Archie’s Law in Microsystems
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- 作者：B. Kozlov (12) kozlovb82@yahoo.fr
M. H. Schneider (12)
B. Montaron (3)
M. Lagu?s (4)
P. Tabeling (1) - 关键词：Archie’s law – Conductivity in rocks – Micromodels – Wettability – Invasion percolation
- 刊名：Transport in Porous Media
- 出版年：2012
- 出版时间：October 2012
- 年：2012
- 卷：95
- 期：1
- 页码：1-20
- 全文大小：1.4 MB
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- ISSN：1573-1634
文摘
Since 1942 Archie’s law is used every day to estimate, from electrical measurements, the quantity of oil present in oil fields. In this article, we perform the first experimental analysis of electric conductivity in well controlled models of porous media. We used microfluidic networks (called micromodels in the oil industry jargon), incorporating thousands of pores, with controlled wettability. Different electrode and pore geometries are considered. In all cases the evolution of the conductivity with the conductive fluid fraction (“saturation”) clearly reveals the presence of percolation thresholds, signaling that as the fraction of the conductive fluid decreases below some critical value, there are no more pathways involving only channels entirely filled with the conductive fluid that connect the electrodes. This behavior is observed in all cases, for all the network/electrode geometries and wetting properties we investigated, and is consequently likely to reflect a genuine behavior for microfluidic “2D” networks. The existing models—based on percolation theory or on mean field approach—reproduce correctly the structure of this behavior, but generally at a semi-quantitative level. The most successful case is obtained with the effective medium theory (EMT) model, with drainage and perpendicular electrodes. This outcome suggests that, despite the complexity of these systems, very simple models can describe correctly the physics of the system. Nonetheless, more precise modeling requires case-by-case studies. Our results are consistent with the current body of knowledge accumulated for decades on three-dimensional samples. The key point is that in 3D systems, owing to topological reasons, the threshold is extremely low in terms of water saturations. Archie’s law completely neglects the threshold effect. Nonetheless the percolation threshold should not be overlooked, and modeling should take this aspect systematically into account, as it is already done by several investigators.