Neville I. Robinson

Vulnerability indicators of sea water intrusion.

In this paper, simple indicators of the propensity for sea water intrusion (SWI) to occur (referred to as SWI vulnerability indicators) are devised. The analysis is based on an existing analytical solution for the steady-state position of a sharp fresh water-salt water interface. Interface characteristics, that is, the wedge toe location and sea water volume, are used in quantifying SWI in both confined and unconfined aquifers. Rates-of-change (partial derivatives of the analytical solution) in the wedge toe or sea water volume are used to quantify the aquifer vulnerability to various stress situations, including (1) sea-level rise; (2) change in recharge (e.g., due to climate change); and (3) change in seaward discharge. A selection of coastal aquifer cases is used to apply the SWI vulnerability indicators, and the proposed methodology produces interpretations of SWI vulnerability that are broadly consistent with more comprehensive investigations. Several inferences regarding SWI vulnerability arise from the analysis, including: (1) sea-level rise impacts are more extensive in aquifers with head-controlled rather than flux-controlled inland boundaries, whereas the opposite is true for recharge change impacts; (2) sea-level rise does not induce SWI in constant-discharge confined aquifers; (3) SWI vulnerability varies depending on the causal factor, and therefore vulnerability composites are needed that differentiate vulnerability to such threats as sea-level rise, climate change, and changes in seaward groundwater discharge. We contend that the approach is an improvement over existing methods for characterizing SWI vulnerability, because the method has theoretical underpinnings and yet calculations are simple, although the coastal aquifer conceptualization is highly idealized.

Contaminant transport in sets of parallel finite fractures with fracture skins

Analysis of flow and transport in double/dual-porosity or fractured formations is a problem with important theoretical and practical applications. We present steady-state and transient solutions for solute transport in a finite system of parallel fractures with fracture skins. Solute transport in the fractures is by advection and hydrodynamic dispersion. Concentrations are attenuated by diffusion into the porous matrix. Radioactive decay and sorption in the skin, the matrix, and along the fracture walls are included. Our analysis extends previous studies by considering both finite fracture lengths and the effects of fracture skins. Our results conform to these studies when considering large, but finite fractures without skins. For transient solutions, we use a numerical inversion of the Laplace transforms and also present a series solution. Steady-state solutions are closed form analytical solutions. The results of these analyses can be used for the verification of numerical models used in predicting or retrodicting flow and transport in fractured porous media and for sensitivity analyses. The steady-state analyses are shown to be satisfactory for sensitivity analyses. We utilize data for cesium-137 and from the Permian Brushy Canyon Sandstone of west Texas in the sensitivity analyses to show the effects of fracture skins. The analyses indicate increased distances of transport with thicker skins of lower porosity and lower diffusivity. Retardation effects were smaller in magnitude. Analysis of transport in dual-porosity systems should consider the effects of fracture skins because they are ubiquitous in nature and are present in many, if not most, hydraulically active near-surface fractures.

Application of Benzo(a)pyrene and Coal Tar Tumor Dose–Response Data to a Modified Benchmark Dose Method of Guideline Development

Assessment of cancer risk from exposure to polycyclic aromatic hydrocarbons (PAHs) has been traditionally conducted by applying the conservative linearized multistage (LMS) model to animal tumor data for benzo(a)pyrene (BaP), considered the most potent carcinogen in PAH mixtures. Because it has been argued that LMS use of 95% lower confidence limits on dose is unnecessarily conservative, that assumptions of low-dose linearity to zero in the dose response imply clear mechanistic understanding, and that “acceptable” cancer risk rests on a policy decision, an alternative cancer risk assessment approach has been developed. Based in part on the emerging benchmark dose (BMD) method, the modified BMD method we used involves applying a suite of conventional mathematical models to tumor dose–response data. This permits derivation of the average dose corresponding to 5% extra tumor incidence (BMD0.05) to which a number of modifying factors are applied to achieve a guideline dose, that is, a daily dose considered safe for human lifetime exposure. Application of the modified BMD method to recent forestomach tumor data from BaP ingestion studies in mice suggests a guideline dose of 0.08 μg/kg/day. Based on this and an understanding of dietary BaP, and considering that BaP is a common contaminant in soil and therefore poses human health risk via soil ingestion, we propose a BaP soil guideline value of 5 ppm (milligrams per kilogram). Mouse tumor data from ingestion of coal tar mixtures containing PAHs and BaP show that lung and not forestomach tumors are most prevalent and that BaP content cannot explain the lung tumors. This calls into question the common use of toxicity equivalence factors based on BaP for assessing risk from complex PAH mixtures. Emerging data point to another PAH compound—7H-benzo(c)fluorene—as the possible lung tumorigen.

Application of the Groenevelt–Grant soil water retention model to predict the hydraulic conductivity

We outline several formulations of the Groenevelt–Grant water retention model of 2004 to show how it can be anchored at different points. The model is highly flexible and easy to perform multiple differentiations and integrations on. Among many possible formulations of the model we choose one anchored solely at the saturated water content, θs, to facilitate comparison with the van Genuchten model of 1980 and to obtain a hydraulic conductivity function through analytical integration: where, k0, k1, and n are fitting parameters. We divided this formulation by θs to obtain the relative water content, θr(h), and inverted the function to produce a form required for integration, namely: in which the parameter β is introduced to accommodate both the ‘Burdine’ and ‘Mualem’ models. The integrals are identified as incomplete gamma functions and are distinctly different from the incomplete beta functions embodied in the van Genuchten–Mualem models. Rijtema’s data from 1969 for 20 Dutch soils are used to demonstrate the procedures involved. The water retention curves produced by our Groenevelt–Grant model are virtually indistinguishable from those produced by the van Genuchten model. Relative hydraulic conductivities produced by our Mualem and Burdine models produced closer estimates of Rijtema’s measured values than those produced by the van Genuchten–Mualem model for 19 of his 20 soils. This work provides an alternative to the widely used van Genuchten–Mualem approach and represents a preamble for the, as yet unsatisfactory, treatment of the tortuosity component of the unsaturated hydraulic conductivity function.

Maximizing Net Extraction Using an Injection‐Extraction Well Pair in a Coastal Aquifer

In this study, we examine the maximum net extraction rate from the novel arrangement of an injection-extraction well pair in a coastal aquifer, where fresh groundwater is reinjected through the injection well located between the interface toe and extraction well. Complex potential theory is employed to derive a new analytical solution for the maximum net extraction rate and corresponding stagnation-point locations and recirculation ratio, assuming steady-state, sharp-interface conditions. The injection-extraction well-pair system outperforms a traditional single extraction well in terms of net extraction rate for a broad range of well placement and pumping rates, which is up to 50% higher for an aquifer with a thickness of 20 m, hydraulic conductivity of 10 m/d, and fresh water influx of 0.24 m(2) /d. Sensitivity analyses show that for a given fresh water discharge from an inland aquifer, a larger maximum net extraction is expected in cases with a smaller hydraulic conductivity or a smaller aquifer thickness, notwithstanding physical limits to drawdown at the pumping well that are not considered here. For an extraction well with a fixed location, the optimal net extraction rate linearly increases with the distance between the injection well and the sea, and the corresponding injection rate and recirculation ratio also increase. The analytical analysis in this study provides initial guidance for the design of well-pair systems in coastal aquifers, and is therefore an extension beyond previous applications of analytical solutions of coastal pumping that apply only to extraction or injection wells.

Impact of permeable conduits on solute transport in aquitards: Mathematical models and their application

[1]xa0The migration of contaminants through porous conduits (for example, sand layers) in aquitards, or any preferential flow feature within a low-permeability matrix, can be significantly retarded via diffusion into the matrix and processes such as sorption and decay. Previous solutions for simulating contaminant transport in these types of environments have been limited to a parallel-plate approach such as that used in studies of fractured rock aquifers. A major drawback of using these approaches is that they cannot account for the radial component of diffusion that occurs from circular- or elliptical-sectioned conduits. We have developed solutions for both of the latter cases and compared results from generic simulations to those obtained with a conventional parallel-plate model. The results demonstrated using a circular conduit approach can produce concentration profiles for both the conduit and surrounding matrix that are up to several orders of magnitude lower than those predicted using parallel-plate models. The solutions for elliptical-section conduits provide concentration profiles that are bounded by the circular- and parallel-plate models. We also present several generic simulations to demonstrate the effects of conduit radius and average groundwater flow velocity on concentration profiles. Finally, the circular conduit model is applied to a clay-rich till aquitard in southern Saskatchewan, Canada to provide insight into an anomalous dissolved chloride peak in the vertical pore water profile. The model demonstrates that the source of the high Cl− could be as far as 10–100 km from the site (although this distance may be unrealistic) and allows estimation of the Cl− concentration at the source. We envisage that the solutions for conduit diffusion will have far wider applications than just aquitard studies, and future uses may include tracer tests in karstic and fractured aquifers.

Second‐order two‐dimensional solution for the drainage of recharge based on Picard's iteration technique: A generalized Dupuit‐Forchheimer equation

[1]xa0Aquifer recharge is one of the most important problems in hydrology from both theoretical and practical points of view. One of the most widely accepted methods to deal with this problem is the use of the Dupuit-Forchheimer theory. This theory assumes that the water table is almost horizontal, the vertical velocity is zero, and the horizontal velocity is uniform with depth. Surfaces of seepage are not considered. Despite these strong limitations the theory is applied, and success is frequently found in many cases despite its fundamental assumptions being violated. In this work an approximate 2-D solution to the problem is sought on the basis of Picards iteration technique, from which a second-order differential equation for recharge problems is found. On the basis of this solution, a modified, analytical Dupuit-Forchheimer (DF) ellipse is found which compares favorably with the full 2-D solution of the problem. The analytical developments of this theory provide a generalized DF theory which permits as an outcome the analytical determination of the surface of seepage.

Development of a Tolerable Daily Intake for N-Nitrosodimethylamine Using a Modified Benchmark Dose Methodology

N-Nitrosodimethylamine (NDMA) is an environmental contaminant that has recently been detected in Australian drinking-water supplies and that is principally generated in chloramination systems. NDMA is acutely toxic to humans at high doses, is genotoxic after cytochrome P-450 metabolism, and is carcinogenic in several animal species. An extremely large lifetime cancer dose-response study reported by Peto and colleagues (1984, 1991a, 1991b) of NDMA in drinking water given to rats is used in risk assessment by various jurisdictions. We have recently reported on use of an Australian modified benchmark dose (mBMD) methodology for developing tolerable daily intakes (TDIs) and guideline values for environmental carcinogens based on cancer dose response in the low-dose region, and have applied this to the NDMA rat liver tumor data. The application of a suite of mathematical models to the incidence data for hepatocellular carcinomas and hemangiosarcomas, followed by arithmetic and exponential-weight averaging of the 5% extra risk dose (mBMD0.05) for the various models, produced an mBMD0.05 range of 0.020–0.028 mg/kg/d. This was then divided by a range of modifying factors to account for seriousness of the carcinogenic endpoint, adequacy of the database, and inter- and intraspecies differences, generating a TDI range of 4.0 to 9.3 ng/kg/d. This may be employed in developing guideline values for NDMA in environmental media.