PERMEABILITY OF UNCONSOLIDATED SANDS AND POROUS ROCKS
PERMEABILITY OF UNCONSOLIDATED SANDS AND POROUS ROCKS
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DOI：
10.1029/jb090ib04p03099
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发表时间：
1985-01-01
期刊：
影响因子：
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通讯作者：
GANGI, AF
中科院分区：
文献类型：
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作者：
GANGI, AF
Krumbein和Monk发现了松散砂渗透率与平均粒径（按重量计）d和标准差σ f（σ = − log 2dfordin mm）的经验关系。对于对数正态粒度分布，它们的表达式为：对于dwin毫米，k = 760 dw 2 exp（−1.31σ），σ单位为100，而对于darcys。他们的数据已被重新分析，以表示的渗透率的平均粒径的数量，dN。该表示是更物理的表示，因为渗透率取决于特定尺寸的孔的数量（即，根据孔径的数量分布函数）。预计孔径分布函数（按数量计）与按数量计的粒度分布函数的关系比与按重量计的粒度分布函数的关系更密切。结果发现，所有数据的拟合结果均为k = 665 dN 2 exp（1.78σ 3）= 665 dw 2exp（−2.88 σ 2+ 1.78σ 3）且k = 648 dN 2（1 + 2.77σ N ~ 3）。发现表达式k = 735 dN ~ 2给出的渗透率值对于松散、松散、松散和松散的情况精确到10%。疏松砂（孔隙度≤ 40%±5%），标准差σ在0 ≤ σ ≤ 0.5范围内。如果采用贝格关于渗透率随孔隙度变化的半理论/经验测定法（孔隙度在30% ≤n≤ 45%范围内），这些结果可以应用于多孔岩石。给出了渗透率随有效围压变化的理论表达式。
Krumbein and Monk found an empirical relationship for the permeability of unconsolidated sand as a function of the mean grain diameter (by weight)dwand the standard deviation σϕ(ϕ = −log2dfordin millimeters). Their expression, for lognormal grain size distributions, isk= 760dw2exp (−1.31σϕ) fordwin millimeters, σϕin ϕ units, andkin darcys. Their data have been reanalyzed to express the permeability in terms of the mean grain diameter by number,dN. This representation is a more physical one because the permeability depends upon the number of pores of particular sizes (i.e., upon the number distribution function of pore sizes). It is expected that the pore size distribution function (by number) is more closely related to the grain size distribution function by number than to the grain size distribution function by weight. It was found that equally good fits of all their data are given byk= 665dN2exp (1.78σϕ3) = 665dw2exp (−2.88 σϕ2+ 1.78σϕ3) andk= 648dN2(1 + 2.77σϕ3).It was found that the expressionk= 735dN2gives permeability values that are accurate to 10% for loose, unconsolidated sands (porosity ≅ ≎ 40%±5%) with standard deviation σϕin the range 0 ≤ σϕ≤ 0.5. These results may be applied to porous rocks if Berg's semitheoretical/empirical determination of the permeability variation with porosity is used (for porosities in the range 30% ≤n≤ 45%). An expression for the theoretical variation of permeability with effective confining pressure is also given.