We have developed a computer model which describes the geochemical and physical processes responsible for acid drainage from waste rock piles. The model is in the form of coupled nonlinear PDEs which describe: the kinetics of the chemical reactions, the release of contaminants, the generation of energy due to the exothermic oxidation of sulphides, the diffusive and convective transport of oxygen and water, and the transport of energy by conduction and convection. The meso-scale and large-scale characterization of waste rock and waste rock piles is discussed. We show that long-term leaching rates are inversely proportional to the square of particle diameter and that the previously used models underestimate the particle size effect on long-term sulphide oxidation. Experimental data on rock fragmentation are used for a fractal statistical characterization of waste rock piles. The acid generation rates, oxygen consumption rates and temperature profiles have been determined for piles containing from fifty thousand to five hundred thousand tonnes of waste rock. The thermodynamic instabilities, which occur at certain critical values of pile height, are responsible for thermodynamic catastrophes which result in a rapid increase of acid generation rates. The critical height is determined by the values of sulphide concentration, particle size, pile porosity and other factors. The numerical code is based on the finite elements method with an adaptive grid generator.
abstract.
[P2.02] Numerical models of thermo-chemical convection in the Earth's mantle
Louise Kellogg (Department of Geology, University of California, Davis CA)
At the elevated pressures and temperatures of the Earth's deep
interior, rock responds to stress by slow, creeping flow, driving
plate tectonics, mountain building, earthquakes, and
volcanoes. Because of the remoteness of the mantle and the long
timescales (millions of years) involved, mantle convection cannot be
observed directly. Computational challenges arise from the complex,
temperature-dependent rheology. Flow is driven both by thermal
stresses and variations in composition. We have developed a
finite-element model of thermochemical convection in the mantle using
a Boussinesq approximation. This talk will focus on the development
and evolution of an iron-rich layer at the base of the mantle, where
the crystalline silicate minerals of the mantle contact the molten
iron-rich core. Such a layer is observed using seismology. In
models, small-scale convection is observed within the layer; the
resulting fine structures can explain seismic anisotropy in the
lowermost mantle.
[P2.03] Challenges for Computational Physics in Underground Imaging of Electrically Conducting Contaminant Plumes
James G. Berryman (Lawrence Livermore National Laboratory, Livermore, CA)
For environmental hazard remediation, optimal strategies for cleanup are aided by knowledge of the location and extent underground of electrically conducting fluid contaminant plumes. As the fluid is transported through connected pores in the earth, time-delay imaging methods using either electrical resistance tomography or electromagnetic induction tomography can delineate both the movement of fluid fronts and local concentrations of these electrically conducting contaminants. The fundamental challenges for computational physics in these problems arise in both the forward modeling and the inversion of field data. For forward modeling, the major challenge is that both the fluid flow itself and the electrical and/or magnetic fields used to probe the fluids are inherently three-dimensional, and therefore computability limits the attainable resolution of the electrical or electromagentic fields on current platforms. For the data inversion (or tomographic) methods used to translate electrical or magnetic boundary measurements into images of conductivity, the contrasts in observed electrical conductivity are typically anywhere from one to several orders of magnitude and therefore not amenable to perturbation methods such as the Born approximation. Recent advances in computational physics for both the forward modeling and the inversion of data in such high contrast electrical systems will be discussed.
[P2.04] Calculating Surface Reaction Enthalpies Using Gas Phase Clusters in a Born-Haber Cycle.
Martin A. Nygren, Furio Cora, David H. Gay, C. Richard A. Catlow (Royal Institution of Great Britain)
Surfaces are by definition exposed to their environment and therefor have the possibility to undergo chemical reactions with it. Whenever the cost of quantum mechanical methods prevents the usage of slabs thick enough (or clusters large enough) to be reliable models of the surface, methods based on interatomistic potentials are preferable for calculating surface energies and relaxations. For a surface that undergoes a chemical reaction the reaction enthalpy must be included into the surface energy. Reaction enthalpies cannot be estimated from calculations employing interatomistic potentials. The way around this problem is to construct a fictious gas phase reaction, a Born-Haber cycle, for which the reaction enthalpies can be calculated or measured. As a generally applicable Born-Haber cycle we suggest that a growth layer is taken of the surface. This layer is then taken apart into clusters that are reacted, and put back together again into a reacted layer. When this reacted layer is put down onto the surface we have completed the reaction. In this cycle the only step that cannot be calculated using interatomistic potentials is the cluster reaction, which thus has to be calculated quantum mechanically. The above procedure will be outlined in some detail together with examples from hydroxilation of Al_2O_3, MgO, Si_2O_4 and Cu_2O.
[P2.05] Numerical Modeling of Ocean Acoustic Wavefields
Frederick Tappert (Applied Marine Physics, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, 33149)
The U.S. Navy requires real-time ``acoustic performance prediction'' models in order to optimize sonar tactics in naval combat situations. The need for numerical models that solve the acoustic wave equation in realistic ocean environments is being met by a collaborative effort between university researchers, industrial contractors, and navy laboratory workers. This paper discusses one particularly successful numerical model, called the PE/SSF model, that was originally developed by the author. Here PE stands for Parabolic Equation, a good approximation to the elliptic Helmholtz equation; and SSF stands for the Split-Step Fourier algorithm, a highly efficient marching algorithm for solving parabolic type equations. These techniques are analyzed, and examples are displayed of ocean acoustic wavefields generated by the PE/SSF model.
[P2.06] Irradiance Fluctuations in Optical Propagation through Atmospheric Turbulence
Stanley M. Flatté (Physics Department, University of California at Santa Cruz, Santa Cruz, CA 95064)
Numerical simulation of optical propagation through atmospheric turbulence has been carried out by use of an FFT implementation of the parabolic approximation to the wave equation. Past work has systematically simulated propagation in the strong-fluctuation regime, in which the irradiance variance is greater than unity, for plane wave initial conditions. Agreement with experiment for irradiance variance has been achieved at the 5% level, and higher moments have been investigated. In this talk, new results for moments of irradiance and log-irradiance for a point-source initial condition will be described. Comparisons will be made with expectations from analytic probability distributions such as the exponential, the exponential convolved with log-normal, and other distributions that have been suggested in the past.