Application of Recursive Estimation to Heat Tracing for Groundwater/Surface-Water Exchange.

We present and demonstrate a recursive-estimation framework to infer groundwater/surface-water exchange based on temperature time series collected at different vertical depths below the sediment/water interface. We formulate the heat-transport problem as a state-space model (SSM), in which the spatial derivatives in the convection/conduction equation are approximated using finite differences. The SSM is calibrated to estimate time-varying specific discharge using the Extended Kalman Filter (EKF) and Extended Rauch-Tung-Striebel Smoother (ERTSS). Whereas the EKF is suited to real-time ("online") applications and uses only the past and current measurements for estimation (filtering), the ERTSS is intended for near-real time or batch-processing ("offline") applications and uses a window of data for batch estimation (smoothing). The two algorithms are demonstrated with synthetic and field-experimental data and are shown to be efficient and rapid for the estimation of time-varying flux over seasonal periods; further, the recursive approaches are effective in the presence of rapidly changing flux and (or) nonperiodic thermal boundary conditions, both of which are problematic for existing approaches to heat tracing of time-varying groundwater/surface-water exchange.

Benefits and Cautions in Data Assimilation Strategies: An Example of Modeling Groundwater Recharge.

Assimilating recent observations improves model outcomes for real-time assessments of groundwater processes. This is demonstrated in estimating time-varying recharge to a shallow fractured-rock aquifer in response to precipitation. Results from estimating the time-varying water-table altitude (h) and recharge, and their error covariances, are compared for forecasting, filtering, and fixed-lag smoothing (FLS), which are implemented using the Kalman Filter as applied to a data-driven, mechanistic model of recharge. Forecasting uses past observations to predict future states and is the current paradigm in most groundwater modeling investigations; filtering assimilates observations up to the current time to estimate current states; and FLS estimates states following a time lag over which additional observations are collected. Results for forecasting yield a large error covariance relative to the magnitude of the expected recharge. With assimilating recent observations of h, filtering and FLS produce estimates of recharge that better represent time-varying observations of h and reduce uncertainty in comparison to forecasting. Although model outcomes from applying data assimilation through filtering or FLS reduce model uncertainty, they are not necessarily mass conservative, whereas forecasting outcomes are mass conservative. Mass conservative outcomes from forecasting are not necessarily more accurate, because process errors are inherent in any model. Improvements in estimating real-time groundwater conditions that better represent observations need to be weighed for the model application against outcomes with inherent process deficiencies. Results from data assimilation strategies discussed in this investigation are anticipated to be relevant to other groundwater processes models where system states are sensitive to system inputs.

Contributing Areas to Domestic Wells in Dipping Sedimentary Rocks under Extreme Recharge Events.

We use particle tracking to determine contributing areas (CAs) to wells for transient flow models that simulate cyclic domestic pumping and extreme recharge events in a small synthetic watershed underlain by dipping sedimentary rocks. The CAs consist of strike-oriented bands at locations where the water table intersects high-hydraulic conductivity beds, and from which groundwater flows to the pumping well. Factors that affect the size and location of the CAs include topographic flow directions, rock dip direction, cross-bed fracture density, and position of the well relative to streams. For an effective fracture porosity (ne ) of 10-4 , the fastest advective travel times from CAs to wells are only a few hours. These results indicate that wells in this type of geologic setting can be highly vulnerable to contaminants or pathogens flushed into the subsurface during extreme recharge events. Increasing ne to 10-3 results in modestly smaller CAs and delayed well vulnerability due to slower travel times. CAs determined for steady-state models of the same setting, but with long-term average recharge and pumping rates, are smaller than CAs in the models with extreme recharge. Also, the earliest-arriving particles arrive at the wells later in the steady-state models than in the extreme-recharge models. The results highlight the importance of characterizing geologic structure, simulating plausible effective porosities, and simulating pumping and recharge transience when determining CAs in fractured rock aquifers to assess well vulnerability under extreme precipitation events.

Incorporating Snowmelt into Daily Estimates of Recharge Using a State-Space Model of Infiltration.

A state-space model (SSM) of infiltration estimates daily groundwater recharge using time-series of groundwater-level altitude and meteorological inputs (liquid precipitation, snowmelt, and evapotranspiration). The model includes diffuse and preferential flow through the unsaturated zone, where preferential flow is a function of liquid precipitation and snowmelt rates and a threshold rate, above which there is direct recharge to the water table. Model parameters are estimated over seasonal periods and the SSM is coupled with the Kalman Filter (KF) to assimilate recent observations (hydraulic head) and meteorological inputs into recharge estimates. The approach can take advantage of real-time hydrologic and meteorological data to deliver real-time recharge estimates. The model is demonstrated on daily observations from two bedrock wells in carbonate aquifers of northwestern New York (USA) between 2013 and 2018. Meteorological inputs for liquid precipitation and snowmelt are compiled from SNODAS (2021). Results for recharge during winter and spring seasons show preferential flow events to the water table from liquid precipitation, snowmelt, or a combination of the two. Recharge estimates summed annually are consistent with previous estimates of recharge reported from groundwater flow and surface-process models. Results from the SSM and KF point to errors in meteorological inputs, such as the snowmelt rate, that are not compatible with hydraulic head observations. Whereas liquid and solid precipitation are measured at discrete stations and extrapolated to 1-km2 grid cells, snowmelt is a meteorological modeled outcome that may not represent conditions in the vicinity of monitoring well locations.

The complex spatial distribution of trichloroethene and the probability of NAPL occurrence in the rock matrix of a mudstone aquifer.

Methanol extractions for chloroethene analyses are conducted on rock samples from seven closely spaced coreholes in a mudstone aquifer that was subject to releases of the nonaqueous phase liquid (NAPL) form of trichloroethene (TCE) between the 1950's and 1990's. Although TCE concentration in the rock matrix over the length of coreholes is dictated by proximity to subhorizontal bedding plane fractures, elevated TCE concentrations in the rock matrix are not continuous along the most permeable bedding plane fractures. A complex configuration of subvertical and subhorizontal fractures appears to be responsible for the TCE distribution from prior TCE releases at land surface. Phase partitioning calculations of TCE in the rock matrix show that most TCE is adsorbed to solid surfaces because of the large fraction of organic carbon (foc) in the mudstone. Large TCE content in some cores indicate the likely presence of the NAPL form of TCE in the rock matrix. Using average values of porosity (n) and foc in phase partitioning calculations identifies a number of locations of possible NAPL occurrence in the rock matrix. Samples of mudstone analyzed for n and foc show variability in these properties over several orders of magnitude. Accounting for this variability in phase partitioning calculations identifies a probability of NAPL occurrence, PNAPL. The spatial variability of PNAPL along coreholes identifies a configuration that may be attributed to a TCE source zone that has evolved after emplacement due to NAPL dissolution, adsorption, and matrix diffusion.

Variability of organic carbon content and the retention and release of trichloroethene in the rock matrix of a mudstone aquifer.

Contaminants diffusing from fractures into the immobile porosity of the rock matrix are subject to prolonged residence times. Organic contaminants can adsorb onto organic carbonaceous materials in the matrix extending contaminant retention. An investigation of spatial variability of the fraction of organic carbon (foc) is conducted on samples of rock core from seven closely spaced boreholes in a mudstone aquifer contaminated with trichloroethene (TCE). A total of 378 samples were analyzed at depths between 14 and 36 m below land surface. Mudstone units associated with deep water deposition have the largest foc, with a maximum value of 0.0396, and units associated with shallow water deposition have the smallest foc. Even though foc correlates with depositional conditions, foc still varies over more than an order of magnitude in continuous mudstone layers between boreholes, and there is large variability in foc over short distances perpendicular to bedding. Simulations of diffusion and linear equilibrium adsorption of TCE using spatially variable foc in the rock matrix show order of magnitude variability in the adsorbed TCE over short distances in the matrix and residence times extending to hundreds of years following remediation in adjacent fractures. Simulations using average values of foc do not capture the range of TCE mass that can be retained in a rock matrix characterized by spatially variable foc. Bounds on TCE mass within the rock matrix can be obtained by simulations with spatially uniform values of foc equal to the maximum and minimum values of foc for a given mudstone unit.

Bioremediation in Fractured Rock: 2. Mobilization of Chloroethene Compounds from the Rock Matrix.

A mass balance is formulated to evaluate the mobilization of chlorinated ethene compounds (CE) from the rock matrix of a fractured mudstone aquifer under pre- and postbioremediation conditions. The analysis relies on a sparse number of monitoring locations and is constrained by a detailed description of the groundwater flow regime. Groundwater flow modeling developed under the site characterization identified groundwater fluxes to formulate the CE mass balance in the rock volume exposed to the injected remediation amendments. Differences in the CE fluxes into and out of the rock volume identify the total CE mobilized from diffusion, desorption, and nonaqueous phase liquid dissolution under pre- and postinjection conditions. The initial CE mass in the rock matrix prior to remediation is estimated using analyses of CE in rock core. The CE mass mobilized per year under preinjection conditions is small relative to the total CE mass in the rock, indicating that current pump-and-treat and natural attenuation conditions are likely to require hundreds of years to achieve groundwater concentrations that meet regulatory guidelines. The postinjection CE mobilization rate increased by approximately an order of magnitude over the 5 years of monitoring after the amendment injection. This rate is likely to decrease and additional remediation applications over several decades would still be needed to reduce CE mass in the rock matrix to levels where groundwater concentrations in fractures achieve regulatory standards.

Bioremediation in Fractured Rock: 1. Modeling to Inform Design, Monitoring, and Expectations.

Field characterization of a trichloroethene (TCE) source area in fractured mudstones produced a detailed understanding of the geology, contaminant distribution in fractures and the rock matrix, and hydraulic and transport properties. Groundwater flow and chemical transport modeling that synthesized the field characterization information proved critical for designing bioremediation of the source area. The planned bioremediation involved injecting emulsified vegetable oil and bacteria to enhance the naturally occurring biodegradation of TCE. The flow and transport modeling showed that injection will spread amendments widely over a zone of lower-permeability fractures, with long residence times expected because of small velocities after injection and sorption of emulsified vegetable oil onto solids. Amendments transported out of this zone will be diluted by groundwater flux from other areas, limiting bioremediation effectiveness downgradient. At nearby pumping wells, further dilution is expected to make bioremediation effects undetectable in the pumped water. The results emphasize that in fracture-dominated flow regimes, the extent of injected amendments cannot be conceptualized using simple homogeneous models of groundwater flow commonly adopted to design injections in unconsolidated porous media (e.g., radial diverging or dipole flow regimes). Instead, it is important to synthesize site characterization information using a groundwater flow model that includes discrete features representing high- and low-permeability fractures. This type of model accounts for the highly heterogeneous hydraulic conductivity and groundwater fluxes in fractured-rock aquifers, and facilitates designing injection strategies that target specific volumes of the aquifer and maximize the distribution of amendments over these volumes.

Porosity and pore size distribution in a sedimentary rock: Implications for the distribution of chlorinated solvents.

Characterizing properties of the rock matrix that control retention and release of chlorinated solvents is essential in evaluating the extent of contamination and the application of remediation technologies in fractured rock. Core samples from seven closely spaced boreholes in a mudstone subject to trichloroethene (TCE) contamination were analyzed using Mercury Intrusion Porosimetry to investigate porosity and pore size distribution as a function of mudstone characteristics, and depth and lateral extent in the aquifer; organic carbon content was also evaluated to identify the potential for adsorption. Porosity and retardation factor varied over two orders of magnitude, with the largest porosities and largest retardation factors associated with carbon-rich mudstone layers. Larger porosities were also measured in the shallow rock that has been subject to enhanced groundwater flow. Porosity also varied over more than an order of magnitude in spatially continuous mudstone layers. The analyses of the rock cores indicated that the largest pore diameters may be accessible to entry of the nonaqueous form of TCE. Although the porosity associated with the largest pore diameters is small (~0.1%), that volume of TCE can significantly affect the total TCE that is retained in the rock matrix. The dimensions of the largest pore diameters may also be accessible to microbes responsible for reductive dechlorination; however, the small percentage of the pore space that can accommodate microbes may limit the extent of reductive dechlorination in the rock matrix.

Effect of cell physicochemical characteristics and motility on bacterial transport in groundwater.

The influence of physicochemical characteristics and motility on bacterial transport in groundwater were examined in flow-through columns. Four strains of bacteria isolated from a crystalline rock groundwater system were investigated, with carboxylate-modified and amidine-modified latex microspheres and bromide as reference tracers. The bacterial isolates included a gram-positive rod (ML1), a gram-negative motile rod (ML2), a nonmotile mutant of ML2 (ML2m), and a gram-positive coccoid (ML3). Experiments were repeated at two flow velocities, in a glass column packed with glass beads, and in another packed with iron-oxyhydroxide coated glass beads. Bacteria breakthrough curves were interpreted using a transport equation that incorporates a sorption model from microscopic observation of bacterial deposition in flow-cell experiments. The model predicts that bacterial desorption rate will decrease exponentially with the amount of time the cell is attached to the solid surface. Desorption kinetics appeared to influence transport at the lower flow rate, but were not discernable at the higher flow rate. Iron-oxyhydroxide coatings had a lower-than-expected effect on bacterial breakthrough and no effect on the microsphere recovery in the column experiments. Cell wall type and shape also had minor effects on breakthrough. Motility tended to increase the adsorption rate, and decrease the desorption rate. The transport model predicts that at field scale, desorption rate kinetics may be important to the prediction of bacteria transport rates.

Bacterial transport experiments in fractured crystalline bedrock.

The efficiency of contaminant biodegradation in ground water depends, in part, on the transport properties of the degrading bacteria. Few data exist concerning the transport of bacteria in saturated bedrock, particularly at the field scale. Bacteria and microsphere tracer experiments were conducted in a fractured crystalline bedrock under forced-gradient conditions over a distance of 36 m. Bacteria isolated from the local ground water were chosen on the basis of physicochemical and physiological differences (shape, cell-wall type, motility), and were differentially stained so that their transport behavior could be compared. No two bacterial strains transported in an identical manner, and microspheres produced distinctly different breakthrough curves than bacteria. Although there was insufficient control in this field experiment to completely separate the effects of bacteria shape, reaction to Gram staining, cell size, and motility on transport efficiency, it was observed that (1) the nonmotile, mutant strain exhibited better fractional recovery than the motile parent strain; (2) Gram-negative rod-shaped bacteria exhibited higher fractional recovery relative to the Gram-positive rod-shaped strain of similar size; and (3) coccoidal (spherical-shaped) bacteria transported better than all but one strain of the rod-shaped bacteria. The field experiment must be interpreted in the context of the specific bacterial strains and ground water environment in which they were conducted, but experimental results suggest that minor differences in the physical properties of bacteria can lead to major differences in transport behavior at the field scale.

Integration of stable carbon isotope, microbial community, dissolved hydrogen gas, and ²HH2O tracer data to assess bioaugmentation for chlorinated ethene degradation in fractured rocks.

An in situ bioaugmentation (BA) experiment was conducted to understand processes controlling microbial dechlorination of trichloroethene (TCE) in groundwater at the Naval Air Warfare Center (NAWC), West Trenton, NJ. In the BA experiment, an electron donor (emulsified vegetable oil and sodium lactate) and a chloro-respiring microbial consortium were injected into a well in fractured mudstone of Triassic age. Water enriched in ²H was also injected as a tracer of the BA solution, to monitor advective transport processes. The changes in concentration and the δ¹³C of TCE, cis-dichloroethene (cis-DCE), and vinyl chloride (VC); the δ²H of water; changes in the abundance of the microbial communities; and the concentration of dissolved H2 gas compared to pre- test conditions, provided multiple lines of evidence that enhanced biodegradation occurred in the injection well and in two downgradient wells. For those wells where the biodegradation was stimulated intensively, the sum of the molar chlorinated ethene (CE) concentrations in post-BA water was higher than that of the sum of the pre-BA background molar CE concentrations. The concentration ratios of TCE/(cis-DCE+VC) indicated that the increase in molar CE concentration may result from additional TCE mobilized from the rock matrix in response to the oil injection or due to desorption/diffusion. The stable carbon isotope mass-balance calculations show that the weighted average ¹³C isotope of the CEs was enriched for around a year compared to the background value in a two year monitoring period, an effective indication that dechlorination of VC was occurring. Insights gained from this study can be applied to efforts to use BA in other fractured rock systems. The study demonstrates that a BA approach can substantially enhance in situ bioremediation not only in fractures connected to the injection well, but also in the rock matrix around the well due to processes such as diffusion and desorption. Because the effect of the BA was intensive only in wells where an amendment was distributed during injection, it is necessary to adequately distribute the amendments throughout the fractured rock to achieve substantial bioremediation. The slowdown in BA effect after a year is due to some extend to the decrease abundant of appropriate microbes, but more likely the decreased concentration of electron donor.