ElectricalMeasurements.v1(1)

7/27/2019 ElectricalMeasurements.v1(1)

1/23

Summary of Lecture 2 Chapter 1

Definition of resistivity

How current is conducted in a rock

Formation resistivity factor

Formation water salinity and temperature

Effect of porosity

Effect of permeability

Relation between resistivity and fluid saturation Shaly Sands

Resistivity of mud and mud components


2/23

Electrical Measurements
http://portalmaritimo.files.wordpress.com/2010/11/conrad-e-marcel-schlumberger.jpg


3/23

Reading Assignment

Bassiouni Ch. 5 Resistivity Logs

Bassiouni Ch. 6 Spontaneous Potential Logs

Homework Assignment(for discussion in class)

Construct a spreadsheet using the parameters of Example 5.3 and theboundary formulas 5.12 5.15 that produced the plot in Fig 5-11. Usedepth increment of 0.1 ft (yes I know that makes a thousand rows).

Cite any discrepancies. Work example 5.4 and be prepared to discuss your interpretation.


4/23

Where are we

heading?

Can I believe the resistivityvalues I read from the log asrepresentative of theformation resistivity?

Thin beds

Radius of investigation


5/23

Generic Electrical Measurement

Current is driven from electrode A to B

Potential (voltage) is measured between N and M

The resistivity of the rock is estimated from these

two measurements using Ohms Law


6/23

Simplest System Homogeneous, isotropic, infinite medium

( imaginary, but could be approximated by a single massive cleansandstone)

Electrode B Current is driven from electrode A to B

Electrode M (closest to source A) is at radius r1

Electrode N(farthest from source A) is at radius r2


7/23

Simplest System Homogeneous, isotropic, infinite medium

( imaginary, but could be approximated by a single massive cleansandstone)

Electrode B Current is driven from electrode B to A

Electrode M (closest to source A) is at radius r1

Electrode N(farthest from source A) is at radius r2

2 2

1 1

2

122

21 12

12

4

4

But Ohm's Law says

Solve for R

What is ?

r

r

T

T

dL dr d R RdA r

drd R

r

V I

VR G

I

G

= =

=

=

=

1 2

2 1

4where

for this particular geometry only!

T

r rG

r r

=


8/23

Example Problem

Resistivity tool at 3000 ft depth. 2-A current driven intoelectrode A (B at surface of earth). 10 mV voltagemeasured between electrode M (17 ft 4 in from A) andelectrode N (20 ft from A). What is the apparentresistivity of the formation in the vicinity of the tool.

4 (17.33 )(20 )converted to meters

(20 17.33)

10converted to Ohms

2

Numerical answer in Example 5.2

T

T

ft ftG

ft

mVR G

A

=

=

Is this the true resistivity of the

formation? Why or why not?


9/23

Lateral Device

(identical to Simplest System)

1 2

2 1

1

2

4where

where = distance from A to M

and = distance from A to N

T

r rG

r r

r

r

=

AO ~ radius of investigation ~ 19 ft

Large radius of investigation is a

double edged sword:

Good to measure formation

past invaded zone

Bad for thin beds


10/23

Normal Device

2 2

1

2

1 21 2

2 1

= distance from A to M

and

= distance from A to N (assume infinite)

44lim lim

T r r

r

r

r rr rG

r r

= = 2r r

11

4 r=

Radius of investigation ~ 2x AM

AM=16 in (short normal) or

AM =64 in (long normal)


11/23

Simplest System

How do the size of equipotential surfacesdepend on resistivity?

1 2 12

2 1

12

1 2

12

2 1

2

4

41 1

41 1

As gets bigger, the second term gets smaller.Subtracting a smaller term makes the right side bigger.

Thus must get smaller for bigger .

r r VR

r r IV

r r IR

V

r r IR

R

r R

=

=

=

Greater resistivity

Lesser resistivity


12/23

Simplest System

How do the size of equipotential surfacesdepend on resistivity?

Greater resistivity

Lesser resistivity


13/23

Response to Resistivity Boundary of

Normal Device

1

negative

1

2 1

A

Ra

A

s

Z

CR R

Z

L

= +

R2 (low)

R1 (high)A

M

Z

2

positive

1

2 1

A s

Ra

A

s

Z L

CR R

Z

L

> = +

+

R2 (low)

R1 (high)

A

MZ

A S

1 2

1 2

positive but Z


14/23

Response to

Resistivity Boundary

of Normal Device


15/23

Example 5.4Amp = 5X

Two tracks


16/23

Response to Resistivity Boundary of

Normal Device


17/23

Focused Current Devices

Designed to perform better on thin

beds

Can be designed for a deep radius of

investigation

Guard electrodes G1 and G2 are tuned

to focus the constant current from A0


18/23

Electrical Transformer

Alternating current

in primary coil

induces alternating

magnetic field

Magnetic field

extends to secondary

coil

Alternating

magnetic field

induces alternating

current in secondary

coil0

0 0

( )Faraday's Law

sin cos sin( )2

d BAV

dt

VdBV t A B t B t

dt A

=

= = =


19/23

Induction DevicesOperate on a completely

different physical principle

Conductive mud not

required, e.g., good for

oil-based mud

Contact with formationnot required

Instead of current

propagated between

electrodes, a magnetic fieldis established

Current is induced only in

the formation (hopefully)


20/23

Corrections to Estimate True Resistivity

Determine whether regions are in series or in

parallel

Radial current outward from tool has zones in

series, e.g., normal, lateral, focused devices

Azimuthal current around the borehole has zones

in parallel, e.g. induction

Re

a i i

i gions

R G R

=

Re

a i i

i gions

C G C

=


21/23


22/23

Correction Charts Different chart for each type of correction for

each type of tool


23/23

Summary of Lecture 3 Chapter 5

Simplest resistivity measurement and calculationof geometric factor to convert resistance intoresistivity

Normal device

Lateral device

Boundary and thin bed behavior

Focused devices Induction devices

Corrections to estimate true resistivity

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