Sonic -2000

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SONIC THEORY

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Sonic energy is generated and detected by devices called

transducers. By definition, a transducer is a “device thatis actuated by power from one system to supply power

in any other form to a second system” ; i.e. , a

transducer converts energy from one form to another. In

sonic logging, the conversion is electrical to acousticenergy (transmitters) or acoustic to electrical energy (

receivers).

Two types of transducers are typically used for logging: 1.

2.

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CREST 

TROUGH 

SINUSOIDAL WAVE TRAIN

A

B

C   A   M

   P   L   I   T   U   D

   E

TIMEE

F

G

HD

T

T

T

T=PERIOD OF THE WAVE 

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THE WAVELENGTH 

A

B

C   A   M

   P   L   I   T   U   D

   E

DISPLACEMENT (POSITION)E

F

G

HD

SINUSOIDAL WAVE TRAIN

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PROPERTIES OF WAVES

••

 

attenuation  

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ACOUSTIC WAVES

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SONIC MONOPOLE THEORY

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COMPRESSIONAL WAVE

DIRECTION OFPROPAGATION

DIRECTION OF

PARTICLE

DISPLACEMENT

RAREFACTION

COMPRESSION

COMPRESSION

RAREFACTION

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SHEAR WAVE

DIRECTION OF

PROPAGATION

DIRECTION OF

PARTICLE

DISPLACEMENT

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THE COMPRESSIONAL AND SHEARVELOCITIES

vK 

v

K BULK MODULUS

SHEAR MODULUS

 BULK DENSITY 

 p

s

( / )4 31/ 2

1/ 2

 

  

 

  

 

  

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 A

F  Modulus

 Angleor Volume Length

Strain

Parameter Parameter inChangeStrain

 Area

ForceStress

Strain

Stress Modulus

,,

ELASTIC MODULI

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FORCE =F 

FORCE  FORCE 

VOLUMETRIC DEFORMATION

V  A

FV  MODULUS BULK K 

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FORCE =  F

FORCE =  F

 

l

l

SHEARING DEFORMATION

l A

Fl

ll

 AF 

Tan

 AF  MODULUSSHEAR

 / 

 /  / 

 

 

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 Rock/ 

 Fluid 

 Mineral Density

(gm/cc)

Young’s

 Modulus

 Bulk

 Modulus

Shear

 Modulus

 Poisson’s

 Ratio

Sandstone Quartz 2.65 0.92 (Mbars) 0.370 (Mbars) 0.424 (Mbars) 0.09

 Limestone Calcite 2.71 0.89 0.732 0.342 0.30

 Dolomite CaMg

(CO3)2

2.87 1.66 0.820 0.500 0.25

Oil  n( CH2) 0.85 - 0.014 0.0 -

Water H2O 1.00 - 0.023 0.0 -Gas - 0.001 - 1.5x10

-60.0 -

MECHANICAL PROPERTIES OF

DIFFERENT MATERIALS

SHEAR WAVE

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SHEAR WAVE 

PROPAGATION 

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CYLINDRICAL DEFORMATION

and POISSON’S RATIO 

FORCE

l

l

FORCE

strainallongitudin

strainlateral

 

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SONIC VELOCITIES AND

POISSON’S RATIO 

 RatiosPoisson

v

v

 p

s

s

 p

'

)2 / 1(

12 / 1

 

  

 

  

  

  

Velocity Ratio

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SNELL’S LAW ANALYSIS 

normal

angle of

incident

angle ofrefraction 

BOREHOLE

FORMATIONi

v

vr 

 f 

bsinsin

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SNELL’S LAW REPRESENTATION OF

SONIC WAVE PROPAGATION

M1 M2

C

r s

is

r s

M1 M2

A

r Pi

M1 M2

B

r pr s

ip

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SNELL’S LAW ANALYSIS 

For wave propagation down the

borehole wall, =90 degress ( sin =1)

so that we now obtain:

sini

v

vcritical

 f 

b

angle ofincidenti 

BOREHOLE

FORMATION

angle of

refraction

SONIC WAVE PROPAGATION

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SONIC WAVE PROPAGATION

T

R1

R2

ipis

st  pt 

S wave

P wave 

ip =CRITICAL

COMPRESSIONAL

ANGLE

Is=CRITICAL

SHEAR

ANGLE

CRITICALLY

REFRACTED

COMPRESSIONAL

AND SHEAR

WAVES

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 QUESTION:

CAN Vf  BE GREATER

THAN Vb ?

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SONIC DIPOLE THEORY 

HALLIBURTON

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12 in

12 in

MONO TRANS

DIPOLE TRANS

MONO

RECVSDIPOLE

RECVS

12 in

LFDT

ISOLATOR

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FLEXURAL WAVE

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DISPERSION PLOT IN A

SLOW SANDSTONE

0 5 10 15291

265

241

222

   I  n  v  e  r  s  e   d

  p   h  a  s  e   d  v

  e   l  o  c   i   t  y

s/ft

Frequency (khz)

tflexuralvs frequency

tshear 

ts

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 p

 f  pV V criticali )(sin

For critically refracted

compressional waves:

SONIC WAVE PROPAGATIONAL

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SONIC WAVE PROPAGATIONAL

PATHS

T

R1

R2

TOOL BODY

BOREHOLE

FLUID

ALTERED

(DAMAGED ZONE)

UNALTERED

(UNDAMAGED)

ZONE

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GUIDED WAVES

•  

 

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THE LEAKY AND NORMAL MODES

Both the Leaky and Normal

modes are produced by

constructive interferencebetween reflected waves at

the borehole wall and body

waves traveling down the

formation 

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Stoneley waves are generatedalong the borehole wall, essentially

by flexing of the wall caused byinteraction of the formation and theborehole fluid

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STONELEY

WAVE

PROPAGATION

PORE FLUID COMPRESSED

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BOREHOLE

MUDCAKE

STONELEY WAVE PROPAGATIONPORE FLUID COMPRESSED

WHICH CAUSES MOVEMENT

INTO FORMATION

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b

smud mud tubestoneley

t t t t 

t OF TERMS IN 

    

22

STONELEY WAVE VELOCITY

AT LOW FREQUENCY

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TOTAL ACOUSTIC WAVEFORM

P wave

Leaky mode

S wave Stoneley

wave

Normal Mode

time

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Time(microseconds)

A

B

C

 

CENTRALIZED TOOL WITH NO WASHOUT

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T

R1

R2

tR1 

tR2 

A

B

C

D

E

tR2= A+B+D+E

tR1

=A+B+C

A,B,C,D,E,=TRAVEL TIMES

tR2 - tR1 = A+B+D+E -(A+B+C)

tR2 - tR1 = D+(E-C)

ASSUME

E=C

tR2 - tR1 = D

 t 2

 D

 s acin

 t t Δt 

R1 R2

TIME TRANSIT 

CENTRALIZED TOOL WITH NO WASHOUT

SLOWNESS

INVERSE

PHASE

VELOCITY

ACOUTIC SIGNAL AT TWO RECEIVERS

pacing

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ACOUTIC SIGNAL AT TWO RECEIVERS

THE ZERO CROSSING THRESHOLD TECHNIQUE 

pacing

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TR

R1

R2

B

A

CD

E

A

B

CD

E

REASONS FOR

BOREHOLE

COMPENSATIONS

CAVED HOLE

(WASHOUT)

TOOL TILT

BOREHOLE COMPENSATION SONIC

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BOREHOLE COMPENSATION SONIC

(BCDT)

TR

R2

TR

R1

3 FT

2 FT

3 FT

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t3

TR

R2

TR

R1

t1

t4

t2

BOREHOLE

COMPENSATION

CAVED HOLE

)2

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BOREHOLE

COMPENSATION

TOOL TILT

t1

t3 

t2 

t4 

 ft 

t t t t 

t c 2

)(

2 / 1

2143

TR

DEPTH DERIVED BOREHOLE

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Z=1 ft

10 ft

TR

R1

R2

t4 

B

TR

R1

R2

t1 

t2 

C

DEPTH DERIVED BOREHOLE

COMPENSATION

DTRCVR = (t2-t1)/z

TR

R1

R2

t3

A

TR 

R1

R2DTXMIT = (t4-t3 )/z

DT(BHC) = (DTXMIT+DTRCVR)/2

TR

DEPTH DERIVED BOREHOLE

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Z=1 ft

10 ft

TR

R1

R2

t1 

t2 

C

DEPTH DERIVED BOREHOLE

COMPENSATION

TR

R1

R2

A,B 

TR 

R1

R2

t3

t4

TR

DEPTH DERIVED BOREHOLE

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TR

R1

R2

t1 

t2 

C

DEPTH DERIVED BOREHOLE

COMPENSATION

TR

R1

R2

t3

A,B 

TR 

R1

R2

t4

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TR

R2

TR

R1

BOREHOLE

COMPENSATION

CAVED HOLE

THE WYLLIE TIME -AVERAGE

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THE WYLLIE TIME -AVERAGE

EQUATION

1- f f

1MATRIX FLUID

THE WYLLIE TIME-AVERAGE

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THE WYLLIE TIME-AVERAGE

EQUATION 

t t t 

s o lv in g fo r p o r o sity

t t 

t t 

 f m a

sm a

 f m a

lo g

lo g

( )

f f 

f f 

1

The fluid in the zone of interest is

typically mud filtrate

is usually considered 189 u sec/ft f t

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The presence of gas in the pore space of a

rock will increase the sonic transit time over

its value in the same liquid-saturated rock.Because of the increase in tlog (cycle

skipping may also add to this effect), the

sonic porosity is optimistic if gas is present inthe flushed zone (using the Wyllie equation,

the input value for tf will be too low).

CYCLE SKIPPING

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THRESHOLD LEVEL 

E4 

E1

E2 

E3 

E3 

E1

E2 E4 

E1

E2 

CYCLE SKIPPING

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GAS EFFECT ON SONIC TOOL RESPONSE

As has already been stated,the presence of gas in the pore spaceof a rock will increase the sonic transit time over its value in the

same liquid-saturated rock. Gas is very compressible; when it

replaces pore liquid, it lower the rock rigidity more than its

density and decreases Sonic velocity. 

The decrease in velocity is almost negligible in deeper low-

porosity formations where pore volume is low and compaction

pressure is high, which means that pore fluid contributes little

to rock rigidity. However, it can be as high as 40 % in shallow,

high -porosity formations where pore volume is large and

compaction pressure is minimum-in which case pore fluid has a

much larger contribution to formation rigidity.

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COMPACTION CORRECTION

 p

s

1

tt

tt

mafluid

malog

 

 

 

 

100

Shale p t C 

EFFECTIVE POROSITY

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EFFECTIVE POROSITY

When shale is present in the formation,

the effective porosity can be calculated

from

  

  

  

  

ma fl

mashsh

shma fl

maeff 

t t 

t t V t t t 

t t  100logf 

Here t sh is from the adjacent (nearby)shale

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Lithology

Sandstone 55.6

Limestone 47.5Dolomites 43.5

) / ( ft st ma  

TYPICAL DELTA-t MATRIX VALUES

f

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Primary

porositySecondary

porosity(Vugs,or 

fractures)

PRIMARY and 

SECONDARY  POROSITY

 D

 sec

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OFFSET 8 FEET = LONG SPACED TOOL

Potential for deeper investigation

LONG SPACED VS SHORT SPACED TOOLS

OFFSET < 8 FEET = SHORT SPACED TOOL

TRANS

REC

OFFSET

Can make measurements in larg

LARGE BOREHOLE EFFECT

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LARGE BOREHOLE EFFECT

TR

R1

A

B

A

B

TR

R1

TR

R1

TR

R1

TR

R1

TR

R1

A

B

A

B

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