Transport in a 2-D saturated porous medium: A new method for particle tracking

A new method for solving the transport equation based on the management of a large numbe of particles in a discretized 2-D domain is presented. The method uses numerical variables to represent the number of particles in a given mesh and is more complex than the 1-D problem. The first part of the paper focuses on the specific management of particles in a 2-D problem. The method also would be valid for three dimensions as long as the medium can be modeled similar to a layered system. As the particles are no longer tracked individually, the algorithm is fast and does not depend on the number of particles present. The numerical tests show that the method is nearly numerical dispersion free and permits accurate calculations even for simulations of low-concentration transport. Because each mesh is considered as a closed system between two successive time steps, it is easy to add adsorption phenomenon without any problem of numerical stability. The model is tested under conditions that are extremely demanding for its operating mode and gives a good fit to analytical solutions. The conditions in which it can be used to best advantage are discussed.     

The age and thermal history of Cerro Rico de Potosi, Bolivia

 Cerro Rico de Potosi, Bolivia, is the world’s largest silver deposit and has been mined since the sixteenth century for silver, and for tin and zinc during the twentieth century, together with by-product copper and lead. The deposit consists primarily of veins that cut an altered igneous body that we interpret to be a dacitic volcanic dome and its underlying tuff ring and explosion breccia. The deposit is compositionally and thermally zoned, having a core of cassiterite, wolframite, bismuthinite, and arsenopyrite surrounded by a peripheral, lower-temperature mineral assemblage consisting principally of sphalerite, galena, lead sulfosalt, and silver minerals. The low-temperature assemblage also was superimposed on the high-temperature assemblage in response to cooling of the main hydrothermal system. Both the dacite dome and the ore fluids were derived from a larger magmatic/hydrothermal source at depth. The dome was repeatedly fractured by recurrent movement on the fault system that guided its initial emplacement. The dome was extruded at 13.8±0.2 Ma (2σ), based on U-Th-Pb dating of zircon. Mineralization and alteration occurred within about 0.3 my of dome emplacement, as indicated by a ⁴⁰Ar/³⁹Ar date of 13.76±0.10 Ma (1σ) for sericite from the pervasive quartz-sericite-pyrite alteration associated with the main-stage, high-temperature, mineralization. The last thermal event able to reset zircon fission tracks occurred no later than 12.5±1.1 Ma (1σ), as indicated by fission-tract dating. Minor sericite, and magmatic-steam alunite veins, were episodically formed around 11 Ma and between 8.3 and 5.7 Ma; the younger episodes occurring at the time of extensional fracturing at Cerro Rico and widespread volcanism in the adjacent Los Frailes volcanic field. None of these younger events appear to be significant thermal/mineralizing events; the exceptionally flat thermal release pattern of ³⁹Ar from sericite and the results of the fission-tract dating of zircon show that none of the younger events was hot enough, and lasted long enough, to cause significant loss of Ar or annealing of zircon fission tracks. U-Th-Pb dating of zircon cores indicates a Precambrian progenitor for some zircons, and REE analyses of dated samples of hydrothermally altered dacite show the presence of a prominent positive Eu anomaly, which constrains interpretations of the origin and evolution of the magmatic/hydrothermal system. Received: 14 October 1995/Accepted: 29 January 1996     

The replacement of anthophyllite by jimthompsonite: a model for hydration reactions in biopyriboles

Anthophyllite crystals found in ultramafic lenses of the Lepontine Alps (Switzerland) contain coherent, submicroscopic intergrowths of ordered and disordered biopyribole polysomes. The chain width distributions of disordered polysomes were analyzed using high resolution transmission electron microscopy (HRTEM). Chains wider than triple were interpreted as intermediate products in the transformation of anthophyllite to the triple chain silicate jimthompsonite. The concentration of individual chain types is strongly correlated with the reaction progress. Based on observed zipper terminations and the transformation rules given by Veblen and Buseck (1980) a scheme of possible reaction paths leading from anthophyllite to jimthomp sonite is proposed. The reaction scheme and a simple kinetic model for elementary reactions allow modeling of the observed chain width distributions. The model suggests that the complex reaction paths involving steps with increasing and decreasing chain width are more important in the formation of jimthompsonite than the direct transformation from anthophyllite. The wide chains (>triple) occurring as intermediate products of the multi-step paths are structurally closer to talc than jimthompsonite. The back-transformation of these wide chains to triple chains is, therefore, a strong argument that jimthompsonite is a stable phase and not only a metastable intermediate product in the transformation of anthophyllite to talc. Received: 8 July 1996 / Accepted: 13 December 1996     

Methodical approach to distribution of epilithic and drifting algae communities in a French subalpine river: Inferences on water quality assessment

In a sub-alpine river, the Asse, with an unpredictable discharge regime, chlorophyll, density and taxonomic diversity of both drifting and periphytic communities were studied from a methodical approach. The investigations based on stamping two close cross-sections to know their spatial distributions in a heterogeneous bed substrate showed a heterogeneous pattern of colonization mainly influenced by hydrological variables as the current velocity, the size of the substrata (gravel-pebble-boulder). For the drifting algae, mainly composed with benthic species temporarily unhooked to the substrata, the heterogeneity of the distribution was reduced in fast flow which induced a mixing of the whole mass of water. For the periphyton, some results indicated that the greatest diversity and the highest chlorophyll concentration were found on pebble substratum where the current velocity was moderate. These results have also shown that the classical methods used to day for investigations were inadequate for most Mediterranean rivers. It was really difficult to estimate the water quality from classical index created for use in regular large plain rivers.     

Bathymetric and geochemical investigation of Kawah Ijen Crater Lake, East Java, Indonesia

A bathymetric survey of Kawah Ijen crater lake was conducted by acoustic sounding in 1996 to compare the lake morphology with those measured in 1922, 1925 and 1938, and to calculate the present lake volume. Even though the lake experienced several hydrothermal eruptions, the maximum depth became shallower (182 m) than before (200 m), resulting in a reduced lake volume (3.0×10⁷ m³).Fifty-two major and minor constituents including rare earth elements and polythionates (PT) of the lake waters at various depths were determined by ICP-AES, ICP-MS and HPLC, respectively. These ions except for several volatile elements are taken up by lake fringe through congruent dissolution of pyroclastics of Kawah Ijen volcano. Most ions are homogeneously distributed throughout the lake, although PT showed a considerable vertical variation. Rare earth elements (REE) in the Kawah Ijen water as well as those from other hyper-acidic crater lakes show distribution patterns likely due to the three rock dissolution (preferential, congruent and residual) types, and their logarithmic concentrations linearly depend upon the pH values of the lake waters.Using the PT degradation kinetics data, production rates of PT, injection rates of SO₂ and H₂S into the lake were estimated to be 114, 86 and 30 tons/day, respectively. Also travel time of the spring water at the Banyupahit Riverhead from Kawah Ijen was estimated to be 600–1000 days through the consideration of decreasing rates of PT. Molten sulfur stocks containing Sn, Cu, Bi sulfides and Pb-barite exposed on the inner crater slope were presumed to be extinct molten sulfur pools at the former lake bottom. This was strongly supported by the barite precipitation temperature estimated through the consideration of the temperature dependence of Pb-chlorocomplex formation.     

Multicomponent ionic diffusion in porewaters: Coulombic effects revisited

The diffusion of an ion in porewaters cannot occur independently of the other ions in solution as a result of Coulombic coupling, as well as from other effects not considered here. Unfortunately, a longstanding disagreement exists about the correct form and meaning of the equations that describe Coulombic coupling in porewaters, i.e., Ben-Yaakov [Am. J. Sci. 281 (1981) 974] vs. Lasaga [Am. J. Sci. 281 (1981) 981]. This paper re-examines this controversy by reformulating the problem starting from fundamental concepts of mass and charge conservation. We show that these antagonistic formulations are both valid and, in fact, equivalent, when the different interpretations of charge balance are resolved. Most of the disagreements between Ben-Yaakov and Lasaga are then shown to result from differing methods of solution, not fundamental disparities in their models. We note, however, that the explanation for the concept of “stationary” gradients of nonreacting ions as given Ben-Yaakov is inaccurate, and such gradients do lead to diffusive fluxes that are counterbalanced by electrochemical migrational fluxes to produce no net flux (excluding advective flux). We further find that the bicarbonate diffusive flux will not balance the diffusional charge flux of sulfate during its reduction if advection is present. This latter imbalance generates compensating fluxes in the other nonreacting ions. We have applied our theory to a simplified case of sulfate reduction in a marine sediment. The results show that nonreacting ions do diffuse and that with normally expected values of porewater advection, the ratio of the bicarbonate to the sulfate flux can be far different than the ideal value of −2.     

Nuclear Waste Disposal Simulations: Couplex Test Cases

We give some results obtained for the Couplex test cases proposed by the ANDRA. In this paper our aim is twofold. Firstly, to compute the release of nuclides out of the repository by concentrating on the 3D near field (Couplex 2). The simulation of the transport phenomena takes into account the dissolution of the glass containers and congruent emissions of the radio-nuclides including filiation chains and some simplified chemistry. Secondly, it is to use the near field computations in order to simulate the nuclide migrations in a 2D far field (Couplex 3). Coupling in between the two simulations takes into consideration the periodicity of the disposal modules and the geometry of the repository described in Couplex 1. The mixed finite element and discontinuous Galerkin methods are used to solve the convection–diffusion equations. In order to handle the nonlinear precipitation/dissolution term, we developed a new iterative technique that combines Picard and Newton–Raphson methods.     

A Finite Volume Scheme for the Transport of Radionucleides in Porous Media

The COUPLEX1 Test case (Bourgeat et al., 2003) is devoted to the comparison of numerical schemes on a convection–diffusion–reaction problem. We first show that the results of the simulation can be mainly predicted by a simple analysis of the data. A finite volume scheme, with three different treatments of the convective term, is then shown to deliver accurate and stable results under a low computational cost.