Naturally occurring radioactive material (NORM) from a former phosphoric acid processing plant

In recent years there has been an increasing awareness of the radiological impact of non-nuclear industries that extract and/or process ores and minerals containing naturally occurring radioactive material (NORM). These industrial activities may result in significant radioactive contamination of (by-) products, wastes and plant installations. In this study, scale samples were collected from a decommissioned phosphoric acid processing plant. To determine the nature and concentration of NORM retained in pipe-work and associated process plant, four main areas of the site were investigated: (1) the 'Green Acid Plant', where crude acid was concentrated; (2) the green acid storage tanks; (3) the Purified White Acid (PWA) plant, where inorganic impurities were removed; and (4) the solid waste, disposed of on-site as landfill. The scale samples predominantly comprise the following: fluorides (e.g. ralstonite); calcium sulphate (e.g. gypsum); and an assemblage of mixed fluorides and phosphates (e.g. iron fluoride hydrate, calcium phosphate), respectively. The radioactive inventory is dominated by U-238 and its decay chain products, and significant fractionation along the series occurs. Compared to the feedstock ore, elevated concentrations (<= 8.8 Bq/g) of U-238 Were found to be retained in installations where the process stream was rich in fluorides and phosphates. In addition, enriched levels (<= 11 Bq/g) of Ra-226 were found in association with precipitates of calcium sulphate. Water extraction tests indicate that many of the scales and waste contain significantly soluble materials and readily release radioactivity into solution. (c) 2005 Elsevier Ltd. All rights reserved.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.