Saturation exponent is an important parameter in Archie’s equations; however, there has been no well-accepted physical interpretation for the saturation exponent. We have theoretically derived Archie’s equations from the Maxwell–Wagner theory on the assumption of homogeneous fluid distribution in the pore space of clay-free porous rocks. Further theoretical derivations showed that the saturation exponent is in essence the cementation exponent for the water–air mixture and is quantitatively and explicitly related to the aspect ratio of the air bubbles in the pores. The results have provided a theoretical backup for the empirically obtained Archie’s equations and have offered a more physical and quantitative understanding of the saturation exponent.

饱和指数是Archie方程中的重要参数。但是，对于饱和指数尚无公认的物理解释。我们从麦克斯韦-瓦格纳理论中理论推导了阿奇方程，该假设基于无粘土多孔岩石孔隙空间中均质流体分布的假设。进一步的理论推导表明，饱和指数本质上是水-空气混合物的胶结指数，并且与孔隙中气泡的纵横比定量且明确地相关。结果为经验获得的阿奇方程提供了理论上的支持，并为饱和指数提供了更多的物理和定量理解。