  In this article we investigate the electrical conductance of an insulating
porous medium (e.g., a sedimentary rock) filled with an electrolyte (e.g.,
brine), usually described using the Archie cementation exponent. We show how
the electrical conductance depends on changes in the drift velocity and the
length of the electric field lines, in addition to the porosity and the
conductance of the electrolyte. We characterized the length of the electric
field lines by a tortuosity and the changes in drift velocity by a constriction
factor. Both the tortuosity and the constriction factor are descriptors of the
pore microstructure. We define a conductance reduction factor to measure the
local contributions of the pore microstructure to the global conductance. It is
shown that the global conductance reduction factor is the product of the
tortuosity squared divided by the constriction factor, thereby proving that the
combined effect of tortuosity and constriction, in addition to the porosity and
conductance of the electrolyte, fully describes the effective electrical
conductance of a porous medium. We show that our tortuosity, constriction
factor, and conductance reduction factor reproduce the electrical conductance
for idealized porous media. They are also applied to Bentheimer sandstone,
where we describe a microstructure-related correlation between porosity and
conductivity using both the global conductance reduction factor and the
distinct contributions from tortuosity and constriction. Overall, this work
shows how the empirical Archie cementation exponent can be substituted by more
descriptive, physical parameters, either by the global conductance reduction
factor or by tortuosity and constriction.
