Propagation of ultrasound through hydrating cement pastes at early times

Propagation of Ultrasound Through Hydrating Cement Pastes at Early Times C.M. Sayers and A. Dahlin Schlumberger Cambridge Research,Cambridge, United Kingdom

Measurements of the velocity and amplitude of ultrasonic compressional waves propagating through neat and accelerated American Petroleum Institute class G cement pastes undergoing hydration are compared with the predictions of the theory of elastic wave propagation through fluid-saturated porous media. The compressional wave velocity is observed to decrease slightly during the first few hours after mixing, followed by a rapid rise as the solid phase becomes interconnected. It is shown that this change in behavior results from a change in character of the observed wave as hydration proceeds. At early times the observed wave involves essentially motion of the fluid phase while at longer times it involves essentially motion of the solid frame. Ultrasonic waves are therefore sensitive to the point at which the solid phase becomes interconnected. This point is of practical significance since the connectivity of the solid phase is responsible for the load-bearing capacity of set cement. The early-time decrease in velocity results from an increasing tortuosity of the pore space due to the formation of hydration products while the increasing velocity at later times results from a stiffening of the porous frame. Wave propagation at early times involves motion of the fluid phase and is extremely sensitive to the presence of air bubbles. Cement pastes containing a sufficiently large number of air bubbles are found to act as high-pass filters over the frequency range employed. This results from the resonant scattering of ultrasound by the bubbles. At longer times the solid frame becomes interconnected and propagation of the low frequency components becomes possible. The amplitude and center frequency of these components are observed to increase with increasing connectivity of the solid phase. ADVANCEDCEMENT BASEDMATERIALS1993, 1, 12-21 KEY WORDS: Cement hydration, Cement pastes, Elastic waves, Entrapped air, Percolation transition, Ultrasonics, Ultrasonic velocity and attenuation

is placed in the annular space between ~ing and borehole wall during oil field g operations to isolate different permeable zones. Fluid may enter the annulus if the pressure Address correspondence to: Colin M. Sayers, SchlumbergerCambridge Research, P.O. Box 153, Cambridge CB3 0HG U.K. © Elsevier Science Publishing Co., Inc. ISSN 1065-7355/93/$6.00

exerted by the cement on a permeable zone falls below the pore pressure in the rock before the c e m e n t achieves sufficient mechanical strength and low enough permeability to prevent fluid invasion. Such invasion may lead to the loss of integrity of the cement sheath and, in the worst case, loss of the well. Hydraulic cements develop mechanical strength and low permeability as a result of hydration, which involves chemical reactions between water and the anhydrous compounds present in the cement. Solid hydration products form both at the surfaces of the cement particles and in the pore space by nucleation and aggregation. As a result, the solid phase becomes highly connected and the material transforms from a viscous suspension of irregularly shaped cement particles into a porous elastic solid with nonvanishing bulk and shear moduli [1]. As the shear modulus increases, the Poisson's ratio is found to decrease from the value of 0.5 characteristic of a fluid to values characteristic of a porous solid. This is shown in Figure 1 for two American Petroleum Institute class G cement pastes containing 1% CaC12 by weight of cement. The transition to an interconnected solid phase is an example of a percolation transition. The connectivity of the solid phase is responsible for the load-bearing capacity of set cement. Measurements of ultrasonic pulse velocities have been used as a nondestructive test for the compressive strength of hardened concrete [2]. Theoretically there is no direct relation between ultrasonic velocity and compressive strength since strength is, in general, a function of defect size. However, under specified conditions the two quantities have been found to be related [2]. The common factor appears to be the density of the concrete: a change in density results in a change in both velocity and strength. However, as pointed out by Keating et al. [3], it is the increase in connectivity of the solid phase, rather than any change in density, which will determine the change in velocity and strength of cement pastes at early times. These authors examined four types of cement paste used in cementReceived January 22, 1993 Accepted April S, 1993

Ultrasound Through Hydrating Cement Pastes 13

Advn Cem Bas Mat 1993;1:12-21

0.5

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G / GPa FIGURE 1. Poisson's ratio v as a function of ultrasonic shear modulus G for two accelerated de-aerated class G cement pastes: 70 hour test using Dyckerhoff + 1% CaCI2 (O), 95 hour test using Cemoil + 1% CaCI 2 (O). This plot extends the results obtained by Sayers and Grenfell [1] to later times. ing oil well casing to see w h e t h e r the early-time strength build-up could be predicted from measurements of ultrasonic velocity [4]. During the first few hours after mixing it was found that ultrasonic velocity is not sensitive to the growth of structure in the cement. However, from the time of initial set onwards, w h e n the solid phase predominates over the fluid phase and strength development is relatively rapid, a correlation was found between ultrasonic velocity and cube strength measured at atmospheric pressure (Figure 2) [4]. A similar correlation based on measurements at higher pressures was reported earlier by Rao et al. [5]. It was pointed out by Keating et al. [3,4] that some of the early-time ultrasonic measurements reported in the literature have been influenced by air trapped in the 9

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Ultrasonic velocity (km/s) FIGURE2. Comparison between ultrasonic velocity and cube strength for cement pastes of four compositions based on American Petroleum Institute class G oil well cements measured at atmospheric pressure during the first 8 hours after mixing: accelerated class G (O), thixotropic (0), neat class G (O), and low density (A) (after Keating et al. [3,4]).

cement paste, and that the degree to which entrapped air influences the results from pulse velocity tests is disputed within the drilling industry. It was also found that in nearly all cases the measured compressional wave velocity decreases slightly during the first few hours after mixing, followed by a rapid increase once the solid phase becomes interconnected [3,4]. This early-time decrease in velocity has not been explained. The purpose of this article is to examine in more detail the early-time propagation behavior of ultrasonic waves in hydrating cement pastes. In the Theory section the propagation of ultrasound through hydrating cement pastes is discussed within the framework of the theory of elastic waves in fluid-filled porous media. An experimental confirmation of earlier findings is presented in the Experimental Results section and the effect of air bubbles on ultrasonic propagation is examined by comparing measurements made on as-mixed and de-aerated cement pastes. Keating et al. [3] have also performed comparative ultrasonic velocity measurements on both as-mixed and de-aerated pastes by determining the time at which the signal first crosses a preset threshold. It is shown that such measurements are inaccurate at early times for cement pastes containing air bubbles.

Theory Cement as a Porous Elastic Solid Once the solid phase becomes interconnected as a result of hydration, it is more appropriate to treat the material as a fluid-saturated porous elastic solid than as a suspension of cement particles in water. The porous "frame" may be characterized by a bulk modulus K and shear modulus G which determine the deformation of the material under "drained" conditions that correspond to the fluid pressure being held constant during the deformation. The propagation of elastic waves in a porous elastic solid saturated with a compressible viscous fluid has been treated by Biot [6]. An important result of this theory is that there exist both a fast and a slow compressional wave in a fluidsaturated permeable solid. At high frequencies both waves are propagatory but at low frequencies the slow wave is the solution of a diffusion equation. The critical frequency separating the low and high frequency regimes corresponds to the viscous skin depth ( X , ~ f c o ) being of the same order as the pore size. Here r/is the viscosity of the pore fluid, pf is the density of the fluid; and co = 2rcf, f being the frequency of the wave. At high frequencies the viscous skin depth is much smaller than the pore size, and the effect of viscosity is confined to a thin boundary layer near the solid/fluid interface. Most of the fluid is there-

14 C.M. Sayers and A. Dahlin

Advn Cem Bas Mat 1993;1:12-21

fore in inviscid flow. At low frequencies the skin depth is much greater than the pore size, so all the fluid is in Poiseuille flow and inertial effects are dominated by viscous effects. In the high frequency limit, the shear wave velocity, vs, and the fast and slow compressional wave velocities, vt(fast) and vl(slow ), are given by [7]: G

2=

Us

(1)

(1 - d?)ps + (1 - a - 1 ) ¢ p f '

vZ(fast, slow)

( P R - Q2) =

( K + 4G/3)Ks~b 2 1 - {b - K/Ks + ~ b K d K f

(11)

In the limit of vanishing frame moduli, (K = G = 0), the shear wave and slow compressional wave velocities vanish, as may be seen from eqs 1 and 2. Johnson [9] has shown that w h e n the pore fluid is much more compressible than the frame (K¢ ~ K, G < Ks), the equations for the fast and slow waves in the high frequency limit simplify considerably:

=

(K + 4G/3)

(2)

+- "V/,d2 - 4(pIlP22 - p~2)(PR - Q2)

(12)

v~(fast) = (1 - q})Ps + (1 - a - 1 ) ¢ p f "

2(PllP22 - p212)

~(slow) Here q) is the porosity and a 1> 1 is the tortuosity which represents the difficulty the fluid experiences in flowing relative to the solid, a is a purely geometrical quantity which is independent of the solid and fluid densities Ps and p[. For the case of isolated spherical particles in a fluid, Berrymann [8] has obtained the following equation for a:

a

1 = ~

(1

+

~b-1).

(3)

The quantities P, Q, R, and A appearing in eq 2 are defined as follows: P = (1 - ~/)[1 - ~ - K/KslKs + c~KsK/Kf -

c~ - K/Ks + c~KdKf

4 + ~ G,

[1 - ~ - K/Kslc)Ks Q = 1 - (a - K/Ks + c~Ks/Kf'

R = 1 -

3.5

(5)

3

(6)

(13)

In this limit the fluid and solid motions are largely decoupled [7]. The fast wave involves essentially motion of the solid only, dragging along some of the fluid, whereas the slow wave involves essentially motion of the fluid. Figure 3 shows the variation of vl(fast) and vt(slow) in the high frequency limit, plotted as functions of the shear wave velocity, vs. Also shown are the stiff frame expressions of eqs 12 and 13. For this calculation the average density of cement grains (Ps = 3160 kg m-3) and a porosity ~b = 0 . 5 8 2 appropriate for American Petroleum Institute class G cement pastes [10] were used. In addition, the values a = 2 . 0 , Poisson's ratio of the frame = 0.2, and bulk modulus of the solid Ks =

.~ 2.5

~ - K/Ks + c ~ K d K f '

K/. apf

(4)

¢%

=

Poisson's ratio of frame = 0.2 Porefluid = water Porosity= 0.582

...'C. / /

Ps = 3160 Kg m"3 KS= 50 GPa

v,~~(fast) // v p= / / ~= 22 " °t 0 ~ / E q u a t i o n ( 1 2 ) ~

and °15---'-------(7)

"~

Kf and K s are the bulk moduli of the fluid and solid. The density terms Pij occurring in eqs 2 and 7 are given by the following equations:

r~

zl = PP2z + RPI1 -

2Qp12.

/ Equation (13) v I (slow)

i

P l l + Pz2 = (1 - c~)p s, P22 + P12 = ~P[, P12 = - (a - 1)r~R. (PR -

Q2) i n eq 2 may be written in the form:

(8) (9) (10)

0

(I.5

i

1 1.5 Shear wave velocity(kin/s)

2

FIGURE3. The variation of vt(fast) (upper curve) and vt(slow) (lower curve) in the high frequency limit as functions of the shear wave velocity vs. Also shown are the stiff frame expressions of eqs 12 and 13.

Advn Cem Bas Mat 1993;1:12-21

Ultrasound Through Hydrating Cement Pastes 1 5

50 GPa were chosen. A Poisson's ratio equal to 0.2 is predicted by the self-consistent approximation at the percolation transition [11]. It is clear from Figure 3 that in the stiff frame limit the fast wave involves essentially motion of the solid and the slow wave involves essentially motion of the fluid. In the weak frame limit the character of these waves is different, the fast wave involves motion of the fluid while the slow wave involves motion of the frame. In this limit the stiff frame expressions of eqs 12 and 13 are clearly inapplicable. Although the expressions given above are only valid in the high-frequency limit, Johnson and Plona [7] have shown that it is possible to obtain results valid for arbitrary frequency by replacing a in the above expressions by-d(co) = a + [ibF(co)/codp&]. Here b = rlc~2/k, where t/is the fluid viscosity and k is the permeability. F(co) allows for the fact that the effective damping is frequency dependent. Well-cured cements have little porosity with characteristic dimension greater than 1 ~m, the bulk of the porosity having dimension less than 0.1 ~m [12]. At later times, therefore, the low frequency limit of Biot's [6] theory is appropriate. In this limit only the fast wave is propagatory, the slow wave being the solution of the diffusion equation. The shear wave velocity and fast longitudinal wave velocity are given in this limit by [6]:

_21r

G 2= Vs (1 - c~)ps + c~pf'

(14)

H = (1 - ~b)ps + ~pf"

(15)

~ast)

x

where mr = 2Xfr, p is the density of the cement paste, Px and vg are the density and ultrasonic velocity of the entrapped air, and a is the radius of the bubbles which are assumed to be spherical. Figures 4 and 5 show the expected attenuation and velocity of ultrasound through a paste containing 1% volume fraction of air bubbles, calculated as functions of ka using the theory in ref 13. Here, k = co/v~ where co = 2~f, f is the frequency, and v° is the velocity of compressional waves in the absence of air bubbles. For the calculations, a density of 1.902 x 1 0 3 kg m - 3 and an early-time velocity of 1.52 km s -1 appropriate for the cement pastes studied in the present work were assumed. For these values, the resonance frequency corresponds to ka = 0.0099. The attenuation plotted in Figure 4 is seen to reach a maximum near resonance, with a strong band of attenuation extending from just below resonance up to ka = 0.2. The attenuation in the range ka = 0.2 to 1 is an order of magnitude less than in the range ka = 0.01 to 0.1. Compressional waves with frequencies in this region will therefore be strongly attenuated. The ultrasonic velocity, plotted in Figure 5, is seen to be much lower than the velocity in an air-free paste for frequencies below resonance, while at high frequencies the velocity is the same as the velocity in an air-free paste. Near the resonance frequency the velocity is seen to be a strong function of frequency.

Experiment Cement P a s t e Preparation The cement pastes were prepared in accordance with the American Petroleum Institute specification 10 [10]

Here:

H = (K + 4G/3) +

101

........

.

.......

K )4 10"1

(16)

Effect of Entrapped Air

g 10 .2

The presence of air bubbles in a cement paste is expected to have a dramatic effect on the ultrasonic waveforms due to resonant scattering by the bubbles [13]. Resonant scattering arises because of the large difference in compressibilities between the gas and liquid phases of the cement paste. The frequency, fr; at which resonance occurs depends on the physical properties of the component phases and on the bubble size [14]:

~

C02r = 3 p ~v2g/(pa2),

,

10 0

K f ( K , - K) 2 Kr(K, - K) + K , ( K , -

........

(17)

10 "a

10 -4

10"5

10 .6 10 .3

/ .

. . . . . . . . . . . . . . . . . . . . . . . 10.2 10 -1 ka

10 °

FIGURE 4. Variation of ultrasonic attenuation with/ca for a cement paste containing 1% by volume of entrapped air.

1 6 C.M. Sayersand A, Dahlin

10 2

.

.

.

.

.

.

.

.

,

.

.

.

Advn Cem Bas Mat 1993;1:12-21

.

.

.

.

.

,

.

.

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.

.

.

.

C e m e n t sample

.

temperature logger

[ /

Perspex wall

///, 101

Receiver

Transmitter .. f/ // .j ,//I r/l.

"g 10°

wave

-a Z

///.. 10 q

10 -2 10 -3

. . . . . . . . . . . . . . . . . . . . . . . . . . i 0 -2 10 "l ka

10 °

P--sll P'n--" I

FIGURE 5. Variation of normalized velocity (vz/v °) with/ca for a cement paste containing 1% by volume of entrapped air. Here v° is the velocity in the absence of entrapped air. for class G oil field cements. Neat class G cement paste was made with 792 g cement and 349 g water, while accelerated class G cement paste contained, in addition, 15.84 g CaC12 (2% by weight of cement). Class G cements are intended for use from surface to 8000 ft (2440 m) depth. The addition of CaC12 accelerator is appropriate for shallow wells. The required amount of water was placed in a Waring blender. With the blender operating at 4000 rpm, the cement, and in the case of the accelerated cement pastes the cement and CaC12 was added within a 15-second interval, after which the paste was mixed at 12,000 rpm for 35 seconds. De-aerated pastes were obtained by pouring the mixed paste from the blender into an open-topped I L beaker which was subsequently put into a dessicator attached to a vacuum pump. The vacuum p u m p maintains a pressure around 0.7 bar below atmospheric for 20 minutes. The paste is gently swirled every few minutes while under reduced pressure.

5058 pulsar

Pre-amplifier

'

~_J Dell 316

PC

LeCroy I U 19400 " ~ i ~ l

[ Ethemet --

SUR

FIGURE 6. The ultrasonic experimental test set-up. pulse obtained for transmission through a 3.81-cm thick perspex plate using the same transducers and ultrasonic couplant as used for the experiments on cement pastes. The transmitter is pulsed by a Panamet-

/ 6000

fit window

~

[

xl0 ~

14

fit spectrum

Amplitude 12

4OO0

Ultrasonic Experimental Test Set-Up The apparatus used is shown schematically in Figure 6 and is similar to that of Sayers and Grenfell [1] and D'Angelo et al. [15]. The cement paste is poured into a perspex cell with internal dimensions 14 cm x 12 cm × 1.208 cm. The perspex walls are 2.416-cm thick to separate the first arrival from the multiple reflections within the perspex walls. Ultrasonic transmission measurements were made using broad-band (Panametrics V101-RB) transducers with a nominal center frequency of 0.5 MHz. The frequency content of the pulse is displayed in Figure 7, which shows the frequency spectrum of the received

10 200O

-6000

°

ii

"~o

~o Travel time / microseconds

°o

o.,'

;

,.~

Frequency / MHz

FIGURE7. Frequency spectrum and measured waveform for propagation through a 3.81-cm thick perspex plate.

Ultrasound Through Hydrating Cement Pastes 1 7

Advn Cem Bas Mat 1993;1:12-21

rics 5058PR high voltage pulser/receiver. A pulse repetition rate of 100 Hz was used. Directly opposite the transmitter, the receiving transducer senses the pulses which are subsequently amplified by a Panametrics 5560B preamplifier. Acoustic contact b e t w e e n the transducers and the perspex cells was made with Panametrics couplant. The amplified signal provides the input for a LeCroy 9400 digital oscilloscope. The first 200 I~s of the received signal was digitized at a 100 MHz sampling rate. Signal averaging is carried out by the oscilloscope using a routine which takes about 10 seconds for 100 averages of the acquired waveform. Averaged waveforms are obtained at intervals of 5 minutes and transferred via a GPIB cable to a Dell 316SX IBM compatible PC. On completion of a test the acquired traces are transferred to a SUN workstation for further analysis.

Determination of Ultrasonic Velocity and Amplitude With a suitable amplification and sampling rate selected on the oscilloscope, the amplitude of the received signal and the time taken for it to travel from the transmitter through the perspex and cement paste to the receiver is determined from the waveform. This time is corrected for the travel time through the perspex and the transducers, which was determined in a separate experiment. The corrected time delay and measured path length are then used to calculate the ultrasonic velocity in the paste.

Experimental Results

25

v"

20

/rf 5

0

r/." / F/ f, 10

20

3O

40

50

60

70

80

90

100

Travel time ! microseconds

FIGURE 8. Normalized ultrasonic waveforms for a deaerated neat class G cement. waveforms for an as-mixed accelerated class G cement paste containing 2% CaC12 are plotted in Figure 11. At early times a relatively high frequency wave is observed to propagate through the as-mixed accelerated cement paste with the onset of a lower frequency signal at later times. This transition is shown in more detail in Figure 12. The measured signal at early times is highly attenuated, as may be seen from the amplitude of the largest positive peak plotted in Figure 13. The amplitude at first decreases with increasing time due to the increasing tortuosity of the pore space, but at later times begins to increase as propagation on the interconnected solid frame becomes possible. The high frequency component seen at early times is interpreted to be the result of wave scattering by entrapped air bubbles following the discussion of the effect of en-

Results for De-Aerated Pastes Ultrasonic waveforms for de-aerated neat and accelerated class G cement pastes are shown in Figures 8 and 9, respectively. These waveforms have been normalized to the amplitude of the largest peak in the waveform. Only a single compressional wave is observed, the velocity of this wave being plotted in Figure 10. In agreement with earlier work, the velocity is observed to decrease slightly before the rapid rise in velocity which occurs once the solid phase becomes interconnected. We suggest that the observed decrease in velocity at early times is due to an increasing tortuosity a due to the formation of hydration products within the pore space as may be deduced from eq 2 in the limit of small frame moduli.

Effect of Entrapped Air It was found that the addition of 2% CaCI2 led to a significant increase in the amount of air trapped in the cement paste due to mixing. Normalized ultrasonic

25

20 rF

d"

F P

lo

20

3o

4o

5o

6o

7~

8~

~

loo

Travel time ! mlctoseconds

FIGURE 9. Normalized ultrasonic waveforms for a deaerated accelerated class G cement containing 2% CaCI2. The intercept on the vertical axis is the time after placing the cement in the cell at which the measurement was made.

18 C.M. Sayers and A. Dahlin

2.4

r

Advn Cem Bas Mat 1993;1:12-21

[

I

[

s

'7

2.2

•

•

o

o

o

2.0

o o o o

O

>

1.8

•

i3

0

0 0

1.6

1.4

•

0

-

0

~+,~oSo°o. J

o°

5

I

I

[

10

15

20

2

~

"

"

"

i

60

70

80

90

100

25

Time / hours FIGURE 10. Measured ultrasonic compressional wave velocities for de-aerated accelerated (@) and neat (O) class G ce-

0

10

20

30

40

50

Travel time / microsecoz~s

ment pastes.

FIGURE 12. Early time ultrasonic waveforms for an as-mixed

trapped air in the Theory section. The peak frequency of the low frequency component is seen to increase with increasing time as the connectivity of the solid frame increases. These observations may be quantified by examining the Fourier spectra shown in Figures 14 to 19 for each of these waveforms. These spectra are normalized to their maximum value, which is shown in Figure 20. At early times (Figures 14 and 15) the paste is seen to behave as a high-pass filter over the frequency range employed, with pass band beginning at about 0.5 MHz. The measured amplitudes in the pass band are small at early times, in agreement with the theoretical curve shown in Figure 4 where the attenuation remains high above/ca = 0.2. Since the travel time of the high frequency component is similar to the travel time in the corresponding de-aerated paste, it follows from Figure 5 that the low frequency cut-off of 0.5 MHz corresponds to the top of the high attenuation band in 25

accelerated class G cement containing 2% CaC12. Figure 4 (/ca = 0.2) and therefore that the characteristic bubble radius is of order 100 p,m. For this value, resonance occurs at a frequency of 0.024 MHz. The characteristic frequency of the transducers used in the present experiment is of order 0.5 MHz. The spectrum obtained for propagation through a 3.81-cm thick perspex plate using the same transducers is shown in Figure 7. It is clear that very little energy is input into the sample at frequencies below the resonant frequency. The above estimate of bubble size was confirmed by breaking the sample several days after the ultrasonic experiments were performed and examining the resultant fracture surface with a scanning electron micro-

10 ]

10"

000000000000000000000 0 0

2O

0

~10 "l 15

1,0

10.2 0

0 0

5

510

20

30

10.3 40

50

60

70

80

90

Travel time / microseconds

FIGURE 11. Normalized ultrasonic waveforms for an as-

mixed accelerated class G cement containing 2% CaC12.

10 15 Time/ Hours

20

25

100

FIGURE 13. Amplitude of the largest positive peak in the waveform for as-mixed accelerated class G cement containing 2% CaC12 to which the waveforms in Figure 11 have been normalized.

Ultrasound Through Hydrating Cement Pastes 1 9

Advn Cem Bas Mat

1993;1:12-21 1

0.9

2

l

l

l

(a) 0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

/

0.1

0 0

(b)

(b)

(a)

1

0.9 0.8 0.7 o 0.6

I

0.9 0.8 0.7 0.6 0.5

0.5

0.4 c) Z

1

0.1~J

0.5

0.5

Frequency / MHz

Frequency/ MHz

'i z

o.3[I

0.4

0.3~

0.2

0.2

0.1

0.1

0 0

01o

0.5 Frequency/ MHz

015 Frequency/ MHz

FIGURE14. Fourier transformed spectrum after (a) 1.2 hours and 0a) 1.6 hours for an as-mixed accelerated class G cement containing 2% CaC12. The amplitudes are normalized to the maximum value.

FIGURE16. Fourier transformed spectrum after (a) 2.8 hours and (b) 3.2 hours for an as-mixed accelerated class G cement containing 2% CaC12. The amplitudes are normalized to the maximum value.

scope. Air bubbles with radii in the range of 50 to 200 p,m were found to be present. It follows from these experiments that at early times the dominant propagation path for ultrasound is through the bubbly fluid with frequencies comparable to the resonant frequency of the air bubbles being strongly scattered. Once the interconnected solid phase forms, a different propagation path becomes available and scattering by the air bubbles in the fluid phase becomes less important. Keating et al. [3,4] found the arrival time by determining the time at which the signal first crossed a preset threshold. Too high a threshold will result in too low a velodty due to cycle skipping for waveforms of

the type seen in Figure 12 at early times. This explains some of the very low velodties at early times reported in the literature. By contrast, the transit time in the present work was obtained manually from the digitized waveform. At later times, when ultrasound is able to travel through the interconnected solid phase, the as-mixed and de-aerated pastes show similar waveforms (compare Figures 9 and 11).

1i

0.9

1

(a)

0.9

Discussion and Conclusion Once the solid phase in a cement paste becomes interconnected, it is more appropriate to treat the material

(b)

1

1

(a)

0.9

0.8

0.8

0.8

0.8

0.7

0.7

0.7

0.7

0.6

0.6

0.6

~

0.5

0.5

~

0.4

0.6

~

0.5 0.4 0.3 0.2 0.1 0

l 0.5

Frequency / MHz

i

0.4

/

0.3~ 0.2 0.1 0 0

~

0.5 Frequency/ MHz

FIGURE 15. Fourier transformed spectrum after (a) 2 hours and (b) 2.4 hours for an as-mixed accelerated class G cement containing 2% CaCl2. The amplitudes are normalized to the maximum value.

~

0.4

0.3

0.3

0.2

0.2

°loi 0

(b)

0.9

o.,°

0.5 Frequency/ MHz

0

0.5 Frequency/ MHz

FIGURE 17. Fourier transformed spectrum after (a) 3.6 hours and (b) 4 hours for an as-mixed accelerated class G cement containing 2% CaCl2. The amplitudes are normalized to the maximum value.

20 C.M. Sayers and A. Dahlin

Advn Cem Bas Mat 1993;1:12-21

1

1

(a)

101

(b)

0.9

0.9

0.8

0.8

O00000000000000OO0000

1¢ 0 0

i

i

0.7

0.7

0.6

0,6

0.5

0.5

0.4 0.3

0.4

0.2

0.2

o.1°

0.1

0

10a

~ 102 ~ 10-s

0.3

O O

~10 4

o

10-s 0

00

0,5

--015

Frequency/ MHz

Frequency / MHz

106

FIGURE18. Fourier transformed spectrum after (a) 4.4 hours and (b) 4.8 hours for an as-mixed accelerated class G cement containing 2% CaC12. The amplitudes are normalized to the maximum value. as a fluid-saturated porous elastic solid than as a suspension of cement particles in water. Two compressional elastic waves are expected in a fluid-saturated porous solid but only one has been observed in hydrating cement pastes using ultrasound. At early times the frame moduli and therefore the velocity of the slow wave are small. The wavelength of the slow wave will therefore also be small, since wavelength is proportional to velocity, and the wave will be strongly scattered [7]. At later times, cements have little porosity with characteristic dimension greater than 1 p~m, the bulk of the porosity having dimension less than 0.1 p,m [12]. At later times, therefore, the low frequency limit ! (b)

0.9

0.9f

(a)

0.8

0.8

0.7

0.7

0'6 f

~

0.6

]

0.5

~

0.5

g

0.4

0.4

Z

0.3

0.3

0.2

0.2

0.1 o.1o

0

0

0.5 Frequency/ MHz

0

0.5 Frequency/ MHz

I

FIGURE 19. Fourier transformed spectrum after (a) 5.2 hours and Co) 5.6 hours for an as-mixed accelerated class G cement containing 2% CaCI2. The amplitudes are normalized to the maximum value.

i

0

5

i

i

10 15 Time / Hours

i

20

25

FIGURE 20. Amplitude of the peak in the spectrum for an as-mixed accelerated class G cement containing 2% CaCl2, normalized to the value at 24 hours.

of Biot's [6] theory is more appropriate. In this limit only the fast wave is propagatory, the slow wave being the solution of the diffusion equation. In agreement with previous measurements, the compressional wave velocity in neat and accelerated American Petroleum Institute class G cement pastes was observed to decrease slightly during the first few hours after mixing, followed by a rapid increase once the solid phase becomes interconnected. It was shown that this change in behavior results from a change in character of the observed wave as hydration proceeds. At early times the observed wave involves essentially motion of the fluid phase while at longer times it involves essentially motion of the solid frame. Ultrasonic waves are therefore sensitive to the point at which the solid phase becomes interconnected. This point is of practical significance since the connectivity of the solid phase is responsible for the load,bearing capacity of set cement. It was concluded that the early,time decrease in veloc, ity is due to an increasing tortuosity resulting from the formation of hydration products within the pore space of the cement paste. The effect of entrapped air was investigated by comparing measurements on as-mixed and de-aerated neat and accelerated class G pastes. At early times the dominant propagation path for ultrasound is through the bubbly fluid with frequencies comparable to the resonant frequency of the air bubbles being strongly scattered. Once the interconnected solid phase forms, a different propagation path becomes available and scattering by the air bubbles in the fluid phase becomes less important. The effect of entrapped air was found to be greater for accelerated than for neat cement pastes. One possible explanation

Advn Cem Bas Mat 1993;1:12-21

for this is that the viscosity of the accelerated cement paste is greater than that of the neat paste so that the time taken for an air bubble to escape from the paste will be greater. The accelerated cement paste would therefore be expected to contain more entrapped air.

Acknowledgments We thank S.N. Davies and C. Hall (SCR)for helpful discussions.

References 1. Sayers, C.M.; Grenfell, R.L. Ultrasonics 1993, 31, 147153. 2. Neville, A.M. Properties of Concrete; Pitman, 1981. 3. Keating, J.; Hannant, D.J.; Hibbert, A.P. Cement and Concrete Research 1989, 19, 554-566.

Ultrasound Through Hydrating Cement Pastes 21

4. Keating, J.; Hannant, D.J.; Hibbert, A.P. Cement and Concrete Research 1989, 19, 715-726. 5. Rao, P.P.; Sutton, D.L.; Childs, J.D.; Cunningham, W.C. Journal of Petroleum Technology 1982, 2611-2616. 6. Biot, M.A.J. Acoust. Am. 1956, 28, 168--191. 7. Johnson, D.L.; Plona, T.J.J. Acoust. Soc. Am. 1982, 72, 556-565. 8. Berrymann, J.G. Appl. Phys. Lett. 1980, 37, 382. 9. Johnson, D.L. Appl. Phys. Lett. 1980, 36, 259. 10. American Petroleum Institute. API Specification 10, Fifth edition, 1990. 11. Sayers, C.M.; Smith, R.L. Ultrasonics 1982, 20, 201-205. 12. Parcevaux, P. Cement and Concrete Research 1984, 14, 419430. 13. Gaunaurd, G.C.; Uberall, H. J. Acoust. Soc. Am. 1980, 69, 362-370. 14. Minnaert, M. London, Edinburgh and Dublin Philosophical Magazine and Journal of Science 1933, 16, 235-248. 15. D'Angelo, R.; Plona, T.J.; Schwartz, L.M.; Coveney, P. Society of Petroleum Engineers, 1993; Paper no: SPE 25403.