This paper presents a 3D vectorial approach model that is capable of calculating traction, bending, cutting effort and torsion stress which are combined through Von Mises’ theory and applied to Goodman fatigue stress analysis and contact load distribution for guide distribution.

Geometry is described by a 3D model that determines tangent, normal and binormal vectors. This model allows calculating Cartesian coordinates and curvature from wellbore drilling data: measured depth, inclination and direction. Using geometry and curvature it is possible to calculate alternating bending effort that adds and subtracts from traction, besides other orthogonal shearing stresses, like cutting effort stress generated by contact load and friction that is added to torsion. These types of stresses are combined and applied through the applicattion of Von Mises’ Theory and Goodman's Analysis in order to verify rod string sizing.

A three-dimensional model is applied to develop an algorithm to perform stress calculations and analysis in a deviated geometry well and this algorithm is included in design software that makes all the possible combinations of rod strings, pumps, tubings, driveheads and prime movers, selecting the best suited combination by the fuzzy logic method. Some well designs are presented and stress analysis results are compared with commercial software results and the differences are highlighted and analysed. These designs include geometry, curvature and stress components, torque, load, fraction of rod strenght, contact loads and guide distribution along well profile. The algorithm includes contact load calculations and optmized rod guide distribution. Applying this model, rod string performance and MTTF can be improved in deviated wells by taking into account stresses that appear in this type of well and they are frequently not considered.

This model combines additional existing stresses in a deviated well like: bending, cutting shear, contatc friction stresses and compose weight and curvature contact loads resultant in inclined plane curve, in a more accurate approach. The fuzzy logic method, which automatically selects the best equipment combination, is another novelty.

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