(PETE 663 — Formation Evaluation Evaluation and the Analysis Analysis of Reservoir 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
Open Openho hole le Well Well Log Log Eva Evalu luat atio ion n Most abundant data for formation evaluation and determination of fluid saturations Well Log SP
Resistivity
Idealized Well Log Set
R=4 = 0.30 R = 0.4
R=8
= 0.07
Shale
Sand
R = 0.3
= 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
Fluid Saturations Grain and matrix
Water Gas
Oil
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
Resi Resist stiv ivit ity y of Rock Rocks s Contai Containin ning g Fluid Fluid
Resi Resist stiv ivit ity y – Defi Defini niti tion on of of the the Ohm Ohm-M -Me eter ter
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 ( .m)
Resistivit y
1 Conductivi ty
Resi Resist stiv ivit ity y Meas Measur urem emen entt
Resistivity V R(ohm − meters)
=
I
2
(ohms) A( m ) L( m)
Resi Resist stiv ivit ity y of Eart Earth h Mat Mater eria ials ls Resistivity
1 Conductivity
(1) Rock (2) Gas y g t i n i v s i a t s e i r s c e n R I
(3) Oil (4) Fresh Water (5) Salt Water
C o n d u c t i v i t y
I n c r e a s i n g
Factors Affecting Resistivity
Resistivity of water
Porosity of the formation,
Pore Pore geo geome metr try y - tort tortuo uosi sity ty
Lithology of the formation
Degree of cementation, and
Type and amount of clay in the rock
From J. Jensen, PETE 321 Lecture Notes
Electricity And Earth Materials
Electrical conduction is by ions in water
Na+ and Cl- are very common
Othe Otherr mon monov oval alen entt ions ions:: K+ and OH-
Common bivalent ions: Ca++, Mg++
Resisti Resistivity vity Multipli Multipliers ers for Various Various Material Materials s
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 ____ 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
75 deg. F
Chart GEN-9
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 0.32 ohm-m ohm-m @ surface surface (25 (25 deg C/77 deg F) – What What is Rm Rm at 145 145 deg deg C (293 (293 deg F)? 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!
Arch Archie ie's 's Firs Firstt Equat Equatio ion n (for Por Poros osit ity) y)
Relates rock resistivity to Rw R o = F R w R o = Resi Resist stiv ivit ity y of a roc rock k tha thatt is is 100 100% % saturated with formation water, -m R w = Resi Resist stiv ivit ity y of of for forma mati tion on water ater,, -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.
Rock containing pores saturated with water water and hydrocarb hydrocarbons ons Non-shaly rock, 100% saturated with water having resistivity, R w
R t
Cube of water having resistivity, R w
φ= 20% Sw = 20% SHC =80%
R o φ= 20% Sw = 100%
R e s si i s st t i i v i i t v t y
R w φ= 100% Sw = 100%
y g t i n i v s i a t s e i r s c e n R I
(1) Rock (2) Gas (3) Oil (4) Fresh Water (5) Salt Water
C o n d u c t i v i t y
I n c r e a s i n g
F = Ro
Rw
=
a
φ m
Formation Factor The The form format atio ion n fact factor or (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 Porosity
For a clean clean formation formation (no shale), shale), the the formati formation on factor can usually be empirically correlated with porosity.
F
=
a
m
φ
a
= constant
1.0 (most formations).
m
= cementation fa factor 2 (most formations).
Common values – F = F = 0.8/ – F = F = 0.8/
2
(Tixier) or 0.62/ 2 for carbonates.
2.15
(Humble) for sandstones.
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) (Blasingame/Unpublished)
Formation Factor Effect of Clay/Shale
The formation factor (F (F ) is constant for a clean sand; F decreases F decreases for shaly sand as value of R of R w increases.
How Archie's Formation Factor Equation Works
Archie's equation is based on the following ing rela relati tion onsh ship ips s 1000 Rock type 1 100 R
F
10
Rock type 2
1 .01
.1
1.0
Saturation
Amount of water per unit volume =
Amount of hydrocarbon per unit volume =
(1-Sw) Sw
S w
Hydrocarbon
Water Matrix
(1 - S w )
Archie Archie's 's Second Second Equati Equation on (For Satur Saturati ation) on)
Relates S w to R t .
If R If R t = R o, then the formation is 100 percent saturated with formation water. However, if R if R t > R o, then the formation contains oil or gas.
General formula: n S w
=
Ro Rt
= F
Rw Rt
=
a Rw m R φ t
For clean sands, n = 2 is common. Like a and m, n is measured in the lab.
Archie Relation for S for S w
Visualization of R of R /R / t R o versus S w
Hydr Hydroc ocar arbon bon Resi Resist stiv ivit ity y Inde Index x (I (I =R /R / t R o) Effects of Clay and Pyrite
Hydr Hydroc ocar arbo bon n Res Resis istiv tivity ity Inde Index x (I (I =R /R / t R o) Effects of Wettability
Hydr Hydroc ocar arbon bon Resi Resist stiv ivit ity y Inde Index x (I (I =R /R / t R o)
Type Curve Curve Solution Solution - No Shale Case Case (Blasingam (Blasingame/Unp e/Unpublish ublished) ed)
Hydr Hydroc ocar arbon bon Resi Resist stiv ivit ity y Inde Index x (I (I =R /R / t R o) Type Type Curve Curve Solutio Solution n - Shale, Shale, n=1.2 (Blasingame/Unpublished)
Hydr Hydroc ocar arbon bon Resi Resist stiv ivit ity y Inde Index x (I (I =R /R / t R o) Type Type Curve Curve Solutio Solution n - Shale, Shale, n=2.0 (Blasingame/Unpublished)
Drilling Disturbs Formation Drilling and rock crushing
Damage Zone
Mud systems and invasion
Oil-based Mud
— Small conductivity mud
Mudcake Damaged zone
— Shallow invasion — Thin cake
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 Uninvaded Zone (Rt) Invaded Zone (Rxo)
Wellbore Mud (Rm)
Uninvaded Zone (Rt)
o n i i o t i n s a T r n e o Z
Mud Cake (Rmc)
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 R w Sw
R m1 Sxo
Rs
di d j
Adjacent bed
(Invasion diameters) ∆r j
dh Hole diameter From NExT, 1999, after Schlumberger
Common Terminology Borehole R m: Borehole mud resistivity R mc : Mud Mud cak cake e res resis isti tivi vity ty Invaded zone R mf : Mud Mud filt filtra rate te resi resist stiv ivit ity y R xo: Inva Invade ded d zon zone e res resiistiv stivit ity y S xo: Inva Invade ded d zon zone e wat water er sat satur urat atio ion n Unin Uninv vaded aded zone zone R w :
Inte Inters rsti titi tial al water ater resi resis stivi tivity ty R t : Uninvaded zone resistivity S w : Uninvaded zone water sa saturation
Summ Summar ary y — Res Resisti istivi vity ty Resistivity is a very important property Resist Resistivit ivity y inver inversel sely y propor proportio tional nal to ion volumes present in water Water resistivity depends on:
Concentration Temperature Ion species
Archie's Archie's First Law relates relates rock rock resistivity resistivity to R w Archie's e's Second Second Law relate relates s S w to R t Archi
(PETE 663 — Formation Evaluation Evaluation and the Analysis Analysis of Reservoir 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
