阿尔奇(Archie)公式:提出背景与早期争论

Archie's formula: historical background and earlier debates

根据关于岩石电学的早期资料,介绍了阿尔奇公式的提出背景和当时身处学术界和测井界的研究者和工程师们围绕阿尔奇公式所展开的一系列研究和论战.回顾与分析证明:围绕阿尔奇公式所进行的早期论战在于地层因子F及指数m和n.具体的论战焦点有四个:(1)地层因子的表达式F=1/φm是否合适;(2)m和n是否具有物理内涵;(3)m和n的值到底是常数还是变数;(4)m和n与岩石的内部结构是否有关.在经过近20年的研究和论争后,即在1960年左右发现指数m和n与岩石的结构、构造以及孔隙流体的饱和度和流体替换的历史有关.此外,还发现岩石的湿润性和超毛细管孔隙度对岩石的电阻率也有很大的影响.虽然阿尔奇公式影响深远而且在岩石物理学和石油测井的发展中具有划时代的意义和里程碑式的作用,但是没有考虑泥质、淡水、低孔隙、非均匀几何参数分布(孔隙度、曲折度)、非均匀饱和度分布、各向异性以及参数a和b对岩石电阻率的贡献和隐藏在这些参数和因素后面的物理机制.因此,在应用阿尔奇公式时必须注意有关的应用条件.此外,根据完全水饱和公式ρ0=FρW=aρW/m和部分水饱和公式ρt=Iρ0=bρ0SW-n来研究F、I、a、b以及m和n与岩石的内部结构、孔隙分布以及孔隙流体和岩石颗粒之间的物理及化学相互作用的关系具有反问题的特点.所以,围绕阿尔奇公式的研究和争论将有可能会伴随着时代的进步和科学技术的发展一直进行下去.

Based on some earlier papers, we present the historical background of Arehie＇s formula and the earlier debates related to Archie＇s work. Reviews and analysis show that the earlier debates related to Archie＇s formula were focused on the following points： （1） Is the formula F= 1/φ^m an adequate form for the formation factor？ （2）Have the exponents rn and n some physical intension？ （3） Are the exponents rn and n constants or variables？ （4） Do rn and n relate to the internal structure and fabric of rocks？ These points were resolved or clarified around the year 1960, after investigations and debates about 20 years. It had been found that the exponents rn and n are controlled by the internal structure of the rocks, by the wettability and microporosity, as well as by the saturation and by the history of the fluid displacement. Although Archie＇s formula has a profound influence on the electricity of reservoir rocks and on the development of geophysical well logging, and although it plays a role of milestone and has the epoch-making significance in the history of rock physics and in the development of electrical well logging methods for petroleum industry, it does not include the contributions to the rock resistivity from clay, fresh water, low porosity, heterogeneous distribution of porosity and saturation, anisotropy, and from the factors characterized by the parameters a and b. As a result, it should be used with care when solving problems in practice. Furthermore, it will results in an inverse problem if the waterbearing formula po - Fρw =aρw/φ^m and the partially saturated formula ρ1=Iρ0=bρ0 Sw^-n are used for finding mathemat- ical relations linking F, I,a ,b,m and n to the internal structure of rocks, the porosity and saturation distribution and to the physical and chemical interaction between rock grains and pore fluids. Because of this fact, studies and debates related to Archie＇s formula will perhaps go on, together with the advances of times and with the developments of science and technology.