Improved designs reduce sucker-rod pumping costs

Gabor Takacs
University of Miskolc
Hungary

To maximize profits from sucker-rod pumped wells, designs must aim at technically and economically optimum conditions.

Assessment of surface and downhole energy losses are basic considerations for improving system efficiency. It is important to properly select the pumping mode, such as the combination of plunger size, pumping speed, stroke length, and rod taper design. The best pumping mode maximizes lifting efficiency and, at the same time, reduces prime-mover power requirements and electrical costs.

Surface equipment operational efficiency can be improved with optimum counterbalancing of the pumping unit, and to achieve an ideal sucker-rod pumping system, a tapered rod string must have a proper mechanical design.

Rod pumping

Rod pumping has been a common form of artificial lift all over the world for a long time. Roughly two thirds of the world's producing oil wells are on this type of lift.

As shown in Fig. 1 [28383 bytes], two of the world's biggest producers, the U.S. and the former Soviet Union, need some kind of artificial lift on most wells.

Total wells in the two countries are considerably different (the former Soviet Union had less than one tenth the number of wells in the U.S.) but the proportion of wells artificially lifted is very similar.¹

Although total liquid volumes produced worldwide do not match the proportions shown in Fig. 1, sucker-rod pumping is still substantial.

In many countries, oil production economics are governed by the production costs for sucker-rod pumping. To maximize profits from rod-pumped wells under prevailing economics, designs must ensure optimum conditions.

Energy efficiency

The profitability of installations can be improved by reducing sucker-rod pump operating costs. Because electric motors drive most installations, electrical costs are an important consideration. Energy losses both downhole and on the surface must be minimized.

An overall efficiency formula, derived in the next part of this article, allows important conclusions to be drawn on determining the most efficient pumping system.

Downhole energy losses

The rod pumping system does its useful work while lifting a given amount of liquid from the bottom of the well to the surface. The hydraulic power is easily calculated with Equation 1 (see equation box) based on the depth of the effective lift and the liquid volume produced.

The sources of downhole energy losses in the sucker-rod pumping system are the pump, the rod string, and the fluid column. In the pump, frictional and hydraulic losses as well as liquid leakage take place. The rod string, while reciprocating in the tubing, rubs against the tubing wall, causing mechanical friction, especially in deviated wells.

Produced liquids impart damping forces on the rod string and cause other hydraulic losses as well. All these losses, in addition to the hydraulic power required for fluid lifting, must be overcome by the mechanical work performed by the pumping unit at the polished rod (Fig. 2 [25707 bytes]).

The energy required for operating the polished rod at the surface is thus the sum of the useful hydraulic work performed by the pump and the downhole energy losses. This power requirement is a basic pumping parameter called the polished-rod power or PRHP. It represents the mechanical power input to the pumping system at the polished rod and can be experimentally found from the area on a dynamometer card taken on the well.

The energy efficiency of the downhole components can be characterized by the relative amount of energy losses in the well. The parameter widely used for this purpose is called lifting efficiency and is the quotient of the useful hydraulic power and the power required at the polished rod, as shown by Equation 2.

Surface losses

On the surface, from the polished rod to the prime mover, mechanical energy losses occur at several places in the rod pumping system. Starting from the polished rod, frictional losses arise in the stuffing box, in the pumping unit's structural bearings, in the speed reducer (gearbox), and in the V-belt drive. It is customary to combine all these energy losses into a single mechanical efficiency hmech.

The prime mover, in most cases an electric motor, converts the electric energy input at its terminals into mechanical work at the motor's shaft and this involves certain inevitable losses. Thus, the electrical power to the motor is always greater than the mechanical power developed at the motor's shaft.

The power losses in an electric motor are classed as mechanical and electrical. Mechanical losses occur in the motor's bearings due to friction. Other mechanical losses include windage loss consumed by air surrounding the rotating parts.

Of the electrical losses, energy loss in the copper winding is the main one. This results in heating of the motor from the electrical current. Usually, an overall efficiency hmot represents all losses in the motor, which, for average electric motors range from 85 to 93%.

Optimum efficiency

If all energy losses occurring from the bottom of the well to the prime mover are considered, an overall efficiency for the pumping system can be defined. Because the system's useful work is represented by the hydraulic power used for fluid lifting, and the total energy input is proportional to the required electric power, the energy efficiency is found by Equation 3.

A more detailed equation can be derived if the individual efficiencies in the system components are substituted in Equation 3 to obtain Equation 4.

An investigation of this overall efficiency equation allows some basic conclusions to be drawn towards attaining a maximum energy efficiency in rod pumping.

First, the relative importance and the usual parameter ranges of the individual terms must be analyzed. Of the parameters included in the equation, the possible values of both the surface mechanical efficiency, hmech, and the motor efficiency, hmot, vary in narrow ranges. At the same time, their values are not easy to improve upon. That is why these values are not very significant for determining the system's total efficiency.

On the other hand, lifting efficiency can be considered as the governing factor because it varies in a broad range depending on the pumping mode selected. Thus, considerable improvements in overall energy efficiency can only be realized by maximizing lifting efficiency.

In summary, the basic requirement for achieving an optimum overall pumping efficiency is increasing the lifting efficiency. Because lifting efficiency mainly depends on the pumping mode selected (such as the combination of plunger size, stroke length, pumping speed, and rod string design), the proper choice of the pumping mode for sucker-rod pumping cannot be overemphasized.

When designing a new pumping system or improving the performance of an existing installation, this must be the primary goal of the rod pumping specialist's efforts.

Mode selection

The pumping mode of a sucker-rod pumping system is defined as the combination of pump size, polished-rod stroke length, pumping speed, and rod string design. The number of standard API pump sizes and stroke lengths is large and pumping speed can be varied within a broad range.

Because many rod-string taper combinations are available, a fairly great number of pumping modes may be possible. For producing a given amount of liquid, however, most of the theoretical pumping modes turn out to be impractical or uneconomical, but the elimination of these still leaves a multitude of options to consider.²

As described previously, the optimum design is chosen from among the remaining pumping modes based on the value of their lifting efficiencies and the one with the maximum hlift is selected.

Maximizing the lifting efficiency coincides with the case of setting the polished-rod power, PRHP, to a minimum. For lifting a given liquid volume from a given depth, such as for a given hydraulic power, lifting efficiency and PRHP are inversely proportional.

Application of this optimization concept, therefore, gives the most energy efficient and thus most economical pumping mode for producing the required liquid rate from the given pump setting depth.

A pumping system design with this principle results in minimum operating costs and in a system with maximum efficiency.

The following example1 illustrates the dominant effect of pumping mode selection on the efficiency of the pumping system. In this example, a pump is set at 6,000 ft with the liquid level at the pump and a desired liquid producing rate of 500 b/d.

The tubing string is anchored, and Grade D sucker rods are used with a service factor of 1.

From the multitude of possible pumping modes, the ones with the best and worst lifting efficiencies are given in Table 1. If the best mode is selected, the energy input at the polished rod is only slightly greater than the pump's hydraulic power, ensuring a lifting efficiency of over 94%.

The worst mode, on the other hand, requires almost three times as much energy as the best one for lifting the same amount of liquid from the same depth. It is also interesting to note that these two extreme pumping modes both require the same pumping unit size.

This example, therefore, demonstrates that large energy and operational cost savings can be realized by choosing the right pumping mode.

Additional calculation results are presented in Fig. 3 [29401 bytes] where maximum values of lifting efficiencies for different rod combinations are plotted vs. pump size. The curves clearly show that by increasing the pump size, the attained maximum lifting efficiency values increase for all tapers. Therefore, use of bigger plungers with correspondingly slower pumping speeds is always advantageous and results in lower energy requirements.

Fig. 3 proves also, in line with practical experience, that heavier rod strings (like API 85 or 86 instead of API 75 or 76) considerably increase power requirement for smaller pump sizes. As pump size increases, however, the difference in power requirement tends to be less pronounced.

This phenomenon is explained by the relative importance of rod string weight in the total pumping load because larger pumps involve greater fluid loads and thus rod string weight becomes a smaller fraction of the total rod load.

Counterbalancing

Proper counterbalancing of a pumping unit evens out the torsional loads on the speed reducer during the pumping cycle. Without counterbalancing, the torque loading on the gearbox would be high during the upstroke because of the high loads on the polished rod.

During the downstroke, on the other hand, the rod string falling in the produced fluid would drive the pumping unit resulting in a negative torque loading on the gear reducer.

Because no motor can operate under such heavily fluctuating loads, some means of counterbalancing the pumping unit had to be devised. These can take the form of beam or rotary counterweights or an air cylinder.

When counterbalancing a pumping unit, ideal counterbalance conditions are desired that can have many beneficial effects on operating the sucker-rod pumping system as follows:

• Gearbox size can be reduced when compared to an unbalanced condition.

• Required prime mover size is smaller.

• Maintenance costs decrease and equipment life increases with smoother operations from a properly balanced speed reducer.

The measure of the evenness of the torsional load on the gear reducer is the mechanical cyclic load factor (CLF). This is calculated by Equation 5 from the variation during the pumping cycle of the net torque on the reducer as the ratio of the root mean square and the average net torques.

Because of its practical and economical importance, optimum counterbalancing of pumping units is a commonly discussed topic. From the many practical solutions developed over the years, several different approaches must be mentioned.⁴ All of these methods try to find the maximum counterbalance moment satisfying one of the following criteria:

• The peak motor currents are equal during the up and downstroke.

• The peak net torques on the up and downstroke are equal.

• The required mechanical powers for the up and downstroke are equal.

• A minimum of the cyclic load factor is achieved.

Minimizing CLF

In this age of computers, the old field procedures for obtaining optimum counterbalance conditions must give way to theoretically more sound procedures. Thus, from the previously discussed models, the sucker-rod pumping specialist's first choice should be the one that minimizes the value of the cyclic load factor (CLF).

The merits of minimizing the CLF for achieving optimum counterbalance conditions are shown in Fig. 4 [31547 bytes], which displays calculated results for an example well.

All parameters are plotted against maximum counterbalance moment on the gearbox because this is the variable that can be changed at will by either moving the existing counterweights on the crank or by replacing them.

As seen in the figure, the CLF curve clearly exhibits a minimum at about 300,000 in.-lb for the given case.

This figure can also serve to compare the recommended and the field procedures. For this reason, the variations of the peaks of up and downstroke net torques are also plotted. The curve intersection represents the counterbalance moment required to set the two peaks equal. This meets one of the optimum counterbalance criteria mentioned previously.

The CLF value valid for this case is greater than the minimum CLF achieved by the recommended optimization model. Therefore, a proper approach to the optimization of counterbalance conditions is to find the counterbalance moment ensuring a minimum CLF.

Rod string design

A properly designed rod string should provide failure-free pumping operations for an extended period of time. Rod string design aims at determining:

• Rod sizes in the string

• Lengths of taper sections

• Rod material.

To find an ideal solution to the above problems, detailed calculations should consider actual well conditions. The two basic problems in rod string design concern how rod loads are calculated and what principle to use for determining taper lengths.

At the time of design, of course, the anticipated rod loads are not known, and they also depend on the taper lengths that are about to be determined. Therefore, one has to rely on approximate calculations to find probable rod loads that will occur during pumping.

Design principles

The early rod string design methods all use the simplifying assumption that the string is exposed to a simple tension loading. Examination of the rod loads during a complete pumping cycle, however, shows that the rod string is under cyclic loading.

The nature of the loading is pulsating tension because the entire string is under tension at all times, but rod stress levels change for the up and downstrokes. This is why, in contrast to early design principles, sucker-rod strings should be designed for fatigue endurance.

After the pioneering work of West, the string design procedure of Neely gained wide acceptance.^{5 6} It was adopted in 1976 by the American Petroleum Institute, and rod percentages calculated by this procedure were included in the editions of API RP 11L.⁷

Since then, the tables published by the API have been used to install thousands of rod strings, saving the time required for detailed string designs.

The API rod taper percentages, as revealed by several investigators, have some inherent errors. These are related to the assumptions that were used but never disclosed for calculating taper lengths.

The API taper percentages, as given in the RP 11L tables, do not vary with well depth, pumping speed, or stroke length. The only input variable is the plunger size. Taper lengths determined from the tables for actual conditions can considerably differ from those calculated with the original Neely procedure.

The discrepancies in rod taper percentages are illustrated in Fig. 5 [29756 bytes] for a two-taper string and a 1.5-in. plunger. The API taper percentages, as shown in the figure, do not vary with total string length or pumping speed. The differences between API tapers and actual calculation results are apparent and lead to the conclusion that accurate rod string designs should be based on actual pumping conditions.

Recommended procedure

A detailed review of sucker-rod string design methods reveals that each method contains either questionable or very simplifying assumptions. The early designs do not consider fatigue loading and are thus inadequate for designing rod strings for cyclic loading. West uses the almost obsolete Mills acceleration factor for calculating dynamic forces.⁵

Neely's design principle and his proposal for the distribution of dynamic loads are also subject to question.⁶ The API tables, as shown previously, were developed for unknown conditions and cannot be used for design purposes without significant errors.⁷

Fig. 6 [26676 bytes] compares these rod design procedures for an example well where rod stresses in the top section of each taper are plotted on the modified Goodman diagram. Early designs that did not consider fatigue loading clearly indicate an unequal loading of the individual tapers. As seen, fatigue loading on the lower tapers is significantly higher than on upper ones. Lower sections are thus more likely to experience premature failure.

The Neely design, on the other hand, gives rod tapers with the upper sections being relatively more loaded.

The best rod string design, of course, would eliminate these disadvantages and would calculate rod loads in each taper section using the solution of the damped wave equation. This approach, however, would involve very complex iterative procedures requiring prohibitive computation time.

To solve this problem, the method of Gault and Takacs gives a more theoretically sound design procedure than previous designs while requiring only moderate computational time.⁸ The goal of this string design method is to have the same degree of safety in every taper section.

As seen in Fig. 6, actual service factor values are the same for all taper sections, and the rod string is subjected to a uniform level of fatigue loading along its entire length.

References

1. Takacs, G., Modern Sucker-rod Pumping, Penn-Well Publishing Co., Tulsa, 1993.

2. Gault, R.H., "Designing a Sucker-Rod Pumping System for Maximum Efficiency," SPE Production Engineering. November 1987, pp. 284-90.

3. Takacs, G., "Program optimizes sucker-rod pumping mode," OGJ, Oct. 1, 1990, pp. 84-90.

4. Gipson, F.W., and Swaim, H.W., "The Beam Pumping Design Chain," 31St Annual Southwestern Petroleum Short Course, Lubbock, Tex., 1984, pp. 296-376.

5. West, P.A., "Improving Sucker-Rod String Design," Petroleum Engineer, July 1973, pp. 68-77.

6. Neely, A.B., "Sucker-Rod String Design," Petroleum Engineer, March 1976, pp. 58-66.

7. Recommended Practice for Design Calculations for Sucker-Rod Pumping Systems (Conventional Units), API RP llL 4th Edition.

8. Gault, R.H., and Takacs, G., "Improved Rod String Taper Design," Paper No. SPE 20676, 65th SPE Annual Technical Conference and Exhibition, New Orleans, Sept. 23-26, 1990.

Bibliography

Takacs, G., "Improved Installation Design Increases the Efficiency of Sucker-Rod Pumping Systems," Distinguished lectures at various SPE section meetings, 1996.

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