Systems and Methods for Modeling Wellbore Trajectories

A computer implemented method for modeling a wellbore trajectory, comprising:

• calculating a tangent vector at each survey point within a wellbore using survey data at each respective survey point, the wellbore comprising two or more survey points;
• calculating a special normal vector and a special binormal vector at each survey point;
• calculating a block tridiagonal matrix using the tangent vector, the special normal vector, and the special binormal vector at each respective survey point;
• calculating a coefficient at each survey point in the direction of the special normal vector at the respective survey point and another coefficient at each survey point in the direction of the special binormal vector at the respective survey point using the block tridiagonal matrix;
• calculating a wellbore curvature at each survey point and a normal vector at each survey point using a first derivative of the tangent vector, the coefficient and the another coefficient at each respective survey point;
• calculating a tangent vector interpolation function for each interval between the survey points using the wellbore curvature, the tangent vector and the normal vector at each respective survey point;
• and
• determining the wellbore trajectory using each tangent vector interpolation function in a torque-drag drillstring model.

A computer readable medium having computer executable instructions for modeling a wellbore trajectory, the instructions being executable to implement:

• calculating a tangent vector at each survey point within a wellbore using survey data at each respective survey point, the wellbore comprising two or more survey points;
• calculating a special normal vector and a special binormal vector at each survey point;
• calculating a block tridiagonal matrix using the tangent vector, the special normal vector, and the special binormal vector at each respective survey point;
• calculating a coefficient at each survey point in the direction of the special normal vector at the respective survey point and another coefficient at each survey point in the direction of the special binormal vector at the respective survey point using the block tridiagonal matrix;
• calculating a wellbore curvature at each survey point and a normal vector at each survey point using a first derivative of the tangent vector, the coefficient and the another coefficient at each respective survey point;
• calculating a tangent vector interpolation function for each interval between the survey points using the wellbore curvature, the tangent vector and the normal vector at each respective survey point;
• and
• determining the wellbore trajectory using each tangent vector interpolation function in a torque-drag drillstring model.