V. Di Federico

Thermal Instability of a Power-Law Fluid Flowing in a Horizontal Porous Layer with an Open Boundary: A Two-Dimensional Analysis

A two-dimensional analysis of the onset of thermal convective instability in a horizontal porous layer with open upper boundary is carried out. The saturating fluid is non-Newtonian of power-law behaviour, and its flow is represented through a suitable extension of Darcy’s law. A model of temperature-dependent viscosity is employed where the consistency index is considered as variable, while the power-law index is assumed to be constant. Numerical data for the neutral stability and for the critical values of a modified Darcy–Rayleigh number have been obtained. The feasibility of an experimental validation of the theoretical results predicted by the stability analysis is discussed in detail. An experimental set-up based on a Hele-Shaw cell is described, and preliminary results relative to the onset of convective cells are described. Observed hysteretic effects and deviations from the rheological model are identified as potential sources of uncertainty.

Propagation of viscous gravity currents inside confining boundaries: the effects of fluid rheology and channel geometry

A theoretical and experimental investigation of the propagation of free-surface, channelized viscous gravity currents is conducted to examine the combined effects of fluid rheology, boundary geometry and channel inclination. The fluid is characterized by a power-law constitutive equation with behaviour index n. The channel cross section is limited by a rigid boundary of height parametrized by k and has a longitudinal variation described by the constant b≥0. The cases k⋛1 are associated with wide, triangular and narrow cross sections. For b>0, the cases k≷1 describe widening channels and squeezing fractures; b=0 implies a constant cross-sectional channel. For a volume of released fluid varying with time like tα, scalings for current length and thickness are obtained in self-similar forms for horizontal and inclined channels/fractures. The speed, thickness and aspect ratio of the current jointly depend on the total current volume (α), the fluid rheological behaviour (n), and the transversal (k) and longitudinal (b) geometry of the channel. The asymptotic validity of the solutions is limited to certain ranges of parameters. Experimental validation was performed with different fluids and channel cross sections; experimental results for current radius and profile were found to be in close agreement with the self-similar solutions at intermediate and late times.

Gravity currents in a linearly stratified ambient fluid created by lock release and influx in semi-circular and rectangular channels

We present an experimental investigation, supported by a theoretical model, of the motion of lock-release, constant inflow, and time varying inflow gravity currents (GCs) into a linearly stratified ambient fluid at large Reynolds number. The aim is the experimental validation of a simple model able to predict the slumping phase front speed and the asymptotic self-similar front speed for rectangular and circular cross section channels. The first investigated system is of Boussinesq type with the dense current (salt water dyed with aniline) released in a circular channel of 19 cm diameter and 400 cm long (605 cm in the inflow experiments), half-filled of linearly stratified ambient fluid (salt water with varying salt concentration). The second system has the same components but with a channel of rectangular cross section of 14 cm width, 11 cm ambient fluid depth, and 504 cm length. The density stratification of the ambient fluid was obtained with a computer controlled set of pumps and of mixing tanks. For t...

Impact of Hydrogeological Uncertainty on Estimation of Environmental Risks Posed by Hydrocarbon Transportation Networks

Ubiquitous hydrogeological uncertainty undermines the veracity of quantitative predictions of soil and groundwater contamination due to accidental hydrocarbon spills from onshore pipelines. Such predictions, therefore, must be accompanied by quantification of predictive uncertainty, especially when they are used for environmental risk assessment. We quantify the impact of parametric uncertainty on temporal evolution of two key risk indices, volumes of unsaturated and saturated soil contaminated by a surface spill of light non-aqueous-phase liquids. This is accomplished by treating the relevant uncertain parameters as random variables and deploying two alternative probabilistic models to estimate their effect on predictive uncertainty. A physics-based model is solved with a stochastic collocation method and is supplemented by a global sensitivity analysis. A second model represents the quantities of interest as polynomials of random inputs and has a virtually negligible computational cost, which enables one to explore any number of risk-related contamination scenarios. For a typical oil-spill scenario, our method can be used to identify key flow and transport parameters affecting the risk indices, to elucidate texture-dependent behavior of different soils, and to evaluate, with a degree of confidence specified by the decision-maker, the extent of contamination and the correspondent remediation costs.

On the propagation of particulate gravity currents in circular and semi-circular channels partially filled with homogeneous or stratified ambient fluid

We present a combined theoretical-experimental investigation of particle-driven gravity currents advancing in circular cross section channels in the high-Reynolds number Boussinesq regime; the ambient fluid is either homogeneous or linearly stratified. The predictions of the theoretical model are compared with experiments performed in lock–release configuration; experiments were performed with conditions of both full-depth and partial-depth locks. Two different particles were used for the turbidity current, and the full range 0≤S≤1 of the stratification parameter was explored (S = 0 corresponds to the homogeneous case and S = 1 when the density of the ambient fluid and of the current are equal at the bottom). In addition, a few saline gravity currents were tested for comparison. The results show good agreement for the full-depth configuration, with the initial depth of the current in the lock being equal to the depth of the ambient fluid. The agreement is less good for the partial-depth cases and is impro...

Multiscale Permeability and Dispersion in Randomly Heterogeneous Geologic Media

Flow and transport in natural soils and rocks have been traditionally described by means of partial differential equations (pde’s). These equations are generally taken to represent basic physical principles (conservation and constitutive laws) that operate on some macroscopic scale (theoretical support volume) at which the geologic medium may be viewed as a continuum. The precise nature of this theoretical macroscopic support scale remains generally unclear though some derive comfort from associating it in the abstract with a “representative elementary volume” (REV). Unfortunately, the concept of an REV is equally difficult to define without ambiguity or to apply in practice. Flow and transport pde’s are local in the sense that all quantities (parameters; forcing functions including initial, boundary and source terms; dependent variables) which enter into them are defined at a single point (x, t) in space-time. Parameters such as permeability, porosity, and dispersivity are generally regarded as macroscopic medium properties that are well-defined, and can thus be determined (at least in principle) experimentally and more-or-less uniquely, at any point x in the flow domain.