Electrical Petrophysics lecture

8/18/2019 Electrical Petrophysics lecture

1/40

Electrical Petrophysics

PETE 3036

Well Logging

Fall 2015


2/40

Objectives1. To understand and quantify the phenomenon of electrical

conduction in porous and permeable rocks,

2. To understand the influence of (a) porosity, (b) connate water

salinity and temperature, (c) grain sorting and cementation, (d)

partial hydrocarbon saturation, (e) wettability, and (f) clay

concentration, on the effective electrical resistivity of rocks,3. To introduce the concepts of formation factor and electrical

resistivity index,

4. To understand the petrophysical limitations of Archie’s

equations,

5. To introduce methods to calculate the electrical resistivity of

connate water, and

6. To perform basic exercises on the calculation of hydrocarbon

saturation.


3/40

Reading Material

Chapter 6 and Chapter 11, Openhole logAnalysis and formation evaluation, byBateman

Chapter 1, Electrical Resistivity of Rocks, pp 1-24 of the book Theory, Measurement, and

Interpretation of Well Logs by Z. Bassiouni,Z.,1994, SPE Textbook Series Vol. 4,Richardson, Texas.


4/40

How is the ELECTRICAL RESISTIVITY of this

rock related to porosity and hydrocarbon

saturation?

EXAMPLE: Fontainebleu Sandstone


5/40

How is the ELECTRICAL RESISTIVITY of this

rock related to porosity and hydrocarbon

saturation?

Large quartz grains

showing quartz-filled

fractures and

porosity filling quartz

(SEM-CL image).


6/40


7/40


8/40


9/40


10/40

ELECTRICAL CONDUCTIVITY AND RESISTIVITY


11/40

ELECTRICAL RESISTIVITY OF ROCK

CONSTITUENTS


12/40


13/40

Electrical Resistivity of Non-NaCl


14/40


15/40


16/40


17/40


18/40


19/40


20/40


21/40


22/40

ELECTRICAL RESISTIVITY OF ROCKS:

MAIN TENDENCIES


23/40


24/40


25/40

Comparison of R w and R o

Let’s consider a cylinder of water with the samevolume as the water volume in the core.

Vp = A L = Ae Le

Ae = A L / Le

rw = Rw Le / Ae = Rw Le2 / ( A L )

To make a comparison, let’s set rw equal to ro.

(In other words, the combination of Le and Aefor the cylinder of water that yields the same

electrical resistance as the water filled core.


26/40

ro = Ro L / A

Recall for the core:

rw = Rw Le2 / ( A L )

And for the water:

R o

= F R w

Comparison of R w and R o (cont.)

Let’s define:

12

L

L R R e

W O

)/(/ 2

L A L R A L ReW O

1

2

L

L F e


27/40

R o = F R w

F is know as the formation resistivity factor:

Comparison of R w and R o (cont.)

Let: Le / L = (Known as tortuosity)

1

2

L

L F e

2 F


28/40

ARCHIE’S “Clean Sand” Equation


29/40


30/40


31/40


32/40

Generalized Formation Resistivity

Relationships• Sandstones

– Humble: F = 0.62 -2.15

–

Simplified Humble: F = 0.81 -2

– Phillips’: F = 1.45 -1.54

– Chevron: F = 1.13 -1.73

• Carbonates

– Caruthers (1968): F = -2

– Shell: F = -1.87+0.019/

Most commonly used


33/40


34/40


35/40


36/40


37/40


38/40

“m” and “n”

• m = cementation exponentvaries with pore geometrysandstones -1.1 to 2.5carbonates -2.9 or higher

• n = saturation exponentreflects path of electric current through porenetwork that is partially full of brineaffected by wettability, clays, residualhydrocarbonsArchie’s equation assumes n = 2, ranges from

1 to 2.5


39/40

Homework

• Problems 1.14, 1.15 and 1.16 from textbook

• Please find resistivity of a fracing water-based

fluid with the following information at 270F

Sulfates, ppm 200

Chlorides, ppm 100

Calcium, ppm 0.01

Bicarbs, ppm 97.60

Magnesium, ppm 14.39


40/40

Review Questions1. Using simple physics arguments, explain why the electrical resistivity of a

rock is related to porosity.

2. Is the electrical resistivity of a rock controlled by its solid or fluid component,

or by both?

3. List four independent petrophysical/measurement conditions that will cause

Archie’s first law to

breakdown?4. The porosity variable used in Archie’s equations, is it total or effective

porosity?

5. Why is it often said that Archie’s second law is not scientifically sound?

6. Why is the electrical conductivity of clays in contact with water relatively

high?7. When does presence of clay/shale in a rock will cause Archie’s first law to

breakdown?

8. Explain why the wettability of a rock could have a sizable influence on the

rock’s electrical conductivity.

Documents

Electrical Petrophysics lecture