Colmenares, Jose B. (2015) Pore-scale modelling of electrical phenomena in porous media
with implications for induced polarization and self-potential methods.
[Ph.D. thesis]

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## Abstract (english)

In this dissertation theoretical and numerical models are proposed for the induced polarization (IP) phenomenon. The theoretical model takes into account the contribution of Stern layer and membrane polarization in variably saturated sandy soils, while the numerical model can be used to get insight into the origins of the membrane polarization mechanism. In this dissertation the frequency-dependent bulk electrical conductivity of the porous medium is calculated using the Hashin-Shtrickman Average model, which describes the dielectric response of variably saturated porous media. Both stern and membrane polarization can be calculated independently, which allows us to study the effect of different physical parameters to each one. The results show that membrane polarization can be obscured by the Maxwell-Wagner polarization. The model was tested against data from laboratory measurements of sands with variable saturation
and a good fit was obtained even though more work has to be done for low saturation levels. Then a numerical model is presented which uses the linearized Poisson-Boltzmann Equation to compute the electrostatic potential of an object in the presence of free ions. The solution is then used to calculate a the dielectric to be used on a numerical solver of Poisson’s equation to calculate the impedance of the system. This result corroborates the assumptions behind the Short Narrow Pore model, a simplified and yet effective model describing
membrane polarization. The methodology used requires a much lower computational effort than solving the Poisson-Nerst-Planck equation since there are no coupled systems.

## Abstract (italian)

In questa tesi sono proposti modelli teorici e numerici per il fenomeno di polarizzazione indotta (IP). Il modello teorico prende in considerazione il contributo della polarizzazione dello strato di Stern e di membrana in terreni sabbiosi di saturazione variabile, mentre il modello numerico può essere utilizzato per ottenere una migliore comprensione degli origini dal meccanismo della polarizzazione di membrana. La conducibilità elettrica del mezzo poroso dipendente dalla frequenza viene calcolata utilizzando il modello Hashin - Shtrickman, che descrive la risposta dielettrica di mezzi porosi con saturazione variabile. Sia la polarizzazione di Stern e di membrana possono essere calcolati indipendentemente, cosa che ci permette studiare l’effetto di diverse parametri fisici. I risultati mostrano che la polarizzazione di membrana può essere oscurato dalla polarizzazione Maxwell - Wagner. Il modello è stato testato contro dati da misure di laboratorio di sabbia con saturazione variabile con buoni risultati anche se più lavoro deve essere fatto per i livelli di bassa saturazione. Il modello numerico presentato utilizza la equazione linearizzata di Poisson - Boltzmann
per calcolare il potenziale elettrostatico di un oggetto in presenza di ioni liberi in soluzione. La soluzione viene quindi utilizzato per calcolare il dielettrico ad essere utilizzato su un risolutore numerico dell’equazione di Poisson per calcolare l’impedenza del sistema. Questo risultato avvalora le ipotesi alla base del modello short narrow pore, un modello semplificato ma efficace che descrive la polarizzazione di membrana. La metodologia utilizzata richiede uno sforzo computazionale molto inferiore che risolvere l’equazione di Poisson-Nerst-Planck poiché non esistono sistemi accoppiati.

EPrint type: Ph.D. thesis Cassiani, Giorgio Ciclo 26 > Scuole 26 > SCIENZE DELLA TERRA 02 February 2015 02 February 2015 porous media, induced polarization, impedance, conductivity Area 04 - Scienze della terra > GEO/11 Geofisica applicataArea 04 - Scienze della terra > GEO/10 Geofisica della terra solida Dipartimenti > Dipartimento di Geoscienze 7961 17 Nov 2015 10:24
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