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Electrical Properties Archie’s Law

Electrical Properties Archie’s Law. Rock containing pores saturated with water and hydrocarbons. Non-shaly rock, 100% saturated with water having resistivity, R w. R t. Cube of water having resistivity, R w. = 20% S w = 20%. R o. = 20% S w = 100%. R w. Saturation Equation.

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Electrical Properties Archie’s Law

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  1. Electrical Properties Archie’s Law

  2. 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

  3. 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

  4. F  Formation Factor Equation • Archie’s equation for formation factor is a power law model: F=a·f-m 1000 Rock type 1 100 10 Rock type 2 1 Note: Sw=1 .01 .1 1.0 From NExT, 1999

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

  6. Formation Factor • F=a·f-m 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

  7. 1000 Rock type 1 100 Rock type 2 10 1 .01 .1 1.0 Rt R0 IR = Sw Saturation Equation • Power Law Model IR=Rt/R0=Sw-n • Each curve for a specific core sample • Neglects effects of conductive materials (clay) From NExT, 1999

  8. 100 n = Slope Log Rt / Ro 10 1 100 10 Log Sw (%) LAB EVALUATION OF N From J. Jensen, PETE 321 Lecture Notes

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

  10. Empirical constant (usually near unity) a R Resistivity of formation water, -m w S w n f m Cementation exponent (usually near 2) Water saturation, fraction R t Saturation exponent (also usually near 2) True formation resistivity, -m Porosity, fraction Archie’s Equation (Combined) From NExT, 1999

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

  12. Mudcake Damaged zone Invading filtrate DRILLING DISTURBS FORMATION • Drilling and rock crushing • Damage zone • Mud systems and invasion • Oil Base Mud • Small conductivity mud • Shallow invasion • Thin cake • Water Base Mud • Moderate to very conductive mud • Shallow to deep invasion • Thin to thick cake From J. Jensen, PETE 321 Lecture Notes

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

  14. 001) BONANZA 1 GRC ILDC RHOC DT 0 150 0.2 200 1.95 2.95 150 us/f 50 SPC SNC CNLLC ILDC -160 MV 40 0.2 200 0.45 -0.15 ACAL MLLCF 0.2 200 6 16 0.2 200 10700 SNC 0.2 200 MLLCF 0.2 200 10800 10900 Resistivity Log EXAMPLE LOG WITH RESISTIVITY From NExT, 1999

  15. Laboratory Resistance From J. Jensen, PETE 321 Lecture Notes

  16. Laboratory Resistivity • Resistivity From J. Jensen, PETE 321 Lecture Notes

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