(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. JensenW.B. Ayers

T.A. BlasingameDepartment of Petroleum Engineering

Texas A&M UniversityCollege Station, TX 77843-3116

Well LogSP Resistivity

Openhole Well Log Evaluation

From NExT, 1999

Most abundant data for formation evaluation anddetermination of fluid saturations

Idealized Well Log Set

φ = 0.30

φ = 0.35

φ = 0.07

R = 0.4

R = 0.3

R = 4

R = 8

Sand

Shale

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

MATRIXFRAMEWORK(QUARTZ)

FRAMEWORK(FELDSPAR)

CEMENT

PORE

Note different use of "matrix"by geologists and engineers

0.25 mm

1.Framework2.Matrix3.Cement4.Pores

Engineering"matrix"

Ayers, 2001

Fluid SaturationsGrain Water Gas Oil

Initially, water fills pores and wets the rock surfaceHydrocarbons migrate into the reservoir rock, displacing some waterHydrocarbon distribution determined by gravity and capillary forces,and by wettability

Modified from NExT, 1999

and matrix

Resistivity of Rocks Containing Fluid

Resistivity – Definition of the Ohm-Meter

From Halliburton (EL 1007)

Resistivity

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

tyConductivi1yResistivit =

Resistivity Measurement

Resistivity

)(

)()()(

2

mL

mAohmsIV

metersohmR =−

Resistivity of Earth Materials

tyConductivi1yResistivit =

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

IncreasingC

onductivity

Incr

easi

ngR

esis

tivity

Factors Affecting Resistivity

Resistivity of waterPorosity of the formation,Pore geometry - tortuosityLithology of the formationDegree of cementation, andType and amount of clay in the rock

From J. Jensen, PETE 321 Lecture Notes

Electricity And Earth Materials

Electrical conduction is by ions in waterNa+ and Cl- are very commonOther monovalent ions: K+ and OH-

Common bivalent ions: Ca++, Mg++

Resistivity Multipliers for Various Materials

Water resistivity controlled by:

Ion concentrations.Type of ions.Temperature.

Chart GEN-4 to convert to NaCl equivalent.Chart GEN-5 for temperature/resist for NaCl.

From Schlumberger

Resistivity of NaCl

Solutions____

ChartGEN-5H

orGEN-9S

From Schlumberger

Ca = 460 ppmS04 = 1,400

Na + Cl = 19,000TDS = 20,860

TDS = 20,850 ppm

0.81

0.45

(460)(0.81)+(1,400)(0.45)+(1)(19,000) = 20,000 ppm

T = 75 deg. F

Chart GEN-8

From Schlumberger

75 deg. F

Chart GEN-9

From Schlumberger

Arp's Formula

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)

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)Relates rock resistivity to RwRo = F RwRo = Resistivity of a rock that is 100%

saturated with formation water, Ω-mRw = Resistivity of formation water, Ω-mF = 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 satu-rated with salt water.As the shale content increases, the rock matrix will become more conductive.

Rock containing pores saturatedwith water and hydrocarbons

Rt

Ro

RwResistivity

Non-shaly rock, 100% saturatedwith water having resistivity, Rw

Cube of waterhaving resistivity, Rw

Incr

easi

ngR

esis

tivity

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

IncreasingC

onductivity

φ= 100%Sw = 100%

φ= 20%Sw = 100%

φ= 20%Sw = 20%SHC =80%

mwo aR

RFφ

==

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.

Formation Factor Correlation with PorosityFor 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 = 0.8/φ2 (Tixier) or 0.62/φ2.15 (Humble) for sandstones.– F = 0.8/φ2 for carbonates.

m

aFφ

=

Archie Relation for Formation Factor

Formation FactorIdeal Considerations

Formation Factor Experiments with Unconsolidated

and Artificially Consolidated Materials

Formation Factor Generalized Correlation (Schlumberger)

Formation Factor Type Curve Solution (Blasingame/Unpublished)

Formation FactorEffect of Clay/Shale

The formation factor (F) is constant for a clean sand; F decreases for shaly sand as value of Rwincreases.

How Archie's Formation Factor Equation Works

Archie's equation is based on the follow-ing relationships

Rock type 1

Rock type 2

1000

100

10

1.01 .1 1.0

φ

F R

When water saturation is 100 percent From NExT, 1999

Saturation

Amount of water per unit volume = φ Sw

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

φ

Matrix1 − φ

WaterHydrocarbonφ (1-Sw)

φ Sw

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

tw

mtw

ton

w RRa

RR

FRR

Sφ

===

For clean sands, n = 2 is common.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

Drilling and rock crushingDamage Zone

Mud systems and invasionOil-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

Mudcake

Invading filtrate

Damaged zone

Effects of Drilling Mud and Mud Filtrate Invasion

Mud Filtrate Invasion

WellboreMud(Rm)

Mud Cake(Rmc)Transitio

n

Zone

Uninvaded Zone(Rt)

Invaded Zone (Rxo)

Uninvaded Zone(Rt)

Modified from J. Jensen, PETE 321 Lecture Notes

Resistivity of zoneResistivity of the water in the zoneWater saturation in the zone

R1

Rs

Rs

Rw

Sw

Rm

Mud

hmc Flushedzone Zone of

transitionor

annulus

didj Adjacent bed

∆rj

dhHole

diameter

Adjacent bed

h

dh

Uninvadedzone

(Bedthickness)

(Invasion diameters)

Sxo

Rm1

Rxd

Rmc

Mudcake

From NExT, 1999, after Schlumberger

Symbols usedin Log

Interpretation

Common Terminology

BoreholeRm: Borehole mud resistivityRmc: Mud cake resistivity

Invaded zoneRmf: Mud filtrate resistivityRxo: Invaded zone resistivitySxo: Invaded zone water saturation

Uninvaded zoneRw: Interstitial water resistivityRt: Uninvaded zone resistivitySw: Uninvaded zone water saturation

Summary — Resistivity

Resistivity is a very important propertyResistivity inversely proportional to ion volumes present in waterWater resistivity depends on:

ConcentrationTemperatureIon species

Archie's First Law relates rock resistivity to RwArchie'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. JensenW.B. Ayers

T.A. BlasingameDepartment of Petroleum Engineering

Texas A&M UniversityCollege Station, TX 77843-3116