Analytical prediction of the formation factor for isotropic mono-sized unconsolidated porous media

被引:1
作者
Awountsa, Y. H. Nkocko [1 ]
Diedericks, G. P. J. [1 ]
Smit, G. J. F. [1 ]
Woudberg, S. [1 ]
机构
[1] Stellenbosch Univ, Dept Math Sci, Div Appl Math, Private Bag X1, ZA-7602 Matieland, South Africa
基金
新加坡国家研究基金会;
关键词
Electrical conductivity; Formation factor; Granular materials; Mathematical modelling; Microstructure; Porous media; ELECTRICAL-CONDUCTIVITY; FLOW; PERMEABILITY; PERCOLATION; TORTUOSITY; DIFFUSION; MODEL;
D O I
10.1016/j.ces.2022.118138
中图分类号
TQ [化学工业];
学科分类号
0817 ;
摘要
Analytical expressions are derived for the formation factor as a function of porosity based on the Representative Unit Cell model for unconsolidated media by applying volume averaging to Ohm's law. Three arrays are considered, namely an over-staggered, fully staggered and regular array. Numerical simulations are performed to compute the formation factor for two-dimensional versions of the arrays by solving the Laplace equation. The absolute relative percentage difference between the numerical data and corresponding model predictions obtained for the over-staggered array is less than 20% and that for both the fully staggered and regular arrays are less than 10%. Two weighted isotropic models are introduced and a percolation threshold porosity incorporated. The models have been validated against experimental data and models from the literature. The improvement in model prediction with the percolation threshold porosity included is between 100 and 200% at the average porosity of the data set considered. (C) 2022 Elsevier Ltd. All rights reserved.
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页数:21
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共 38 条
  • [1] Pore geometrical model for the resistivity of brine saturated rocks
    Abousrafa, E. M.
    Somerville, J. M.
    Hamilton, S. A.
    Olden, P. W. H.
    Smart, B. D. G.
    Ford, J.
    [J]. JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING, 2009, 65 (3-4) : 113 - 122
  • [2] THE FORMATION FACTOR OF RECONSTRUCTED POROUS-MEDIA
    ADLER, PM
    JACQUIN, CG
    THOVERT, JF
    [J]. WATER RESOURCES RESEARCH, 1992, 28 (06) : 1571 - 1576
  • [3] The electrical resistivity log as an aid in determining some reservoir characteristics
    Archie, GE
    [J]. TRANSACTIONS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS, 1942, 146 : 54 - 61
  • [4] EXPERIMENTAL-STUDY OF SOME HYDROGEOPHYSICAL PROPERTIES OF UNCONSOLIDATED POROUS-MEDIA
    BIELLA, G
    LOZEJ, A
    TABACCO, I
    [J]. GROUND WATER, 1983, 21 (06) : 741 - 751
  • [5] Electrical conductivity models in saturated porous media: A review
    Cai, Jianchao
    Wei, Wei
    Hu, Xiangyun
    Wood, David A.
    [J]. EARTH-SCIENCE REVIEWS, 2017, 171 : 419 - 433
  • [6] GENERAL EXPRESSION FOR CORRELATION OF RATES OF TRANSFER AND OTHER PHENOMENA
    CHURCHILL, SW
    USAGI, R
    [J]. AICHE JOURNAL, 1972, 18 (06) : 1121 - +
  • [7] FLOW OF GASES THROUGH CONSOLIDATED POROUS MEDIA
    CORNELL, D
    KATZ, DL
    [J]. INDUSTRIAL AND ENGINEERING CHEMISTRY, 1953, 45 (10): : 2145 - 2152
  • [8] Failure of the Conventional Expression of Tortuosity in Granular Porous Solids
    Diaz-Curiel, J.
    Biosca, B.
    Arevalo-Lomas, L.
    Miguel, M. J.
    [J]. SURVEYS IN GEOPHYSICS, 2021, 42 (04) : 943 - 960
  • [9] Electrical conduction and formation factor in isotropic porous media
    Diedericks, GPJ
    duPlessis, JP
    [J]. ADVANCES IN WATER RESOURCES, 1996, 19 (04) : 225 - 239
  • [10] PERMEABILITY, CONDUCTIVITY, AND PORE GEOMETRY OF SANDSTONE
    DOYEN, PM
    [J]. JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH AND PLANETS, 1988, 93 (B7): : 7729 - 7740