Resistivity Log

(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 77843-3116

Openhole Well Log Evaluation Most abundant data for formation evaluation and determination of fluid saturations Well Log SP

Resistivity

From NExT, 1999

Idealized Well Log Set

R=4 R = 0.4

R=8

φ = 0.30

φ = 0.07

Shale

Sand

R = 0.3

φ = 0.35

Four Components of Sandstone (Schematic Diagram) Geologist’s Classification

1.Framework 2.Matrix 3.Cement 4.Pores

Engineering "matrix"

Note different use of "matrix" by geologists and engineers

PORE CEMENT

FRAMEWORK (QUARTZ)

MATRIX

FRAMEWORK (FELDSPAR)

0.25 mm

Ayers, 2001

Fluid Saturations Grain and matrix

Water Gas

Oil

z Initially, water fills pores and wets the rock surface z Hydrocarbons migrate into the reservoir rock, displacing some water z Hydrocarbon distribution determined by gravity and capillary forces, and by wettability Modified from NExT, 1999

Resistivity of Rocks Containing Fluid

Resistivity – Definition of the Ohm-Meter

From Halliburton (EL 1007)

Resistivity Resistivity zThe voltage required to cause one amp to pass through a cube having a face area of one square meter zUnits are ohm-m2/m; usually ohm-m (Ω.m)

1 Resistivit y = Conductivi ty

Resistivity Measurement z Resistivity

V 2 (ohms) A(m ) R(ohm − meters) = I L ( m)

Resistivity of Earth Materials

(1) (2) (3) (4) (5)

Rock Gas Oil Fresh Water Salt Water

Increasing Conductivity

Increasing Resistivity

1 Resistivity = Conductivity

Factors Affecting Resistivity zResistivity of water zPorosity of the formation, zPore geometry - tortuosity zLithology of the formation zDegree of cementation, and zType and amount of clay in the rock

From J. Jensen, PETE 321 Lecture Notes

Electricity And Earth Materials

z Electrical conduction is by ions in water z Na+ and Cl- are very common z Other monovalent ions: K+ and OHz Common bivalent ions: Ca++, Mg++

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

Resistivity of NaCl Solutions ____ Chart GEN-5H or GEN-9S

From Schlumberger

Chart GEN-8 TDS = 20,850 ppm

0.81 0.45 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

75 deg. F

Chart GEN-9

From Schlumberger

Arp's Formula z For constant solution – R1(T1 + 7) = R2(T2 + 7) (T in deg F) – R1(T1 + 21.5) = R2(T2 + 21.5) (T in deg C)

z Example – – – – –

Rm = 0.32 ohm-m @ surface (25 deg C/77 deg F) What is Rm at 145 deg C (293 deg F)? R2 = R1(T1 + 21.5)/(T2 + 21.5) R2 = 0.32(25+21.5)/(145+21.5) = 0.089 ohm-m Check this on the chart!

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

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

φ= 20% Sw = 20% SHC =80%

Ro R es

φ= 20% Sw = 100%

istiv ity

Rw φ= 100% Sw = 100%

Increasing Resistivity

(2) Gas (3) Oil (4) Fresh Water (5) Salt Water

Increasing Conductivity

(1) Rock

F = Ro

Rw

=

a

φm

Formation Factor The formation factor (F) depends on: zPorosity of the formation. zPore geometry. zLithology of the formation. zDegree of cementation. zType and amount of clay in the rock.

Formation Factor Correlation with Porosity z For a clean formation (no shale), the formation factor can usually be empirically correlated with porosity.

F=

a

φ

m

a = constant ≅ 1.0 (most formations). m = cementation factor ≅ 2 (most formations).

z Common values – F = 0.8/φ2 (Tixier) or 0.62/φ2.15 (Humble) for sandstones. – F = 0.8/φ2 for carbonates.

Archie Relation for Formation Factor

Formation Factor Ideal Considerations

Formation Factor Experiments with Unconsolidated and Artificially Consolidated Materials

Formation Factor Generalized Correlation (Schlumberger)

Formation Factor Type Curve Solution (Blasingame/Unpublished)

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

How Archie's Formation Factor Equation Works z Archie's equation is based on the following relationships 1000 Rock type 1

FR

100

10

1 When water saturation is 100 percent

Rock type 2

.01

φ

.1

1.0 From NExT, 1999

Saturation z Amount of water per unit volume = φ Sw z Amount of hydrocarbon per unit volume = φ (1 - Sw)

φ 1−φ

φ (1-Sw) φ Sw

Hydrocarbon

Water Matrix

Archie's Second Equation (For Saturation) z Relates Sw to Rt . z If Rt = Ro, then the formation is 100 percent saturated with formation water. However, if Rt > Ro, then the formation contains oil or gas. z General formula:

Rw a Rw n Ro Sw = =F = Rt Rt φ m Rt z For clean sands, n = 2 is common. z Like a and m, n is measured in the lab.

Archie Relation for Sw

Visualization of Rt/Ro versus Sw

Hydrocarbon Resistivity Index (I=Rt/Ro) Effects of Clay and Pyrite

Hydrocarbon Resistivity Index (I=Rt/Ro) Effects of Wettability

Hydrocarbon Resistivity Index (I=Rt/Ro)

Type Curve Solution - No Shale Case (Blasingame/Unpublished)

Hydrocarbon Resistivity Index (I=Rt/Ro) Type Curve Solution - Shale, n=1.2 (Blasingame/Unpublished)

Hydrocarbon Resistivity Index (I=Rt/Ro) Type Curve Solution - Shale, n=2.0 (Blasingame/Unpublished)

Drilling Disturbs Formation zDrilling and rock crushing „Damage Zone zMud systems and invasion „Oil-based Mud — Small conductivity mud — Shallow invasion — Thin cake

Damaged zone

Mudcake

„Water-based Mud — Moderate to very conductive mud — Shallow to deep invasion — Thin to thick cake

Invading filtrate

Effects of Drilling Mud and Mud Filtrate Invasion

Mud Filtrate Invasion

Invaded Zone (Rxo)

Uninvaded Zone (Rt)

Wellbore Mud (Rm)

Uninvaded Zone (Rt)

i on t i s an r T ne o Z

Mud Cake (Rmc)

Modified from J. Jensen, PETE 321 Lecture Notes

Resistivity of zone Resistivity of the water in the zone Water saturation in the zone Mud

Symbols used in Log Interpretation

Rm

Adjacent bed Rs

hmc Rmc dh

(Bed thickness)

Mudcake

h

Flushed zone Zone of transition or annulus Rxd

Uninvaded zone R1 Rw Sw

Rm1 Sxo Rs

di dj

Adjacent bed

(Invasion diameters) ∆rj dh Hole diameter From NExT, 1999, after Schlumberger

Common Terminology Borehole Rm: Borehole mud resistivity Rmc: Mud cake resistivity Invaded zone Rmf: Mud filtrate resistivity Rxo: Invaded zone resistivity Sxo: Invaded zone water saturation Uninvaded zone Rw: Interstitial water resistivity Rt: Uninvaded zone resistivity Sw: Uninvaded zone water saturation

Summary — Resistivity z Resistivity is a very important property z Resistivity inversely proportional to ion volumes present in water z Water resistivity depends on: „ Concentration „ Temperature „ Ion species

z Archie's First Law relates rock resistivity to Rw z Archie's Second Law relates Sw to Rt

(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 77843-3116