阿尔奇公式的理论本原

Theoretical roots of Archie formulas

在岩石导电机理上,纯水层阿尔奇公式有两点必须改进.第一,岩石骨架不导电,岩石孔隙中的地层水导电,当孔隙度为零时,岩石的电导率为零,电阻率为无穷大.但在现在使用的双对数坐标系下,此坐标点(Ф=0,F=∞)无法实现.须将电阻率之比改为电导率之比,并采用普通坐标.第二,地层因素F是导体容量孔隙Ф和导体几何性质——孔道迂曲度τ两个因素的函数.但是纯水层阿尔奇公式F仅为Ф一个因素的函数.测井无法获得τ的数值.但通过观察实验数据,τ和Ф存在内在关联,将τ与Ф融合,得到1/F=Ф^2/a的关系式.普遍消除了F~Ф关系曲线左、右斜率不同或低孔门限的"非阿尔奇"现象.将公式中的导电因子Ф^2扩展为(ФSw)^2,得到含油层阿尔奇公式:R1/R0=1/sw^2.在油(气)成藏过程中湿性附着液首先被驱替,润湿性对原始油(气)藏不起作用.饱和度指数n值等于2.

According to the electrical conduction mechanism in rocks,the Archie formula for reservoirs completely saturated with brine needs to be improved in two aspects.First,given the rock matrix is not conductive and the formation water in pores is conductive,if the porosity is zero,then the rock conductivity is zero and F is infinite.However,the point(Ф=0,F=∞)cannot be realized in the F~Фdouble logarithm coordinate system.Therefore the ratio of resistivity needs to be changed to the ratio of conductivity and the ordinary coordinate system be utilized.Secondly,the formation factor F is related to conductor capacityФand conductor geometry,the tortuosityτ.But F is only related toФin Archie formula.The tortuosityτcannot be obtained by well logging.Observing the experimental data,there is a relation betweenτandФ.MergingФandτ,the relation 1/F=Ф^2/a is derived,which universally eliminates the"non-Archie"phenomena that the F~Фrelation shows a line in low-porosity range and another line with a different slope in high-porosity range or a line with a porosity threshold.ExtendingФ^2 in the formula above to(ФSw)^2,the Archie formula for oil bearing formation will be obtained,R1/R0=1/sw^2.Because wetting fluids are displaced first in the process of hydrocarbon accumulation,wettability has no effect on the original hydrocarbon reservoirs.The saturation index n is equal to 2.