Continuous geomechanically stable wellbore trajectories

A computer program product, comprising a non-transitory computer readable medium having a computer readable program code embodied therein, said computer readable program code containing instructions for causing a computer processor to:

• calculate a number of reachable position by drilling relative to a starting position wherein the number of reachable positions by drilling is 2 or greater and each reachable position by drilling is a first distance from the starting position;
• determine hoop stresses around a circumference of a borehole at each reachable position by drilling from a geomechanical model of the subterranean formation using a poro-elastic solution based on an inclination-azimuth plane of the borehole and principal stresses from the geomechanical model at each reachable position;
• select a set of stable positions from the reachable positions by drilling by determining whether all the hoop stresses around the circumference of the borehole at each reachable position by drilling have a magnitude of shear or tensile failure less than a predetermined magnitude using a Mohr-Coulomb failure criterion;
• repeat the calculate, determine and select instructions for each of the stable positions wherein each stable position is a new starting position until a final position is reached;
• and
• outputting results of the iterative calculate, determine and select instructions in tangible form.

Apparatus for calculation of a continuous geomechanically stable trajectory in a subterranean formation comprising:

• a machine that calculates a number of reachable positions by drilling relative to a starting position wherein the number of reachable positions by drilling is 2 or greater and each reachable position by drilling is a first distance from the starting position;
• determining hoop stresses around a circumference of a borehole at each reachable position by drilling from a geomechanical model of the subterranean formation using a poro-elastic analytic solution based on an inclination-azimuth plane of the borehole and principal stresses from the geomechanical model at each reachable position;
• selecting a set of stable positions from the reachable positions by drilling by determining whether all the hoop stresses around the circumference of the borehole at each reachable position by drilling have a magnitude of shear or tensile failure less than a predetermined magnitude using a Mohr-Coulomb failure criterion;
• repeating the calculating, determining and selecting for each of the stable positions wherein each stable position is a starting position until a final position is reached;
• and
• an interface that outputs results of the iterative calculating, determining and selecting elements in tangible form.

A method of drilling a borehole in a subterranean formation comprising the steps of:

• calculating a number of reachable positions by drilling relative to a starting position wherein the number of reachable positions by drilling is 2 or greater;
• determining hoop stresses around a circumference of a borehole at each reachable position by drilling from a geomechanical model of the subterranean formation using a poro-elastic analytic solution based on an inclination-azimuth plane of the borehole and principal stresses from the geomechanical model at each reachable position;
• selecting a set of stable positions from the reachable positions by drilling by determining whether all the hoop stresses around the circumference of the borehole at each reachable position by drilling have a magnitude of shear or tensile failure less than a predetermined magnitude using a Mohr-Coulomb failure criterion;
• repeating the calculating, determining and selecting steps for each stable position wherein each stable position is a starting position until a final position is reached;
• selecting at least one trajectory from the from the sets of stable positions;
• and
• employing a representation of the at least one selected trajectory to drill at least one borehole in the formation.