Andrew R. Piggott

Fractal relations for the diameter and trace length of disc-shaped fractures

Analytic relations are developed between the fractal parameters of a random, isotropic population of disc-shaped fractures and the parameters of the corresponding population of fracture traces expressed in outcrop. These relations indicate that a fractal distribution of fracture diameters translates to a fractal distribution of trace lengths and that the parameters for diameter may be uniquely determined from the parameters for trace length. Probabilistic results demonstrate the accuracy of the analytic relations and identify nonideal behaviors at the limits of the computed trace length data. It is expected that these relations will be useful in the three-dimensional characterization of fracture systems in rock from in situ trace length data.

Laboratory assessment of the equivalent apertures of a rock fracture

Hydraulic, electrical, and tracer test results are presented for a natural fracture in granite. The hydraulic and electrical apertures of the fracture are similar and suggest minimal fracture surface-to-surface contact. Tracer aperture exceeds hydraulic aperture indicating transport at a rate less than that predicted on the basis of hydraulic aperture. Numerical simulation of tracer transport reveals that transport within the fracture is not explicable in terms of parallel plate flow and that transport occurs locally at rates in excess of the overall rate defined by tracer aperture.

Analytical models for flow through obstructed domains

The effects of low- or zero-conductivity inclusions on flow through two- and three-dimensional domains are represented using an analogy to percolation theory. Here, the term flow refers to the analogous processes of fluid, electrical current, and heat conduction. Mapping functions are derived from renormalization group models as a solution to the percolation analogy. These functions relate the extent to which a domain is obstructed to the probability that the domain is conductive and to the bulk conductivity of the domain. Stochastic methods are used to define a relation between the proportion of a domain which is isolated from flow and the proportion which is obstructed. A description of the influence of the scale of the obstructions, relative to that of the domain, is inherent in the formulation. Data obtained from numerical and electrical analogues are used to verify the mapping functions and assess the limitations of the representation.

Publicly accessible software for groundwater modelling and analysis

Abstract Practitioners of hydrogeology and groundwater engineering have access to a range of topical software that may be freely used, modified and redistributed. Many of these software may be obtained at no cost using the Internet. Implementing publicly accessible software achieves software reuse and rapid prototyping, may reduce the cost of software acquisition and development, and provides authors with increased flexibility in the distribution of their products. Software that are useful within groundwater studies include operating systems, editors, language compilers, models and components such as mathematical subroutines and routines for discretization and plotting and visualization. Public distribution of software may achieve personal and corporate objectives and should be undertaken with due regard for issues such as the potential impact on subsequent commercial deployment of the software.

Static and dynamic calculation of formation fluid displacement induced by hydraulic fracturing

Hydraulically fracturing a geological formation results in the displacement of the fluids that are distributed within the formation in response to fracturing fluid loss and poroelasticity effects. This process will limit the application of hydraulic fracturing in conjunction with groundwater contamination remediation if the resulting fluid displacement translates to deleterious mobilization of the target contaminants. A dynamic solution for determining the fluid displacement accompanying hydraulic fracturing is developed and compared to a simpler, static solution. The static solution is shown to be adequate for characteristic formation and fracture treatment parameters.