Based on fluid migration essence, the tortuosity calculation formula described by seepage velocity is derivated; according to the fracture profile shape in various accuracy, the random profile is split into V shape, curvature curve and groove structure; the shear slipping fracture which includes contact area is simplified into parallel plate model with randomly filled cylinder, spherome and cuboid; then combined with Kozeny-Carmann equation, the tortuosity equation accuracy is checked by random profile units, randomly filled parallel plate model; finally, the relationship between tortuosity and porosity is fitted. The results show that the tortuosity could be described by the ratio of velocity along the fluid flow direction to the total seepage velocity; the derived tortuosity formula satisfies the calculation accuracy. The porosity-tortuosity relationships of the cylinder, cuboid and spherome contact area equivalent bodies fit well.
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