Determining the rheological properties of a fluid through a non-linear response

1. A method for determining rheological properties of a fluid, comprising:

actuating a resonator disposed in a volume that contains a fluid sample to operate the resonator in the fluid sample at a predetermined actuation scheme;

actuating the resonator with an actuation protocol that actuates the resonator in at least one of a steady state motion or a time-dependent motion, wherein actuating the resonator with an actuation protocol comprises inducing a measurable change on a motion of the resonator based at least in part due to one or more deformations in the fluid sample;

measuring, with a photodetector positioned to receive a reflected laser beam that originates with a laser beam source and reflects from the operating resonator, at least one response characteristic of the resonator based on the operation of the resonator in the fluid sample;

comparing the at least one measured response characteristic to a rheological model that associates the at least one response characteristic of the resonator to one or more rheological properties of the fluid sample; and

based on the comparison, determining one or more rheological properties of the fluid sample.

2. The method of claim 1 , wherein the resonator comprises a mechanical oscillator.

3. The method of claim 2 , wherein the mechanical oscillator comprises a piezoelectric crystal, a cantilever beam, a MEMS device, a torsional spring, a vibrating wire, or a tuning fork.

4. The method of claim 3 , wherein the fluid sample comprises a non-Newtonian liquid.

5. The method of claim 4 , wherein the non-Newtonian liquid comprises a hydrocarbon liquid, a completion liquid, or a petroleum-derived liquid.

6. The method of claim 1 , wherein actuating the resonator comprises actuating motion on the resonator through one or more signals to induce harmonic or anharmonic motion.

7. The method of claim 6 , wherein the one or more signals comprises one or more capacitive, piezoelectric, magnetic, or optical signals.

8. The method of claim 1 , wherein the time-dependent motion comprises at least one sequence of displacements of the resonator with at least one of a plurality of amplitudes or frequencies.

9. The method of claim 1 , wherein measuring at least one response characteristic of the resonator comprises measuring at least one response characteristic in a transduction domain that provides a measurable signal from the operation of the resonator.

10. The method of claim 9 , wherein measuring at least one response characteristic in a transduction domain that comprises at least one of a capacitive, a piezoelectric, a magnetic, or an optical characteristic.

11. The method of claim 1 , wherein measuring at least one response characteristic of the resonator comprises measuring at least one of a velocity or a displacement of amplitude or phase of the resonator in at least one of a time domain or a frequency domain.

12. The method of claim 1 , wherein comparing the at least one measured response characteristic to a rheological model comprises comparing at least one motion response characteristic of the resonator to at least one of a mathematical model or a computational model.

13. The method of claim 12 , wherein the at least one of the mathematical model or the computational model relates a change in the at least one motion response characteristic to at least one of a deformation amplitude or a deformation rate induced in the fluid sample.

14. The method of claim 1 , wherein actuating the resonator disposed in the volume that contains the fluid sample to operate the resonator in the fluid sample at the predetermined actuation scheme comprises actuating a mechanical oscillator disposed in the volume that contains the fluid sample to vibrate the mechanical oscillator in the fluid sample at a predetermined vibration protocol.

15. The method of claim 14 , wherein measuring the at least one response characteristic of the resonator based on the operation of the resonator in the fluid sample comprises measuring at least one motion response characteristic of the mechanical oscillator based on a non-linear response of the mechanical oscillator in the fluid sample.

16. The method of claim 15 , wherein comparing the at least one measured response characteristic to a rheological model that associates characteristics of the fluid sample to one or more rheological properties comprises comparing the at least one measured motion response characteristic to the rheological model that associates motion characteristics of the fluid sample to one or more rheological properties.

17. The method of claim 15 , wherein measuring the at least one motion response characteristic of the mechanical oscillator comprises measuring the at least one motion response characteristic with the photodetector positioned to receive the reflected laser beam that originates with the laser beam source and reflects from the vibrating mechanical oscillator.

18. The method of claim 1 , further comprising circulating the fluid sample into the volume during actuation of the resonator.

19. The method of claim 1 , wherein determining one or more rheological properties of the fluid sample comprises iteratively determining the one or more rheological properties of the fluid sample with a numerical inversion or optimization protocol.

20. The method of claim 1 , wherein the one or more rheological properties comprises at least one of a complex viscosity, a storage modulus, a loss modulus, an apparent viscosity, a flow index, or a consistency factor of the fluid sample.

21. The method of claim 1 , wherein the rheological model comprises at least one of a Bingham Plastic model, a power law model, a Hershel-Bulkley model, or a Carreau model.

22. The method of claim 1 , wherein the fluid sample comprises a non-Newtonian liquid.

23. The method of claim 22 , wherein the non-Newtonian liquid comprises a hydrocarbon liquid, a completion liquid, or a petroleum-derived liquid.