Nonlinear Acoustics Applications for Near-Wellbore Formation Evaluation (2021)

We present experimental and modeling results and a downhole logging tool concept resulting from a research collaboration between Chevron Energy Technology Company and Los Alamos National Laboratory investigating using nonlinear acoustics applications for natural fracture characterization and assessing near-wellbore mechanical integrity or drilling-induced damage. The generation of a scattered wave by noncollinear mixing of two acoustic plane waves in an acoustically nonlinear medium was first documented several decades ago. If the frequency ratio and convergence angle of the two waves and the compressional-to-shear velocity ratio of the medium where they intersect meet certain conditions, their interaction creates a scattered third wave, propagating in a predictable direction, with a frequency equal to the sum or difference between the two primary wave frequencies and an amplitude dependent on the nonlinearity at the intersection location. The conditions resulting in this scattering and the properties of the scattered wave are thus governed by the physics of the interaction, resulting in a set of “selection rules” that are the key to the measurement principle introduced here. If the two transmitted plane waves are oriented such that the third wave returns to the borehole, the phenomenon may be used as the basis for a logging tool measuring acoustic nonlinearity around the wellbore circumference, with a secondary measurement of the compressional-to-shear velocity ratio. Laboratory measurements supported by finite-difference and analytical modeling confirmed that the mixing of two plane compressional waves generated a shear wave as predicted by the selection rules in a large Berea sandstone block, confirming the potential for a downhole tool with a depth of investigation in the range 15 to 20 cm. Historical data show that nonlinearity in core samples is primarily caused by a lack of mechanical integrity. In the oil field, this may be microfractures in tight rock unconventional reservoirs or incipient near-wellbore failure while drilling. This prompts applications to fracture characterization and calibration of mechanical earth models. The main practical challenge for a downhole logging tool is injecting powerful directional acoustic energy into the formation. We envisage an openhole tool making sequential station measurements using transmitters built into hydraulically controlled pads contacting the borehole wall. Noncollinear mixing may be activated by maintaining the frequency of one transmitter constant while sweeping the other through the range of frequency ratios predicted by the selection rules, resulting in a received sum or difference frequency signal that rises to a peak and then falls. Alternatively, the frequency ratio may be maintained while steering one of the acoustic beams. The peak signal amplitude indicates the coefficient of nonlinearity, which is sensitive to lack of mechanical integrity caused by natural fractures or mechanical disaggregation. The frequency ratio at which it occurs is an indicator of the shear-to-compressional velocity at the location where the two beams cross. In this manner, a record of nonlinearity along or around the borehole can be envisaged. The physics of acoustic nonlinearity is well established, and our laboratory measurements have determined that the phenomenon of interest should occur and be measurable in the subsurface. Overcoming the engineering challenges would bring new formation evaluation insights unique to this measurement principle.