what is archie equ and why it is important?how we use it?sir i need complete understanding of this equation
Thank you so much for putting an interesting question. Infact Archie is the basis for all the modern Petrophysics.
In 1942 Archie gave his classical empirical formula which set the basis of petrophysics. At that time only clean formations were assumed to be HC bearing and there were no concepts of shaly sand, thin beds and unconventional reservoirs. Obviously petrophysics went from simple to complicated reservoirs.
Archie took clean clastic core plugs from the producing horizons of Gulf Cost in his experiments. He measured the samples porosity, permeability and electrical resistivity saturating them with brines of varying salinity from 20 to 100,000 ppm Nacl. He noted that the resistivity of each brine saturated rock sample, Ro, increased linearly with brine resistivity, Rw. He called the proportionality constant the rock's formation factor F, and wrote
Ro = F*Rw
He then plotted formation factor against porosity, on double logarithmic graph paper, finding another linear trend, which is
F = 1/Phi ^ m
Archie next considered partially saturated, hydrocarbon-bearing rock. He proposed a second factor, later called the resistivity index, I, to further raise the rock's resistivity.
Rt = IRo
Forgoing the enormous difficulties of experimenting with partially saturated rock, he combed the literature for already reported data and plotted them again using double logarithmic graph paper, Archie noted
I = 1/ Sw^n
In which Sw is water saturation, and n, later called the saturation exponent, appeared about 2. Combining the two double logarithmic trends gives Archie's law
Rt = Rw/ Phi^m * Sw^n
Since 1942, petrophysicists have measured the electrical resistivity of just about every conceivable type of porous rock, igneous and metamorphic rock and found that Archie’s law satisfactorily describes their experimental data.
We use it to get the Sw of the clean formations, we usually get the Phi, Rt and Rw data from the wireline logs and electrical properties (a,m,n) from core data. Picket plot gives us good relation of Rw, m and n.
Hope it helps