Spatial characterization of dysfunction in downhole systems

A method for determining spatial variation of vibration along a bottomhole assembly (BHA) including a drill bit, the method comprising:

• obtaining first data including a first vibrational amplitude with a first sensor at a first distance from the drill bit;
• obtaining second data including a second vibrational amplitude with a second sensor at a second distance from the drill bit, the second distance being greater than the first distance;
• and
• using, via at least one processor that is part of or coupled to the BHA, acoustic velocity and the first and second data to determine data characterizing spatial variation of vibration along at least a portion of a length of the BHA, wherein using the first and second data includes deriving a vibrational frequency.

A downhole system, comprising:

• a bottomhole assembly (BHA) including a drill bit;
• a first sensor disposed at a first distance from the drill bit;
• a second sensor disposed at a second distance from the drill bit, wherein the second distance is greater than the first distance;
• and
• at least one processor that is part of or coupled to the BHA, the at least one processor configured to:
• obtain data from the first sensor and the second sensor and use the data to determine data characterizing spatial variation of vibration along at least a portion of a length of the BHA;
• and
• determine a maximum amplitude of the vibration by solving a system of equations that relates the maximum amplitude of the vibration to vibrational amplitudes measured by the first and second sensors, wherein the system of equations further includes a distance to a first vibrational node, the first distance between the first sensor and the drill bit, the second distance between the second sensor and the drill bit, and a wavelength.

A method for determining spatial variation of vibration along a bottomhole assembly (BHA) including a drill bit, the method comprising:

• obtaining first data with a first sensor at a first distance from the drill bit;
• obtaining second data with a second sensor at a second distance from the drill bit, the second distance being greater than the first distance;
• using, via at least one processor that is part of or coupled to the BHA, the first and second data to determine data characterizing spatial variation of vibration along at least a portion of a length of the BHA;
• and
• determining, via the at least one processor that is part of or coupled to the BHA, a maximum amplitude of the vibration by solving a system of equations that relates the maximum amplitude of the vibration to vibrational amplitudes measured by the first and second sensors, wherein the system of equations further includes a distance to a first vibrational node, the first distance between the first sensor and the drill bit, the second distance between the second sensor and the drill bit, and a wavelength.