Directional Acoustic Surveying Instrument
- D.M. Trehome (Heriot-Watt U.) | P.G. Harper (Heriot-Watt U.) | D. Su (Heriot-Watt U.)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling Engineering
- Publication Date
- June 1989
- Document Type
- Journal Paper
- 104 - 108
- 1989. Society of Petroleum Engineers
- 4.1.2 Separation and Treating, 4.3.4 Scale, 1.5 Drill Bits, 1.6 Drilling Operations, 4.1.5 Processing Equipment
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A new type of acoustic detector capable of determining the direction of a noise source was developed. Under granite transmission at a depth of 600 m [1,970 ft] and ranges up to 200 m [655 ft], directional accuracies of 1 to 2 degrees were achieved. Detectable sources included quasi-continuous (e.g., drill-bit) noise and pulses (e.g., explosive or sparker tool). The sensing element is a symmetric resonator whose flexural modes are readily excited by an external acoustic source. The physical principle is that the phase plane of a strong acoustic spectral component fixes the nodal directions of the resonant flexural vibrational mode, thus establishing the propagation direction in relation to the modal symmetry. The resonator is encapsulated in oil to damp the vibrations and to retain and communicate the acoustic signal. (The vibrational modal pattern is detected with strain gauges and processed to provide directionality.) This paper presents (1) vibrational response theory; (2) construction details; and (3) analysis of field data leading to directionality.
Conventional methods for locating subsea/underground noise sources require hydro- and geophones in net-arrays with minimum separations on the order of mean acoustic wavelength. Correlation techniques then provide directional information. This paper describes the principles, design, and performance of an instrument comprising a single noise tool that operates in a surveyed borehole, allowing real-time determination of the noise orientation.
Acoustic directional sensing was first systematically studied in 1982 and concerns the vibrations of a circular, symmetric shell in response to a resonant acoustic signal. At resonant frequencies, four-, six-, eight-fold, etc., modes align themselves with diametric antinodes along the direction of propagation. Therefore, m principle, strain measurements are sufficient to fix the propagation direction relative to one or more vibrational patterns. The practical difficulties, however, are numerous and formidable because the noise source is not only spectrally broad, but also incoherent to some degree.
The instrument consists of a thin, brass, hemispherical shell equipped with strain gauges and mounted at the base (or-pole). The whole instrument is immersed in oil to damp the vibration and to serve as an acoustic coupling medium. Imbalance in the resonator can lead to ambiguous or false directionality. Matching the resonant frequencies to expected spectral peaks in the acoustic signal requires consideration of shell thickness, diameter, type of mounting, and immersion oil. Details are discussed later.
In the present design, the strain field is sampled near the resonator rim by semiconductor gauges, but other methods have been studied, notably holographic, optical fiber, and piezoelectric polyvinylidene fluoride (PVdF). The Analysis and Discussion section describes a method of extracting the directional response from noisy signals and presents results that relate to field trials at the Rogaland Research Inst. in Stavanger, Norway.
Principle of Directional Vibrational Response
The earliest theoretical work on the free vibrations of thin hemispherical shells is from Rayleigh in 1881; Kalnins and others have since advanced the general linear theory. Su computed modes of incomplete hemispherical shells. For the lowest-frequency (n=2) modes (i.e., the fundamental flexural modes), the maximum radial displacement occurs near the free boundary rim, and treating it as a narrow cylindrical section or ring is sufficient. The vibrations of acoustic interest, the inextensible or flexural modes, are easily understood as those that leave the ring perimeter unchanged (to first order in the strain). Modes of higher frequencies that involve stretching require the full-shell theory and include those of four-fold and higher symmetry.
An ideal freely vibrating cylindrical shell section (approximating the hemispherical rim) has two orthogonal, flexural (n = 2) modes of the same frequency, , represented by radial displacements proportional to (cos 2 , sin 2 ) and related to the tangential components by the Love relations (see Figs. la and b). Here the azimuthal angle, , is measured around the rim from some arbitrary reference direction. The orthogonal linear combination [(a cos 2 2 ) -(b cos2 +a sin 2 )] is equally acceptable because it is equivalent to a (rescaled) ring rotation.
Suppose now that the ring (radius r) vibrates in an isotropic fluid acoustic medium, is subject to a plane pressure wave (amplitude P) that acts on the outer surface only, and propagates at an angle of to the reference direction. Then, denoting the wave number by Nk, the spatial phase around the rim is Nkr cos( ). For rings of a few centimeters in radius and at frequencies less than 1.0 kHz [ 1,000 cycles/sec], Nkr less than 1 so that the wave amplitude becomes very nearly
(1) The vibrational response to the driving pressure (Eq. 1) can be uniquely resolved into dependent components that match the three separate terms of Eq. 1. The first response, independent of , is the "breathing" mode, a stretching or membrane mode with a typical frequency of several kilohertz. The second response is a swinging motion with no change of shape and a restorative force provided only by the ring mounting.
The third response term is our main interest. If COS2( -a) is written as 1/2 [cos 2( - a) + 1 ], then it matches the flexural mode cos 2 ( - a), taking bla = tan 2 . (The constant term only augments the breathing mode.) The important principle is that the spatial phase of the flexural mode is fixed by the sound direction. Also note that the orthogonal (odd) mode, sin 2( - ), is unexcited.
A coherent acoustic wave with a fixed propagation direction (reference direction, 0 = 0) is represented by the sinusoidal driving force field f cos 2 cos f . This allows the steady resonant (even) response to have the expected nodes at = Fig. 2 represents the ( , ) dependence for five values.
There are, however, complications in practice. The acoustic medium (transformer oil in the present device) provides an inertial and dissipative resistance that leads to lowered and broadened spectral response. Small asymmetries lead to dynamic Unbalance in the hemispherical shell and a consequent splitting of the resonant frequency, f, into two components. A good resonator has its fundamental frequency (100 or 200 Hz [100 or 200 cycles/sec]) split by about 1.0 Hz [1.0 cycle/sec] in air. Directional response in air is complicated by asymmetric pinning. Fortunately, the broadening effect of medium damping can compensate for this.
Instrument Construction and Operation
As noted, the resonator is ideally designed of materials and dimensions to match its natural frequencies to the expected spectral character of the signal. Overall size is limited by the borehole diameter. AH resonators used in the field tests were turned from marine brass (e.g., shell radius r=3.5 cm [1.4 in.] and thickness h=0.6 nun [0.02 in.]), determining a fundamental flexural mode frequency (in oil) of = 196 Hz [ 1 96 cycles/sec], and a higher four-fold mode frequency of 1.906 kHz [1,906 cycles/sec]. The inevitable frequency splitting caused by manufacture and assembly is reduced to a minimum by testing and balancing in air.
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