Determination of Formation Properties in Cased Boreholes Using Full Waveform Acoustic Logs_massachusetts Institute of Technology

8/11/2019 Determination of Formation Properties in Cased Boreholes Using Full Waveform Acoustic Logs_massachusetts Institute of Technology

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DETERMINATION OF FORMATION PROPERTIES IN CASED BOREHOLESUSING UIJ WAVEFORM ACOUSTIC LOGS

by

Kenneth l l Tubman R Cheng an d l l Nat Toksoz

Earth Resources LaboratoryDepartment of Earth Atmospheric an d Planetary Sciences

lIassachusetts Institute of TechnologyCambridge llA 02139

ABSTRACT

Wave propagat ion in bonded a nd u nb on de d c ase d boreholes is examinedth rough the calculat ion i synthetic full waveform acoustic logs. T he m od el sconsist of a central fluid borehole surrounded by a number of fl uid and solidannuli. Waveforms calculated fo r a variety of formation a n d c em e nt parametersdemonst ra te tha t the f ir st a rr iv al s o bs er ve d o n full waveform acoustic logs inwell bonded cased holes are those of the formation and not the casing. Wavesref racted along the casing are generally too small to be observed. Thepresence of the steel and cement can make th e determination of formationvelocities more ditll.cult than in an open hole. The formation body wave arrivalsare decreased sUbstantially if th e cement velocities are near or greater thanthe formation velocities. A fluid layer between the stee l and th e cemen tes sent ia l ly f r ees the pipe from the cement. The steel arrival then becomes al ar ge , r in gi ng s ig na l which obscures the formation a rri va l. T he presence of thislayer is a more importan t fac tor than i ts t hi ck ne s s i n c a us in g such behavior. the fluid layer is between the cement and the formation, the ce men t c an dampout the ringing of the pipe. a th ick cement layer is b on de d t o the pipe and

the fluid layer is thin. the casing arrival is small and the formation arrivals arediscernible. A th inner cement layer resu l t s in the observation of a body wavetha t has a velocity t h a t is an average of the s te el a nd c em e nt velocities.

INTRODUCTION

Previous studies have examined wave propagation i n c as ed boreholes. Mosthave been fo r bond logging app li ca tions though , and so concentrated ondetermining c e m en t p a ra m e te r s and bonding conditions Walker, 1968; Riddle,1962; Pardue et tzl 1963; Brown et al 1970 . Tubman et l 1984 made th eassumption tha t the stee l wa s com ple tely b ond ed to the cement which was intu rn completely bonded to the formation. Chang an d Everhart, 1983accounted fo r other than perfec t b on din g by allOWing discontinuities in th eaxial displacement a t the s te e l- c em e nt i n te r fa c e a n d reqUiring the axial stressto go to zero a t th is boundary. Their formulation di d no t include any addit ionalfluid layers.

In this s tudy we examine full waveform acoustic logs in boreholes withu nb on de d i n a dd it io n to well -bonded casing. The si tuat ion of unbonded casingand cement is modeled th rough the inclusion of f lu id layers in termixed with the


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58 Tubmane taL

solid layers of the steel, cement, and formation.

SYNTHETIC :MlCROSEISllOGRAllS

Synthetic full waveform acoustic logs are generated fo r cased holegeometries. The borehole geometry is modeled as a number of homogeneous,i s ot ropic annu l i s u rround ing a central flUid cylinder. Th e n u mb er of annuli isarbitrary, as well as whether each is a solid or fluld The only res t r ic t ions aretha t the central cylinder is fluid and the outer. inflnite formation is solidAttenuation is included in the calculations th rough th e use of complex layervelocities. Th e synthe t ic waveforms are ca lcu la ted using the method of discretewavenumber integrat ion Cheng and Toksi:iz 1981; Tubman at a 1984 andconta in al l body and gUided waves. Th e source t he same as tha t used byTubman at a l 1984 is centered at 13 kHz Layers of s tee l and cement areWithin an infinite formation in th e model of a well b on de d c as ed hole. A flu ldlayer is p la ce d b et we en th e s tee l and the cement to model poor pipe-cementbonding, and between the cement and th e formation to model poor cement

formation bonding. More details of th e method are given in Tubm an at aI1984 and Cole 1983 . Th e parameters used in t h e g e ne r at io n of the synthetic

microseismograms are given with each flgure.

Well Bonded Casing and Cement

Figure 1 shows the micro seismogram fo r a model consisting of layers ofsteel, cement. and formation surrounding the central fluld cylinder. This is th eg eo me try us ed to represent a well bonded cased hole. There are fairly c learbody and gUided wave arrivals. Th e velocities of these waves are determined byfinding th e move out of the arr ivals with increasing source-receiver separation.The body wave velocities determined in this m an ne r c or re sp on d to theformation velocities and n ot those of the casing or cement. This isdemonst ra ted fur ther by modifying individual parameters of the model. Theformation velocities are lowered in the model used in the calculation of themicro seismogram of Figure 2 ll o the r parameters remain unchanged. Thecompressional and shear velocities are lowered so as to maintain a constant I ratio fo r th e two formations. t th e observed arr ivals were from thecasing. a nd n ot from the formation. l i tt le di tIerence would be expected betweenth e waveforms. It is c le ar , t ho ug h. tha t the velocities determined from themicroseismograms in Figure 2 are d it Ie re nt f ro m those in Figure 1 Thevelocities measured f rom F igure 2 again correspond to the formation velocities.It is in te re sti ng to n ote that . while th e body wave arrival t imes have changedsignificantly, the Stone ley wave arrival time has changed only slightly. Thisindicates t ha t th e d om i na nt i nf lu en ce o n the Stone le y wave aside from that ofthe borehole fiuid is from t he s te el and the cement, with the formation having

very little etIect. The thickness of t he c em en t l ayer is importan t in controllingthe nature of th e StoneIey wave The formation has m or e i nf lu en ce i th ecement layer is very th in o r non-existent.

Th e presence of the steel and the cement can make determinat ion of theformation velocities more difficult though. This is i l lustrated in th emicrose ismograms shown i n F ig ur es 3 and 4 The cement velocities used in th em od el f or F ig ur e 3 have been raised so tha t they ar e no w close to th os e of the

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60 TubmanetaL

Good Steel Cement Bond No Cement Formation ond

A no th er c om mo n occurrence in cased holes is good steel-cement bondingbut poor cement-formation bonding. In Figures 8 - 12 we present synthetic

microseismograms modeling this situation. The intermediate fiuid layer isbetween th e cement an d the formation so the steel casing is now clad with alayer of cement. In Figure 8 the thickness of the fiuid layer is 0.0625 inchesand the thickness of the cement layer is 1.6875 inches. The cement issufficiently thick here to damp out th e ringing of th e c as in g o bs er ve d in thefree pipe situation. The a rr ival f rom the casing is very small. The velocity ofth e first obvious arrival corresponds to th e P wave velocity of the formation.Th e formation S wave arrival is also clear. To check tha t th es e a re indeed th eformat ion arrivals . th e casing parameters are held constant and th e formationvelocities are modified. Th e resulting microseismograms are shown in Figure 9.It is clear from this figure tha t th e a rr iv al t im es and velocities of th e bodywaves have c ha ng ed a s the formation velocities change. Velocities determinedfrom this figure confirm tha t the observed arrivals are from the formation andnot from the casing.

the cement layer is th inner it will not be able to damp out the casingarrivals effectively. Figure 10 shows th e synthetic micros e is mograms f rom amodel w ith a cement layer thickness of 0.5 inches and a fiuid l ay er t h ick ness of1.25 inches. Th e amplitude of th e first a rr iv al h as increased relative to theprevious cases of th icker cement. The durat ion of this portion of th e waveformhas also increased substantially. Th e formation shear and pseudo-Rayleighwave arrivals are no w m uc h m ore difficult to identify due t o o ve rl ap ping withth e ringing of the earl ier arrival. Changing the formation parameters has littleeffect on the shape anc;l velocity of this first arrival. This is seen in Figure 11,which was calculated with the same geometry bu t with a slower formation. Thefirst wave packets on waveforms in both Figures 10 and ar e virtuallyidentical. The veloc ity of this f ir st a rr ival is determined to be b et we en t he p la tevelocity of the s te el a nd the velocity of th e cement. I n F ig ur e 12 the velocitiesof th e cement have be increased so tha t they are no w comparable to th eformation velocities. This r el at io ns hi p b et we en the cement and formationv elo ci ti es i n the well-bonded cased hole resulted in significantly reducedamplitudes of th e f i rs t ar rival Figure 3 . Here, t h e amp li tu d es and shape of thef ir st a r riva l are almost unchanged. The velocity has increased slightly though,due to t he f as te r cement. The amplitUde and velocity of this wave increase Withdecreasing thickness of the cement layer. A s imilar ampli tude variat ion of th ecas ing s igna l with cemen t t h ick ness was observed by Walker 1968 using datafrom tes t wells.

ON LUS ONS

T hre e t yp es of bonding situations commonly encountered in cased holesare studied th ro ug h t he calculation of synthetic full waveform acoustic logmicro seismograms.

In the case of g oo d b o nd in g between s te el a nd c em e nt and b e tween cemen tand formation, th e layers of stee l an d cem en t generally have only a smallinf iuence on the formation body wave arrivals. It is possible fo r these l ay er s t omake the determination of formation velocities more difficult than in an open

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Cased o l llicroseismograms 61

hole the cement velocities are comparable to those of the formation theamplitude of the formation arrivals can be significantly reduced Th e s te el a ndcement along with the flUid e xe rt t he dominant influence on the Stonely wave

A fluid layer between the steel and cement effectively frees the steelcasing Th e result is tha t th e c as in g a rr iv al b ec om es larger i n a mp li tu de an dl on ge r i n d u ra ti on The cas ing s ignal in this s i tua t ion dominates th e formationP wave signal There is little chan ge in the nature of the w av ef or m a s th e thickness of th e fluid layer is changed It is t he t he p re se nc e of this layer noti ts t h ick ness tha t is th e most impor tan t f acto r in th e behavior of th e casingarrival

When there is poor bonding between the cement and the formation butgood b ond ing between the steel and the cement the situation is morecomplicated It may be possible to d is cer n the formation body wave arrivalseven in t he p re s en c e of a fluid layer between th e c em ent a nd th e formationthe flUid layer is t hi n a nd there is a large amount of cement bonded to th e pipethe cement will act to damp out the ringing of th e pipe making the formationarrivals clear t he c em en t layer is sufficiently thin it will ring along with th esteel casing Th e flrst arriv al in th is si tuat ion will be from th e combination ofthe steel and th e cem ent and will have a velocity intermediate to thei rvelocities

KNOWLEDGEllENTS

This work was supported by the Full Waveform Acoustic Logging Consortiuma t M T Kenneth Tubman was partially supported by a Phillips PetroleumCompany Fellowship

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62 u b man e ta

R F R N S

Brown H D Grijalva V.E. and 1.L. Raymer 1970 New developments in sonicwave train display and analysis i n c as ed holes: Trans. S.P.W.L.A. paper F.

Chang S. K and Everhart A H 1983 A s tudy of sonic logging in a casedborehole: J. Pet. Tech. v.35. p.1745 1750.

Cheng C H and Toksoz M N 1981 Elastic wave propagation in a fluid-fil ledborehole and synthet i c acoustic logs: Geophysics; v.46 p.1042 1053.

Cole S.P. 1983 Guided wave dispersion in a borehole containing muit iple fluidlayers B.S. Thesis Department of Physics Massachusetts Insti tute ofTechnology Cambridge MA

Grosmangin M Kokesh F.P. and Majani P. 1961. A sonic method o r analyzingthe quali ty of cementation of borehole casings: J. Pet. Tech. p.165 171.

Pardue G.H. Morris R L Gollwitzer 1.H. and Moran J.H. 1963 Cement bond log- A study of c em e nt a nd casing variables: J. Pet. Tech. p.545 555.

Riddle G A 1962 Acoustic wave p ro p ag a ti o n i n bonded and unbonded oi l wellcasing: S.P.E. paper number 454.

Tubman KM. Cheng C H and Toksoz M N 1984 Synthetic u l waveformacoustic logs in cased boreholes: Geophysics i n p re ss .

Walker T 1968 A full-wave display of acoustic signal in cased holes: J. Pet.Tech. p.818 824.

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se d o l lficroseismogr ms

R VP VS RHa OP os FT T S] T S] IGM/CCI

1 5 ~ 1 6 7 5 5 O. 12000 2 O. 1875 2 0000 7 5 1 1

333333 9 259 5 67 1 92 ~ O O O 3O. 16 8 53 2 16 6 6

TIME IMSl 5 1 1 5 2 5 3 3 5

Q Q QQ Q

- NQ QQ Q

T TI I

N : QQ Q

- ~ QQ Q

IQ QQ Q

- nQ 0Q 0

5 00 50 2 2 5 3 3 5TIME IMSl

63

FIG. 1. Synthetic microseismograrns in a well b on de d c a se d hol e fo r offsetsvarying from 1 ft. to 15. ft a t .5 i t intervals is the outer radius of th elayer; p and V th e compressional and shear velocities; p the density; and p and the compressional and shear quality factors Th e bottom layer = 0. is the infinite formation

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64 ubm n e t a

R VP VS RHO OP OS1FT) 1FT IMS) 1FT IMS) CGM/CCI

1 5 ~ 1 6 7 5 5 O. 1 2 2 O. 1875 2 I 0000 7 5 1 1333333 9 259 5 67 1 92 ~ O O O 3

O. 13 12 7 2 16 6 6

TIME IMS)

0>

0>

'

N0>

N

''

0>0>

>'

' '

3 551 5 2TIME (MSl

5

5 1 1 5 2 5 3 3 5

- 1/\A 0> ~ v I.0> \Jvv>

- \ v

I0>

>

- l{\rv'0>0>

- \VV V- \ ptv0>0> ~ J V

rJ v>

0>

- >

0>,

N

FIG 2. S am e a s F ig ure 1 with a slower formation

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u e ole licroseismograms 65

Noo

...l

oo

o

oo

3.50.0 0.5 0

R O OP OS GM CCI

I.2000

20.00 O7.5000 1000.00 1000.00I .9200 YO OO 30.002.1600 60.00 60.00

VS1FT IMS

O11.0000

8.30008.5300

TIME IMSl

1.00 1.50 2.00TIME IMSl

VP1FT IMS

5.500020.000013.500016.0000

0.50

R FTJ

0.1541670.1875000.333333O

0.00

0.00 0 .50 1 .00 1.50 .0 0 2 .50 3 .00 3 .50,

- JIQ V

V IfAv J

- fJ\ vQ

V - JQQ

V

- V QQ

Ir -- \Q

,

l

N

FIG 3. Microseismograms fo r a m od el w it h cement velocities close to theformation velocities. Th e amplitude scale gain is twice that of the othe rfigures.

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66 Tubman e t aL

R VP VS R OP OSlFT lFTIMS lFT M3 CGM/CCI

1 5 ~ 1 6 7 5 5 O 1 2 2 O1875 2 11 7 5 1 1333333 9 259 5 67 1 92 YO OO 3

O 19 5 1 5 2 3 95 69

TIME IMSl 5 1 1 5 2 5 3 3 5

- 0Q 00 0

N:- :-NQ 0Q 0

- 0

-l lQ 00 0

- 00 0l-

00 0 5 00 1 5 2 2 5 3 3 5

TIME MSl

FIG. 4 Microseismograms fo r a model with formation velocities comparableto the casing velocities

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sed o l llicroseismog r ms

R VP VS R I OP OSeFT 1FT IMS 1FT IMS eGM/CCl

1 5 ~ 1 6 7 5 5000 O. 1 2000 20 00 O.0 187500 20 0000 I I 0000 7 5000 1000 00 1000 000 229167 5 5000 O. 1 2000 20 00 O.0 333333 9 2590 5 6700 1 9200 40 00 30 00O. 13 1200 7 0000 2 1600 60 00 60 00

TIME (MSl0 00 0 50 1 00 1 50 00 2 5 0 3 0 0 3 5 0

0 0

0 00 0

67

N

00

i

00

~0

?

00

oo

N

00

n i

0

00

0

0

0

0 0 0 0 50 1 00 1 5 0 2 0 0TIME IMSJ

2 5 0 3 0 0 3 5 0

FIG. 5. Microseismograms fo r th e f re e pipe situation There is a .5 inch fluidlayer between the steel and the cement

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68 ubm n e t a

R VS RHCI OP OS1FT) 1FT IMS) 1FT IMS) (GM/CCI

1 5 ~ 1 6 7 5 5 O. 1 2000 2 O. 1875 2 11 7 5 1 1

187583 5 5 O. 1 2000 2 O. 333333 9 259 5 67 1 92 YO.OO 3O. 16 8 53 2 16 6 6

TIME (MSl5 1 1 5 2 2 5 3 3 5

T1 T1

~.

~

5 1 00 1 5 2 2 5 3 3 5TIME IMSl

FIG. 6. Microseismograms fo r a model of a microannulus The fluid layerbetween th e pipe a n d c em e nt is 001 inches thick

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Cased ole licroseismograms 69

R VP VS RHO OP asIFTl 1FT IMS 1FT IMS IOM/eel

1 5 ~ 1 6 7 5 5 O 1 2 2 O1875 2 11 0000 7 5 1 1187583 5 5 O 1 2 2 O333333 9 259 5 67 1 9 2 ~ O O O 3

O 13 12 7 2 1600 6 6

TIME IMSl0 00 0 50 I 00 1 50 2 00 2 50 3 00 3 50

Q Q

Q >

N : N

> >Q >

> > > >

~ ~Q >Q >

>

Q >

U1

Q > > >

0 00 0 50 1 00 1 50 2 00 2 50 3 00 3 50TIME IMSl

FIG 7 Same as Figure 6 with lower formation velocities

3 3


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70 ubma n et a

R VP VS R P aseFT) WT MS T MS IGMICCI

1 5 ~ 1 6 7 5 5000 o. 1 2000 20 00 O.0 187500 20 0000 0000 7 5000 1000 00 1000 000 328125 9 2590 5 6700 1 9200 YO.OO 30 060 333333 5 5000 O. 1 2000 20 00 O.O. 16 0000 8 5300 2 1600 60 00 60 00

TIME fMSl0 00 0 50 1 00 1 50 a 2 50 3 00 3 50

0 0

0 00 0

N N0 00 0

n l l

00 0

0

I- 0

0 00 0

0 00 0 50 00 1 50 2 00 2 50 3 00 3 50TIME fMSl

FIG. 8 Microseismograms for a model with good steel cement bonding butno cement formation bonding There is a t hi ck c e me n t layer b on de d t o thepipe

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se d o l lficroseismogr ms 7

R VP VS ~ QP QSfFTJ fFT IMSJ 1FT IMSJ fGM/CCI

1 5 ~ 1 6 7 5 5000 O 1 2000 20 00 O0 187500 20 0000 11 0000 7 5000 1000 00 1000 000 328125 9 2590 5 6700 19200 ~ O O O 30 000 333333 5 5000 O 1 2000 20 00 OO 13 1200 7 0000 2 1600 60 00 60 00

TIME [MSl0.00 0.50 1.50 2.50 3.00 3.50

:c cc c

c 0c 0

T .I I

c

~

cc c

oC.C 0C c

c cc c

0.00 0.50 1.00 5 2.00 2.50 3.00 3.50TIME [MSl

FIG 9 Same as Figure 8 with lower formation velocities

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72 u b m a n e t a

R VP VS RHO QP QS1FT) 1FT IMS) 1FT IMS) fGM/CCI

1 5 ~ 1 6 7 5 5 O 1 2 2 O1875 2 7 5 1 1229167 9 259 5 67 1 92 YO OO 3333333 5 5 O 1 2 2 O

O 16 8 53 2 16 6 6

TIME (MSl 5 l 00 l 5 2 5 3 3 5

0

00

N0 00 0

T1

0 00 0

-~ ~0 0

0

- 0 00 0

-. ~0 00 0

5 l 00 l 50 2 2 5 3 3 5TIME (MSl

F1G 1 Microseismograms lo r a model with a t hi n l ay er 1 cemen t bondedto the pipe and a th ick tl uid l ay er b et we e n t he cemen t and the formation

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Cased ol llicroseismograms

R VP VS R O OP OSeFT) 1FT IMS) 1FT IMS) IGM/CCl

154167 5 5 O. I 2 2 O. 1875 2 11. 0000 7 5 1 1

229167 9 259 5 67 1 92 4 3333333 5 5 O 1 2 2 O.

O. 13 12 7 2 1600 6 6

TIME IMSl0.00 0.50 J. 00 J.50 .00 2.50 3.00 3.50

N

-

.

;= 0

0 0

0.00 0.50 J. 00 J. 50 2.00 2.50 3.00 3.50TIME IMSl

F1G. 11. Same a s F ig ur e 10 with lower formation velocities

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74 Tubman e t aL

oo

oo

oo

\ N v V . / V \ / V - - - ; -. c

oo

1 j I j v V \ A ~ - - ; ; ;

oo

M f \ / o ~ - - - - - h ,

R VP VS RHO Of OSefT 1FT MS FT MS IGM CCl

0.154167 5.5000 O 1 .2000 20.00 O

0.187500 20.0000 11.0000 7.5000 1000.00 1000.000.229167 13.5000 8.3000 1.9200 40.00 30.000.333333 5.5000 O 1.2000 20.00 OO 16.0000 8.5300 2.1600 60.00 60.00

TIME IMSl0.00 0.50 1.00 1.50 .0 0 2.50 3 .. 00 3.50

-

o

TJ

~

0.00 0.50 1.00 1.50 2.00T M IMSJ

2.50 3.00 3 . 50

FIG 12 Same as Figure 10 with higher cement velocities.

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Documents

Determination of Formation Properties in Cased Boreholes Using Full Waveform Acoustic Logs_massachusetts Institute of Technology