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(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