Analytical Solution for Modeling Discharge into a Tunnel Drilled in a Heterogeneous Unconfined Aquifer

Predicting transient inflow rates into a tunnel is an important issue faced by hydrogeologists. Most existing analytical solutions overestimate the initial discharge due to the assumption that drilling was instantaneous over the entire tunnel length. In addition, they assume a homogeneous system. An alternative model was recently developed for tunnels intersecting heterogeneous formations, but its application was reduced to the case of confined flow to deep tunnels in weakly diffusive aquifers. In this paper, we adapt existing analytical solutions for drainage systems to the specific case of a tunnel progressively drilled in a highly diffusive heterogeneous unconfined aquifer. The case of a tunnel overlying an impervious layer is analytically solved by applying the superposition principle, while the case of a tunnel constructed some distance above an impervious layer is solved by discretizing the tunnel length into subsectors. Both models can simulate transient discharge into a tunnel drilled at various speeds through a heterogeneous unconfined aquifer, and allow the prediction of discharge rates in shallow tunnels located in highly diffusive aquifers. We successfully applied this approach to a tunnel in heterogeneous volcanic rock.     

Numerical Modeling of the Observed Wiechert Seismograph Magnification

—The paper presents results of experiments designed to measure the actual dynamic magnification of the Wiechert 1000 kg horizontal seismometer when excited by seismic waves. This is accomplished by comparing 51 digital records of seismic events recorded by the Wiechert and a well calibrated reference seismometer. The results obtained indicate that the magnification of the Wiechert seismometer is influenced by the interaction of its mass and frame, especially for high frequencies. This interaction has been modeled by considering a system of two coupled pendulums, yielding a theoretical dynamic magnification curve which exhibits main features of the observed magnification. The dis crepancy between the nominal and the actual response of the Wiechert seismograph may lead to errors in studies involving spectral analyses of recorded seismograms, and to overestimation of local earth quake magnitudes.     

Evaluation of Noble Gas Recharge Temperatures in a Shallow Unconfined Aquifer

Water table temperatures inferred from dissolved noble gas concentrations (noble gas temperatures, NGT) are useful as a quantitative proxy for air temperature change since the last glacial maximum. Despite their importance in paleoclimate research, few studies have investigated the relationship between NGT and actual recharge temperatures in field settings. This study presents dissolved noble gas data from a shallow unconfined aquifer heavily impacted by agriculture. Considering samples unaffected by degassing, NGT calculated from common physically based interpretive gas dissolution models that correct measured noble gas concentrations for "excess air" agreed with measured water table temperatures (WTT). The ability to fit data to multiple interpretive models indicates that model goodness-of-fit does not necessarily mean that the model reflects actual gas dissolution processes. Although NGT are useful in that they reflect WTT, caution is recommended when using these interpretive models. There was no measurable difference in excess air characteristics (amount and degree of fractionation) between two recharge regimes studied (higher flux recharge primarily during spring and summer vs. continuous, low flux recharge). Approximately 20% of samples had dissolved gas concentrations below equilibrium concentration with respect to atmospheric pressure, indicating degassing. Geochemical and dissolved gas data indicate that saturated zone denitrification caused degassing by gas stripping. Modeling indicates that minor degassing (<10% ΔNe) may cause underestimation of ground water recharge temperature by up to 2°C. Such errors are problematic because degassing may not be apparent and degassed samples may be fit by a model with a high degree of certainty.     

Contamination of an Unconfined Sand Aquifer by Waste Pulp Liquor: A Case Study

A zone of contaminated ground water has been identified in an unconfined sand aquifer adjacent to a pit into which spent pulp liquor was intermittently discharged from 1970 to 1979. A network of multilevel sampling, bundle-type piezometers was installed. Up to seven depthspecific sampling points were incorporated into each piezometer providing a cost-effective means for three-dimensional mapping of hydraulic head and water quality in the unconfined sand aquifer. Ground-water samples retrieved from this network showed an area of contamination 900 m long, 400 m wide, and more than 25 m deep. This plume is dispersed about the ground-water flow lines passing beneath the waste disposal pit, and it terminates at a vigorous ground-water discharge area located 800 m from the pit. The contaminated ground water is characterized by elevated concentrations of sodium (3,000 mg/1), chloride (590 mg/1), alkalinity (2,700 mg/1), total organic carbon (2,000 mg/1), chemical oxygen demand (10,800 mg/1), biological oxygen demand (2,000 mg/1), tannin and lignin (780 mg/1), and lower sulphate (1 mg/1) compared to background ground waters in the area. The apparent rate of sodium migration is more than 50 m/yr and is close to the average linear ground-water velocity. Removal of some organic matter by biological transformation has produced the increased alkalinity in the contaminated ground water and somewhat reduced pH. Tannin and lignin are relatively inert compared to other organic compounds found in the waste liquor. Extremely low sulphate levels occurring in the highly contaminated ground waters indicate the existence of conditions favorable for microbially-mediated sulphate reduction.     

Water Table Uncertainties due to Uncertainties in Structure and Properties of an Unconfined Aquifer

We consider two sources of geology‐related uncertainty in making predictions of the steady‐state water table elevation for an unconfined aquifer. That is the uncertainty in the depth to base of the aquifer and in the hydraulic conductivity distribution within the aquifer. Stochastic approaches to hydrological modeling commonly use geostatistical techniques to account for hydraulic conductivity uncertainty within the aquifer. In the absence of well data allowing derivation of a relationship between geophysical and hydrological parameters, the use of geophysical data is often limited to constraining the structural boundaries. If we recover the base of an unconfined aquifer from an analysis of geophysical data, then the associated uncertainties are a consequence of the geophysical inversion process. In this study, we illustrate this by quantifying water table uncertainties for the unconfined aquifer formed by the paleochannel network around the Kintyre Uranium deposit in Western Australia. The focus of the Bayesian parametric bootstrap approach employed for the inversion of the available airborne electromagnetic data is the recovery of the base of the paleochannel network and the associated uncertainties. This allows us to then quantify the associated influences on the water table in a conceptualized groundwater usage scenario and compare the resulting uncertainties with uncertainties due to an uncertain hydraulic conductivity distribution within the aquifer. Our modeling shows that neither uncertainties in the depth to the base of the aquifer nor hydraulic conductivity uncertainties alone can capture the patterns of uncertainty in the water table that emerge when the two are combined.     

Three-Dimensional Numerical Investigation of Pore Water Pressure and Deformation of Pumped Aquifer Systems

Excessive groundwater withdrawal has caused severe land subsidence worldwide. The pore water pressure and the deformation of pumped hydrostratigraphic units are complex. A fully coupled three-dimensional numerical simulation was carried out for different pumping plans in this paper. When groundwater is pumped from a confined aquifer, the great compaction occurs in the pumped aquifer and its upper and lower adjacent aquitard units. Land subsidence is smaller and the area affected by land subsidence is greater when groundwater is pumped from the deeper confined aquifer. The pore water pressure in the pumped confined aquifer changes immediately with pumpage. In the adjacent aquitard units, however, the pore water pressure increases in the early pumping time and decreases in the early recharging time. The decrease in the pore water pressure vertically spreads from the interface between aquitard and pumped aquifer to the other surface of the aquitard. The pumped aquifer compacts and rebounds immediately with pumping and non-pumping or recharging actions, while the compaction and rebounding of the aquitard units clearly lag behind. The compaction of the adjacent aquitard unit first occurs near the interface between aquitard and pumped aquifer units, and the compaction zone spreads outward as the pumping goes on. The aquitards may expand vertically within some zones. Due to the inelastic deformation of soil skeleton, different pumping plans result in different land subsidence. For the same net pumpage, maximal land subsidence and horizontal displacement are the smallest for constant discharge and the greatest for recharge-discharge cycle.     

Prediction of Remediation of a Heterogeneous Aquifer: A Case Study

Contaminant plumes whose characteristic length is smaller than the horizontal integral scale of the hydraulic conductivity, K, are abundant in shallow, phreatic aquifers. In such cases, the aquifer can be regarded as layered, with K being only a function of the vertical coordinate. The heterogeneity of K has a critical role upon the efficiency of remediation of such sites, for example, by Pump and Treat schemes. The expected efficiency is a random variable, with uncertainty. Quantifying this uncertainty can be of great importance to decision making. In this study, we focus on a case study in the coastal aquifer of Israel and compare two different approaches for constructing realizations of K: continuous and indicator. We observe a significant difference between the constructed realizations, which results in a considerable difference in the predicted remediation efficiency and its uncertainty. Furthermore, we study the effect of conditioning the realizations by a rather limited number of K data points. We find that the conditioning results in a major reduction of the uncertainty. In addition, we compare the results of the transport model to a simplified semi‐analytical solution that is based on assuming radial flow. We find a good agreement with the three‐dimensional numerical model. This result illustrates that the simplified solution can be used for prediction of the remediation efficiency when the flow at the plume vicinity can be regarded as radial.     

A Comparison of Office-Derived vs. Field-Derived Water Table Maps for a Sandy Unconfined Aquifer

This study compares the accuracy of two types of water table maps both of which were constructed with the object of optimizing future mapping efforts in similar environments. The. first type of map is based solely on office information, with no field verification. The second type of map is based on careful field mapping using numerous measurement points.
The office-derived maps were based on topography, surface water features, existing reports, maps and data in the files of the Wisconsin Geological and Natural History Survey; the data were not field-verified. The field-derived maps used a dense network of 236 piezometers at 176 sites in an area of approximately 170 square miles. The field project was much more expensive and labor-intensive than was the construction of office-derived maps for the same area.
The two methods produce water table maps which agree to an appreciable extent, the greatest agreement being in areas having ground water-fed streams. Differences in water table elevations indicated by the two methods range from negligible to approximately 5 feet. Thus, depending upon the availability of existing information, relatively accurate water table elevations can be delineated in similar sandy unconfined aquifers without time-consuming and expensive field work that drilling and piezometer installation entails.
Preliminary construction of office-derived water table maps enables researchers to use their resources efficiently. In some situations, expensive installation of wells and piezometers for a regional monitoring network may add little accuracy to the regional map. For localized problems, collection of additional field data will always be necessary, but can be guided by the office-derived maps. The authors caution that this technique may only be applicable to sandy, unconfined aquifers in humid climates.