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Castelletto, Nicola (2010) Thermoporoelastic Modelling of Deep Aquifer Injection and Pumping by Mixed Finite Elements and Finite Volumes. [Tesi di dottorato]

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Abstract (inglese)

The present work concerns the mechanics of porous media and focuses on the development of a thermo-poro-elastic model, with particular emphasis on the simulation of fluid injection/pumping operations into geological formations. A non-linear model for coupled fluid flow and heat transfer in saturated porous media has been developed based on Mixed Hybrid Finite Elements (MHFEs) and Finite Volumes (FV). In particular, the MHFE discretization for the flow equation leads to an element-wise mass-conservative scheme, providing an accurate discrete velocity field. In the heat transfer equation, a time-splitting tecnique has been used solving separately the convective term by means of a FV scheme, and the conductive term by the MHFE method. The model can simulate problems characterized by very sharp temperature fronts, introducing no spurious oscillation in the numerical solution and negligible numerical diffusion, and does not required an excessive mesh resolution in order to ensure accuracy and stability. A fully coupled 3-D Mixed Finite Element model has also been developed for the numerical solution to the Biot equations of 3-D consolidation, combining Mixed Finite Elements (MFEs) and traditional Finite Elements (FEs) to discretize the fluid flow and the structural equilibrium equations, respectively. MFEs are used in order to alleviate the pore pressure numerical oscillations at the interface between materials with different permeabilities. An ad hoc solution algorithm based on conjugate gradients is implemented that takes advantage of the block structure of the discretized problem. The proposed models have been validated against well-known analytical solutions, and successfully experimented with in engineering applications.

Abstract (italiano)

Il presente lavoro di tesi si inserisce nell'ambito dello studio della meccanica dei mezzi porosi ed ha avuto come oggetto principale lo sviluppo di un modello termo-poro-elastico per la simulazione di processi di iniezione/pompaggio in formazioni geologiche. E' stato implementato un modello non-lineare per lo studio del flusso di massa accoppiato al trasferimento di calore utilizzando Elementi Finiti Misti Ibridi (MHFE) e Volumi Finiti (FV). In particolare, nel caso dell'equazione di flusso del fluido, l'uso degli Elementi Finiti Misti Ibridi garantisce la proprietà di conservazione della massa, assicurando così un campo di velocità accurato. Nel caso dell'equazione di trasporto è stata adottata una tecnica time-splitting andando a risolvere separatamente il termine convettivo con uno schema ai FV, e quello diffusivo con il metodo degli MHFE. Il codice sviluppato è in grado di riprodurre fenomeni caratterizzati da fronti di temperatura molto marcati, senza introdurre oscillazioni spurie nella soluzione numerica, e non richiede l'impiego di griglie di calcolo estremamente raffinate al fine di assicurare un'adeguata accuratezza. E' stato sviluppato inoltre un modello 3D per lo studio accoppiato di problemi di flusso e deformazione sfruttando l'uso combinato di Elementi Finiti Misti (MFE) e di Elementi Finiti (FE) nella discretizzazione, rispettivamente, dell'equazione di flusso e di equilibrio strutturale. L'impiego di MFE è stato scelto in modo da limitare le oscillazioni numeriche della soluzione che caratterizzano il problema di flusso-deformazione in regioni con forti contrasti di permeabilità. Il sistema lineare che scaturisce dalla discretizzazione delle equazioni di bilancio è stato risolto implementando una tecnica iterativa ad hoc basata sui gradienti coniugati precondizionati. I modelli proposti sono stati testati su alcuni problemi di letteratura e applicati, con successo, a casi di interesse ingegneristico.

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Tipo di EPrint:Tesi di dottorato
Relatore:Gambolati, Giuseppe
Correlatore:Ferronato, Massimiliano
Dottorato (corsi e scuole):Ciclo 22 > Scuole per il 22simo ciclo > SCIENZE DELL'INGEGNERIA CIVILE E AMBIENTALE
Data di deposito della tesi:NON SPECIFICATO
Anno di Pubblicazione:Gennaio 2010
Parole chiave (italiano / inglese):Mixed Finite Elements, Finite Volumes, Thermoporoelasticity, Geomechanics
Settori scientifico-disciplinari MIUR:Area 01 - Scienze matematiche e informatiche > MAT/08 Analisi numerica
Struttura di riferimento:Dipartimenti > Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate
Codice ID:2688
Depositato il:11 Ott 2010 10:24
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