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# Difference between revisions of "Rod and tubing design for PCP systems"

The rod string and tubing are important components of the overall progressing cavity pump (PCP) system. This page discusses considerations in the design of these systems.

In a PCP system, the rod string must be capable of carrying axial load and transmitting torque between the bottomhole pump and the surface drive. Therefore, rod-string design encompasses an evaluation of the axial tension and torque loading conditions for the full range of anticipated operating conditions. An appropriate size and grade of rod string can then be selected on the basis of appropriate design criteria, such as ensuring that the maximum calculated combined stress does not exceed the yield capacity or manufacturer’s recommended values. Fatigue-loading considerations must also be addressed in certain applications.

The axial load and torque at any location along a rod string is made up of several different components (Fig. 1). Several major load components (pump hydraulic torque and pump axial load) are applied to the rod string at the pump; others (resistive torque and rod weight) are developed in a distributed manner along the length of the rod string. In almost all cases, the rod-string axial load and torque are maximum at the polished-rod connection at surface. Rod-string axial load at any location is equal to

where,

Fr = rod-string axial load (N [lbf]),

Fp = pump pressure load (N [lbf]),

ΣFw = sum of rod-string weight below location (N [lbf]),

ΣFu = sum of uplift forces below location (N [lbf]).

Rod-string weight is a function of the unit weight and vertical length of the rod string. The uplift forces result from fluid flow effects, as discussed previously. The pump pressure load results from the differential pressure across the pump acting on the pump rotor and is analogous to the plunger load in a beam pump. There has been some controversy over how this load develops on the rotor, and several different formulations have been published. One correlation that provides a reasonable approximation of the pump pressure load is as follows[1]:

where,

Fp = pump pressure load (N [lbf]),

pd = pump discharge pressure (kPa [psi]),

pi) = pump intake pressure (kPa [psi]),

d = nominal rotor diameter (mm [in.]),

e = pump eccentricity (mm [in.]),

dr = rod-string diameter (mm [in.]),

C = constant (7.9 × 10–4 [0.79]).

At any rod-string location, the torque is equal to

where,

Tr = rod-string torque (N•m [ft•lbf]),

Th = pump hydraulic torque (N•m [ft•lbf]),

Tf = pump friction torque (N•m [ft•lbf]),

Tv = viscous pump torque (N•m [ft•lbf]),

ΣTR = sum of rod-string resistive torque below location (N•m [ft•lbf]).

The pump torque components were discussed above. Resistive torque is usually smaller than the other two components but should be considered in high-fluid-viscosity applications.[2]

Rod-string axial loads increase with increases in well depth, rod-string diameter, and pump displacement. In applications with high fluid viscosities, changes in axial load with flow rate depend on the offsetting effects of the flow losses and rod-string uplift forces. Rod-string torque increases with increases in pump differential pressure, pump displacement, and pump friction. In applications with high fluid viscosities, torque will increase with both flow rate (because of higher flow losses that increase the pump discharge pressure) and rotational speed (because of an increase in resistive torque).

### Combined stress

The combined loading of a rod string (i.e., rod body) as a result of axial load and torque can be represented by the effective (Von Mises) stress calculated as follows:

where

σe = effective stress (MPa [ksi]),

Fr = rod-string axial load (N [lbf]),

Tr = rod-string torque (N•m [ft•lbf]),

dr = rod-string diameter (mm [in.]),

C1 = constant (16.0 or [1.6 × 10–5]),

C2 = constant (7.680 × 108 or [0.1106]).

Because the connections (couplings) used in standard rods are usually designed to have greater strength than the rod body, only the effective stresses of the rods typically need to be checked. However, proper makeup during installation is essential to ensure that the connections will function as designed by the manufacturers and provide the specified minimum load capacity. Some vendors offer sucker rods with reduced connection sizes (e.g., 25.4 mm [1 in.] rods fabricated with 22.2 mm [7/8 in.] pin connections); connection capacity can be the limiting factor in such cases. Fig. 2 shows the magnitude of the maximum effective stress that develops in a 25.4 mm [1 in.] rod string for a wide range of axial load and torque conditions. These results clearly show that effective stress is primarily a function of torque and that the impact of tension on the stress magnitude at lower torque values is normally of little consequence. From these results, it becomes quite evident that there is little advantage to using tapered rod strings in PCP applications.

In contrast to the inherent cyclic rod stress that occurs in beam pumping, the rod stresses in PCP applications tend to be relatively constant. As a result, the effective rod stresses may approach the yield stress of the rod material without causing failures in PCP applications, although fatigue induced by bending is an issue in directional and horizontal wells (see below). The minimum yield stress for Grade D sucker rods is 690 MPa [100 ksi], although several manufacturers also offer higher-strength grades with yield strengths up to 860 MPa [125 ksi]. For continuous-rod products, the minimum yield stress typically ranges from 586 MPa [85 ksi] at the low end to 790 MPa [115 ksi] for the higher-strength materials. The most common continuous-rod size is 25.4 mm [1.0 in.].

In PCP system design, rod loading should be evaluated for the full range of anticipated operating conditions to ensure that the selected rod string will have adequate capacity. It is advisable to use at least a 20% safety factor in rod sizing. This will allow for unanticipated torque increases that might be brought about by such factors as sand slugs, stator swelling, or startup friction. In addition, it will provide a margin of safety in the case of rod-strength reductions caused by rod-body wear or corrosion damage. Note that a 20% decrease in rod diameter can produce a 100% increase in rod stress and a 50% reduction in the load capacity of the rod.

### Rod string fatigue

It is well established that mechanical components subjected to alternating loads are susceptible to metal fatigue, even if the peak stress level in the material is well below the yield strength. The fatigue life of a component is affected by the average (mean) stress it experiences, the magnitude of fluctuations in the applied stress, and the frequency of the stress fluctuations. Load fluctuations, coupled with a high mean stress, result in a more severe fatigue situation than in a load case with fluctuations of a similar magnitude but negligible mean stress. This is important in the context of PCP applications, which usually will involve a high mean stress in the rod string. Most steels exhibit an endurance limit, which corresponds to the maximum alternating stress that will result in an “infinite” fatigue life (i.e., for polished materials without any corrosion). Designing rod strings for alternating stress levels below the endurance limit is an excellent design criterion.[3][4]

The operating conditions in many PCP applications expose rod strings to severe load fluctuations. Variations in pump discharge pressure caused by gas in the production tubing or increases in pump friction as a result of sand or fluid slugs can cause significant fluctuations in pump torque and axial load. However, the use of PCP systems in directional wells typically presents a more critical fatigue situation, because the rods are subjected to cyclic bending stresses at a frequency matching the rotational speed of the pump. Given the typical operating speeds of PCPs, the number of loading cycles can reach several million in a relatively short time (weeks or months). Fatigue analyses should be considered when these loading conditions are expected. In calculations of fatigue life, both the high frequency (i.e., bending effects in deviated wells) and low frequency (e.g., gas slugging effects) should be considered, given the different impacts they may have on stress levels.

## Rod string/tubing wear

Rod-string and tubing wear is an important consideration in the design of surface-driven PCP systems for directional, slant, and horizontal wells. The rod-string configuration, magnitude of the contact loads that develop between the rod string and tubing, produced-fluid conditions, and rotational speed of the rod string all interact to determine the wear mechanisms that will predominate and the corresponding component wear rates that will occur in different circumstances. From a design perspective, the goal is to assess the potential for wear problems and then to select a PCP system configuration that will maximize the service life of the installation.

For standard rod strings, contact between the rod string and tubing tends to be concentrated at the couplings or rod guides, although rod-body contact can also develop under certain loading conditions. In contrast, continuous sucker rods tend to contact the tubing uniformly along the wellbore. As a result, the contact load magnitudes differ considerably between these two rod configurations for the same wellbore geometry and rod-tension conditions. Particularly for standard rods, contact loads can be quite high in moderate- to high-curvature well segments, such as the angle-build sections of directional and horizontal wells. Also, well shapes that allow the tension/curvature contact loading to act in tandem with the gravity loads acting on the rod string (common in slant wells) can be particularly prone to wear problems. Fig. 3 and Fig. 4 present charts that can be used to estimate contact loads for standard and continuous rod strings, respectively, as a function of the well-curvature and rod-tension conditions.

Field experience[5] has shown that tubing wear rates correlate with(in decreasing order)

• Sand cut
• Centralizer type
• Rotational speed
• Water cut

In general, tubing wear rates increase exponentially with increasing sand cut (to a limit) and linearly with increasing contact load. Because of reduced lubrication, wear rates may increase significantly in situations in which the water cut increases substantially. Coated centralizers exhibit lower wear rates than standard couplings, with the degree of reduction being a function of the coating material. Note that field experience has shown some coating materials to be prone to the embedding of sand, which resulted in accelerated instead of reduced tubing wear rates. Spin-thru centralizers eliminate tubing wear very effectively as long as they remain functional. Because of the much lower uniform contact loads, tubing wear rates associated with continuous rod tend to be substantially (e.g., 5 to 20 times) lower than standard rod strings with metal couplings (material hardness and size factors play a role in the reduction). In applications using high-volume PC pumps and large-diameter standard rods, the increased surface velocity of the couplings may contribute to a form of hydrodynamic lubrication that tends to reduce wear rates relative to the expected rates based on the load conditions involved.

Although failures resulting from rod-string/tubing wear usually occur infrequently in vertical-well applications, failures are not uncommon within weeks or even days in directional or slant wells producing sandy fluids. Although there are costs associated with wear prevention (centralizers, continuous-rod or tubing rotator systems), they are often justified by the increased workover and equipment replacement costs (e.g., couplings/centralizer and tubing) that would otherwise be incurred in such cases. In many cases, repeated failures occur because of the operating practices used and the lack of data collected during workovers to characterize the source and locations of the wear problem properly. Operators must develop an understanding of wear processes and become familiar with the workover histories and operating characteristics of a variety of wells that have experienced wear failures to become effective at designing, equipping, and operating wells to prevent wear failures.

One of the most common locations for severe rod/tubing wear is the first couple of joints above the pump. In many instances, failures have occurred in this section of the well despite the well curvature and rod tensions being higher at various uphole locations. The increased wear rates directly above the pump can be attributed to the eccentric motion of the rotor, which may cause the rod string directly above the pump to develop an impacting/rotating interaction with the tubing. This interaction results in a more severe wear mechanism. The use of robust rod centralizers as opposed to standard couplings is recommended for at least the first two or three rod connections above the pump. Ensuring that a full-length standard rod (7.6 m [25 ft]), as opposed to a short pony rod, is attached directly to the pump rotor is important. The pony rod may restrict the required orbital motion of the rotor head, causing damage to the pump stator or failure of the rotor pin.

## Pump speed considerations

As the equipment has improved and operators have gained familiarity with PCP systems, pump operating speeds have increased substantially. Although the initial heavy oil well installations were typically run at speeds between 30 and 100 rpm, speeds in the 300 to 500 rpm range are now common, and some operators have been known to produce high-water-cut wells at speeds up to 1,000 rpm. Generally, speeds exceeding 500 rpm are not recommended because they typically lead to reduced pump and surface equipment life, increased potential for sucker-rod fatigue failures, and vibration problems.

### Vibrations

Rod strings commonly experience excessive vibrations within certain speed ranges because of the resonant frequencies of the system. The potentially harmful vibrations can usually be minimized by adjusting the speed slightly up or down. Some speed control systems even allow the locking out of frequencies that cause harmonic problems. However, it is important to recognize that the resonant frequencies of the system will likely change over time with variations in the load and fluid flow conditions. Harmonics are an especially important consideration for the portion of the rod string directly above the pump that naturally experiences a “whipping” action because of the orbital motion of the rotor. The various factors influencing the severity of the whipping motion include the mass and eccentricity of the rotor, the extent to which the rotor sticks out above the stator, the well configuration, operating speed, anchored vs. unanchored tubing, and rod-string configuration. At higher speeds, this whipping action can lead to accelerated rod and tubing wear and fatigue failures of the sucker rod. In wells that experience repeated problems, additional rod centralization or different types of centralizers should be used.

### Damaged caused by shutdowns

Ensuring that PCP installations are equipped with effective braking systems and tubing-string torque anchors becomes very important for high-speed operations, particularly in deeper wells. These devices help to prevent failures associated with parted rod or tubing strings and surface equipment damage during shutdowns.

### Tubing string failures

Tubing-string failure is another problem that has been encountered in some higher-speed PCP applications. The failures were characterized by a parting of one or more tubing joints at the last thread on the pin adjacent to a coupling. The failures occurred at many different locations in the wells, including near surface, midstring, and above the pump, and attempts to solve the problem with tubing anchors and tubing centralizers simply led to a subsequent failure at another location in some cases. The failures occurred after only a few weeks in some wells and after many months in others. Available anecdotal information suggests that the problems were more prevalent in wells with:

• Large-volume pumps
• High speeds
• Improper rotor space-out (i.e., substantial rotor stickup above the stator)

The evidence points to tubing fatigue failure induced by vibration. Consideration should be given to possible corrosion-enhanced fatigue. Possible remedies may include changes in pump speed or pump seating depth.

## References

1. Matthews, C.M., Skoczylas, P., and Zahacy, T.A. 2001. Progressing Cavity Pumping Systems: Design, Operation and Performance Optimization: Short Course Notes, CFER Technologies.
2. Blanco, L.B. and Ribeiro, P.R. 1999. Finite Element Modeling of Heavy Oil Production Using PCP. Presented at the Latin American and Caribbean Petroleum Engineering Conference, Caracas, Venezuela, 21-23 April 1999. SPE-53961-MS. http://dx.doi.org/10.2118/53961-MS.
3. Shigley, J.E. 1986. Mechanical Engineering Design, 227-281. New York City: McGraw-Hill Book Co. Inc.
4. Bannantine, J.A. et al. 1990. Fundamentals of Metal Fatigue Analysis. New York City: Prentice Hall.
5. Matthews, C.M. and Dunn, L.J. 1993. Drilling and Production Practices To Mitigate Sucker-Rod/Tubing-Wear-Related Failures in Directional Wells. SPE Prod & Oper 8 (4): 251-259. SPE-22852-PA. http://dx.doi.org/10.2118/22852-PA.