The permeability anisotropy is related to the electric resistivity anisotropy and the pore throat cross-section anisotropy as, (equation), where the subscript H and V indicate the conduction in the horizontal and vertical direction, respectively. RH and RV are the horizontal resistivity and vertical resistivity of brine filled rock formation. FH and FV are the formation factor measured in the horizontal and vertical directions. Similarly, (equation) and (equation) are the average pore throat cross-sections to the horizontal and vertical conductions, respectively.
The permeability anisotropy is an important parameter in evaluating reservoir performance. The above relation will help to identify permeability-anisotropic formation from the electrical anisotropy measurements. If the formation is electrically anisotropic and RV≠RH (FV≠FH) when it is wet, then the formation is also permeability-anisotropic and KV≠KH. By examining the macroscopic anisotropy of the permeability and electric conductivity in thinly laminated formations, we show that the KH/KV is bound by the RV/RH of the wet formation: KH _ (equation) On the other hand, the permeability is anisotropic even if the formation is electrically isotropic and RV=RH (FV=FH) when it is wet: (equation)
To estimate the permeability anisotropy, the pore throat cross-section anisotropy (equation), has to be known. Although the (equation) and hence, (equation), can be measured petrographically when proper core samples are available, these are generally unknown. When the cores are not available, they may be estimated from pore size distribution measurements using NMR log data.
Sealing sands in some reservoirs may be interpreted as an example of laminated anisotropic rocks. The permeability-resistivity relation may be used to identify such sealing sands from log measurement of resistivity anisotropy.
The relation between permeability (flow conductivity) and electric conductivity has been known if the electric conduction through the rock surface is ignored or negligible (Purcell, 1949). The relation relates the permeability k to the formation factor F as,