Resistivity of material is an intrinsic property of material which measures how strongly that material opposes the flow of electric current.Its unit is Ohm-meter.
The potential difference V between two ends of wire of length L,cross section area A and supplied by electric current I is given as :-
V= I*r …………………………..eq 1
Where r is resistance of wire ,which is constant for that wire,unit of r is ohms,Unit of potential difference V is volts and unit of electric current I is ampere
Resistance offered by wire is directly proportional to length of wire and inversely proportional to cross sectional area A.
r a L/A ………………………….eq 2
In the above equation constant of proportionality is resistivity R ,hence equation 2 can written as:-
r = R (L/A) …………………………eq 3
Resistivity is a physical property of material ,its value is constant for same material at same temperature.
Re-arranging equation 3 we get:-
R = r (A/L)
As A is cross-section area with unit in meter2 , L is length with unit in meter and r is resistance in ohms,unit of resistivity R comes out as Ohm- m2 /m or Ohm-m.
Reciprocal of resistance is conductance and reciprocal of resistivity is conductivity.
Unit of conductivity as used in logging for practical reasons is mili mho / meter
Applications of resistivity log:-
1.Water Saturation:- Resistivity is important input for water saturation estimation.Archie equation provides relation for resistivity based water saturation calculation as below:-
Sw = [ (a* Rw)/(qm *Rt)]1/n
Sw = Water Saturation
a = Cementation factor
Rw = Formation Water resistivity
q = Porosity
m = Cementation exponent
Rt = True formation resistivity
n = Saturation exponent
As we can see in above equation true formation resistivity and formation water resistivity are important input for water saturation calculation and resistivity tools help us in getting it.
There are certain assumptions associated with Archie equation as given below :-
1a. Only water in pores acts as electrical conductor,matrix and hydrocarbon acts as insulator.
1b. There is no shale in sands.As most of the reservoirs around the world have shales in matrix so several shaly sand equations are developed such as Indonesian equation,Simandoux equation,Waxman-smits and Dual-water.Most of these equations are modified form of archie equation.
1c. Diameter of invasion:- Diameter of mud filtrate invasion is determined during resistivity environmental correction during determination of true resistivity.Tornado chart is used for determination of true resistivity and diameter of invasion.
2.Well to well Correlation:- Doing well to well correlation using resisistivity curves has distinct advantage as correlation of resistivity is correlation of fluid volume and salinity in formation.
3.Pore pressure estimation:- Resistivity can also be used for pore pressure estimation as per below equation:-
Pp = Phyd Rn / Rlog