A method for drilling, comprising steps of:
- extending a borehole from a surface location to a borehole end with a drill string being comprised of a bottom hole assembly with a drill bit,
- wherein the drill bit is positioned on the bottom hole assembly at said borehole end so as to set a bit location,
- wherein said surface location is comprised of a surface sensor,
- wherein said bottom hole assembly is comprised of a downhole sensor at a downhole location,
- wherein said downhole sensor is separated by a plurality of segments from said bit location,
- wherein said plurality of said segments has a length S, said bit location and said downhole locations being separated by said length S,
- wherein each segment has a segment length s less than said length, and
- wherein the step of extending is comprised of following steps:
- Step A:
- setting said drill bit at an initial location (K) in the borehole, said bit location being at said initial location K, said downhole location being at a K−S location;
- Step B:
- measuring with said surface sensor at said surface location for said bit location at said initial location (K) so as to determine an initial location (K) surface sensor measurement;
- Step C:
- measuring with said downhole sensor at said downhole location for said bit location at said initial location (K) so as to determine a location (K−S) downhole sensor measurement;
- Step D:
- applying an initial Kalman filter to said initial location (K) surface sensor measurement and said location (K−S) downhole sensor measurement, so as to generate a projection of said borehole end for steering said drill bit,
- wherein said initial Kalman filter is comprised of an initial error correction based on said initial location (K) surface sensor measurement and said location (K−S) downhole sensor measurement;
- Step E:
- moving said drill bit to a location (K+(n)s) in the borehole according to the projection of Step D, said bit location being at said location (K+(n)s), said downhole location being at a (K−S+(n)s) location,
- wherein n is a positive integer;
- Step F:
- measuring with said surface location sensor at said surface location for said bit location at said location (K+(n)s) so as to determine a location (K+(n)s) surface sensor measurement;
- Step G:
- measuring with said downhole sensor at said downhole location for said bit location at said location (K+(n)s) so as to determine a location (K−S+(n)s) downhole sensor measurement;
- Step H:
- applying a first level adjusted Kalman filter to said location (K+(n)s) surface sensor measurement and said location (K−S+(n)s) downhole sensor measurement, so as to generate a first level adjusted projection of said borehole end for steering said drill bit,
- wherein said first level adjusted Kalman filter is comprised of a first level adjusted error correction based on said initial location (K) surface sensor measurement, said location (K+(n)s) surface sensor measurement, and said location (K−S) downhole sensor measurement;
- Step I:
- repeating the Steps E-H until (n)s is equal to S, wherein said projection of Step D is replaced with a corresponding first level adjusted projection of a respective Step H during a subsequent step of repeating Step E;
- Step J:
- moving said drill bit to said location (K+(n)s) in the borehole according to the corresponding first level adjusted projection of the respective repeated Step H when (K+(n)s) is equal to (K+S), said bit location being at said location (K+(n)s), said downhole location being at said (K−S+(n)s) location when (K−S+(n)s) is equal to (K);
- Step K:
- measuring with said surface location sensor at said surface location for said bit location at said location (K+S) so as to determine a location (K+S) surface sensor measurement;
- Step L:
- measuring with said downhole sensor at said downhole location for said bit location at said location (K) so as to determine a location (K) downhole sensor measurement;
- Step M:
- applying a second level adjusted Kalman filter to said location (K+S) surface sensor measurement and said location (K) downhole sensor measurement, so as to generate a second level adjusted projection of said borehole end for steering said drill bit,
- wherein said second level adjusted Kalman filter is comprised of a second level adjusted error correction based on said initial location (K) surface sensor measurement, said location (K+(n)s) surface sensor measurement, said location (K+S) surface sensor measurement, said location (K−S) downhole sensor measurement and said location (K) downhole sensor measurement;
- Step N:
- moving said drill bit to a location (K+S+(z)s) in the borehole according to the second level adjusted projection of Step M, said bit location 26 being at said location (K+S+(z)s), said downhole location being at said (K+(z)s) location,
- wherein z is a positive integer;
- Step O:
- measuring with said surface location sensor at said surface location for said bit location at said location (K+S+(z)s) so as to determine a location (K+S+(z)s) surface sensor measurement;
- Step P:
- measuring with said downhole sensor at said downhole location for said bit location at said location (K+(z)s) so as to determine a location (K+(z)s) downhole sensor measurement;
- Step Q:
- applying a third level adjusted Kalman filter to said location (K+S+(z)s) surface sensor measurement and said location (K+(z)s) downhole sensor measurement, when z is equal to n, so as to generate a third level adjusted projection of said borehole end for steering said drill bit,
- wherein said third level adjusted Kalman filter is comprised of a third level adjusted error correction based on said initial location (K) surface sensor measurement, said location (K+(n)s) surface sensor measurement, said location (K+S) surface sensor measurement, said location (K+S+(z)s) surface sensor measurement, said location (K−S) downhole sensor measurement, said location (K−S+(n)s) downhole sensor measurement, said location (K) downhole sensor measurement, and said location (K+(z)s) downhole sensor measurement;
- repeating the Steps N-Q for completing the borehole, wherein the second level adjusted projection of Step M is replaced with a corresponding third adjusted projection of a respective Step Q during the step of repeating Step N.