# US 8,788,207 B2 · Precise borehole geometry and BHA lateral motion based on real time caliper measurements > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 8,788,207 B2 - Document ID: US8788207B2 - Status: Granted - Kind: B2 - Application number: 13/194,179 - Filed: 2011-07-29 - Published: 2013-01-31 - Granted: 2014-07-22 - Earliest claimed: 2011-07-29 - Assignees: Baker Hughes Incorporated - Applicants: Jianyong Pei; Thomas Dahl; John Macpherson - Inventors: Jianyong Pei; Thomas Dahl; John Macpherson - Web page: https://patentgrep.com/patent/US8788207B2 ## CPC - E21B 47/085: using radiant means, e.g. acoustic, radioactive or electromagnetic - E21B: EARTH OR ROCK DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS ## Abstract Disclosed is a method for estimating a geometry of a borehole penetrating the earth. The method includes: performing a plurality of borehole caliper measurements with N transducers at a plurality of times, wherein for each time a measurement set comprises measurements made by the N transducers at that time; dividing a cross-section of the borehole into S sectors; obtaining an estimate of the borehole geometry by connecting representative radius points in adjacent sectors; 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. ## Claims ### Claim 1 A method for estimating a geometry of a borehole penetrating the earth, the method comprising: performing a plurality of borehole caliper measurements with N transducers at a plurality of times, wherein for each time a measurement set comprises measurements made by the N transducers 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 using a processor; 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 using a processor; 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 using a processor; iterating the obtaining an estimate of the borehole geometry and the displacing each measurement set based on a latest displacement vector using a processor; 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 using a processor. ### Claim 2 (depends on 1) The method according to claim 1, wherein the N transducers are disposed on a perimeter of a bottom hole assembly or downhole sensor sub configured to be conveyed through the borehole, a center C of the perimeter being a reference point from which the borehole caliper measurements are referenced. ### Claim 3 (depends on 2) The method according to claim 2, wherein the bottom hole assembly has a circular cross-section in the X-Y plane and the perimeter is a circumference of the bottom hole assembly. ### Claim 4 (depends on 3) The method according to claim 3, wherein a radius r for each measurement is calculated by adding a distance from the center C and a standoff measured by one of the N transducers performing the measurement. ### Claim 5 (depends on 4) The method according to claim 4, wherein the obtaining a first estimate of the borehole geometry comprises creating a histogram for each sector, the histogram comprising a number or measurement points versus a range of radii that the measurement points fall into. ### Claim 6 (depends on 5) The method according to claim 5, wherein the first representative radius for each sector comprises a radius in a range of radii having a highest density of measurement points. ### Claim 7 (depends on 2) The method according to claim 2, wherein the displacing comprises: creating an N-sided polygon for each measurement set wherein each vertex represents one measurement; creating a straight line from the center C through each vertex wherein the line intersects the first estimate of the borehole geometry; determining an offset vector di for each vertex, the offset vector comprising a distance and direction along the straight line to the intersection of the first estimate of the borehole geometry; summing the offset vectors di for each polygon to obtain a vector sum D where D = ∑ i = 1 N ⁢ d i . ### Claim 8 (depends on 7) The method according to claim 7, wherein the displacing further comprises moving each polygon that exceeds the selection criterion a distance δ where δ=D/(N−1) in the direction of D. ### Claim 9 (depends on 8) The method according to claim 8, further comprising estimating the center C of the BHA at the time the associated measurement set was performed by summing all move vectors δi for all iterations Niteration where ∑ δ = ∑ i = 1 N iteration ⁢ δ i and moving from the center point C according to δ. ### Claim 10 (depends on 9) The method according to claim 9, further comprising estimating the trajectory of the center C of the BHA by connecting ends of each successive move vector δi corresponding to a sequence of measurement times for the associated polygon. ### Claim 11 (depends on 1) The method according to claim 1, further comprising determining a mean displacement of the first displacement vectors and setting the selection criteria to the mean displacement. ### Claim 12 (depends on 1) The method according to claim 1, wherein the N transducers comprises a first set of sensors spaced a distance L from a second set of sensors along a longitudinal axis of the borehole and the method further comprises estimating a rate of penetration (ROP) of the first and second set of sensors into the borehole by dividing L by a time T it takes for the second set of sensors to measure a same borehole geometry as the first set of sensors where ROP=L/T. ### Claim 13 (depends on 1) The method according to claim 1, wherein a sensor in the plurality of sensors is not operable. ### Claim 14 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. ### Claim 15 (depends on 14) The apparatus according to claim 14, wherein carrier comprises a bottom hole assembly (BHA). ### Claim 16 (depends on 15) The apparatus according to claim 15, wherein the plurality of sensors is evenly distributed about a circumference of the BHA. ### Claim 17 (depends on 15) The apparatus according to claim 15, wherein the plurality of sensors is unevenly distributed about a circumference of the BHA. ### Claim 18 (depends on 14) The apparatus according to claim 14, wherein the plurality of sensors comprises a first set of sensors spaced a distance L from a second set of sensors along a longitudinal axis of the borehole. ### Claim 19 (depends on 14) The apparatus according to claim 14, wherein the plurality of sensors comprise acoustic transducers. ### Claim 20 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.