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At least 1,063 records · Page 59Linked to original sources
USGS2010

Chlorofluorocarbons as tracers of groundwater transport processes in a shallow, silty sand aquifer

Detailed depth profiles of Chlorofluorocarbons CFC-11(CFCl 3 (, CFC-12 (CF 2 Cl 2 ) and CFC-113 (C 2 F 3 Cl 3 ) have been obtained from a well-characterized field site in central Ontario. Aquifer materials comprise predominantly silty sands, with a mean organic carbon content of 0.03%. Nearly one-dimensional flow exists at this site, and the vertical migration of a well-defined 3 H peak has been tracked through time. Detailed vertical sampling has allowed CFC tracer velocities to be estimated to within 10%. Comparison with 3 H profiles enables estimation of chlorofluorocarbon transport parameters. CFC-12 appears to be the most conservative of the CFCs measured. Sorption at this site is low ( K d < 0.03), and degradation does not appear to be important. CFC- 113 is retarded both with respect to CFC-12 and with respect to 3 H ( K d = 0.09−0.14). CFC-11 appears to be degraded both in the highly organic unsaturated zone and below 3.5 m depth in the aquifer, where dissolved oxygen concentrations decrease to below 0.5 mg L −1 . The half-life for CFC-11 degradation below 3.5 m depth is less than 2 years. While apparent CFC-12 ages match hydraulic ages to within 20% (up to 30 years), apparent CFC-11 and CFC-113 ages significantly overestimate hydraulic ages at our field site.

Water Resources Research↗
USGS2010

Evaluation of 11 equations for determining evaporation for a small lake in the North Central United States

Eleven equations for calculating evaporation were compared with evaporation determined by the energy budget method for Williams Lake, Minnesota. Data were obtained from instruments on a raft, on land near the lake, and at a weather station 60 km south of the lake. The comparisons were based on monthly values for the open-water periods of 5 years, a total of 22 months. A modified DeBruin-Keijman, Priestley-Taylor, and a modified Penman equation resulted in monthly evaporation values that agreed most closely with energy budget values. To use these equations, net radiation, air temperature, wind speed, and relative humidity need to be measured near the lake. In addition, thermal surveys need to be made to determine change in heat stored in the lake. If data from distant climate stations are the only data available, and they include solar radiation, the Jensen-Haise and Makkink equations resulted in monthly evaporation values that agreed reasonably well with energy budget values.

Minnesota↗
USGS2010

Modeling the effects of variable groundwater chemistry on adsorption of molybdate

Laboratory experiments were used to identify and quantify processes having a significant effect on molybdate (MoO 4 2− ) adsorption in a shallow alluvial aquifer on Cape Cod, assachusetts. Aqueous chemistry in the aquifer changes as a result of treated sewage effluent mixing with groundwater. Molybdate adsorption decreased as p H, ionic strength, and the concentration of competing anions increased. A diffuse-layer surface complexation model was used to simulate adsorption of MoO 4 2− , phosphate (PO 4 3− ), and sulfate (SO 4 2− ) on aquifer sediment. Equilibrium constants for the model were calculated by calibration to data from batch experiments. The model was then used in a one-dimensional solute transport program to successfully simulate initial breakthrough of MoO 4 2− from column experiments. A shortcoming of the solute transport program was the inability to account for kinetics of physical and chemical processes. This resulted in a failure of the model to predict the slow rate of desorption of MoO 4 2− from the columns. The mobility of MoO 4 2− ncreased with ionic strength and with the formation of aqueous complexes with calcium, magnesium, and sodium. Failure to account for MoO 4 2− speciation and ionic strength in the model resulted in overpredicting MoO 4 2− adsorption. Qualitatively, the laboratory data predicted the observed behavior of MoO 4 2− in the aquifer, where retardation of MoO 4 2− was greatest in uncontaminated roundwater having low p H, low ionic strength, and low concentrations of PO 4 3− and SO 4 2− .

Water Resources Research↗
USGS2010

Transport of chromium and selenium in a pristine sand and gravel aquifer: Role of adsorption processes

Field transport experiments were conducted in an oxic sand and gravel aquifer using Br (bromide ion), Cr (chromium, injected as Cr(VI)), Se (selenium, injected as Se(VI)), and other tracers. The aquifer has mildly acidic p H values and low concentrations of dissolved salts. Within analytical errors, all mobile Cr was present as Cr(VI). All mobile Se was probably present as Se(VI). Adsorption of Cr and Se onto aquifer sediments caused retardation of both tracers. Breakthrough curves for Cr and Se had extensive tails, which caused large decreases in their maximum concentrations relative to the nonreactive Br tracer after only 2.0 m of transport. A surface complexation model was applied to the results of laboratory studies of Cr(VI) adsorption on aquifer solids from the site based on adsorption onto hydrous ferric oxide. The modeling results suggested that the dominant adsorbents in the aquifer solids have lower affinities for anion adsorption than pure hydrous ferric oxide. The steep rising limbs and extensive tails observed in most of the breakthrough curves are qualitatively consistent with the equilibrium surface complexation model; however, slow rates of adsorption and desorption may have contributed to these features. Variations during transport in the concentrations of Cr, Se, and other anions competing for adsorption sites likely gave rise to variations in the extent of adsorption. Adequate description of the observed retardation of Cr and Se would require a coupled transport-adsorption model that can account for these effects. Companion experiments in the mildly reducing zone of the aquifer (Kent et al., 1994) showed a loss of Cr mass, probably resulting from reduction to Cr(III), and little retardation of mobile Cr and Se during transport; this contrast illustrates the influence of aquifer chemistry on the transport of redox-sensitive solutes.

Water Resources Research↗
USGS2010

Effects of carbon and nitrate on denitrification in bottom sediments of an effluent-dominated river

Nitrogen and carbon limitation of denitrification in the bed sediments of an effluent-dominated stream were investigated by quantifying the effects of nitrate and glucose additions on the rate of sediment N 2 O production. Bed sediment samples were collected from a 30-km stretch of the South Platte River where up to 95% of the base flow discharge consists of effluent from a water treatment plant in Denver, Colorado. The rate of denitrification in upstream sediment samples incubated under in situ nitrate and carbon conditions was primarily limited by nitrate supply. The stimulatory effect of nitrate additions on the rate of bed sediment denitrification decreased with increasing distance downstream of the treatment plant. Approximately 35 km downstream of the treatment plant, denitrification in the bed sediment samples was carbon limited. The observed decreases in the concentration of total inorganic nitrogen (as NH 4 + NO 3 ) dissolved in the river and the organic carbon content of the bed sediments with increasing distance downstream of the treatment plant suggest that bed sediment denitrification is a significant sink for nitrogen in this stretch of the river.

Colorado↗
USGS2010

Chemical evolution of groundwater near a sinkhole lake, northern Florida: 2. Chemical patterns, mass-transfer modeling, and rates of chemical reactions

Chemical patterns along evolutionary groundwater flow paths in silicate and carbonate aquifers were interpreted using solute tracers, carbon and sulfur isotopes, and mass balance reaction modeling for a complex hydrologic system involving groundwater inflow to and outflow from a sinkhole lake in northern Florida. Rates of dominant reactions along defined flow paths were estimated from modeled mass transfer and ages obtained from CFC-modeled recharge dates. Groundwater upgradient from Lake Barco remains oxic as it moves downward, reacting with silicate minerals in a system open to carbon dioxide (CO 2 ), producing only small increases in dissolved species. Beneath and downgradient of Lake Barco the oxic groundwater mixes with lake water leakage in a highly reducing, silicate-carbonate mineral environment. A mixing model, developed for anoxic groundwater downgradient from the lake, accounted for the observed chemical and isotopic composition by combining different proportions of lake water leakage and infiltrating meteoric water. The evolution of major ion chemistry and the 13 C isotopic composition of dissolved carbon species in groundwater downgradient from the lake can be explained by the aerobic oxidation of organic matter in the lake, anaerobic microbial oxidation of organic carbon, and incongruent dissolution of smectite minerals to kaolinite. The dominant process for the generation of methane was by the CO 2 reduction pathway based on the isotopic composition of hydrogen (δ 2 H(CH 4 ) = −186 to −234‰) and carbon (δ 13 C(CH 4 ) = −65.7 to −72.3‰). Rates of microbial metabolism of organic matter, estimated from the mass transfer reaction models, ranged from 0.0047 to 0.039 mmol L −1 yr −1 for groundwater downgradient from the lake.

Water Resources Research↗
USGS2010

Chemical evolution of groundwater near a sinkhole lake, northern Florida: 1. Flow patterns, age of groundwater, and influence of lakewater leakage

Leakage from sinkhole lakes significantly influences recharge to the Upper Floridan aquifer in poorly confined sediments in northern Florida. Environmental isotopes (oxygen 18, deuterium, and tritium), chlorofluorocarbons (CFCs: CFC-11, CCl 3 F; CFC-12, CCl 2 F 2 ; and CFC-113, C 2 Cl 3 F 3 ), and solute tracers were used to investigate groundwater flow patterns near Lake Barco, a seepage lake in a mantled karst setting in northern Florida. Stable isotope data indicated that the groundwater downgradient from the lake contained 11–67% lake water leakage, with a limit of detection of lake water in groundwater of 4.3%. The mixing fractions of lake water leakage, which passed through organic-rich sediments in the lake bottom, were directly proportional to the observed methane concentrations and increased with depth in the groundwater flow system. In aerobic groundwater upgradient from Lake Barco, CFC-modeled recharge dates ranged from 1987 near the water table to the mid 1970s for water collected at a depth of 30 m below the water table. CFC-modeled recharge dates (based on CFC-12) for anaerobic groundwater downgradient from the lake ranged from the late 1950s to the mid 1970s and were consistent with tritium data. CFC-modeled recharge dates based on CFC-11 indicated preferential microbial degradation in anoxic waters. Vertical hydraulic conductivities, calculated using CFC-12 modeled recharge dates and Darcy's law, were 0.17, 0.033, and 0.019 m/d for the surficial aquifer, intermediate confining unit, and lake sediments, respectively. These conductivities agreed closely with those used in the calibration of a three-dimensional groundwater flow model for transient and steady state flow conditions.

Florida↗
USGS2010

State-dependent anisotrophy: Comparison of quasi-analytical solutions with stochastic results for steady gravity drainage

Anisotropy in large-scale unsaturated hydraulic conductivity of layered soils changes with the moisture state. Here, state-dependent anisotropy is computed under conditions of large-scale gravity drainage. Soils represented by Gardner's exponential function are perfectly stratified, periodic, and inclined. Analytical integration of Darcy’s law across each layer results in a system of nonlinear equations that is solved iteratively for capillary suction at layer interfaces and for the Darcy flux normal to layering. Computed fluxes and suction profiles are used to determine both upscaled hydraulic conductivity in the principal directions and the corresponding “state-dependent” anisotropy ratio as functions of the mean suction. Three groups of layered soils are analyzed and compared with independent predictions from the stochastic results of Yeh et al. (1985b). The small-perturbation approach predicts appropriate behaviors for anisotropy under nonarid conditions. However, the stochastic results are limited to moderate values of mean suction; this limitation is linked to a Taylor series approximation in terms of a group of statistical and geometric parameters. Two alternative forms of the Taylor series provide upper and lower bounds for the state-dependent anisotropy of relatively dry soils.

Water Resources Research↗
USGS2010

Estimating 14C groundwater ages in a methanogenic aquifer

This paper addresses the problem of 14 C age dating of groundwaters in a confined regional aquifer affected by methanogenesis. Increasing CH 4 concentrations along the groundwater flow system and 13 C and 14 C isotopic data for dissolved inorganic carbon, dissolved organic carbon, and CH 4 clearly show the effect of methanogenesis on groundwater chemistry. Inverse reaction path modeling using NETPATH indicates the predominant geochemical reactions controlling the chemical evolution of groundwater in the aquifer are incongruent dissolution of dolomite, ion exchange, methanogenesis, and oxidation of sedimentary organic matter. Modeling of groundwater 14 C ages using NETPATH indicates that a significant part of groundwater in the Alliston aquifer is less than 13,000 years old; however, older groundwater in the range of 15,000–23,000 years is also present in the aquifer. This paper demonstrates that 14C ages calculated using NETPATH, incorporating the effects of methanogenesis on the carbon pools, provide reasonable groundwater ages that were not possible by other isotopic methods.

Water Resources Research↗
USGS2010

Transient hydrogeological controls on the chemistry of a seepage lake

A solute mass balance method was used to estimate groundwater inflow and outflow rates for Nevins Lake, Michigan, a seepage lake in the upper peninsula that historically has shown extremely variable water chemistry compared with most other seepage lakes. A 4-year study (1989–1992) of the hydrology and geochemistry of Nevins Lake and its contiguous groundwater system revealed that changes in the mass of dissolved solutes are the result of annual hydraulic gradient reversals. A pronounced acidification of Nevins Lake from 1986 to 1988 was likely caused by drought-induced diminished groundwater inflow rates. In this study, dissolved calcium (the major cation in water of Nevins Lake, groundwater, and precipitation) was used for estimating mass flow rates. During the 1989–1992 period, Nevins Lake showed a reproducible annual cycle in calcium mass. Immediately following spring snowmelt and the resulting hydraulic gradient reversal, the mass of dissolved calcium in the lake increases rapidly, and then it decreases steadily throughout the summer and early fall, at which time the lake becomes hydraulically mounded and receives no groundwater inflow. Groundwater flow rates estimated by the solute mass balance method are sensitive to assumed solute concentrations in discharging groundwater. Pore water samples from the lake bed are shown to be more representative of water discharging to the lake than are samples from piezometers near the lake shore, but spatial and temporal variability in pore water chemistry must be considered. Stable isotope analyses ( 18 O and 2 H) of lake water, groundwater, and pore water samples show that water discharging to Nevins Lake in the spring is entirely recycled lake water, and no groundwater derived from terrestrial recharge reaches the lake. The conceptual model formulated during this study linking lake chemistry and the contiguous groundwater system and general groundwater flow patterns surrounding highly transient lake systems are likely transferable to other similar systems.

Michigan↗
USGS2010

Combined use of groundwater dating, chemical, and isotopic analyses to resolve the history and fate of nitrate contamination in two agricultural watersheds, Atlantic coastal plain, Maryland

The history and fate of groundwater nitrate (NO 3 − ) contamination were compared in 2 small adjacent agricultural watersheds in the Atlantic coastal plain by combined use of chronologic (CCl 2 F 2 , 3 H), chemical (dissolved solids, gases), and isotopic (δ 15 N,δ 13 C, δ 34 S) analyses of recharging groundwaters, discharging groundwaters, and surface waters. The results demonstrate the interactive effects of changing agricultural practices, groundwater residence times, and local geologic features on the transfer of NO 3 − through local flow systems. Recharge dates of groundwaters taken in 1990–1992 from the surficial aquifer in the Chesterville Branch and Morgan Creek watersheds near Locust Grove, Maryland, ranged from pre-1940 to the late 1980’s. When corrected for localized denitrification by use of dissolved gas concentrations, the dated waters provide a 40-year record of the recharge rate of NO 3 − , which increased in both watersheds by a factor of 3–6, most rapidly in the 1970's. The increase in groundwater NO 3 − over time was approximately proportional to the documented increase in regional N fertilizer use, and could be accounted for by oxidation and leaching of about 20–35% of the fertilizer N. Groundwaters discharging upward beneath streams in both watersheds had measured recharge dates from pre-1940 to 1975, while chemical data for second-order reaches of the streams indicated average groundwater residence times in the order of 20+ years. At the time of the study, NO 3 − discharge rates were less than NO 3 − recharge rates for at least two reasons: (1) discharge of relatively old waters with low initial NO 3 − concentrations, and (2) local denitrification. In the Chesterville Branch watershed, groundwaters remained oxic throughout much of the surficial aquifer and discharged relatively unaltered to the stream, which had a relatively high NO 3 − concentration (9–10 mg/L as N). In the Morgan Creek watershed, groundwaters were largely reduced and denitrified before discharging to the stream, which had a relatively low NO 3 − concentration (2–3 mg/L as N). Chemical and isotopic data indicate that quantitative denitrification occurred within buried calcareous glauconitic marine sediments that are present at relatively shallow depths beneath the Morgan Creek watershed. NO 3 − removal by forests, wetlands, and shallow organic-rich soils in near-stream environments was largely avoided by groundwaters that followed relatively deep flow paths before converging and discharging rapidly upward to the streams.

Maryland↗
USGS2010

Processes controlling the chemistry of two snowmelt‐dominated streams in the Rocky Mountains

Time‐intensive discharge and chemical data for two alpine streams in the Loch Vale watershed, Colorado, were used to identify sources of runoff, flow paths, and important biogeochemical processes during the 1992 snowmelt runoff season. In spite of the paucity of soil cover the chemical composition of the streams is regulated much as in typical forested watersheds. Soils and other shallow groundwater matrices such as boulder fields appear to be more important in controlling surface‐water chemistry than their abundance would indicate. The chemical composition of the major source waters (usually thought of as end‐members whose chemical composition is relatively constant over time) changes at the same time that their mixing ratio in streams changes, confounding use of end‐member mixing models to describe stream‐water chemistry. Changes in the chemical composition of these source waters are caused by the ionic pulse of solutes from the snowpack and the small size of the shallow groundwater reservoir compared to the volume of snowmelt passing through it. The brief hydrologic residence time in the shallow groundwater indicates that concentrations of most dissolved constituents of stream water were controlled by fast geochemical processes that occurred on timescales of hours to days, rather than slower processes such as weathering of primary minerals. Differences in the timing of snowmelt‐related processes between different areas of the watershed also affect the stream‐water chemical composition. Cirque lakes affect discharge and chemical composition of one of the streams; seasonal control on stream‐water NO 3 and SiO 2 concentrations by diatom uptake in the lakes was inferred. Elution of acidic waters from the snowpack, along with dilution of base cations originating in shallow groundwater, caused episodes of decreased acid‐neutralizing capacity in the streams, but the streams did not become acidic.

Colorado↗
USGS2010

Use of a reactive gas transport model to determine rates of hydrocarbon biodegradation in unsaturated porous media

A mathematical model is presented that simulates the transport and reaction of any number of gaseous phase constituents (e.g. CO 2 , O 2 , N 2 , and hydrocarbons) in unsaturated porous media. The model was developed as part of a method to determine rates of hydrocarbon biodegradation associated with natural cleansing at petroleum product spill sites. The one-dimensional model can be applied to analyze data from column experiments or from field sites where gas transport in the unsaturated zone is approximately vertical. A coupled, non-Fickian constitutive relation between fluxes and concentration gradients, together with the capability of incorporating heterogeneity with respect to model parameters, results in model applicability over a wide range of experimental and field conditions. When applied in a calibration mode, the model allows for the determination of constituent production/consumption rates as a function of the spatial coordinate. Alternatively, the model can be applied in a predictive mode to obtain the distribution of constituent concentrations and fluxes on the basis of assumed values of model parameters and a biodegradation hypothesis. Data requirements for the model are illustrated by analyzing data from a column experiment designed to determine the aerobic degradation rate of toluene in sediments collected from a gasoline spill site in Galloway Township, New Jersey.

Water Resources Research↗
USGS2010

Modeling hexavalent chromium reduction in groundwater in field-scale transport and laboratory batch experiments

A plausible and consistent model is developed to obtain a quantitative description of the gradual disappearance of hexavalent chromium (Cr(VI)) from groundwater in a small-scale field tracer test and in batch kinetic experiments using aquifer sediments under similar chemical conditions. The data exhibit three distinct timescales. Fast reduction occurs in well-stirred batch reactors in times much less than 1 hour and is followed by slow reduction over a timescale of the order of 2 days. In the field, reduction occurs on a timescale of the order of 8 days. The model is based on the following hypotheses. The chemical reduction reaction occurs very fast, and the longer timescales are caused by diffusion resistance. Diffusion into the secondary porosity of grains causes the apparent slow reduction rate in batch experiments. In the model of the field experiments, the reducing agent, heavy Fe(II)-bearing minerals, is heterogeneously distributed in thin strata located between larger nonreducing sand lenses that comprise the bulk of the aquifer solids. It is found that reducing strata of the order of centimeters thick are sufficient to contribute enough diffusion resistance to cause the observed longest timescale in the field. A one-dimensional advection/dispersion model is formulated that describes the major experimental trends. Diffusion rates are estimated in terms of an elementary physical picture of flow through a stratified medium containing identically sized spherical grains. Both reduction and sorption reactions are included. Batch simulation results are sensitive to the fraction of reductant located at or near the surface of grains, which controls the amount of rapid reduction, and the secondary porosity, which controls the rate of slow reduction observed in batch experiments. Results of Cr(VI) transport simulations are sensitive to the thickness and relative size of the reducing stratum. Transport simulation results suggest that nearly all of the reductant must be located in the reducing stratum. Within this context and as long as there is adequate reductive capacity present, the transport simulation results are insensitive to the parameters important for the batch simulations. The results illustrate how a combination of field measurements and batch laboratory studies can be used to improve predictive modeling of contaminant transport.

Water Resources Research↗
USGS2010

Hydrologic and geochemical effects on oxygen uptake in bottom sediments of an effluent-dominated river

More than 95% of the water in the South Platte River downstream from the largest wastewater treatment plant serving the metropolitan Denver, Colorado, area consists of treated effluent during some periods of low flow. Fluctuations in effluent-discharge rates caused daily changes in river stage that promoted exchange of water between the river and bottom sediments. Groundwater discharge measurements indicated fluxes of water across the sediment-water interface as high as 18 m 3 s −1 km −1 . Laboratory experiments indicated that downward movement of surface water through bottom sediments at velocities comparable to those measured in the field (median rate ≈0.005 cm s −1 ) substantially increased dissolved oxygen uptake rates in bottom sediments (maximum rate 212 ± 10 μmol O 2 L −1 h −1 ) compared with rates obtained when no vertical advective flux was generated (maximum rate 25 ± 8.8 μmol O 2 L −1 h −1 ). Additions of dissolved ammonium to surface waters generally increased dissolved oxygen uptake rates relative to rates measured in experiments without ammonium. However, the magnitude of the advective flux through bottom sediments had a greater effect on dissolved oxygen uptake rates than did the availability of ammonium. Results from this study indicated that efforts to improve dissolved oxygen dynamics in effluent-dominated rivers might include stabilizing daily fluctuations in river stage.

Colorado↗
USGS2010

Simulation of aerobic and anaerobic biodegradation processes at a crude oil spill site

A two-dimensional, multispecies reactive solute transport model with sequential aerobic and anaerobic degradation processes was developed and tested. The model was used to study the field-scale solute transport and degradation processes at the Bemidji, Minnesota, crude oil spill site. The simulations included the biodegradation of volatile and nonvolatile fractions of dissolved organic carbon by aerobic processes, manganese and iron reduction, and methanogenesis. Model parameter estimates were constrained by published Monod kinetic parameters, theoretical yield estimates, and field biomass measurements. Despite the considerable uncertainty in the model parameter estimates, results of simulations reproduced the general features of the observed groundwater plume and the measured bacterial concentrations. In the simulation, 46% of the total dissolved organic carbon (TDOC) introduced into the aquifer was degraded. Aerobic degradation accounted for 40% of the TDOC degraded. Anaerobic processes accounted for the remaining 60% of degradation of TDOC: 5% by Mn reduction, 19% by Fe reduction, and 36% by methanogenesis. Thus anaerobic processes account for more than half of the removal of DOC at this site.

Water Resources Research↗
USGS2010

Eolian transport, saline lake basins, and groundwater solutes

Eolian processes associated with saline lakes are shown to be important in determining solute concentration in groundwater in arid and semiarid areas. Steady state mass balance analyses of chloride in the groundwater at Double Lakes, a saline lake basin in the southern High Plains of Texas, United States, suggest that approximately 4.5 × 10 5 kg of chloride is removed from the relatively small (4.7 km 2 ) basin floor each year by deflation. This mass enters the groundwater down the wind gradient from the lake, degrading the water quality. The estimates of mass transport were independently determined by evaluation of solutes in the unsaturated zone and by solute mass balance calculations of groundwater flux. Transport of salts from the lake was confirmed over a short term (2 years) by strategically placed dust collectors. Results consistent with those at Double Lake were obtained from dune surfaces collected upwind and downwind from a sabkha near the city of Abu Dhabi in the United Arab Emirates. The eolian transport process provides an explanation of the degraded groundwater quality associated with the 30–40 saline lake basins on the southern half of the southern High Plains of Texas and New Mexico and in many other arid and semiarid areas.

Water Resources Research↗
USGS2010

Comment on "Horizontal aquifer movement in a theis-theim confined system" by Donald C. Helm

In a recent paper, Helm [1994] presents an analysis of horizontal aquifer movement induced by groundwater withdrawal from a confined aquifer in which fluid and grains are incompressible. The analysis considers the aquifer in isolation (ignoring overlying and underlying strata) and assumes that the aquifer deforms purely in the horizontal direction (with no vertical movement). Helm's solution for grain displacement is obtained through introduction of a quantity known as bulk flux, q b , defined as q b = n v w + (1 - n )v s where n is porosity, v w is velocity of water, and v s is the velocity of the solid grains. On the basis of the bulk flux concept, Helm develops an explanation for the driving force on the bulk material. It is our view that Helm's analysis is subject to four limitations. First, Helm's assumption of zero vertical displacement is not supported by field observations and could result in over- estimation of radial displacement. Second, in ignoring the role of overlying and underlying strata, Helm's solution does not yield reliable estimates of aquifer deformation. Third, Helm's solution method works only for problems that involve one spatial coordinate (for example, x or r) but does not generally work for problems involving three-dimensional flow and de- formation. Fourth, Helm's explanation of the driving force on the bulk material is faulty for general three-dimensional problems. The purpose of our comment is to discuss these four issues.

Water Resources Research↗