Resonating sensor for high-pressure and high-temperature environments

1. An apparatus comprising:

a substrate;

a sensor element including a double-ended tuning fork piezoelectric resonator having a first tine and a second tine, wherein:

the double-ended tuning fork piezoelectric resonator is formed in the substrate;

the double-ended tuning fork piezoelectric resonator is configured to vibrate at a first frequency;

the substrate includes an additional piezoelectric resonator;

the additional piezoelectric resonator is configured to vibrate at a second frequency that is at least two orders of magnitude greater than the first frequency;

the first tine and the second tine are positioned within an aperture of the substrate;

the first tine and the second tine are spaced apart from one another so as to form a slot between the first tine and the second tine;

a width of the slot from the first tine to the second tine, the width of the slot measured orthogonally to lengths of the first tine and the second tine, varies along the lengths of the first tine and the second tine;

opposite sides of the first tine are inwardly tapered continuously toward a middle of the first tine; and

opposite sides of the second tine are inwardly tapered continuously toward a middle of the second tine; and

a body including caps coupled to the sensor element, wherein the double-ended tuning fork piezoelectric resonator is enclosed within a cavity of the body.

2. The apparatus of claim 1 , wherein the sensor element and the caps are hermetically sealed, and wherein the cavity is filled with an inert gas.

3. The apparatus of claim 1 , wherein the lengths of the first tine and the second tine each extend between a first anchor and a second anchor.

4. The apparatus of claim 1 , wherein:

an outer edge of the second tine is inwardly tapered continuously toward the middle of the second tine at a first taper angle; and

an inner edge of the second tine is inwardly tapered continuously toward the middle of the second tine at a second taper angle.

5. The apparatus of claim 1 , wherein the first tine is symmetrical with the second tine.

6. The apparatus of claim 1 , wherein the opposite sides of the first tine are symmetrical with each other, and wherein the opposite sides of the second tine are symmetrical with each other.

7. The apparatus of claim 1 , wherein the first tine and the second tine are formed of a piezoelectric crystal material that has a melting point above 1000° C. and a Curie temperature at or above 1000° C.

8. The apparatus of claim 1 , wherein the sensor element comprises a resistance temperature detector.

9. The apparatus of claim 1 , wherein the additional piezoelectric resonator comprises:

a beam, wherein the beam is formed in the substrate between the aperture and an additional slot in the substrate spaced from the aperture; and

two electrodes on the beam configured to enable excitation of an acoustic standing wave in the beam.

10. A method comprising:

measuring pressure of a fluid in a well using a double-ended tuning fork piezoelectric resonator having a first tine and a second tine;

estimating resistivity of an excitation electrode of the double-ended tuning fork piezoelectric resonator;

measuring a temperature of the fluid in the well based on the estimated resistivity of the excitation electrode; and

using the measured pressure and the measured temperature to control the well.

11. The method of claim 10 , further comprising using the measured temperature to perform temperature compensation on the measured pressure.

12. The method of claim 10 , wherein:

the first tine and the second tine are spaced apart from one another so as to form a slot between the first tine and the second tine;

opposite sides of the first tine are inwardly tapered continuously toward a middle of the first tine; and

opposite sides of the second tine are inwardly tapered continuously toward a middle of the second tine.

13. A system comprising:

memory storing instructions;

a processor configured to execute the instructions to:

receive data from a sensor in a well, the data including pressure of a fluid in the well, the sensor including a double-ended tuning fork piezoelectric resonator having a first tine and a second tine;

estimate resistivity of an excitation electrode of the double-ended tuning fork piezoelectric resonator;

measure a temperature of the fluid in the well based on the estimated resistivity of the excitation electrode; and

use the pressure and the measured temperature to control the well.

14. The system of claim 13 , wherein:

the first tine and the second tine are spaced apart from one another so as to form a slot between the first tine and the second tine;

opposite sides of the first tine are inwardly tapered continuously toward a middle of the first tine; and

opposite sides of the second tine are inwardly tapered continuously toward a middle of the second tine.

15. The system of claim 13 , wherein:

the double-ended tuning fork piezoelectric resonator is formed in a substrate;

the double-ended tuning fork piezoelectric resonator is configured to vibrate at a first frequency;

the substrate includes an additional piezoelectric resonator;

the additional piezoelectric resonator is configured to vibrate at a second frequency that is at least two orders of magnitude greater than the first frequency; and

the first tine and the second tine are positioned within an aperture of the substrate.