Cavitation, a novel drilling concept

Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. I 1, pp. 115-119. Pergamon Press 1974. Printed in Great Britain.

Cavitation, A Novel Drilling Concept F. A. ANGONA* An experimental investigation of cavitation erosion as a possible drilling mechanism is described. A focusin 0 acoustic system enclosed in a pressure chamber permitted the sound pressure and the hydrostatic pressure to be independently varied over the range of 1-20 atm. The intensity of cavitation, as measured by the erosion rate of Lueders limestone and aluminum, was found to increase as the third power of hydrostatic pressure. Experimental results obtained in this pressure range correlate with published Soviet data taken at pressures up to 75 atm. Extrapolation of data to 10,000-ft drilling conditions indicate penetration rates higher than those for rotary drilling provided a borehole transducer with an acoustic output in excess of 100 h.p. can be developed.

1. I N T R O D U C T I O N Some years ago we became interested in cavitation erosion as a possible mechanism for drilling deep oil wells. Since a liquid filled hole is required for most drilling the relatively high hydrostatic pressure at the bottom of the hole could appreciably alter the cavitation phenomenon. A comprehensive literature survey revealed little information on the effect of elevated pressure on the intensity of cavitation. Consequently, we conducted an experimental investigation of this subject. In [1], we discuss these experiments and the results of elevated pressure on cavitation erosion of aluminum. In this current paper, the effect of pressure on the erosion of Lueders limestone is discussed. The results for Lueders limestone are extrapolated to a hypothetical oil well drilling situation and penetration rates are estimated. Cavitation is the phenomenon associated with the for. mation and violent collapse of bubbles in a liquid. The energy associated with the collapse of a single bubble is small, but the spherical convergence of the collapsing bubble generates an energy density sufficient to erode materials with strengths as high as that of tungsten. Understanding of both the threshold and intensity of cavitation at high pressures is necessary to evaluate cavitation as a drilling mechanism. The threshold is the magnitude of the acoustic signal required to induce cavitation and is primarily dependent on the hydrostatic pressure and the properties of the liquid. The intensity of cavitation determines its destructiveness, once cavitation is initiated. It is generally accepted that cavitation erosion is caused by the shock wave generated as the bubble collapses. The intensity is determined by the magnitude and number of these shock waves. Jones and Edwards [2], in their study of cavity dynamics at atmospheric pressure, have measured shockwave amplitudes in excess of 104 atm. Benjamin and * Mobil Research and Development Corporat.ion, Field Research Laboratory, Dallas, TX, U.S.A.

ROCK I 1 / 4 - A

Ellis [3], have shown by high-speed photography that the collapsing cavities deform and liquid jets are formed. They believe these jets could be as important as the shock waves in causing cavitation erosion. During the early stages of this investigation, Sirotyuk [4] reported on a cavitation study at elevated hydrostatic pressure. He experimentally confirmed our contention that the intensity of cavitation can be considerably enhanced by increasing the hydrostatic pressure. Sirotyuk's results are directly related to this study and are used to extrapolate laboratory results to deep drilling conditions. Equipment The equipment for this investigation was designed to permit the sound pressure and the hydrostatic pressure to be independently varied over the range of 1-20 atm. A focusing acoustic system was used to attain the acoustic pressures required to produce cavitation at these pressures. This system also offered the advantage of confining the cavitation zone to a small volume in the interior of the pressure chamber, thus minimizing wall effects and eliminating erosional damage to the equipment. The basic components of the equipment are a highpowered acoustic transducer driven by a heavy-duty power amplifier, a paraboloidal aluminum reflector, and a pressure chamber. Details of the equipment and the experimental procedures employed are given in [1]. A schematic drawing of the pressure chamber with the transducer and reflector in place is shown as Fig. 1.

2. RESULTS

The results of the initial cavitation experiments bordered on the spectacular and demonstrated that rock could be effectively drilled by cavitation. Figure 2 shows a photograph of a Lueders limestone core which was exposed to cavitation for three minutes at a hydrostatic 115

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pressure of 250 psi. Rocks both weaker (Berea sandstone) and stronger (Solenhofen limestone) than Lueders have been eroded by cavitation. In addition metals of various hardnesses ranging from lead to stainless steel have been eroded by cavitation. The observed weight loss per unit time of exposure decreased with increasing hardness.

Fig. 3. Lueders limestone core drilled by cavitation. Radial cracks demonstrate violence of cavitation.

observed as a fountainlike spray extending as much as 2 in. above the sample. Evidence of the impact action of the shock wave from individual cavities can be seen on the eroded aluminum samples of Fig. 5.

Qualitative The violence of cavitation erosion is demonstrated by the radial cracks evident in Fig. 3. When the acoustic and hydrostatic pressures were adjusted for maximum cavitation activity, the ejection of rock fragments obscured the core within a fraction of a second. The five motion picture frames (64 frames/sec) of Fig. 4 show the rapid build up of the ejected debris from a Lueders limestone core. A few seconds exposure of an aluminum sample caused the sample surface to become roughened with craters and pits. Ridges were formed around and between the craters; these often protruded above the original sample surface. Also, fine particles of metal were torn loose as the craters were formed and could be

Fig. 2. Lueders limestone core 1 in. dia and length drilled by cavitation erosion.

Fig. 4. Frames from motion picture of Lueders limestone core being eroded by cavitation. Time interval between frames is 15.6 msec; core is 1 in. dia.

Cavitation, a novel drilling concept

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Fig. 5. Detail of erosion craters on 1-in. dia aluminum samples. Crater at center right is approximately 0"05 in. in diameter.

Effect of hydrostatic pressure Since the primary objective of our study was to determine the effects of hydrostatic pressure on the erosional characteristics of cavitation, the bulk of the work was confined to Lueders limestone and alloy I100F aluminum. These materials were selected because they are relatively soft and respond readily to cavitation in the power range of the equipment and also because of their uniformity from sample to sample. As shown in Fig. 6, the weight loss for Lueders limestone increases appreciably as the hydrostatic pressure is increased. The driving voltage was set slightly above the value required to initiate cavitation for each setting of the hydrostatic pressure, PLo. A similar curve for aluminum was shown in 1-1-1,Fig. 7. These data demonstrate that the intensity of cavitation does indeed increase as the hydrostatic pressure is raised.

When weight loss is plotted against hydrostatic pressure for a constant value of applied acoustic pressure, PA, curves such as those shown in Fig. 7 are obtained. For each value of PA there is a range of hydrostatic pressures where cavitation erosion is a maximum. The general shape of the curves can be explained by the dynamics of the cavitation bubbles. Noltingk and Neppiras I-5] have shown in their numerical study that for a fixed PA and a fixed frequency, there exist both a lower and a higher limit for PLo. The lower limit occurs because as P~.o is decreased the cavitation bubbles grow larger. Because of the bubble growth, the collapse time for each bubble increases and eventually exceeds the half period of the acoustic signal; that is, the cavity does not collapse completely before the acoustic signal reverses into its negative phase. As PLO is increased beyond the value for maximum cavitation erosion, fewer and fewer cavitation

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Fig. 8. Relative weight loss of Lueders limestone as a function of hydrostatic pressure for various settings of the applied acoustic pressure.

events occur until finally the hydrostatic pressure is sufficiently high that the fixed value of PA is below the threshold of cavitation, and cavitation does not occur. Similar curves for aluminum are shown in [1], Fig. 8. 3. ANALYSIS O F RESULTS In spite of efforts to minimize the effects of variations in gas content and the size of nuclei in the liquid by using degassed distilled water, there was considerable scatter in the raw data. Consequently, the experimental data were smoothed by plotting AW vs PA for each setting of the hydrostatic pressure. Values of AW were taken from the smoothed curves, normalized to facilitate comparison between data for different samples and published results, and plotted as a function of PL0 with PA as a parameter. Normalization was accomplished by dividing the weight loss at elevated pressure by the measured weight loss at atmospheric pressure for each value of the applied acoustic pressure. The normalized curves for Lueders limestone are displayed as Fig. 8.

200~ / / ~ ~ . . . . ~ 5. 67 a t m 0

4 8 12 16 HYDROSTATIC PRESSURE(atm)

Fig. 9. Weight loss of Lueders limestone compared to radiation equation (equation 1).

The calculated weight loss is plotted in Fig. 9 and shows fair agreement with the experimental data. In order to apply the results of this laboratory investigation to the drilling of an oil well, an order of magnitude extrapolation is required. To accomplish this, the weight loss for Lueders limestone, as predicted by equation (1) is plotted in Fig. 10. The required acoustic pressure in atmospheres is noted on each curve. At a drilling depth of 3000 ft, the l09 700

Extrapolation of laboratory data In [1], a reasonably good correlation between our aluminum results and those of Sirotyuk was established. In addition, a correspondence between cavitation erosion and blackbody radiation was developed. These lead to two independent means for extrapolating data to higher pressures. Encouraged by the agreement of the two independent methods of extrapolating the aluminum data, an equation comparable to equation (4) of [1] was derived for the Lueders limestone data. The weight loss per 5 sec exposure for Lueders limestone as predicted by the modified radiation equation is 1

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Fig. 10. Extrapolation ofexperimental data by equation 1. The weight loss is in mg for a 5 sec exposure.

Cavitation, a novel drilling concept hydrostatic pressure is 100 atm, and the erosion rate as read from Fig. 10 is 1200 g for a 5 sec exposure. This is equivalent to drilling a 10 in. dia hole at a rate of 25 ft/hr, which is comparable to the rate obtained by conventional drilling methods. The extrapolated erosion rate for drilling the same hole at 10,000 ft is 900 ft/hr. This appreciable increase in the penetration rate with depth contrasts with the decrease associated with conventional drilling. In addition, cavitation drilling is potentially a bit-less system, since there need be no physical contact between the drill (transducer) and the formation, thus eliminating tripping and the associated problems. In order to cavitate at a depth of 10,000 ft, an acoustic pressure of the order of 340 atm would be required. According to the plane wave theory, the acoustic intensity is I = -2pc

(2)

when PA is the required acoustic pressure and pc is the acoustic impedance of the fluid in the hole. For PA equal to 340 atm and water as the fluid, the intensity is 38.5 kW/cm 2. This intensity is extremely high and most likely could only be achieved with focusing. Assuming a focal area of the order of 2 cm 2, the area of our laboratory equipment, the power output of the downhole transducer would have to be 100 h.p. At present this is an order of magnitude above the power levels of commercially available acoustic transducers.

4. C O N C L U S I O N S The feasibility of &filing by cavitation has been experimentally investigated in a laboratory study designed to determine the relationship between cavitation intensity, acoustic pressure, and hydrostatic pressure. The signifi-

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cant findings and principal conclusions drawn from this study are: (1) Cavitation erosion is an effective mechanism for drilling through rock. (2) The intensity of cavitation increases as the third power of hydrostatic pressure over the pressure range of 1-20 atm. (3) Our cavitation data correlate well with published Soviet data obtained at pressures up to 75 atm. (4) Effectiveness of cavitation erosion as a drilling mechanism should increase with depth so long as the acoustic signal generating the cavitation field can be increased to necessary threshold levels. (5) Extrapolation of laboratory results to pressures which occur at 10,000 ft drilling depths indicates significantly higher penetration rates may be obtained by cavitation than with rotary drilling. (6) A downhole acoustic transducer with an output in excess of 100 h.p. would be required to drill at 10,000 ft. Received 30 July 1973.

Aelmowledgements~The author wishes to thank the Mobil Research and Development Corporation for permission to publish this material. Appreciation is also extended to Wilton Gravley and Paul M. Berry with whom I had numerous discussions.

REFERENCES 1. Angona F. A., Cavitation erosion of aluminum at elevated pressure, J. Acoust. Soc. Amer. 50, 277-285 (1971). 2. Jones I. R. and Edwards D. H, An experimental study of the forces generated by the collapse of transient cavities in water, J. Fluid Mech. 7, 596 (1960). 3. Benjamin T. B. and Ellis A. T., The collapse of cavitation bubbles and the pressure thereby produced against solid boundaries, Phil. Trans. Roy. Soc. London, Ser. A, 260, 221-224 (1966). 4. Sirotyuk M. G., Ultrasonic cavitation processes at elevated hy• drostatic pressures, Soy. Phys. Acoust. 12, 199-204 (1966). 5. Noltingk B. E. and Neppiras E. A., Cavitation produced by ultrasonics, Proc. Phys. Soc. (London) 63B, 674-685 (1950); 64B, 10321038 (1951).