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当垂直井井眼穿过水平地层时 ,电法测井仪器的响应不受各向异性的影响。这不是因为地层是各向同性的 ,而是由于长期以来商用测井仪器所测的电阻率张量的分量恰巧与通常在岩心分析中测得的分量一致 ,而其它张量分量则在测量结果中没有反映 ,以致在地层评价中人们往往忽略这些分量。但是随着大斜度井和水平井的出现 ,在测井解释理论中就不能再忽视储层的各向异性了。人们一直习惯于使用标量阿尔奇公式从由测井仪器测得的电阻率来计算含水饱和度。但如何解决各向异性对含水饱和度计算的影响 ,通常的办法是根据标量阿尔奇公式分别建立电导率张量各个主轴分量关于含水饱和度的关系式 ,据此不加证明地将其扩展到张量形式 ,其中既包含张量成份 ,比如电导率 ,也包含标量成份 ,比如孔隙度和含水饱和度 ,这就是张量阿尔奇公式。从中推出的含水饱和度的表达式也具有张量的形式 ,直接求解将涉及到对数和指数矩阵函数的计算。另一种办法是从阿尔奇含水饱和度理论的一种修正形式——电效率理论出发 ,同样以相似的思路将其推广到张量形式 ,这就是张量电效率公式 ,可以由此得到含水饱和度的另一种张量表达式。无论是从张量阿尔奇公式出发 ,还是从张量电效率公式出发 ,计算含水饱和度时都牵涉到较为复杂的矩阵运算。为避?
When a vertical wellbore crosses a horizontal formation, the response of the electrical logging tool is not affected by the anisotropy. This is not because the formation is isotropic but rather because the components of the resistivity tensor measured by commercial logging tools coincide with the components normally measured in core analysis and the other tensor components are the result of measurements Is not reflected in the evaluation of strata so that people often overlook these components. However, with the advent of highly deviated wells and horizontal wells, reservoir anisotropy can no longer be neglected in well logging interpretation theory. It has always been customary to use the scalar Archie formula to calculate the water saturation from the resistivity measured by the logging tool. However, how to solve the anisotropy of water saturation calculation, the usual approach is based on the scalar Archie formula to establish the conductivity tensor of the various spindle components of water saturation, which accordingly without its extension to Tensor forms, which include both tensor components, such as conductivity, but also scalar components, such as porosity and water saturation, are the tensor Archie’s formula. The expression of water saturation derived therefrom also has the form of a tensor, which is directly related to the calculation of logarithmic and exponential matrix functions. Another approach is based on a modified form of Archie’s water saturation theory - the electrical efficiency theory, which is also extended to the tensor form in a similar way, which is the tensor electrical efficiency equation, from which water-containing Another Tensor Expressions of Saturation. Whether it is based on the tensor Archie’s formula or the tensor’s electric efficiency formula, calculating the water saturation involves more complex matrix operations. To avoid?