acoustic logging

Chapter 51 Acoustic Logging A. (Turk) Timur. chc\,roa COT.

Introduction Acoustic wave propagation methods have become an in- tegral part of formation evaluation since the first downhole measurement of velocities was conducted in 1927. ’ These early measurements were conducted to obtain time/depth curves to use in interpreting seismic data.’ In the 1930’s, proposals were made to conduct velocity measurements in a fashion similar to electric logging, by using an acoustic transmitter and one or more receivers. First successful implementation of this technology was in the late 1940’s and early 1950’~.~-’ Commercial acoustic velocity logs were first introduced in 1954 by Seismograph Service Corp. in the U.S. and by United Geophysical in Canada.

Since then, technology involving borehole measurements of acoustic wave propagation properties has developed significantly and has become established as a major formation evaluation method. These acoustic wave propagation methods used in well logging can be broadly classified into two groups: transmission and reflection. Properties measured in each method and their applications in formation evaluation are listed in Table 51.1

Compressional wave velocities measured by acoustic logging were found to be related to porosity so closely that the acoustic log became a standard porosity tool. which it still is in many areas. The second most common use of borehole acoustic measurements is in evaluating cement jobs by measurements inside casing.

This chapter describes the use of acoustic wave propagation properties in formation evaluation after a brief description of elasticity. acoustic wave propagation properties in rocks, and methods of recording these in the borehole.

Elasticity Introduction The theory of elasticity investigates relationships between external forces applied to a body and resulting

changes in its size and shape.’ In this theory, it is assumed that displacements are small and the body returns to its original condition after the forces are removed. Ap- plied forces and the resulting deformations are described by stresses and strains.

Stress is the force, F, per unit area. A, applied; strain, t, is deformation per unit length, t. or volume, V, as illustrated in Fig. 5 1.1.

Within the elastic limit, as shown in Fig. 51.2. stresses are found to be proportional to strains (Hooke’s law). The ratio of stress to strain is a different constant for different loading conditions. These proportionality constants are defined as elastic moduli. which are fun damental properties of a material.

Young’s Modulus, E. This is the ratio of tensile or compressive stress (FL/A) to the resultant strain (tL, =ALlL):

FLiA E=-

ALIL

Shear (or Torsion) Modulus, G. The ratio of shearing stress (F,IA) to the shearing strain E,, =(AL/L) is

F,7 IA G=-.

6 s

Bulk Modulus, K. Bulk modulus describes the change of V under hydrostatic pressure, p:

K=P AVIV

where K is also the reciprocal of compressibility, c.

51-2 PETROLEUM ENGINEERING HANDBOOK

TABLE 51.1-ACOUSTIC WAVE PROPAGATION METHODS

Property Applicatton

Transmission seismic and geological interpretation

porosity Compressional- and shear- lithology

wave velocttles hydrocarbon content geopressure detection mechanical properties of

rocks

Compressional- and shear- cement bond quality wave attenuations location of fractures

rock consolidation permeability indication

Reflection location of vugs and fractures

Transit time and amplitude orientation of fractures and of reflected waves bed boundaries

channeling and microannulus casing quality

Poisson’s Ratio, p, This is a measure of the geometric change of shape under uniaxial stress. It is expressed as the ratio of the fractional change in diameter, d, (transverse strain, eT) to the fractional change in length (longitudinal strain, EL):

Adld

p=aL,L..

Relationships Among Elastic Parameters. These four elastic parameters are not independent; any one parameter can be expressed in terms of two others:

E=2(1 +p)G

Acoustic Waves Acoustic waves propagate mechanical energy. For in- stance, if an elastic material is subjected to an instan- taneous force at one end. it is compressed (Fig. 51.3).

Fig. 51.1-Longitudinal, transverse, and shear deformations.

This disturbance is then transmitted along the material by a series of compressions and rarefactions. The disturbance travels at a constant velocity that is a fundamental property of the material. The elastic moduli and the density determine the velocity of propagation for each material.

Two types of mechanical wave propagation will be described qualitatively. Detailed discussions of acoustic wave propagation are given in Refs. 7 through 11.

Compressional Waves. Compressional waves are those in which the mechanical disturbance is transmitted by a particle motion parallel to the direction of wave propagation (Fig. 51.3). They are also called longitudinal, pressure, primary, or P-waves. Particles of the material oscillate around this rest position in simple harmonic motion. As they move from equilibrium, they push or pull their neighbors, thereby transmitting the disturbance through the material. The velocity of this compressional wave motion, lip, is a constant for a given material:

v,=+(K+4/,G)“, . . . . . . .(I) P

where p is the density.

Shear Waves. Shear waves, also called transverse, tor- sional, or S-waves, are those where particle motion is perpendicular to the direction of wave propagation (Fig. 51.4).

Particles in the material again move about their rest position with simple harmonic motion. For this motion to be transmitted, however, each particle must have a force of attraction to its neighbor. Whereas compressional waves can be propagated simply by elastic colli- sion of one molecule with the next, attractive forces must exist between adjacent molecules to transmit shear waves. Since these forces are very small in gases and liquids, fluids do not transmit shear waves.

The velocity of shear waves, v,, , is also a constant for a given material:

G % v,,=

0 - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P

(2)

Yield StrengIh

Breaking Point

Elastic Limit

STRESS t

Hooke’s Law Region

STRAIN -

Fig. 51 .P-Stress/strain diagram for an elastic material

ACOUSTIC LOGGING 51-3

a A B A B A . . . . . . . . . . . . . . ..I.. . . .-. . * . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..a... . . me.* . . . . . . . . ..I....... . . ..-.. . . ..m. * * . . . . . . . . . . a. . . . . . . . . . . . . . . s.... . . . ..-. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . w...... . . . . . . . . . . . . . . . . . . . . . . . . . _ ..-.. . ..-.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .” . . . . . .“. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .-. . . . . . . . . . . . . . . . . . ..I.. *... . . . . . . . . . . . . . . * . . . . . . . . . . . . . . . . . . . . . . . . . . ..“.. . . ..m.* . . . . . . . . . . . . .

- * Dlrecllon cd L-A- rJileCtion PartIck W.Wde”gth 0‘ wave MOllO” Propagalion

Fig. 51.3-Compressional wave.

Characteristics of Acoustic Waves Acoustic waves have many characteristics similar to light waves. They undergo interference, diffraction, reflection, and refraction. At a boundary separating materials of two different velocities, they are mode converted, reflected, and refracted according to Snell’s law.

For either compressional or shear waves, velocities are related to frequency, f, by

L’= hf,

where X is the wave length. Motion of either compressional or shear waves in an

extended medium is characterized by an infinite number of particles, each vibrating in simple harmonic motion. A simple description of this wave propagation is given by a plane wave solution of the wave equation:

u=A cos(2+2n~).

where u is the particle motion at a given point, s, away from the source and at any given time, t. At any given time, t=O, the displacement along the wave varies as cos(2as/X); hence, the u is equal to signal amplitude A, where s is equal to even multiples of wavelength-i.e., s=O, X, 2X. Motion of each particle, on the other hand, is described by a simple harmonic motion given by

u=A cos(27rjl).

An additional feature of acoustic waves to be considered is attenuation. As one moves away from the source, the intensity of sound decreases. This decrease of acoustic waves results from (1) geometric spread of energy, reflection, refraction. and scattering, and (2) absorption, whereby mechanical energy is converted into heat.

The decrease in intensity because of absorption is given by

,=I e-2cu.\ 0

where I,, is the acoustic intensity at the source, I is intensity at a distance, s, from the source, and 01 is the coefficient of absorption.

The acoustic intensity is proportional to the square of the amplitude; therefore, the amplitude, A. of a wave at a

:*.... *:::: :* r-- . . . . . *.

. . . . . . :.::*..* .“..:. ..*** .*...*. :..*..:::: .*:::a .*...*.*:::. .,..

Dlrecllon 01Parllcle “lbM,lO” I

. . ..*......:::::f:.............‘*....... : :. . . - . . . . . .*...*a-...-,- *. . . . -.*: . . . . . :.:::...:..,.,....:.::::. . . . . .*a.. .*... . .,.* ,..... *.-- . . . . . . . . * . . . . *... Z.“.. .*... * . . . . .**... .*... :.: :::.. :::::::.....: .*,,.. ..: . . . . .:...:.a ***... .:.*, .,.*.

. . . . ::::::. *.a *...- *.-...a.. a.. .-

.-.-.::e:

-a Dlrecllon Of

Ware PmpagafK.n

Fig. 51.4-Shear wave.

distance, s, from the source is

A=A e-ffs 0 1

where A,, is the amplitude at the source. A schematic diagram of an experimental apparatus is

given in Fig. 51.5 to illustrate the measurement of acoustic properties. Two piezoelectric elements are at- tached to the specimen as shown. A pulser provides the electric pulse to the transmitting piezoelectric element and also triggers the oscilloscope trace. The transmitter vibrates according to the change of voltage with time, generating a mechanical pulse in the specimen. As it travels through the specimen, the mechanical pulse is attenuated. The receiving piezoelectric element converts this attenuated pulse into an electric pulse that is displayed on the oscilloscope screen.

The travel time of the mechanical pulse through the specimen is read on the horizontal scale of the oscilloscope, and the velocity is calculated from

L v=-.

t

By using a set of either P-wave or S-wave transducers, both velocities, vp and v,?, can be measured as described. These velocities, assuming an infinite, isotropic, homogeneous, and elastic medium, are related to elastic moduli by

4 v,~~=P=K+~G, . . . . . . _. (3)

v,‘p=G, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...(4)

Fig. 51.5-Experimental apparatus for measurement of velocity and attenuation.


Acoustic Properties I

\ Models /

Fig. 51 .&Factors affecting acoustic properties of rocks.

and

o.s(v,/v,)* - 1 /A= (v,,v,)2 -1 , . . . . . (5)

where P, K, and G are P-wave, bulk, and shear moduli, respectively, p is Poisson’s ratio, and p is density.

As mentioned earlier, these same elastic constants can be obtained directly by measuring lateral and longitudinal strains as functions of stress. Elastic constants measured in this manner are referred to as static elastic constants in contrast to dynamic elastic constants measured through the use of acoustic wave propagation techniques.

One method for measurement of attenuation requires specimens of two different lengths from the same material. Assuming that the voltage amplitude of the received signal from the specimen of length L t is A I and from the specimen of length L2 is AZ, and that voltage amplitudes are proportional to the amplitudes of mechanical pulses, the two amplitudes can be expressed as

A, =A,CaLI

and

A 2 =A e-uL2 0

Hence, the coefficient of absorption, nepers/cm, is obtained from

1 cy=- InA’.

L2-L, A2

Or, in more common units, attenuation is given in decibels per unit length, defined as

20 a=- log A’.

L2-L1 A2

Other parameters defining attenuation are the quality factor, F,, and the logarithmic decrement, 6. Coeffi- cients of compressional and shear wave attenuation (op, as) are related to the respective quality factors (Fqp, F,,y) and the logarithmic decrements (6,,, 8,) by

1 ffv 6 -=-=- . . . . . F, of a, . . . . . . . . . . (6)

where v is velocity and f is frequency.

Acoustic Wave Propagation in Rocks Introduction Acoustic wave propagation properties of rocks are known to depend on porosity, rock matrix composition, stress (overburden and pore fluid pressures), temperature, fluid composition, and texture (structural framework of grains and pore spaces), as illustrated in Fig. 51.6. I2 A unified approach involving measurements of compressional and shear-wave velocities, analyses of rock composition, and use of theoretical models to interpret these data was described in Refs. 13 through 16.

Acoustic Properties Acoustic wave propagation properties were described in the preceding section for homogeneous, elastic media. Applications of these relationships to rocks, however, are complicated by the presence of pores and cracks, and fluids contained in them. A simplified, theoretical development is described in the Appendix to illustrate some of these complications by incorporating rock- frame, pore-fluid, and rock-grain compressibilities into the velocity equations.

As indicated earlier, acoustic wave properties in rocks are functions of numerous independent variables. Therefore, evaluation of various theories of acoustic wave propagation requires laboratory experiments conducted on rock samples under controlled pressure, temperature, and saturation conditions.

Various experimental methods have been developed for measuring acoustic wave propagation properties of rock samples. Detailed description of one of the laboratory systems is given by Timur. ” It is designed to conduct sequential measurements of properties of both the compressional and the shear waves on rock samples subjected to simulated subsurface conditions. A typical experimental setup is shown in Fig. 51.7, where a rock sample is assembled between two transducers in a sample holder. This assembly is placed in a pressure vessel and subjected to varying overburden and pore fluid pressures and temperatures. A minicomputer digitally records the compressional and shear-wave pulses transmitted through the rock samples, as well as sample temperature, overburden and pore fluid pressures, and sample length changes.

ACOUSTIC LOGGING

Insulated

Thermocouple

Linear Variable Differential Transformer

2iirifT@

Pore Fluid

P and S Wave Transmitter

_ Sample (Jacketed)

_ P and S Wave

Fig. 51.7-A typical sample (d= 8.9 cm, L = 5.1 cm) assembled for acoustic measurements.

A typical set of compressional and shear-wave velocity data obtained with this apparatus is shown in Fig. 5 1.8. The rate of change of porosity in this sample with varying overburden and pore fluid pressures is shown in Fig. 5 1.9. These data were obtained from concurrcnt measurements of changes in the sample pore and bulk volumes during acoustic measurements.

Fig, 5 1.10 illustrates typical compressional and shear wave attenuation data. obtained from the amplitude spectra of transmitted pulses.

Porosity

Porosity dependence of v,, in rocks has been intensively investigated. “W This forms the basis for estimating porosities from in-situ measurements with an acoustic velocity log.

Results of early laboratory measurement of compressional-wave velocities determined on water- saturated sandstones are plotted vs. porosities in Fig. 5 1.1 I. ” The porosity/velocity relationship is within the indicated statistics as long as the lithology remains relatively constant.

Es v,

Navalo Sandstone

” I

Porosity 11.5. Density 2.46 vi PO/P1 2.30

I OVERBURDEN PRESSURE, PSI x 101 00.00 4.00 8.00 12.00 16.00 20.00 24.00 26.00 r 1 7 - 0.00 0.16 0.31 0.47 0.62 0.78 0.94 109 z

Fig. 51.8-Pressure dependence of compressional- and shear- wave velocities in a Navajo sandstone.

Porosity dependence of v,, has also been investigated to some extent.25m28 A change in shear-wave travel times (lit),$) per unit change in porosity ($J) is found to be almost twice the corresponding change in I /II,,

Rock Composition

Rock composition affects the velocities in significant ways, as illustrated in Fig. 51.12.‘” Laboratory data plotted in this figure are for cores saturated with brine and subjected to an overburden pressure of 3,000 psi. The two principal minerals in the rock were quartz. in the form of tripolite, and calcite. They were mixed in relative proportions ranging from approximately 50% calcite/50% quartz to 80% calcite/20% quartz. The samples with lower porosity had a continuous calcite matrix, whereas the samples with a higher porosity had a continuous quartz matrix.

Effects of rock composition usually are taken into account by establishing velocity/porosity relationships for each group of rocks of similar composition through correlations of both the laboratory and the field data. This is illustrated in Fig. 51.12 by two separate groupings, one for calcite matrix and the other for quartz.

Rock composition plays a significant role in acoustic wave propagation properties. A procedure for comprehensive analyses needed for this purpose was described by Jones et al. I3 First, they conducted a combination of measurements of X-ray diffraction, elemental analysis, clay analysis, and grain density measurements. Each of these then was assigned an experimental error, and linear programming was used to establish the rock mineral composition, as shown in Table 51.2.

PETROLEUM ENGINEERING HANDBOOK

tf

W

,L 0 4 8 12 16 20 24 28

OVERBURDEN PRESSURE. PSI x 101

Fig. 51.9-Pressure dependence of porosily of Navajo sandstone.

Stress Pressure dependence of velocities of compressional and shear waves also has been the subject of numerous studies. Velocities of elastic waves traveling in a porous medium are known to be functions of both the external (overburden) pressure, pO, and the internal (pore fluid) pressure, pf. Some of the experimental results indicating dependence of compressional-wave velocity on confining pressure are given in Fig. 5 1.13 for various rock

2.5 1

VELOCITY, km/s

3 3.5 4 4.5 5 6 I I T r --- -1

ft/sec x 103 B ;ci II!-- _12 13 15 17 1

35

30

5

\

Time Average ft/sec (m/s) Malrix 19500 (5944)

’ ,I Fluid 5000 (1524) 0 0

‘9

, 1 I /

120 110 100 90 80 70 60 RECIPROCAL VELOCITY. sec/ft x 10m6

50

Fig. 51 .l I-Velocttylporosity data determined in laboratory for water-saturated sandstones compared with time- average relation for quartz/water system.

100

60

Fq 40

20 4

1

0

Berea Sandstone h r 16

I , I I 2000 4000 6000 8000

DIFFERENTIAL PRESSURE, psi

Fig. 51 .I+Pressure dependence of compresslonal and shear attenuation in a Berea sandstone saturated with brine.

samples including dolomite, limestone, and sandstone and for a sandpack. 29 In general, velocities increase with increasing p0 and decrease with increasing pt.

From a theoretical analysis of elastic wave propaga- ion in sphere packs, Brandt3’ predicted velocities to be unctions of (p, -npf), where n is a number between 0

and 1. Experimental data of Hicks and Berry”’ and yliie et al. I9 indicated n to be close to unity, whereas

data obtained by Banthia et al. 32 indicated values of n to

VELOCITY, km/s 3 3.5 4 5 6 7 I I I I--II

ft/sec x lo3 10 12 15 20 I 1 I r-1 7

\p Calcite ft/sec (m/s) Matrix 22500 (6858) Brine 5235 (1596)

10

5

0

4

Quartz (Tripolite)

Matrix 19200 (5852) Brine 5235 (1596) I

I , I I I \I \ 100 90 80 70 60 50 40

P-WAVE TRAVEL TIME, sec/ft x 10m6

Fig. 51.12-Comparison of compressional-wave velocities as function of porosity for brine-saturated tripolite samples under confining pressure of 3,000 psi.

ACOUSTIC LOGGING

TABLE 51.2-ROCK COMPOSITION

Sample Navajo sandstone Petrography medium-porosity, well-sorted quartzite Grain density 2.60 Grain porosity 19.4 X-ray, wt%

Quartz 93.0 Calcite 1 Dolomite - Clay 1.7 Feldspar 0.7 Pyrite Anhydrite 0.4

NAA and AAS, wt% Si 42.60 Al 1.20 Ti 0.79 Fe 0.20 MQ 0.02 Ca 0.20 Na 0.00

:: 0.16

54.00 Phyllo-silicate 6.00 Computed volume, %

Quartz 68.37 Calcite - Dolomite - Clay 4.73 Feldspar 0.57 Pyrite Anhydrite - Silica 6.93 Siderite -

rwts

FAecbft

be significantly less than 1. To investigate this discrepancy, Gardner et al. 33 conducted experiments taking into account the past pressure history of samples. They found that p n and pi are equally effective in chang- ing velocities-i.e., n = 1, provided that the differential pressure (pd =po -pf) follows a pressure cycle previously imposed on the sample (Fig. 51.14).

Temperature The effect of temperature on elastic wave velocities is considered to be of second order and usually is neglected in seismic exploration and acoustic log interpretations. To study this effect, early laboratory experiments’4-38 were conducted by measuring velocity as a function of overburden pressure at constant values of temperature instead of as a function of temperature at constant pressure. Also, the effects of pore fluid pressure were not considered. Later, the effects of temperature on the velocities were investigated through laboratory measurements on rock samples subjected to simulated subsurface pressure conditions ” (Fig. 51.15). On the average, the compressional wave velocities were found to decrease by 1.7% and the shear-wave velocities by 0.9% for 100°C increase in temperature.

Below freezing temperatures, however, the effect of temperature on elastic wave velocities become much more significant. An increase of 50% or more in compressional wave velocities is observed upon freezing the pore fluid in some rock samples.39 Below freezing, compressional wave velocity in water-saturated rocks was found to increase with decreasing temperature, whereas it was nearly independent of temperature in dry

z G 13 0

i

-Y Sandstone

11 d = 18

0 2000 4000 6000 8000 10.000 PRESSURE, psi

Fig. 51.13-Compressional-wave velocity vs. confining pressure for brine-saturated carbonates, sandstone and sand pack.

ocks. The shapes of the velocity vs. temperature curves ere functions of rock composition, pore structure, and

he pore fluids. Some of the velocity vs. porosity data at ubfreezing temperature is illustrated in Fig. 5 1.16. 39-43

luid Composition n understanding of the effects of fluid composition on

lastic wave properties has become much more signifi- ant with the increasing interest in detection of hydrocar- ons with seismic measurements. As a result, these ef- ects have been the subject of many studies, both heoretical and experimental, in the recent literature. The

Fig. 51.14-Compressional-wave velocity as a function of differential pressure.


Berea Sandstone

0 0 ,A h (,po = 1360, pf = 600 bars) a

Do v o (PO = 345, pf = 150 bars)

0 a

0 7 = = , 138, 60 tars) 9 c Lp? pf

0 Compressional Wave Velocity A Shear Wave Velocity

(p. = 1380, pf = 600 bars c ,i ? fi-~ x -A%

I 3.05

2.30

L--~ .~ I 0 20 40 60 80 100 120 140 160 lE0 200

TEMPERATURE. “C

Fig. 51.15-Temperature dependence of compressional- and shear-wave velocities in brine-saturated Berea sandstone.

0.40

0.35

E % p- 0.30 k

:: ii ’ 0.25 i

8 E 5 0.20

ii

0.15

0.10

Simpson (Ref. 41)

Umiat

6

7 l Laboratory Measuremenls

/ 0

AField Measurements from Alaska g

10 20 30 40 50 60 -10

70 60 90 100

9

10

14 c G

0 d

'6 >

16

20 22

is:

SE! 32

POROSITY, PERCENT

Fig. 51.16-Compressional-wave velocity of frozen rocks as a function of porosity.

first important theoretical contribution was made by Gassmann,44 who described the relationships between pore fluid, rock skeleton (or frame), and the rock grains by starting with first principles of the theory of elasticity. Later, Biot45,46 developed a more comprehensive theory of elastic wave propagation in a fluid-saturated, isotropic and microhomogeneous porous solid over a wide frequency range. Biot’s theory, which reduces to that of Gassmann at low frequencies, incorporates the effects of fluid composition through the density and compressibility of the saturant fluid (see Appendix).

Geertsma4’ investigated the applications of Biot’s theory to the interpretation of acoustic logs and estimated expected range of velocity dispersion by comparing velocities at zero and infinitely high frequencies. Since the estimated velocity dispersion was found to be generally less than 3%, the low frequency approximation of Biot’s theory and, hence, Gassmann’s theory is useful for most applications. Brown and Korringa” further generalized Gassmann’s theory and succeeded in remov- ing the requirement of macrohomogeneity.

The experimental data of King, 4’ shown in Fig. 5 1.17 for brine-, kerosene-, and air-saturated (dry) Boise sandstone ($=25 %), illustrated the predicted behavior; compressional-wave velocity is greater in brine-saturated rocks than in comparable gas-saturated rocks, with the reverse true for shear-wave velocity.

On the other hand, experimental data of Gregory 5o in Fig. 51.18 indicate that for some rocks, shear-wave velocity behavior upon the change of saturation from gas to brine is opposite to the predictions of the Biot theory. This may be due to the presence of isolated microcracks in these rocks, whereas the BiotiGassmann theories assume the pore structure to be open and interconnected.

Texture

Texture in this context is the structural framework of the rock consisting of solid matrix and pore structure. Its im- portance in elastic wave propagation has been

dramatically illustrated in Fig. 51.19. The data in this figure are the compressional and shear-wave velocities in dry and water-saturated Troy granite with a porosity of 0.3 %. 5’ Velocities were measured as functions of confining pressure by maintaining pore fluid pressure (pf) at 1 bar. Compressional-wave velocities are higher when the rock is water-saturated, whereas the shear-wave velocities are unchanged between the two states. What is most interesting, however, is that a porosity of only 0.3% is affecting the velocities b 20% or more.

Classical bounding theories5z-5r obviously cannot account for these large changes in the respective moduli because of large differences between the properties of rock matrix and fluid in the pores. This is because they used the total porosity without considering how it is distributed.

Scanning electron micrographs (SEM’s) shown in Fig. 5 1.20 show pore space in Troy granite to consist mainly of thin cracks, typical of most granites. 56

The effects of these cracks on elastic wave propagation properties have been investigated extensively, and many theoretical models have been developed. 14q5’ The theoretical curves shown in Fig. 51.19 were obtained by fitting the velocity data with the noninteractive scattering theory. I4 For these theoretical formulations, the rock is

ACOUSTIC LOGGING

2.9 -r? E x 5 2.7

ti d 2.1 >

1.9

1.7

1.5

1.3

---O Brine

- -A Kerosene -0 Dry

Boise Sandstone 6 = 25%

0 0.1 0.2 0.3 0.4 0.5 DIFFERENTIAL PRESSURE, k bar

Fig. 51.17-Observed and theoretical compressional- and shear-wave velocities in Boise sandstone as a function of pressure for three saturation flulds. The circles, triangles, and squares are laboratory data from King for brine-, kerosene- and air-saturated (dry) samples.

assumed to consist of a solid matrix and pores of spherical and oblate spheroidal shapes. Using the SEM’s as a guide and the porosity as a constraint, the pore space was modeled by a spectrum of pore shapes ranging from spheres to very fine cracks. Theoretical velocities were calculated as a function of pressure by first determining the ranges in pore shapes at each pressure condition. Depending on the fit, the pore aspect ratio (ratio of minor to major axis of an ellipsoid) spectra were adjusted and calculations were repeated until good fits were obtained to all velocities. Theoretical curves plotted on Fig. 5 1.19 are based on the final model.

Effects of various pore shapes on acoustic velocities as predicted by the noninteractive scattering theory are illustrated in Fig. 51.21. The effects shown in this figure are for a rock with matrix properties of K,,, =0.44 megabar, G=0.37 megabar, and pm=2.7 g/cm’; for water with K,,, =23.2 kilobar and pw, = 1 g/cm”; and for gaswithK,=1,5XlO-‘kilobarandp,=lO-’g/cm’. As indicated, for a given porosity, the thinner (smaller aspect ratio) pores affect the velocities much more than the spherical pores.

0.90

0.85

0 5 10 15 20 25 30 35 40

POROSITY, O/o

Fig. 51.18~S-wave velocity ratio vs. porosity for dry, (v,),, and fully water-saturated, (v,),. rocks.

DEPTH, km

--- 0 Sat’d

- 0 Dry

1:: 1~ , , Troyyranite

0 0.2 0.4 0.6 0.8

DIFFERENTIAL PRESSURE, k bar

Fig. 51.19-Observed and theoretical compresslonal (v,) and shear (w,) velocities in dry and water-saturated Troy granite as a function of differential pressure. The data (points) are from Ref. 51.


Fig. 51.20~-Scanning electron micrographs of pore system cn Troy granite


This theory also was used to analyze the “well- behaved” (according to Biot/Gassmann) experimental data of Fig. 51.17, where the results are plotted as solid and long- and short-dashed curves. Additionally, however, it also can explain the “unexpected’ ’ behavior of the experimental data of Fig. 5 I. 18, as illustrated in Fig. 5 1.2 1 by its predictions for the S-wave velocities in rocks with pores of various shapes.

Modeling of the real rock can be achieved by approximating the regular pores by spheres and rounded spheroids and by approximating the grain boundary spaces and flat pores by low-aspect-ratio cracks. However, there is no practical way to measure a pore aspect-ratio spectrum independently. An extensive study by Hadley 58 involved counting hundreds of cracks on three SEM’s, each covering about 1 mm2 of rock surface. These results are being used for testing “crack” theories. So far, these theories have added much to our understanding of acoustic wave propagation; their practical applications, however, have not yet materialized.

Summary Factors affecting acoustic wave propagation properties of rocks were illustrated in a qualitative fashion with emphasis on compressional and shear-wave velocities, mostly because attenuation properties are much less understood. Among the factors influencing velocities, porosity, lithology (mineral composition and structural framework), saturation and differential pressure are considered primary, and the others, with certain qualifica- tions, secondary. As the previous discussion indicates, significant advances have been made in understanding the properties of acoustic wave propagation in rocks. Further advances will be made because of the significance of this work, not only in formation evaluation, but also in seismic exploration.

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\ 0.01 \o.os

1

\,,,,r ::,“:r;a:r

P-Wave S-Wave I I I I I I / 1 I 1 1

POROSITY, % POROSITY, %

Fig. 51.21-Normalized P- and S-wave velocities vs. columr 1

concentration of inclusions (porosity) of different aspect ratios for water- and -gas-saiurated pores, respectively.

Acoustic Wave Propagation Methods Introduction

Acoustic wave propagation methods used in well logging can be classified into two groups: transmission and reflection (Table 51.1). In the transmission method, one or more transmitters emit acoustic energy, which is transmitted by formation and/or casing and is detected by one or more receivers. In the reflection method, one or more transducers emit acoustic energy, part of which is reflected by the borehole wall and/or casing and is detected by the same transducer.

In this section, both the transmission and reflection methods will be described, starting with a description of acoustic wave propagation in a borehole and followed by various methods of recording acoustic data.

(A) Wavefronts

Fig. 51.22-Compressional, P, and shear, S, wave propagation in or around a fluid-filled borehole.


Pseudo-Rayleigh

Compressional

i I Airy Phase

IIMt+

Fig. 51.23-Acoustic waveform.

Acoustic Wave Propagation in a Fluid-Filled Borehole The propagation of elastic waves in a borehole filled with liquid has been studied extensively.60-70 Only a qualitative description of the phenomenon will be given here for identifying the components of an acoustic pulse reoorded in a borehole.

The general geometry for the transmission method is illustrated in Fig. 51.22, which shows a single receiver logging sonde. Two pressure transducers are spaced on an acoustically insulated body, the upper one to generate compressional waves in the borehole fluid and the lower one to detect compressional waves reaching it. The receiver converts these waves to electrical signals. These are transmitted to the surface and displayed on an oscilloscope as a record of received-signal amplitude vs. time and recorded either in analog form on film or digitally on magnetic tape.

This received signal, which is referred to as the acoustic waveform, represents several acoustic waves and is illustrated by the synthetic waveform trace shown in Fig. 51.23. For the usual case of a liquid-filled borehole in a formation with both the compressional- and shear-wave velocities higher than borehole fluid velocity, two body (or head) waves and two guided waves are propagated. These waves are shown in Fig. 5 1.23 in the order of their arrival time at the receiver: (I) compressional wave, (2) shear wave. (3) pseudo-Rayleigh waves, and (4) Stoneley waves.

Compressional and shear waves, which are also called P. primary, and S, secondary waves, respectively, are head or body waves because they travel in the body of the formation. Pseudo-Raylcigh and Stoneley waves, which also are called reflected conical (or normal mode) and tube wave (or water arrival). respectively, arc guided waves because they require the presence of the borehole for their existence.

A description of the various ray paths of these waves may help further in understanding elastic wave propagation in and around the borehole. The acoustic transmitter shown in Fig. 51.22 generates compressional waves

traveling with a velocity, vf. in the mud. When these waves reach the borehole face, they are both reflected and refracted. For angles of incidence less than the Pm wave critical angle tI1,,

part of the energy is transmitted into the formation in the form of compressional wave and another part as a shear wave, and the remainder is reflected back into the mud as a compressional wave, all according to Snell’s law.

At or near the P-wave critical angle, a shear wave is still transmitted into the formation and P-wave reflected back into the mud, but a P-wave is critically refracted and travels with the v,’ in the formation, close and parallel to the borehole wall, while continuously radiating P-wave energy back into the mud at the same P-wave critical angle (Fig. 5 I .22).

At the S-wave critical angle (o,,).

O,y=sin-’ “f , ( > v 5

the S-wave is critically refracted and travels with the \J,, in the formation along a path similar to that of the refracted P-wave. It also continuously radiates P-wave energy back into the mud at the S-wave critical angle (Fig. 51.22). Beyond the S-wave critical angle, all the incident energy is reflected back into the mud to form the guided pseudo-Rayleigh waves (Fig. 5 1.24).

To summarize, the compressional wave travels as a P- wave between the transmitter and the formation, in the formation, and also between the formation and the receiver (PPP); the shear wave travels as a P-wave between the transmitter and the formation, an S-wave in the formation, and again as a P-wave between the formation and the receiver (PSP). If the formation shear-wave velocity is slower than borehole fluid velocity, shear waves cannot be refracted along the borehole wall; therefore, no shear head wave is generated.

As described earlier, compressional and shear waves travel at velocities determined by the elastic moduli and the density of the formation:

.(7)

and

( . . . .

p,, is the bulk density of formation, and I,, and I, are compressional- and shear-wave transit times.

The body waves travel at all frequencies at speeds given by Eqs. 8 and 9. They are nondispersive (variation of velocity with frequency is negligible), and undergo attenuation and geometric spreading. Attenuation, 01, of the body waves is proportional to the logarithmic ratio of the amplitudes, A 1 and A?, at distances s t and s? from the source 15,t6:

51-13 ACOUSTIC LOGGING

where (Y is in decibelift and F,, is a geometrical spreading factor.

The tingy packet shown between the compressional and shear waves is called the leaky or PL mode. 66 It is a guided wave generated by the interaction of the formation with totally reflected compressional waves between the compressional and shear critical angles. Paillet and White@ have shown that the leaky mode propagates at a velocity close to that of compressional waves in the formation and its phase velocity decreases with increasing frequency. They also have shown that the leaky mode amplitude, and hence the shape of the compressional wave train, varies with a change of Poisson’s ratio.

Pseudo-Rayleigh and Stoneley waves are the two main guided waves. They both arrive after the shear wave, have larger amplitudes and longer durations than cithcr the compressional or the shear wave, and are disper- aivc.67 The pseudo-Rayleigh wave is gcneratcd by the total internal reflection of the acoustic energy at the borehole face beyond the shear critical angle. It travels within the borehole by multiple internal reflections without loss of energy into the formation; therefore, it is a guided wave. Its amplitude decays exponentially in the formation away from the borehole face, but is oscillatory in the fluid. A pseudo-Rayleigh wave is not generated unless I’., > l’f and it travels with a velocity 11,. such that vf< I’,. s v,> with an Airy phase traveling slower than ‘f.

Fig. 5 I .25 shows the dispersion characteristics for the phase and group velocities of the guided waves in a fluid-filled borehole. ” The parameters used are (1) for the formation, P-wave velocity= I5 x IO3 ftisec, S-wave velocity=9~ 10’ ftisec, density=2.3 g/cm”, and (2) for the borehole fluid, P-wave velocity=6x 10’ ftisec, density = 1.2 g/cm3 : the borehole diameter is 8 in. The phase and group velocities plotted are normalized to the P-wave velocity of the borehole fluid.

As shown in this figure, the pseudo-Rayleigh waves are very dispersive. At the low-frequency end. there is a cutoff frequency below which these waves are not generated. At this frequency, the pseudo-Rayleigh wave phase velocity is equal to the shear-wave velocity of the formation and it steeply decreases with increasing frequency and asymptotically approaches at high frequencies the velocity of the fluid in the mud. Group velocity of pseudo-Rayleigh wave has an Airy phase that travels more slowly than the borehole fluid velocity (Fig. 5 1.25). Pseudo-Rayleigh waves have large amplitudes and arrive after the refracted shear wave, often making identification of the smaller-amplitude S-wave arrival difficult. However, only a small error is made if the velocity estimates are made by using the pscudo- Rayleigh arrivals.

The second type of guided waves is the Stoneley wave. which is the true surface wave coupled between the borehole fluid and the formation. The particular motion of these waves is shown in Fig. 5 1.26. 7’ where Y is the borehole radius. Their amplitudes decay exponentially both in the fluid and in the formation away from the borehole face. As shown in Fig. 51.24, they are slightly dispersive. have no geometric spreading, and travel at

<

----- p

- s -. -. Guided Waves

Fig. 51.24-Two-receiver sonde and the ray paths of body and guided waves.

CUtOIl Frequency

- - Group

I I I 0 10 20 30

FREQUENCY. ktiz

Fig. .51.25-Dispersion characteristics of the pseudo-Rayleigh and Stoneley waves.


i Rock I

r 0 r=R

Elorehole F.X.?

Fig. 51.26-Stoneley (or tube) wave particle motions

Formrtlo”

Fig. 51.27-Transit time measurement by a single-receiver tool.

ou1put From Receiver 1

OlAput From Receiver 2

Fig. 51.28-Transit time measurement by a two-receiver tool.

velocities slightly slower than that of the borehole fluid or formation shear wave velocity, whichever is less.

Unlike the formation shear wave or pseudo-Rayleigh waves, Stoneley waves always are present, whether or not v,~ is greater than vf. They arrive as a compact pulse slightly later than that for a direct fluid arrival or shear arrival if v,~ < vf. Stoneley wave amplitudes are high at low fre

9 uencies and decay rapidly with increasing fre-

quency. ’ In the low-frequency end, the Stoneley waves are called tube waves and travel with a velocity, v,, given by’

v, = “f

( >

. . . . . . . . . . . . . . . . . . . . . . . . . Kf ,~,

57

where Kf is the bulk modulus of the fluid, given by

Q=P~; >

and

(9)

Therefore, in formations with v, < vf, so that neither shear nor pseudo-Rayleigh waves are present, the Stoneley wave can be used to estimate formation shear- wave velocity if formation bulk density is available from a density log.

The dispersion characteristics described so far (of the pseudo-Rayleigh and the Stoneley waves) are for a borehole containing a point source. The effects of the logging sonde on dispersion behavior also have been investigated by Cheng and Toks6z.67 Their study indicated, first, that the dispersion curves for the pseudo- Rayleigh wave are shifted to lower frequencies as the borehole radius increases. They further found that for a relatively rigid tool, presence of a logging sonde simply makes the borehole diameter appear smaller, thus shift- ing the dispersion curves to higher frequencies.

As stated at the beginning of this section. only a qualitative description was given of the elastic wave propagation in a fluid-filled borehole. Ray theory is only an approximation when describing elastic wave properties in a cylindrical geometry. Accurate description of this phenomenon requires solution of the wave equation for cylindrical boundary conditions. The reader is referred to the references given at the beginning of this section for a more quantitative treatment.

Methods of Recording Acoustic Data As described in the previous section, an acoustic waveform is rich in information. It may have four component waves: compressional, shear, pseudo-Rayleigh, and Stoneley. Each of these, in turn, has four measurable properties: velocity, amplitude, amplitude attenuation, and frequency. 27

Various methods of logging were developed to record one or more of these properties. A brief description of some of these logging techniques, with emphasis on those in more common use. follows.


-------- MeasuredTnnsltTlmr

Fig. 51.29-The effect of hole enlargement on the response of acoustic velocity logging tools: (a) one-receiver type and (b) two-receiver type.

Conventional Acoustic Logging

The most commonly used property of acoustic waves in a borehole is the velocity of compressional waves. In conventional acoustic logging, the time, t, required for a compressional wave to travel through 1 ft of formation is recorded as a function of depth. This parameter, 1, referred to as the interval transit time, transit time, or travel time, is the reciprocal of the velocity of the compressional waves:

,=,,J- “P

Transit time also is referred to as compressional-wave slowness and is identified as fP to differentiate it from shear wave transit time:

Velocities observed in acoustic logging vary from 4,000 to 25,000 ft/sec; hence, the travel times range from 40 to 250 ~s/ft.

Tool Characteristics. The original acoustic logging tool, as mentioned earlier, used one transmitter and one receiver (Fig. 51.27). Values of L recorded in this ar- rangement, however, also include travel time of sound in mud in the borehole. To remove this component, a dual-receiver commercial tool was introduced74 to measure the time difference between the arrival of the signal at the first receiver and at the second receiver (Fig. 51.28).

Two-receiver systems, however, also were found to be unsatisfactory, especially at boundaries of hole ir- regularity, 75 as illustrated in Fig. 5 1.29.

To improve accuracy of 1 measurement further, a borehole-compensated sonde (Fig. 51.30) with two

Transmitter

lr Transmitter

Fig. 51.30-Borehole-compensated acoustic log


Measurements from Lower Transmftler LT +I

Fig. 51.31-Travel time measurement with the borehole-compensated acoustic log.

transmitters and four receivers was developed.76 This borehole-compensated tool may be considered to be composed of two separate two-receiver systems. As illustrated by the measurement scheme in Fig, 5 1.3 1, per- turbations caused by hole irregularities are oppositely directed; therefore, they cancel. These sondes usually have a 2-ft span between the receivers with a 3-ft spacing between each transmitter and its near receiver.

h

ib,

Fig. 51.33-The effect of bed thickness on the response of an acoustic velocity logging device: (a) bed thinner than the span and (b) bed thicker than the span.

Caliper Hole Diam.

Inches

i 16

BHC Sonic Log 2’ Span

t p see/it

100 70 40

Fig. 51.32-Presentation of acoustic log

Log Presentation. Transit time 1 measured by acoustic velocity logs is recorded as a function of depth across Tracks 2 and 3 in units of microseconds per foot (psecift). The typical example shown in Fig. 51.32 also has the integrated travel time recorded at the left edge of Track 2 as a series of pips, placed at l-millisecond intervals.

Additional Curves Recorded. A three-arm caliper and a gamma ray curve can be recorded simultaneously in Track I of the conventional acoustic logs (Fig. 51.32). The gamma ray curve can be replaced or supplemented by a spontaneous-potential (SP) curve; however, this SP should be used only for qualitative interpretation because of proximity of the electrode to the metal in the sonde.

Tool Span. The usual span for the acoustic log receivers is 2 ft; however, tools with receiver spacings of 3 in.77 to 1 rn” or longer also have been developed for special applications.

The shorter the span, of course, the more detail given by the tool. The relative effects of bed thickness. h, and tool span on measured transit times are illustrated in Fig. 5 1.33. The log measures only the formation between the receivers. The measured transit time is the weighted average of transit times in formations between the receivers.

Cycle Skipping and Triggering on the Noise. In transit time logging, the first arrival of the acoustic pulse must trigger both receivers of the sonde to yield correct values

ACOUSTIC LOGGING

Detection Levels

Near Receiver -

Far Receiver

I I + 1 Cycle 14

Fig. 51.34-Cycle skip and triggering on the noise

of t. Under certain conditions, even though the first arrival is strong enough to trigger the first receiver, it may be attenuated to such an extent that by the time it reaches the far receiver it may be too weak to trigger it (Fig. 5 I .34). Instead, the far receiver may be triggered by a later arrival in the same acoustic pulse. This causes large and abrupt increases in the recorded transit time values. This phenomenon, known as “cycle skipping,” may occur when the signal is strongly attenuated by (1) gas sands, especially if they cause gas in the mud; (2) poorly consolidated formations: (3) recently drillstem-tested intervals, because of the release of gas; (4) fractured formations: and (5) aerated mud.

If the detection levels are set too low, however, either one or both receivers may be triggered by noise, which is always present as the tool is being dragged up the hole. Depending on the receivers involved, triggering may cause 1 spikes either too short or too long. Examples of cycle skipping and trig ering by noise are illustrated in Figs. 51.35 and 51.36. $9

Calibration. The precision of measurement of acoustic transit time with the acoustic log is determined by the precision of the timing circuitry, which, in turn. is controlled by the frequency of the quartz crystal used. For the usual crystals of 2.5 MHz, the potential resolution of the transit time measurement is f0.4 psecift.

The accuracy of the transit time measurement, however, depends on many other factors in addition to the precision of the timing circuitry. A discussion of some of the factors affecting the measurement of transit time is given by Thomas.‘j

51-17

SP 1 / 1’Span

5 L-

- I

3’Span

7; P 4

3’Span Cycle Sklpptng .Accentuated

Fig. 51.35-Sonic log run in Edwards limestone: (a) 1-ft span, (b) 34 span, and (c) 34 span with intentionally accentuated cycle-skipping.

An essential factor is to ensure the proper calibration of the logging system. Calibration procedures of each commercially available acoustic velocity system are described in respective service company manuals. These should be required before and after logging to ensure the accuracy of the surface equipment. It is important to emphasize, however, that most calibration procedures do

Induction Resistivity

(API Units) (f]M) 50 100 0.2 2.0

Interval Travel Time

(psecht)

200 150 100

-7- x

Fig. 51.36-Cycle skip and noise on acoustic log


TIME, @SEC

2000 3000

Fig. 51.37-Acoustic waveform recording

L Sonde

Fig. 51.38-Approximate volume of investigation of conventional acoustic logs.

just that. They merely check linearity of some of the circuitry in the surface instrumentation without any input from the downhole sonde.

A true calibration requires measuring the response of the complete system, surface instrumentation, and sonde in a standard environment. For this purpose, the tool is placed in a fluid-filled steel sleeve and transit time is checked against the known value of 57 psec/ft. In addition, some free pipe in the surface casing should be logged while going in and coming out of the hole, and checked against the value for steel of 57 psec/ft. Anhydrite beds, with a transit time of 50 pseclft, and other formations with known transit times sometimes can be used to check the accuracy of the log; however, these methods are useful only if the downhole velocities in naturally occurring rocks are known not to vary from location to location or with depth of burial.

Amplitude/Time Recording

As described earlier, the acoustic wave (Fig. 51.37a) contains information other than compressional wave velocity. One of the methods developed to record some of this formation is the amplitude/time recording. In this method, which is also called the “X-Y mode,” the amplitude of acoustic energy is recorded as a function of time at preassigned depths along the wellbore (Fig. 5 1.37~). Usually, this is achieved by analog recording of the output of one of the receivers on film.

Within the last few years, however, the introduction of wellsite and downhole computers has made possible the digital recording of waveforms from an array of acoustic receivers. For example, with one of these tools, a waveform is digitized at every %-in. depth interval of the borehole to obtain more than 500 data points. Pro- cessing of this wealth of new information is a current area of research that is expected to increase significantly the usefulness of borehole acoustic measurements.

Intensity/Time Recording

For most applications, analog recordings of waveforms at %-in. depth intervals are rather cumbersome to use. Hence, for routine use, to obtain a continuous recording or a log, waveforms are recorded in the intensity/time mode. In this presentation, each waveform is reduced to a series of dashes of varying width and intensity, depending on its frequency and amplitude (Fig. 51.37b). The process can be visualized by rotating the acoustic waveform of Fig. 51.37b by 90” on its horizontal axis and then recording the positive-going portions of the wave train as series of dashes and leaving the negative- going portions as blank spaces, as shown in Fig. 51.37 c. The intensity/time log (Fig. 51.37d) is obtained by stacking these dashed lines from each depth interval.

Unfortunately, this process has not been standardized. Some service companies have the negative part of the waveform as the dark dashes and the positive part as the light blanks; other companies, vice versa. Also, some service companies have the time increasing from left to right, while other companies increase in the opposite direction. The various trade names for this presentation are Variable Density Log’” (VDL) by Schlumberger and Dresser, 3-D Log’” by Birdwell, and Micro-Seismogram Log’” by Welex.


Long-Spaced Acoustic Logging Introduction. Conventional acoustic logs have a relatively shallow depth of investigation, Di. The approximate bulk volume of the rock investigated by conventional acoustic logs is illustrated in Fig. 51.38. so

This region is most subject to alterations because of stress relief, mechanical damage caused by drilling, and chemical alteration (clay hydration) caused by drilling fluid. An important early study by Hicks” clearly demonstrated that acoustic velocities in certain formations sensitive to damage were significantly lower when measured near the borehole face than when measured deeper in the formation. Hicks” clearly demonstrated that these borehole effects on acoustic velocities diminish with increased transmitter-to-receiver spacing. Since then, many investigators have observed drastically poor logging data caused by borehole enlargement and formation alteration around the borehole.

Borehole Size, Effects of borehole geometry on log measurements can be considered in terms of hole rugosity and hole enlargement. Borehole rugosity, which can cause significant errors in pad-type tools (such as density. sidewall neutron porosity, microrcsistivity, and high- frequency dielectric measurements) can produce diffrac- tions in acoustic waves propagating along the borehole. In general, these should not affect the first-arrival compressional transit time measurements but can affect the

190

160

170

160

- 150 7 i 140

2 130

120

110

100

90

Long Spacing 8-10 ft Sonde

Conventional 3-5 ft Sonde

Transmitter-Near Receiver Spacing

6 8 10 12 14 16

HOLE DIAMETER. IN.

16 20

Fig. 51.39-Maximum detectable formation transit time, various transmitter-to-near-receiver spacing.

Fig. 51.40-Effects of cavity on density, sldewell neutron, and acoustic logs.


Long Spacing Acoustic Log

Conventional Acoustic Log

R

R

- R

R

T

‘r\;; i e :::I d :_p

:. :. 1 g z:i; i o::: n .’ n I; e::jI ; :. ::. ::: ‘. :. .’ ::: r ., :.:.:. :. m ‘. :.

:. a t

&

‘. :, ‘. ‘... .. ‘. .,.I. i .‘. ‘. ‘. .’ 0 ‘. .. n

Fig. 51.41-Comparison of depth of investigations of conventional and long-spacing acoustic logs.

amplitudes. The hole size, however, can have a significant effect on the transit time measurements if the hole is large enough and the tool is centralized because the acoustic energy traveling directly down the hole in the mud might arrive at the receiver before the formation compressional wave.

Hole size effects on acoustic measurements have been investigated extensively. ‘%** For a centralized tool, Goetz et al. 8L computed the travel times along the direct mud path and the refracted path in the formation, for various hole sizes. Some of their results are illustrated in Fig. 5 I .39 in terms of I vs. borehole diameter. Below the line labeled conventional 3- to 5-ft sonde, a centered tool will read the formation transit time. Between this line and the dashed line (computed for a receiver with a 5ft spacing from the transmitter), a centered tool will record a value intermediate between formation and mud transit times. Above the dashed line, a conventional acoustic log measures the velocity of compressional waves in the mud. The upper solid line is for a longer-spacing acoustic log with 8- to lo-ft receiver spacing. Below this

Conventional (3-5 11)

Long Spacing (E-10 11)

40 120 100 150

5

I a 150 < 30

120

’

9 100

f

E 20

2

p a 10

A

I

1 2 3 4 5 6 7 8 9 IO 11 12 13 14 1s ALTERATION DEPTH

(Inches from Borehole Wall)

Fig. 51.42-Effects of formation alteration on measurements with convemional (3 lo 5 ft) and long-spacing (8 to 10 ft) acoustic sondes.

line, the long-spaced tool measures high formation transit times in larger-diameter holes in the range where conventional tools would record incorrectly low formation travel times.

Even though these borehole size effects are important. conventional borehole-compensated acoustic logs can record reliable measurements under much more adverse borehole conditions than other porosity tools, such as density and neutron tools. The influence of a cavity on the density, sidewall neutron, and conventional acoustic tools is compared in Fig. 5 1.40. s3 In this figure, over the elliptical cavity indicated by the calipers on the density and acoustic logs, both the density and sidewall neutron curves are useless, whereas the acoustic log provides reliable data. This feature of the acoustic log is used to complement density and neutron porosity that are not reliable because of poor hole conditions.

Formation Alteration. A more important factor affecting the borehole acoustic measurements is formation alteration or damage around the borehole (Fig. 51.41). This can occur because of stress relaxation near the borehole wall, mechanical damage caused by prolonged exposure to drilling, or chemical alteration of the foma- tion by interaction of drilling fluid with sensitive clays in the formation. Under these conditions, accurate measurements of acoustic velocities depend on hole size and transmitter receiver spacing, as well as velocities of both altered and unaltered zones around the borehole.

Formation alteration was investigated by Goetz et ul. ** by assumi g n a step profile transit time around the borehole, with the altered or damaged zone having a transit time kd that is greater than the undisturbed formation 1 and a mud transit time of 200 psec/ft. They computed the depths of investigation of conventional acoustic (3- to 5-ft) and long-spacing (8- to lo-ft) acoustic logs in a 10.in.-diameter borehole. They also


12'

10'

10'

LTl

Fig. 51.43-Schlumberger long-spacing sonic log.

calculated formation alteration (td-t) as a function of alteration depth for unaltered formation transit times of 100, 120, and 150 psec/ft. Their results, plotted in Fig. 5 I .42, illustrate the ability of the longer-spacing tool to overcome the effects of formation damage. In this figure, the area to the left of each curve represents the conditions for reliable measurements. For example, at an alteration of 20 psecift, a conventional tool can handle an alteration of 5 in. if the formation transit time, I, is 100 psec/ft, but only 3 in. if t= 150 psec/ft.

Long-Spacing Acoustic Logging Tool. Both the borehole enlargement and the formation alteration effects can be accommodated by acoustic tools with longer transmitter-to-receiver spacings. A schematic diagram of one such tool, the Long Spacing Sonic’” by Schlumberger, s4 is shown in Fig. 5 1.43. Two transmitters, 2 ft apart, are at the bottom, and two receivers, 2 ft apart, are at the top, with 8ft spacing between the two sections. Two long-spacing logs are recorded concur- rently, one with 8- to IO-ft spacing and the other with lo-

,’ LTd’

Fig. 51.44-Borehole-compensated transit time measurements: (a) conventional and (b) depth derived.

to 12-ft spacing. Borehole compensation is accomplished by a depth-derived measurement scheme illustrated in Fig. 51.44b, rather than the inverted array technique shown in Fig. 5 1.44a, which was described earlier (Fig. 5 1.3 1). To obtain the transit time at depth level, first the transmitter Tr is pulsed twice and the respective times fI =Tr -RI, t? =Tr --‘RI are recorded. The transit time for this case is given by

II -tz tI =- psecift,

2

which is subject to errors discussed earlier if the hole size is different at the two receiver positions.

After the tool has moved 9 ft 8 in. up hole, the transmitters will be spanning the same depth interval between the points of refraction. This time they are each pulsed, and the travel times, t3 =Tt -+R? and f4 =Tz +Rz are recorded by the second receiver (Rz). For this second case, the transit time is given by

f4 -13 11 = - psecift,

2

which is subject to the same errors as t, but in an opposite direction. The depth-derived transit time for the 8 to IO-ft spacing is obtained by averaging these two measurements:

II +t2 t-

2

A similar borehole compensation is obtained for the lo- to 12-ft spacing by using the second transmitter T2 in the first position, instead of T , , and the first receiver R r in the second position, instead of RZ


BHC Sonic Travel Time

(psedft) 140

Hole O::n 4 Days 40

--------_---_ --Hole Open 79 Days -r-r-~Ir-lr-~-r1-l r y-r 7 T r

.

r- -;

<T- ., -'

i ..- -I

C'> CT ,,

_ ' r

. j

Fig. 51.45-Formation alteration caused by exposure to mud; bit size 12% in.

Effects of prolonged exposure to drilling and drilling mud on acoustic velocities measured with a conventional borehole-compensated acoustic log are illustrated in example logs in Fig. 5 1.45 taken from the reference by Misk et al. *’ The dashed curve is obtained after the hole has been exposed to drilling for 4 days with the borehole relatively undamaged; the solid curve is after 79 days of exposure. During this period, the formation over much of the interval has been damaged enough to increase the 1 by 30 psecift or more.

As described previously, long-spacing acoustic logs are less affected by altered zones A comparison of conventional and long-spaced acoustic logs is shown in Fig. 51.46 for a sand/shale section.73 In the upper section, the conventional log is reading higher values of I than those by the long-spacing tool, probably because of shale alteration. In Sand Z, both logs are in agreement. whereas in sections directly above and below Sand Z. the conventional log is reading significantly higher values of t. probably because of hole washouts.

250 pseclft

LJJ

‘( :. Spacing

Fig. 51.46-Conventional and long-spacing acoustic logs tn a sand/shale section.

The example in Fig. 5 1.47 is a comparison of the two acoustic tools in shallow and deeper Louisiana gulf coast sand/shale sequences. s6 Physical characteristics of both the shale at 3,470 ft and the sand at 3.500 ft have been altered by drilling and interaction with mud filtmte. The conventional spaced tool is reading 15 psecift higher because of this alteration. This is also reflected by a lo-millisecond difference between the respective transit time integration curves shown in the depth tract. In the deeper section, as the formations become more compacted, the formation alteration is reduced; hence, the conventional and long-spacing measurements are in agreement within the interval 8,500 to 8,600 ft.

Even though, in most instances. the t values from 8- to IO-ft and lo- to 12-ft spaced receivers are in agreement, very deep formation alteration can sometimes affect the I values recorded by the S- to IO-ft receivers. The example in Fig. 51.48 is from a shallow well with modified depths. ” In the upper zone, the 8- to IO-h spacing is reading values higher by IO psecift than those given by


il b : I i i

-

-

Fig. 51.47-Conventional (BHC) and long-spacing (LSS) acoustic logs in a Louisiana gulf coast sand/shale sequence.

the lo- to 12-ft spacing, because of very deep formation alteration. In the lower section, the 8 to IO-ft spacing still reads a few microseconds higher down to the compacted formations below depth 227 ft.

In the final example shown in Fig. 51.49, the better response of the long-spaced logs in enlarged boneholes is illustrated. In the upper section, the conventional spaced tool is reading the mud transit time in a hole washed out

GR - psedft

160 60

Fig. 51.48-Very deep formation alteration.

to 20 in. In the lower section, the borehole is not washed out but the conventional tool is reading up to 60 ,usec/ft too high because of formation alteration. Below 8,700 ft, all three curves (i.e., the 3- to 5-ft, 8 to lo-ft, and IO- to 12-ft curves), are in agreement.

Summary. Borehole size and formation alteration can significantly affect the properties of acoustic waves


\ ’ 1

I-

I -

\ I /

c

I

1 I- I I - I I_

I

/ I-

,‘“L

I 3’-5’+\ BHC :

-I i

Fig. 51.49~-Response of conventional and long-spacing acoustic logs In an enlarged borehole.

Fig. 51.50-Identification of shear arrivals on analog recording of (a) acoustic waveforms and (b) variable-density (3D) presentations.

traveling in a borehole. The long-spaced acoustic tools are much less affected by borehole conditions and yield more reliable values of compressional-wave transit times under borehole conditions in which conventional tools would be grossly in error. The vertical bed boundary resolution of the long-spaced tool is the same as that of the conventional tool since the receiver spacing is 2 ft for both. Because of the longer transmitter-to-receiver spacing, the acoustic energy has to travel farther; therefore, it is attenuated more. This has caused more frequent spik- ing and cycle skipping on the long-spaced acoustic logs; however, this technology is improving through the introduction of more powerful transmitters, more sensitive receivers, downhole digitizing, and surface processing of waveforms.

Shear-Wave Logging The borehole acoustic measurement methods described so far have been for obtaining compressional wave velocities. The desirability of obtaining other information contained in the acoustic waveform has long been recognized. I7 Most of the effort has been directed toward obtaining the velocity of shear waves.

Early attempts involved hand-picking the shear-wave arrivals on the analog recording of either waveforms or variable-density-microseismogram or three-dimensional (3.D)-presentations as illustrated in Fig. 5 1 .50e3

Another method involves automatic recording of shear-wave travel times by a bias technique. “v’)’ In this method, a high-amplitude event following the compressional-wave arrivals is assumed to be the shear wave arrival. The transit time of these waves is measured by setting the voltage bias level higher than the compressional-wave amplitudes.

A thorough investigation of conventional methods for determining shear-wave velocities from long- and short- spaced acoustic logs was conducated by Koerperich.” In this study. borehole experiments were conducted by using a conventional Schlumberger Borehole Compen- sated Sonic Log@ (BHC) with two transmitters and four receivers at 3- and 5-ft spacing and a Schlumberger experimental long-spaced tool with a single transmitter and four receivers located at 10, 12. 14. and 16 ft from the


transmitter. Waveforms recorded with these tools in a carbonate section are shown in Fig. 51.51 for several transmitter-to-receiver spacings. As indicated in this figure, it is easier to identify the later arrivals on the longer-spacing waveforms because of the greater separation in arrival times.

Some measurement results from this study are shown in Figs. 51.52 and 51.53 for a carbonate and a sand/shale section, respectively. For both compressional and shear waves, long spacings generally yield slightly lower travel times (higher velocities) than short spacings. Another important aspect of this study involved laboratory measurements of acoustic velocities on core samples. Compressional and shear-wave velocities were measured on core plugs subjected to simulated subsurface overburden and pore pressure conditions. These results are lotted as circles in Figs. 51.52 and 51.53. Koerperich r, states that average agreement between the laboratory and log shear velocities (for both the long- and short-spaced tools) is within 2% for carbonates and 8% in sandstones, and that it is slightly better for the compressional waves. He states further that these differences between the laboratory and the log values are nonsystematic.

The foregoing discussion demonstrates that determination of shear transit times in a borehole by hand-picking the arrival times from waveforms or from variable- density presentations is at best a tedious and not very accurate process. Further, attempts to automate this process by threshold detection have been subject to errors when using an axial transmitter/receiver logging technology designed primarily for measurement of compressional-wave travel times. The reasons for these errors are explained by some of the recent modeling studies of acoustic wave propagation in a fluid-filled borehole. 6sm67 These studies demonstrate that the shear- wave arrival is indistinguishable from the onset of the reflected conical waves on the synthetic acoustic waveforms. However, the phase and group velocities of the reflected conical wave at its low-frequency cutoff are equal to the formation shear-wave velocity (see Fig. 5 1.25). Hence. if the onset of the reflected conical wave is measured in error, the transit time will be close to that of the shear wave. This might be the case in some of the previously discussed studies.

Acoustic Array Logging Borehole modeling of acoustic wave propagation has demonstrated the need for a new generation of acoustic logging technology to extract more information from acoustic waveforms. Acoustic logging tools having arrays of transmitters and receivers, and complex digital signal processing capabilities have been developed to analyze the data obtained.

One such tool is shown in Fig. 51.54.” It has a Iower- frequency transmitter (1 1 kHz vs. the conventional 20 kHz), an array of four receivers placed at a longer spacing from the transmitter, and a downhole digitizer to record waveforms without cable distortions. Surface instrumentation records the signals digitally. The processing method, using a four-fold correlation algorithm. analyzes waveforms from the four receivers simultaneously to obtain compressional and shear-wave transit times (Fig. 51.55).

Depth. II

591.6

591.6

r “S‘ Wave Time Pick T-R Spacing

3’

5

5946-v - 10’

594 7 12’

0 1000 2000 Time.qec

Fig. 51.51-Acoustic waveforms recorded at various transmitter-to-receiver spacings in a carbonate section.

Another acoustic array log is a 12-receiver experimental sonde developed by Schlumberger. ” It has a single IO-kHz transmitter and an array of 12 receivers. The receivers have been arranged both in a nonuniform array spanning 4 ft with spacings of 0, 6, 9, 12, 1.5, 18, 21, 24, 27, 30, 36, 42, and 48 in. and in a uniform array spanning 5.5 ft with 6 in. between the receivers. The spacing between the transmitter and a receiver array is adjustable between 5 and 25 ft.

An experimental tool developed by Elf Aquitaine uses an array of transmitters and an array of receivers. ” The transmitting array has five transmitters uniformly spaced at 0.25 m apart; hence, it has a span of 1 m. The receiving array has 12 receivers uniformly spaced at I-m intervals. The distance between the receiving and the transmitting arrays is set at 1 m.

Finally, the prototype sonde by Schlumberger (shown in Fig. 51.56) has an eight-receiver array and two transmitters.‘j In addition, it has two additional receivers spaced at 3 and 5 ft from the transmitter to simulate conventional tools. It also has the capability to measure the compressional-wave velocity of the borehole fluid. Again, waveforms are digitized downhole and transmitted to the surface for recording and analysis.

As apparent from the previous discussion, this is a very active area of development. Tools are constantly being developed to explore the extraction of additional information, such as pseudo-Rayleigh and Stoneley wave velocities, from acoustic waveforms. Capabilities are being developed to record large amounts of data. For example, more data are obtained with one of these array tools in a l-mile-deep well than are recovered in a l-mile seismic section.

A parallel and complementary area of development is signal processing methods for analyzing these data. Processing methods such as direct phase determination, y4 slowness time coherence, 93 and semblance 77,95 have been developed to permit automated analysis of shear-wave transit times. Array processors are being added to wellsite data acquisition systems to permit real- time signal processing.


Fig. 51.52-Borehole and laboratory measurements of compressional- and shear-wave transit times in a carbonate section.

Fig. 51.53-Borehole and laboratory measurements of compressional- and shear-wave transit times in a sand/shale section.

ACOUSTIC LOGGING

r---- -------------

-;rx;]

, L------------------l

Van Cartridge

1 (Telemetry. Analog-to-

0.3 Ill

0.3 Ill

0.3 In

Digital bonvertk)

spacers

Fig. 51.54-A four-receiver acoustic array log with a downhole digitizer.

So far, emphasis has been on extraction of shear-wave velocity from acoustic waveforms. With continued im- provement in tool design and signal processing, it is expected that in the not too distant future, acoustic logs will record not only the velocities of compressional, shear, pseudo-Rayleigh and Stoneley waves, but their attenuations as well.

Reflection Method The reflection method of acoustic wave propagation logging is basically similar to sonar. A single transducer rotates at constant speed, emitting acoustic pulses in the megahertz range and recording their echoes from the borehole face (Fig. 51.57). As in the transmission method, both travel times and amplitudes are used. The azimuth of the beam also is recorded.

The first such logging tool, the borehole televiewer, Vh used only the amplitude of the reflected signals to

51-27

I Gamma

Ray

0 APIU ,

Compr. T&&tP -

C

iii

Fig. 51.55-Compressional- and shear-wave transit time log obtained by analysis of the waveforms recorded with the sonde in Fig. 51.54.

generate a picture of the borehole wall. When the borehole wall is smooth, the amplitude of the reflected signal is high; it is recorded as a light spot. Low- amplitude reflections from fractured or vuggy walls are recorded as dark spots. The resulting log is essentially a black and white picture of the borehole wall, split ver- tically along magnetic north and flattened (Figs. 51.58 through 5 1.60).

For the borehole televiewer (BHTV) log, the vertical scale is depth and the horizontal scale corresponds to azimuth of the borehole wall. An isometric view of a vertical fracture intersecting the wellbore in an east-west direction is shown on the left in Fig. .51.58.97 The corresponding BHTV log on the right shows the fracture as two vertical dark lines 180” apart. Similarly, an isometric of a south-dipping fracture or bedding plane is shown with the corresponding BHTV log in Fig. 5 1.59.

An example of a BHTV log (SeisvieweP by Bird- we1198) based on amplitude imaging is shown in Fig.


R Receiver Electronics

~ Fluid-Delta T Measurement

Wideband Receivers Spaced 6” Apart

Rg \ Two Standard Ceramic Receivers

UT\ LT/’

Two Low-Frequency Transmitters

Transmitter Electronics

l-l Fig. 51.56-An eight-recerver acoustic array sonde.

Fig. 51.5743lock diagram of BHTV logging system.

E

S

N

il

*o- --_ --.

W

1 III. .

N E S W N

Vertical Fracture Intersecting Well Bore

BHTV Log

Fig. 51.58-Isometric of a vertical fracture intersecting a borehole and corresponding BHTV log.

51.60 for a borehole intersected by two fractures. The corresponding isometric on the right describes the two different dips and strikes.

Significant hardware and signal processing improvements have been made to early BHTV technology. 97,99-101 Current technology uses transit time information to obtain an image, in addition to the image obtained from the amplitudes of the reflected signals. Transit time images complement amplitude images in many ways. Transit time measurement is essentially a near-perfect borehole geometry tool with a resolution of 0.05 in. BHTV images developed from the transit time measurements can be considered as two- dimensional (2D) relief maps of the borehole.

Further use of transit time measurements is made in generating tilted polar scan displays. 99 These are essentially 3D casts of the borehole, which can be viewed from all directions. The tilted polar scan of Fig. 51.61 shows a damaged section of a casing viewed from two angles, which also can be viewed from any desired angle.

Applications Introduction Some present and possible future applications of acoustic logging will be presented to illustrate the use of borehole acoustic measurements described earlier and listed in Table 51.1. Discussion here will emphasize the more important uses, and only references will be given to more routine and less significant ones.

Seismic and Geological Interpretation Borehole measurements of acoustic properties were developed originally to obtain time/depth curves to use in seismic interpretation. lo2 In addition to recording transit times of the compressional waves as functions of depth, acoustic logs also integrate these data and record a tick mark on the log for each millisecond of elapsed time. These marks are then used in conjunction with check-shot surveys for seismic interpretation. 79,‘03

Recent advances in borehole shear-wave velocity recording also have allowed this technology to be used with surface seismic shear surveys in a way similar to the compressional-wave velocity log use with the seismic compressional surveys. ‘04


An important geological application of acoustic logs has been for correlating geologic sections. As described earlier (see Fig. 51.39), acoustic log response is much less affected by borehole irregularities than are some of the other porosity logs. As a result, acoustic logs provide valid data over a large proportion of the borehole.

Further, acoustic logs usually show much character and detail. Therefore, they have been useful for locating bed boundaries, identifying gas/oil interfaces, and determining subsurface geology. An example of geological correlation is shown in Fig. 5 1.62; even though the two wells in this figure are 10 miles apart, the character of the compressional transit time curves is quite similar.

Porosity Borehole measurements of acoustic velocities were in- strumental in the development of quantitative formation evaluation in the 1950’s, although they were developed initially to aid seismic interpretation. Over the years, the primary use of acoustic logs in formation evaluation has been the determination of porosity from measurements of compressional-wave transit time (t= l/v,). Earlier in this chapter, factors affecting acoustic properties were described through both theoretical and experimental studies of elastic wave propagation in porous media. On the basis of these discussions, it would be at best naive to expect a simple linear relationship between porosity and compressional-wave transit time. However, empirical observations have indeed demonstrated the validity of such a relationship under certain special conditions.

Consolidated Rocks. A commonly used linear relationship for estimating porosity from acoustic measurements (based on laboratory measurements of acoustic velocity and porosity in porous rocks and other materials) was proposed by Wyllie et al. 18,t9 Commonly referred to as the Wyllie time-average equation, it is expressed as

1 G , (l-4) . . . . . . (10)

VP “L V,

or in terms of transit times, as

t=&+(l-4)1,, . . . . . . . . . . . . . . . . . . . . (11)

where ( (= 1 lvP) = transit time of the compressional

waves for the liquid-saturated porous medium,

I~(= l/vL) = transit time for saturant liquid that forms the solid frame of the porous medium,

t, (= l/v,) = transit time for rock matrix that forms the solid frame of the porous medium, and

$I = porosity.

This relationship can be rearranged as

1’(hL -tm)++t, . . . . . . . . . . . . . . (12)

BHTV Log

Dip: Orientation of Minimum Angle: tan-’ h/d

Fig. 51.59~isometric of fracture or bedding plane intersecting borehole at moderate dip angle, and corresponding BHTV log.

N E S W N 5560

5561

5562

5563

5564

5565

Dip Angle q ir ec lia n

58’ N 70 E

Angle Direction 740 N 46 w

Fig. 51.60-BHTV indicating two fractures of different dips and strikes.

Fig. 51.61-BHTV tilted polar image of a section of a damaged casing.


Fig. 51.62-Acoustic log correlation between two wells

Porosity Evaluation from I

t -t, I d=-X-

Ipwtm FCP

,I/(//.//.. 30 40 50 60 70 60 90 100 110 120 130

I,, /Jsec/ll

v, ftlsec i,. @?c/ft

Sandsloner 16,000 - 19,500 55.5 - 51.3

Limestones 21,000 - 23,000 47.6 - 43.5

Dolomites 23,000 - 26,000 43.5 - 38.5

Fig. 51.63-Porosity evaluation from acoustic log

where the slope is m=tL-t,,, and the intercept is b=t,. The most attractive feature of Eq. 12 is its simplicity.

It states that the transit time of an acoustic wave in a porous rock is the porosity-weighted average of its transit times in the matrix and the liquid in its pores. Also, it extrapolates to correct values for 0 and 100% porosities-i.e., I, and tL, respectively.

This simplicity coupled with pedagogically pleasing qualities made Eq. 12 popular and, more importantly, established acoustic logging as an important tool in formation evaluation. As stated, however, there is no theoretical justification for such a simple relationship. In the Appendix, the linear relationship, Eq. 13, is shown to be a second-order approximation of a comprehensive relationship, Eq. A-9, with the intercept h approximately equal to the matrix transit time and the slope m strongly dependent on elastic properties of the porous rock frame and the compressibility of pore fluid. Nevertheless, under the right conditions, a linear dependence of transit time on porosity has been established through literally hundreds of empirical observations.

A graphical representation of the time-average equation, Eq. 11, is given in Fig. 51.63. lo5 This is a good beginning for determining porosity from acoustic log measurements when no other information is available. It provides acceptable values of porosity for well- compacted rocks with uniform pore size distribution and under effective stress (difference between the overburden stress and pore fluid pressure) of at least 4,000 psi.

In most applications, the linear relationship of Eq. 13 has been found to be more useful than the time-average equation, Eq. 11, provided that the values of b and m can be determined. As indicated in the Appendix, the parameter b is approximately equal to (l/v,,,); therefore, it depends on rock matrix properties. Published values for b range from 50 to 60 yseclft for sandstones, from 45 to 50 for limestones, and from 40 to 48 for dolomites.

Velocities of compressional and shear waves for a large number of materials are given in handbooks by Clark lo6 and by Simmons and Wang. lo7 An extensive list of compressional and shear transit times have been compiled by Wells et al. lo8 for minerals and rocks encountered in oil and mineral exploration. Probably the most comprehensive compilation of compressional and shear-wave velocities for marine sediments, rock- forming minerals, and rocks is given, for various pressures and temperatures, in a recent handbook by Carmichael. ‘09 A set of compressional and shear-wave velocity data from the literature is listed in Table 5 1.3 ” for selected materials, to illustrate the range of velocities encountered in and around the borehole.

The values of m depend on the elastic moduli of the rock frame, which in turn are controlled by the effective stress and pore structure and by the compressibility of the pore fluid. Changes in velocities have been observed to become smaller with increasing effective stress. Therefore, pressure dependence of m may be small enough to be neglected in normally pressured sections below 7,000 ft. Effects of pore structure might be


TABLE 51.3-ACOUSTIC VELOCITIES

Material v,(fllsec) v,(ftlsec)

Nonporous solrds

anhydrite calcite cement (cured) dolomite granite gypsum limestone quartz salt steel

20,000 20,100* 12,000 23,000 19,700 19,000 21,000 16,900 * 15,000* 20,000

Water-saturated porous rocks in situ Porosity (o/o)

dolomites 5 to 20 20,000 to 15,000 limestones 5 to 20 18.500 to 13.000 sandstones 5 to 20 16,000 to 11,500 sands (unconsolidated) 20 to 35 11,500 to 9,000 shales‘ 7,000 to 17,000 -

Liquids’ *

water (pure) water (100,000 mg NaCIIL) water (200,000 mg NaCIIL) drilling mud petroleum

4,800 5,200 5.500 61000 4,200

Gases

air (dry or motst) 1,100 hydrogen 4,250 methane 1,500

11,400 -

12,700 11,200

- 11,100 12,000 8,000 9,500

11,000 to 7,500 9,500 to 7,000 9,500 to 6,000

-

described qualitatively by stating that the magnitude of m increases with decreasing grain contact areas. Thus, m is small for crystalline rocks and larger for granular and shalier rocks, ranging from 0.5 to 1.5 psec/ft for carbonates and from I to 3 psec/ft for sandstones.

Compressibility of the pore fluid depends on whether it is gas, oil, or water and becomes significant in poorly consolidated rocks (see Eq. A-7). In well-consolidated rocks under high effective stress, the relative contribution of pore fluid compressibility to the overall rock elastic moduli is small; therefore, variations of m because of pore fluid content may be neglected.

The large range in values of b and m necessitates the use of core analysis data to calibrate the acoustic log for estimating porosity. For this purpose, porosities and travel times are measured on core samples under the equivalent subsurface pressure conditions, and the linear relationship between the two is established by statistical analysis. If laboratory measurements of I are not available, restored pressure measurements of porosity, or porosity corrected for equivalent subsurface conditions can be correlated to I from the acoustic log to establish the linear relationship. provided that adequate depth correspondence between core and log data can be established.

There are numerous field examples of acoustic log measurements yielding reliable estimates of porosity in well-compacted, clean sandstones and carbonates, provided that the lithology is known. Fig. 51.64 illustrates

the close agreement between acoustic-log-measured transit times and core-measured porosities for carbonate sections in two wells.

In fact, the acoustic log in certain areas is the most consistently reliable porosity device. To reiterate, the conditions required are (1) lithology is accurately known, (2) porosity is largely intergranular, and (3) rocks are well compacted and subjected to a differential stress of at least 4,000 psi.

As with other conventional porosity logs, variations in lithology make porosity estimates from compressional- wave transit times unreliable. To overcome this. acoustic logs are used with density and/or neutron logs, or with measurements of shear-wave transit times described in the next section.

Secondary Porosity. Another application of the acoustic log is for estimation of “secondary porosity” in vugular and/or fractured rocks. For this, it is assumed that compressional wave velocity is affected only by the primary or intergranular porosity. The density and neutron logs are assumed to respond to total porosity. Hence, any difference between these is assumed to be secondary porosity consisting of vugs and/or fractures. An example of this is shown in Fig. 5 1.65, where the section contains anhydrite with fracture porosity. ’ ‘u Notice that while the transit time I remains approximately constant over the entire section, density oh decreases from 2.97 to 2.83


South Ralph

Wevburn Saskatchewan

Mlsswpplan LImestone

Tranr,, Tlrn.3 /Jsec/tt

100 85 70 55 40

Salt Potential Spacing - 1 ft, 2 Receivws

millivolts Poro.lfy - (%)

Steelman (Kvqsford) Field

M~ss~rs~pp~en Limestone

Saskatchewan

Tranl,, Tlrnl? /.lsecm

100 85 70 55 40

Specsng - 1 ft. 2 Receivers

Porolltv - (%)

Self Potential

mdlivolts 35 30 25 21 15 10 5 0

~--

3

/

> L-

Sonic Log /---- ore Analysis

Zore I 4naIySiS-j-

t

/ / I I --_--

t ‘?. ’

+-I ----i--1

I r ;

-

I~<-,

i +

-1 L L-

Note: Porosity Scale Based on Matrix Velocity , Vm q 23,000 ft/sec q 23,000 ft/sec

Fig. 51.64-Acoustic log vs. core analysis porosity

ACOUSTIC LOGGING

g/cm 3 . and the neutron porosity 4 W increases from 0 IO 4%. thereby indicating a secondary porosity of 4%.

Poorly Consolidated Rocks. In poorly consolidated sandstones, reliability of porosity estimates from acoustic logs is rather poor. In these cases, usually a combination of density and neutron logs is preferred. One significant advantage of the acoustic log is that it is much less affected by the hole conditions, such as washouts and rugosity. This was illustrated in Fig. 5 I .39 where the density and sidewall neutron logs were responding to hole conditions whereas the acoustic log was found to yield reliable estimates of porosity.

Several methods have been developed to obtain porosity information from acoustic logs in poorly compacted sands. 21.1’1 One approach 2’ involves adjustment of porosity calculated from the time-average equation using a compaction correction factor Fc,,. First. the apparent porosity $,, is computed from

‘-‘,,I I$,=-. . . . . . .(14) ~1‘ - ’ 01

Then this value is corrected by F,, to obtain the corrected porosity, 4,.. from

&=$. . . .(15) ‘P

The values of Fc7, (Fig. 5 1.63) range from 1 to 1.6 or higher. One method used to estimate F,, is based on estimating the compaction of sands from the compaction of adjacent shales. If the transit time of adjacent shales is 100 psecift or less, they are assumed to be compacted. Hence. to obtain the correction factor, the transit time L,,,~ observed in the nearby shales is divided by 100.

FcP=*. . . . . . . . . . . . . . . 100

.(16)

Other methods for determining F,, include determination of porosity either from a resistivity log in a water- bearing sand or from other porosity logs such as density and/or neutron, and then comparing the value with 4,, obtained from the acoustic log.

More recently another empirical relationship for estimating porosity from compressional-wave velocity was developed by Raymer et al. ’ ’ ’ on the basis of extensive field observations of transit time vs. porosity. The relationship reported is for the full porosity range from 0 to 100%; however, for the porosity range of interest, 0 to 37%, it is expressed as

where v, is 17,850 filsec for sandstone, 20,500 ftisec for limestone, and 22,750 ftisec for dolomite, respectively; and of is velocity of sound in the pore fluid.

-

t

Fig. 51.65~Secondary porosity in the Auquilco formation. Neu- quen basin, Argentina.

TRANSIT TIME, psedlt

Fig. 51.66-An empirical relationship for estimating porosity in sandstone, limestone, and dolomite.


Time Average Eq.

1, 56 psec/li.

l Clean Sands

A Shaly Sands

Velocity, ft/sec

80 90 100 110 120 130 140 150 7J60

50 I, INTERVAL TRANSIT TIME, vsec/ft

Fig. 51.67-Velocity/porosity correlations for moderately consolidated to unconsolidated sands.

fif 9 - 5 0 - Laminated 1 -- Structural

-.- Dispersed

Compressional

10 20 30 40 50 60

CLAY/SHALE FRACTION OF FORMATION, %

Fig. 51.69-Estimated shale effects on compressional and shear velocities.

Fig. 51.68-Shaly sand models for acoustic wave propagation

a) Laminated c) Grain Boundary Structural

b) Framework Structural

studies.

d) Dispersed

0 Sandstone

CD Clay

A graphical representation of this empirical relationship is given in Fig. 51.66. Raymer et al. t It found this relationship to be a better estimator of porosity than the time-average equation. They also reported that it is applicable to both consolidated and unconsolidated rocks.

Predictions from this relationship and from the time- average equations were investigated by Hartley It* for the moderately consolidated to unconsolidated sands of the Gulf of Mexico. The lack of agreement indicated in Fig. 5 1.67 led Hartley to the universally applicable conclusion that empirical relationships “may provide er- roneous porosities if they are applied outside of the data set from which they were developed.”

Shaly Sands. Another aspect of Hartley’s study t ” con- siders the effects of shaliness in porosity interpretation. In Fig. 5 1.67, porosity predictions from the empirical relations are worse for the shaly sands. Effects of shales on acoustic velocities are not very well understood; as a result, they are difficult to account for. A recent theoretical study by Mineart’” shed much light on this problem by relating clay effects to their distribution within the rock framework. Minear used the Kuster- Toksoz ‘I4 model of porous media and divided clay distributions into four groups. As illustrated in Fig. 51.68, these four groups are (1) the laminated model (Fig. 51.68a), in which clay-mineral-rich and shaly layers alternate with clean sandstone layers. (2) the framework structural model (Fig. 51.68b), in which shale grains substitute for quartz grains randomly, (3) the grain boundary structural model (Fig. 5 1.68c), in which shale grains occur at some, but not all. boundaries between the quartz grains, and (4) the dispersed clay model (Fig. 51.68d), in which clays occur dispersed in the pore fluid or lining the pores but not between the grain contacts.


90 100 110 120 130 140 150

I,, dn

Laboralory Data (Ref. 27) Field Data (hiked Lithologlar Excluded)

C Limestone OLtmertone ADolomite QDolomltc 1 Sandstones 0 Sandntone

Fig. 51.70-Compressional-wave transit time vs. shear-wave transit time.

One of the obvious conclusions in this study is that the time-average equation is applicable to the laminated model. A more interesting conclusion, however, states that the framework (Fig. 51.68b) and grain-boundary (Fig. 5 1.68~) shales seem to have the same effect on acoustic velocities. Further results of this study are summarized in Fig. 51.69. The differences, t&ly -tclean, between the transit times of the shaly and clean formation for both the compressional and shear waves are plotted vs. the clay or shale fraction for a sandstone with a porosity of 30%. Structural and laminated shales have approximately the same effect on I,, and l-5 but increase t,, more than I,, Dispersed clay, if it has a density close to that for sandstone, has about the same effect on L,, as the structural and the laminated clays: however, its effect on I,, is only about one-third of that by the other two.

Lithology Estimation of lithology from conventional acoustic log measurements may be made by solving for the matrix travel time from the time-average equation if the porosity is known from another source. Even though this technique has been used under certain conditions, matrix transit times of the most common rock types determined in this fashion are not distinct enough to make this a very useful method.

A more deterministic method for establishing lithology from acoustic log measurements is based on the relationships shown in Fig. 5 1.70. In this figure, laboratory- and borehole-measured values of compressional-wave transit times are plotted against shear-wave transit times. Laboratory data cover a porosity range of 5 to 30% for sandstones and 5 to 2.5 % for carbonates. and an effective stress range of 0 to 6.000 psi.” As indicated, each lithology has a well-defined trend, regardless of porosity or effective stress (depth). Lines of equal velocity ratio

Fig. 51.71-Compressional- to shear-wave velocity ratio vs. compressional-wave velocity. Data from Fig. 51.70.

(v,Iv,) are closely spaced for dolomites and limestones- 1.8 and I .9, respectively. The sandstones range from 1.6 for low-porosity sands to 1.75 for high- porosity sands under low effective stress.

Lithology identification is also illustrated in Fig. 51.71 by replotting the velocity ratio data of Fig. 5 1.70 vs. compressional wave velocities.

Use of borehole measurements of compressional and shear transit times is described by NationsEX for determining porosity and lithology in mixed-lithology rocks. He assumes that velocity ratio is a constant for a “pure” rock type: 1.6 for sandstones, 1.8 for dolomites, and 1.9 for limestones. He further assumes that mixed-lithology rocks will exhibit a ratio that is directly proportional to the content of the two minemls and that porosity is distributed equally between the two. From the velocity ratio, he first determines the mineralogical composition; then, on the basis of this information, assigns the ap- propriate matrix transit time for calculating porosity. An example of the results of this technique is illustrated in Fig. 5 1.72 for dolomite/sandstone and dolomite/ limestone mixtures.

Hydrocarbon Content Acoustic signals on microseismogram or variable- density logs are known to disappear sometimes in oil and gas zones in unconsolidated formations. This property is used to locate oil/water contacts. as well as gas caps, but is not completely reliable. Sometimes, even within the bame zone, signal disappearance may or may not be in- dicative of presence of hydrocarbons.

Laboratory studies conducted by Gardner and Har- ris”’ on sandpacks indicate that shear-wave velocities decrease when liquid is added to sandpacks, whereas the compressional-wave velocity increases (Fig. 51.73).


Lithology Set

0 Dolomite-Sandstone *Dolomite-Limestone

Dolomitlc Sandstone With Part of Pore Space Not Connecte

FDC-CNL POROSITY,

Fig. 51.72-Porosity from compressional-wave transit time corrected for lithology by the velocity ratio vs. porosity from density/neutron crossplot for complex lithologies.

\ \

\ -we_

,y 5000 psig

\ \

I I 20 40

POROSITY, 40

Fig. 51.73-Variation of compressional-wave and shear-wave velocilles of wet and dry sands with porosity at 5,000 psig differential pressure.

Water Saturated 4 \ 200 PSI

3 c - 1000 ps,

0 I I I I I I 0 10 20 30 40 50 60

POROSITY. ‘.

3 0. 0. 0

Fig. 51.74-Ratio of compressional-wave to shear-wave velocity for sands and consolidated rock.

These observed differences between compressional and shear-wave velocities are illustrated by plotting velocity ratio as a function of porosity and pressure (Fig. 5 1.74). Also shown in this figure is the velocity ratio range of 1.75 & 0.20 for the consolidated sedimentary rocks. A velocity ratio greater than two indicates an unconsolidated sand saturated with liquid. Below this value it may be either an unconsolidated sand containing gas or a consolidated rock.

For the consolidated rocks, the ranges of velocity ratios for liquid and gas saturation were obtained by Gregory50 through laboratory measurements. The results of his study are summarized in Fig. 51.75.

Additional experimental data obtained on a sandpack are shown in Fig. 51.76. ’ I6 Laboratory measurements of compressional- and shear-wave velocities are measured as a function of water saturation and plotted on this figure together with measured values of density.

These data and the previous observations may be inter- preted in general terms through use of the Gassmann- Biot theory described in the Appendix. Taking the square roots of Eqs. A-l and A-2 gives, respectively,

I L’,, = -

Ph ‘% [ PC/ +f(Kf)

and

G % v,,= - .

( > Ph

Predictions of these equations also are plotted on Fig. 5 1.76 as dashed lines. One of the predictions of Eq. A-l is that for 100% gas saturation, incompressibility of pore

ACOUSTIC LOGGING

1 .QO

,.20 _ Consolidated Sedimentary Rocks Pressure Range - O-10,000 psi

1.10 I I I I I 1 1 1 0 5 10 15 20 25 30 35 40

POROSITY, %

Fig. 51.75-Variations of velocity ratio with porosity for water- saturated and gas-saturated rocks.

fluid (K$ is much smaller than that of the rock matrix (K,,,); hence, f(Kf) becomes negligibly small (see Eq. A-4). Therefore, P-wave velocities calculated from this equation for the gas-saturated rocks are smaller than those for the liquid-saturated rocks.

The S-wave velocity, however, becomes the function of gas saturation through dependence on the bulk density because the shear modulus G is the same for the rock whether it contains gas or liquid. Hence, as indicated in Eq. A-2, shear-wave velocity increases upon introduction of gas to the extent that the bulk density decreases.

Returning to the P-wave velocities, since the compressibility of gas is much larger than that of water, a small amount of gas reduces pore fluid compressibility essentially to that of gas as predicted by Eq. A-7 (see Appendix).

Cf=S,,.c,,. i-(1 -S,,.)c,,

where cX is gas compressibility. Hence, a small amount of gas reduces compressional-wave velocities significantly, but additional gas saturation has little further effect. This was illustrated by the laboratory data and theoretical prediction plotted in Fig. 5 I .76. A field example shown in Fig. 51.77 confirms this by

demonstrating that compressional-wave transit time does not differentiate the upper zone at 90% gas saturation from the lower one containing 20% gas, because the I curve essentially is responding to the velocity of the mud in both intervals.

Effects of gas saturation on the compressional to shear-wave velocity ratio is illustrated in Fig. 5 1.78 for a deep dolomite reservoir. ‘I7 Over the 18,500 to 18,520-ft interval the v,,Iv, ratio is 1.8; this is as expected for a dolomite lithology. Over the gas zone below 18,520 ft, however, this ratio is reduced to 1.6, and clearly differentiates the gas zone. A similar gas effect is shown in Fig. 5 I .79 for a sandstone reservoir. In this case, the vp/v, ratio is reduced from 1.67 to 1.5 1, again clearly dehneating the gas zone.

fii $J 5.0 I I = I i Measured (VP) ,

Ii 1 e 4.0’7 -- I ---L-__-!-- i 1.

i

Computed rvp)’ / -----/ I

I

0 0.2 0.4 0.6 0.8 1.0

WATER SATURATION, S,

Fig. 51.76-Compressional- and shear-wave velocity and bulk density vs. saturation for a sand pack.

Sonic, ii secift -200 180 130 Induction Log

Resistivily f!M 1 I I I

1 .o 10.0 100.0 I I I

Fig. 51.77-Gas effect on acoustic log


Fig. 51.78-Gas effect on compressional- to shear-wave velocity ratio in a dolomite reservoir.

1.6 1.7

t Velocity Ralio rllT

Fig. 51.79-Gas effect on compressional- to shear-wave velocity ratio in sandstone reservoir.

t

Fig. 51.80-Typical gulf coast induction log indicating Iwo gas sands.

l

Fig. 51.81-Scope pictures from selected levels in the log on Fig. 51.80.

In general, the effects of gas saturation on acoustic velocities in rock may be summarized as follows.

1. Compressional-wave velocity is greater in liquid- saturated rocks than in comparable gas-saturated rocks, whereas the reverse is true for shear-wave velocities.

2. The difference in compressional-wave velocity for the liquid- and gas-saturated states becomes negligibly small with increasing depth, whereas the equivalent difference for the shear-wave velocities remains constant.

3. Under equivalent pressure conditions, compressional-wave velocity decrease upon gas saturation (in poorly consolidated rocks) is much greater than that in well-consolidated rocks.

Attenuations of elastic waves are also used to identify gas zones. ’ I8 This is illustrated in the typical Gulf Coast sandsshowninFigs.51.80and51.81.InFig.51.80,the induction log indicates two gas zones: one in a thin stringer at 5,476 ft and the other in a massive sand at 5,520 ft underlain by water. Scope pictures in Fig. 5 1.8 1 were recorded with a single-transmitter, dual-receiver acoustic log while going into the hole described in the previous figure. In Fig. 51.81a, the lower-receiver signal is just becoming affected as it moves very close to the gas stringer. One foot lower, at 5,477 ft, the lower receiver is in the top of the gas zone. In Fig. 5 1.8 lc, the lower receiver is in the gas sand and the upper receiver is being affected. In the massive gas sand at 5,540 ft, both receivers are showing almost total compressional wave loss, whereas in the water sand at 5,580 ft, a strong signal is apparent at both receivers. For comparison, a typical shale response at 5,462 ft is given in Fig. 5 1.8lf.


Geopressure Detection Geopressure refers to a buried rock/fluid system in which the fluid pressure is greater than the hydrostatic pressure of a full column of formation water. Geopressure also is called abnormal pressure or over- pressure. Abnormally high fluid pressures are found worldwide. Such pressures occur when fluid in the pore space begins to support more overburden than just fluids-i.e., not all the compressional forces are transmitted by the rock matrix only.

The ability to predict the occurrence and magnitude of abnormal pressures is a requirement in planning efficient drilling and, ultimately, completion procedures. Hott- man and Johnson”’ established a procedure for determining the first occurrence of geopressure and the precise depth vs. pressure relationship. They observed that for hydrostatic-pressure formations in a given geological province, a plot of the logarithm of compressional-wave travel time in shales, i,,h, vs. depth is generally a straight line. The divergence of the observed travel time kc,,, from that obtained with the established normal trend kli is a measure of the pore-fluid pressure in the shale and, hence, in the adjacent permeable formation (Fig. 51.82). They also established a trend of resistivity vs. depth for shales and used it similarly in conjunction with acoustic log data.

A field example showing acoustic log response in an abnormal pressure section in the North Sea is given on the right track of Fig. 5 1.83. ‘*” A remarkably accurate prediction of abnormal pressure by surface seismic measurements is shown for comparison in the left track.

A procedure for evaluation of formation pressure is summarized as follows. “’

1. Plot shale velocity or transit time and establish a normal compaction trend line.

2. Locate the anomalous pressure top at the depth at which plotted data points diverge from the normal trend.

3. Take the difference between observed shale transit time and normal shale transit time.

4. Convert the difference to formation pressure gradient by means of an empirically derived curve for a given age and for a given area (Fig. 5 1.84 was used for the example shown in Fig. 51.83).

5. Multiply the pressure gradient obtained by depth to compute the formation fluid pressure at that depth.

Another approach for evaluating abnormal pressures is suggested by Eaton. ‘*’ He proposes the following empirical relationship for predicting pore fluid pressure

(Pf):

where D = depth, ft

p/D = pore fluid pressure gradient, psi/ft, p,/D = overburden stress gradient, psi/ft,

(P/D) ,r = normal hydrostatic pressure gradient (0.456 psiift for Gulf Coast, 0.434 for

fresh waters),

1, = transit time on the extrapolated normal curve at depth,

0

2

4

6

8

10

12

14

-

-

-

'ob

/ I

Fig. 51.82-Prediction of Qeopressure from shale transit time.

Predicted

Abnormal

Pressure TopL

Normal

Pressure or

Lithology Change

Abnormal-’

Pressure

i

I,,‘,-‘n = 38 Mud Wt. = 13.3 1( 1

Top Chalk

Actual

Abnormal

Pressure Top

t&-f, = 36

Mud Wt. = 14.0 ____.~.~

Top Chalk

Fig. 51.83-Comparison of seismic prediction and actual downhole pressure environment.


17

MEASURED, I&, - NORMAL fs,,

Fig. 51.84-Transit-time/pressure correlation, North Sea.

0 200 I400 600 600 1000 ..,

.#,,I ,I..

‘I ‘I ‘; ,I I- Caring Travel

Fig. 51.8%Free pipe

Time

-. \

Fig. 51.86-Good bond to casing and formation

‘oh = observed transit time at depth, and m = empirical exponent varying regionally

around a value of three.

Cement Bond Quality The primary purposes of oilwell cementing are to secure casing to prevent leakage to the surface and to isolate producing zones from water zones. With the increasing cost of completing wells, accurate determination of the quality of the casing cementation has become necessary to avoid costly recompletion and squeeze cementing jobs.

The successful cementing of a well is affected by many factors: cement setting time, pressure, temperature, hole size and deviation, formation and cement characteristics, casing surface, and damage to the cement bond by perforating or squeezing operations. These and many other factors must be considered when evaluating the effectiveness of a cement job.

Early in acoustic logging, it was observed that the amplitude of an acoustic signal in a firmly cemented pipe is only a fraction of that of a free pipe. tZ3 Since then, downhole acoustic measurements have been firmly established as the primary technology for determining cement bondin not only to the casing but to the formation as well ” .‘25 Under favorable conditions even the . % compressive strength of cement can be determined. ‘I6

Free Pipe. A schematic axial transmitter and receiver configuration is shown in Fig. 5 1.85 for cement bond logging. ‘*’ In a free pipe, most of the energy is confined to the casing and the borehole fluid, as indicated in Fig. 5 I .85. The resulting acoustic waveform as recorded by the receiver is also shown in this figure. The following observations characterize waveforms observed in free, unbonded casing.

1. The first arrival of the waveform is equal to the total travel time in casing between transmitter and receiver, plus the travel time in fluid between the tool and the pipe.

2. The amplitude of the entire waveform is high. 3. The waveform exhibits a highly uniform frequency. 4. The waveform is persistent and lasts a relatively

long time.

Good Bond to Casing and Formation. When the cement is perfectly bonded to both the casing and the formation, a very favorable acoustic coupling is developed. As a result, maximum energy is transferred to the formation, and very little energy is transmitted through the casing and cement sheath. As shown in Fig. 51.86, the waveform shows practically no signal at the casing arrival time and very little amplitude until the formation arrival time.

Bond to Casing and to a High-Velocity Formation. In areas of high-velocity formations, signals from the formation arrive at the same time as or earlier than the casing signal, thereby complicating the interpretation significantly (Fig. 51.87).

Cement Bond to Casing Only. A commonly occurring condition is that the periphery of the casing is totally surrounded and bonded by a hardened sheath of cement that


1 ,-Casing Travel Time I

Fig. 51.87-Bond to casing and to a high-velocity formation.

is not bonded to the formation (Fig. 5 1.88). This might happen because the cement does not bond with mudcake of poorly consolidated formations, or the mudcake dries and shrinks away from cement.

Under this condition, energy traveling through the casing is attenuated drastically because of the highly at- tenuating cement sheath. The annulus outside the cement sheath offers very unfavorable acoustic coupling; hence. very littlc energy is transferred to the annular fluid and virtually none into the formation. This is indicated by the lack of later-arriving formation energy in the waveform of Fig. 51.88. The energy observed at Y!O psec is the beginning of the fluid wave for the transmitter-to- receiver spacing of 5 ft.

Partial Bonding. A most difficult situation in evaluating cement bond quality is the condition of partial bond (Fig. 5 I .89). A small gap may be formed between the casing and cement in an otherwise well-bonded casing. In this situation the waveform typically contains two distinct wave energies. The first wave energy arrives at casing time, since part of the casing is free to vibrate. The second wave energy arrives at a time indicated by the velocity of the formation. Hence, both a moderately strong casing arrival and a moderate-to-strong formation arrival exists.

The typical partial-bonding waveform is characteristic of either a microannulus or a channel in the cement. A microannulus is a very small separation between casing and cement. Normally, a hydraulic seal exists with a microannulus. but not with a channel in the cement. Thus. it is important to differentiate between the two. The best way is to rerun the bond log with pressure on the casing. If a microannulus exists, the casing will ex- pand, decreasing the separation and transferring acoustic energy to and from the formation. The casing signal will decrease and formation signals will then become more evident. However, if only channeling exists, pressuring the casing will not greatly alter the log.

Another way to differentiate between microannulus and channeling is by noting the length of section over which the condition exists. ‘I5 Since microannulus is thought to be caused by the condition of the exterior surface of the casing, such as the presence of grease or mill

0 200 ,; 400 600 800 1000 1

.I : 1

.*:

‘1

t.-. I,

i I- Casing ikeI Time

Fig. 51.88-Cement bond to casing only.

varnish, the effect tends to appear over a long section of log. Channeling ordinarily occurs over shorter sections.

Examples of various bonding conditions are illustrated by the variable-density (3D) log shown in Fig. 5 I .90. “’ The interval from X552 to X614 ft shows a good pipe bond but no formation bond. Only a few formation arrivals can be seen, indicating a lack of acoustical coupling between the cement sheath and the formation itself. Above and below this interval are sections of poorly bonded pipe. This probably is due to channeling. This is suggested by the strong pipe signal overriding a weak formation signal. The interval from X468 to X518 ft i$ well bonded, as evidenced by the strong formation signal. However, there is evidence of a microannulus between X506 and X518 ft. Here the fonnation signal is distorted somewhat by a casing signal. “’

A recently introduced technology, the Cement Evalua- tion Tool by Schlumberger. shows great promise in dif- ferentiating between microannulus and channeling. I”’ This tool is based on the acoustic reflection method; however, unlike the boreholc telcviewcr with one rotating transducer, it has eight transducers placed on a centralized sonde at 45” from each other in a helical path. These transducers, emitter and receiver. are about

0 200 ,400 600 800 1000 ‘I I -f~ ,‘I,.

-~ ., 4 ,

_I /

- C&g Tk~el Time

Fig. 51.89-Partial bonding


I- usec lncreasina

Good Bond

Probable Micro-Annulus

Channel-Poor Bond

Good Bond to Casing No Bond to Formation

Channel-Poor Bond

Fig. 51.90-Good bond to casing-no bond to formation

Maxlmwn

Fig. 51.91-Ultrasonic cement evaluation log

Fig. 51.92-Full waveforms and variable-density log for different bonding conditions.

1 in. in diameter and operate at 500 kHz. They repeated- ly send a short ultrasonic pulse toward the casing to make it resonate in its thickness mode. Cement behind the casing is detected as a rapid damping of this resonance, whereas a lack of cement gives a longer resonance decay.

An example of a cement evaluation log is shown in Fig. 5 1.91. I30 The right track can be viewed as a map of cement behind the casing. It is divided into eight chan- nels, each one representing one transducer with a shading from white (free pipe) to black (good cement). In this example, a channel is clearly visible as a white streak.

Summary of Bonding Conditions. Typical full waveforms for various bonding conditions are summarized in Fig. 51.92. 128

When there is no cement bonded to the casing, a free casing signal is indicated on the variable-density log as straight dark lines with distortion at the collars. This distortion occurs for a vertical distance equal to the spacing between the transmitter and receiver of the logging instrument (6 ft on the example shown in Fig. 51.92).

When there is good cement bonding both to the casing and to the formation, there is no casing signal. but there is a strong formation signal. The difference in response for the low- and high-velocity arrivals for a well-bonded section is clearly illustrated in the lower section of the variable-density log of Fig. 51.92.

Cased-Hole Evaluation Most existing wells were completed before the advent of reliable porosity logging devices; therefore, accurate porosity data for planning of enhanced recovery operations must be obtained through existing casing. Radioac- tivity logging measurements commonly are used for this purpose; this information, however, can be supplemented by the acoustic log measurements in wells


where a good cement bond exists between casing and the formation. 13’ A recent study ‘X2 involving laboratory modeling and computer simulations has indicated that acoustic logging can be successful in both bonded and unbonded casing.

Through-casing acoustic logs have provided reliable measurements of compressional and shear-wave velocity data for evaluating porosity and lithology. An openhole and cased-hole comparison is shown in Fig. 5 1.93 for the compressional and shear-wave transit times t,, and I,, The logs were obtained by analysis of the waveforms digitally recorded with the acoustic logging system shown in Fig. 51.54. The agreement between compressional and shear transit time logs run in open and cased holes is excellent. This further enhances the role of acoustic measurements in cased-hole evaluation.

Mechanical Properties A knowledge of the mechanical properties of rocks is important in drilling, production, and formation evaluation. Mechanical properties include the elastic properties such as Young’s modulus, shear modulus, Poisson’s ratio, and bulk pore compressibilities, as well as the inelastic properties such as fracture pressure gradient and formation strength. Borehole measurements of acoustic properties in combination with density log measurements are being used more and more for in-situ determination of mechanical properties of rocks.

Elastic Moduli. Elastic constants describe the mechanical properties of matter: Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio. Knowledge of these moduli for rocks is needed in study- ing the propagation of acoustic waves, as well as in practical engineering problems connected with drilling, formation fracturing. and predicting reservoir performance.

A commonly used approach to gather this information is to obtain core samples and to conduct laboratory experiments. For meaningful results. these measurements must be made at equivalent subsurface conditions. Needless to say, these are time-consuming and costly. Even then the results are suspect because the process of coring removes the overburden stress from the sample and causes other disturbances that may not be reversible.

Numerous studies have been conducted that compared elastic moduli obtained by the static (from measurements of stress and strain) and the dynamic (from acoustic velocities and density) methods. In rocks subjected to lower effective stresses, the dynamic elastic moduli are higher than the static values; as the stress increases, however, these differences decrease. ‘33.‘31 Theoretical studies by Walsh ‘X predicted that this could be caused by the resence of cracks in rocks. In fact, Simmons and Brace’ P ’ found the static and dynamic moduli to be in close agreement when rocks are subjected to higher stresses (30,000 psi) so that the cracks are closed.

The relationship of the in-situ-measured elastic moduli to those determined in the laboratory was investigated by Myung and Helander. “’ They made laboratory measurements of compressional- and shear-wave velociL ties on core samples under simulated subsurface pressure conditions and reported a close agreement between in- situ and laboratory-determined values of dynamic elastic moduli.

Interval Transit Time 1

500 pslm A0 I I

, I

2 Cased Hole

Fig. 51.93-Comparison of digital-sonic logs in a well before and after casing.

Since then, many other investigators have used borehole acoustic measurements to determine elastic moduli. 89,‘37,‘38 Compressional- and shear-wave velocities obtained from the acoustic log measurements are used with values of density from a density log to calcu- late Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio by assuming an infinite, isotropic, homogeneous, and elastic medium (see Eqs. 3 through 6).

Applications of these in-situ-determined values of moduli include predicting sand production and sub- sidence, and determining fracturing characteristics of formations. An application involving fracture characteristics is shown in Fig. 51.94.h” The core and log data are from a section of igneous and metamorphic rocks. The fracture characteristics of the core are shown graphically as well as plotted quantitatively as rock quality designation (RQD), which is the ratio of the cumulative length of unfractured core to the unit length of core. Elastic moduli curves are quite similar to the RQD curve.


R.Q.D.

mo4oobooaoomoonoouoo 91aJw

Elastic Properties 3-D Velocity

,&EC INCREASING I

Fig. 51.94-Comparison of rock quality designatton (R.Q.D.), elastic properties, and 3D velocity log

Fracturing. Fracturing of formations is a commonly used well stimulation technique. To detennine the best zoncb for fracturing. laboratory compressibility tests can be run on rock samples from the zones of interest. Frac- ture design requires a knowledge of elastic moduli. which can be obtained from borehole measurements.

An earlier use of boreholc acoustic measurements was for the identification of zones favorable for fracturing. Hi@amplitude and high-velocity Lhear w;1vc\ have been associated with zonch that can be fractured sue- w\fully. whereas Tones with low-velocity and low- amplitudc S-waves wcrc found to be quite plastic. In the example shown in Fig. 51 .c)S. Anderson and Walker”” inclicatc 3 wcil-defined shear wave in the /lone from 4.600 to 4.54.5 ft and none ahovc this LOW.

During drilling. control of hydrostatic prcssurc in the horeholc is nccc.shaQ to not cscccd fracturing prczsuro ot the formations. thcrcby causing circulation 10~.

However, a knowledge of fracture pressure is needed for proper design of fracturing operation to stimulate hydrocarbon production from tight formations. An estimate of fracture pressure (p/,.) is given by Hubbert and Willis: “”

where 1~0 = overburden pressure. 11, = pore-fluid pressure.

p = Poisson’> ratio. and D = depth.

Recent applications of this relationship are discusxcd hy Atkinson. I41


Am&ude an +

4500

4600

Comp. 1 Shear

Fig. 51.95-Evaluation of fracturing prospects.

Sand Control. Sand-production control has been a costly problem affecting the economics of oil and gas production in many areas. To avoid unnecessary sand- control measures, various techniques have been developed that use borehole measurements of acoustic propertics, 13X.IJ?~l4~

In the example shown in Fig. 5 I .96. the need for sand control is predicted by assuming that hydrocarbon effects on acoustic properties are predominant in poorly consolidated formations. “’ In the oil zones shown, transit times are significantly higher than the value in the water zone, and the amplitudes are reduced, thereby indicating poorly consolidated rocks.

Fracture Evaluation

Many of the important reservoirs in the world produce from naturally occurring fractures, yet evaluating the

performance of these reservoirs is much less understood. Techniques for evaluating naturally fractured reservoirs are reviewed in the literature by Aguilera and van Poollen, IJ5 Suau and Gartner, ‘A6 and Aguilera. “’ Among these, techniques based on measurements of acoustic properties are prominent. Cycle skipping observed on the transit time curve has been associated with fracturing in certain formations. Also. reduction of signal amplitude has been correlated with fractures. More successful applications, however. involve the use of variable-density or waveform logs. ‘4x.‘4y For these logs, when fractures occur, anomalies also occur in the acoustic wave banding pattern. Sometimes these are diagonal patterns. but more often they occur as sudden breaks in the banding.

Fig. 51.97 shows a variable-density log (3-D log) from a granite section in New Hampshire. “’ In Zone C.


RESISTIWTY ohm mVm

0 18” Normal

5650.. t

Fig. 51.96-Hydrocarbon effects indicate the need for sand control.

125-130

Fig. 51.97-Variable density (3D) log in fractured granite.

the compressional wave is not attenuated, whereas the shear-wave amplitude is reduced significantly. A theoretical study by Knopoff and McDonald”’ would predict this to be due to a low-angle (or horizontal) fracture. High-amplitude compressional and shear energies indicate that Zone B has no fractures. High attenuation of the compressional and shear waves in Zone A is inter- preted to be caused by an oblique fracture. The diagonal energy pattern below Zone C is caused by the presence of a reflector (fracture) near the borehole.

In the foregoing analysis, fractures are considered to be thin reflectors causing distortion in wave propagation because of acoustic impedance mismatch with the sur- rounding rock. Since abrupt changes in lithology and porosity also can cause similar acoustic impedance mismatches, this simplified interpretation becomes much more complex.

When the hole conditions are favorable and there is no mudcake or heavy muds in the hole, the borehole reflection method provides a more straightforward technique for the evaluation of fractures. A borehole televiewer sonde operating in a circular borehole intersectin a vertical fracture is shown on the left in Fig. 51.98. 8 (” The borehole televiewer log obtained in this configuration. shown on the right. clearly depicts the vertical fracture as two dark lines.


Fig. 51.98-Vertical fracture intersecting a circular borehole and its representation on BHTV amplitude log

The amplitude image from the BHTV, however, cannot distinguish whether the fracture is open or filled. An open fracture produces an image on the amplitude log because little or no signal returns to the sonde. A filled fracture also can produce an image if there is sufficient acoustic impedance contrast between the filling material and the host rock to produce a weaker signal. Therefore, both open and filled fractures may produce similar dark images on the amplitude log.

Transit time imaging, however, responds not to variations of signal amplitude but rather to the travel time (and, hence, the distance) from the borehole wall. On the transit time log, the distance to the borehole face is represented by a gray scale designating white for far, dark for near, and black for no signal. Therefore, an open fracture produces a black image on the transit time image, whereas a filled fracture does not. Fig. 51.99 shows a vertical fracture on the amplitude log on the left. The similar black outline on the transit time log on the right confirms that this is an open fracture.

Permeability

Theoretical studies by Biot45.46 have indicated that changes in acoustic attenuation may reflect the fluid mobility (the ratio of permeability to viscosity). Later studies by Wyllie et al. 24 and Gardner and Harris”’ considered the logarithmic decrement (Eq. 6) of acoustic energy to be a result of solid friction (“jostling” decrement) in the rock matrix and viscous drag (“sloshing” decrement) within the saturant fluid.

The solid matrix losses (jostling losses) were studied experimentally by Gardner and Harris, ‘I5 with respect to the effects of overburden pressure and fluid saturation. The results of their investigation indicate the jostling decrement of a sandstone under overburden pressures to be almost independent of fluid saturation and signal frequency. Hence, changes in the logarithmic decrement can be attributed to sloshing loss, which, according to Biot,45.46 reflects changes in fluid mobility.

Later, iv a theoretical study, RosenbaumM applied Biot’s theory to the investigation of propagation of acoustic pulses in a fluid-filled borehole surrounded by a porous medium. He predicted that permeability could be estimated from an analysis of tube wave data contained in the acoustic waveform recorded in a borehole. He suggested that, for a sealed interface between the borehole and formation, maximum sensitivity to permeability was obtained in the interval between S-wave arrival and the fluid wave. For the open interface (no mudcake), the entire signal following the S-wave arrival could be used. The P-wave arrival was least sensitive to permeability and could be used for normalization.

Results of this study were first tested by Staai and Robinson 15’ in the Groningen gas field, The Netherlands. They recorded acoustic waveforms and analyzed them to obtain a permeability profile, which compared favorably with the core analysis data.

More recently, Rosenbaum’s prediction@ of the relationship between the energy loss of the tube (Stoneley) wave and permeability was investigated more extensively by Williams et al. ‘52 Using a special long-spacing acoustic logging tool, they measured the tube wave transit time and energy ratio in wells located in different geographic locations with formations of varying lithology, permeability, saturating fluid, depth, and geological age. From these wells, they also obtained whole core samples for measurements of permeability. For these widely varying conditions, they report qualitative correlations between core-measured permea- bilities and the tube wave data.

An example shown in Fig. 5 1.100 for a Cretaceous carbonate section is highly promising as it indicates that both tube amplitude ratio, Am /AR’ , and transit time cor- relate well with a permeability increase of three orders of magnitude in the center zone.

Conclusions Borehole measurements of acoustic properties have a wide range of applications in exploration, production,

51-46

5210

5220

5230

AMPLITUDE

Dark-Weak Slgnal While-Strong SIgnal

I E S W N

TRANSIT TIME

Black-No Slgnal Dark-Near White-Far

N E S W N

Fig. 51.99-Vertical fracture of the BHTV amplitude log on the left, confirmed to be open by the BHTV transit time log on the right..

and formation evaluation. Theoretical and experimental studies have significantly improved our understanding of the relationships between acoustic wave propagation and formation evaluation parameters, such as porosity, fluid saturation, and lithology. This, in turn, has prompted the development of new and improved borehole acoustic measurement technology and sophisticated digital signal processing technology to analyze the large amount of data. Even then. current applications often use only a small fraction of the information available in acoustic waveforms.

Advances in the understanding of acoustic wave propagation are interactively complementing improvements in downhole recording and transmission technology. and developments in signal processing. This should result not only in a broader and more quantitative use of the present applications, but also in the development of many new applications.

Fig. 51.100-Permeability correlation with tube wave data

Nomenclature A = area; or signal amplitude

A,, = signal amplitude at the source h = intercept defined by Eq. 13 c = compressibility d = diameter

Di = depth of investigation E = Young’s modulus

f‘ = frequency f(Kf) = function of incompressibility of a fluid

in pore spaces F = force

F,, = compaction correction factor F, = quality factor

G = shear modulus I = intensity

I,, = acoustic intensity at the source K = bulk modulus L = length m = slope n = number p = pressure

pCi = differential pressure pf = internal (pore fluid) pressure

pf/D = pore fluid pressure gradient. psiift

(pf./D) ,I = normal hydrostatic pressure gradient (0.456 psiift for U.S. gulf coast)

P.fr = fracture pressure

PO = external (overburden) pressure p,,lD = overburden stress gradient. psiift

P,l = P-wave modulus for the rock frame (or the dry rock)


r = borehole radius s = arbitrary point S = saturation f = travel time t = transit time

I( = I/Y,,) = transit time for the compressional waves for a liquid-saturated porous medium

I~~( = I/Y~,) = transit time for saturant liquid

‘,I = damaged zone transit time I,,,( =1/t,,,,) = transit time for rock matrix that forms

the solid frame of a porous medium

1,, = transit time on the extrapolated normal curve at depth

1 oh = observed transit time at depth N = particle motion at s 1’ = velocity

“f = compressional-wave velocity of drilling

I’,, =

\‘r =

\‘,, =

\‘, =

O!=

6=

E=

CL =

t, =

CT =

0, =

X=

P”=

P=

4=

Subscripts

a= C=

(1 =

f= ,? =

hc = L=

/n =

N=

0 =

P= .s =

S/l =

1\’ =

mud compressional-wave velocity pseudo-Rayleigh-wave velocity shear-wave velocity tube- or Stoneley-wave velocity coefficient of absorption; or attenuation

coefficient logarithmic decrement strain longitudinal strain shearing strain transverse strain S-wave critical angle wave length Poisson’s ratio density porosity

apparent corrected dry rock pore fluid gas hydrocarbon liquid matrix neutron overburden or oil pore volume; or P-wave modulus S-wave modulus shale water

Acknowledgments I wish to thank A.A. Brown, G.S. De, and K.J. Dunn of Chevron Oil Field Research Co. and M.N. Toksoz of the Massachusetts Inst. of Technology for reviewing the manuscript. Debbie Ivey for typing. and. more importantly. the participants of the Chevron Formation Evaluation seminar durmg the past 20 years for many helpful suggestions toward the evolution of this chapter.

APPENDIX Theory of Elastic Wave Propagation in Rocks The first theoretical expression of elastic behavior of a saturated porous medium was given by Gassmann.U Later, Biot45,46 developed a more comprehensive theory of elastic wave propagation in a fluid-saturated, isotropic, porous solid over a wide frequency range. The predicted velocity dispersion by this theory is. in general, less than 3% ” ; therefore, the low-frequency approximation should be useful for most applications.

Velocities predicted by this theory at the lower frequencies can be expressed simply by

7 \‘; = P‘l +mf)

. (A-1) Ph

and

G Lj,,Z = - . . . . . . . . . . . . . . . . . . . . . . (A-2)

Pb

where Pd is the P-wave modulus for the rock frame (or the dry rock), and f(Kf) is the function of the incompressibility of the fluid in the pore spaces. The P-wave modulus for the dry rock can be expressed, in turn, by

Pd=Kd+;Gd: .t.. (A-3)

and the functionf(Kf), by

flKf.1 =Kj (1 -K,,/K,,,)’ (I-K$K,,,M+(K,,, -K,,)K+K,,,’ ’

(A-4)

in which K is incompressibility (or bulk modulus), G is shear modulus, and the subscripts d, f, and m refer to the rock frame (or the dry rock), fluid, and rock matrix.

For rocks containing both water and hydrocarbons, the bulk density is expressed as

p/,=$p,.+(l -d)p,,,, . .(A-5)

where

Pf=S,,P,,.+(l -S,,.)p,,(,, .(A-6)

and the fluid incompressibility. K,, which is the inverse of compressibility, cf, is given by

c, =S,,.c,,.+(l -S,,,)C,,< , (A-7)

where S denotes saturation, and the subscript hc refers to hydrocarbon.

Rock frame incompressibility, K,,. in Eq. A-3. which is the inverse of compressibility of dry rock, (‘,I, is related to PV compressibility, c,, . by

c,,=&.,~ +c,,$. (A-X)


on the basis of Van der Knaap’s” definitions. Substitu- tion of this equation into Eq. A-l, after some manipula- tion, results in

3 1-p CL -= Ph”‘,i 2 1 +!J (cf-CJ’ SC, -’

fc ,,,. (A-9)

Further substitutions into this equation for density from Eq. A\5 and rearranging yields a quadratic equation in p. Negleciing terms involving I” 2 (since p is a fraction) and assuming p to be independent of porosity yields an equation expressing l/v,,2 as a linear function of porosity. For lower porosities.

i=mt$+b. . . . (A-10) v P

If the Poisson ratios for the saturated rock and the rock matrix are assumed to be close in value, then b becomes approximately equal to l/v,,,. The parameter m in Eq. A- IO, however, is a strong function of c,, .

As the foregoing discussion indicates, Eq. A-10 is an approximation of Eq. A-9. Therefore, the commonly used time-average equation, ‘8.‘9 which is of the same form as Eq. A-10,

(A-11)

(where vf is the velocity of saturant liquid) also may be considered to be an approximation of the more general theory.

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