Gabor Takacs
Technical University of Miskolc
Miskolc, Hungary
Direct energy costs for sucker-rod pumping can be optimized by selecting the right pump size, stroke length, and pumping speed for the required liquid production rate.
Calculation procedures for a computer program are developed for optimizing the design of conventional pumping units. The developed program is an alternative to API Bulletin RP 11L and improves the accuracy of pumping system design.
ARTIFICIAL LIFT
The aim of artificial-lift design is to ensure the most economical means of liquid production within the constraints imposed by the given well and reservoir. For sucker-rod pumping this usually means selecting the right size of pumping unit and gear reducer, as well as determining the pumping mode to be used. Pumping mode variables include plunger size, stroke length, and pumping speed.
The size of the pumping unit and gear reducer can only be selected if the operating conditions (loads, torques, etc.) are known. These can vary with different pumping modes.
Therefore, the basic task of design lies in the optimal determination of the pumping mode.
For surface pumps (e.g., mud pumps), the calculation of the required plunger size, stroke length, and speed is quite straightforward. This is because pump displacement is a direct function of these variables which can be changed at will.
The situation is dramatically different in the case of sucker-rod pumps because downhole-pump stroke length is far from being equal to the stroke length set at the surface. This is due to the plunger being moved by a long elastic rod string.
Pump displacement cannot be directly determined from surface parameters, and this condition is a very basic problem of a sucker-rod system design.
The calculation of the liquid rate produced by a sucker-rod pump relies on the accurate determination of plunger stroke length from surface data. A well-proven method for actual stroke-length calculations is the procedure described in API RP 11 L.1 Generally, this calculation model gives reliable predictions because it accounts for most of the effects that impact plunger movement.
Therefore, API RP11L is widely used to solve suckerrod pumping problems and to design installations.
This article deals with a particularly important design problem for sucker-rod pumping systems. Namely, what is the most economical way a prescribed liquid rate can be lifted from a given well?
Basically, solution of this problem requires the determination of optimum values for plunger size, stroke length, and pumping speed, i.e., finding the optimum pumping mode.
It is quite easy to see that a desired liquid rate can be achieved by a multitude of pumping modes. Denoting one of these as optimal is a matter of preferences, which the designer has to decide beforehand.
One can say that the optimum pumping mode does not exist. But at the same time, there may be several optimum pumping modes, depending on actual requirements .2
A review of the different approaches used to optimize pumping modes shows that some are quite simple procedures, requiring only hand calculations and the use of tables published in API documents.
Others rely on sophisticated computer programs and are not readily available.
The optimization procedure described in this article is valid for conventional pumping units and is based on RP 11 L calculations, with some modifications and improvements. The goal set forth for the optimization process is to assure minimum energy usage for the production of the required liquid rate.
A significant feature of the model is the designing of the rod string for each pumping mode used in the process of selecting the optimum mode. The resulting iterative calculation scheme can easily be adapted to computers.
The program developed by the author gives fair running times on personal computers.
PREVIOUS WORK
The RP 11L procedure cannot be directly applied to optimization of pumping modes because pump displacement is a result of the calculations and not an input variable. If one starts from the desired production rate and wants to find the pumping modes which achieve that rate, a tedious trial-and-error procedure has to be followed.
To ease the solution of this problem, API published RP 11L3, which contains several tens of thousands of precalculated pumping modes . 3 This design book gives the pumping modes that would produce the given volumes for different liquid rates, pump setting depths, and rod taper combinations.
Along with the details of the pumping mode, all the parameters that can be found with RP 11 L are given. This feature allows one to select the pumping mode which is considered to be the best for producing the desired liquid rate under the conditions at hand.
The use of RP 11L3 tables, however, has inherent errors, some of which are limitations of the original RP 11 L calculation model. These include such assumptions as an anchored tubing string, pumped-off conditions, 1 00% volumetric efficiency, etc.
Some problems arise also from the way rod-string design was treated during the development of these tables. Namely, pumping modes were calculated utilizing the taper percentages given in RP 11L. But these taper lengths do not account for the effects of stroke length and pumping speed on rod design. Taper lengths only change with plunger size, as can be seen from the table of recommended taper percentages published in succeeding editions of RP 11 L.
Although the latest edition of RP 11 L adopted a comprehensive rod-design method developed by A.B. Neely,4 this situation did not change. The tables in RP 11L3, therefore, can contain some inherent errors, and their use is limited to anchored tubing and near pumped-off conditions.
The next significant contribution to pumping-mode optimization was made by M.A. Estrada, who used the solution of the wave equation to find the surface operational parameters of sucker rod pumping.5 He developed optimization tables for Mark 11 pumping units and proposed the use of an economic index (El) to rate the effectiveness of different pumping modes.
The economic index includes the values of peak polished rod load (PPRI), peak net torques (PT), polished rod horsepower (PRHP), and lifting efficiency (LE), into a single formula, and assigns the same importance to each of these.
After sorting by ascending El values, the pumping modes that give the desired rate, one has to select the pumping mode which is feasible under the given conditions and has the lowest possible El values. Estrada's rating principle was later used by J.P. Byrd.6
R.H. Gault showed the importance of proper pumping 7 mode selection. He followed the logic of API RP 11L3 and used its tables. He proved that the selection of the right pumping mode can have a very significant effect on power usage and operating costs.
The latest contribution to the problem of pumping mode selection came from J.P. Byrd,8 who proposed a very comprehensive rating system. The performance-effectiveness rating system considers most of the dominant factors of sucker-rod pumping and rates pumping modes according to their performance effectiveness (PE) values. However, the use of his method requires preparation of optimization tables not yet available.
PROPOSED OPTIMIZATION
The goal of optimization, as used here, is to find that pumping mode which ensures the maximum value of lifting efficiency, defined as:
LE = Ph
-------
PRHP
This requirement coincides with the case of setting the PRHP to be a minimum. This is because lifting a given liquid volume from a given pump setting depth, i.e., for a given hydraulic power (Ph), lifting efficiency, and PRHP are inversely proportional.
The pumping mode thus determined will need the least amount of prime-mover power, as the system's total energy requirement is a direct function of PRHP.
Application of the proposed optimization concept, therefore, gives the most energy-efficient and thus most economical pumping mode for the production of the required liquid rate from the given pump setting depth.
The above principle was used to solve the following practical design problem: Given the surface pumping unit and gear reducer, what is the optimal pumping mode to lift the desired liquid volume?
The use of a given pumping unit limits the number of possible pumping modes by imposing constraints on operational parameters such as:
- Maximum PPRL (limited by structural capacity)
- Maximum PT (limited by torque rating)
- Available polished-rod stroke lengths
- Available pumping speed range.
Selection of pumping unit and gear reducer size is also possible using the proposed technique, in which case calculations are made with no limits set to the above variables.
IMPROVEMENTS TO RP 11L
The original RP 11 L calculation method has been modified to include some features not originally available and to speed up calculations. These were proposed by J.D. Clegg9 and the authors and include: The effect of wellhead pressure, pump volumetric efficiencies other than 100%, and an iterative model for frequency-factor calculations.
ROLE OF ROD STRING
To use the RP 11 L technique for the calculation of sucker-rod pumping parameters, the mechanical properties of the rod string in use have to be known. Because these properties change with different taper percentages, the rod string must be designed first.
But all the proper string-design procedures require plunger size, stroke length, and pumping speed as input variables.
The selection of pumping modes, therefore, can only be achieved by an iterative scheme. This is not the case with RP 11L3 in which taper percentages recommended by API were used, eliminating the need for iterations.
The optimization method proposed here accounts for the iterative nature of pumping mode selection. The rod string will be designed throughout the calculation process, thus ensuring a more exact solution of the problem.
This approach reduces errors that may be present in RP 11L3 optimization tables under such conditions when API taper lengths (used for the development of these tables) and rod percentages actually calculated differ considerably.
CALCULATION PROCEDURE
The details of the optimization method are described by flowcharts of a computer program in Figs. 1-4. The program calculates for a given pumping unit and gear reducer all the pumping modes that would produce the required liquid volume. Basic input data are the following:
- The unit's API designation
- Available polished rod stroke length values
- Range of available pumping speeds
- Fluid properties
- Wellhead pressure
- Whether the tubing string is anchored or not
- Rod string data that include API rod number, type of rods (coupled or continuous), and service factor
- Estimated pump volumetric efficiency.
After these data, the desired production data are entered: qD (required liquid production rate), L (pump setting depth), and LDYN (dynamic liquid level).
The calculations start with the selection of the smallest possible plunger diameter, d, and the first polished rod stroke length, s (Fig. 1). Now only the pumping speed that would produce the desired volume has to be determined. This value is calculated in a subroutine.
Assume that this pumping speed (spm) is already known, which means that one pumping mode has already been found. The next step is to check the pumping unit for overload conditions.
In case the PPRL is below the unit's structural capacity, and the resulting PT does not exceed the rating of the gear reducer, one valid pumping mode has been found.
This calculation scheme gives one combination of plunger size, stroke length, and pumping speed that assures the production of the desired liquid rate. Further, additional operational parameters are calculated, such as PRHP, LE, etc. (Fig. 2).
These parameters are then output, and another pumping mode is sought. The next value of polished rod stroke length, s, is chosen, and the calculations are repeated. When all values of the pumping unit's available stroke lengths have been used, the next plunger size is selected and the whole procedure repeated.
The operation of the subroutine mentioned above is illustrated in the flowcharts in Figs. 3-4. These calculations find the pumping speed needed to achieve the production rate desired, for the case of given plunger size and given surface stroke length.
In the first part of the procedure (Fig. 3), checks are made to ensure that the desired liquid rate qD falls between the maximum and minimum pump displacements attainable with the given pumping unit. For this reason, pump displacement, qp, is calculated for the lowest and highest values of available pumping speeds.
If these pump displacements bracket the desired volume, an iterative calculation follows that determines the necessary pumping speed.
Fig. 4 illustrates the principle of the iteration method used. The "Regula Falsi" type of solution is applied to find the required pumping speed, N3, starting from the given two points of the pump displacement-pumping speed function.
With N3 known, the rod string can already be designed, as every variable that affects string design is known at this point: plunger size, stroke length, pumping speed, etc.
Taper lengths having been determined, the RP 11 L procedure can be used to find the pump displacement, qp, that corresponds to the pumping speed calculated before.
In case the pump displacement valid for pumping speed N3 equals the desired production rate, qD, the required pumping speed, and accordingly the required pumping mode, is found. Otherwise, the iteration method is repeated until the necessary pumping speed is arrived at.
At the end of the calculations described, those pumping modes will be available, which on one hand ensure the pumping of the required liquid rate from the given well, and on the other, do not result in overloaded conditions using the given pumping unit and gear reducer.
The program lists these pumping modes on the output, from which the optimal one with the highest value of the lifting efficiency can be determined. This optimal pumping mode will result in the least amount of electric power usage and power costs as well.
In case this pumping mode is not feasible for some reason (e.g., restriction on tubing size) another one is selected which has the next highest lifting efficiency value.
EXAMPLE PROBLEM
To illustrate the optimization procedure and the developed computer program, the following example problem will be shown. In this example, the same input data are used as those given by R.H. Gault.7
These data involved a desired liquid production of 500 b/d from 6,000 ft pump setting depth with an anchored tubing string and pumped-off conditions. Pumping this amount of liquid requires hydraulic horsepower of 22.1.
To facilitate the selection of pumping unit and gear reducer sizes for the job, the program was run with no limits set on torque rating and structural capacity values. The pumping modes with the best and worst lifting efficiency, selected from the calculated ones, are listed in Table 1.
Using the best pumping mode, the energy input at the polished rod is only slightly greater than the hydraulic power, 22.1 hp. This is a very efficient operation.
On the other hand, the worst mode uses almost three times as much energy as the best one. It is also interesting to see that these two extreme pumping modes both require the same size of pumping unit.
As total energy costs are directly related to polished rod horsepower, big savings can be realized by choosing the right pumping mode.
Fig. 5 shows the maximum values of lifting efficiencies obtained for different rod combinations vs. pump size. It is clearly seen that increasing the plunger size increases maximum lifting efficiency for all API rod numbers. Therefore, use of bigger plunger diameters with correspondingly slower pumping speeds is always advantageous because these result in lower energy requirements.
Another observation, in line with practical experience, is that use of heavier rod strings (85 or 86 instead of 75 or 76) can greatly increase the power requirements for smaller pumps. The difference is not so pronounced for bigger pumps, as in those cases rod weight becomes a smaller fraction of the total load.
OPERATING COSTS
The operating costs of sucker rod pumping can be calculated using an approximate method that is based on motor-shaft horsepower requirements and gives the energy costs of pumping.
The input power needed at the motor shaft, Pm, can be found from the value of polished-rod power, Ps, using the formula below:
PM = Ps
-----
Nn Nm (2)
Annual energy costs are determined from this power requirement. Taking into account the specific cost of electric energy, one arrives at:
K = Ps(24)(365) c (3)
Under average conditions, mechanical efficiency, Nh, Of the pumping unit is around 80%; average efficiency of electric motors, Nm, is approximated as 75%. Substituting these values and the specific electric cost of c = 2.45 ft/kw-hr into Equation 2, a good approximation of annual energy costs is reached:
K = 35,770 Ps (4)
EXAMPLES FOR COST REDUCTION
The developed computer program was used to optimize the operation of four wells in the Hungarian oil field Nagylengyel. Table 2 lists, for all wells, the most and the least economical pumping modes calculated.
Comparisons of polished-rod power values show an average ratio of two between the worst and best modes.
Improper pumping mode selection, therefore, can result in energy requirements and in consequence energy costs twice as much as in optimized cases.
Actual conditions of the wells included in this study are compared to calculated ones in Table 3. The rows with the well numbers contain the actual production parameters. The table's following rows display calculated pumping modes with decreasing effectiveness.
In every case, annual energy costs are given along with the possible savings related to present conditions. Evaluation of the results permits the following conclusions to be drawn.
- In Well 126, an increase of pump size alone to 2 3/4 in. reduces energy costs by 5.3%.
- In Well 331, string oversizing is less pronounced than in Well 113. Running of a larger pump alone, or in combination with a lighter string, ensures savings of 4.4 or 7.8%, respectively.
- In Well 429, using the present pump with a lighter string results in 6.3% savings of operating costs.
It can be observed, in general, that rod-string oversizing results in heavier strings requiring more power from the prime mover.
The use of larger pumps, on the other hand, decreases energy costs as an effect of the lower pumping speeds required.
REFERENCES
- "Recommended Practice for Design Calculations for Sucker Rod Pumping Systems (Conventional Units)," API RP 11L 4th Edition, 1988.
- Szilas, P.A., Production and Transport of Oil and Gas, Elsevier Scientific Publ. Co., 1985.
- "Sucker Rod Pumping System Design Book," API Bul. 11L3 1st Edition, 1970
- Neely, A.B., "Sucker Rod String Design," Petroleum Engineer, March 1976, pp. 58-66.
- Estrada, M.E., "Design and Optimizing Tables for the Mark II Oil Field Pumping Unit," MS Thesis, University of Tulsa, 1976.
- Byrd, J.P., "Pumping Deep Wells with a Beam and Sucker Rod System," Paper SPE 6436, Deep Drilling and Production Symposium of SPE, Amarillo, Tex., Apr. 17-19, 1977.
- Gault, R.H., "Designing a SuckerRod Pumping System for Maximum Efficiency," J. Pet. Tech., November 1987, pp. 284-90.
- Byrd, J.P., "Rating the Effectiveness of Beam and Sucker Rod Pumping Modes," 36th Southwestern Petroleum Short Course, Lubbock, Tex., 1989, pp. 280-92.
- Clegg, J.D., "Rod Pump Design Using Personal Computers," 33d Southwestern Petroleum Short Course, Lubbock, Tex., 1986, pp. 232-42.
- Takacs, G., Cziczlavicz, L., and Juratovics, A., "Computer Application of RP 11 L," (in Hungarian) Koolaj es Foldaz, December 1981, pp. 353-8.
Copyright 1990 Oil & Gas Journal. All Rights Reserved.
