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Uncertainty assessment of subsurface solute transport by transmissivity conditioning in finite heterogeneous domains
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An approach to subsurface transport in statistically inhomogeneous velocity fields
No full textTo solve the general case of dispersion in heterogeneous porous media, an application based on first order stochastic analysis coupled with the finite, element method is proposed to evaluate statistically non homogeneous Eulerian velocity fields. In natural formations analyses the spatial nonstationarity of flow may derive from statistical nonhomogeneity of medium properties, spatial sinks and/or sources, finite boundaries, and conditioning on measurements. These situations are commonly encountered, and the assumption of location independent statistics, of flow is often violated to adapt real life cases to synthetic schemes where spatially stationary approaches that can be found in literature can be utilized. While the impact of these simplifications has been analyzed in some cases, e.g., by checking the influence of boundaries conditions on the velocity variance, only few attempts to found a general solution are given in the literature. In the present note, a numerical solution for inhomogeneous velocity fields like those found in bounded domains is obtained by first-order stochastic analysis and the finite element method. In this general context, the hydraulic properties of the media are not necessarily, statistically homogeneous and/or the hydraulic conductivity integral scale may be comparable with the domain extension, so that a significant portion of the flow field is affected by conditions imposed on the boundaries. A discussion of the results of some test cases in comparison with known literature solutions gives a measure of the capabilities of the proposed method
Criteri per la manutenzione dei sistemi di distribuzione idropotabile
No full textLe prestazioni dei sistemi di distribuzione idropotabile, intese come soddisfacimento della richiesta dell’utenza in termini piezometrici e di portata, tendono naturalmente a diminuire con gli anni. Il processo è legato all’invecchiamento delle condotte sia in ter-mini idraulici (complessivo aumento della scabrezza per il deterioramento del rivesti-mento o della stessa parete interna e/o per l’eventuale riduzione di sezione dovuta ai depositi), sia in termini di integrità strutturale (riduzione delle caratteristiche di resi-stenza alle sollecitazioni interne ed esterne dei giunti e delle stesse tubazioni con un ge-nerale incremento del tasso di fallanza e delle perdite). L’accorta pratica progettuale può ridurre in qualche misura gli effetti legati all’invecchiamento idraulico, tenendone preventivamente conto e dimensionando le reti con valori cautelativi di scabrezza, ma l’invecchiamento in termini di integrità strutturale può essere contrastato solo con un incremento della frequenza degli interventi di manutenzione a cui corrisponde un au-mento dei costi di gestione. Al punto che può risultare conveniente procedere alla sosti-tuzione di un intero tratto di tubazione piuttosto che continuare ad operare con inter-venti di manutenzione sempre più frequenti. Con riferimento alla singola condotta, il problema della determinazione dell’istante temporale che riduce al minimo i costi com-plessivi (di manutenzione e sostituzione), è un classico problema di minimo, dipendente dall’andamento del tasso di guasto nel tempo e dai costi (annualizzati) di riparazione e sostituzione, risultando univoca l’individuazione di un istante nella vita della condotta in cui risulti ottimale dal punto di vista economico la sua sostituzione. Più complessa risulta invece l’analoga valutazione in un sistema di distribuzione, dovendo in tal caso individuare non solo un valore ottimale per il tempo di sostituzione, ma anche indicare una priorità di scelta fra diverse condotte. Tali aspetti sono esaminati nella presente nota, mettendo a confronto soluzioni note in letteratura e una proposta originale per la definizione di una tecnica di pianificazione degli interventi di riparazione e/o sostitu-zione che contempla contemporaneamente sia criteri di carattere economico che consi-derazioni relative all’affidabilità del sistema
Simulations of non ergodic transport induced by inhomogeneous flow fields in heterogeneous porous formations of hierarchical sedimentary architecture
No full textDealing with subsurface flow and transport in naturally heterogeneous formations neither statistical homogeneity nor ergodicity are usually met in real world applications. If the stationarity is obeyed by Lagrangian velocity field the ergodicity of transport can be ascribed to the only size of the injection area, but this is not the case in all situations where flow field doesn't meet statistical homogeneity. In this case not only the size of the area where the concentration is injected, but also its location as well as the spatial variability of mean flux play a relevant role in the expected plume evolution. Among other causes, the hierarchical sedimentary architecture of porous formations combined with the finite size of the domain may be considered as one of the main causes of the flow field inhomogeneity and of the subsequent evidences of the non ergodic transport in real cases. To give a better understanding of this phenomenon synthetic 2-D cases of isotropic log conductivity field with integral scale λ1 whose expected value is assumed as a periodic function of the space coordinates of prescribed amplitude are investigated. The wave length of the mean log conductivity fluctuation is λ2, properly chosen to satisfy the relationship λ1 < λ2 < L, being L the characteristic dimension of the finite domain. The time evolution of the spatial moments of the plume driven by a statistically inhomogeneous steady state random velocity field is analyzed by varying the amplitude of the periodic mean flow and its wave length λ2 and by taking into account different sizes of injection area. These moments are achieved by space- time integration of the velocity field covariance structure derived according to the first-order Taylor series expansion by the stochastic finite element method. The discussion of the results leads to a better understanding into the ergodicity lack that affects solute transport in heterogeneous aquifers, by giving a comparative measure of the relevance of two possible causes, that is the flow field inhomogeneity due to the hierarchical sedimentary architecture of porous formations combined with a limited domain and the injection area of finite size
Flow and transport in heterogeneous porous formations subject to uncertainty in statistical description of the hydraulic log-conductivity spatial behaviour
No full textThe effect of a periodic spatial behaviour of the mean log-conductivity (logK) in random heterogeneous aquifers was investigated by numerical simulations. The adopted schematization reflects the spatial inhomogeneity due to an inexact definition of spatial statistical properties of media and can be considered a rough description of the hierarchical sedimentary architecture of porous formations. The solution of investigated cases was achieved by use of both the stochastic finite element method (SFEM) and the Monte Carlo simulations (MC). From the results it was possible to distinguish the contribute of the fluctuating mean log-conductivity field in the plume evolution. Comparison between SFEM and MC outcome reveals strong nonlinearity effects related to the spatial variability of the mean of the logK field also when its variance is negligible
Reply to 'Comment on Nonstationary flow and nonergodic transport in random porous media by N. Suciu and C. Vamos [#2007WR005946]'
No full textThe paper reports the replay to comment by Suciu and Vamoş [2007] on a published paper [Darvini and Salandin, 2006] and demonstrates the correctness of the previously obtained results. New insights about the fulfillment of the ergodic hypothesis in numerical experiments are also added
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