Optimizing of Centralizer Distribution
Authors: Fonseca Carlos Fernando Humbert , Salies Jacques Braile 
Published: December 2007

Abstract
There are two procedures for the distribution of centralizers along the casing: rules o thumb for vertical wells and the widespread theoretical model developed in API SPEC 10D. This paper presents a new approach for placement of centralizers. The casing deflection is modelled in more realistic way than the API algorithm, through the use of better boundary conditions. A computer program was developed to integrate information on hole trajectory, casing properties and centralizer performance for optimizing centralizer performance for optimizing centralizer spacing. Some comparative examples with other models are presented. The results of the proposed a algorithm are less conservative than proposed a algorithm are less conservative than those of the API model. This reduces the number of centralizers to be run in a particular well. particular well

Introduction
One of the most important aspects of the displacement efficiency of the drilling fluid by the cement slurry is the casing centralization in the well. The cement slurry tends to pass by the zone of least resistance to the flow, that is, through the widest part of the well-casing annulus, forming thus preferential circulation channels. This preferential circulation channels. This problem is critical for highly deviated wells. problem is critical for highly deviated wells. To correctly program a cementing job, the positioning of the centralizers must be positioning of the centralizers must be planned, looking for conditions more favorable planned, looking for conditions more favorable to the displacement of the cement slurry. This involves the analysis of the forces due to t he weight of the casing and of the bending forces due to the curvature of the well for the deflection calculation of the centralizer and the casing. The lateral force in the centralizers is obtained through the balance of all the forces in a 3-dimension space, similar to that which is a developed in the literature. The centralizer deflection is then calculated based on its restoring force. For the casing deflection between two centralizers a more realistic approach to the problem was utilized. To model the problem, a problem was utilized. To model the problem, a system with a bi-fixed beam was assumed, instead of a bi-supported beam according to API SPEC 10D. For the solution of the problem the theory described in Timoshenko was utilized.
This paper does not focalize aspects relating to Fluid Mechanic, such as the influence of descentralization on fluid velocity. It approaches the distribution of centralizers under the point of view of Strength of Materials.

EFFECT OF BUOYANCE ON AXIAL STRESS
One of the controversial aspects of the literature is the calculation of axial forces (compressive and tensile forces) along the casing.
There are basically two modellings widely utilized. The first theory considers the force extremity of string, generating a stress diagram of compressive forces in the lower section of the string and tensile forces in the upper interval. The second modelling considers that the stress diagram consists of tensile forces only, assuming that the tension is calculated based on the buoyanced weight of the string.
The first model is widely utilized in the determination of the neutral tension point and in problems of string buckling, The second, on its turn, is utilized in problems involving the calculation of the side forces on the bit and the stabilizers to evaluate the behavior of the bottom-hole composition of drill strings. This latter model was adopted in this work for the calculation of the stresses, that is, only tensile forces are present along the string.