Onsager’s reciprocal relation and the hydraulic permeability of porous media

Li, Sidney X.; Pengra, David B.; Wong, Po‐zen

doi:10.1103/physreve.51.5748

Cited by 59 publications

(40 citation statements)

References 11 publications

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“…1b). Compilation of published experimental data, a) k versus /, b) F versus / and c) k versus F, in unconsolidated monodisperse glass beads (Glover and Walker, 2009;Glover and Déry, 2010; black dots), well-sorted, rounded sands (Biella and Tabacco, 1981;Biella et al, 1983; blue dots), sintered glass beads (Wong et al, 1984;Guyon et al, 1987;Li et al, 1995;Blair et al, 1996; purple, red and orange squares corresponding to different grain sizes as indicated in the inset) and Fontainebleau sandstone (Doyen, 1988;Fredrich et al, 1993;Zamora, unpublished data;black diamonds;Revil et al, 2014; grey diamonds). The colored lines are inserted to highlight power-law trends in the various materials (note that the three families of sintered glass obey fairly similar power laws).…”

Section: Sintered Glass Beadsmentioning

confidence: 99%

“…Sintered glass beads have often been used as rock proxies to study the effect of porosity on the physical properties of rocks. In particular, Wong et al (1984), Guyon et al (1987), Li et al (1995) and Blair et al (1996) reported measurements of k, F and / in sintered monodisperse glass beads. They used three main types of glass beads with radii of around 25, 50 and 100 lm (materials with grain radii as low as 90 lm and as high as 160 lm are included in the last group).…”

Section: Sintered Glass Beadsmentioning

confidence: 99%

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Pore Space Connectivity and the Transport Properties of Rocks

Bernabé

Tang

et al. 2016

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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-Pore connectivity is likely one of the most important factors affecting the permeability of reservoir rocks. Furthermore, connectivity effects are not restricted to materials approaching a percolation transition but can continuously and gradually occur in rocks undergoing geological processes such as mechanical and chemical diagenesis. In this study, we compiled sets of published measurements of porosity, permeability and formation factor, performed in samples of unconsolidated granular aggregates, in which connectivity does not change, and in two other materials, sintered glass beads and Fontainebleau sandstone, in which connectivity does change. We compared these data to the predictions of a Kozeny-Carman model of permeability, which does not account for variations in connectivity, and to those of Bernabé et al. (2010Bernabé et al. ( , 2011 ]. Both models agreed equally well with experimental data obtained in unconsolidated granular media. But, in the other materials, especially in the low porosity samples that had undergone the greatest amount of sintering or diagenesis, only Bernabé et al. model matched the experimental data satisfactorily. In comparison, predictions of the Kozeny-Carman model differed by orders of magnitude. The advantage of the Bernabé et al. model was its ability to account for a continuous, gradual reduction in pore connectivity during sintering or diagenesis. Although we can only speculate at this juncture about the mechanisms responsible for the connectivity reduction, we propose two possible mechanisms, likely to be active at different stages of sintering and diagenesis, and thus allowing the gradual evolution observed experimentally.Résumé -Connectivité de l'espace poreux et propriétés de transport des roches -La connectivité porale est probablement l'un des plus importants facteurs affectant la perméabilité des roches réservoir. En outre, les effets de connectivité ne sont pas limités aux seuls matériaux approchant un seuil de percolation mais peuvent avoir lieu progressivement dans des roches soumises à des processus tels que la diagénèse mécanique ou chimique. Dans cette étude, nous avons compilé plusieurs jeux, préalablement publiés, de mesures de porosité, perméabilité et facteur de formation, obtenues sur des agrégats granulaires non-consolidés, pour lesquels la connectivité ne change pas, ainsi que dans deux autres matériaux, billes de verre frittées et grès de Fontainebleau, pour lesquels elle varie. Nous avons comparé ces données aux prédictions d'un modèle de perméabilité de type Kozeny-Carman, qui ne tient pas compte des variations de connectivité, et à celles du modèle de Bernabé et al. (2010Bernabé et al. ( , 2011

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Section: Sintered Glass Beadsmentioning

confidence: 99%

Section: Sintered Glass Beadsmentioning

confidence: 99%

Pore Space Connectivity and the Transport Properties of Rocks

Bernabé

Tang

et al. 2016

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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“…In electrokinetic conditions (EK), the capillary is electrically insulated (i.e., J=0), Vp is externally applied, and therefore a potential gradient called the streaming potential (i.e., VO) is induced. Conversely, in electroosmosis conditions (EO), V• is externally applied, the capillary is sealed at both ends (i.e., Q=0), and consequently, a pressure gradient is generated [Li et al, 1995]. In EK conditions, (8) and (9) can be rewritten in a new form using parameters with clearer physical interpretations ---•-Vp + --VO, …”

Section: Introductionmentioning

confidence: 99%

Streaming potential in heterogeneous networks

Bernabé¹

1998

J. Geophys. Res.

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Abstract. It is well-known that when in contact with an electrolyte, the surfaces of minerals like quartz become charged. In porous rocks, this causes coupling of fluid flow and electrical conduction. In this paper, the theory of electrokinetic coupling in a single capillary is first reviewed. The rest of the paper is concerned with the upscaling of the microscopic (i.e., pore scale) equations and parameters into their macroscopic counterparts. Upscaling was explicitly performed here in a large number of arbitrarily heterogeneous, two-dimensional networks. As a result, the macroscopic equations were established in a new form using C, the macroscopic coupling coefficient, and 6k, a dimensionless correction to permeability. In particular, it was shown that Onsager's [ 1931] reciprocity holds at macroscopic scales and that the scale invariant Helmholtz-Smoluchowski formula is not always valid. Accordingly, the macroscopic coupling coefficient C may not always be independent of permeability. In the networks considered here, the coupling coefficient appeared to be controlled by Johnson and Schwartz's [1989] weighted average length scale A. Another goal of this paper was to examine the spatial and statistical distributions of electrical currents and potential gradients in networks with varying heterogeneity levels. Similar to local fluid fluxes and pressure gradients, local electrical currents and potential gradients become localized in highly heterogeneous networks. The current field can equivalently be described in terms of current loops, and their spatial distribution can be analyzed. It was found that the current loop field becomes increasingly structured as the level of heterogeneity augments. One important consequence of the spatial distribution of currents and current loops is that at high levels of heterogeneity, the possibility exists to generate a magnetic field of significant intensity over wide areas of the networks. It was also observed that the magnitude of the local electric field appears normally distributed at low variance of the pore radii distribution and becomes increasingly non-Gaussian as the heterogeneity is increased. Owing to the fact that the total current is zero, the local currents have an unusual distribution, i.e., uniform with a high-end, -1 power, tail.

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“…(Sprunt et al 1994;Pozzi 1995a, 1997;Li et al 1995;Jiang et al 1998;Pengra et al 1999); [2] sandstone with NaCl as a function of permeability/microstructure (pH5) (Jouniaux and Pozzi 1995b); [3] St. Bees, Stainton, and Fontainebleau sandstones with NaCl (Jaafar et al 2009;Vinogradov et al 2010); [4] sandstone with KCl (Alkafeef and Alajmi 2007); [5] sand with NaCl (Guichet et al 2003;Block and Harris 2006);[6] granite with NaCl (Morgan et al (1989)); [7] glass with NaCl (Pengra et al 1999;Block and Harris 2006);[8] zeolitized tuffs with NaCl (Revil et al 2002);[9] basalt with NaCl (Revil et al 2003 (Tardif et al 2011;Glover et al 2012a).…”

Section: Introductionmentioning

confidence: 99%

Measurements of the Relationship Between Microstructure, pH, and the Streaming and Zeta Potentials of Sandstones

Walker

Glover

2017

Transp Porous Med

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A large number (1253) of high-quality streaming potential coefficient (C sp ) measurements have been carried out on Berea, Boise, Fontainebleau, and Lochaline sandstones (the latter two including both detrital and authigenic overgrowth forms), as a function of pore fluid salinity (C f ) and rock microstructure. All samples were saturated with fully equilibrated aqueous solutions of NaCl (10 −5 and 4.5 mol/dm 3 ) upon which accurate measurements of their electrical conductivity and pH were taken. These C sp measurements represent about a fivefold increase in streaming potential data available in the literature, are consistent with the pre-existing 266 measurements, and have lower experimental uncertainties. The C sp measurements follow a pH-sensitive power law behaviour with respect to C f at medium salinities (C sp = − 1.44 × 10 −9 C − 1.127 f , units: V/Pa and mol/dm 3 ) and show the effect of rock microstructure on the low salinity C sp clearly, producing a smaller decrease in C sp per decade reduction in C f for samples with (i) lower porosity, (ii) larger cementation exponents, (iii) smaller grain sizes (and hence pore and pore throat sizes), and (iv) larger surface conduction. The C sp measurements include 313 made at C f > 1 mol/dm 3 , which confirm the limiting high salinity C sp behaviour noted by Vinogradov et al., which has been ascribed to the attainment of maximum charge density in the electrical double layer occurring when the Debye length approximates to the size of the hydrated metal ion. The zeta potential (ζ ) was calculated from each C sp measurement. It was found that ζ is highly sensitive to pH but not sensitive to rock microstructure. It exhibits a pH-dependent logarithmic behaviour with respect to C f at low to medium salinities (ζ = 0.01133 log 10 (C f ) + 0.003505, units: V and mol/dm 3 ) and a limiting zeta potential (zeta potential offset) at high salinities of ζ o = − 17.36 ± 5.11 mV in the pH range 6-8, which is also pH dependent. The sensitivity of both C sp and ζ to pH and of C sp to rock microstructure indicates that C sp and ζ measurements can only be interpreted together with accurate and equilibrated measurements of pore fluid conductivity and pH and supporting microstructural and surface conduction measurements for each sample.

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Onsager’s reciprocal relation and the hydraulic permeability of porous media

Cited by 59 publications

References 11 publications

Pore Space Connectivity and the Transport Properties of Rocks

Pore Space Connectivity and the Transport Properties of Rocks

Streaming potential in heterogeneous networks

Measurements of the Relationship Between Microstructure, pH, and the Streaming and Zeta Potentials of Sandstones

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