Numerical Investigation of Parameters Affecting. Seismoelectric Coupling Coefficient in. Partially-Saturated Porous Media

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1 Contemporary Engineering Sciences, Vol. 9, 16, no. 5, HIKARI Ltd, Numerical Investigation o Parameters Aecting Seismoelectric Coupling Coeicient in Partially-Saturated Porous Media Ulugbek Djuraev 1, Shieraw Regassa Juar 1,*, Pandian Vasant, Sonny Irawan 1 and Luluan Almanna Lubis 3 1 Department o Petroleum Engineering Universiti Teknologi PETRONAS, 361 Seri Iskandar Perak Darul Ridzuan, Malaysia Department o Fundamental & Applied Sciences Universiti Teknologi PETRONAS, 361 Seri Iskandar Perak Darul Ridzuan, Malaysia 3 Department o Petroleum Geosciences Universiti Teknologi PETRONAS, 361 Seri Iskandar Perak Darul Ridzuan, Malaysia Copyright 16 Ulugbek Djuraev et al. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract We conducted a numerical investigation on the eects o brine concentration, water saturation, and requency o seismic wave on the seismoelectric coupling response in a two-phase saturated porous media. The numerical model was ormulated based on Pride s theoretically developed seismoelectric coupling coeicient that accounts or the conversion o seismic wave to electromagnetic wave. The results show that in oil-water system brine concentration has signiicant inluence on the coupling coeicient at higher water saturation. When water saturation is less than about., the eect o brine concentration and seismic requency on the coupling coeicient is insigniicant. * Corresponding author

2 144 Ulugbek Djuraev et al. The general characteristics is that at the given water saturation, there is a critical requency beyond which requency does not have much impact on the seismoelectric coupling coeicient. When the water saturation is., such critical requency is about 1 khz. The value o the critical requency increases as water saturation increases suggesting that it is a unction o water saturation. In general, the seismoelectric response is stronger at higher water saturation, lower brine concentration and lower seismic requency. Keywords: Seismoelectric, Saturation, Porous medium, Oil 1 Introduction Solid surace minerals, in contact with electrolyte solution such as brine, essentially develop electrical charges on the solid surace due to amphoteric reactions [6]. Subsequently, the surace charges are counter balanced by electrical charges o the electrolyte solution in the Stern layer; where other electrical charges remain in a so-called diuse layer. Subsequently, this leads to ormation o the electrical double layer (EDL) that is shown in Fig. 1. When a seismic wave propagates through luid-containing porous media it induces relative luid-to-solid motions at the microscale, where such motions result in a relative-to-solid surace motion o electrical charges in the double layer. This, in turn, triggers conversion o mechanical to electromagnetic energy, also known as the seismoelectric conversion. Furthermore, this transient electrokinetic phenomenon o seismoelectric eects can be observed at the macroscale using dipole receivers placed on the ground surace [9] or installed in wellbores [3]. Fig. 1 Electrical Double Layer The electrokinetic conversions make up the oundation o the seismoelectric method, which combines the sensitivity o electrical methods to subsurace hydrological properties with high resolution o seismic surveys. The distinctive characteristic o this method is the detection o subsurace interaces prompted by contrasts in rock properties and in luid electrical properties, such as porosity and permeability, water saturation and electrical conductivity, respectively [7]. Recent

3 Numerical investigation o parameters 145 ield experiments have shown promising results o using the seismoelectric method to investigate hydrocarbon and hydraulic reservoirs. Moreover, it has also been highlighted that the interpretation o amplitudes o converted signals can be used or imaging the geometry o a reservoir [11]. The seismoelectric method has a long history [4, 5], however the irst principal comprehensive theory o the method was developed by Pride in the early 9s [8]. Ever since, his canonical groundwork has led to numerous breakthroughs. Despite the advances made to understand the complex physics that govern the conversion, theoretical calculations o coeicients aecting the seismoelectric phenomenon are diicult because o a large number o parameters, such as porosity, permeability, rock and luid properties and so orth [15]. In spite o that, results obtained rom such studies can provide some insight on what is anticipated beore conducting an actual laboratory and/or ield experiment. Thereore, we intend to conduct a theoretical investigation to study the impact o water saturation, brine concentration and seismic requency on seismoelectric coupling in ully- and partially-saturated conditions prior to perorming a laboratory experiment. Methodology Seismoelectric coupling is directly dependent on reservoir rock properties, luid density and luid conductivity, and the electric double layer [7]. For instance, zetapotential, as a key element o the EDL, is directly dependent on brine concentration, and this in turn, has a substantial eect upon the magnitude o the seismoelectric amplitudes [15]. Additionally, recent studies revealed that seismoelectric eects are also greatly aected by changing luid saturations in a porous medium [, 1]. Thereore, the methodology o our study begins with determining the magnitude o zeta-potential using an empirically derived model. Moreover, we assume that water is the wetting phase o the porous medium, and thus varying water saturation does not aect neither the EDL nor zeta-potential. Thereater, we expand Pride s equation o seismoelectric coupling coeicient or ully- and partially-saturated porous media saturated with oil and water as a unction o seismic requency and brine concentration..1 Zeta-potential model The zeta-potential is the electrical potential on the slipping plane within the double layer [1]. A number o researchers conducted experiments to measure zetapotential or brine-saturated porous media, and thus they state that the magnitude o zeta-potential reduces with increasing salinity [1]. Since the measurement o zeta-potential in luid-saturated porous media is complex, it can be estimated by using empirically derived Eq.1 below. Researchers report various equation coeicients and validity limits, because measurements were obtained rom dierent equipment conigurations, brine compositions and porous media. For this reason, a care must be taken beore using one s correlation.

4 146 Ulugbek Djuraev et al. alog C b (1) 1 Vinogradov, et al. [1] conducted a number o experiments to measure the magnitude o zeta-potential or a wide range o brine concentration. They compared their results with other published data, where the values o measured zeta-potential in mvolt were plotted on a semi-log plot with the x-axis representing the concentration with units o mol/l. Subsequently, they proposed the model shown in Eq.. In this study, we adopted their model with an assumption that the brine composition consists solely o sodium chloride (NaCl) and is valid or concentrations less than.4 mol/l. 19.log1C 9.67 (). Pride s Model or Partially-Saturated Conditions Pride [8] developed a complete set o equations that characterizes the coupling between seismic and electromagnetic wave propagation by combining Biot s poroelasticity theory and Maxwell s equations via requency-dependent seismoelectric coupling shown in Eq. 3 [7]. The coupling equation is considered to be quite complex, since it takes into account multiple variables that aect both seismic and electromagnetic ields. L( ) L ~ m d 1 i 1 4 c 1 i 3/ ~ d 1/ (3) where L is the low-requency electrokinetic coupling, m is a dimensionless number, d is the Debye length, Λ is a geometry term o the porous material, ω c is the transition angular requency, and ω is the angular requency. Subsequently, the coupling can be calculated with an additional set o equations shown below in Eq. 4 to Eq. 8. where L ~ d 1 ~ k BT d e z N A 1/ (4) (5) c (6) k

5 Numerical investigation o parameters 147 m (7) k (8) Due to complexity o Pride s coupling coeicient, Walker, et al. [13] proposed to use a simpliied version o the equation assuming that the Debye length can be neglected when compared to the characteristic pore size. Moreover, they modiied the ollowing parameters: 8 m (9) r e where r e is eective pore radius. The transition angular requency is given by equation 1. 8 c (1) r e And thus, the simpliied Pride s electrokinetic equation or ully-saturated porous medium becomes where 1/ ( ) 1 L L i (11) c r e L 1 o (1) F Early theoretical developments accounted or seismoelectric eects that occur only in ully-saturated conditions [4, 8]. However, the practical potential o using the seismoelectric method is realized when it takes into account both ully- and partially-saturated conditions in porous media. Thereore, or our theoretical study, we adopted the simpliied version o Pride s seismoelectric coupling coeicient modiied by Walker, et al. [13] and extended it or partially-saturated conditions with water and oil saturating the porous medium. The calculations were perormed in the requency range o 1 khz 15 khz. Brine concentration was varied rom.1 mol/l to.1 mol/l. Water saturation was varied rom.1 to 1.. The remaining parameters used in our calculations are listed in Table 1 shown below.

6 148 Ulugbek Djuraev et al. Water density Oil density (Baronia) Water dynamic viscosity Oil dynamic viscosity Table1 Parameters used in the calculations Notation Value Unit 1 3 kg / m w kg / m o. 894 Pa * s w. 8 Pa * s o Vacuum permittivity F / m Water dielectric constant Oil dielectric constant w o.1 Porosity % Tortuosity Boltzmann s constant 4 m k E 3 J / K B Temperature T K Charge o an electron e E 19 Coulumb Ionic valence (NaCl) z 1 Avogadro s number N 6.E 6 3 ions / m A Formation actor F Eective pore radius r 8 m e Pore geometry length. 8 m 3 Results and Discussion Eect o brine concentration on the seismoelectric coupling coeicient L was studied numerically. Fig. a shows the variation o the coupling coeicient at various water saturation values when requency was ixed at 1 khz. The results show that the eect o brine concentration is prominent at high water saturation. In general, the coupling coeicient shows a declining trend as brine concentration increases. However, the rate o decline is slightly lower at low water saturation. When the saturation is increased rom. to.6 at brine concentration.1 mol/l,

7 Numerical investigation o parameters 149 the coupling coeicient increased rom.15 nv/pa to.45 nv/pa, respectively. This is about 34 % increase in seismoelectric coupling coeicient. In comparison, when water saturation is increased rom. to.6 at brine concentration.1 mol/l, the coupling coeicient increased rom.54 nv/pa to.18 nv/pa, which is about 337% increase. Fig. b shows the eect o brine concentration at constant water saturation o.4 at three dierent requencies. There is a general declining trend when brine concentration increases at ixed water saturation. When low and high requencies are compared, the coupling coeicient is higher at lower requencies. This observation suggests that at lower requency excitations, the relaxation time and eect o nonlinearities are lower which results in less dissipation. Fig. Eect o brine concentration on coupling coeicient. (a) = 1 khz, (b) Sw =.4 Figure 3a shows eect o water saturation on the coupling coeicient at various requencies. Brine concentration was ixed at.1 mol/l. At higher water saturations, the contrast between the coupling coeicients at dierent requencies is larger. When the requency is increased rom 5 khz to 15 khz in the ully saturated case, the value o the coupling coeicient is reduced by 57 %, i.e. rom.51 nv/pa to.9 nv/pa. On the contrary, when water saturation is low, the contrast between the coupling coeicient at various values o requency is rather insigniicant. Our results are consistent with previous studies such as Bordes, et al. [1] and Strahser, et al. [1]. Fig. 3b shows eect o water saturation on the coupling coeicient at various brine concentrations when the requency is ixed at 1 khz. The result exhibits similar trend that is shown in Fig. 3a. At water saturation less than., brine concentration does not seem to have signiicant eect. However, at higher water saturations, the seismoelectric coupling is sensitive to brine concentration. The response is higher at lower brine concentration.

8 15 Ulugbek Djuraev et al. Warden, et al. [14] highlights that the seismoelectric signal properties vary with water saturation, because the content o aqueous phase aects seismic velocity and seismic attenuation, electrical conductivity o a luid-containing porous medium, and propagation and diusion o electromagnetic waves. On the contrary, in a porous medium saturated with gas and water, water saturation has entirely dierent eect on the seismoelectric coupling, Bordes, et al. []. Fig. 3 Eect o water saturation on coupling coeicient. (a) C =.1 mol/l, (b) = 1 khz. Eect o seismic requency on the seismoelectric coupling coeicient at various water saturation is present in Fig.4a. Brine concentration is ixed at.1 mol/l. Although the general trend is that the seismoelectric coupling coeicient decreases as requency increases, it seems that or a particular water saturation there is a critical requency beyond which the eect o requency is insigniicant. When the water saturation is., this critical requency is about 1 khz. The critical requency shits to the right when water saturation increases. Fig. 4b shows the eect o requency when water saturation is ixed at.4 and brine concentration is varied. The seismoelectric coupling coeicient is higher at lower requencies. As requency increases, the coupling coeicient declines. However, the rate o decline is becoming lower at higher requencies. The declining trend o the coupling coeicient as requency increases might be related to the nonlinearities that occur at high requency. Also, high requency aects relaxation time which in turn eeds into the nonlinearities producing higher dissipation. As such, the seismoelectric coupling becomes lower at higher requencies.

9 Numerical investigation o parameters 151 Fig. 4 Eect o requency on coupling coeicient. (a) C =.1 mol/l, (b) Sw =.4 4 Conclusion In this paper, we extended Pride s theoretical seismoelectric coupling ratio to a partially-saturated medium, where the coupling was ormulated as a unction o water saturation, brine salinity and requency o seismic wave. The resulting model is applied to a porous media saturated with oil and water. Our results show that there is a general declining trend in the seismoelectric coupling coeicient when brine concentration is increased at ixed water saturation. When lower and higher requencies are compared at ixed water saturation, the coupling coeicient is higher at lower requencies. This observation suggests that at lower requencies, the relaxation time and eect o nonlinearities are lower, which results in less dissipation. As such, more mechanical energy can be converted to electromagnetic energy as the seismic wave propagates through the medium as maniested by the characteristics o the coupling coeicient as shown in our study. At water saturation less than., brine concentration and seismic requency do not seem to have signiicant eect on the coupling coeicient. However, at higher water saturations, the seismoelectric coupling is sensitive to both brine concentration and requency. The general characteristics is that at the given water saturation, there seem to be a critical requency beyond which requency does not seem to have much impact on the seismoelectric coupling coeicient. When the water saturation is., such critical requency is about 1 khz. When water saturation increases, the critical requency also increases. Acknowledgements. The authors grateully acknowledge inancial support rom the UTP-TU Delt Shell project at the Universiti Teknologi PETRONAS under grant No. 153AB-DA5.

10 15 Ulugbek Djuraev et al. Reerences [1] C. Bordes, S. Garambois, L. Jouniaux, P. Senechal, Seismoelectric Measurements or the Characterization o Partially Saturated Porous Media, AGU Fall Meeting Abstracts, 9, pp [] C. Bordes, P. Sénéchal, J. Barrìère, D. Brito, E. Normandin, D. Jougnot, Impact o water saturation on seismoelectric transer unctions: a laboratory study o coseismic phenomenon, Geophysical Journal International, (15), [3] J.C. Dupuis, K.E. Butler, A.W. Kepic, B.D. Harris, Anatomy o a seismoelectric conversion: Measurements and conceptual modeling in boreholes penetrating a sandy aquier, Journal o Geophysical Research, 114 (9). [4] J. Frenkel, On the theory o seismic and seismoelectric phenomena in a moist soil, J. Phys. J. Phys. (Soviet), 8 (1944), [5] A. Ivanov, Eect o electrization o earth layers by elastic waves passing through them, Doklady Akademii Nauk SSSR, 4 (1939), [6] A. Jardani, A. Revil, Seismoelectric couplings in a poroelastic material containing two immiscible luid phases, Geophysical Journal International, (15), [7] L. Jouniaux, C. Bordes, Frequency-dependent streaming potentials: a review, International Journal o Geophysics, 1 (1), [8] S.R. Pride, Governing equations or the coupled electromagnetics and acoustics o porous media, Physical Review B, 5 (1994), [9] A. Revil, G. Barnier, M. Karaoulis, P. Sava, A. Jardani, B. Kulessa, Seismoelectric coupling in unsaturated porous media: theory, petrophysics, and saturation ront localization using an electroacoustic approach, Geophysical Journal International, 196 (13), [1] M. Strahser, L. Jouniaux, P. Sailhac, P.-D. Matthey, M. Zillmer, Dependence o seismoelectric amplitudes on water content, Geophysical Journal International, 187 (11), [11] A. Thompson, J.R. Sumner, S.C. Hornbostel, Electromagnetic-to-seismic conversion: a new direct hydrocarbon indicator, The Leading Edge, 6 (7), 48-

11 Numerical investigation o parameters [1] J. Vinogradov, M. Jaaar, M. Jackson, Measurement o streaming potential coupling coeicient in sandstones saturated with natural and artiicial brines at high salinity, Journal o Geophysical Research: Solid Earth, 115 (1). [13] E. Walker, P.W. Glover, Permeability models o porous media: Characteristic length scales, scaling constants and time-dependent electrokinetic coupling, Geophysics, 75 (1), E35-E46. [14] S. Warden, S. Garambois, L. Jouniaux, D. Brito, P. Sailhac, C. Bordes, Seismoelectric wave propagation numerical modelling in partially saturated materials, Geophysical Journal International, 194 (13), [15] Z. Zhu, M. Toksӧz, X. Zhan, Seismoelectric measurements in a porous quartzsand sample with anisotropic permeability, Geophysical Prospecting, 64 (15), Received: July 5, 16; Published: September 19, 16

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