J.A. Barker

A comparison of some simple adsorption isotherms for describing divalent cation adsorption by ferrihydrite

Abstract An adsorption model for divalent cation (M2+) adsorption by ferrihydrite (iron hydrous oxide gel) was developed. The model was used to describe the pH and concentration dependence of M2+ adsorption in 1 M NaNO3. The model was derived by initially considering the statistical thermodynamics of H+−M2+ exchange on a uniform surface. The competitive Langmuir isotherm so derived was characterized by three parameters: a site affinity, a maximum adsorption capacity, and a parameter describing the H+/M2+ exchange stoichiometry. The problem of surface heterogeneity was then formulated in terms of the distribution of sites obeying this local isotherm. The distribution was estimated for ferrihydrite by fitting experimental Ca and Zn adsorption data to four closely related composite isotherms, each with a characteristic distribution of site affinities. The Toth isotherm (four adjustable parameters) and two-site Langmuir isotherm (five adjustable parameters) fitted the experimental data best. The resultant isotherms enabled Ca and Zn adsorption to be estimated within a factor of 1.5 or better over a wide range of pH and concentration. The associated site affinity distributions suggest that the surface of ferrihydrite is composed of a relatively large number of low affinity sites and a small number of high affinity sites.

The implications of groundwater velocity variations on microbial transport and wellhead protection – review of field evidence

Current strategies to protect groundwater sources from microbial contamination (e.g., wellhead protection areas) rely upon natural attenuation of microorganisms between wells or springs and potential sources of contamination and are determined using average (macroscopic) groundwater flow velocities defined by Darcys Law. However, field studies of sewage contamination and microbial transport using deliberately applied tracers provide evidence of groundwater flow paths that permit the transport of microorganisms by rapid, statistically extreme velocities. These paths can be detected because of (i) the high concentrations of bacteria and viruses that enter near-surface environments in sewage or are deliberately applied as tracers (e.g., bacteriophage); and (ii) low detection limits of these microorganisms in water. Such paths must comprise linked microscopic pathways (sub-paths) that are biased toward high groundwater velocities. In media where microorganisms may be excluded from the matrix (pores and fissures), the disparity between the average linear velocity of groundwater flow and flow velocities transporting released or applied microorganisms is intensified. It is critical to recognise the limited protection afforded by source protection measures that disregard rapid, statistically extreme groundwater velocities transporting pathogenic microorganisms, particularly in areas dependent upon untreated groundwater supplies.

Hydrogeothermal studies in the United Kingdom

Following the increase in oil prices in the mid‐1970s, Britain assessed its geothermal resources. Low‐temperature, hot‐water resources, in the range 40°C to 100°C, occur in Permo‐Triassic sandstones in several deep sedimentary basins. In total these resources are estimated at 69.1 × 1018 joules (J) (2576 million tonnes coal equivalent). Resources also occur in Upper Palaeozoic aquifers but, as the permeability of these aquifers depends upon fissures, exploitation is difficult. The only surface manifestations of hot water at depth are the warm springs at Bath and Bristol and in the Peak District and Taff Valley, which issue from the Carboniferous Limestone. The potential of radiothermal granites for Hot Dry Rock (HDR) development has also been investigated, particularly in the Carnmenellis granite in Cornwall. Three boreholes drilled in the granite to depths of over 2 km have been connected by developing natural fractures. Water circulation between the boreholes and through the fractured rock has been successful.

Convergent Radial Tracing of Viral and Solute Transport in Gneiss Saprolite

Deeply weathered crystalline rock aquifer systems comprising unconsolidated saprolite and underlying fractured bedrock (saprock) underlie 40% of sub-Saharan Africa. The vulnerability of this aquifer system to contamination, particularly in rapidly urbanizing areas, remains poorly understood. In order to assess solute and viral transport in saprolite derived from Precambrian gneiss, forced-gradient tracer experiments using chloride and Escherichia coli phage PhiX174 were conducted in southeastern Uganda. The bacteriophage tracer was largely unrecovered; adsorption to the weathered crystalline rock matrix is inferred and enabled by the low pH (5.7) of site ground water and the bacteriophages relatively high isoelectric point (pI = 6.6). Detection of the applied PhiX174 phage in the pumping well discharge at early times during the experiment traces showed, however, that average ground water flow velocities exceed that of the inert solute tracer, chloride. This latter finding is consistent with observations in other hydrogeological environments where statistically extreme sets of microscopic flow velocities are considered to transport low numbers of fecal pathogens and their proxies along a selected range of linked ground water pathways. Application of a radial advection-dispersion model with an exponentially decaying source term to the recovered chloride tracer estimates a dispersivity (alpha) of 0.8 +/- 0.1 m over a distance of 4.15 m. Specific yield (S(y)) is estimated to be 0.02 from volume balance calculations based on tracer experiments. As single-site observations, our estimates of saprolite S(y) and alpha are tentative but provide a starting point for assessing the vulnerability of saprolite aquifers in sub-Saharan Africa to contamination and estimating quantitatively the impact of climate and abstraction on ground water storage.

A tracer methodology for identifying ambient flows in boreholes

Identifying flows into, out of, and across boreholes is important for characterizing aquifers, determining the depth at which water enters boreholes, and determining the locations and rates of outflow. This study demonstrates how Single Borehole Dilution Tests (SBDTs) carried out under natural head conditions provide a simple and cheap method of identifying vertical flow within boreholes and determining the location of in-flowing, out-flowing, and cross-flowing fractures. Computer simulations were used to investigate the patterns in tracer profiles that arise from different combinations of flows. Field tracer tests were carried out using emplacements of a saline tracer throughout the saturated length of boreholes and also point emplacements at specific horizons. Results demonstrated that SBDTs can be used to identify flowing fractures at the top and bottom of sections of vertical flow, where there is a change in vertical flow rate within a borehole, and also where there are consistent decreases in tracer concentration at a particular depth. The technique enables identification of fractures that might be undetected by temperature and electrical conductance logging, and is a simple field test that can be carried out without pumping the borehole.

Modelling doublets and double porosity

Abstract A simple model has been developed as a scoping tool for transport between an injection well and an abstraction well pumping at the same rate (i.e. a doublet) in a fractured porous rock. This model is aimed primarily at the planning and preliminary interpretation of tracer tests and trial heat exchange using thermal doublets in the Chalk aquifer. The model is essentially a particular case of transport along multiple flow paths and relies on the invariance of double-porosity transport with respect to velocity variations along a flow path. Hypothetical simulations demonstrate that solute tracer tests need to be supplemented by information on fracture porosity in order to be able to predict thermal breakthrough.

Pumping tests using large-diameter observation wells

Abstract The drawdown in a large-diameter observation well during a pumping test, using a production well of negligible diameter, is shown to be identical to the drawdown that would be observed if the roles of the wells were reversed. The drawdown is therefore given by the well function for a large-diameter well.

Re-evaluating dual-porosity effects at the site of a seminal groundwater modelling study: Tilmanstone, southern England

Abstract The first numerical model of solute transport to incorporate Fickian diffusive exchange between mobile fracture water and immobile porewater for an actual case of groundwater contamination at catchment scale was applied to the Chalk aquifer at Tilmanstone in SE England by Bibby (Water Resources Research, 1981, 17, 1075–1081). The unconfined aquifer at Tilmanstone had been contaminated by coalfield brine leaking from disposal lagoons operating throughout much of the twentieth century. Recent observations show that the Bibby model underestimates dual-porosity diffusive retardation, and hence underestimates the persistence of contamination, probably by several decades. 2D representation of the aquifer in plan ignored the hydrostratigraphy, and model calibration was limited by the lack of time-variant paired profiles of fracture water and porewater. Vertical profiles through the Chalk determined by packer testing, borehole dilution testing and geophysical logging, together with a new depth profile of chloride concentration in Chalk matrix porewater, are described. The hydrostratigraphy is interpreted in relation to the Chalk lithostratigraphy of SE England, and incorporated into a vertical-section model of chloride transport along the axis of the valley, consistent with the new and historical profiles of fracture water and porewater chloride concentrations. New predictions of the longevity of the chloride contamination at Tilmanstone are presented.

Models of tracer breakthrough and permeability in simple fractured porous media

Abstract Tailing and bimodal behaviour of tracer breakthrough curves from tracer tests conducted in fractured porous media are commonly presented as ‘deviations’ from the Fickian model for homogeneous porous media. Tailing is mainly attributed to: (1) tracer storage brought about by diffusion between mobile and static regions of fluid; (2) a concentration of flow towards the wider (aperture) and, thus, more permeable fracture zones; and (3) the high variance in fracture conductivity and consequent mixing of tracer. Bi- (or multi-) modality has been attributed to solute following a few highly permeable flow paths. Systematic numerical simulations of flow and transport in geometrically simple fractured porous media were conducted using a 2D finite difference flow code and a particle tracking transport model. As a simplification only advective dispersion was considered. The modelling study produced a large variety of tracer breakthrough curves, including two patterns commonly seen in field data — the backward tailed uni-modal type and the Gaussian type. The study demonstrates that different types of breakthrough might be characteristic of particular sets of conceptual models for heterogeneities and, as such, may provide a useful pointer in the application and interpretation of tracer tests.

Discussion on ‘The application of analytical solutions to the thermal plume from a well doublet ground source heating/cooling scheme’ Quarterly Journal of Engineering Geology and Hydrogeology Vol. 44, 191–197

In his paper, Banks (2011) discusses the possibility of deriving an exact analytical solution to the hydraulic travel time along a flow line of his well-doublet scenario. The solution is given as follows, providing a general solution for the (hydraulic) travel time, t t, along the x -axis from any point to an abstraction well (or from the injection well to any point on the x -axis). The third solution (β > 1, α = −1) already appears in Banks’s paper as equation (5). The …