Improved Rod String Taper Design

Abstract

This study presents an improved method for designing sucker rod taper percentages. percentages. The API RP11L is the usual source for sucker rod taper percentages. When it was last revised, in 1976, it was necessary to make several simplifying assumptions because the complete calculations were too laborious for hand calculation. Introduction With a personal computer, it is now possible to design accurate tapers for possible to design accurate tapers for each specific system with minimal computational time and effort. This paper presents the logic and formulae necessary to presents the logic and formulae necessary to design optimum taper percentages, with equal service factors, for any sucker rod system. A flow chart for a computer program is included. program is included. A brief history is given of the earlier methods of rod taper calculations. This study examines each method and describes why it was inadequate. Rod designs using equal service factors will have a significant impact on operating costs and system efficiency. The calculations for rod taper percentages need to be updated to the state of the art. The Equal Service Factor method:Eliminates the use of simplifying assumptions and permits the calculation of the optimum design, with equal service factors, for each system.Permits accurate calculations for rod tapers which include sinker bars.Provides a more accurate method for calculating the loads at the top of each taper. ROD STRING DESIGN FUNDAMENTALS The sucker rod string is a vital part of the pumping system, since it provides the link between the surface pumping unit and the subsurface pump. Proper design of the rod string has a great impact on the system efficiency. Rod failures always involve servicing costs and lost production. The proper design of rod strings assures good operating conditions and will reduce total production costs and increase income. To introduce the fundamentals of rod design, a discussion of the nature of rod loads and previous rod design methods will be given. Then a detailed discussion of the proper method of balanced taper rod design will be presented. Rod Loads The sucker rod string is a peculiar piece of mechanical equipment, having piece of mechanical equipment, having almost no analogies in man-made structures. Being several thousand feet long and having a maximum diameter of 1.25 inches, the solid steel rod string can be considered a perfect "slender bar". Since its weight is perfect "slender bar". Since its weight is distributed along its length, any section has to carry at least the weight of the rods below it. This results in stretch and suggests that an ideal construction would be a continuous taper from top to bottom. Since such a shape is impractical, the use of tapered strings with sections of decreasing diameters is a common design practice. practice. The most basic property of any sucker rod string is its elastic behavior. P. 605

An Enhanced Model for the Design of Tapered Sucker-Rod Strings

“…Neely's approach (Neely 1976) to load calculations includes buoyancy as well as dynamic loads for which he recommends an empirical correlation. The Gault and Takacs (1990) model is the only one that tries to include the effect of the force wave reflections in the rod string when calculating rod loads and finds the surface dynamic loads from API TR 11L (2008) calculations.…”

“…Setting the SFs equal in each taper, as done by West (1973a, b) and Gault and Takacs (1990), ensures the same amount of safety for every taper section. Rod strings designed this way have the same safety factor included in every taper and do not have any weak points.…”

“…The fatigue loading of the individual tapers, however, is different for the four designs. The models of West (1973a, b) and Gault and Takacs (1990) have their three points belonging to the three tapers located on SF ¼ constant lines; these strings are, therefore, uniformly loaded and have tapers designed with the same safety against fatigue failure. The string designed by Neely's procedure (Neely 1976) is not uniformly loaded because the three tapers have different SFs.…”

“…The best possible solution of the problem involves the calculation of rod loads from the solution of the damped-wave equation written on the rod string. This approach is justified by experience gained since the introduction of the wave equation in the late 1960s by Gibbs (1967), proving that the predictive solution of the damped wave equation gives loads that very closely match measurements. Because mechanical stresses in the rods must be calculated from "true" loads, the solution must include the effects of buoyant forces that occur on the different tapers (Lea et al 1995).…”

“…The latest design procedure proposed by Gault and Takacs (1990) is the only one that includes the effects of the reflections of force waves in the rod string when calculating rod loads. These dynamic loads are distributed along the string in proportion to the mass being moved.…”