Anti-collision well trajectory design
Techniques for determining trajectories for a plurality of wells while avoiding collision between wells are presented. The techniques can include determining a zone of uncertainty for individual wells of the plurality of wells, determining a minimum separation factor for individual wells of the plurality of wells, determining a gradient of a separation factor for at least one pair of wells of the plurality of pairs of wells, updating a nudge position for at least one well, and providing nudge positions for the individual wells of the plurality of wells.
1. A computer-implemented method of determining trajectories for a plurality of wells while avoiding collision between wells, the method comprising:
determining, by one or more processors of the computer, a zone of uncertainty for individual wells of the plurality of wells, whereby a plurality of zones of uncertainty are determined, and wherein each of the plurality of zones of uncertainty comprises a range of potential deviated locations for a location of a borehole of the respective individual well with respect to an expected location of the borehole;
determining, by the one or more processors of the computer, based on the plurality of zones of uncertainty, a minimum separation factor for individual wells of the plurality of wells, whereby a plurality of minimum separation factors is determined, and wherein determining the minimum separation factor for a respective individual well comprises:
determining a plurality of separation factors for the respective individual well, wherein the plurality of separation factors includes a separation factor for each pair of the respective individual well and another well of the plurality of wells, and wherein determining the separation factor for each respective pair is based on a distance between a first center of the respective individual well and a second center of the other well, a first zone of uncertainty of the respective individual well, and a second zone of uncertainty of the other well; and
determining the minimum separation factor from the plurality of separation factors;
determining, by the one or more processors of the computer, a gradient of a separation factor for at least one pair of the respective individual well and other well based on the respective plurality of separation factors, first zone of uncertainty, and second zone of uncertainty;
updating, in a memory system of the computer, a nudge position for at least one well of the plurality of wells, based on the separation factor gradient and the plurality of separation factors;
providing, by the one or more processors of the computer, based on the updating, nudge positions for the individual wells of the plurality of wells; and
outputting, by the one or more processors of the computer, a set of recommended collision-free nudging vectors to a display of the computer.
2. The method of claim 1 , wherein the nudge positions for the individual wells of the plurality of wells cause the individual wells to avoid an obstacle.
3. The method of claim 1 , wherein the nudge positions for the individual wells of the plurality of wells cause at least one well to intersect a target.
4. The method of claim 1 , wherein the plurality of wells comprises at least three wells.
5. The method of claim 1 , wherein the plurality of minimum separation factors is based on an oriented separation factor formula.
6. The method of claim 1 , wherein at least one zone of uncertainty of the plurality of zones of uncertainty lies in a plane and comprises at least one of an ellipse or a pedal curve.
7. The method of claim 1 , wherein the updating the nudge position comprises updating a position matrix with a move matrix comprising a plurality of nudge vectors.
8. The method of claim 1 , further comprising iterating, prior to the providing, the determining the zone of uncertainty, the determining the minimum separation factor, the determining the gradient of the separation factor, and the updating, until a stop condition occurs.
9. The method of claim 8 , wherein the stop condition comprises at least one of a global minimum separation factor being above a predetermined threshold or a number of iterations exceeding a predetermined iteration ceiling, wherein the global minimum separation factor is based on the plurality of minimum separation factors.
10. The method of claim 1 , further comprising not updating a nudge position for at least one well based on its minimum separation factor exceeding a threshold.
11. A computer system for determining trajectories for a plurality of wells while avoiding collision between wells, the system comprising at least one electronic processor that executes instructions to perform operations comprising:
determining, by the at least one electronic processor, a zone of uncertainty for individual wells of the plurality of wells, whereby a plurality of zones of uncertainty are determined, and wherein each of the plurality of zones of uncertainty comprises a range of potential deviated locations for a location of a borehole of the respective individual well with respect to an expected location of the borehole;
determining, by the at least one electronic processor, based on the plurality of zones of uncertainty, a minimum separation factor for individual wells of the plurality of wells, whereby a plurality of minimum separation factors is determined, and wherein determining the minimum separation factor for a respective individual well comprises:
determining a plurality of separation factors for the respective individual well, wherein the plurality of separation factors includes a separation factor for each pair of the respective individual well and another well of the plurality of wells, and wherein determining the separation factor for each respective pair is based on a distance between a first center of the respective individual well and a second center of the other well, a first zone of uncertainty of the respective individual well, and a second zone of uncertainty of the other well; and
determining the minimum separation factor from the plurality of separation factors;
determining, by the at least one electronic processor, a gradient of a separation factor for at least one pair of the respective individual well and other well based on the respective plurality of separation factors, first zone of uncertainty, and second zone of uncertainty;
updating, in a memory system of the system, a nudge position for at least one well of the plurality of wells, based on the separation factor gradient and the plurality of separation factors;
providing, by the at least one electronic processor, based on the updating, nudge positions for the individual wells of the plurality of wells; and
outputting, by the at least one electronic processor, a set of recommended collision-free nudging vectors to a display of the system.
12. The system of claim 11 , wherein the nudge positions for the individual wells of the plurality of wells cause the individual wells to avoid an obstacle.
13. The system of claim 11 , wherein the nudge positions for the individual wells of the plurality of wells cause at least one well to intersect a target.
14. The system of claim 11 , wherein the plurality of wells comprises at least three wells.
15. The system of claim 11 , wherein the plurality of minimum separation factors is based on an oriented separation factor formula.
16. The system of claim 11 , wherein at least one zone of uncertainty of the plurality of zones of uncertainty lies in a plane and comprises at least one of an ellipse or a pedal curve.
17. The system of claim 11 , wherein the updating the nudge position comprises updating a position matrix with a move matrix comprising a plurality of nudge vectors.
18. The system of claim 11 , wherein the operations further comprise iterating, prior to the providing, the determining the zone of uncertainty, the determining the minimum separation factor, the determining the gradient of the separation factor, and the updating, until a stop condition occurs.
19. The system of claim 18 , wherein the stop condition comprises at least one of a global minimum separation factor being above a predetermined threshold or a number of iterations exceeding a predetermined iteration ceiling, wherein the global minimum separation factor is based on the plurality of minimum separation factors.
20. The system of claim 11 , wherein the operations further comprise not updating a nudge position for at least one well based on its minimum separation factor exceeding a threshold.