An effective medium model for the electric conductivity of an N-component anisotropic and percolating mixture

Koelman, J.M.V.A.; Kuijper, Arno

doi:10.1016/s0378-4371(97)00385-3

Cited by 48 publications

(32 citation statements)

References 14 publications

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“…Depending on the SBVP solution different statistical models can be distinguished. The numerous ways of closing the integral equations were offered -the method of effective medium (Hashin 1968;Buyevich 1992;Koelman and de Kuijper 1997), differential method (Milton 1985;Zimmerman 1996;PhanThien and Pham 2000), Mori-Tanaka-Eshelby method of the average fields (Hatta and Taya 1985;Benveniste 1986;Chen and Wang 1996;Weber et al 2003), the singular approximation method (Shermergor 1977;Shvidler 1985), the strong isotropy hypothesis and method of conditional moments (Khoroshun et al 1993), correlation approximation and multipoint approximation (Volkov and Stavrov 1978;Tashkinov et al 2012;Tashkinov 2015). Some of the techniques are described below.…”

Section: Statistical Characterization Of Local Stress and Strain Fieldsmentioning

confidence: 99%

Statistical methods for mechanical characterization of randomly reinforced media

Tashkinov

2017

Mech Adv Mater Mod Process

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Advanced materials with heterogeneous microstructure attract extensive interest of researchers and engineers due to combination of unique properties and ability to create materials that are most suitable for each specific application. One of the challenging tasks is development of models of mechanical behavior for such materials since precision of the obtained numerical results highly depends on level of consideration of features of their heterogeneous microstructure. In most cases, numerical modeling of composite structures is based on multiscale approaches that require special techniques for establishing connection between parameters at different scales. This work offers a review of instruments of the statistics and the probability theory that are used for mechanical characterization of heterogeneous media with random positions of reinforcements. Such statistical descriptors are involved in assessment of correlations between the microstructural components and are parts of mechanical theories which require formalization of the information about microstructural morphology. Particularly, the paper addresses application of the instruments of statistics for geometry description and media reconstruction as well as their utilization in homogenization methods and local stochastic stress and strain field analysis.

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Section: Statistical Characterization Of Local Stress and Strain Fieldsmentioning

confidence: 99%

Statistical methods for mechanical characterization of randomly reinforced media

Tashkinov

2017

Mech Adv Mater Mod Process

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“…According to the symmetrical anisotropic effective medium theory at low frequency and basic principles of the SATORI resistivity model proposed by Koelman et al [26] and de Kuijper et al [27] , the conductivity of dispersed shaly sand with the five components can be expressed as…”

Section: The Effective Medium Resistivity Model For Dispersed Shaly Smentioning

confidence: 99%

“…Because effects of extrinsic factors on log interpretation accuracy are decreased to some extent by selecting right drilling conditions and formation water resistivity, and correcting for invasion effect, only intrinsic factors should be considered in establishing a generalized resistivity model for low resistivity reservoirs. Until now, resistivity models applied in low resistivity reservoirs are mainly as follows: 1) Archie equation [14] , applied in low resistivity reservoir caused by high saline formation water; 2) electric double layer resistivity models [15][16][17][18][19][20] , applied in low resistivity reservoir caused by high saline formation water and excess conductivity of dispersed clay; 3) conductive rock matrix models [1,2] , applied in low resistivity reservoir caused by high saline formation water, microscopic capillary pores, conductive minerals or clay in rock matrix; 4) three-water conduction model [21] , describing conductance mechanism for low resistivity reservoir better, and applied in low resistivity reservoir caused by high saline formation water, microscopic capillary pores, and excess conductivity of dispersed clay; 5) dual water clay matrix conductive model [22] , applied in low resistivity reservoir caused by high saline formation water, microscopic capillary pores, and excess conductivity of dispersed clay; 6) effective medium HB resistivity model in laminated and dispersed shaly sand [23 -25] , applied in low resistivity reservoir caused by high saline formation water, excess conductivity of dispersed clay, conductive minerals in rock matrix and thin sand-shale interlayers; and 7) symmetrical effective medium resistivity model in laminated and dispersed shaly sand [26][27][28] , applied in low resistivity reservoir caused by high saline formation water, excess conductivity of dispersed clay, conductive minerals in rock matrix and thin sand-shale interlayers. To sum up, since resistivity models in current use cannot completely describe conductance mechanism in the complex hydrocarbon-bearing reservoirs, especially when dispersed clay, laminated shale, conductive minerals in rock matrix, microscopic capillary pores, and high saline formation water coexist in hydrocarbon-bearing shaly sand reservoir, conductance mechanism in the complex hydrocarbon-bearing reservoir becomes more complicated and a generalized resistivity model is needed to describe the conductance mechanism for low resistivity reservoir with presence of the five intrinsic factors.…”

mentioning

confidence: 99%

Generalized effective medium resistivity model for low resistivity reservoir

Song

Xiao-min

2008

Sci. China Ser. D-Earth Sci.

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With the advancement in oil exploration, producible oil and gas are being found in low resistivity reservoirs, which may otherwise be erroneously thought as water zones from their resistivity. However, the evaluation of low resistivity reservoirs remains difficult from log interpretation. Since low resistivity in hydrocarbon bearing sands can be caused by dispersed clay, laminated shale, conductive matrix grains, microscopic capillary pores and high saline water, a new resistivity model is required for more accurate hydrocarbon saturation prediction for low resistivity formations. Herein, a generalized effective medium resistivity model has been proposed for low resistivity reservoirs, based on experimental measurements on artificial low resistivity shaly sand samples, symmetrical anisotropic effective medium theory for resistivity interpretations, and geneses and conductance mechanisms of low resistivity reservoirs. By analyzing effects of some factors on the proposed model, we show theoretically the model can describe conductance mechanisms of low resistivity reservoirs with five geneses. Also, shale distribution largely affects water saturation predicted by the model. Resistivity index decreases as fraction and conductivity of laminated shale, or fraction of dispersed clay, or conductivity of rock matrix grains increases. Resistivity index decreases as matrix percolation exponent, or percolation rate of capillary bound water increases, and as percolation exponent of capillary bound water, or matrix percolation rate, or free water percolation rate decreases. Rock sample data from low resistivity reservoirs with different geneses and interpretation results for log data show that the proposed model can be applied in low resistivity reservoirs containing high salinity water, dispersed clay, microscopic capillary pores, laminated shale and conductive matrix grains, and thus is considered as a generalized resistivity model for low resistivity reservoir evaluation. low resistivity reservoir, symmetrical anisotropic effective medium conductance theory, microscopic capillary pores, dispersed clay, laminated shale, conductive matrix grain, generalized resistivity model Now hydrocarbon-bearing low resistivity reservoirs have been found in most of oilfields in China. Since low resistivity reservoirs have commercially-produced oil and potential oil reserves, they have become an important source for increasing oil reserves and oil productions in oilfields. Many analysts have studied geneses of low resistivity reservoirs in detail. Their achievements show that low resistivity in shaly sands can be caused by intrinsic factors, extrinsic factors and complex factors [1][2][3][4][5][6][7][8][9][10][11][12][13] . Intrinsic factors include high saline formation water, high irreducible water saturation caused by microscopic capillary pores, excess conductivity of dispersed clay, conductive minerals in rock matrix and thin sand-shale interlayers. Extrinsic factors contain salt mud invasion, different conditions between hydrocarbon b...

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“…By introducing a hypothetical homogeneous medium of non-zero electrical conductivity ó 0 and applying the general effective medium theory, the electrical conductivity of saturated cement paste, ó cp , satisfies the following equation 19 ó…”

Section: Relative Electrical Conductivity Of Saturated Cement Pastementioning

confidence: 99%

“…According to Koelman and de Kuijper, 19 the electrical conductivity of the hypothetical homogeneous medium, ó 0 , can simply be expressed as…”

Section: Relative Electrical Conductivity Of Saturated Cement Pastementioning

confidence: 99%

Prediction of relative electrical conductivity of saturated cement paste

Zheng¹,

Zhou²

2008

Magazine of Concrete Research

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Owing to its importance both in assessing the microstructural development and in computing the ionic diffusivity and permeability, it is of great practical significance to determine the relative electrical conductivity of saturated cement paste. This paper presents an analytical solution for the relative electrical conductivity of saturated cement paste. By modelling saturated cement paste as a two-phase composite material, consisting of capillary pores, and hydrated products and unhydrated cement grains, an analytical solution is derived for the relative electrical conductivity of saturated cement paste based on the general effective medium theory. Two parameters involved in the analytical solution are then determined by experimental calibration. After verifying the analytical solution with two sets of experimental results obtained from the literature, the effects of the water/cement (w/c) ratio and the degree of hydration on the relative electrical conductivity of saturated cement paste are evaluated in a quantitative manner. It is found that the relative electrical conductivity of saturated cement paste decreases with the decrease of the w/c ratio and/or with the increase of the degree of hydration. The paper concludes that the analytical solution presented can predict the relative electrical conductivity of saturated cement paste with reasonable accuracy. Notation aintermediate coefficient H(V 1 ÀV 1c ) Heaviside step function in terms of V 1 and V 1,c h 1 , h 2 coefficients between zero and one m percolation exponent in terms of n n parameter R cp relative electrical conductivity of saturated cement paste to pore solution t parameter larger than or equal to zero V 1 , V 2 , volume fractions of phase 1 (capillary pores) and phase 2 (hydrated products and unhydrated cement particles) V 1,c critical volume fraction of phase 1 V cap volume fraction of capillary pores V hyd volume fraction of hydrated products V unhyd volume fraction of unhydrated cement grains w/c water/cement ratio AE degree of hydration ó 1 , ó 2 electrical conductivities of phases 1 and 2 ó s , ó cp , ó 0 electrical conductivities of pore solution, saturated cement paste and hypothetical homogeneous medium

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An effective medium model for the electric conductivity of an N-component anisotropic and percolating mixture

Cited by 48 publications

References 14 publications

Statistical methods for mechanical characterization of randomly reinforced media

Statistical methods for mechanical characterization of randomly reinforced media

Generalized effective medium resistivity model for low resistivity reservoir

Prediction of relative electrical conductivity of saturated cement paste

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