A fuzzy logic based explicit declustering technique.

During the spatial estimation of geoscience resource variables, the quantity or quality of minerals and hydrocarbons can be represented by a broad range of properties, including geochemical, geotechnical, or other physical measures. Preferential sampling within the region of interest causes biased global parameters due to clustered sampling patterns. Unbiased sample distribution is essential for conducting conditional simulations to model uncertainty of spatially distributed attributes, e.g. geochemical content of metal or porosity. Therefore, declustering procedures are applied during resource estimation to estimate an unbiased statistical distribution of the measured variables. Traditional techniques such as cell declustering do not consider grade clustering, i.e., the similarity of measured variables within a spatially clustered neighbourhood. This paper presents a declustering technique that explicitly accounts for spatial clustering and the similarity of measured samples' attributes within these spatially clustered samples. In the proposed method, samples were first classified explicitly into spatial and geochemical (grade) clusters using the Fuzzy c-means algorithm. Declustering weights were derived using the Mamdani based Fuzzy Inference System using various T-norm operations. The technique was applied to the publicly available GSLib and Walker Lake datasets. It was shown that the proposed scheme produced more accurate results than those obtained with the traditional declustering technique.

Assessment of physical leaching processes of some elements in soil upon ingestion by continuous leaching and modeling.

The physical processes controlling the desorption of some elements (B, Cd, Co, Mn, Ni, and Sr) from soils in a continuous leaching system representing the human stomach are investigated here by fitting experimental leaching data to a mathematical particle diffusion model. Soil samples (50 mg) from Cornwall, UK, contained in a flow-through extraction chamber (ca. 6.5 mL) were intimately contacted with artificial gastric solution at various flow rates (0.42-1.42 mL min(-1)) for up to ca. 4 h, followed by analysis of the fractions collected with inductively coupled plasma mass spectrometry (ICP-MS). The leaching profiles of the various elements were fitted to a mathematical model incorporating two mass transfer processes (liquid film diffusion and apparent solid phase diffusion) to determine the effective external mass transfer coefficient (beta) and the apparent intraparticle soil diffusion coefficient (D(a)). A system of partial differential equations was solved numerically with a finite difference discretization of the computational domain allowing the rate limiting physical desorption process(es) for each element to be determined. The (thermodynamic) driving force of the leaching process is defined by the distribution coefficient (K(d0)) between soil and leachant. Although the K(d0) values investigated are very similar (ca. 6-15 L kg(-1)) for the elements studied with the exception of B (ca. 2.7 L kg(-1)), the leaching profiles are very different due to diffusion-limited processes. The elements may be classified as limited by beta (B, Sr, and Cd), by D(a) (Co, and Mn) or by beta and D(a) (Ni). This results in quantifiable parameters for the liability of elements in soil upon ingestion which may be implemented in future risk assessment protocols.