Static spontaneous potential. The maximum SP that would be recorded when the SP electrode passes from a position well inside a very thick, porous, permeable clean sand (or other reservoir rock) to a point well within a thick shale. The static spontaneous potential given by the sum of the components of the electrochemical potential is:
;#; SSP = –K log10 (aw / amf) , ;#;
where
and aw and amf are the activities of the formation water and mud filtrate, respectively. Because of the inverse relationship between activity and equivalent resistivity in dilute solutions, this equation is approximated by
SSP = –K log10 (Rmfe / Rwe)
where Rmfe and Rwe are the equivalent resistivities of mud filtrate and formation water, respectively. For NaCI solutions which are not too saline, Rmfe = Rmf and Rwe = Rw; for more concentrated solutions, an activity correction should be made. Since the static SP in a sandstone is equal to the potential causing current (I) to flow in a mud column of resistance (Rm), shale of resistance (Rsh), and a sandstone of resistance (Rss), then
SSP = IRm + IRsh + IRss
where the measured SP is IRm.