Precise borehole geometry and BHA lateral motion based on real time caliper measurements

An apparatus for estimating a geometry of a borehole penetrating the earth, the apparatus comprising:

• a carrier configured to be conveyed through the borehole;
• a plurality of sensors disposed at the carrier and configured to perform borehole caliper measurements at a plurality of times, wherein for each time in the plurality of times a measurement set comprises measurements made by the plurality of sensors at that time;
• and
• a processor configured to implement a method comprising:
• receiving a measurement set for each time in the plurality of times;
• dividing a cross-section of the borehole into S sectors, the cross-section being in an X-Y plane that is perpendicular or sub-perpendicular to a Z-axis that is a longitudinal axis of the borehole;
• obtaining an estimate of the borehole geometry by connecting in adjacent sectors a representative radius point that represents a radius representative of measurements in each sector;
• displacing each measurement set according to a displacement vector related to an offset of each measurement set from the estimated geometry if the displacement vector exceeds a selection criterion;
• iterating the obtaining an estimate of the borehole geometry and the displacing each measurement set based on a latest displacement vector;
• and
• providing a latest obtained estimate as the geometry of the borehole when all of the displacement vectors no longer exceed the selection criterion for the displacing.

A non-transitory computer readable medium comprising computer executable instructions for estimating a geometry of a borehole penetrating the earth by implementing a method comprising:

• receiving a plurality of borehole caliper measurements performed with a plurality of sensors at a plurality of times, wherein for each time in the plurality of times a measurement set comprises measurements made by the plurality of sensors at that time;
• dividing a cross-section of the borehole into S sectors, the cross-section being in an X-Y plane that is perpendicular or sub-perpendicular to a Z-axis that is a longitudinal axis of the borehole;
• obtaining an estimate of the borehole geometry by connecting in adjacent sectors a representative radius point that represents a radius representative of measurements in each sector;
• displacing each measurement set according to a displacement vector related to an offset of each measurement set from the estimated geometry if the displacement vector exceeds a selection criterion;
• iterating the obtaining an estimate of the borehole geometry and the displacing each measurement set based on a latest displacement vector;
• and
• providing a latest obtained estimate as the geometry of the borehole when all of the displacement vectors no longer exceed the selection criterion for the displacing.