Module for: Resistivity Theory (adapted/modified from lectures in PETE 321 (Jensen/Ayers))

Transcription

1 (PETE 663 Formation Evaluation and the Analysis of Reservoir Performance (Fall 2003)) Module for: Resistivity Theory (adapted/modified from lectures in PETE 321 (Jensen/Ayers)) J. L. Jensen W.B. Ayers T.A. Blasingame Department of Petroleum Engineering Texas A&M University College Station, TX

2 From NExT, 1999 Openhole Well Log Evaluation Most abundant data for formation evaluation and determination of fluid saturations SP Well Log Resistivity

3 Idealized Well Log Set R = 4 R = 0.4 φ = 0.30 R = 8 φ = 0.07 Shale Sand R = 0.3 φ = 0.35

4 Four Components of Sandstone (Schematic Diagram) Geologist s Classification 1.Framework 2.Matrix 3.Cement 4.Pores PORE CEMENT Engineering "matrix" FRAMEWORK (QUARTZ) Note different use of "matrix" by geologists and engineers MATRIX FRAMEWORK (FELDSPAR) 0.25 mm Ayers, 2001

5 Fluid Saturations Grain Water Gas Oil and matrix Initially, water fills pores and wets the rock surface Hydrocarbons migrate into the reservoir rock, displacing some water Hydrocarbon distribution determined by gravity and capillary forces, and by wettability Modified from NExT, 1999

6 Resistivity of Rocks Containing Fluid

7 Resistivity Definition of the Ohm-Meter From Halliburton (EL 1007)

8 Resistivity Resistivity The voltage required to cause one amp to pass through a cube having a face area of one square meter Units are ohm-m 2 /m; usually ohm-m (Ω.m) Resistivit y = 1 Conductivi ty

9 Resistivity Measurement Resistivity R ( ohm meters) = V I ( ohms) A( m L( m) 2 )

10 Resistivity of Earth Materials Resistivit y = 1 Conductivity Increasing Resistivity (1) Rock (2) Gas (3) Oil (4) Fresh Water (5) Salt Water Increasing Conductivity

11 Factors Affecting Resistivity Resistivity of water 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

12 Electricity And Earth Materials Electrical conduction is by ions in water Na + and Cl - are very common Other monovalent ions: K + and OH - Common bivalent ions: Ca ++, Mg ++

13 Resistivity Multipliers for Various Materials z Water resistivity controlled by: Ion concentrations. Type of ions. Temperature. z Chart GEN-4 to convert to NaCl equivalent. z Chart GEN-5 for temperature/resist for NaCl. From Schlumberger

14 Resistivity of NaCl Solutions Chart GEN-5H or GEN-9S From Schlumberger

15 Chart GEN-8 TDS = 20,850 ppm Ca = 460 ppm S04 = 1,400 Na + Cl = 19,000 TDS = 20,860 (460)(0.81)+(1,400)(0.45)+(1)(19,000) = 20,000 ppm T = 75 deg. F From Schlumberger

16 75 deg. F Chart GEN-9 From Schlumberger

17 Arp's Formula For constant solution R 1 (T 1 + 7) = R 2 (T 2 + 7) (T in deg F) R 1 (T ) = R 2 (T ) (T in deg C) Example Rm = 0.32 surface (25 deg C/77 deg F) What is Rm at 145 deg C (293 deg F)? R 2 = R 1 (T )/(T ) R 2 = 0.32( )/( ) = ohm-m Check this on the chart!

18 Archie's First Equation (for Porosity) Relates rock resistivity to Rw R o = F R w R o = Resistivity of a rock that is 100% saturated with formation water, Ω-m R w = Resistivity of formation water, Ω-m F = Formation factor As the salt water content increases, the formation resistivity will decrease. A rock containing oil or gas will have a higher resistivity than the same rock completely saturated with salt water. As the shale content increases, the rock matrix will become more conductive.

19 Rock containing pores saturated with water and hydrocarbons Non-shaly rock, 100% saturated with water having resistivity, R w R t φ= 20% Sw = 20% SHC =80% R o φ= 20% Sw = 100% Cube of water having resistivity, R w Resistivity R w Increasing Resistivity (1) Rock (2) Gas (3) Oil (4) Fresh Water (5) Salt Water Increasing Conductivity F = R o R w = a φ m φ= 100% Sw = 100%

20 Formation Factor The formation factor (F) depends on: Porosity of the formation. Pore geometry. Lithology of the formation. Degree of cementation. Type and amount of clay in the rock.

21 Formation Factor Correlation with Porosity For a clean formation (no shale), the formation factor can usually be empirically correlated with porosity. a = constant 1.0 (most formations). m = cementation factor 2 (most formations). Common values F = φ F = 0.8/φ 2 (Tixier) or 0.62/φ 2.15 (Humble) for sandstones. F = 0.8/φ 2 for carbonates. a m

22 Archie Relation for Formation Factor

23 Formation Factor Ideal Considerations

24 Formation Factor Experiments with Unconsolidated and Artificially Consolidated Materials

25 Formation Factor Generalized Correlation (Schlumberger)

26 Formation Factor Type Curve Solution (Blasingame/Unpublished)

27 Formation Factor Effect of Clay/Shale The formation factor (F) is constant for a clean sand; F decreases for shaly sand as value of R w increases.

28 How Archie's Formation Factor Equation Works Archie's equation is based on the following relationships 1000 Rock type F R 10 Rock type When water saturation is 100 percent From NExT, 1999 φ

29 Saturation Amount of water per unit volume = φ S w Amount of hydrocarbon per unit volume = φ (1 - S w ) φ 1 φ φ (1-S w ) φ S w Hydrocarbon Water Matrix

30 Archie's Second Equation (For Saturation) Relates S w to R t. If R t = R o, then the formation is 100 percent saturated with formation water. However, if R t > R o, then the formation contains oil or gas. General formula: S n w = R R o t = F R R w t = φ a m R R w t For clean sands, n = 2 is common. Like a and m, n is measured in the lab.

31 Archie Relation for Sw

32 Visualization of Rt/Ro versus Sw

33 Hydrocarbon Resistivity Index (I=R t /R o ) Effects of Clay and Pyrite

34 Hydrocarbon Resistivity Index (I=R t /R o ) Effects of Wettability

35 Hydrocarbon Resistivity Index (I=R t /R o ) Type Curve Solution - No Shale Case (Blasingame/Unpublished)

36 Hydrocarbon Resistivity Index (I=R t /R o ) Type Curve Solution - Shale, n=1.2 (Blasingame/Unpublished)

37 Hydrocarbon Resistivity Index (I=R t /R o ) Type Curve Solution - Shale, n=2.0 (Blasingame/Unpublished)

38 Drilling Disturbs Formation Drilling and rock crushing Damage Zone Mud systems and invasion Oil-based Mud Small conductivity mud Shallow invasion Thin cake Water-based Mud Moderate to very conductive mud Shallow to deep invasion Thin to thick cake Damaged zone Mudcake Invading filtrate

39 Effects of Drilling Mud and Mud Filtrate Invasion

40 Mud Filtrate Invasion Invaded Zone (R xo ) Uninvaded Zone (R t ) Uninvaded Zone (R t ) Transition Zone Wellbore Mud (Rm) Mud Cake (Rmc) Modified from J. Jensen, PETE 321 Lecture Notes

41 Resistivity of zone Resistivity of the water in the zone Water saturation in the zone Symbols used in Log Interpretation (Bed thickness) R mc Mud R m h mc d h Mudcake Flushed zone R xd Zone of transition or annulus Adjacent bed R s Uninvaded zone R 1 R w S w h R m1 S xo R s d i d j Adjacent bed (Invasion diameters) r j d h Hole diameter From NExT, 1999, after Schlumberger

42 Common Terminology Borehole R m : Borehole mud resistivity R mc : Mud cake resistivity Invaded zone R mf : Mud filtrate resistivity R xo : Invaded zone resistivity S xo : Invaded zone water saturation Uninvaded zone R w : Interstitial water resistivity R t : Uninvaded zone resistivity S w : Uninvaded zone water saturation

43 Summary Resistivity Resistivity is a very important property Resistivity inversely proportional to ion volumes present in water Water resistivity depends on: Concentration Temperature Ion species Archie's First Law relates rock resistivity to R w Archie's Second Law relates S w to R t

44 (PETE 663 Formation Evaluation and the Analysis of Reservoir Performance (Fall 2003)) Module for: Resistivity Theory (adapted/modified from lectures in PETE 321 (Jensen/Ayers)) End of Presentation J. L. Jensen W.B. Ayers T.A. Blasingame Department of Petroleum Engineering Texas A&M University College Station, TX