Modeling of Acceptable Hole Curvature for Running Casing Strings - Preliminary Study
Authors: Lagreca Alejandro J. , Miska Stefan Z. , Sorem James R. 
Published: December 2007

Abstract
A mathematical model is presented to analyze insertion forces for casing strings in high hole curvatures (dogleg severity) and high deviation angles. This mathematical model allows simulation of forces acting on casing strings in short and long doglegs with constant curvature. The equations for predicting the acceptable hole curvature are obtained by modifying of an existing governing differential equation. An approximating function, which satisfies the geometrical boundary conditions, is proposed as a solution. This approximating function describes the equilibrium configuration of the casing centerline and provides a method to predict forces acting below the neutral point. The influence of hole curvature on these forces was simulated for some casing strings. Calculated forces are described and presented in graphical form.

Introduction
An effective casing weight that exceeds the friction forces is required when running a casing string. Estimation of the resisting loads is beneficial for well planning and selecting casing strings. In wellbores with high curvature (dogleg severity) or inclination, the friction forces can become quite high causing insertion problems (Fig. 1). Besides bending stresses due to curvature and compressive loads, sizable friction forces can produce compressive stresses in the casing that can cause plastic deformation and/or localized buckling of the casing string.
To resolve the effect of the friction forces on the casing running operation several practices have been developed. For instance: circulation and top-drive weight are used as contingency measure. Hydraulic tools are developed to assist the setting operation. Drag modeling is studied for projecting forces, or for calculating friction factors to determine the minimum requirements to successfully case a hole.
In 1988, Christian reported casing weights "lower than expected" while running a 10–3/4" casing string in a shallow and high-angle well. This author also reported that the location of the KOP proved important because it gave enough casing weight, accumulated in the vertical section, to push the casing.
In addition, in 1988, Maidla and Wojtanowicz introduced a procedure to calculate the coined term "borehole friction factor" through data analysis and mathematical modeling. This concept was used to calculate casing hook loads during either pulling-out or running-in. The borehole friction factors calculated for running-in were greater than for pulling-out. "Ledges, washouts or bridges causing by sloughing the wellbore would work against the insertion". These authors suggested that these effects might be called "borehole conditions" which are not related to mechanical friction.
In 1996, Payne and Abbasian reported casing weight losses by about 70 klbs while running a 9–5/8" casing in an ERD well. Several contingency measures were taken during insertion to regained weight. These authors attributed the running weight reduction to mechanical effects where they must be recognized and not combined with the frictional effects in one single factor.
In 1997, Batchelor, Edwards and Moyer modeled, designed and used an inverted tapered 7–5/8"x7" production casing for a shallow, long-reach well. These authors used drag modeling for simulating the running weights. The modeling revealed a high probability for casing the production hole with a single string.
Determination of the acceptable hole curvature for a given casing size is a proposed method to determine loads for well planning. Conversely, if the wellplan (shape) is given the method can be useful for selecting casing sizes. In principle, the method is based on Lubinsky's equation and simple cases were modeled considering short and long doglegs with constant curvature. A casing in a short dogleg is depicted in Fig. 2. The hole is inclined and composed by two sections: a straight section, AB and a curved section BC. P. 473^