Отправлено: 31.07.15 08:05. Заголовок: The effect of a variable pore radius on formation resistivity factor

The effect of a variable pore radius on formation resistivity factor
Edith Mьller-Huber, Jьrgen Schцn b, Frank Bцrner

Journal of Applied Geophysics 116 (2015) 173–179


Formation resistivity factor Fwas introduced as the ratio of the resistivity of a rock fully saturated with conductive
water to the resistivity of the conductive water based on results of laboratory measurements. It was also found
that the formation factor is a function of the type and character of a formation and is related to porosity by a relationship
including an exponentm. For model calculations of the formation factor, capillary channel models describing
a straight tube with a constant circular cross-sectional area are frequently used. However, the pore
channel radius is not constant in natural rocks.
Amodified capillarymodel that describes a straight pore channel with a radius varying between its two extreme
values rt (pore throat) and rb (pore body) is presented. The proposed model can therefore explain the effect of
pore shape upon formation factor and porosity. In this case, exponent m is controlled by the porosity itself and
the ratio rb/rt. Different rock types have a specific position in a plot of formation factor versus porosity including
a forward calculated grid for varying ratio rb/rt. Sand and gravel are characterized by low ratios rb/rt of 2.5 to 4.5,
while sandstones possess intermediate rb/rt of 5.0 to 20.0. Carbonates show the greatest variability with ratios of
1.0 to 40.0.
This newapproach can be used to derive the ratio rb/rt from a determination of porosity and formation factor and
thus enhances the understanding of pore space geometries in different formation types, which is also of importance
for hydraulic conductivity.