Equivalent diffusion coefficient of clay-rich geological formations: comparison between numerical and analytical estimates

Laboratory experiments in rock samples collected from clay-rich formations indicate that the effective molecular diffusion coefficient (D) is a heterogeneous and anisotropic property. Since laboratory measurements of D are representative of a very small volume, upscaling is necessary in order to incorporate these data in large-scale numerical models of diffusive transport. In this work we address the problem of the estimating the equivalent diffusion coefficient (D _eq ), in terms of total diffusive flux, in a three-dimensional domain characterized by a heterogeneous and anisotropic spatial distribution of D. D _eq was estimated from the results of steady-state diffusive transport simulations through several realizations of the D field. The ensemble averages of D _eq from fields with different degrees of heterogeneity and anisotropy were then compared with estimates from analytical upscaling expressions based on stochastic as well as power-averaging approaches. These expressions are largely based on similar expressions developed for calculating the effective hydraulic conductivity in heterogeneous and anisotropic domains. Comparisons showed that stochastic expressions provide accurate estimates of D _eq only for fields characterized by low heterogeneity. Within the range of heterogeneity and anisotropy considered, our results showed that a power-averaging expression is very accurate in predicting D _eq especially when the parameter p _i is estimated through fitting of the numerical results. Nonetheless, the relationship between this parameter and the anisotropy ratio is linear.     

Effects of climate, invasive species and anthropogenic impacts on the growth of the seagrass Posidonia oceanica (L.) Delile in Liguria (NW Mediterranean Sea)

Eight shallow water Posidonia oceanica meadows were sampled in June 1999 along 300 km of the Ligurian coast and were compared through shoot density and lepidochronology. The growth of the seagrass was examined in the light of climate fluctuations and local stresses, colonisation by alien, invasive alga Caulerpa taxifolia, and effects of the oil spill from the tanker "Haven", and other anthropogenic impacts. Both shoot density and lepidochronology pointed to a generalised state of regression of all the meadows. The analysis of long-term growth curves of the rhizomes showed a positive trend parallel to the increase of air temperature. Two main groups of meadows were individuated on the basis of growth curve similarity. The first included four meadows, namely Ventimiglia, Imperia, Noli and Prelo, that were characterised by average values of rhizome growth of 8-9.1 mmyear(-1) and shoot density greater than 200 shootsm(-2). Although the Imperia meadow was the only one where the alien invasive alga C. taxifolia was found, it did not show differences for rhizome growth in comparison to the other meadows. The second group was formed by meadows that had suffered past anthropogenic impacts: Arenzano and Monterosso al Mare. They showed higher rhizome growth rates (9.4-10.6 mmyear(-1)) and shoot densities between 200 and 100 shootsm(-2). At Arenzano, where "Haven" oil was stranded in April 1991, no rhizome older than 8 years was found, thus confirming the shoot mortality induced by the oil spill event. The two last meadows exhibited growth curves very different from all the others: Portovenere, is a shallow meadow where P. oceanica merely survives in an extremely degraded situation with highest rhizome growth rate (12 mmyear(-1)), the other, Riva Trigoso, is the only meadow implanted on rock and had the lowest growth rates (7.1 mm year(-1)).