Advances and benefits of fractal models to predict streaming potentials in partially saturated porous media

2021 ◽  
Author(s):  
Damien Jougnot ◽  
Luong Duy Thanh ◽  
Mariangeles Soldi ◽  
Jan Vinogradov ◽  
Luis Guarracino
Keyword(s):  
Porous Media ◽  
Fractal Theory ◽  
Electrical Potential ◽  
Streaming Potential ◽  
Excess Charge ◽  
Distribution Law ◽  
Distribution Models ◽  
Streaming Potentials ◽  
Fractal Models ◽  
Partially Saturated Porous Media

<p>Understanding streaming potential generation in porous media is of high interest for hydrological and reservoir studies as it allows to relate water fluxes to measurable electrical potential distributions in subsurface geological settings. The evolution of streaming potential <span>stems</span> from electrokinetic coupling between water and electrical fluxes due to the presence of an electrical double layer at the interface between the mineral and the pore water. Two different approaches can be used to model and interpret the generation of the streaming potential in porous media: the classical coupling coefficient approach based on the Helmholtz-Smoluchowski equation, and the effective excess charge density. Recent studies based on both approaches use a mathematical up-scaling procedure that employs the so-called fractal theory. In these studies, the porous medium is represented by a bundle of tortuous capillaries characterized by a fractal capillary-size distribution law. The electrokinetic coupling between the fluid flow and electric current is obtained by averaging the processes that take place in a single capillary. In most cases, closed-form expressions for the electrokinetic parameters are obtained in terms of macroscopic hydraulic variables like permeability, saturation and porosity. In this presentation we propose a review of the existing fractal distribution models that predict the streaming potential in porous media and discuss their benefits compared against other published models.</p>

The Streaming Potential and the Rheology of Foam

1967 ◽  
Vol 7 (04) ◽  
pp. 359-368 ◽  
Author(s):  
S.H. Raza ◽  
S.S. Marsden
Keyword(s):  
Porous Media ◽  
Apparent Viscosity ◽  
Streaming Potential ◽  
Newtonian Fluids ◽  
Flow In Porous Media ◽  
Flow Rates ◽  
Foaming Agents ◽  
Streaming Potentials ◽  
Foam Flow ◽  
Order Of Magnitude

Abstract An experimental study of the flow of fine-textured, aqueous foams through Pyrex tubes is described. The foams range in quality F (ratio of gas volume to total volume) from 0.70 to 0.96 and behave like pseudoplastic fluids. At lower flow rates they exhibit laminar flow and have apparent viscosities which increase with quality, and which cover a range of 15 cp to 255 poise for tubes of 0.25- to 1.50-mm radius ri. At higher flow rates a plug-like type of flow is developed, the extent of which increases with both and ri. When the same foams flow through either open or packed Pyrex tubes, remarkably high streaming potentials phi E are often generated. These can easily reach 50v if nonionic foaming agents are used, but are at least an order of magnitude less for ionic foaming agents. A linear relationship between phi E and the pressure differential phi p is observed; this usually extrapolates to positive values of phi p at phi E of zero. The slope of the line increases with both F and ri. An equation was derived to describe the streaming potential of non-Newtonian fluids in circular tubes and was used to correlate experimental results. The calculated potential is are of the right order of magnitude. Introduction Foams are both unusual and intriguing in their physical properties, and have been the subject of many scientific studies. However, present knowledge of foams is still fragmentary, specific and often contradictory. Apparent viscosity of foam is the physical property of greatest interest to both rheologists and engineers. Sibree reported that the apparent viscosity decreased with increasing shear rate in a manner similar to some non-Newtonian fluids. Penny and Blackman reported that fire-fighting foams had both a limiting shear stress and a tensile yield stress. There is little doubt that some foams at least behave like non-Newtonian fluids, and have apparent viscosities considerably higher than those of either constituent phase. The high apparent viscosity of foam with its concomitant effect on mobility ratio and sweep efficiency no doubt prompted several attempts by research groups to use foam as a displacing agent in porous media. Based on recent experience, most of these groups probably succeeded in completely blocking fluid flow in the porous media and then abandoned their efforts. Two groups apparently found the successful combination of experimental parameters at about the same time. Others have recently added to our knowledge-of foam flow in porous media and its use as a displacing agent. An experimental problem encountered by Fried was a transient blockage of foam flow in porous media when distilled water was used to prepare the foam-producing solution. Fried surmised that this was due to an electrokinetic effect and he eliminated it by using electrolytes in preparing foaming solutions. He also measured the streaming potential of a number of foams in capillary tubes which he found to be appreciably higher than those obtained when the constituent liquid flowed under comparable conditions. This paper presents results of a more comprehensive study of the streaming potential generated by aqueous foam flowing in both open and packed Pyrex tubes. It also adds to knowledge of the rheology of these foams as deduced from their flow behavior in open tubes. APPARATUS AND PROCEDURE A diagram of the apparatus used is shown in Fig. 1. Details of its construction, testing and use are described elsewhere. Careful selection of materials, extreme cleanliness and rather elaborate electrical insulation and shielding were necessary to obtain reproducible results (15 percent). Both streaming potential and streaming current were measured with an electrometer. The design of the foam generator developed for this work is novel (Fig. 2). SPEJ P. 359ˆ

scholarly journals Spatially Resolved Streaming Potentials of Human Intervertebral Disk Motion Segments Under Dynamic Axial Compression

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
James C. Iatridis ◽  
Masaru Furukawa ◽  
Ian A. F. Stokes ◽  
Mack G. Gardner-Morse ◽  
Jeffrey P. Laible
Keyword(s):  
Axial Compression ◽  
Electrical Potential ◽  
Streaming Potential ◽  
Human Motion ◽  
Intervertebral Disk ◽  
Applied Force ◽  
Central Nucleus ◽  
Streaming Potentials ◽  
Spatially Resolved ◽  
Electrode Potentials

Intervertebral disk degeneration results in alterations in the mechanical, chemical, and electrical properties of the disk tissue. The purpose of this study is to record spatially resolved streaming potential measurements across intervertebral disks exposed to cyclic compressive loading. We hypothesize that the streaming potential profile across the disk will vary with radial position and frequency and is proportional to applied load amplitude, according to the presumed fluid-solid relative velocity and measured glycosaminoglycan content. Needle electrodes were fabricated using a linear array of Ag∕AgCl micro-electrodes and inserted into human motion segments in the midline from anterior to posterior. They were connected to an amplifier to measure electrode potentials relative to the saline bath ground. Motion segments were loaded in axial compression under a preload of 500N, sinusoidal amplitudes of ±200N and ±400N, and frequencies of 0.01Hz, 0.1Hz, and 1Hz. Streaming potential data were normalized by applied force amplitude, and also compared with paired experimental measurements of glycosaminoglycans in each disk. Normalized streaming potentials varied significantly with sagittal position and there was a significant location difference at the different frequencies. Normalized streaming potential was largest in the central nucleus region at frequencies of 0.1Hz and 1.0Hz with values of approximately 3.5μV∕N. Under 0.01Hz loading, normalized streaming potential was largest in the outer annulus regions with a maximum value of 3.0μV∕N. Correlations between streaming potential and glycosaminoglycan content were significant, with R2 ranging from 0.5 to 0.8. Phasic relationships between applied force and electrical potential did not differ significantly by disk region or frequency, although the largest phase angles were observed at the outermost electrodes. Normalized streaming potentials were associated with glycosaminoglycan content, fluid, and ion transport. Results suggested that at higher frequencies the transport of water and ions in the central nucleus region may be larger, while at lower frequencies there is enhanced transport near the periphery of the annulus. This study provides data that will be helpful to validate multiphasic models of the disk.

scholarly journals A Physically Based Model for the Streaming Potential Coupling Coefficient in Partially Saturated Porous Media

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1588
Author(s):  
Luong Duy Duy Thanh ◽  
Damien Jougnot ◽  
Phan Van Do ◽  
Nguyen Xuan Ca ◽  
Nguyen Thi Hien
Keyword(s):  
Porous Media ◽  
Coupling Coefficient ◽  
Water Saturation ◽  
Streaming Potential ◽  
Saturated Porous Media ◽  
Physically Based Model ◽  
Partially Saturated ◽  
Proposed Model ◽  
Physically Based ◽  
Partially Saturated Porous Media

The electrokinetics methods have great potential to characterize hydrogeological processes in porous media, especially in complex partially saturated hydrosystems (e.g., the vadose zone). The dependence of the streaming coupling coefficient on water saturation remains highly debated in both theoretical and experimental works. In this work, we propose a physically based model for the streaming potential coupling coefficient in porous media during the flow of water and air under partially saturated conditions. The proposed model is linked to fluid electrical conductivity, water saturation, irreducible water saturation, and microstructural parameters of porous materials. In particular, the surface conductivity of porous media has been taken into account in the model. In addition, we also obtain an expression for the characteristic length scale at full saturation in this work. The proposed model is successfully validated using experimental data from literature. A relationship between the streaming potential coupling coefficient and the effective excess charge density is also obtained in this work and the result is the same as those proposed in literature using different approaches. The model proposes a simple and efficient way to model the streaming potential generation for partially saturated porous media and can be useful for hydrogeophysical studies in the critical zone.

scholarly journals Effective Excess Charge Density in Water Saturated Porous Media

2018 ◽  
Vol 34 (4) ◽  
Author(s):  
Luong Duy Thanh
Keyword(s):  
Porous Media ◽  
Zeta Potential ◽  
Double Layer ◽  
Electric Double Layer ◽  
Electrical Potential ◽  
Debye Length ◽  
Excess Charge ◽  
Geophysical Research ◽  
Colloid Science ◽  
Capillary Pore

A model for the effective excess charge in a capillary as well as in porous media is developed for arbitrary pore scales. The prediction of the model is then compared with another published model that is limited for a thin electric double layer (EDL) assumption. The comparison shows that there is a deviation between two models depending on the ratio of capillary/pore radius and the Debye length. The reasons for the deviation between two models are not only due to the thin EDL assumption to get electrical potential and charge distribution in pores but also to some other approximations for integral evaluations. The results suggest that the model developed in this work can be used with arbitrary capillary/pore scale and thus is not restricted to the thin EDL assumption. Keywords: Zeta potential, porous media, electric double layer, effective excess charge. References [1] M. Aubert, Q.Y. Atangana, Groundwater, 34 (1996) 1010–1016.[2] A. Finizola, J.-F. Lénat, O. Macedo, D. Ramos, J.-C. Thouret, F. Sortino, J. Volcanol. Geoth. Res., 135 (2004) 343–360.[3] C. Doussan, L. Jouniaux, J.-L. Thony, Journal of Hydrology 267 (2002) 173–185.[4] F. Perrier, M. Trique, B. Lorne, J.-P. Avouac, S. Hautot, P. Tarits, Geophys. Res. Lett. 25 (1998) 1955–1958.[5] Martinez-Pagan, P., A. Jardani, A. Revil, and A. Haas, Geophysics 75 (2010) WA17–WA25.[6] Naudet, V., A. Revil, J.-Y. Bottero, and P. Bgassat, Geophysical Research Letters 30 (2003).[7] V. Naudet, M. Lazzari, A. Perrone, A. Loperte, S. Piscitelli, V. Lapenna, Engineering Geology 98 (2008) 156-167.[8] A. Perrone, A. Iannuzzi, V. Lapenna, P. Lorenzo, S. Piscitelli, E. Rizzo, F. Sdao, Journal of Applied Geophysics 56 (2004) 17-29.[9] Jouniaux, L., A. Maineult, V. Naudet, M. Pessel, and P. Sailhac, C. R. Geoscience 341 (2009).[10] Revil, A., and A. Jardani, The Self-Potential Method: Theory and Applications in Environmental Geosciences, Cambridge University Press, 2013.[11] Hunter, R., Zeta Potential in Colloid Science: Principles and Applications, Colloid Science Series, Academic Press, 1981.[12] Leroy, P., and A. Revil, Journal of Colloid and Interface Science, 270 (2004) 371–380.[13] T. Ishido, H. Mizutani, Journal of Geophysical Research 86 (1981) 1763-1775.[14] P. W. J. Glover, E. Walker, M. Jackson, Geophysics 77 (2012) D17–D43.[15] Revil, A., and P. Leroy, Journal of Geophysical Research 109 (2004).[16] Linde, N., D. Jougnot, A. Revil, S. K. Matthäi, T. Arora, D. Renard, and C. Doussan, Geophys. Res. Lett. 34 (2007) L03306.[17] Revil A. and Mahardika H, Water Resources Research 49 (2013) 744–766.[18] Jardani, A., A. Revil, A. Bolève, A. Crespy, J. Dupont, W. Barrash and B. Malama, Geophysical Research Letters, 34 (2007) L24,403.[19] L. Guarracino, D. Jougnot, Journal of Geophysical Research - Solid Earth 123 (2018) 52-65.[20] Jackson M.D., Leinov E., International Journal of Geophysics 2012 (2012).[21] Gierst L., J. Am. Chem. Soc. 88 (1966) 4768.[22] Rice, C., and R. Whitehead, J. Phys. Chem. 69 (1965) 4017–4024.[23] Pride, S., Physical Review B 50 (1994) 15,678–15,696.[24] Bear, J., Dynamics of Fluids in Porous Media, Dover Publications, New York, 1988. [25] Chan I. Chung, Extrusion of Polymers: Theory & Practice, Hanser-2nd edition, 2010.[26] J. Vinogradov, M. Z. Jaafar, M. D. Jackson, Journal of Geophysical Research 115 (2010).

FRACTAL ANALYSIS OF HYDRAULICS IN POROUS MEDIA WITH WALL EFFECTS

Fractals ◽  
2014 ◽  
Vol 22 (03) ◽  
pp. 1440001 ◽  
Author(s):  
MINGCHAO LIANG ◽  
BOMING YU ◽  
SHANSHAN YANG ◽  
MINGQING ZOU ◽  
LONG YAO
Keyword(s):  
Porous Media ◽  
Power Law ◽  
Fractal Theory ◽  
Analytical Models ◽  
Wall Effects ◽  
Average Mass ◽  
Fractal Models ◽  
Power Law Fluids ◽  
Power Law Index ◽  
Analytical Expressions

The analytical expressions for the normalized average mass flux and pressure drop for power law fluids for wall effects in porous media are presented by using the fractal theory and technique for porous media. The proposed models are expressed as functions of power law index and structure parameters. These model predictions show that the proposed models can provide a good agreement with the experimental and other analytical results. This indicates that the fractal models may be helpful to much better understand the mechanisms of flow than other analytical models for porous media.

scholarly journals The strain-generated electrical potential in cartilaginous tissues: a role for piezoelectricity

2021 ◽  
Vol 13 (1) ◽  
pp. 91-100
Author(s):  
Philip Poillot ◽  
Christine L. Le Maitre ◽  
Jacques M. Huyghe
Keyword(s):  
Physiological Response ◽  
Numerical Models ◽  
Measurement Techniques ◽  
Electrical Potential ◽  
Evidence Base ◽  
Piezoelectric Response ◽  
Mechanical Forces ◽  
Streaming Potentials ◽  
Cartilaginous Tissues ◽  
Electrical Potentials

AbstractThe strain-generated potential (SGP) is a well-established mechanism in cartilaginous tissues whereby mechanical forces generate electrical potentials. In articular cartilage (AC) and the intervertebral disc (IVD), studies on the SGP have focused on fluid- and ionic-driven effects, namely Donnan, diffusion and streaming potentials. However, recent evidence has indicated a direct coupling between strain and electrical potential. Piezoelectricity is one such mechanism whereby deformation of most biological structures, like collagen, can directly generate an electrical potential. In this review, the SGP in AC and the IVD will be revisited in light of piezoelectricity and mechanotransduction. While the evidence base for physiologically significant piezoelectric responses in tissue is lacking, difficulties in quantifying the physiological response and imperfect measurement techniques may have underestimated the property. Hindering our understanding of the SGP further, numerical models to-date have negated ferroelectric effects in the SGP and have utilised classic Donnan theory that, as evidence argues, may be oversimplified. Moreover, changes in the SGP with degeneration due to an altered extracellular matrix (ECM) indicate that the significance of ionic-driven mechanisms may diminish relative to the piezoelectric response. The SGP, and these mechanisms behind it, are finally discussed in relation to the cell response.

Sign in / Sign up

Export Citation Format

Share Document