Electrical Properties Archie’s Law

Formation Factor Equation Rock containing pores saturated with water and hydrocarbons Non-shaly rock, 100% saturated with water having resistivity, Rw Rt Cube of water having resistivity, Rw = 20% Sw = 20% Ro = 20% Sw = 100% Rw Saturation Equation = 100% Sw = 100% Resistivity Formation Factor Equation

Formation Factor The formation factor (F) depends on Porosity of the formation, Pore geometry - tortuosity Lithology of the formation Degree of cementation, and Type and amount of clay in the rock From J. Jensen, PETE 321 Lecture Notes

Formation Factor Equation Archie’s equation for formation factor is a power law model: F=R0/Rw=a·f-m 1000 Rock type 1 100 F Note: When  = 100%, Ro must equal Rw; thus, a = 1.0 (if a is constant) Ro is the resistivity of a formation 100% saturated with water. If we think about a core sample, there is only one major component that conducts electricity, and that is the water in the pore space. The magnitude of the resistivity is a function of the amount of fluid (porosity and water saturation), the resistivity of the saturating fluid, and the interconnectedness of the pore space. The graph above illustrates that there is a relationship between the formation factor and porosity. The slope of the line is a function of the pore structure (or tortuosity) which is called the cementation exponent. The cementation exponent is a measure of the degree of interconnectivity of the pore space. 10 Rock type 2 1 Note: Sw=1 .01 .1 1.0  From NExT, 1999

Formation Factor - Example Core Data From J. Jensen, PETE 321 Lecture Notes

F=a·f-m Formation Factor a = constant  1.0 for most formations m = cementation factor  2 for most formations Other commonly used values Sandstones: F = 0.8/f2 (Tixier) 0.62/f2.15 (Humble) Carbonates F = 0.8/f2 From J. Jensen, PETE 321 Lecture Notes

Saturation Equation Power Law Model IR=Rt/R0=Sw-n Each curve for a specific core sample No conductive materials (clay) present Rock type 1 Rock type 2 1000 100 10 1 .01 .1 1.0 Sw IR = Rt R0 Note: When Sw = 100%, Rt must equal Ro As we stated earlier, the resistivity of a formation is controlled by the water in the formation. It is a function of the amount of water, the resistivity of that water, and the interconnectivity of the pore space. Both porosity and water saturation control the amount of water in the pore space. When porosity is constant, the resistivity relationships are solely affected by water saturations. The figure above clearly shows that the ratio of resistivities is a strong function of water saturation where the saturation exponent is a measure of the interconnectivity of the fluids in the pore space (which is related to capillary pressure and relative permeability). Saturation exponent is related to the cementation exponent discussed in the previous slide. From NExT, 1999

Laboratory Determination of Saturation Exponent, n 100 10 1 0.1 1.0 Sw (fraction) Rt / Ro n = Slope From J. Jensen, PETE 321 Lecture Notes

R0 Appears in Both Equations when Sw = 100% when  = constant From NExT, 1999

Archie’s Equation (Combined) Empirical constant (usually near unity) a Resistivity of formation water, -m w R Water saturation, fraction w S Saturation exponent (also usually near 2) n Porosity, fraction f Cementation exponent (usually near 2) m True formation resistivity, -m t R Archie’s equation is the basic equation used by petrophysicists to determine whether a formation has water or hydrocarbons in the pore space. As you can see, the water saturation is a function of several variables: the resistivity of the water in the pore space, the total composite formation resistivity, porosity, and several other variables that are a function of the rock. From NExT, 1999

IDEALIZED LOG SET R = 4  = 0.30 R = 0.4 R = 8  = 0.07 Shale R = 0.3  = 0.35  = 0.07 R = 0.4 R = 0.3 R = 4 R = 8 Sand Shale IDEALIZED LOG SET From J. Jensen, PETE 321 Lecture Notes

Effect of Filtrate Invasion - Rnear_well  Rt (permeability present) Wellbore Mud (Rm) Mud Cake (Rmc) Transition Zone Uninvaded (Rt) Invaded Zone (Rxo) Modified from J. Jensen, PETE 321 Lecture Notes

EXAMPLE LOG WITH RESISTIVITY GRC 150 SPC MV -160 40 ACAL 6 16 ILDC 0.2 200 SNC MLLCF RHOC 1.95 2.95 CNLLC 0.45 -0.15 DT us/f 50 001) BONANZA 1 10700 10800 10900 SNC 0.2 200 MLLCF ILDC Deep Resistivity Log (ILDC), Rt From NExT, 1999

Laboratory Resistance From J. Jensen, PETE 321 Lecture Notes

Laboratory Resistivity From J. Jensen, PETE 321 Lecture Notes