Semi-empirical equations for the systematic decrease in permeability with depth in porous and fractured media

Permeability loss with depth is a general trend in geological media and plays an essential role in subsurface fluid flow and solute transport. In the near surface zone where groundwater movement is active, the decrease in permeability with depth is dominated by the mechanical compaction of deformable media caused by the increase in lithostatic stress with depth. Instead of using empirical equations from statistical analysis, by considering the well-defined relationships among permeability, porosity, fracture aperture and effective stress under lithostatic conditions, new semi-empirical equations for the systematic depth-dependent permeability are derived, as well as the equations for the depth-dependent porosity in a porous medium and the depth-dependent fracture aperture in a fractured medium. The existing empirical equations can be included in the new equations as special cases under some simplification. These new semi-empirical equations perform better than previous equations to interpret the depth-dependent permeability of the Pierre Shale (with a maximum depth of approximately 4,500 m) and the granite at Stripa, Sweden (with a maximum depth of about 2,500 m).