The Ultimate Sucker-Rod String Design Procedure

Abstract

A properly designed sucker-rod string should provide failure-free pumping operations for an extended period. Improper design of rod tapers can lead to early mechanical failures (rod breaks) with a complete termination of pumping action and an inevitable loss of production. Because of its prime importance in sucker-rod pumping technology several rod string design procedures based on different assumptions were developed in the past. Since most sucker rod breaks are fatigue failures the mechanical design of sucker-rod string must consider the cyclic nature of rod loading and the appropriate fatigue endurance limit of the rod material. This is why most string designs utilize the modified Goodman diagram for calculating the lengths of rod tapers.Available sucker-rod string design models calculate rod taper lengths that ensure proper operation without premature fatigue failures. Their common design problems are (a) defining the principle of taper length determination, and (b) calculating the true mechanical stresses along the string. The universally accepted principle of taper length calculations is to provide the same level of safety against fatigue failures in each taper section. Mechanical loads and stresses, on the other hand, are usually found in most of the design procedures from very approximate formulas. These loads, therefore, can greatly deviate from the true mechanical loads that would be measured in the rod string run in the well. The paper details the main features of available rod string designs and discusses their main characteristics; it provides a thorough comparison of designs involving the calculation of loads and stresses predicted from the solution of the damped wave equation. Using a predictive analysis program rod stresses are calculated that, plotted on the modified Goodman diagram, provide a proper comparison of the merits of the different rod string design methods.Rod strings designed by available design procedures usually do not have identical safety included in the different tapers. This is due to the improper calculation of rod string loads that form the basis of calculating rod taper percentages. Based on the evaluation of the different available rod string designs the paper introduces a novel procedure that estimates rod loads from the predictive solution of the damped wave equation during the design process. Since loads calculated that way simulate actual loads very accurately, the most important limitation of previous rod string design procedures is eliminated. Strings designed using the proposed model, therefore, will have identical safeties against fatigue failures in each taper; the new design model provides the ultimate safety over previous designs.

Simulation of the Sucker Rod Column Dynamics for Different Pumping Regimes

“…D [kN] where the piston diameter D is expressed in meters; is the friction force into extraction pipes that occurs because of the transport of the oil therethrough: (5) where: λ is the hydraulic loss coefficient (it can be considered λ=0.046, that is a typical value for rough pipes [5]); A p is the net sectional area of the piston; A t is the interior passage sectional area of the extraction pipes; L is the length of the sucker rod column and v is its speed; F o is the force due to the free oscillations of the sucker rod column that occur when changing the conditions from phase I to phase II and from phase III to phase IV. When changing the conditions from phase I to phase II, F o can be calculated with the relation [5]: (6) where: t 1 is the time corresponding to the crank angle ϕ 1 ; p is the pulsation of intrinsic oscillations of the sucker rod column (it can be calculated with the formula [5]: p=8000/ L); m is the total mass of the sucker rods; ν 1 is the speed of the polished rod when the crank angle is equal to ϕ 1 ;α=0.2 . T ; (T is the period of the pumping cycle); ψ=k t / (k t + k p ) where k p and k t are the elastic constants corresponding to the sucker rod column and to the extraction pipes column, respectively: (7) where: k pi and k ti are the elastic constants corresponding to the section i of the sucker rod column and to the extraction pipes column, respectively: (8) where: E is Young's modulus of the steel from which are made the sucker rods and the extraction pipes; l pi and l ti are the length of the section i of the sucker rod column and of the extraction pipes column, respectively, and A pi and A ti are the corresponding sectional areas.…”

“…Much of further research on the design and the behavior during operation of these installations focused mainly on the study of the dynamics of the sucker rod column and on issues related to the analysis and synthesis of the mechanism of the pumping units. In this respect, a number of interesting results that have strongly helped to the achievement of the research from this paper are presented in [5][6][7][8][9].…”

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

“…As a consequence, the basic objective of the design procedure (i.e., having identical SFs at the top of each taper) will not be met. This is a general problem with all known rod-string designs that stems from the fact that rod loads required in the design process are estimated from approximate formulas only, as proved by Takacs and Gajda (2013). The use of predicted loads obtained from the solution of the damped-wave equation, on the other hand, ensures the highest possible approximation of measured loads, and can thus provide a reliable foundation to further investigations.…”

Optimal Stress Calculations for Sucker Rod Pumping Systems

“….etc. the rod string might be more susceptible to failure at different locations of the taper, see [14,15].…”