REVIEW OF SCIENTIFIC INSTRUMENTS 86, 044902 (2015)
Non-intrusive, high-resolution, real-time, two-dimensional imaging of multiphase materials using acoustic array sensors M. Cassiède and J. M. Shaw Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 2G6, Canada
(Received 15 September 2014; accepted 9 March 2015; published online 7 April 2015) Two parallel multi-element ultrasonic acoustic arrays combined with sets of focal laws for acoustic signal generation and a classical tomographic inversion algorithm are used to generate real-time two-dimensional micro seismic acoustic images of multiphase materials. Proof of concept and calibration measurements were performed for single phase and two phase liquids, uniform polyvinyl chloride (PVC) plates, and aluminum cylinders imbedded in PVC plates. Measurement artefacts, arising from the limited range of viewing angles, and the compromise between data acquisition rate and image quality are discussed. The angle range of scanning and the image resolution were varied, and the effects on the quality of the reproduction of the speed of sound profiles of model solids and liquids with known geometries and compositions were analysed in detail. The best image quality results were obtained for a scanning angle range of [−35◦, 35◦] at a step size of 2.5◦ post processed to generate images on a 40 µm square grid. The data acquisition time for high quality images with a 30 mm × 40 mm view field is 10 min. Representation of two-phase solids with large differences in speed of sound between phases and where one phase is dispersed in the form of macroscopic objects (greater than 1 mm in diameter) proved to be the most difficult to image accurately. Liquid-liquid and liquid-vapor phase boundaries, in micro porous solids by contrast, were more readily defined. Displacement of air by water and water by heptane in natural porous limestone provides illustrative kinetic examples. Measurement results with these realistic cases demonstrate the feasibility of the technique to monitor in real time and on the micrometer length scale local composition and flow of organic liquids in inorganic porous media, one of many envisioned engineering applications. Improvement of data acquisition rate is an area for future collaborative study. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4915894] I. INTRODUCTION
Non-intrusive, real-time measurement of local composition and fluid movement in porous media presents numerous data acquisition and data processing challenges, but equipment with this capability is relevant to many fields of science and engineering from earth science to petroleum engineering and from biomedical engineering to industrial catalysis. Optimization and compromise are needed to realize successful applications in three dimensions, two dimensions (2D), and along one dimensional (1D) paths in porous media. Some compromises are application specific and concern limitations to the range of angles that can be viewed, to the spatial resolution requirements, the total areas or volumes explored, to the speed of process kinetics that can be surveyed, and the possible need for additives to improve contrast. Successful imaging techniques have been based on X-ray, acoustic, thermo-acoustic, and more recently photoacoustic1 devices, where the structure of cells and internal organs in biology and biomedical applications, and where thermophysical phenomena such as diffusion, chemical reaction, phase change, and natural gas hydrate formation in chemical engineering have been monitored. Within this spectrum of activity, acoustic techniques are of growing interest because they are often convenient, cheaper, and have fewer side effects in the case of biomedical 0034-6748/2015/86(4)/044902/13/$30.00
applications. While the data acquisition and image processing times required to obtain individual high-resolution three-dimensional images can be long,2 current commercial multi-element acoustic devices permit the generation of two-dimensional high-resolution acoustic images based on ultrasonic emission from an array of sensors at shorter time intervals, and arrays provide one-dimensional images rapidly, thus opening up a number of potential useful applications in science, medicine, and engineering. For example, in medical applications of ultrasonic imaging, in which high-frequency sound waves are used to construct detailed cross-sectional images of internal organs, acoustic emitters and receivers are placed in a circle or on the surface of a sphere that surrounds the object of interest. Images are then constructed based on straight-line propagation of sound energy from individual emitters to individual receivers on opposing sides of the array. Even so, refraction phenomena occurring at the boundary of tissues presenting variations in speed of sound are often responsible for strong artifacts3 and these must be eliminated in image processing. The more widespread use of phased array systems across a variety of industrial sectors starting during the early 2000s has made them less expensive, and nonintrusive tools have been developed for diverse geometries. Two-dimensional acoustic or seismic measurement methods have become common tools in engineering applications, from non-destructive product testing, to archeology, and resource
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mapping. These images are obtained rapidly but lack spatial resolution, or target identification of specific features, readily distinguished from backgrounds, such as flaws, cracks, or fissures in metal objects and these applications do not address time varying phenomena. The present work builds upon proof of concept studies presented previously where the same phased array was used to measure liquid-liquid phase separation, kinetics of separation and end states, for methanol + mixed hexanes and methanol + heptane mixtures4 and for asphaltene + polystyrene + toluene mixtures5 based on 1D imaging. The liquid-liquid and liquidvapor interfaces arising in these measurements were detected from the presence of discontinuities (in speed of sound) and peaks (in acoustic wave attenuation) arising in 1D profiles at fixed elevations measured along the probe length. Two 64-element acoustic arrays were used and the interface location was assessed with a precision of 300 µm. Phase separation kinetics was readily tracked at fixed elevations because all elevations were scanned at a rate of 1 Hz. These results opened new possibilities for investigating local thermophysical property and local phase behavior of fluids including key applications as diverse as the energy sector (asphaltenic mixtures such as live oils) and consumer products and pharmaceutics where monitoring and controlling emulsion formation or breakage phenomena in real time are important issues in formulation control. To date, only pulseecho and transmission measurements have been performed at fixed elevations. In this work, the experimental technique is extended to 2D and 2D acoustic images are constructed based on the use of a classic tomographic inversion algorithm.7 More specifically, a procedure and benchmark measurements related to tracking local fluid composition and phase boundaries in porous media at high resolution as functions of time are elucidated. Envisioned applications include flow, imbibition, diffusion, and other processes arising in synthetic and natural porous media such as reservoir rock and coal. The envisioned applications impose acute and oblique angular geometry between emitters and receivers rather than a simpler circular geometry. This limited-view geometry is more prone to distortion effects than a circular geometry and the additional challenge in this case is to measure small changes in speed of sound values with adequate spatial and temporal resolution, while minimizing the impact of artefacts in both 1D and 2D images. New results relying on this data acquisition approach and novel data processing features are presented. Real-time, two-dimensional, high-resolution images of fluid flow and fluid composition within inorganic porous media are presented, and limitations of the technique requiring further development are discussed.
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The probes and signal generator/data acquisition system are commercial products and their operation is also illustrated elsewhere.3 The sensors (10L64-A2, Olympus NDT) have a central acoustic frequency of 10 MHz and comprise an array of 64 individual piezoelectric ceramic composite elements. Each element is 7 mm × 0.6 mm (a little less than 0.6 mm in reality due to the cutting-line between the elements) and the center-to-center distance or pitch between two successive elements is 0.6 mm. The sensors are electrically driven by a data acquisition unit TomoScan Focus LT. The acoustic waveforms are then recorded, visualized, and analysed using the TomoView software. The acoustic measurement files generated from this device are further analyzed and processed, as described below, to obtain 1D or 2D speed of sound images. Cell I, designed around liquid and colloid applications, where a sample is injected into a cavity machined from a block of Polybenzimidazole (PBI), was described previously.3,4 For Cell I, the two acoustic probes, placed opposite one another within an aluminum frame, abut the exterior walls of the PBI cell and are used to send and receive acoustic signals. Cell II, designed specifically for the current study, holds porous blocks with a rectangular geometry between the two probes, and the bottom part of the blocks can be immersed in a liquid contained in a reservoir at the base of the holder, as shown in Fig. 1. B. Methods
Acoustic beams are fired through test materials by exciting groups of piezoelectric elements simultaneously. The direction of a beam is controlled by applying a small delay, on the order of a few nanoseconds, between the pulses of consecutive elements in a group. The choice of the number
II. EXPERIMENTAL APPARATUS AND METHODS A. Apparatus
The experimental device comprises two custom-made thermally sealed acoustic cells, a pair of acoustic array probes, and a programmable and proprietary acoustic signal generation and acquisition system, supplied by Olympus NDT.
FIG. 1. Schematic for acoustic Cell II. (1) Acoustic probe; (2) shim; (3) porous block; (4) reservoir for liquid; (5) jacket for heat carrier fluid circulation; (6) Teflon plates for thermal insulation.
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of elements and the delay time define a focal law. A focal law takes into account probe and shim characteristics as well as the geometries and the acoustic properties of the test material in order to generate the desired beam shape through the interaction of waves from individual elements. The probes are used in transmission mode. A shim is inserted between the test material and the probe surface to avoid direct contact of the sensor with a liquid medium or a rough rock surface. The probe face is matched acoustically to the shim using ultrasonic coupling gel (Couplant for Ultrasonic Testing OG-1, NDT-Europa) comprising water, surface-active agents, corrosion inhibitors, and a gelling agent. The gel permits excellent acoustic transmission on diverse surfaces. In the present work, each beam is generated by exciting eight or nine adjacent elements of the transmitting array. This number was chosen according to the length and the width of individual piezoelectric elements as well as their spacing to comprise a square base for the composite wave. The acoustic beams were focused at infinity. This configuration maximizes the transmitted sound energy and the generation of deformed beams is avoided. A data acquisition unit (TomoScan Focus LT) is used to transmit the delays to the elements of the emitting phased array probe and to receive and sum the delays of the resulting signal. The group of receiving elements is selected according to the trajectory of the ultrasound beam in the medium and in the shim where changes in the speed of sound may occur. In principle, the sound wave generated by a group of transducers travels in a straight line until it encounters an interface. The impact of shims or other materials between the sensors and the test material must be factored into the selection of receiver elements to avoid unnecessary distortions in the output signals. The change in direction of the transmitted ultrasound energy occurring at a boundary between the shim and the test material is given by the Snell-Descartes law υshim sin α = , sin β υtest material
(1)
where α and β are the incident and transmitted angles, υshim and υtest material are the speeds of sound in the shim and the test material. Sound energy follows a straight-line trajectory when the speed of sound is the same in the two media or when the beam has a 90◦ incidence angle. If the acoustic wave propagation occurs along a path that is longer than a certain length, known as the near-field distance, N, the diameter of the beam diverges as illustrated in Fig. 2. The near field distance N for an element or group of elements in a phased array can be calculated6
FIG. 2. Illustration of spreading of an ultrasonic beam generated by a group of transducers.
N=
k L 2element f , 4υtest piece
(2)
where k is a near field correction factor. It depends on the ratio between the width and the length of the probe element.7 f is the frequency and L element is the length or aperture of probe element. If the probe is mounted on a shim, the effective aperture then depends on the refracted angle and the effective near field length takes the form6 ) ( cos β 2 f k L element L shimυshim cos α − , (3) Neff = 4υtest piece υtest piece where L shim represents the ultrasound path length in the shim. Beyond the near field region, the sound pressure gradually decreases as the beam diameter expands and the energy dissipates. The reduction in amplitude of the acoustic signal is also related to dissimilarities in material properties across an interface. The transmission (refracted) coefficient T at a planar boundary between two media, defined as the percentage of sound energy traveling in the first medium which is transmitted into the second medium, takes the form 2Z2 , (4) (Z1 + Z2) where Z1 and Z2 are the acoustic impedances in the first and second media. From Eq. (4), it can be seen that as the acoustic impedances of two materials become similar, the transmission coefficient increases, and as the acoustic impedances become dissimilar, the transmission coefficient decreases. These intrinsic effects of sound energy propagation lead to a decrease in the amplitude of the acoustic signal transmitted through a test material. In order to compare all the acoustic waveforms using the same criteria, the gain of the acoustic signal is adjusted so that the amplitude of the first peak reaches 80% of the screen height for each focal law, as illustrated in Fig. 3. An example of beam steering between four pairs of transmitter-receiver groups of elements in a sample with a homogeneous speed of sound is presented in Fig. 4. In this illustration, no beam spreading occurs. The complete ray coverage during a classic tomography survey is much more complex. Fig. 5 depicts full ray coverage where beams traverse an object over a range of angles from −25◦ to +25◦ with a 2.5◦ step. The concentration of rays is greater in the central portion of the image than near the upper and lower edges. T=
FIG. 3. Example of an acoustic waveform, visualized using TomoView software, for beam steering with an angle of 20◦.
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variations in the horizontal dimension of the PVC plates, fluid in cell I and limestone samples in Cell II with elevation were ignored.
III. RESULTS AND DISCUSSION
FIG. 4. Example of beam steering with angle β for which beam spreading does not occur.
Ultrasonic settings and signal visualization were performed using TomoView and the data are exported to Matlab for post-processing. From the analysis of the resulting acoustic waveform for each beam, the time of flight of the acoustic wave that propagates through the sample is detected as the first peak exceeding an amplitude threshold. From the time of flight data between different transmitter-receiver pairs, twodimensional speed of sound images were generated using an inversion algorithm based on the LSQR method8 launched on the local supercomputing cluster WestGrid. To facilitate acoustic data post processing, small systematic and random
In this section, illustrative benchmark experiments linked to key applications are explored in detail in relation to the principle compromises envisioned for them. For example, a wider sweep angle range provides a richer database for creating 2D images but increases data acquisition time per image. Improved image resolution increases acoustic data post processing time and imposes constraints on the nature of the computing cluster needed to perform the post processing. For these illustrations, the sweep angle range is varied from [−20◦, 20◦] to [−35◦, 35◦] and the grid resolution used to construct the images is varied from 200 µm down to 40 µm. Comparisons between average speeds of sound at specific elevations calculated from the 2D images and the values obtained from 1D measurements at the same elevation act as a check for the 2D image generation algorithm. The first illustration concerns two-dimensional images of a uniform solid and a uniform liquid. The second illustration concerns two-dimensional speed of sound images of model two-phase solids with known geometries. The third illustration concerns two-dimensional speed of sound images for two-phase liquids with known compositions and geometries. The fourth and fifth illustrations concern speed of sound images where local compositions vary in time within a porous natural limestone block resulting from water and organic liquid imbibition and diffusion in the presence of a vapour and a liquid cap, respectively. Each application presents specific challenges and outcome qualities as discussed below. A. Uniform solid and liquid fields
FIG. 5. Complete ray coverage for a tomography scan in Cell I over a range of angles from −25◦ to +25◦ with a 2.5◦ step, where the horizontal acoustic path length is 15.8 mm.
Polyvinyl chloride (PVC) is essentially amorphous but may include up to 5%–10% crystalline material. Microstructure may also be altered along the edges during processing due to stress and thermal effects leading to local variations in density and speed of sound. These effects are expected to be secondary and the 30 × 40 mm PVC plates used in this study are treated as uniform. The two acoustic probes were attached to each side of the plate in Cell II, 30 mm apart, and the horizontal dimension of the elements (7 mm) is equal to the thickness of the plate. Ten minutes were needed to acquire all the data for a scan from −35◦ to 35◦, with a step size of 2.5◦. The data acquisition time drops to seven minutes for a −20◦ to 20◦ scan with the same step size. The transmission times between transmitter-receiver pairs were then input into the inversion code run on a supercomputing cluster, and 2D acoustic images were available within 2 to 8 h depending on the usage rates for the cluster. Acoustic images for the polyvinyl chloride plates with the two angle ranges and constructed using grid resolution of 40 µm are presented in Fig. 6. The one-dimensional speed of sound data acquired with horizontal beams over the probe length as well as the twodimensional speed of sound values averaged over horizontal
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FIG. 6. 2D speed of sound images for a 30 × 40 mm PVC plate at 25 ◦C constructed using a grid resolution of 40 µm: (a) angle range [−20◦, 20◦] with an angle step of 2.5◦, (b) angle range [−35◦, 35◦] with an angle step of 2.5◦. Black filled diamonds: one-dimensional data, pink filled squares: averaged two-dimensional data for [−20◦, 20◦] angle range, and green filled triangles: averaged two-dimensional data for [−35◦, 35◦] angle range at each elevation.
bands of fixed width at each elevation is superimposed to the 2D image for comparison. First, it can be observed that the image obtained with broader scanning angle range presents more angular artefacts such as oblique lines and areas with more pronounced speed of sound contrasts especially in the left lower and right upper parts. The image obtained with a [−20◦, 20◦] angle range shows a more uniform speed of sound distribution with the bottom and top edges of the image presenting slightly higher speed of sound values. The average
speed of sound value deviates from a reported speed of sound value in PVC6 (2395 m/s at 25 ◦C) by 38 m/s in the case of a [−20◦, 20◦] angle range, by 36 m/s in the case of a [−35◦, 35◦] angle range, and by 39 m/s for the 1D profile. These differences in average speed of sound value are small and may reflect differences in the degree of crystallinity or temperature. The average absolute deviation (AAD) from the mean speed of sound value were found to be 3.7 m/s for the angle range [−20◦, 20◦], 3.6 m/s for the angle range [−35◦,
FIG. 7. Two dimensional speed of sound images of a uniform liquid medium (water, with a speed of sound of 1497 m/s at 25 ◦C) constructed using a grid resolution of 40 µm with angle range: (a) [−20◦, 20◦] and (b) [−25◦, 25◦] at an angle step size of 2.5◦. Black filled diamonds: one-dimensional data, pink filled squares: averaged two-dimensional data for [−20◦, 20◦] angle range, and green filled triangles: averaged two-dimensional data for [−25◦, +25◦] angle range.
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FIG. 8. 30 × 40 mm PVC plate with an aluminum cylinder 15 mm diameter in the center: (a) drawing, (b) acoustic image constructed using a 200 µm grid resolution, a −35◦ to +35◦ angle range with a 2.5◦ step.
35◦], and 4.2 m/s for the 1D measurements, suggesting that the PVC plate is effectively uniform. The one-dimensional data display the same trend as the 2D results with increasing speed of sound values at the lower and upper edges of the images. However, the speed of sound profiles obtained from averaged two-dimensional data is smoother for both angle ranges with a slightly higher mean value for the [−35◦, 35◦] angle range. The shape of the speed of sound profiles obtained from the 2D images only differs from the 1D profiles near the upper and lower edges of the images. Water comprised the second medium with a uniform composition. For this experiment, Cell I was used. Again, two acoustic images were generated: [−20◦, 20◦] and [−25◦, 25◦] with step sizes of 2.5◦ using a grid resolution of 40 µm. Again, the one dimensional speed of sound data was superimposed along with the averaged 2D speed of sound results on the 2D speed of sound images shown in Fig. 7. The reference value9 for the speed of sound at 25 ◦C is 1497 m/s. The measured average speeds of sounds, the AAD, and maximum absolute
deviations (MAD) for 1D measurements are 1495 m/s, 1.2 m/s, and 4.0 m/s; for 2D measurements with an angle range [−20◦, 20◦] are 1498 m/s, 1.2 m/s, and 2.6 m/s; and for 2D measurements with an angle range [−25◦, 25◦] are 1500 m/s, 2.6 m/s, and 5.2 m/s. The averaged two-dimensional values over specific elevations confirm this trend and reveal that the speed of sound values are overestimated in the central area of the image obtained with angle range [−25◦, 25◦]. These discrepancies may be due to mode conversion of sound wave propagation occurring at the water/PBI interface.6 As the incident angle of the longitudinal wave in the water (slower) medium increases, the refracted angle in the PBI (faster) medium increases, resulting in a progressive conversion of the longitudinal wave energy to a lower velocity shear wave that is refracted at an angle predicted by Snell-Descartes law. Consequently, interference of longitudinal waves with shear waves can occur and the estimation of the first-arrival travel time can be affected, leading to artefacts in the images, especially in the central portion where the ray coverage is the densest.
FIG. 9. 30 × 40 mm PVC plate with an aluminum cylinder 7.5 mm diameter in the center: (a) drawing, (b) acoustic image constructed using a 200 µm grid resolution, a −35◦ to +35◦ angle range with a 2.5◦ step.
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FIG. 10. 30 × 40 mm PVC plate with an aluminum cylinder 3.75 mm diameter in the center: (a) drawing, (b) acoustic image constructed using a 200 µm grid resolution, a −35◦ to +35◦ angle range with a 2.5◦ step.
Irrespective of these modest distortions, the representation of uniform fields is good for solids and excellent for liquids in absolute terms, and the representation of average speed of sound values at specific elevations obtained from the 2D inversion algorithm and the simpler 1D measurements is excellent. For kinetics measurements, where the focus is on difference measurements, the small speed of sound distortions arising in uniform fields can be eliminated as part of the envisioned background subtraction. This topic is addressed below. B. Two phase solids with known geometries
Representation of two phase solids with known geometries was addressed using PVC plates into which aluminum cylinders were imbedded. The preliminary screening case comprised a rectangular 30 × 40 × 4.9 mm PVC plate with a 15 mm diameter aluminum cylinder embedded in the center (Fig. 8(a)). A two-dimensional speed of sound image was then constructed using 200 µm square sided grids and a
range of angles from −35◦ to +35◦ with a 2.5◦ step. The resulting image (Fig. 8(b)) shows good reproduction of the outlines of the central object in the vertical dimension but the shape of the cylinder is not well represented in the horizontal dimension. Artefacts inherent in this kind of image reconstruction method10 are also present in the image. The average speed of sound value calculated in the PVC, 2675 m/s, deviates from the expected speed of sound value in PVC from the literature by 280 m/s and from measurements above by 317 m/s and possesses an AAD of 180 m/s. The speed of sound in the aluminum cylinder is underestimated significantly as the average speed of sound value calculated in this area deviates from the theoretical value6 (6320 m/s) by 3058 m/s and the AAD is 113 m/s. This weak resolution in some areas of the image arises because of the lack of spatial coverage of the rays. There are only two probes facing each other on two lateral sides of the object. Further, straight-line propagation of ultrasound energy through the test material is assumed in the algorithm. In reality, when the sound wave encounters the PVC-aluminum boundary with an incidence that does not
FIG. 11. 30 × 40 mm PVC plate with three aluminum cylinders (3.75 mm diameter): (a) drawing, (b) acoustic image constructed using a 200 µm grid resolution, a −35◦ to +35◦ angle range with a 2.5◦ step.
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lie perpendicular to the tangent at this point, a large portion of the wave energy is reflected straight back due to the large difference in acoustic impedance between the two media. Only a small portion continues straight ahead and is refracted in the aluminum cylinder. The difference between the angle of incidence and the angle of refraction is also high because of the large speed of sound contrast between the two media. Finally, as the near field length in the material calculated from Eq. (3) is equal to 5 mm and is smaller than the acoustic path length in the test piece, the ultrasonic beam increases in diameter before striking the receiver array. Consequently, the area of highest energy of the beam may not strike the group of selected elements on the receiving probe but may be collected by adjacent elements. This phenomenon can also explain the ghost effects and artefacts encountered in the image. This test case for two phase solids represents a “worst case” scenario for the data acquisition method and assumptions built into the inversion algorithm. By reducing the size of the cylinders to 7.5 mm (Fig. 9) and 3.75 mm (Fig. 10), but keeping the other test conditions the same, the central speed of sound value computed in the PVC portion deviates by less than 30 m/s from the theoretical value and the average absolute deviation decreases to 65 m/s for the test piece with the 3.75 mm cylinder. Artefacts persist especially in the corners of the images. These common artefacts have no physical meaning. They consist of an accentuation of speed of sound values in a small portion of the reconstructed image that can lead to misinterpretation of the structure of a material.10 Fortunately, object resolution improves as the size of objects
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diminishes and ghost imaging becomes less pronounced with smaller objects. Screening tests with two-phase solids also explored the impact of the number of embedded cylinders which was increased to three, and the role of cylinder size and image resolution on image quality, both with respect to object definition and artefact reduction. For a PVC plate with three 3.75 mm diameter aluminum cylinders with the configuration shown in Fig. 11(a), the resulting 2D image, Fig. 11(b) with the same resolution and focal law as for Figs. 8–10, shows good representation of the central cylinder but the shapes and positions of the other two cylinders are poorly represented. Various forms of filtering and focal law variation were attempted but were unsuccessful at eliminating these distortions. By reducing cylinder size to 1.2 mm, Fig. 12(a) and decreasing the grid resolution of the acoustic images from 200 µm to 40 µm, the quality of the reproduction of the speed of sound profile of the test pieces was improved significantly as shown in the series of acoustic images—Figs. 12(b)-12(g). While image quality improvement appears to be continuing for grid sizes less than 40 µm, this is the current computational limit at the available supercomputing cluster because a system memory limit is otherwise exceeded. The resulting image presented in Fig. 12(g) shows a significant improvement in both the size and placement of cylinders and artefacts in the corners of the image vis-à-vis Fig. 12(b), at the cost of significantly increased computational intensity. In an effort to reduce data acquisition and computational time, the angle
FIG. 12. 30 × 40 mm PVC plate with three aluminum cylinders (1.2 mm diameter): (a) drawing, and acoustic image using grid resolutions (b) 200 µm, (c) 150 µm, (d) 100 µm, (e) 80 µm, (f) 60 µm, (g) 40 µm obtained with a [−35◦, 35◦] angle range with 2.5◦ step size.
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FIG. 13. 30 × 40 mm PVC plates with aluminum cylinders (1.2 mm diameter): (a) drawing, acoustic images constructed with angle ranges: (b) [−35◦, 35◦], (c) [−30◦, 30◦], (d) [−25◦, 25◦], (e) [−20◦, 20◦], at 2.5◦ angle step size, and a 40 µm grid resolution.
range for beam steering was reduced from [−35◦, 35◦] to [−20◦, 20◦] in 5◦ increments while maintaining the 2.5◦ step size, to study the impact on the resolution of the cylinders. However, as the resulting acoustic images, Figs. 13(b)-13(e), clearly show, the best reproductions of the speed of sound profiles, particularly in the central region of the image, are obtained for an angle range [−35◦, 35◦] and with the lowest grid size of 40 µm, i.e., for the conditions that require the longest data acquisition and image processing times. Despite the density of the ray coverage, Fig. 5, and the small grid size of the image processing algorithm, 40-200 µm, the smallest individual solid objects visible in a uniform solid field must exceed the dimensions of the individual acoustic probes, in this case, 0.6 mm. This is illustrated in Fig. 14. Acoustic images of a 0.6 mm aluminum cylinder embedded
at the centre of a PVC plate, constructed using angle ranges: Fig. 14(a) [−35◦, 35◦], Fig. 14(b) [−20◦, 20◦], with a 2.5◦ angle step size and a 40 µm grid resolution cannot be distinguished from images of a uniform PVC plate, Figs. 6(a) and 6(b), even in the central area of the image, where the ray density is greatest. Reconstructed image smearing at the length scale of the sensors is a known limitation for devices based on linear scans performed with standard flat piezoelectric detectors. Spatial resolution of 2D images can only be improved with this geometry by reducing sensor size. Higher resolution 2D images can also be obtained by performing circular scans over a closed surface with a 360◦ view. The reconstructed image distortions and spatial resolution limitations described here were expected compromises in the development of the technique and the apparatus and a consequence of the impact
FIG. 14. Acoustic images of a 30 × 40 mm PVC plate with an aluminum cylinder 0.6 mm diameter in the center constructed using angle ranges: (a) [−35◦, 35◦], (b) [−20◦, 20◦], with a 2.5◦ angle step size and a 40 µm grid resolution.
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FIG. 15. Speed of sound image for a two phase liquid—water (below) with a nominal speed of sound of 1497 m/s and cooking oil (above) with a nominal speed of sound of 1469 m/s: (a) obtained with angle range [−20◦, 20◦], (b) obtained with angle range [−25◦, 25◦], black filled diamonds: local one-dimensional speed of sound data, pink filled squares: averaged two-dimensional data for [−20◦, 20◦] angle range, and green filled triangles: averaged two-dimensional data for [−25◦, +25◦] angle range. The images were constructed using 40 µm square sided grids.
of what is described in the medical imaging literature as limited-view tomography.11,12 C. Two phase liquids with known compositions and liquid-liquid interface location
Experiments for this test case, comprising a water layer beneath a cooking oil layer with a horizontal interface, were performed in Cell I. The speeds of sound in each phase, the interface and the meniscus, are well represented in the 2D images as shown in Figs. 15(a) and 15(b). The theoretical
value for the speed of sound in water, 1497 m/s at 25 ◦C, is well represented by the 2D averaged values found in this experiment (1497 m/s for the [−20◦, 20◦] angle range and 1499 m/s for the [−25◦, 25◦] angle range). The absolute deviations from the average speed of sound values within each phase obtained from the 1D measurements are 1.9 m/s in the water phase where the mean value is 1496 m/s and 0.7 m/s in the cooking oil phase where the mean value is 1469 m/s. These deviations fall at and within measurement uncertainty, respectively, and coexisting phases possessing similar speed of sound values are readily distinguished. By
FIG. 16. Acoustic images of an Indiana Limestone plate using a grid resolution of 40 µm, obtained with an angle range of (a) [−20◦, 20◦] and (b) [−35◦, 35◦].
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FIG. 17. 2D speed of sound difference images for water imbibition into air filled pores of Indiana Limestone using a grid resolution of 40 µm. (I) t = 1 h, (II) t = 5 h, (III) t = 9 h. (a) Angle range [−20◦, +20◦], (b) angle range [−35◦, +35◦]. Black filled diamonds: one-dimensional data, pink filled squares: two-dimensional data for [−20◦, +20◦] angle range, and green filled triangles: two-dimensional data for [−35◦, +35◦] angle range.
increasing the angle range from [−20◦, 20◦] to [−25◦, 25◦], the convex shape of the meniscus at the interface becomes better defined and the spatial resolution appears to approach the sensor size (0.6 mm). Nevertheless, distortions at the
upper and lower edges of the image persist as also seen in Fig. 5. These distortions are small in absolute terms and as noted above, for kinetics measurements, where the focus is on difference measurements, the small static distortions in speed
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of sound arising in uniform fields can be eliminated as part of the envisioned background image subtraction procedure. D. Observation of liquid vapour interfaces in porous media
For these experiments, a (30 mm × 40 mm × 6 mm) plate of Indiana Limestone with a 70 mD-brine and a 200 mDhelium gas permeability, and an overall porosity of 18%, was cleaned in toluene and then dried at 150 ◦C. All surfaces, except the base, were then sealed with the ultrasonic coupling agent and background images were prepared as shown in Figs. 16(a) and 16(b) for angle ranges [−20◦, 20◦] and [−35◦, 35◦], respectively, with a spatial resolution of 40 µm. The reservoir at the base of Cell II was then filled with water and the background images were subtracted from corresponding images obtained as water imbibed into the plate from the reservoir over a period of 9 h. Speed of sound difference images, showing water penetration with time, is reported in Figs. 17(a)-17(c). The upward movement of water through the pore network and local water saturation of the pore network, averaged over a depth of (6 mm) and with an imaging grid size of 40 µm, are clearly seen as a function of time and are comparably defined for both [−20◦, 20◦] and [−35◦, 35◦] angle ranges. The 1D and elevation-averaged 2D speeds of sound difference data at fixed elevation, superimposed on the images, are also comparable except at the lower and upper edges of the plate (below an elevation of 3 mm and above an elevation of 33 mm). Small differences in apparent local saturation and the boundary defining the upper limit of water penetration are also evident for the [−20◦, 20◦] and [−35◦, 35◦] angle range cases. Based on the extensive calibrations performed to date, the representation obtained for [−35◦, 35◦] is preferred. The data acquisition times for an image with an angle range of [−35◦, 35◦] and an angle step size of 2.5◦ are 10 min. As the upward velocity of water in the pore network is less than 2 mm per hour, the impact of water movement during data acquisition on image quality is negligible. E. Observation of liquid-liquid interfaces in porous media
For these experiments, the Indiana Limestone plate used in Sec. III D was soaked in water for 24 h, and the plate surfaces, other than the base, were resealed with the ultrasonic coupling agent. Background images were again obtained and were subtracted from corresponding images obtained as heptane imbibed into the plate from the reservoir over a period of 13 h. A time series of speed of sound difference images with a grid size of 40 µm, showing water displacement by heptane, are reported in Figs. 18(I)-18(IV). The profiles of averaged 2D speed of sound differences at fixed elevation are comparable to the 1D profiles but are smoother for both the [−20◦, 20◦] and [−35◦, 35◦] angle ranges. The net upward movement of heptane through the pore network within the limestone plate is clearly observed in the sequence of images that show a decrease in speed of sound with time in the lower portion of the plate. This decrease is expected9 because the speed of sound in heptane (1128 m/s) is lower than the speed of sound
FIG. 18. 2D difference speed of sound images for heptane imbibition in water filled pores of Indiana Limestone using a grid resolution of 40 µm. (I) t = 1 h, (II) t = 5 h, (III) t = 9 h, (IV) t = 13 h. (a) Angle range [−20◦, +20◦], (b) angle range [−35◦, +35◦]. Black filled diamonds: one-dimensional data, pink filled squares: two-dimensional data for [−20◦, +20◦] angle range, and green filled triangles: two-dimensional data for [−35◦, +35◦] angle range.
in water (1497 m/s) at 25 ◦C. The speed of sound contrasts is lower than in the case of water imbibition into air filled pores in the same plate and artifacts appearing in the images are more pronounced particularly for the images obtained using the angle range [−35◦, 35◦]. While the distribution of heptane
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in the pore structure over time, with a peak concentration at an elevation of 11 mm, is a subject of an ongoing investigation, the sensitivity of the technique to fluid and interface movement within porous media is evident.
IV. CONCLUSION
In this work, the capacity of an acoustic imaging technique to provide laboratory-scale, non-intrusive, highresolution, real-time, two-dimensional images of multiphase materials, with an engineering focus where “limited-view” rectilinear as opposed to circular geometries are typically preferred, is demonstrated. Artefacts arising with this geometry and their resolution are discussed and illustrative kinetics examples including visualization of liquid-vapour and liquidliquid movement occurring in porous natural limestone are provided. Restrictions, including the scale of the device, to avoid beam spreading for cases of specific interest and the scale of features in the materials of interest to avoid distortions in images are identified and discussed for diverse cases. Compromises between data acquisition rate and the resulting 2D image quality are illustrated and limitations imposed by post processing computer power are discussed. While it is expected that the latter limitation will relax in the future with improvements to computer power, the compromise between data acquisition rate and image quality will remain for cases with more rapid kinetics. Improvement of data acquisition rate is a priority topic for future study. Future work will also comprise specific studies related to diffusion phenomena of light hydrocarbons in heavy oil and bitumen within porous media, as well as the detection of local speed of sound variations in beds of coal particles arising during bioconversion. ACKNOWLEDGMENTS
J. M. Shaw thanks l’Université de Pau et des Pays de l’Adour (UPPA) for a visiting professorship and Total E&P
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(Centre Scientifique et Technique Jean-Féger) for a visiting appointment. This project was launched during a sabbatical leave hosted jointly by these institutions. Both authors thank Dr. Jean-Luc Daridon and Dr. Jerome Pauly for hosting part of this study in their laboratories at (UPPA) and for valuable discussions. Their assistance is much appreciated. We also thank Djamel Nasri (UPPA) and L’Atelier de Physique (UPPA) for helping with the design and manufacture of the acoustic cell; Mildred Becerra for her help in the laboratory at the University of Alberta; and Compute Canada for use of the WestGrid high-speed computing facility. Financial support from the sponsors of the NSERC Industrial Research Chair in Petroleum Thermodynamics: Alberta Innovates Energy and Environment Solutions, British Petroleum, ConocoPhillips, Inc., NEXEN Energy ULC, Shell Canada, Total E&P Canada, VMG, Inc., and the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. 1R.
G. H. Willemink, S. Manohar, Y. Purwar, C. H. Slump, F. Van Der Heijden, and T. G. Van Leeuwen, “Imaging of acoustic attenuation and speed of sound maps using photoacoustic measurements,” Proc. SPIE 6920, 692013 (2008). 2R. A. Kruger, R. B. Lam, D. R. Reinecke, S. P. Del Rio, and R. P. Doyle, Med. Phys. 37, 6096 (2010). 3J. T. Bushberg, J. A. Seibert, E. M. Leidholdt, Jr., and J. M. Boone, The Essential Physics of Medical Imaging (Lippincott Williams & Wilkins, 2001). 4M. Khammar and J. M. Shaw, Rev. Sci. Instrum. 82, 104902 (2011). 5M. Khammar and J. M. Shaw, Energy Fuels 26, 1075 (2012). 6Olympus, Phased Array Testing: Basic Theory for Industrial Applications (Olympus NDT, 2010). 7N. Dube, Introduction to Phased Array Ultrasonic Technology Applications: R/D Tech Guideline (Olympus NDT, 2004). 8B. Giroux, E. Gloaguen, and M. Chouteau, Comput. Geosci. 33, 126 (2007). 9E. W. Lemmon, M. O. McLinden, and D. G. Friend (National Institute of Standards and Technology, Gaithersburg MD, 2005), http://webbook.nist. gov. 10A. Rosenthal, D. Razansky, and V. Ntziachristos, IEEE Trans. Med. Imaging 29, 1275 (2010). 11G. Paltauf, R. Nuster, and P. Burgholzer, Phys. Med. Biol. 54, 3303 (2009). 12A. Rosenthal, V. Ntziachristos, and D. Razansky, Curr. Med. Imaging Rev. 9, 318 (2013).
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Non-intrusive, high-resolution, real-time, two-dimensional imaging of multiphase materials using acoustic array sensors M. Cassiède and J. M. Shaw Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 2G6, Canada
(Received 15 September 2014; accepted 9 March 2015; published online 7 April 2015) Two parallel multi-element ultrasonic acoustic arrays combined with sets of focal laws for acoustic signal generation and a classical tomographic inversion algorithm are used to generate real-time two-dimensional micro seismic acoustic images of multiphase materials. Proof of concept and calibration measurements were performed for single phase and two phase liquids, uniform polyvinyl chloride (PVC) plates, and aluminum cylinders imbedded in PVC plates. Measurement artefacts, arising from the limited range of viewing angles, and the compromise between data acquisition rate and image quality are discussed. The angle range of scanning and the image resolution were varied, and the effects on the quality of the reproduction of the speed of sound profiles of model solids and liquids with known geometries and compositions were analysed in detail. The best image quality results were obtained for a scanning angle range of [−35◦, 35◦] at a step size of 2.5◦ post processed to generate images on a 40 µm square grid. The data acquisition time for high quality images with a 30 mm × 40 mm view field is 10 min. Representation of two-phase solids with large differences in speed of sound between phases and where one phase is dispersed in the form of macroscopic objects (greater than 1 mm in diameter) proved to be the most difficult to image accurately. Liquid-liquid and liquid-vapor phase boundaries, in micro porous solids by contrast, were more readily defined. Displacement of air by water and water by heptane in natural porous limestone provides illustrative kinetic examples. Measurement results with these realistic cases demonstrate the feasibility of the technique to monitor in real time and on the micrometer length scale local composition and flow of organic liquids in inorganic porous media, one of many envisioned engineering applications. Improvement of data acquisition rate is an area for future collaborative study. C 2015 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4915894] I. INTRODUCTION
Non-intrusive, real-time measurement of local composition and fluid movement in porous media presents numerous data acquisition and data processing challenges, but equipment with this capability is relevant to many fields of science and engineering from earth science to petroleum engineering and from biomedical engineering to industrial catalysis. Optimization and compromise are needed to realize successful applications in three dimensions, two dimensions (2D), and along one dimensional (1D) paths in porous media. Some compromises are application specific and concern limitations to the range of angles that can be viewed, to the spatial resolution requirements, the total areas or volumes explored, to the speed of process kinetics that can be surveyed, and the possible need for additives to improve contrast. Successful imaging techniques have been based on X-ray, acoustic, thermo-acoustic, and more recently photoacoustic1 devices, where the structure of cells and internal organs in biology and biomedical applications, and where thermophysical phenomena such as diffusion, chemical reaction, phase change, and natural gas hydrate formation in chemical engineering have been monitored. Within this spectrum of activity, acoustic techniques are of growing interest because they are often convenient, cheaper, and have fewer side effects in the case of biomedical 0034-6748/2015/86(4)/044902/13/$30.00
applications. While the data acquisition and image processing times required to obtain individual high-resolution three-dimensional images can be long,2 current commercial multi-element acoustic devices permit the generation of two-dimensional high-resolution acoustic images based on ultrasonic emission from an array of sensors at shorter time intervals, and arrays provide one-dimensional images rapidly, thus opening up a number of potential useful applications in science, medicine, and engineering. For example, in medical applications of ultrasonic imaging, in which high-frequency sound waves are used to construct detailed cross-sectional images of internal organs, acoustic emitters and receivers are placed in a circle or on the surface of a sphere that surrounds the object of interest. Images are then constructed based on straight-line propagation of sound energy from individual emitters to individual receivers on opposing sides of the array. Even so, refraction phenomena occurring at the boundary of tissues presenting variations in speed of sound are often responsible for strong artifacts3 and these must be eliminated in image processing. The more widespread use of phased array systems across a variety of industrial sectors starting during the early 2000s has made them less expensive, and nonintrusive tools have been developed for diverse geometries. Two-dimensional acoustic or seismic measurement methods have become common tools in engineering applications, from non-destructive product testing, to archeology, and resource
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mapping. These images are obtained rapidly but lack spatial resolution, or target identification of specific features, readily distinguished from backgrounds, such as flaws, cracks, or fissures in metal objects and these applications do not address time varying phenomena. The present work builds upon proof of concept studies presented previously where the same phased array was used to measure liquid-liquid phase separation, kinetics of separation and end states, for methanol + mixed hexanes and methanol + heptane mixtures4 and for asphaltene + polystyrene + toluene mixtures5 based on 1D imaging. The liquid-liquid and liquidvapor interfaces arising in these measurements were detected from the presence of discontinuities (in speed of sound) and peaks (in acoustic wave attenuation) arising in 1D profiles at fixed elevations measured along the probe length. Two 64-element acoustic arrays were used and the interface location was assessed with a precision of 300 µm. Phase separation kinetics was readily tracked at fixed elevations because all elevations were scanned at a rate of 1 Hz. These results opened new possibilities for investigating local thermophysical property and local phase behavior of fluids including key applications as diverse as the energy sector (asphaltenic mixtures such as live oils) and consumer products and pharmaceutics where monitoring and controlling emulsion formation or breakage phenomena in real time are important issues in formulation control. To date, only pulseecho and transmission measurements have been performed at fixed elevations. In this work, the experimental technique is extended to 2D and 2D acoustic images are constructed based on the use of a classic tomographic inversion algorithm.7 More specifically, a procedure and benchmark measurements related to tracking local fluid composition and phase boundaries in porous media at high resolution as functions of time are elucidated. Envisioned applications include flow, imbibition, diffusion, and other processes arising in synthetic and natural porous media such as reservoir rock and coal. The envisioned applications impose acute and oblique angular geometry between emitters and receivers rather than a simpler circular geometry. This limited-view geometry is more prone to distortion effects than a circular geometry and the additional challenge in this case is to measure small changes in speed of sound values with adequate spatial and temporal resolution, while minimizing the impact of artefacts in both 1D and 2D images. New results relying on this data acquisition approach and novel data processing features are presented. Real-time, two-dimensional, high-resolution images of fluid flow and fluid composition within inorganic porous media are presented, and limitations of the technique requiring further development are discussed.
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The probes and signal generator/data acquisition system are commercial products and their operation is also illustrated elsewhere.3 The sensors (10L64-A2, Olympus NDT) have a central acoustic frequency of 10 MHz and comprise an array of 64 individual piezoelectric ceramic composite elements. Each element is 7 mm × 0.6 mm (a little less than 0.6 mm in reality due to the cutting-line between the elements) and the center-to-center distance or pitch between two successive elements is 0.6 mm. The sensors are electrically driven by a data acquisition unit TomoScan Focus LT. The acoustic waveforms are then recorded, visualized, and analysed using the TomoView software. The acoustic measurement files generated from this device are further analyzed and processed, as described below, to obtain 1D or 2D speed of sound images. Cell I, designed around liquid and colloid applications, where a sample is injected into a cavity machined from a block of Polybenzimidazole (PBI), was described previously.3,4 For Cell I, the two acoustic probes, placed opposite one another within an aluminum frame, abut the exterior walls of the PBI cell and are used to send and receive acoustic signals. Cell II, designed specifically for the current study, holds porous blocks with a rectangular geometry between the two probes, and the bottom part of the blocks can be immersed in a liquid contained in a reservoir at the base of the holder, as shown in Fig. 1. B. Methods
Acoustic beams are fired through test materials by exciting groups of piezoelectric elements simultaneously. The direction of a beam is controlled by applying a small delay, on the order of a few nanoseconds, between the pulses of consecutive elements in a group. The choice of the number
II. EXPERIMENTAL APPARATUS AND METHODS A. Apparatus
The experimental device comprises two custom-made thermally sealed acoustic cells, a pair of acoustic array probes, and a programmable and proprietary acoustic signal generation and acquisition system, supplied by Olympus NDT.
FIG. 1. Schematic for acoustic Cell II. (1) Acoustic probe; (2) shim; (3) porous block; (4) reservoir for liquid; (5) jacket for heat carrier fluid circulation; (6) Teflon plates for thermal insulation.
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of elements and the delay time define a focal law. A focal law takes into account probe and shim characteristics as well as the geometries and the acoustic properties of the test material in order to generate the desired beam shape through the interaction of waves from individual elements. The probes are used in transmission mode. A shim is inserted between the test material and the probe surface to avoid direct contact of the sensor with a liquid medium or a rough rock surface. The probe face is matched acoustically to the shim using ultrasonic coupling gel (Couplant for Ultrasonic Testing OG-1, NDT-Europa) comprising water, surface-active agents, corrosion inhibitors, and a gelling agent. The gel permits excellent acoustic transmission on diverse surfaces. In the present work, each beam is generated by exciting eight or nine adjacent elements of the transmitting array. This number was chosen according to the length and the width of individual piezoelectric elements as well as their spacing to comprise a square base for the composite wave. The acoustic beams were focused at infinity. This configuration maximizes the transmitted sound energy and the generation of deformed beams is avoided. A data acquisition unit (TomoScan Focus LT) is used to transmit the delays to the elements of the emitting phased array probe and to receive and sum the delays of the resulting signal. The group of receiving elements is selected according to the trajectory of the ultrasound beam in the medium and in the shim where changes in the speed of sound may occur. In principle, the sound wave generated by a group of transducers travels in a straight line until it encounters an interface. The impact of shims or other materials between the sensors and the test material must be factored into the selection of receiver elements to avoid unnecessary distortions in the output signals. The change in direction of the transmitted ultrasound energy occurring at a boundary between the shim and the test material is given by the Snell-Descartes law υshim sin α = , sin β υtest material
(1)
where α and β are the incident and transmitted angles, υshim and υtest material are the speeds of sound in the shim and the test material. Sound energy follows a straight-line trajectory when the speed of sound is the same in the two media or when the beam has a 90◦ incidence angle. If the acoustic wave propagation occurs along a path that is longer than a certain length, known as the near-field distance, N, the diameter of the beam diverges as illustrated in Fig. 2. The near field distance N for an element or group of elements in a phased array can be calculated6
FIG. 2. Illustration of spreading of an ultrasonic beam generated by a group of transducers.
N=
k L 2element f , 4υtest piece
(2)
where k is a near field correction factor. It depends on the ratio between the width and the length of the probe element.7 f is the frequency and L element is the length or aperture of probe element. If the probe is mounted on a shim, the effective aperture then depends on the refracted angle and the effective near field length takes the form6 ) ( cos β 2 f k L element L shimυshim cos α − , (3) Neff = 4υtest piece υtest piece where L shim represents the ultrasound path length in the shim. Beyond the near field region, the sound pressure gradually decreases as the beam diameter expands and the energy dissipates. The reduction in amplitude of the acoustic signal is also related to dissimilarities in material properties across an interface. The transmission (refracted) coefficient T at a planar boundary between two media, defined as the percentage of sound energy traveling in the first medium which is transmitted into the second medium, takes the form 2Z2 , (4) (Z1 + Z2) where Z1 and Z2 are the acoustic impedances in the first and second media. From Eq. (4), it can be seen that as the acoustic impedances of two materials become similar, the transmission coefficient increases, and as the acoustic impedances become dissimilar, the transmission coefficient decreases. These intrinsic effects of sound energy propagation lead to a decrease in the amplitude of the acoustic signal transmitted through a test material. In order to compare all the acoustic waveforms using the same criteria, the gain of the acoustic signal is adjusted so that the amplitude of the first peak reaches 80% of the screen height for each focal law, as illustrated in Fig. 3. An example of beam steering between four pairs of transmitter-receiver groups of elements in a sample with a homogeneous speed of sound is presented in Fig. 4. In this illustration, no beam spreading occurs. The complete ray coverage during a classic tomography survey is much more complex. Fig. 5 depicts full ray coverage where beams traverse an object over a range of angles from −25◦ to +25◦ with a 2.5◦ step. The concentration of rays is greater in the central portion of the image than near the upper and lower edges. T=
FIG. 3. Example of an acoustic waveform, visualized using TomoView software, for beam steering with an angle of 20◦.
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variations in the horizontal dimension of the PVC plates, fluid in cell I and limestone samples in Cell II with elevation were ignored.
III. RESULTS AND DISCUSSION
FIG. 4. Example of beam steering with angle β for which beam spreading does not occur.
Ultrasonic settings and signal visualization were performed using TomoView and the data are exported to Matlab for post-processing. From the analysis of the resulting acoustic waveform for each beam, the time of flight of the acoustic wave that propagates through the sample is detected as the first peak exceeding an amplitude threshold. From the time of flight data between different transmitter-receiver pairs, twodimensional speed of sound images were generated using an inversion algorithm based on the LSQR method8 launched on the local supercomputing cluster WestGrid. To facilitate acoustic data post processing, small systematic and random
In this section, illustrative benchmark experiments linked to key applications are explored in detail in relation to the principle compromises envisioned for them. For example, a wider sweep angle range provides a richer database for creating 2D images but increases data acquisition time per image. Improved image resolution increases acoustic data post processing time and imposes constraints on the nature of the computing cluster needed to perform the post processing. For these illustrations, the sweep angle range is varied from [−20◦, 20◦] to [−35◦, 35◦] and the grid resolution used to construct the images is varied from 200 µm down to 40 µm. Comparisons between average speeds of sound at specific elevations calculated from the 2D images and the values obtained from 1D measurements at the same elevation act as a check for the 2D image generation algorithm. The first illustration concerns two-dimensional images of a uniform solid and a uniform liquid. The second illustration concerns two-dimensional speed of sound images of model two-phase solids with known geometries. The third illustration concerns two-dimensional speed of sound images for two-phase liquids with known compositions and geometries. The fourth and fifth illustrations concern speed of sound images where local compositions vary in time within a porous natural limestone block resulting from water and organic liquid imbibition and diffusion in the presence of a vapour and a liquid cap, respectively. Each application presents specific challenges and outcome qualities as discussed below. A. Uniform solid and liquid fields
FIG. 5. Complete ray coverage for a tomography scan in Cell I over a range of angles from −25◦ to +25◦ with a 2.5◦ step, where the horizontal acoustic path length is 15.8 mm.
Polyvinyl chloride (PVC) is essentially amorphous but may include up to 5%–10% crystalline material. Microstructure may also be altered along the edges during processing due to stress and thermal effects leading to local variations in density and speed of sound. These effects are expected to be secondary and the 30 × 40 mm PVC plates used in this study are treated as uniform. The two acoustic probes were attached to each side of the plate in Cell II, 30 mm apart, and the horizontal dimension of the elements (7 mm) is equal to the thickness of the plate. Ten minutes were needed to acquire all the data for a scan from −35◦ to 35◦, with a step size of 2.5◦. The data acquisition time drops to seven minutes for a −20◦ to 20◦ scan with the same step size. The transmission times between transmitter-receiver pairs were then input into the inversion code run on a supercomputing cluster, and 2D acoustic images were available within 2 to 8 h depending on the usage rates for the cluster. Acoustic images for the polyvinyl chloride plates with the two angle ranges and constructed using grid resolution of 40 µm are presented in Fig. 6. The one-dimensional speed of sound data acquired with horizontal beams over the probe length as well as the twodimensional speed of sound values averaged over horizontal
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FIG. 6. 2D speed of sound images for a 30 × 40 mm PVC plate at 25 ◦C constructed using a grid resolution of 40 µm: (a) angle range [−20◦, 20◦] with an angle step of 2.5◦, (b) angle range [−35◦, 35◦] with an angle step of 2.5◦. Black filled diamonds: one-dimensional data, pink filled squares: averaged two-dimensional data for [−20◦, 20◦] angle range, and green filled triangles: averaged two-dimensional data for [−35◦, 35◦] angle range at each elevation.
bands of fixed width at each elevation is superimposed to the 2D image for comparison. First, it can be observed that the image obtained with broader scanning angle range presents more angular artefacts such as oblique lines and areas with more pronounced speed of sound contrasts especially in the left lower and right upper parts. The image obtained with a [−20◦, 20◦] angle range shows a more uniform speed of sound distribution with the bottom and top edges of the image presenting slightly higher speed of sound values. The average
speed of sound value deviates from a reported speed of sound value in PVC6 (2395 m/s at 25 ◦C) by 38 m/s in the case of a [−20◦, 20◦] angle range, by 36 m/s in the case of a [−35◦, 35◦] angle range, and by 39 m/s for the 1D profile. These differences in average speed of sound value are small and may reflect differences in the degree of crystallinity or temperature. The average absolute deviation (AAD) from the mean speed of sound value were found to be 3.7 m/s for the angle range [−20◦, 20◦], 3.6 m/s for the angle range [−35◦,
FIG. 7. Two dimensional speed of sound images of a uniform liquid medium (water, with a speed of sound of 1497 m/s at 25 ◦C) constructed using a grid resolution of 40 µm with angle range: (a) [−20◦, 20◦] and (b) [−25◦, 25◦] at an angle step size of 2.5◦. Black filled diamonds: one-dimensional data, pink filled squares: averaged two-dimensional data for [−20◦, 20◦] angle range, and green filled triangles: averaged two-dimensional data for [−25◦, +25◦] angle range.
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FIG. 8. 30 × 40 mm PVC plate with an aluminum cylinder 15 mm diameter in the center: (a) drawing, (b) acoustic image constructed using a 200 µm grid resolution, a −35◦ to +35◦ angle range with a 2.5◦ step.
35◦], and 4.2 m/s for the 1D measurements, suggesting that the PVC plate is effectively uniform. The one-dimensional data display the same trend as the 2D results with increasing speed of sound values at the lower and upper edges of the images. However, the speed of sound profiles obtained from averaged two-dimensional data is smoother for both angle ranges with a slightly higher mean value for the [−35◦, 35◦] angle range. The shape of the speed of sound profiles obtained from the 2D images only differs from the 1D profiles near the upper and lower edges of the images. Water comprised the second medium with a uniform composition. For this experiment, Cell I was used. Again, two acoustic images were generated: [−20◦, 20◦] and [−25◦, 25◦] with step sizes of 2.5◦ using a grid resolution of 40 µm. Again, the one dimensional speed of sound data was superimposed along with the averaged 2D speed of sound results on the 2D speed of sound images shown in Fig. 7. The reference value9 for the speed of sound at 25 ◦C is 1497 m/s. The measured average speeds of sounds, the AAD, and maximum absolute
deviations (MAD) for 1D measurements are 1495 m/s, 1.2 m/s, and 4.0 m/s; for 2D measurements with an angle range [−20◦, 20◦] are 1498 m/s, 1.2 m/s, and 2.6 m/s; and for 2D measurements with an angle range [−25◦, 25◦] are 1500 m/s, 2.6 m/s, and 5.2 m/s. The averaged two-dimensional values over specific elevations confirm this trend and reveal that the speed of sound values are overestimated in the central area of the image obtained with angle range [−25◦, 25◦]. These discrepancies may be due to mode conversion of sound wave propagation occurring at the water/PBI interface.6 As the incident angle of the longitudinal wave in the water (slower) medium increases, the refracted angle in the PBI (faster) medium increases, resulting in a progressive conversion of the longitudinal wave energy to a lower velocity shear wave that is refracted at an angle predicted by Snell-Descartes law. Consequently, interference of longitudinal waves with shear waves can occur and the estimation of the first-arrival travel time can be affected, leading to artefacts in the images, especially in the central portion where the ray coverage is the densest.
FIG. 9. 30 × 40 mm PVC plate with an aluminum cylinder 7.5 mm diameter in the center: (a) drawing, (b) acoustic image constructed using a 200 µm grid resolution, a −35◦ to +35◦ angle range with a 2.5◦ step.
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FIG. 10. 30 × 40 mm PVC plate with an aluminum cylinder 3.75 mm diameter in the center: (a) drawing, (b) acoustic image constructed using a 200 µm grid resolution, a −35◦ to +35◦ angle range with a 2.5◦ step.
Irrespective of these modest distortions, the representation of uniform fields is good for solids and excellent for liquids in absolute terms, and the representation of average speed of sound values at specific elevations obtained from the 2D inversion algorithm and the simpler 1D measurements is excellent. For kinetics measurements, where the focus is on difference measurements, the small speed of sound distortions arising in uniform fields can be eliminated as part of the envisioned background subtraction. This topic is addressed below. B. Two phase solids with known geometries
Representation of two phase solids with known geometries was addressed using PVC plates into which aluminum cylinders were imbedded. The preliminary screening case comprised a rectangular 30 × 40 × 4.9 mm PVC plate with a 15 mm diameter aluminum cylinder embedded in the center (Fig. 8(a)). A two-dimensional speed of sound image was then constructed using 200 µm square sided grids and a
range of angles from −35◦ to +35◦ with a 2.5◦ step. The resulting image (Fig. 8(b)) shows good reproduction of the outlines of the central object in the vertical dimension but the shape of the cylinder is not well represented in the horizontal dimension. Artefacts inherent in this kind of image reconstruction method10 are also present in the image. The average speed of sound value calculated in the PVC, 2675 m/s, deviates from the expected speed of sound value in PVC from the literature by 280 m/s and from measurements above by 317 m/s and possesses an AAD of 180 m/s. The speed of sound in the aluminum cylinder is underestimated significantly as the average speed of sound value calculated in this area deviates from the theoretical value6 (6320 m/s) by 3058 m/s and the AAD is 113 m/s. This weak resolution in some areas of the image arises because of the lack of spatial coverage of the rays. There are only two probes facing each other on two lateral sides of the object. Further, straight-line propagation of ultrasound energy through the test material is assumed in the algorithm. In reality, when the sound wave encounters the PVC-aluminum boundary with an incidence that does not
FIG. 11. 30 × 40 mm PVC plate with three aluminum cylinders (3.75 mm diameter): (a) drawing, (b) acoustic image constructed using a 200 µm grid resolution, a −35◦ to +35◦ angle range with a 2.5◦ step.
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lie perpendicular to the tangent at this point, a large portion of the wave energy is reflected straight back due to the large difference in acoustic impedance between the two media. Only a small portion continues straight ahead and is refracted in the aluminum cylinder. The difference between the angle of incidence and the angle of refraction is also high because of the large speed of sound contrast between the two media. Finally, as the near field length in the material calculated from Eq. (3) is equal to 5 mm and is smaller than the acoustic path length in the test piece, the ultrasonic beam increases in diameter before striking the receiver array. Consequently, the area of highest energy of the beam may not strike the group of selected elements on the receiving probe but may be collected by adjacent elements. This phenomenon can also explain the ghost effects and artefacts encountered in the image. This test case for two phase solids represents a “worst case” scenario for the data acquisition method and assumptions built into the inversion algorithm. By reducing the size of the cylinders to 7.5 mm (Fig. 9) and 3.75 mm (Fig. 10), but keeping the other test conditions the same, the central speed of sound value computed in the PVC portion deviates by less than 30 m/s from the theoretical value and the average absolute deviation decreases to 65 m/s for the test piece with the 3.75 mm cylinder. Artefacts persist especially in the corners of the images. These common artefacts have no physical meaning. They consist of an accentuation of speed of sound values in a small portion of the reconstructed image that can lead to misinterpretation of the structure of a material.10 Fortunately, object resolution improves as the size of objects
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diminishes and ghost imaging becomes less pronounced with smaller objects. Screening tests with two-phase solids also explored the impact of the number of embedded cylinders which was increased to three, and the role of cylinder size and image resolution on image quality, both with respect to object definition and artefact reduction. For a PVC plate with three 3.75 mm diameter aluminum cylinders with the configuration shown in Fig. 11(a), the resulting 2D image, Fig. 11(b) with the same resolution and focal law as for Figs. 8–10, shows good representation of the central cylinder but the shapes and positions of the other two cylinders are poorly represented. Various forms of filtering and focal law variation were attempted but were unsuccessful at eliminating these distortions. By reducing cylinder size to 1.2 mm, Fig. 12(a) and decreasing the grid resolution of the acoustic images from 200 µm to 40 µm, the quality of the reproduction of the speed of sound profile of the test pieces was improved significantly as shown in the series of acoustic images—Figs. 12(b)-12(g). While image quality improvement appears to be continuing for grid sizes less than 40 µm, this is the current computational limit at the available supercomputing cluster because a system memory limit is otherwise exceeded. The resulting image presented in Fig. 12(g) shows a significant improvement in both the size and placement of cylinders and artefacts in the corners of the image vis-à-vis Fig. 12(b), at the cost of significantly increased computational intensity. In an effort to reduce data acquisition and computational time, the angle
FIG. 12. 30 × 40 mm PVC plate with three aluminum cylinders (1.2 mm diameter): (a) drawing, and acoustic image using grid resolutions (b) 200 µm, (c) 150 µm, (d) 100 µm, (e) 80 µm, (f) 60 µm, (g) 40 µm obtained with a [−35◦, 35◦] angle range with 2.5◦ step size.
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FIG. 13. 30 × 40 mm PVC plates with aluminum cylinders (1.2 mm diameter): (a) drawing, acoustic images constructed with angle ranges: (b) [−35◦, 35◦], (c) [−30◦, 30◦], (d) [−25◦, 25◦], (e) [−20◦, 20◦], at 2.5◦ angle step size, and a 40 µm grid resolution.
range for beam steering was reduced from [−35◦, 35◦] to [−20◦, 20◦] in 5◦ increments while maintaining the 2.5◦ step size, to study the impact on the resolution of the cylinders. However, as the resulting acoustic images, Figs. 13(b)-13(e), clearly show, the best reproductions of the speed of sound profiles, particularly in the central region of the image, are obtained for an angle range [−35◦, 35◦] and with the lowest grid size of 40 µm, i.e., for the conditions that require the longest data acquisition and image processing times. Despite the density of the ray coverage, Fig. 5, and the small grid size of the image processing algorithm, 40-200 µm, the smallest individual solid objects visible in a uniform solid field must exceed the dimensions of the individual acoustic probes, in this case, 0.6 mm. This is illustrated in Fig. 14. Acoustic images of a 0.6 mm aluminum cylinder embedded
at the centre of a PVC plate, constructed using angle ranges: Fig. 14(a) [−35◦, 35◦], Fig. 14(b) [−20◦, 20◦], with a 2.5◦ angle step size and a 40 µm grid resolution cannot be distinguished from images of a uniform PVC plate, Figs. 6(a) and 6(b), even in the central area of the image, where the ray density is greatest. Reconstructed image smearing at the length scale of the sensors is a known limitation for devices based on linear scans performed with standard flat piezoelectric detectors. Spatial resolution of 2D images can only be improved with this geometry by reducing sensor size. Higher resolution 2D images can also be obtained by performing circular scans over a closed surface with a 360◦ view. The reconstructed image distortions and spatial resolution limitations described here were expected compromises in the development of the technique and the apparatus and a consequence of the impact
FIG. 14. Acoustic images of a 30 × 40 mm PVC plate with an aluminum cylinder 0.6 mm diameter in the center constructed using angle ranges: (a) [−35◦, 35◦], (b) [−20◦, 20◦], with a 2.5◦ angle step size and a 40 µm grid resolution.
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FIG. 15. Speed of sound image for a two phase liquid—water (below) with a nominal speed of sound of 1497 m/s and cooking oil (above) with a nominal speed of sound of 1469 m/s: (a) obtained with angle range [−20◦, 20◦], (b) obtained with angle range [−25◦, 25◦], black filled diamonds: local one-dimensional speed of sound data, pink filled squares: averaged two-dimensional data for [−20◦, 20◦] angle range, and green filled triangles: averaged two-dimensional data for [−25◦, +25◦] angle range. The images were constructed using 40 µm square sided grids.
of what is described in the medical imaging literature as limited-view tomography.11,12 C. Two phase liquids with known compositions and liquid-liquid interface location
Experiments for this test case, comprising a water layer beneath a cooking oil layer with a horizontal interface, were performed in Cell I. The speeds of sound in each phase, the interface and the meniscus, are well represented in the 2D images as shown in Figs. 15(a) and 15(b). The theoretical
value for the speed of sound in water, 1497 m/s at 25 ◦C, is well represented by the 2D averaged values found in this experiment (1497 m/s for the [−20◦, 20◦] angle range and 1499 m/s for the [−25◦, 25◦] angle range). The absolute deviations from the average speed of sound values within each phase obtained from the 1D measurements are 1.9 m/s in the water phase where the mean value is 1496 m/s and 0.7 m/s in the cooking oil phase where the mean value is 1469 m/s. These deviations fall at and within measurement uncertainty, respectively, and coexisting phases possessing similar speed of sound values are readily distinguished. By
FIG. 16. Acoustic images of an Indiana Limestone plate using a grid resolution of 40 µm, obtained with an angle range of (a) [−20◦, 20◦] and (b) [−35◦, 35◦].
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FIG. 17. 2D speed of sound difference images for water imbibition into air filled pores of Indiana Limestone using a grid resolution of 40 µm. (I) t = 1 h, (II) t = 5 h, (III) t = 9 h. (a) Angle range [−20◦, +20◦], (b) angle range [−35◦, +35◦]. Black filled diamonds: one-dimensional data, pink filled squares: two-dimensional data for [−20◦, +20◦] angle range, and green filled triangles: two-dimensional data for [−35◦, +35◦] angle range.
increasing the angle range from [−20◦, 20◦] to [−25◦, 25◦], the convex shape of the meniscus at the interface becomes better defined and the spatial resolution appears to approach the sensor size (0.6 mm). Nevertheless, distortions at the
upper and lower edges of the image persist as also seen in Fig. 5. These distortions are small in absolute terms and as noted above, for kinetics measurements, where the focus is on difference measurements, the small static distortions in speed
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of sound arising in uniform fields can be eliminated as part of the envisioned background image subtraction procedure. D. Observation of liquid vapour interfaces in porous media
For these experiments, a (30 mm × 40 mm × 6 mm) plate of Indiana Limestone with a 70 mD-brine and a 200 mDhelium gas permeability, and an overall porosity of 18%, was cleaned in toluene and then dried at 150 ◦C. All surfaces, except the base, were then sealed with the ultrasonic coupling agent and background images were prepared as shown in Figs. 16(a) and 16(b) for angle ranges [−20◦, 20◦] and [−35◦, 35◦], respectively, with a spatial resolution of 40 µm. The reservoir at the base of Cell II was then filled with water and the background images were subtracted from corresponding images obtained as water imbibed into the plate from the reservoir over a period of 9 h. Speed of sound difference images, showing water penetration with time, is reported in Figs. 17(a)-17(c). The upward movement of water through the pore network and local water saturation of the pore network, averaged over a depth of (6 mm) and with an imaging grid size of 40 µm, are clearly seen as a function of time and are comparably defined for both [−20◦, 20◦] and [−35◦, 35◦] angle ranges. The 1D and elevation-averaged 2D speeds of sound difference data at fixed elevation, superimposed on the images, are also comparable except at the lower and upper edges of the plate (below an elevation of 3 mm and above an elevation of 33 mm). Small differences in apparent local saturation and the boundary defining the upper limit of water penetration are also evident for the [−20◦, 20◦] and [−35◦, 35◦] angle range cases. Based on the extensive calibrations performed to date, the representation obtained for [−35◦, 35◦] is preferred. The data acquisition times for an image with an angle range of [−35◦, 35◦] and an angle step size of 2.5◦ are 10 min. As the upward velocity of water in the pore network is less than 2 mm per hour, the impact of water movement during data acquisition on image quality is negligible. E. Observation of liquid-liquid interfaces in porous media
For these experiments, the Indiana Limestone plate used in Sec. III D was soaked in water for 24 h, and the plate surfaces, other than the base, were resealed with the ultrasonic coupling agent. Background images were again obtained and were subtracted from corresponding images obtained as heptane imbibed into the plate from the reservoir over a period of 13 h. A time series of speed of sound difference images with a grid size of 40 µm, showing water displacement by heptane, are reported in Figs. 18(I)-18(IV). The profiles of averaged 2D speed of sound differences at fixed elevation are comparable to the 1D profiles but are smoother for both the [−20◦, 20◦] and [−35◦, 35◦] angle ranges. The net upward movement of heptane through the pore network within the limestone plate is clearly observed in the sequence of images that show a decrease in speed of sound with time in the lower portion of the plate. This decrease is expected9 because the speed of sound in heptane (1128 m/s) is lower than the speed of sound
FIG. 18. 2D difference speed of sound images for heptane imbibition in water filled pores of Indiana Limestone using a grid resolution of 40 µm. (I) t = 1 h, (II) t = 5 h, (III) t = 9 h, (IV) t = 13 h. (a) Angle range [−20◦, +20◦], (b) angle range [−35◦, +35◦]. Black filled diamonds: one-dimensional data, pink filled squares: two-dimensional data for [−20◦, +20◦] angle range, and green filled triangles: two-dimensional data for [−35◦, +35◦] angle range.
in water (1497 m/s) at 25 ◦C. The speed of sound contrasts is lower than in the case of water imbibition into air filled pores in the same plate and artifacts appearing in the images are more pronounced particularly for the images obtained using the angle range [−35◦, 35◦]. While the distribution of heptane
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in the pore structure over time, with a peak concentration at an elevation of 11 mm, is a subject of an ongoing investigation, the sensitivity of the technique to fluid and interface movement within porous media is evident.
IV. CONCLUSION
In this work, the capacity of an acoustic imaging technique to provide laboratory-scale, non-intrusive, highresolution, real-time, two-dimensional images of multiphase materials, with an engineering focus where “limited-view” rectilinear as opposed to circular geometries are typically preferred, is demonstrated. Artefacts arising with this geometry and their resolution are discussed and illustrative kinetics examples including visualization of liquid-vapour and liquidliquid movement occurring in porous natural limestone are provided. Restrictions, including the scale of the device, to avoid beam spreading for cases of specific interest and the scale of features in the materials of interest to avoid distortions in images are identified and discussed for diverse cases. Compromises between data acquisition rate and the resulting 2D image quality are illustrated and limitations imposed by post processing computer power are discussed. While it is expected that the latter limitation will relax in the future with improvements to computer power, the compromise between data acquisition rate and image quality will remain for cases with more rapid kinetics. Improvement of data acquisition rate is a priority topic for future study. Future work will also comprise specific studies related to diffusion phenomena of light hydrocarbons in heavy oil and bitumen within porous media, as well as the detection of local speed of sound variations in beds of coal particles arising during bioconversion. ACKNOWLEDGMENTS
J. M. Shaw thanks l’Université de Pau et des Pays de l’Adour (UPPA) for a visiting professorship and Total E&P
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(Centre Scientifique et Technique Jean-Féger) for a visiting appointment. This project was launched during a sabbatical leave hosted jointly by these institutions. Both authors thank Dr. Jean-Luc Daridon and Dr. Jerome Pauly for hosting part of this study in their laboratories at (UPPA) and for valuable discussions. Their assistance is much appreciated. We also thank Djamel Nasri (UPPA) and L’Atelier de Physique (UPPA) for helping with the design and manufacture of the acoustic cell; Mildred Becerra for her help in the laboratory at the University of Alberta; and Compute Canada for use of the WestGrid high-speed computing facility. Financial support from the sponsors of the NSERC Industrial Research Chair in Petroleum Thermodynamics: Alberta Innovates Energy and Environment Solutions, British Petroleum, ConocoPhillips, Inc., NEXEN Energy ULC, Shell Canada, Total E&P Canada, VMG, Inc., and the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged. 1R.
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