ABSTRACT
A material fluid element within a porous medium experiences deformations due to the disordered spatial distribution of the Darcy scale velocity field, caused by the heterogeneity of hydraulic conductivity. A physical consequence of this heterogeneity is the presence of localized kinematical features such as straining, shearing and vorticity in the fluid element. These kinematical features will influence the shape of solute clouds and their fate. Studies on the deformation of material surfaces highlighted the importance of stretching and shearing, whereas vorticity received so far less attention, though it determines folding, a deformation associated with the local rotation of the velocity field. We study vorticity in a three-dimensional porous formation exploring how its fluctuations are influenced by the spatial structure of the porous media, obtained by immersing spheroidal inclusions into a matrix of constant hydraulic conductivity. By comparing porous formations with the same spatial statistics, we analyse how vorticity is affected by the different shape and arrangement of inclusions, defined as the medium 'microstructure'. We conclude that, as microstructure has a significant impact on vorticity fluctuations, the usual second-order statistical description of the conductivity field is unable to capture local deformations of the plume.
ABSTRACT
Spatial heterogeneity of the hydraulic properties of geological porous formations leads to erratically shaped solute clouds, thus increasing the edge area of the solute body and augmenting the dilution rate. In this study, we provide a theoretical framework to quantify dilution of a non-reactive solute within a steady state flow as affected by the spatial variability of the hydraulic conductivity. Embracing the Lagrangian concentration framework, we obtain explicit semi-analytical expressions for the dilution index as a function of the structural parameters of the random hydraulic conductivity field, under the assumptions of uniform-in-the-average flow, small injection source and weak-to-mild heterogeneity. Results show how the dilution enhancement of the solute cloud is strongly dependent on both the statistical anisotropy ratio and the heterogeneity level of the porous medium. The explicit semi-analytical solution also captures the temporal evolution of the dilution rate; for the early- and late-time limits, the proposed solution recovers previous results from the literature, while at intermediate times it reflects the increasing interplay between large-scale advection and local-scale dispersion. The performance of the theoretical framework is verified with high resolution numerical results and successfully tested against the Cape Cod field data.
Subject(s)
Models, Theoretical , Porosity , Water Pollutants, Chemical/chemistry , Anisotropy , Groundwater , Solutions/chemistry , Time Factors , Water MovementsABSTRACT
Fez-se um levantamento de 260 placentas examinadas pelo Servico de Anatomia Patologica da Maternidade Nossa Senhora de Lourdes, Goiania, no periodo de janeiro de 1978 a janeiro de 1979. Procurou-se relacionar os achados histopatologicos aos aspectos clinicos e obstetricos das pacientes, bem como com os motivos que levaram o tocologo a solicitar o exame anatomopatologico de placenta. Observou-se que 55,76% das placentas apresentaram alteracoes divididas em oito categorias: infeccoes inespecificas, sofrimento vascular, incompatibilidade sanguinea materno-fetal, placenta imatura, tumores benignos, patologias do cordao umbilical e sofrimento fetal cronico, constatando-se a existencia de relacao entre os varios tipos de alteracoes e os quadros clinico e obstetrico das pacientes, confirmando, uma vez mais, a importancia do exame anatomopatologico de placenta na investigacao e conclusao diagnostica em obstetricia.}
