "hydroschizophrenia." Adding to the problem, the hydrologic relationships between surface and ground water supplies are only known at a reconnaissance level in even the most studied international basins, and thus even basic questions regarding the territorial sovereignty of ground water resources often remain unaddressed or even unasked. Despite the tensions inherent in the international setting, riparian nations have shown tremendous creativity in approaching regional development, often through preventive diplomacy, and the creation of "baskets of benefits," which allow for positive-sum, integrative allocations of joint gains. In contrast to the notion of imminent water wars, the history of hydropolitical relations worldwide has been overwhelmingly cooperative. Limited ground water management in the international arena, coupled with the fact that few states or countries regulate the use of ground water, begs the question: will international borders serve as boundaries for increased "flows" of hydrologic information and communication to maintain strategic aquifers, or will increased competition for shared ground water resources lead to the potential loss of strategic aquifers and "no flows" for both ground water users?     

Grid resolution study of ground water flow and transport

Three-dimensional grids representing a heterogeneous, ground water system are generated at 10 different resolutions in support of a site-scale flow and transport modeling effort. These grids represent hydrostratigraphy near Yucca Mountain, Nevada, consisting of 18 stratigraphic units with contrasting fluid flow and transport properties. The grid generation method allows the stratigraphy to be modeled by numerical grids of different resolution so that comparison studies can be performed to test for grid quality and determine the resolution required to resolve geologic structure and physical processes such as fluid flow and solute transport. The process of generating numerical grids with appropriate property distributions from geologic conceptual models is automated, thus making the entire process easy to implement with fewer user-induced errors. The series of grids of various resolutions are used to assess the level at which increasing resolution no longer influences the flow and solute transport results. Grid resolution is found to be a critical issue for ground water flow and solute transport. The resolution required in a particular instance is a function of the feature size of the model, the intrinsic properties of materials, the specific physics of the problem, and boundary conditions. The asymptotic nature of results related to flow and transport indicate that for a hydrologic model of the heterogeneous hydrostratigraphy under Yucca Mountain, a horizontal grid spacing of 600 m and vertical grid spacing of 40 m resolve the hydrostratigraphic model with sufficient precision to accurately model the hypothetical flow and solute transport to within 5% of the value that would be obtained with much higher resolution.     

Influence of calibration methodology on ground water flow predictions

We constructed a numerical model of transient ground water flow and solute transport for a portion of the Biscayne Aquifer in Florida, and calibrated the model with three different combinations of data from a 193-day period: head (h) data alone, data on h and ground water discharge to a canal (q), and data on h, q, and ground water chloride concentration (C). We used each of the three calibrated models to predict h and q during a 182-day test period separate from the calibration period. All three calibrated models predicted h equally well during the test period (r = 0.95, where r = 1 indicates perfect agreement between measured and simulated values), though the model calibrated on h alone had significantly different parameter values than the other two models. Predictions of q during the test period depended on calibration methodology; models calibrated with multiple targets simulated q more accurately than the model calibrated on h alone (r = 0.79 compared to r = 0.49). Based on the results of these simulations, we conclude: (1) Post-calibration prediction is important in assessing the value of different data types in automated calibration; (2) inverse-solution uniqueness is not a requirement for accurate h predictions; (3) relatively simple models can predict with reasonable accuracy transient ground water flow in a complex aquifer, and parameters governing this prediction can be estimated by nonlinear regression methods that incorporate both h and q data; (4) addition of C data to the calibration did not improve model predictive capacity because the information in the C data was similar to that in the q data, from the perspective of model calibration (the subsurface chemical signal in question was controlled mainly by seepage of high-chloride canal water into the low-chloride ground water system).     

Heat flow and ground water flow in the Great Plains of the United States

Regional groundwater flow in deep aquifers adds advective components to the surface heat flow over extensive areas within the Great Plains province. The regional groundwater flow is driven by topographically controlled piezometric surfaces for confined aquifers that recharge either at high elevations on the western edge of the province or from subcrop contacts. The aquifers discharge at lower elevations to the east. The assymetrical geometry for the Denver and Kennedy Basins is such that the surface areas of aquifer recharge are small compared to the areas of discharge. Consequently, positive advective heat flow occurs over most of the province. The advective component of heat flow in the Denver Basin is on the order of 15 mW m⁻² along a zone about 50 km wide that parallels the structure contours of the Dakota aquifer on the eastern margin of the Basin. The advective component of heat flow in the Kennedy Basin is on the order of 20 mW m⁻² and occurs over an extensive area that coincides with the discharge areas of the Madison (Mississippian) and Dakota (Cretaceous) aquifers. Groundwater flow in Paleozoic and Mesozoic aquifers in the Williston Basin causes thermal anomalies that are seen in geothermal gradient data and in oil well temperature data. The pervasive nature of advective heat flow components in the Great Plains tends to mask the heat flow structure of the crust, and only heat flow data from holes drilled into the crystalline basement can be used for tectonic heat flow studies.     

A simple borehole dilution technique in measuring horizontal ground water flow

Borehole dilution techniques use repeated fluid column profiling after establishment of an initial uniform condition to monitor the rate at which ambient ground water moves into a borehole. Application of the dilution technique in a monitoring well makes it possible to estimate the horizontal Darcy flow velocity of ground water in the aquifer surrounding the borehole. Previous investigators have demonstrated the technique using either relatively concentrated saline solutions or deionized water to produce a fluid column with properties distinctly different from those of local ground water. We present a new dilution technique using the food color Brilliant Blue FCF (Euro code E-133) to mark the fluid column and using a specially constructed photometric sensor to characterize the dilution of this dye over time. The effective application of this technique is documented by two practical examples.     

Modeling time series of ground water head fluctuations subjected to multiple stresses

The methods behind the predefined impulse response function in continuous time (PIRFICT) time series model are extended to cover more complex situations where multiple stresses influence ground water head fluctuations simultaneously. In comparison to autoregressive moving average (ARMA) time series models, the PIRFICT model is optimized for use on hydrologic problems. The objective of the paper is twofold. First, an approach is presented for handling multiple stresses in the model. Each stress has a specific parametric impulse response function. Appropriate impulse response functions for other stresses than precipitation are derived from analytical solutions of elementary hydrogeological problems. Furthermore, different stresses do not need to be connected in parallel in the model, as is the standard procedure in ARMA models. Second, general procedures are presented for modeling and interpretation of the results. The multiple-input PIRFICT model is applied to two real cases. In the first one, it is shown that this model can effectively decompose series of ground water head fluctuations into partial series, each representing the influence of an individual stress. The second application handles multiple observation wells. It is shown that elementary physical knowledge and the spatial coherence in the results of multiple wells in an area may be used to interpret and check the plausibility of the results. The methods presented can be used regardless of the hydrogeological setting. They are implemented in a computer package named Menyanthes (www.menyanthes.nl).     

Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion

Nonlocal moment equations allow one to render deterministically optimum predictions of flow in randomly heterogeneous media and to assess predictive uncertainty conditional on measured values of medium properties. We present a geostatistical inverse algorithm for steady-state flow that makes it possible to further condition such predictions and assessments on measured values of hydraulic head (and/or flux). Our algorithm is based on recursive finite-element approximations of exact first and second conditional moment equations. Hydraulic conductivity is parameterized via universal kriging based on unknown values at pilot points and (optionally) measured values at other discrete locations. Optimum unbiased inverse estimates of natural log hydraulic conductivity, head and flux are obtained by minimizing a residual criterion using the Levenberg-Marquardt algorithm. We illustrate the method for superimposed mean uniform and convergent flows in a bounded two-dimensional domain. Our examples illustrate how conductivity and head data act separately or jointly to reduce parameter estimation errors and model predictive uncertainty.This work is supported in part by NSF/ITR Grant EAR-0110289. The first author was additionally supported by scholarships from CONACYT and Instituto de Investigaciones Electricas of Mexico. Additional support was provided by the European Commission under Contract EVK1-CT-1999-00041 (W-SAHaRA-Stochastic Analysis of Well Head Protection and Risk Assessment).     

Modeling ground water flow in alluvial mountainous catchments on a watershed scale

In large mountainous catchments, shallow unconfined alluvial aquifers play an important role in conveying subsurface runoff to the foreland. Their relatively small extent poses a serious problem for ground water flow models on the river basin scale. River basin scale models describing the entire water cycle are necessary in integrated water resources management and to study the impact of global climate change on ground water resources. Integrated regional-scale models must use a coarse, fixed discretization to keep computational demands low and to facilitate model coupling. This can lead to discrepancies between model discretization and the geometrical properties of natural systems. Here, an approach to overcome this discrepancy is discussed using the example of the German-Austrian Upper Danube catchment, where a coarse ground water flow model was developed using MODFLOW. The method developed uses a modified concept from a hydrological catchment drainage analysis in order to adapt the aquifer geometry such that it respects the numerical requirements of the chosen discretization, that is, the width and the thickness of cells as well as gradients and connectivity of the catchment. In order to show the efficiency of the developed method, it was tested and compared to a finely discretized ground water model of the Ammer subcatchment. The results of the analysis prove the applicability of the new approach and contribute to the idea of using physically based ground water models in large catchments.     

Analysis of steady ground water flow toward wells in a confined-unconfined aquifer

A confined aquifer may become unconfined near the pumping wells when the water level falls below the confining unit in the case where the pumping rate is great and the excess hydraulic head over the top of the aquifer is small. Girinskii's potential function is applied to analyze the steady ground water flow induced by pumping wells with a constant-head boundary in a mixed confined-unconfined aquifer. The solution of the single-well problem is derived, and the critical radial distance at which the flow changes from confined to unconfined condition is obtained. Using image wells and the superposition method, an analytic solution is presented to study steady ground water flow induced by a group of pumping wells in an aquifer bounded by a river with constant head. A dimensionless function is introduced to determine whether a water table condition exists or not near the pumping wells. An example with three pumping wells is used to demonstrate the patterns of potentiometric surface and development of water table around the wells.     

Calculating ground water transit time of horizontal flow through leaky aquifers

The calculation of ground water transit times is one important factor in ground water protection. In this paper, we present an analytical solution for the transit time for a Dupuit-type flow system applicable to saturated flow through a horizontal leaky aquifer discharging to a downgradient fixed-head boundary under steady-state conditions. We investigate the influence of leakage when comparing the resulting travel times of our model based on head-dependent leakage with the commonly used model with no leakage and a simplified model with constant leakage. The results show significant differences in the position of the water divide and transit time, suggesting that leakage cannot be ignored.     

Michigan basin regional ground water flow discharge to three Great Lakes

Ground water discharge to the Great Lakes around the Lower Peninsula of Michigan is primarily from recharge in riparian basins and proximal upland areas that are especially important to the northern half of the Lake Michigan shoreline. A steady-state finite-difference model was developed to simulate ground water flow in four regional aquifers in Michigan's Lower Peninsula: the Glaciofluvial, Saginaw, Parma-Bayport, and Marshall aquifers interlayered with the Till/"red beds," Saginaw, and Michigan confining units, respectively. The model domain was laterally bound by a continuous specified-head boundary, formed from lakes Michigan, Huron, St. Clair, and Erie, with the St. Clair and Detroit River connecting channels. The model was developed to quantify regional ground water flow in the aquifer systems using independently determined recharge estimates. According to the flow model, local stream stages and discharges account for 95% of the overall model water budget; only 50% enters the lakes directly from the ground water system. Direct ground water discharge to the Great Lakes' shorelines was calculated at 36 m3/sec, accounting for 5% of the overall model water budget. Lowland areas contribute far less ground water discharge to the Great Lakes than upland areas. The model indicates that Saginaw Bay receives only approximately 1.13 m3/sec ground water; the southern half of the Lake Michigan shoreline receives only approximately 2.83 m3/sec. In contrast, the northern half of the Lake Michigan shoreline receives more than 17 m3/sec from upland areas.     

Estimating ground water recharge using flow models of perched karstic aquifers

The fraction of rain that is annually recharged to ground water is a function of the transient quantities of precipitation (wet vs. dry years) as well as other meteorological and geologic factors, and thus it is very difficult to estimate. In this study, we have used long records (20 to 30 years) of precipitation and spring discharge to reconstruct the transient character of yearly recharge. These data sets were used to calibrate numerical ground water flow models on the less than 3 km(2) scale for four separate perched karstic aquifers in the Judean and Samarian Mountains of Israel. The stratification and karstic character of the local carbonate rock aquifers cause ground water to flow through discrete dissolution channels and to discharge at isolated springs. An innovative, dual-porosity approach was used where a finite-difference solution simulates flow in the rock matrix, while the karstic channels are simulated using computationally simple drains. Perched conditions are also simulated innovatively using MODFLOW by treating the bottom unsaturated layer as if it is saturated, but by assuming zero pressure head throughout the "unsaturated" layer. Best fitting between measured and computed spring hydrograph data has allowed us to develop a set of empirical functions relating measured precipitation to recharge to the aquifer. The generic methodology presented gives insight into the suspected changes in aquifer recharge rates between particularly wet or dry years.     

An assessment of aquifer storage recovery using ground water flow models

Owing to increased demands on ground water accompanied by increased drawdowns, technologies that use recharge options, such as aquifer storage recovery (ASR), are being used to optimize available water resources and reduce adverse effects of pumping. In this paper, three representative ground water flow models were created to assess the impact of hydrogeologic and operational parameters/factors on recovery efficiency of ASR systems. Flow/particle tracking and solute transport models were used to track the movement of water during injection, storage, and recovery. Results from particle tracking models consistently produced higher recovery efficiency than the solute transport models for the parameters/properties examined because the particle tracking models neglected mixing of the injected and ambient water. Mixing between injected and ambient water affected recovery efficiency. Results from this study demonstrate the interactions between hydrogeologic and operational parameters on predictions of recovery efficiency. These interactions are best simulated using coupled numerical ground water flow and transport models that include the effects of mixing of injected water and ambient ground water.