Modeling of a detailed bow spring centralizer description in stiff-string torque and drag calculation

Abstract

Flexible bow spring centralizers are commonly used in the drilling industry to ensure a good centralization of casings inside the borehole. A bow spring centralizer consists of multiple bows evenly spaced around the tubular. They are attached to the casing at multiple locations via connections or rings, and run-in hole such that the bows are sliding against the borehole. To provide a good centralization, the bows must be stiff enough to push the casing away from the borehole. Also, it must be flexible enough to avoid large contact forces and consequently friction forces that can cause excessive drag. This paper aims to present a theoretical model for bow-spring centralizers and its implementation in a stiff-string torque and drag model based on the finite element method.Our modeling approach assumes that the flexible centralizer bows are identical. Each bow acts independently from the others and could be in contact with the borehole or not, depending on the lateral displacement and orientation of the centralizer. The bow force follows a power law based on a constant stiffness and a stiffness power coefficient that are computed based on test measurements provided by the manufacturer.When introduced in a stiff-string torque and drag model, the contact forces are computed on each individual bow. For drag forces, the bows are assumed to be non-rotating inside the borehole, so the axial friction force at a bow spring is related to the algebraic sum of all bow contacts. When the casing is rotating inside the centralizer, a tangential friction force is generated between the casing and bow spring rings. It is related to the resultant contact force i.e., the vector sum of all bow contacts.An example of the calibration for a bow-spring centralizer is studied in this paper. The theoretical bow-spring model showed its capacity to have a good interpretation of the measurements. It also showed the importance of specifying the testing condition with regards to the possible clearance between the casing and centralizer rings. The finite element torque and drag model is firstly validated against another model. When applied to a case study of running in hole a casing string with bow-spring centralizers, the model shows its effectiveness to describe the casing centralization along the wellbore as well as the tension variations at the surface.