sensors Article
Passive Downhole Pressure Sensor Based on Surface Acoustic Wave Technology Sully M. M. Quintero *, Sávio W. O. Figueiredo, Victor L. Takahashi and Arthur M. B. Braga
ID
, Roberth A. W. Llerena
Mechanical Engineering Department, Pontifical Catholic University of Rio de Janeiro, Rua Marquês de São Vicente 225, 22453-900 Rio de Janeiro, Brazil;
[email protected] (S.W.O.F.);
[email protected] (V.L.T.);
[email protected] (R.A.W.L.);
[email protected] (A.M.B.B.) * Correspondence:
[email protected]; Tel.: +55-21-3527-2800 Received: 20 June 2017; Accepted: 13 July 2017; Published: 15 July 2017
Abstract: A passive surface acoustic wave (SAW) pressure sensor was developed for real-time pressure monitoring in downhole application. The passive pressure sensor consists of a SAW resonator, which is attached to a circular metal diaphragm used as a pressure transducer. While the membrane deflects as a function of pressure applied, the frequency response changes due to the variation of the SAW propagation parameters. The sensitivity and linearity of the SAW pressure sensor were measured to be 8.3 kHz/bar and 0.999, respectively. The experimental results were validated with a hybrid analytical–numerical analysis. The good results combined with the robust design and packaging for harsh environment demonstrated it to be a promising sensor for industrial applications. Keywords: pressure sensor; downhole application; SAW device; wireless sensor
1. Introduction Throughout the last few decades, the use of permanent well monitoring systems has been experiencing a remarkable growth in the oil and gas industry [1]. Information such as downhole pressure and temperature are valuable in order to optimize production and also help in identifying or avoiding problems that may lead to an undesired shut-down of an oil well. For a long time now, technologies based on quartz crystals and fiber optics have dominated the market for downhole pressure gauges. Both require the use of downhole cables (electrical or optical), which increases the cost of the monitoring solution. With the downturn in the oil and gas industry, with oil prices expected to remain well below where they were in the first half of the decade, any solution that provides cost reductions is welcomed by oil producers. As a consequence, the use of downhole wireless telemetry has been gaining increased attention in the last few years [2–6]. However, in order to reach its full potential, wireless solutions will require low power consumption, opening a window of opportunity for surface acoustic wave (SAW) devices in monitoring systems for oil wells. This paper presents a passive SAW-based pressure sensor developed for these applications. The first pressure sensor based on SAW was proposed in 1975 by Reeder et al. [7]. It consisted of SAW delay line transducers fabricated on the surface of a pressure-dependent membrane made of ST-X quartz. It was integrated into an oscillator, and its phase and time delay changed linearly with the applied pressure. Some years later, in 1997, Buff et al. [8] proposed a similar pressure sensor design, but using a SAW resonator instead of a delay line. This design used 36◦ Y cut quartz and could store electromagnetic energy captured with an antenna, thus being a passive remote pressure sensor. The versatility of SAW devices was also used to measure soil pressure, as addressed in 2014 by Wang et al. [9], who proposed a passive wireless SAW sensor consisting of a hollow cylinder with a sealing membrane in which the SAW transducers were fabricated, producing a delay line.
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A more current and successful employment of SAW pressure sensors is in the automotive industry in conjunction with tire pressure monitoring systems (TPMS). The SAW sensors are integrated to the vehicle’s wheels and communicate wirelessly with a central transponder. These sensors require no battery, and are what is called the second generation of TPMS [10]. The first generation TPMS was also based on Micro-Electro-Mechanical Systems (MEMS) pressure sensors and required battery to supply energy to an active transmitter [11]. Alternative materials other than quartz have been investigated for pressure sensor fabrication. In 2013, Rodriguez-Madrid and Iriart [12] developed a high-frequency (GHz) SAW pressure sensor for gases made from aluminum nitrate (AlN) as the piezoelectric material deposited on nanocrystalline diamond (NCD) membrane structure. The materials allowed the sensor to be used in high-temperature environments, and has achieved extreme pressure sensibility. Aiming at reducing the production cost of SAW pressure sensors, S. Grousset et al. [13] depicted a wafer-level approach to transfer single-layer Quartz crystal onto Silicon substrate. This allowed for batch production, better control of all sensors characteristics, and better integration with the electronics. While the majority of SAW pressure sensors have been designed as membrane-like devices, in 2014, Della Lucia et al. [14] proposed a different way to use SAW devices for this application. The essence of their design consisted of subjecting a SAW device to compression loading instead of bending loading such as the one a membrane is subjected to. The packaging comprised a capsule where the device was fixed and compressed with the aid of a mechanical plunger connected to a membrane. Under pressure, the membrane presses the plunger, which in turn compresses the SAW device. This pressure sensor was mentioned to be used in the oil offshore and gas industry, and was able to measure pressures ranging from 0 to 1000 bar—far above the upper pressure limits of the aforementioned designs. As can be noticed in Table 1, the maximum operating pressure capability reported by most researchers is generally low. Since the mechanical strength of the piezoelectric materials used is relatively low, the sensors cannot be used to measure high levels of pressure. This is a limiting factor when one desires to use these sensors in high-pressure environments like inside a wellbore, where pressure conditions may reach up to 2700 bar in extreme cases [15]. Table 1. Summary of the main parameters related to pressure sensors based on surface acoustic wave (SAW) technology. Author
Sensitivity
Range (bar)
Substrate
Technology
Wireless
0–3.5
ST-X Quartz
Delay Line
No
0–10
35 Y Quartz AIN on CVD Nanocrystaline
Resonator 1-port Resonator 2-port Resonator 2-port Resonator 1-port Resonator
Yes
Buff et al. [8]
44–145 ppm/bar 76 ppm/bar
Wang et al. [9]
330 kHz/bar
0–4
Rodriguez-Madrid and Iriart [12]
0.125 kHz/bar
0–1000
Della Lucia et al. [14]
203 Hz/bar
0–1034
ST-X Quartz
0–4.8
AT-Cut Quartz (YXl)/37◦
Reeder et al. [7]
Grousset et al. [13]
25.8 kHz/bar
ST-X Quartz
No No No No
In order to measure pressure values in the vicinity of 100 bar with relatively enhanced sensitivity, we propose an alternative way to deploy SAW devices for pressure measurement. By bonding a SAW resonator on a metallic membrane previously designed to stand to pressures of up to 200 bar, the mechanical strength limitation of quartz membranes is overcome. The strain levels in the membrane do not reach harmful values, thus the SAW device is kept safe. The design also includes passive and wireless operation of the sensor.
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2. Design and Numerical Simulation 2. Design and Numerical Simulation 2.1. 2.1. Design Design The workingprinciple principleofof this sensor is detection the detection the produced strain produced by the pressure applied The working this sensor is the of theofstrain by the applied pressure on a circular diaphragm instrumented with a SAW resonator. The pressure sensor is on a circular diaphragm instrumented with a SAW resonator. The pressure sensor is mounted directly mounted directly on a mandrel specifically developed up to accommodate up to two The on a mandrel specifically developed to accommodate to two transducers. Thetransducers. diaphragm was diaphragm was designed so as to remain uncoupled from the deformations of the mandrel. designed so as to remain uncoupled from the deformations of the mandrel. As As depicted depicted in in Figure Figure 1, 1, the the pressure pressure sensor sensor consists consists of of aa base, base, aa diaphragm, diaphragm, aa cover, cover, and and aa SAW SAW resonator. All metallic parts, designed and machined in our laboratory, were made of stainless resonator. All metallic parts, designed and machined in our laboratory, were made of stainless steel steel AISI except the the diaphragm, diaphragm, which made of of Inconel™ Inconel™ 718. 718. The the diaphragm diaphragm AISI 316, 316, except which was was made The material material of of the was thermally treated to achieve achieve its its maximum maximum strength strength (precipitation (precipitation hardening hardening at at 718 718 ◦℃). was thermally treated to C). Figure Figure 11 also shows the mandrel designed to accommodate the pressure sensor. The dashed red line points also shows the mandrel designed to accommodate the pressure sensor. The dashed red line points out out the place where they are to be placed. The main parts of the sensor are schematically shown in the place where they are to be placed. The main parts of the sensor are schematically shown in the the exploded The “A” detail “A” the shows theofpicture the the base with thealready diaphragm already exploded view.view. The detail shows picture the baseofwith diaphragm instrumented. instrumented. The base has grooves for O-rings and backup rings (made from a fluoroelastomer marketed ® brand). The has groovesThese for O-rings backup ringsthe (made a fluoroelastomer marketed under thebase Viton O-ringsand have two roles: first from is to isolate the lower chamber of ® under the Viton brand). These O-rings have two roles: the first is to isolate the lower chamber of the the diaphragm, on which the pressure to be measured acts, from the upper chamber instrumented diaphragm, onresonator; which thethe pressure from thefrom upper instrumented with with the SAW secondtoisbe tomeasured isolate theacts, diaphragm thechamber deformations coming from the SAW resonator; the second is to isolate the diaphragm from the deformations coming from the base and cover of the transducer, and to avoid position offset. Regarding the cover, it keeps the the base and cover of the transducer, and to avoid position offset. Regarding the cover, it keeps the diaphragm from detaching and protects the SAW from any possible contamination. The SAW device diaphragm from detaching and protects the SAW from of any possible contamination. Theconfiguration SAW device shown in the detail “B”, attached to the upper surface the diaphragm, is a one-port shown in the detail “B”, attached to It the upper of surface of the diaphragm, is a (IDT) one-port resonator operating at 433.92 MHz. consists one interdigital transducer andconfiguration two banks of resonator operating at 433.92 MHz. It consists of one interdigital transducer (IDT) and two reflectors on a ST-cut quartz piezoelectric substrate with the acoustic aperture of 0.2 mm andbanks pitch of of reflectors on a ST-cut quartz piezoelectric substrate with the acoustic aperture of 0.2 mm and pitch of 1.5 µm. Basically, the IDT is a series of interleaved metallic electrodes responsible for generating the 1.5 µ m. waves. Basically, the IDT is a series of interleaved metallic electrodes responsible for generating the surface surface waves.
Figure in the Figure 1. 1. Pressure Pressure sensor sensor assembly. assembly. In In detail detail A: A: diaphragm diaphragm mounted mounted in the base. base. In In detail detail B: B: top top view view of the SAW sensor. of the SAW sensor.
2.2. Numerical Simulations 2.2. Numerical Simulations Although the strain straindistribution distributioninina rigidly a rigidly clamped diaphragm under uniform pressure is Although the clamped diaphragm under uniform pressure is well well understood, we have chosen to perform numerical simulations in order to better understand understood, we have chosen to perform numerical simulations in order to better understand the the distribution and effective deformation transferred from the diaphragm to the SAW resonator. distribution and effective deformation transferred from the diaphragm to the SAW resonator. We We employed ANSYS Workbench 16.0 finite element analysis (FEA) software to analyze the strains employed ANSYS Workbench 16.0 finite element analysis (FEA) software to analyze the strains transferred to the SAW device when the diaphragm is subjected to pressures of up to 100 bar. The transferred to the SAW device when the diaphragm is subjected to pressures of up to 100 bar. following parameters were used as input in the simulations: The following parameters were used as input in the simulations: Diaphragm: modeled as AISI 316 steel, with thickness and diameter of 0.6 and 15 mm, • Diaphragm: modeled as AISI 316 steel, with thickness and diameter of 0.6 and 15 mm, respectively. respectively.
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Adhesive layer: considered to be a 30 µ m-thick isotropic material with Young’s modulus • Adhesive of 3.5layer: GPa. considered to be a 30 µm-thick isotropic material with Young’s modulus of 3.5 GPa. SAW resonator: 0.7 mm wide, 3.6 mm long, and 0.35 mm thick, and modeled as ST-cut • SAW resonator: 0.7 mm wide, 3.6 mm long, and 0.35 mm thick, and modeled as ST-cut quartz quartz material, with the wave propagation direction parallel to radial direction. material, with the wave propagation direction parallel to radial direction. Every domain was meshed with tetrahedral elements—specifically the element SOLID187, domain wastetrahedral. meshed with tetrahedral elements—specifically element SOLID187, which whichEvery is a 3-D 10-node The total number of nodes in the FE the model was 411128. is a Figure 3-D 10-node tetrahedral. Thestrain total number nodes in the FE model was 411128. 2a shows the radial field onof the diaphragm-SAW system, and in the inset, the Figure 2a shows the radial strain field on the diaphragm-SAW system, and in the inset,along the detail detail of the mesh surrounding the SAW. Figure 2b shows the radial strain distribution the of the mesh surrounding the SAW. Figure 2b shows the radial strain distribution along the longitudinal longitudinal axis of the SAW device for different pressure values, at the upper surface. The grey axis of area the SAW device for values, at the upper surface. shadedThe area shaded corresponds to different the IDT pressure region, from which the surface wavesThe aregrey launched. corresponds to the IDT region, from which the surface waves are launched. The maximum strain maximum strain variation between the center point and the IDT edge is approximately of 6% of the variation full scale. between the center point and the IDT edge is approximately of 6% of the full scale.
(a)
(b)
Figure 2. (a) Radial strain distribution (in the inset: mesh density close to the SAW device). (b) Radial Figure 2. (a) Radial strain distribution (in the inset: mesh density close to the SAW device). (b) Radial strain straindistribution distributionon onthe thetop topsurface surfaceofofthe theSAW SAWdevice deviceatatincreasing increasingpressures. pressures.
3. Experimental Setup 3. Experimental Setup In order to characterize the sensor’s response to pressure, the sensor was screw-fastened to a In order to characterize the sensor’s response to pressure, the sensor was screw-fastened to pressure vessel with identical docking to that of the mandrel designed for field test. For this purpose, a pressure vessel with identical docking to that of the mandrel designed for field test. For this purpose, a calibrated dead-weight tester purchased from DH-Budenberg (580) (Salford, Manchester, England) a calibrated dead-weight tester purchased from DH-Budenberg (580) (Salford, Manchester, England) and a pressure gauge purchased from Fluke (700P29) (Everett, WA, USA) were used, respectively, as and a pressure gauge purchased from Fluke (700P29) (Everett, WA, USA) were used, respectively, as the the standard and pressure reference. The resonance frequency was monitored using a vector standard and pressure reference. The resonance frequency was monitored using a vector network network analyzer (VNA) purchased from Keysight (E5061B) (Bayan Lepas, Penang, Malaysia). analyzer (VNA) purchased from Keysight (E5061B) (Bayan Lepas, Penang, Malaysia). The pressure test setup is shown in Figure 3. The dead-weight tester’s port is connected to the The pressure test setup is shown in Figure 3. The dead-weight tester’s port is connected to the inlet port of the mandrel. The mandrel's outlet port is connected to the pressure gauge. In one of the inlet port of the mandrel. The mandrel's outlet port is connected to the pressure gauge. In one of insets in the picture, it is possible to see the antennas used for the wireless performance tests. The the insets in the picture, it is possible to see the antennas used for the wireless performance tests. wireless arrangement consists of a pair of custom dipole antennas with an offset of 5 cm, using the The wireless arrangement consists of a pair of custom dipole antennas with an offset of 5 cm, using mandrel as the ground plane. The output power and the number of points of the VNA was set to 10 the mandrel as the ground plane. The output power and the number of points of the VNA was set to dBm and 1601, respectively. 10 dBm and 1601, respectively. In addition, the left inset picture shows the top-surface of the diaphragm instrumented with the In addition, the left inset picture shows the top-surface of the diaphragm instrumented with the SAW resonator. SAW resonator. All experiments were performed at room temperature (25 ℃). The pressure load was increased All experiments were performed at room temperature (25 ◦ C). The pressure load was increased step by step, in about seven steps, up to a maximum of 96 bar. Each step was kept for 3 min and step by step, in about seven steps, up to a maximum of 96 bar. Each step was kept for 3 min and simultaneously monitored by the pressure gauge and the VNA. To test the sensor reproducibility, simultaneously monitored by the pressure gauge and the VNA. To test the sensor reproducibility, three three load cycling tests were performed. load cycling tests were performed.
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Figure 3. Setup for the pressure the inset, the diaphragm instrumented with thethe SAW; at Figure pressuretests: tests:in theleft left inset, the diaphragm instrumented with SAW; Figure 3. 3. Setup for the pressure tests: ininthe left inset, the diaphragm instrumented with the SAW; at the center of of thethe figure, the side the inset, aa plot at the center figure, the sideview viewof themandrel mandrelwith withantennas; antennas;and andin inthe thetop-right top-right the center of the figure, the side view ofofthe mandrel with antennas; and in the top-right inset, inset, a plot plot of one of the load cycles. of ofone oneof ofthe theload loadcycles. cycles.
4. 4. Results and Discussion 4.Results Resultsand andDiscussion Discussion Figure of the sensor measured at pressure levels (0 Figure 4ashows showsthe thefrequency frequencyresponse response sensor measured at different pressure levels Figure4a shows the frequency response ofof thethe sensor measured atdifferent different pressure levels (0to to ◦ 97 bar) and at the temperature of 25 ℃. We clearly notice the shift in the resonance frequency as the (0 to 97 bar) and at the temperature of 25 C. We clearly notice the shift in the resonance frequency 97 bar) and at the temperature of 25 ℃. We clearly notice the shift in the resonance frequency as the applied pressure increases. The curve the sensor in 4b, as the applied pressure increases. The calibration curve the is sensor is reproduced in Figure 4b, applied pressure increases. The calibration calibration curve for for thefor sensor is reproduced reproduced in Figure Figure 4b, which which presents the frequency changes corresponding to scattering parameter S11. There is which presents the frequency changes corresponding to scattering parameter S11.There Thereisisaa linear linear presents the frequency changes corresponding to scattering parameter S11. linear dependence of the frequency with sensitivity of This dependence frequency on on the pressure, with calculated sensitivity of 8.4 kHz/bar. This behavior dependenceof ofthe the frequency on the the pressure, pressure, with calculated calculated sensitivity of 8.4 8.4 kHz/bar. kHz/bar. This behavior is expected, since the diaphragm’s strain response to pressure is linear, and strain transfer is expected, the diaphragm’s strain response toresponse pressure to is linear, andisstrain occurs from behavior is since expected, since the diaphragm’s strain pressure linear,transfer and strain transfer occurs from diaphragm to the diaphragm the SAW resonator. occurs fromthe theto diaphragm tothe theSAW SAWresonator. resonator.
S11(dBm) (dBm) S11
0 0
1 bar 1 barbar 66.7 66.7 bar
26.8 bar 26.8 bar 76.7bar 76.7bar
46.8 bar 46.8 86.7bar bar 86.7 bar
56.7 bar 56.7 96.7bar bar 96.7 bar
-10 -10 -20 -20 -30 -30 -40 -40 432.8 432.8
433.0 433.0
433.2 433.2
433.4 433.4
433.6 433.6
Frequency Frequency(MHz) (MHz)
(a) (a)
(b) (b)
Figure 4. (a) S11 curve for all applied pressures. (b) Comparison of the variation of the SAW Figure 4. (a) S11 curve for all applied pressures. (b) Comparison of the variation of the SAW Figure 4. (a) S11 curveasfor all applied pressures.calibration (b) Comparison of ambient the variation of the SAW resonance frequency a function of pressure curve at temperature (25resonance ℃). resonance frequency as a function of pressure calibration curve at ambient temperature (25 ℃). frequency as a function of pressure calibration curve at ambient temperature (25 ◦ C).
These These results results were were compared compared to to an an analytical analytical formula formula presented presented by by Sinha Sinha et et al. al. [16] [16] for for the the Theseofresults were compared toSAW an analytical formula presented by Sinha et al.Their [16] formethodology the behavior behavior the frequency of a resonator undergoing biaxial strain. behavior of the frequency of a SAW resonator undergoing biaxial strain. Their methodology of the frequency of of aofSAW resonator undergoing biaxial strain. Theirforce, methodology considered the considered the aacircular piezoelectric disk to where considered thecase case circular piezoelectric disksubjected subjected tonormal normal force, whereaaSAW SAWresonator resonator case of a circular disk normalelement force, where SAW resonator was built was directly on our case, sensing (SAW isis attached to was built built directlypiezoelectric on its its top. top. In In oursubjected case, the theto sensing element (SAWaresonator) resonator) attached to aa directly on its top. In our case, the sensing element (SAW resonator) is attached to a circular metal circular metal diaphragm, which transfers flexural strain to the SAW resonator through circular metal diaphragm, which transfers flexural strain to the SAW resonator through the the diaphragm, which transfers flexural strain to the SAW resonator through the adhesive. The transferred adhesive. The transferred strain induces changes in the pitch of the interdigital transducer, elastic adhesive. The transferred strain induces changes in the pitch of the interdigital transducer, elastic strain induces in the pitch of the interdigital transducer, elastic constants, the and density of the constants, and density medium. expression for fractional constants, andchanges densityof ofthe thepropagating propagating medium.The The expression forpredicting predicting thetotal total fractional change in frequency may be given by the expression change in frequency may be given by the expression
∆𝑓 = −1.39 11 + 0.39 33 𝑓
(1)
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where f is the reference frequency, 11 is the strain in the wave propagation direction, and 33 is the strain perpendicular to the direction of for propagation. Thefractional corresponding 11 and may 33 were obtained propagating medium. The expression predicting the total change in frequency be given by thesimulations expression from the numerical described in Section 2.2. The red curve in Figure 4b, based upon the ∆f = −to 1.39strain. ε 11 + 0.39 ε 33 disagreement between our(1) above equation, is almost 20% more sensitive The experimental f results andwhere thosef obtained by Sinha et al. [16] may be related to the lower strain transfer performance is the reference frequency, ε 11 is the strain in the wave propagation direction, and ε 33 is the of the sensor configuration. Strain in theofdiaphragm absorbed the adhesive strain perpendicular to the direction propagation. is Thepartially corresponding ε 11 and by ε 33 were obtained when it is the SAW numerical simulations described in Section 2.2. The red curve Figure 4b, based upon is thesensed. transferredfrom to the resonator, and thus only a part of the total in membrane’s strain above equation, is almost 20% more sensitive to strain. The disagreement between our experimental In order to verify and understand these discrepancies, tensile specimens were instrumented results and those obtained by Sinha et al. [16] may be related to the lower strain transfer performance with the same type ofconfiguration. SAW and adhesive in theis development presented pressure sensor. of the sensor Strain in theused diaphragm partially absorbedof bythe the adhesive when it is to theresults SAW resonator, thus only to a part of theanalytical total membrane’s strain proposed is sensed. In this case,transferred the tensile were and compared other formula by Sinha and In order to verify and understand these discrepancies, tensile specimens were instrumented with Locke [17]. Similar discrepancies were observed, confirming that the disagreements are effectively the same type of SAW and adhesive used in the development of the presented pressure sensor. In this associated to the performance of analytical the sensor configuration case, thestrain tensile transfer results were compared to other formula proposed by Sinha and Locke [17]. Finally, the sensor was were characterized for temperatures rangingare from 30 toassociated 70 ℃. Figure 5 shows Similar discrepancies observed, confirming that the disagreements effectively to the strain transfer performance of the sensor configuration a nonlinear response of the relative frequency drift as a function of the◦ temperature. The square Finally, the sensor was characterized for temperatures ranging from 30 to 70 C. Figure 5 shows fitting indicates a second-order temperature coefficient value of −37 ppb/℃ It is slightly higher than a nonlinear response of the relative frequency drift as a function of the temperature. The square ◦ C about the second-order temperature coefficient forcoefficient the ST value cut quartz (i.e., −34higher ppb/℃). fitting indicates a second-order temperature of −37 ppb/ It is slightly than This slight ◦ the second-order temperature coefficient for the ST cutmaterials quartz (i.e., with about mismatched −34 ppb/ C). This slight expansion difference may be a result of the interaction between thermal difference may be a result of the interaction between materials with mismatched thermal expansion coefficients such as quartz, stainless steel, and the adhesive. coefficients such as quartz, stainless steel, and the adhesive. F/F F/F= 16.57 + 0.605 * T -0.037 * T
F/ F (ppm)
0
2
-50
-100
-150
30
40
50
60
70
Temperaure ( C) Figure 5. Variation the SAW resonance frequency as aas function of temperature (25 ◦ C). Figure 5. Variation of theofSAW resonance frequency a function of temperature (25 °C).
5. Conclusion
5. Conclusion
Other authors have already demonstrated the applicability of pressure sensors based on SAW Other resonators; authors have already theof applicability pressure sensors based on SAW however, the lowdemonstrated mechanical strength quartz limits the of sensors’ maximum operating pressure and restricts their applicability. In this paper, we proposed and demonstrated a wireless resonators; however, the low mechanical strength of quartz limits the sensors’ maximum operating pressure sensor based on a SAW resonator with outstanding results with respect to the balance between pressure and restricts their applicability. In this paper, we proposed and demonstrated a wireless operating range and sensitivity. The linear pressure sensitivity was estimated to be 8.3 kHz/bar, and ◦ C. pressure sensor basedsecond-order on a SAW resonator with value outstanding results with respect to the balance the measured temperature coefficient was −37 ppb/ ◦ Although the sensor tested only upThe to 70 linear C, the current design can be improvedwas to allow for between operating range andwassensitivity. pressure sensitivity estimated to be higher temperatures. One could use a SAW resonator fabricated on Langasite substrate, which has 8.3 kHz/bar, and the measured second-order temperature coefficient value was −37 ppb/℃. been proven to operate at a temperature of 500 ◦ C [18], and bond it to the diaphragm using a ceramic Although the sensorThis was tested only up to high 70 ℃, the current canused be improved to allow cement adhesive. adhesive type withstands temperatures, and isdesign successfully to install
for higher temperatures. One could use a SAW resonator fabricated on Langasite substrate, which has been proven to operate at a temperature of 500 ℃ [18], and bond it to the diaphragm using a ceramic cement adhesive. This adhesive type withstands high temperatures, and is successfully used to install resistive strain gages. This combination was demonstrated in the work of [19], which described the behavior of a high-temperature SAW strain sensor, and reported low hysteresis
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resistive strain gages. This combination was demonstrated in the work of [19], which described the behavior of a high-temperature SAW strain sensor, and reported low hysteresis values. A numerical analysis in conjunction with an analytical formula was used to study the behavior of the frequency change under different strain distributions, and discrepancies were found. Initially, it was not clear whether the error stemmed from the hybrid analysis or the experimental measurements. However, the results of tensile tests confirmed that the disagreements were associated mainly with the performance of the strain transfer coefficient. Acknowledgments: This research was funded by Shell Brazil through the project BG-40, and received education financial support from the Technological Development (CNPq) and the Coordination for the Improvement of Higher Education Personnel (CAPES). Author Contributions: S.M.M.Q. and S.W.O.F. conceived the SAW pressure sensor and performed the experiments; V.L.T. selected the instruments and assembled the experimental setup; R.A.W.L. and A.M.B.B. designed the mandrel and diaphragm, and performed the numerical simulations. All authors contributed to the writing of the manuscript. Conflicts of Interest: The authors declare no conflict of interest.
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