Mansfield P, Issa B
Department of Physics, University of Nottingham, UK.
Magn Reson Imaging. 1994;12(2):275-8. doi: 10.1016/0730-725x(94)91535-0.
Attempts to quantify the permeability constant that appears in Darcy's equation in terms of the porosity, tortuosity and surface area have been made by Kozeny and Carman. These results in turn have been translated by Seevers into expressions involving spin-lattice relaxation times. When this work was done originally in the mid-1960s, NMR imaging and spatially localised T1 maps had not been invented. Therefore, bulk T1 average values were used and it is not surprising to see substantial deviations from predicted permeabilities in bore core material. In this paper we re-examine the Kozeny-Carman and Seevers theories in the light of new techniques development for the localised measurement of both T1 maps and fluid velocity maps. New results show spatially correlated T1 and flow maps obtained from Bentheimer sandstone samples. These are discussed in terms of a localised permeability constant. By this means we show that the relationship between T1 and permeability does not hold at the local level for isolated pixels within a larger specimen.
科曾尼（Kozeny）和卡曼（Carman）曾尝试根据孔隙率、曲折度和表面积来量化达西方程中出现的渗透率常数。这些结果又被西弗斯（Seevers）转化为涉及自旋晶格弛豫时间的表达式。这项工作最初是在20世纪60年代中期完成的，当时核磁共振成像和空间定位T1图尚未发明。因此，使用的是整体T1平均值，并且在岩芯材料中观察到与预测渗透率存在显著偏差也就不足为奇了。在本文中，我们根据用于局部测量T1图和流体速度图的新技术发展，重新审视科曾尼 - 卡曼理论和西弗斯理论。新结果展示了从本特海默砂岩样品获得的空间相关T1图和流图。这些结果将根据局部渗透率常数进行讨论。通过这种方式，我们表明对于较大样本内的孤立像素，T1与渗透率之间的关系在局部层面并不成立。
