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PEH:Progressing Cavity Pumping Systems
Petroleum Engineering Handbook
Larry W. Lake, Editor-in-Chief
Volume IV - Production Operations Engineering
Joe Dunn Clegg, Editor
Copyright 2006, Society of Petroleum Engineers
Chapter 15 – Progressing Cavity Pumping Systems
Introduction Progressing cavity pumping (PCP) systems derive their name from the unique, positive displacement pump that evolved from the helical gear pump concept first developed by Rene Moineau in the late 1920s. Although these pumps are now most commonly referred to as progressing cavity (PC) pumps, they also are called screw pumps or Moineau pumps. PC pumps initially were used extensively as fluid transfer pumps in a wide range of industrial and manufacturing applications, with some attempts made to use them for the surface transfer of oilfield fluids. However, it was not until after the development of synthetic elastomers and adhesives in the late 1940s that PC pumps could be applied effectively in applications involving petroleum-based fluids. Except for several limited field trials, it was not until the late 1970s that a concerted effort was made to use PC pumps as a method of artificial lift for the petroleum industry. Over the past two decades, with the technical contributions and persistence of many individuals and companies, PCP systems have experienced a gradual emergence as a common form of artificial lift.  Although precise numbers are difficult to obtain, it is estimated that more than 50,000 wells worldwide currently are being produced with these systems.
This chapter serves as a guideline for the design and operation of the various PCP systems currently being used in various downhole applications worldwide. The chapter is broken into five major parts as follows: Part 1—PCP Lift System Equipment, Part 2—PCP System Design, Part 3—Specific Application Considerations, Part 4—PCP System Installation, Automation, Troubleshooting and Failure, and Part 5—Design Example.
Readers are encouraged to refer to the numerous references at the end of this chapter for additional details on PC pumps and PCP systems.
The two key features that differentiate PCP systems from other forms of artificial lift are the downhole PC pump and the associated surface drive systems. Although other major components, such as the production tubing and sucker rod strings, are found in other downhole lift systems, the design and operational requirements typically differ for PCP applications. Also, many additional equipment components may be used in conjunction with PCP systems to contend with specific application conditions.
The basic surface-driven PCP system configuration illustrated in Fig. 15.1 is the most common, although electric and hydraulic downhole drive systems and various other hybrid PCP systems are also available (see Alternative PCP System Configurations). The downhole PC pump is a positive displacement pump that consists of two parts: a helical steel "rotor" and a "stator" comprised of a steel tubular housing with a bonded elastomeric sleeve formed with a multiple internal helix matched suitably to the rotor configuration. The stator is typically run into the well on the bottom of the production tubing, while the rotor is connected to the bottom of the sucker rod string. Rotation of the rod string by means of a surface drive system causes the rotor to spin within the fixed stator, creating the pumping action necessary to produce fluids to surface.
- High overall system energy efficiency, typically in the 55 to 75% range.
- Ability to produce high concentrations of sand or other produced solids.
- Ability to tolerate high percentages of free gas.
- No valves or reciprocating parts to clog, gas lock, or wear.
- Good resistance to abrasion.
- Low internal shear rates (limits fluid emulsification through agitation).
- Relatively low power costs and continuous power demand (prime mover capacity fully utilized).
- Relatively simple installation and operation.
- Generally low maintenance.
- Low profile surface equipment.
- Low surface noise levels.
PCP systems, however, also have some limitations and special considerations:
- Limited production rates (maximum of 800 m 3 /d [5,040 B/D] in large-diameter pumps, much lower in small-diameter pumps).
- Limited lift capacity (maximum of 3000 m [9,840 ft]). Note that the lift capacity of larger displacement PC pumps is typically much lower.
- Limited temperature capability (routine use to 100°C [212°F], potential use to 180°C [350°F] with special elastomers).
- Sensitivity to fluid environment (stator elastomer may swell or deteriorate on exposure to certain fluids, including well treatment fluids).
- Subject to low volumetric efficiency in wells producing substantial quantities of gas.
- Sucker rod strings may be susceptible to fatigue failures.
- Pump stator may sustain permanent damage if pumped dry for even short periods.
- Rod-string and tubing wear can be problematic in directional and horizontal wells.
- Most systems require the tubing to be pulled to replace the pump.
- Vibration problems may occur in high-speed applications (mitigation may require the use of tubing anchors and stabilization of the rod string).
- Paraffin control can be an issue in waxy crude applications (rotation as opposed to reciprocation of the rod string precludes use of scrapers for effective wax removal).
- Lack of experience with system design, installation, and operation, especially in some areas.
Many of these limitations continue to change or be alleviated over time with the development of new products and improvements in materials and equipment design. If configured and operated properly in appropriate applications, PCP systems currently provide a highly efficient and economical means of artificial lift.
PCP Lift System Equipment
The basic system components include the downhole pump, sucker rod and production tubing strings, and surface drive equipment, which must include a stuffing box. However, a PCP installation may also include different accessory equipment, such as gas separators, rod centralizers, tubing-string rotator systems, and surface equipment control devices. The following sections describe the various components of a PCP installation in further detail.
Downhole PC PumpPC pumps are classified as single-rotor, internal-helical-gear pumps within the overall category of positive displacement pumps.  The rotor comprises the "internal gear" and the stator forms the "external gear" of the pump. The stator always has one more "tooth" or "lobe" than the rotor. The PC pump products currently on the market fall into two different categories based on their geometric design: single lobe or multilobe. Currently, the vast majority (i.e., estimated at > 97%) of PC pumps in use downhole are of the single-lobe design and thus are the primary focus of this chapter. Other variations of these basic configurations include semi-elliptical rotor/stator geometries and uniform-thickness elastomer pumps.
The geometric design of a single-lobe PC pump is illustrated in Fig. 15.2. The longitudinal cross-section in Fig. 15.2 shows the single external helical shape of the rotor and the corresponding double internal helical geometry of the stator. Note that the stator pitch length (Ls) is exactly double the rotor pitch length in single-lobe pumps. With the mating of the rotor and stator in a single-lobe PC pump, two parallel, helical cavities are formed (180° apart and one rotor pitch out of phase) that spiral around the outside of the rotor along the pump length, with each cavity having a length equal to the stator pitch length. Note that the parallel cavities are offset lengthwise, with the end of a cavity on one side of the rotor corresponding to the maximum cavity cross-section on the opposite side. In a single-lobe pump, the rotor is circular in cross section (with a minor diameter, d), whereas the cavity within the stator has a semi-elliptical geometry. Another important geometric parameter is the pump eccentricity (e), which is equal to the distance between the centerlines of the major and minor diameters of the rotor. The distance between the stator axis and rotor major diameter axis is also equal to the eccentricity value. The rotor creates an interference fit seal with the stator elastomer on both sides of the semi-elliptical opening and a seal over the semicircular end of the stator opening at the positions corresponding to the ends of the longitudinal fluid cavities. The fluid-filled cavities are formed by the open areas left between the rotor and stator at each cross section. Fig. 15.3 shows a section view of a single-lobe PC pump and the different rotor and stator geometries of several different pump models.
During production operations, the rotor translates back and forth across the stator opening as it is rotated within the fixed stator. This occurs because of a combination of two motions: rotation of the rotor around its own centroidal axis in the clockwise direction and eccentric reverse rotation (i.e., nutation) of the rotor about the centroidal axis of the stator. Fig. 15.4 illustrates the rotor movement within the stator opening at a given longitudinal position through one full revolution. The rotor movement causes the series of parallel fluid cavities formed by the rotor and stator to move axially from the pump suction to discharge on a continuous basis. The nutation of the rotor about the stator centerline is also shown in Fig. 15.4.
Typically, rotors are precision machined from high-strength carbon steel (e.g., ASTM 1045 or 4140) into an external helix, although some manufacturers have recently developed techniques that allow rotors to be fabricated through a metal forming process. In most cases, the rotors are coated with a thin layer of wear-resistant material, usually chrome, to resist abrasion and then are polished to a smooth finish to reduce rotor/stator friction. Rotors are also fabricated from various stainless steels for service in corrosive or acidic environments because these materials are less susceptible to corrosive fluid attack. These rotors, however, tend to be far more susceptible to abrasion wear than chrome-coated rotors. For most applications, the chrome plating thickness is typically 0.254 mm (0.01 in.) on the rotor major diameter. However, for severe wear applications, vendors typically offer rotors with a "double" chrome thickness to prolong service life. Other processes used by vendors to fabricate rotors with more abrasion-resistant coatings include boronizing, nitriding, and also thermal spray methods which are used to apply carbide-based coatings materials.
Stators typically are fabricated by placing a machined core (i.e., with the shape of the helical stator opening) inside a steel tubular and then injecting and subsequently curing an elastomer material within the annular space. Achieving a good bond between the elastomer sleeve and the steel tubular is essential. Depending on the chemical composition and the curing process of the elastomer, the chemical and mechanical properties of the material can vary considerably, as discussed in detail later.
Multilobe PC Pumps. In response to increasing demand for higher displacement PC pumps, several manufacturers have developed various models of multilobe PC pumps. Although the basic operating principles are the same, multilobe designs can be differentiated from single-lobe pumps by the presence of three or more parallel cavities within the stator and by rotor geometries with two or more lobes. The stator must always have one more lobe than the matching rotor; thus, the multilobe pump geometries are often referenced according to their rotor/stator lobe ratio (e.g., 2:3 and 3:4 pumps). Although it is possible to manufacture pumps with higher ratios, the multilobe pump models currently available have a 2:3 lobe ratio configuration. The cross-sectional shapes of the rotors and stators can also be varied somewhat from the original Moineau geometry, which has round (i.e., circular) lobes. All the major pump manufacturers have adopted semi-elliptical rotor and matching stator geometries for their multilobe pump products. This decision was based primarily on fabrication considerations, because it is possible to machine the rotors in the same manner as single-lobe rotors, which is substantially less costly than cutting rotors with a milling machine. Fig. 15.5 presents cross-sectional diagrams of the two pump designs to illustrate the differences in the rotor and stator shapes. Note that the interference fit that develops between the rotor and stator is also affected by the different component geometries, and this can affect the pressure integrity of the seals between the pump cavities, which in turn can influence pump performance and life.
The primary advantage that multilobe pumps have over single-lobe designs is their ability to achieve higher volumetric and lift capacity with shorter pumps of the same diameter. The increased displacement can be attributed to a larger stator cavity area and the fact that each stator cavity is swept multiple times during a single revolution of the rotor (i.e., twice in a 2:3 lobe geometry), as opposed to only once for a single-lobe pump. As a result, the fluid is advanced multiple stator pitch lengths per revolution. Because the cavities also tend to overlap more along the pump length than in single-lobe designs, a shorter pump is typically required to achieve the same pressure capacity. The shorter lengths also help to reduce product costs.
Multilobe pumps also have some disadvantages: (1) higher flow velocities through the pump, which can lead to increased fluid shear rates and flow losses and greater potential for erosion of the elastomer; (2) higher frequency of stator flexing, which increases hysteretic heat generation and may impact pump life; (3) greater potential for inflow problems to develop when high-viscosity fluids are pumped; (4) more prone to cause vibration problems because of the larger rotor mass and increased nutation speeds; and (5) increased torque requirements corresponding to the typically larger pump displacements. In general, the potential problems associated with these various disadvantages can be avoided through proper system design and operation.
Uniform-Thickness PC Pumps. An example of another type of hybrid PC pump product, the "uniform-thickness" pump, is illustrated in Fig. 15.6. These products were first introduced in the mid-1990s as one approach to overcome non-uniform distortion of the stator cavity caused by swelling or thermal expansion of the elastomer. A variety of manufacturing techniques have since been developed to fabricate stators with an elastomer sleeve of uniform thickness around the entire stator opening. Note that only the stator component differs and that conventional rotors are typically used with these pump models. Because the potential for stator distortion is minimized, these pumps should perform better in light-oil or high-temperature applications. Note, however, that because of the relatively thin elastomer sleeve, proper pump sizing is critical for these pump models if reasonable run lives are to be achieved.
Pump Models and SpecificationsA wide variety of PC pump models are available from many different manufacturers. It is important to note that currently no industry standards (e.g., API) govern PC pump designs and that pump geometries and materials vary considerably between vendors. In addition, although it is typical among vendors to specify pump models according to their volumetric displacement and pressure differential capabilities, the rating criteria may vary (i.e., particularly with respect to pressure ratings) and should be understood for proper pump selection. Fig. 15.7 shows the wide range of displacement and pressure capabilities associated with currently available PC pumps categorized according to the minimum casing size in which they can be installed with reasonable clearances.
Pump Displacement. The displacement of a PC pump is defined as the volume of fluid produced for each turn of the rotor. When the rotor completes a full revolution, the series of cavities within the pump have advanced one full stator pitch length, thus discharging a corresponding fluid volume to the production tubing. Because the cavity area between the rotor and stator remains constant at all cross sections along the pump length, a PC pump delivers a uniform nonpulsating flow at a rate directly proportional to pump speed.
The volumetric displacement of a single-lobe PC pump (s) is a function of the pump eccentricity (e), rotor minor diameter (d), and stator pitch length (Ls) and can be calculated as follows:
For convenience, most pump manufacturers specify pump displacement in terms of volume per day at a certain pump speed, typically 1, 100, or 500 rpm. Although product selection varies among manufacturers, PC pump displacements generally range from 0.02 m3/d/rpm [0.13 B/D/rpm] to > 2.0 m3/d/rpm [12.6 B/D/rpm]. This requires using an appropriate conversion factor with Eq. 15.1.
It is apparent from Eq. 15.1 that different combinations of the parameters e, d, and Ls can be used to obtain equivalent pump displacements. The performance and serviceability of a PCP system can be influenced strongly by these geometrical variations under certain completion and production conditions. Unfortunately, the potential impacts associated with using different pump geometries are usually difficult to assess because these geometric specifications are typically considered proprietary and thus are not published by pump manufacturers.
The theoretical flow rate of a PC pump is directly proportional to its displacement and rotational speed and can be determined by
where qth = theoretical flow rate (m3/d [B/D]), s = pump displacement (m3/d/rpm [B/D/rpm]), and ω = rotational speed (rpm).
However, as the differential pressure across the pump increases, some fluid slips backward through the seal lines between the rotor and the stator, reducing the discharge flow rate and volumetric efficiency of the pump. As a result, the actual flow rate of a PC pump is the difference between its theoretical flow rate and the slippage rate:
where qa = actual flow rate (m3/d [B/D]), qth = theoretical flow rate (m3/d [B/D]), and qs = slippage rate (m3/d [B/D]).
The slippage rate is dependent on rotor/stator fit, elastomer properties, fluid viscosity, and pump differential pressure capacity. Note that the actual displacement of a PC pump may vary from the manufacturer’s published values even without consideration for slippage in cases when the stator cavity volume is reduced because of expansion or swelling of the elastomer under downhole conditions. In some cases, the displacement reduction can exceed 10% of the published value.
Pressure Ratings. The overall pressure capacity of a PC pump is controlled by the maximum pressure that can be developed within individual cavities and the number of cavities (i.e., full stator pitches) along the pump. The maximum pressure capacity of each cavity is a function of the seal integrity between the rotor and stator and the properties of the produced fluid. In general, the differential pressure capacity of the seal lines increases with tighter rotor/stator interference fits and higher-viscosity fluids. However, the pump geometric parameters and the properties of the stator elastomer can significantly influence seal capacity. For example, long pitch pumps tend to have more effective seals (i.e., all other variables being equal) as a result of minimal cavity distortion or elastomer deformation in the axial direction of the pump during operation. The rotor diameter and eccentricity also affect the nature of the rotor/stator interaction, which can affect sealability during pump operation. The elasticity and stiffness of the elastomer also govern sealability. For metal-elastomer interference fits, the pressure differential per cavity typically ranges from 410 to 620 kPa [60 to 90 psi]. Determination of appropriate pressure ratings for multilobe and uniform-thickness PC pumps must also consider the different leak paths and/or seal behavior compared with single-lobe pumps. Pressure ratings for both single-lobe and multilobe PC pumps are generally considered to be insensitive to pump speed.
Historically, PC pump pressure ratings were often referenced to the number of pump "stages" or cavities, which led to substantial confusion given that different vendors used different stage definitions. As a result, most manufacturers now specify pump pressure capabilities in terms of maximum differential pressure (or equivalent head of water). Fig. 15.7 shows the range of pressure ratings for most of the currently available PC pumps. Currently, no industry standards govern the setting of pressure ratings by individual PC pump manufacturers.
Operating a PC pump at excessive differential pressures leads to high fluid slippage rates across the rotor/stator seal lines, which causes excessive stator deformation. Sustained operation under such conditions will lead to accelerated deterioration of the elastomer material properties and will likely result in the premature failure of the stator.
Elastomer Types, Properties, and Selection MethodsIn downhole applications, most PC pump failures involve the stator elastomer and often result from chemical or physical elastomer breakdown induced by the wellbore environment. The environment can vary considerably between different reservoirs and individual operations. The bottomhole temperature may range from 15 to 200°C [60 to 360°F]; the well may be pumped off or have a high bottomhole pressure; and the produced fluids may contain solids (e.g., sand, coal fines), gases (e.g., CH4, CO2, H2S), and a wide range of other constituents, including water, paraffins, naphthenes, asphaltenes, and aromatics. Additionally, the methods and fluids used to drill, treat, and stimulate wells introduce a variety of other chemicals into the wellbore, such as drilling muds, completion fluids (heavy salt solutions), treatment fluids (e.g., diluents, hot oil, strong acids), corrosion inhibitors (e.g., amines), and flooding materials (e.g., CO2).
Successful use of PC pumps, particularly in the more severe downhole environments, requires proper elastomer selection and appropriate pump sizing and operation. PC pump manufacturers continue to develop and test new elastomers; over time, these efforts have resulted in performance improvements and an expanded range of practical applications. Despite this success, the elastomer component still continues to impose severe restrictions on PC pump use, especially in applications with lighter oils or higher temperatures.
Mechanical and Chemical Properties. The performance of an elastomer in a PCP application depends heavily on its mechanical and chemical properties.  Although many different mechanical properties can be quantified for elastomers, only a few are highly relevant to PC pump performance. One important property is hardness because it characterizes the relationship between the rotor/stator interference fit and the resulting sealing force. Tear strength is also important because it provides a measure of an elastomer’s resistance to tearing and indicates its fatigue and abrasion resistance. Although abrasion resistance is a critical parameter in many applications, the ASTM abrasion tests (drum, tabor, pico) do not represent the PC pump wear mode and should be interpreted with caution. Dynamic properties, which characterize the hysteretic heat buildup behavior, are not overly critical in PC pumps because the flexing frequencies of the single-lobe geometries are generally not high enough to result in significant temperature rise, except when the fit is very tight or heat removal is minimal. Although tensile strength and elongation are commonly referenced properties, they have little practical relevance to PC pumps other than their relationship to other mechanical properties because the elastomer is strained to only a fraction of its capacity. Table 15.1 summarizes the most commonly referenced mechanical properties, along with any corresponding ASTM and DIN test references. The range of values typical of commercially available PC pump elastomers is included to show the variations that exist in these properties.
Chemical resistance is normally evaluated through compatibility testing with the fluids in question. Elastomer samples are exposed to the fluid in an autoclave environment for a predetermined period of time (typically 72 or 168 hours); then, the volume and mass change are measured. To be representative, these tests should also assess the change in mechanical properties through measurements of hardness and, if possible, tensile strength and elongation. Because these tests are performed on small samples (which seldom come from actual pumps) for a limited period of time, they are most useful for ranking elastomers as opposed to determining the actual swell level within a stator.
The chemical and mechanical properties of an elastomer are very sensitive to temperature, and the nature of changes in these properties can vary dramatically between elastomers. Although testing is normally done at room temperature, in most cases the mechanical properties will deteriorate significantly with increasing temperature. The rate of fluid swell will also increase at higher temperatures, although in most cases the ultimate level of swell will remain the same. Whenever possible, any testing to evaluate elastomers should be done as close to the anticipated downhole conditions as practical.
PC Pump Elastomers. Most PC pump manufacturers have stator products available with several different elastomer types. Because the formulations of these elastomers are considered proprietary, there is no standard naming convention. Certain generic names are common to the different manufacturers, but elastomer properties may vary significantly.
Although there is a wide range of different elastomer types, almost all PC pumps use some variation of a synthetic nitrile elastomer. Within the class of nitrile elastomers, there is a virtually unlimited number of different formulations possible with an associated wide range of mechanical and chemical properties. A discussion of the more common types of elastomers used in PC pumps follows.
Nitrile (NBR). Most elastomers in PC pumps can be classified as conventional nitrile (NBR).  The base polymers for these elastomers are manufactured by emulsion copolymerization of butadiene with acrylonitrile (ACN). ACN contents in nitrile elastomers typically vary from 30 to 50%, with the cost of the elastomer increasing marginally with increasing ACN level. Most manufacturers distinguish between a medium nitrile (sometimes called Buna, which typically has an ACN content < 40%) and a high nitrile (> 40% ACN). Increasing ACN levels produce increasing polarity, which improves the elastomer’s resistance to nonpolar oils and solvents. However, higher ACN levels result in increased swell in the presence of such polar media as esters, ketones, or other polar solvents and leads to a decline in certain mechanical properties. It is important to note that aromatics such as benzene, toluene, and xylene swell NBR elastomers considerably, regardless of ACN level.
NBR elastomers are normally sulfur cured, and the combination of sulfur with the natural unsaturation of the elastomer can result in additional cross-linking and associated hardening in the presence of heat. As a result, NBR elastomers are not recommended for continuous use at temperatures that exceed 100°C [212°F]. For a similar reason, NBR elastomers also are not recommended for applications that contain high levels of H2S because the sour gas contributes additional sulfur, which leads to post-vulcanization and surface hardening. These changes result in a loss of resilience and elasticity, typically causing premature stator failure.
Historically, the hardness of NBR elastomers has been between 65 and 75 Shore A. More recently, manufacturers have introduced soft medium NBRs (55 to 60 Shore A) for abrasive, heavy oil applications. The rationale was that they would be more forgiving to the gravel and iron pyrite solids that are produced occasionally and have a tendency to tear the stator material. The soft elastomer requires the use of a higher degree of rotor/stator interference fit, which has the advantage of maintaining some sealing even after extensive wear of the rotor or stator.
Hydrogenated NBR (HNBR). Conventional NBR elastomers, especially when sulfur cured, often contain a large degree of unsaturation in the form of double and triple carbon-carbon bonds in the base polymer. Relative to a more stable single bond, these unsaturated hydrocarbon groups are susceptible to chemical attack or additional cross-linking. This is the primary reason why NBRs experience problems upon exposure to high temperatures, H2S, and aggressive chemicals.
Through a hydrogenation process, it is possible to increase the saturation (i.e., decrease the number of double and triple carbon-carbon bonds) of the NBR polymer, thus stabilizing the associated elastomer. The degree of saturation can vary, but typically it is > 90% and can be as high as 99.9%. If the saturation is very high, then a sulfur cure system is no longer effective, and a peroxide cure must be used. These compounds are typically referred to as highly saturated nitriles (HSN) or hydrogenated nitriles (HNBR).  For an equivalent volume, the cost of an HNBR elastomer is typically four times that of a conventional NBR, making the stators made from such elastomers considerably more expensive.
The primary advantage of an HNBR is increased heat resistance. Sulfur-cured HNBRs can ideally be used up to 125°C [257°F], whereas higher-saturation peroxide-cured compounds can potentially be used in applications with temperatures up to 150°C [300°F]. Other advantages, especially if the elastomer is peroxide cured, include improved chemical resistance and H2S tolerance. The mechanical properties of HNBR elastomers usually are similar to those of NBR elastomers.
Most PC pump manufacturers offer HNBR stators, but the limited number of applications that warrant the higher cost have kept their use to relatively low levels. Historically, the HNBR polymers have been highly viscous and difficult to inject into stators, increasing manufacturing costs substantially. However, within the last few years, the polymer manufacturers have introduced lower-viscosity, high-ACN HNBR elastomers. As a result, pump manufacturers have taken a renewed interest in these elastomers, which may lead to more use of HNBR compounds in stator products in the future.
Fluoroelastomers (FKMs). FKMs have been expanding in availability and use over the last decade. Although a number of different varieties of FKMs are available, common to all is the presence of high levels of fluorine that saturate the carbon chain. The carbon-fluorine bonds in FKMs are extremely strong, giving this formulation heat and chemical resistance superior to that of most other elastomers.
FKMs are, to a large extent, made up of the fluoro-polymer and thus contain a low level of fillers and additives. As a result, the mechanical properties of FKMs tend to be inferior to those of NBR and HNBR elastomers. In terms of chemical stability, they have excellent resistance to heat, although their mechanical properties tend to deteriorate further at high temperatures from already relatively low initial levels. A variety of cure systems are used for FKM elastomers, including peroxide, but they require an extended post-curing session to optimize their properties, adding considerably to manufacturing process costs. As a result, the cost for an equivalent volume of FKM elastomer may range from 20 to several hundred times that of a conventional NBR. This makes all but the lower-cost grades of FKMs uneconomical for PC pump stators, and even those that are viable carry a high cost premium.
The primary advantage of an FKM elastomer is the increased heat and chemical resistance. FKM elastomers have the potential to be used up to 200°C [400°F] as long as they are not subject to excessive mechanical loading (proper sizing of PC pumps is critical). In terms of fluid resistance, they have minimal swell with most oilfield fluids, including aromatics.
General use of FKM elastomers in PC pump applications is relatively recent, with several PC pump manufacturers now offering these products. Some success has notably been encountered in lighter-oil applications in which NBR stators swell, necessitating multiple rotor changes. Despite being expensive, FKM stator products appear to be viable in certain applications, especially if the pumps are sized properly and extended run times are achieved.
Elastomer Selection. Elastomer selection for a particular application involves deciding on a particular formulation or type (i.e., medium or high NBR, HNBR, or FKM) and a specific stator supplier because the basic formulations differ between manufacturers. For the most part, elastomer selection is based on the downhole conditions and required fluid resistance. Although mechanical properties are also important, sufficient detailed information is not routinely available from the PC pump manufacturers to make this a consideration in elastomer selection.
Most manufacturers publish guidelines for elastomer selection that are based on anticipated downhole conditions, including fluid type, gases, solids, and operating temperature. Historically, API fluid gravity has been used as the primary measure of fluid aggressiveness in terms of elastomer swell and associated property deterioration. Although a strong trend does exist directionally, problems can arise when API gravity is used as the main selection criterion (i.e., especially at the higher end), given that fluids of the same gravity can have vastly different compositions of the aromatic components that cause swell. There are exceptions to this rule, such as the heavy oil fields in Venezuela, where the gravity is low but the quantity of aromatics is relatively high and can lead to problems with fluid swell. Although the exact value varies somewhat between manufacturers, the crossover point for medium to high NBR use is typically about 25°API. Most manufacturers do not recommend the use of a conventional NBR beyond 35 to 40°API. At the higher API gravities, the only options are FKM or perhaps HNBR formulations, although these elastomers are available only from certain manufacturers and their use is usually restricted to a narrow range of applications.
When a question exists as to the best elastomer to use, it is common practice to perform compatibility tests with the wellbore fluid and selected elastomer samples. These tests generally provide an effective means to rank the suitability of different elastomers (i.e., especially of the same type from different manufacturers) and can be helpful in establishing appropriate rotor sizing. Results almost always consist of volume, mass, and hardness change and, in some cases, may include changes in mechanical properties. From previous testing experience and tracking of pump performance, most pump suppliers have established limits for the maximum volume and hardness change for which they recommend use of their products.
Although compatibility testing provides a more scientific way to select elastomers, it is not practical in many cases because it is difficult to get the well fluids, representative elastomer samples, and a laboratory that does the specialized testing all in the same location. Nevertheless, there are a number of techniques based solely on fluid analyses that may be used to assist in elastomer selection. Hydrocarbon analysis through chromatographic techniques has been the most widely used method, but for it to be helpful in assessing elastomer compatibility, the analysis must include detection of the hexanes plus. This results in a breakdown (mole, mass, and volume percent) by component up to C30+, so the test is often referred to by this name (i.e., C30+). Results are normally divided into paraffin, aromatic, and naphthene groups, with breakdowns of specific components within each group. The most useful information includes the total percent aromatics and levels of individual aromatic components. Most PC pump manufacturers are familiar with this testing method and have guidelines on the maximum percent aromatics recommended for each of their elastomers. A less expensive, more readily available method for fluid analysis is an aniline point test (ASTM D611). Aromatic hydrocarbons exhibit the lowest aniline point (e.g., 60°C [140°F] for diesel), whereas oils with low aromatics typically have values that are > 100°C [212°F]. This test has been used extensively to assess elastomer compatibility in the drilling industry, but its use for PC pumps is new, so relationships between aniline point and recommended elastomers are still being compiled.
The limitations to the elastomer selection "rules" associated with API gravity or hydrocarbon analysis are usually the result of temperature or H2S. Conventional NBR elastomers are normally not recommended for temperatures > 100°C [212°F] or with H2S concentrations > 2% because of the elastomer hardening that occurs over time, frequently leading to cracking and fatigue. In these cases, HNBR or FKM elastomers are more appropriate choices. However, caution must be exercised when these elastomers are considered because the fluid resistance of the HNBR elastomers varies significantly by manufacturer and mechanical loading considerations must be addressed with FKM elastomers.
Despite all these selection methods, it is important to point out that operators are typically faced with using a "trial-and-error" approach to determine optimal elastomer selection and pump sizing when applying PCP systems in new areas.
Rod Strings and Production Tubing. Surface-driven PCP systems require a sucker-rod string to transfer the torsional and axial loads from the surface drive system down to the bottomhole PC pump. Although conventional sucker rods continue to be used in many PCP applications, some rod manufacturers have developed products designed especially for PCP applications: (1) larger-diameter rods (e.g., 25.4 mm [1.0 in.] and 37.5 mm [1.5 in.]) to handle the high loads associated with large-displacement PCPs; (2) hollow rods designed to handle high loads and to facilitate downhole injection of diluents or treatment fluids; (3) rods with different connection designs that minimize the coupling diameter to reduce flow losses (typically, the pin diameter is reduced one size relative to standard rods, e.g., 25.4 mm [1 in.] rods fabricated with 22.2 mm (7/8 in.) pin connections, which allows the use of smaller-diameter couplings); and (4) relatively large-diameter (e.g., up to 29.2 mm [1.15 in.]) round continuous rod.
Several different rod-string configurations are commonly used in PCP applications. These include continuous rods, standard rods with couplings (including hollow rods), standard rods with centralizers, and standard rods with bonded/molded rod guides. Within these categories are numerous additional variations resulting from differences in centralizer and rod guide design. The centralizers can be divided into two groups based on functionality. The first group consists of "coated" centralizers that have a urethane, plastic, or elastomer sleeve bonded to either a coupling or the rod body. The second group consists of "spin-thru" centralizers that have an outer stabilizer that is free to rotate on either an inner core or the rod body. With the spin-thru design, the rod string rotates inside the stabilizer, which remains stationary against the tubing. Fig. 15.8 shows several different types of centralizers and rod guides. Continuous-rod products are not currently available in all countries but are used extensively in Canada, Venezuela, and selected regions of the U.S.
The production tubing strings used in most PCP applications are typical of those used in most other oil and gas production operations. The tubulars conform to API product standards,  with EUE and NU connections and Grade 55 pipe used in most cases. In some situations, large-diameter tubing strings are warranted to contend with high flow losses or to facilitate the use of an alternative PC pumping system (see below), and small-diameter casing products are used instead. Some special internally coated tubing-string products, including boron-coated tubing and tubing with polyethylene liners, are available for use in applications in which wear and/or corrosion problems may occur.
Surface Drive Systems. The surface equipment used in a conventional surface-driven PCP system must perform the following functions: suspend the rod string and carry the axial loads; deliver the torque required at the polished rod; safely rotate the polished rod at the required speed; provide for safe release of the stored energy during shutdowns; and prevent produced fluid from escaping the system. To facilitate these requirements, all surface equipment systems include a wellhead drive unit (drive head), a stuffing box, power transmission equipment, and a prime mover, as illustrated in Fig. 15.9. In addition, the surface equipment may also include safety shutdown devices, torque limiters, recoil control devices, and electronic speed control (ESC) and monitoring systems.
Wellhead Drive Units. The wellhead drive unit consists of a wellhead frame, thrust bearing, a polished-rod braking system (in most cases), and sometimes a fixed gear or belt and sheave system. Fig. 15.10 shows two types of drive heads. In many cases, the wellhead frame threads directly onto the tubing head. However, there is a growing trend toward the use of flanged connections, especially for applications involving drive systems that are 60 hp or larger. These systems facilitate proper alignment of the drive on the wellhead to help prevent stuffing box leakage and provide sufficient strength to carry the much heavier drive heads and motors used today. The drive heads typically mount onto composite pumping tees, which in turn mount onto the casing head. Note that the wellhead frame usually incorporates the stuffing box assembly and that some units are fabricated to allow mounting of either electric prime movers or hydraulic motors.
One important function of the drive head is to support the axial rod-string load. The thrust bearing, contained in the wellhead frame, supports this load while allowing the rod string to rotate with minimal friction. Most wellhead frames are available with a variety of thrust bearings to suit different loading applications. The expected life of the thrust bearing is usually quantified by an L 10 rating. Within a large sample, the median bearing life is typically between four and five times the L10 life.
Most drive heads have either a hollow shaft or an integral shaft design that facilitates the connection of the drive to the polished rod. With the most common hollow shaft design, the polished rod passes through the entire wellhead and is suspended by a polished-rod clamp that seats into a drive slot on top of the wellhead frame. In a modification of this design, a hexagonal rod substitutes for the polished rod, and the drive unit has a mating hollow shaft through which torque is applied to the rod. Polished rod and stuffing box exposure depends on whether the particular design incorporates an open (Fig. 15.10a) or closed (see Fig. 15.10b) frame. The hollow shaft design allows some repositioning of the rod string without removal of the wellhead. This is done by loosening the polished rod clamp, raising or lowering the polished rod as required, and then tightening the clamp. This flexibility to reposition the rod string simplifies rod space-out procedures, flush-bys, and the repositioning of the rod string to prevent wear-related failures. In drives with an integral shaft design, the polished rod threads directly into the drive mechanism as opposed to passing through it. As a result, the only way to reposition the rod string is to add pony rods of different lengths to change the string length. Initial space-out procedures and flush-bys are not easily accommodated with the integrated shaft design.
Drive heads also incorporate a stuffing box that seals on the rotating polished rod to control fluid leakage from the production string and wellhead. The two basic types of stuffing boxes available are conventional and specialty (i.e., rotating) systems. The conventional stuffing boxes function similar to those used with beam-pump systems. They use a special packing material compressed against the polished rod to effect a seal; (i.e., the rod rotates directly against the packing material, so the compressive loading imposed by tightening the stuffing box must balance the resultant friction forces against fluid seal integrity). These stuffing boxes require regular inspection and maintenance (i.e., greasing and tightening). Rotating stuffing boxes are designed to seal differently, typically incorporating an inner sleeve that seals against the polished rod and rotates with it during operation. Additional seals designed to operate in a clean fluid environment provide a seal between the rotating sleeve and the fixed outer housing of the stuffing box. A clean lubricating oil environment is ideally maintained in this interstitial region during operation. One key consideration for stuffing box selection is access for packing material or seal replacement, and another is tightening of the packing as required. To minimize stuffing box leakage and maintenance requirements, it is also important to ensure that the polished rod has not been bent. Some new stuffing box designs rely on injectable packing materials (viscous materials that require an injection pressure of approximately 7 MPa [1,000 psi] that readily facilitate repacking of a stuffing box).
Normally, drive heads are connected to the power transmission equipment by a vertical shaft (Fig. 15.10b). However, horizontal connections can be facilitated by incorporating right-angle gearboxes directly into the drive head (Fig. 15.10a). These gearboxes typically enclose gears that provide a reduction ratio of up to 4:1. To prevent gearbox failure, operators should adhere to manufacturer guidelines for maximum gearbox speed and torque.
Power Transmission Equipment. Power transmission equipment is used to transmit power (torque and speed) from the prime mover to the polished rod. This equipment almost always incorporates some type of speed reduction/torque transfer system that permits the prime mover to operate at a higher speed and lower torque than the polished rod. In some cases, power transmission components, such as gearboxes and fixed speed belts and sheaves, are integrated into the drive head.
Power transmission equipment can be arranged in a variety of different configurations as is illustrated in Fig. 15.11. The various configurations can include almost any combination of hydraulic equipment, belts and sheaves, and gearboxes to provide the desired operating speed and torque characteristics. Note that power transmission equipment is usually classified as either direct drive or hydraulic on the basis of whether or not it incorporates hydraulic system components.
Hydraulic power transmission systems incorporate a hydraulic system between the prime mover and the input shaft of either a gearbox or fixed speed belt and sheave system that is integrated into the drive head. The hydraulic system itself consists of a hydraulic pump connected to the output shaft of the prime mover, various intermediate valves and plumbing, and a hydraulic motor attached to the input shaft of the drive head (Fig. 15.12a). Note that variable displacement hydraulic pumps and motors are typically used. Additional required components include a hydraulic fluid reservoir and fluid filtration system. All hydraulic equipment, except the hydraulic motor and connecting hoses, is usually mounted on a skid (Fig. 15.12b). The torque delivered by the hydraulic motor to the drive head is proportional to the hydraulic system pressure and a function corresponding to the hydraulic motor design. The hydraulic system flow rate may be controlled with either prime-mover speed control systems or, more commonly, pump displacement adjustments (i.e., through changes in the swash plate position in variable-displacement pumps) to set the rotational speed of the hydraulic motor. The relationship between prime-mover speed and hydraulic motor speed is a function of the relative displacements of the hydraulic pump and motor. As an alternative, some vendors also sell in-line hydraulic drive units that use high-torque, low-speed hydraulic motors to drive the polish rod directly without any gear or belt and sheave reduction. These units tend to be relatively compact and quiet compared with the more standard systems.
Direct-drive power transmission systems can be categorized as mechanical fixed speed, mechanical variable speed, or electronic. Mechanical fixed speed refers to a direct-drive system with a fixed gear ratio powered by a prime mover that can operate at a single speed (i.e., typically an AC electric motor). Mechanical variable-speed systems have either internal combustion prime movers that can operate at variable speeds or a belt and sheave system that accommodates a variety of sheave sizes. To vary pump speed in the latter case, the well must be shut down to permit changing of the sheaves. Electronic systems consist of an electric motor with an ESC system. Fig. 15.13 shows different types of direct-drive systems.
The features of the different types of power transmission systems are compared in Table 15.2. Although hydraulic systems are typically less efficient than direct electric drives, they generally require little field infrastructure and have a high variable-speed turndown rate, which makes them popular for low-rate, high-viscosity applications in which prime-mover speeds are much higher than pump speeds and flexible speed control is desirable. The simplicity of mechanical fixed- and variable-speed systems makes them practical for applications in which fluid rates are relatively stable and speed adjustment requirements are limited. The direct-electric-drive systems typically have better energy efficiency than hydraulic drives, although they typically are more expensive and can be more difficult to repair. Field electrification is usually required for effective use of electric-drive systems.
Prime Movers. The prime mover provides the energy to drive the surface equipment and ultimately the rod string and downhole pump. The amount of power that the prime mover must deliver depends on the power demand at the polished rod and the efficiency of the power transmission system. Typical prime-mover power ratings range from 4 to 75 kW [5 to 100 hp], although higher capacity wellhead units designed to accommodate twin electric motors providing power up to 225 kW [300 hp] have recently been introduced by several vendors in conjunction with new large displacement PC pumps.
The two types of prime movers commonly used to drive PCP systems are internal combustion engines and electric motors. Internal combustion engines (Fig. 15.13b) have the advantages of a simple setup with minimum capital investment and variable-speed capability. They are often used on wells in remote areas where electricity is not available. In some situations, depending on gas production and composition, it is possible to fuel the engine with produced gas. Nevertheless, electric motors are the most common form of prime mover used for PCP systems because of low maintenance requirements, high efficiency, low energy costs, easy operation, and low noise levels. The major disadvantage of using electric motors for the prime mover is that the cost of powering the motor can be prohibitively high unless the well site is electrified. Another drawback is that speed adjustment is possible only through sheave changes, motor rewiring, or the use of ESC systems.
Most electric motors used as prime movers in PCP applications are three-phase, squirrel-cage induction motors. The operating characteristics of an induction motor are illustrated in the speed-vs.-torque curve in Fig. 15.14. During motor startup, the difference between the developed torque and load torque determines the rate at which the motor will accelerate up to speed. If sustained, the large current draw during startup would cause permanent motor stator damage. Therefore, the startup torque capabilities of the system must be well above (e.g., 1.25–1.5×) that required by the system operating load. Note that in PCP applications, the static friction within the pump, combined with initial system inertial loads, can, in some cases, cause the torque required at startup to be substantially higher than the normal operating torque. In particular, the startup or breakaway torque of the pump can be affected by excessive compression set or swelling of the elastomer. Fig. 15.14 shows that the normal operating range for motors is the linear region below the full-load torque (i.e., torque required to produce rated power at rated speed). Continuous operation at torques above the full-load torque may result in excessive heat generation, which will cause permanent motor damage.
High-efficiency motors designed to NEMA B standards (see Chap. 8 in the Facilities and Construction Engineering section of the Handbook ) are typically used in PCP applications. They characteristically have startup torques of between 125 and 150% of full load (i.e., for motors with synchronous speeds of 1,200 rpm), breakdown torques of 200% of full load, and a slip of < 5%. In addition, because the motors are unsheltered in most PCP installations, totally enclosed fan-cooled motor enclosures are typically used for these applications. The fans are considered critical for providing adequate cooling to prevent damage to the motor under warm-climate operating conditions. Most PCP drive systems use six pole motors that operate at slightly < 1,200 rpm with supply power of 460 V and 50 to 60 Hz.
Nominal power factors are sometimes quoted by manufacturers based on operation at full load under the rated voltage, current, and frequency conditions. For the induction motors used in PCP applications, nominal power factors typically range from 0.80 to 0.90. However, motors are designed to operate with a maximum power factor when loaded to full capacity, and this is often not the case in the field. Actual power factors can be measured during motor operation with specialized equipment.
Nominal overall energy conversion efficiency values for electric motors are often quoted by manufacturers based on operation at full load under the rated voltage, current, and frequency conditions. In the range of motor sizes used in PCP applications, nominal efficiencies range between approximately 90 and 95%. However, as for the power factor, motors are designed to operate at maximum efficiency when loaded to full capacity. Operation above or below full capacity or deviations from rated conditions will result in lower efficiencies.
Motor power factors and efficiency values may decrease when a motor is used in less-than-ideal operating environments (e.g., high ambient temperatures) or with increased motor age. Thus, differences between summer and winter operating conditions should be taken into consideration with respect to motor performance and efficiency.
Safety Shutdown Devices. Surface equipment components, such as the hydraulic system or the prime mover, may be at risk of sustaining costly damage if allowed to operate continuously under certain conditions. As a result, surface drive systems usually incorporate devices that automatically shut the system down when adverse conditions exist. For example, hydraulic systems often have a switch to shut the system down if the hydraulic fluid level drops too low; internal combustion engines usually have high-engine-temperature and low-oil-pressure shutdown switches; and many electronic systems are equipped with high-current shutdown switches.
Torque Limiters. Bottomhole pump seizures resulting from sanding or elastomer swelling, parted tubing, and blocked flowlines can all result in a sudden escalation in rod-string torque. If uninterrupted, the power transmission equipment will continue to increase the applied torque until the rod string or some other component fails. To prevent such failures, torque limiters are installed on the surface equipment to ensure that polished-rod torque cannot exceed some preset limit. Hydraulic systems, for example, typically use a pressure control valve that allows some hydraulic fluid to bypass the hydraulic motor when the system pressure becomes too high. This reduces rod-string speed while allowing the prime mover to keep operating at a safe torque level. Electronic drives either receive torque feedback from a mechanical device on the drive head or determine torque directly with special algorithms. When this operating torque exceeds the preset limit, the electronic drive will reduce the rod-string speed in an attempt to lower torque. If that fails, the drive will eventually shut the prime mover off.
ESC Sytems. ESC systems are used to vary the speed of direct-drive systems. ESC systems incorporate an inverter operating from a three-phase power source, a control system that directs and excites the inverter, and an induction motor. Currently, several variations of ESC systems are being used in PCP applications. The primary difference between these systems is in the control system strategy and types of inverters used. Motor speed is controlled by adjusting the frequency of the input power signals generated by the inverter on the basis of the control system algorithms.
Most ESC systems typically operate the electric motor at a speed setpoint, although more advanced systems also allow torque-based control. Three-phase AC power is fed into a rectifier circuit that produces a DC bus. The pulse-width-modulated inverter draws energy from this bus and creates three-phase AC power at the frequency commanded by the control system. Although basic speed control is typically open loop, the more elaborate systems often use closed-loop speed control capabilities. The control modules of more advanced ESC systems may incorporate sophisticated motor algorithms, microprocessors, and digital signal processors to perform a multitude of motor current, magnetic flux, rotor slip, winding resistance, temperature correction, and magnetizing reactance calculations using several different feedback signals from the motor. The system then uses this information to achieve the desired motor operating condition. Fig. 15.15 shows a block diagram illustrating the typical configuration for these systems.
Most ESC systems allow programming of such basic control options as torque limits, speed ramping, and regenerative braking. More advanced systems include features like automatic restart after fault trips and delays, frequency skipping to avoid resonance, and power-loss ride-through. Many ESC systems also have an optional serial communications interface that enables digital links to programmable logic controllers or computers for remote access to monitoring, adjustment, and control functions.
Rod-String Backspin Control Devices. When a surface-driven PCP system is in operation, a significant quantity of energy is stored in the torsional strain of the rods and within the fluid column above the pump within the tubing string. The development and use of larger-displacement and higher-pressure-capacity PC pumps have led to a substantial increase in the magnitude of the torsional strain and fluid energy that become stored in the production system during normal pumping operations. The stored energy is released with backspin of the pump and/or rod string whenever the PCP system is shut down through routine operator intervention or automatic power cutoff in high-torque-overload cases. When the power supply to the drive is lost or interrupted, the potential energy that remains in the system will cause the surface equipment and drive string to accelerate in the direction opposite its normal operating mode. Uncontrolled backspin can lead to surface equipment damage and backed-off rod strings or tubing. These conditions also pose a significant hazard to field personnel working on or near the surface equipment. Thus, it is essential that brakes be used to control the release of rod-string torque and restrict rod recoil to a safe speed. In many applications, if unrestrained by the surface drive/brake equipment, backspin speeds can increase to the point at which the drive-head sheaves or motor fans fragment and "explode" radially outward because of the high centrifugal forces generated.
Typically, two different types of backspin events may occur: the seized pump scenario, in which the pump rotor seizes within the stator, and the normal shutdown scenario that occurs during routine shutdowns of the pumping system. Upon shutdown in the seized pump case, the pump has stopped turning and the torsional strain energy (i.e., twists) stored in the rod string causes the surface system to start spinning in the reverse direction until all the energy is dissipated. The response period is generally short, and little or no fluid drains from the production tubing because of the seized-pump condition. In the normal shutdown case, fluid remaining in the production tubing drains back to the well through the pump, causing both the pump and the drive system to accelerate backward. This continues until the fluid energy in the tubing (i.e., fluid level) is balanced by the fluid column in the annulus and the pump friction, which can take anywhere from several minutes to hours, depending on the circumstances.
Several incidents have occurred in which uncontrolled backspin of a PCP system drive head has led to explosive sheave fragmentation. In a few cases, personnel were struck by sheave fragments and seriously injured. This has led to a heightened awareness by equipment manufacturers and operators of the need to ensure that surface equipment (i.e., particularly the braking system) is properly sized for each application and to implement operating and workover procedures that enhance worker safety.
Most drive heads are equipped with some type of brake system to limit backspin speeds to the allowable speed ratings of the drive-head and sheave components. Table 15.3 summarizes the major types of recoil control devices used in PCP systems.
In hydraulic systems, when the rods backspin, the hydraulic motor becomes a pump, causing the hydraulic fluid to flow in the reverse direction through the system. Braking is usually accomplished by forcing the fluid to pass through a flow restriction. Standalone hydraulic constriction devices use a hydraulic pump driven by rod backspin to force fluid through a flow restriction. Torque converters provide braking by forcing vanes to rotate within a viscous fluid. Another basic type of recoil control device uses brake pads activated either mechanically or through the use of a hydraulic pump driven by rod backspin. Regenerative braking has been incorporated into some of the newer ESC systems. With this type of braking, the electric motor is loaded during the backspin, causing it to act as a generator and convert recoil energy into electrical energy. However, the utility of these systems relies on the integrity of the drive-system components (e.g., belts and sheaves) that link the polished rod and electric motor, which poses additional risk of failure.
It is important for operators to ensure that the brake specifications of the drive equipment installed are adequate for their specific application conditions under both backspin scenarios described above. Apart from physical compatibility with the drive system being used, it is important to consider the speed at which the braking device engages, the torque that it can resist, and the energy that it can dissipate safely. If the recoil control device does not engage until the rods reach a relatively high speed or if it cannot handle the amount of torque applied by the rods, it may prove ineffective in preventing excessive backspin speeds.
This section outlines some auxiliary equipment commonly used with PCP systems. a brief description of the design and application features of each product is provided.
Tag Bar Assemblies and Tail Joints. A tag bar or "rotor stop" is normally required to facilitate installation and spaceout of the rod string. Several different tag bar designs are available, but they usually consist simply of a steel rod or bar (approximately 25 mm [1 in.] in diameter) fastened widthwise across the middle of a short (e.g., 0.6 m [2 ft]) perforated tubing pup joint that is threaded to the pump intake. In some designs, the rod is replaced with a steel plate with holes to permit fluid flow. The number and shape of the perforations in the pup joint vary among manufacturers. A large perforated area is particularly important in highly viscous fluid applications to minimize flow losses and to facilitate sand flow to the pump intake. The pump vendor usually supplies a tag bar joint with the PC pump.
Although the tag bar pup is usually the bottom component of the tubing string in a PC pump completion, an additional length of tubing is sometimes run below the tag bar as a tail joint to lower the pump intake. For example, in horizontal wells, the pump may be seated in the vertical section to alleviate wear problems while a tail joint is installed to allow fluid to be drawn from the curved or horizontal sections of the wellbore. This technique can also be used effectively to increase the fluid flow velocity below the pump, which can be important for maintaining solids in suspension. In some cases, tail joints can be used to reduce the gas-to-liquid ratio at the pump intake, although the pressure losses through the tail joint may lead to additional solution gas breakout, resulting in little or no improvement in volumetric pump efficiency. If tail joints are used, they should not be centralized and the string should be landed at a position where the intake is on the low side of the wellbore to minimize the amount of free gas that enters the pumping system.
Tubing Anchors. Most PCP systems operate in the clockwise direction, so the resistive (i.e., friction) torque in the system tends to unthread the production tubing connections. As a result, tubing anchors are often run below or above the PC pump so that the resistive torque loading is transferred directly to the casing. They also alleviate the need to over-torque the tubing connections during makeup, which can substantially increase the number of makeups possible before thread damage occurs. Tubing anchors should be run with large-volume pumps and in high-speed applications in which the high resistive torques and system vibrations increase the potential for tubing backoff problems. Although several vendors supply conventional tubing anchors that can be used in this application, several manufacturers sell products specifically designed for PC pumping systems that differ from conventional anchors in that they resist torque while providing minimal axial load resistance. This facilitates removal of the tubing string from a well that has sanded in.
Tubing Rotators. When tubing wear is a major issue, such as in slant and horizontal wells, tubing rotator systems can be used to substantially improve the service life of the tubing string. Rotating tubing hangers that allow the tubing to be rotated while the pump is in operation have been designed. The tubing is suspended by a thrust bearing, and a rotator mechanism that can be ratcheted manually or can be equipped to rotate the tubing continuously is provided. Rotating tubing hanger products are available from several different vendors.
Tubing Drain. Tubing drains provide an alternative means to drain produced fluid from the production tubing string in PCP applications when the rotor cannot be pulled from the stator. These devices are commonly run in wells that are prone to experiencing seized rotors because of a buildup of produced sand above the pump or excessive elastomer swell. The drains are run with the production tubing string and are typically located a few tubing joints above the pump. To activate the drain, the production tubing is pressurized from surface to the point at which the drain "blows" (i.e., a plate ruptures or shear pins fail), allowing the fluid column in the tubing string to drain back to the casing annulus. The existing tubing drain products cannot be reset (i.e., closed) from surface; therefore, the tubing string must be tripped to replace them once they have been activated.
Tubing Centralizers. PCP systems can experience severe vibration problems in some wells, particularly those operating at high speeds. Tubing centralizers can be run in conjunction with the production tubing to help stabilize the string and reduce the vibration amplitudes, which helps to mitigate tubing failures caused by backoff and/or fatigue.
Downhole Gas Separators. Downhole gas separators are used routinely in the oil industry to separate free gas from the production fluid before it enters the pump. Eliminating free gas from the produced fluid reduces its compressibility and therefore increases the volumetric efficiency of the downhole pump (which is determined based on liquid volume only). The gas separators used in PCP applications are normally passive devices that simply create a flow path that encourages the free gas to flow up the casing annulus. As a result, the completion details (e.g., casing size, pump seating location, and use of torque anchors) can have a significant influence on the effectiveness of these devices. Flow losses within the separator may also affect the amount of free gas entering the pump. A gas separator device designed specifically for directional- and horizontal-well applications uses a weighted cam and swivel system to ensure that the intake remains on the low side of the wellbore.
Monitoring and Control Systems. Since the early 1990s, operators have begun to incorporate field instrumentation and logic functions into process control systems for PCP systems.  These systems monitor a variety of production-related parameters, make decisions that are based on their values, and then automatically implement these decisions. For example, some pumpoff control systems measure fluid levels or bottomhole pressures, compare the measured values with preset upper and lower limits, and then adjust the pump speed to maintain the fluid level within the desired range. These systems hold considerable promise for reducing manual monitoring time, decreasing downtime, and increasing productivity.
Pressure and Flow Switches. Pressure switches are used to shut down the PCP system in the event of either excessive or low flowline pressures to prevent damage to or failure of the surface or downhole equipment. Flow switches are used to control flow rates within prescribed upper and lower limits and to shut down the system if the rates move outside the desired operating range (i.e., usually low-flow conditions).
Alternative PCP System ConfigurationsSeveral nonstandard PCP systems have been developed by various companies to improve pumping capacity, performance, and serviceability for certain applications. These include a number of different downhole drive systems that inherently eliminate tubing wear problems and reduce fluid flow losses. Rod-insert PC pump designs are available that preclude the need to pull the tubing string for pump replacement. Charge pumps and fluidizer pumps are currently being used to increase the gas- and solids-handling capabilities of PCP systems. The following sections provide a brief description of the rationale for developing each hybrid system and a description of the basic operating principles of the product where applicable.
Electric Downhole Drive PCP Systems. The use of PC pumps driven by conventional electric submersible pump (ESP) motors was first attempted by a Canadian operator in a heavy oil well in 1966, unfortunately with little success, and then to a much greater extent by Russian operators in the 1970s. However, only within the last decade have these downhole drive (DHD) PCP systems been more fully developed and successfully deployed on a commercial basis.  Several major ESP vendors now market motors, gear boxes, and other equipment for DHD PCP systems; as a result, these systems have begun to see wider use. The entire surface unit drive system and rod string required in a conventional PCP system are replaced with a DHD unit that typically consists of an ESP motor (either a 2- or 4-pole design that has synchronous speeds of 3,600 and 1,800 rpm, respectively), a gearbox and flex-shaft assembly, and a pump intake unit. Fig. 15.16 shows a schematic of a generic DHD system.
A key feature of the DHD systems is the gearbox/seal/flex-shaft assembly. Although various vendors use different designs and configurations for these components, the overall functions are typically the same: (1) to isolate the motor oil from the well fluids; (2) to provide a speed reduction between the motor and the pump; (3) to isolate the motor and gearbox from the pump’s eccentric motion; (4) to support the thrust load generated by the pump; and (5) to provide a path for the produced fluid to flow from the wellbore past the motor (i.e., for cooling) to the pump inlet. The speed reduction is necessary because 2- and 4-pole ESP motors normally rotate at 3,600 and 1,800 rpm, respectively (i.e., synchronous speed at 60 Hz), which is much higher than the ideal operating speed for PC pumps. The eccentric motion of the pump is typically absorbed by a specially designed flex-shaft or knuckle-joint assembly positioned between the pump and the gear box.
DHD systems offer certain advantages in applications in which neither an ESP nor a rod-driven PCP can be used optimally. For example, PC pumps generally perform better than conventional ESPs in viscous-oil, high-sand-cut, or high-GOR applications. In deviated or horizontal wells, the rod strings required in surface-driven PCP systems create potential for severe wear or fatigue problems, particularly if there is a large differential pressure on the pump. In such cases, a DHD system may offer a better overall solution by combining the pumping capabilities of a PC pump with the benefits of a rodless drive system. Eliminating sucker rods also results in lower flow losses, which may, in some cases, allow less expensive, smaller-diameter production tubing to be used. In addition, there are no backspin safety issues because the rotating parts are all run downhole. A DHD system also eliminates the need for a stuffing box at surface, thereby reducing the potential for leaks. Drawbacks of the DHD systems include the additional capital and servicing costs associated with the power cable for the downhole motor, some size restrictions, and in most cases, additional coordination between the ESP and PCP vendors for equipment design, supply, installation, and service. In practice, these systems are normally used only in higher-rate applications because their use in low-productivity wells generally is not economical.
It is imperative to design a DHD system properly because changing equipment once the system has been installed in a well is costly. Once installed, speed control can be achieved only with a variable-frequency drive. It is important to ensure that the cable and seal systems chosen are compatible with the well fluids to prevent premature system failure. Also, the pump is not normally "sumped" because there must be liquid flow past the motor at all times during operation to ensure that the motor is adequately cooled.  Manufacturers recommend a 0.3 m/s [1 ft/s] minimum liquid flow velocity past the motor, but this recommendation is based on high-water-cut ESP system designs in which the flow is turbulent. With viscous oil, it is possible that the flow will be laminar, even at 0.3 m/s [1 ft/s], which may result in insufficient motor cooling and thus increased potential for motor failure. Shrouded systems may be used when seating the pump below the perforations is desirable or when the flow velocity past the motor is expected to be too low for adequate cooling. Note, however, there may be additional flow losses through the shroud that should be taken into consideration. During installation of DHD systems, the susceptibility of the power cable to damage is a concern; thus, particularly in directional- and horizontal-well applications, the use of cable protectors is recommended.
Wireline-Retrievable DHD PCP Systems. Recently, DHD PCP systems have been developed in which the motor, drive assembly (i.e., seals and gearbox) are run into the well on the tubing string, and the pump (both rotor and stator) are run in and latched to the drive system by wireline. This allows relatively fast and inexpensive pump replacement when necessary, which is attractive in regions where rig costs are high or when frequent pump replacement is required. These systems typically require large casing (e.g., typically 177 mm [7 in.]) and tubing string sizes (e.g., 114 mm [4.5 in.] and larger) to accommodate the use of PC pumps with adequate displacement capacities.
Hydraulic DHD PCP Systems. There are two types of hydraulic DHD systems for PC pumps that are either commercially available or are under development by different manufacturers. These include a closed-loop hydraulic system with a downhole hydraulic motor driving a PC pump and a closed- or open-loop fluid-driven PC motor coupled to a PC pump. Both of these hydraulic drive systems require a surface pump and a fluid handling system to provide power fluid to the downhole hydraulic motor. In an open-loop system, the power fluid is commingled with the produced fluid for return to surface; in a closed-loop system, a separate flowline is required for the return stream. In the closed-loop systems, hydraulic oil is typically used as the power fluid, whereas water is normally used in open-loop systems. The systems in which a second PC pump is used as a motor to drive the production pump are typically open-loop designs, and the two pumps are sized relative to one another so that the power fluid used to drive the motor pump is produced with the formation fluid back to surface by the production pump. In viscous-fluid applications, this arrangement can provide the advantage of viscosity reduction and lower flow losses.
The major advantages of these systems are the elimination of the backspin hazard, stuffing-box leaks, and wear and failure problems associated with rod strings. Drawbacks include the added complexity of the surface facilities and downhole completion, higher workover costs, and limited production rate capacity. The availability and use of these systems have been quite limited.
Rod-Insert PCPs. Rod-insert PCP systems are configured the same as the conventional surface-driven systems, with the exception that both the rotor and stator are run on the rod string. This design allows the stator to be pulled without removal of the tubing string. The obvious benefit to this design is savings in service rig time. The major drawback is the limitations imposed by standard tubing-string diameters on the size (i.e., displacement) of the PC pump that can be deployed. Problems with latching and release of the downhole assembly can also be an issue in some cases (e.g., sand buildup above the pump). Note that some of these systems rely on the use of conventional pump hold-down subs designed for beam pump systems.
Tubing-Driven PCP Systems. This type of system, currently at the prototype development stage, is another hybrid of the conventional surface-driven PCP system in which the tubing string is used to drive the downhole pump and to provide a conduit for fluid production to surface. The surface-drive system must support, rotate, and seal the tubing string, and the downhole completion must be modified to include an anchoring system for the stator, a swivel fixture to facilitate rotation of the rotor within the stator, and tubing centralizers to prevent casing wear. They are capable of delivering much higher torque to the pump than the conventional rod-driven systems. The tubing strings should also be equipped with centralizers designed to alleviate casing wear concerns.
Charge Pump Systems. For many years, Canadian operators have successfully used PCP systems specially configured with two pumps run in series with common rod and tubing strings.  These so-called charge pump systems consist of a higher-displacement, low-lift pump run below a lower-displacement, normal-lift pump, as illustrated in Fig. 15.17. The two pumps are separated by one or more joints of tubing to facilitate the different rotor eccentricities and the "timing" of the two rotor/stator pairs. Charge pumps are used to raise volumetric pumping efficiency in gassy wells by using the larger-volume pump to compress the produced fluid substantially before it enters the second pump (on which the efficiency is based). This can allow increased drawdown under gassy conditions and helps to ensure adequate fluid cooling of the main PC pump, which facilitates longer run life. The drawbacks of charge pump systems include their increased capital cost, increased energy consumption because of the higher mechanical friction of the system, and increased pump length, which makes them more difficult to handle and install. A number of vendors supply these pumps on a special-order basis.
Fluidizer Pumps. Fluidizer or recirculating pumps are simply a variation of the charge pump configuration. The basic difference between the two systems is that the tubing segment separating the two pumps is perforated in a fluidizer pump configuration. This design allows some of the fluid produced by the larger pump to be recirculated back into the casing annulus while still helping to improve the efficiency of the second pump. Fluidizer pumps are typically used to help prevent sand bridging and settlement as a means to decrease the workover frequency in wells producing sand-laden fluids. 
Water Reinjection Systems. In addition to common use in dewatering coalbed methane wells, PCPs have been used to dewater gas wells. They have also seen use in conjunction with downhole water injection systems and in various configurations of downhole oil/water separation systems.  In a gas-well dewatering system with downhole injection, a packer and sealbore assembly are used to isolate the producing zone from the lower water-disposal zone and a bypass sub is run below the PC pump (typically a rod-insert pump design which latches into the bypass sub assembly). The PCP system operates in a normal manner, pumping the water, which separates by gravity from the gas and collects above the packer, into the production tubing above the pump, while the gas flows to surface in the casing/tubing annulus. The water builds up sufficient head in the tubing string to create flow down past the PC pump through the bypass sub into the disposal zone. The PCP downhole oil/water separation systems tend to be more complex in terms of the downhole equipment configuration given the added requirement of performing effective oil/water separation and downhole water reinjection. These systems represent an emerging technology with relatively few field trials completed to date.
As mentioned, despite the large number of installations worldwide, PC pumps and drive systems do not, in general, conform to any industry standards or common specifications. As a result, there is significant variation in the products available from different vendors, which generally precludes interchangeability of equipment components. The nomenclature (e.g., naming conventions, ratings) used in conjunction with both pumps and drive units also varies considerably, which can make it difficult for users to easily compare and select products from different suppliers. Nevertheless, there have been some recent efforts to develop industry standards for PCP systems.
In the late 1990s, the International Organization for Standardization (ISO) commissioned the development of a standard for downhole PC pumping systems. This effort led to the issuance of ISO Standard 15136-1, Part 1: Pumps in 2001, with further work currently being undertaken to develop a Part 2 dealing with drive units. The published standard provides guidelines related to PC pump manufacturing, design, and bench testing; therefore, it is useful from an informational perspective. However, the provisions of the standard tend to be very general, and it does not attempt to preclude individual vendors from continuing to offer a unique line of pump products with different elastomers. Although many provisions are consistent with the current practices of major suppliers of PC pump products, the standard as a whole does not appear to have been widely adopted by the industry at this time, in part because of some of the nomenclature requirements.
In response to a number of drive/sheave failures in the mid- to late-1990s, a group of surface-drive manufacturers in Canada initiated the development of an industry standard for surface drives that encompassed braking systems.  The standard provides guidelines for the design, specification, and use of PCP surface-drive units in an effort to support safe operation of this equipment.
PCP System Design
PCP systems are, in general, highly flexible in terms of their ability to function effectively in a diverse range of applications. As with other artificial-lift systems, the basic objective in the design of a PCP system is to select system components and operating parameters (e.g., pump speed) that can achieve the desired fluid production rates while not exceeding the mechanical performance capabilities of the equipment components to facilitate optimal service life and system value. When a PCP system is designed for a particular application, both the system components and operating environment must be considered to ensure that a suitable system design is achieved.
Overview of the Design ProcessFig. 15.18 presents a "design process" flow chart that outlines the many factors and considerations that should be addressed in the selection of an effective overall system configuration and operating strategy. At each step, the designer selects certain operating parameters or specific equipment components and must then assess the impacts of these decisions on system performance. For example, selection of a particular tubing size is based on such design considerations as flow losses and casing size. Some considerations apply to more than one decision, as is the case with flow losses that affect pump, tubing, and rod-string selection. Other design considerations may produce conflicting results, which complicates the decision-making process. For example, the use of rod-string centralizers may minimize wear but may also increase flow losses. As with other artificial-lift systems, the design process is generally iterative, and individual parameters are often adjusted to achieve an optimal design for a particular application. As Fig. 15.18 shows, the primary design considerations for a PCP system are pump selection and sizing, fluid flow effects, rod loading and fatigue, rod and tubing wear, and power transmission selection.
The first step in the design process is to gather information for the application of interest. Past experience, fluid properties, production, well records, and reservoir data are all useful sources of relevant information. Next, it is necessary to determine the anticipated fluid rates. These can be estimated from historical data or by setting a dynamic fluid level and calculating production rates based on reservoir data and an inflow performance relationship.  Initial values must then be set for the wellbore geometry, pump-seating location, dynamic fluid level, tubing size, and rod-string configuration. If the design is for an existing well, some of these parameters may already be constrained.
Once these equipment and operating parameters are established, flow losses can be calculated. If the estimated flow losses are unacceptably high, they can be reduced by increasing the tubing size, reducing the rod-string induced flow restrictions, or decreasing the fluid rate. Next, initial values for pump intake and discharge pressures, net lift, pump speed, and pump displacement can be set. This allows the designer to select a range of pump models capable of satisfying the desired pump displacement and lift requirements. However, if there are no pumps available that meet both requirements, then the prescribed pump displacement and lift specifications must be relaxed by decreasing the fluid rate expectations, increasing pump speed, reducing discharge pressure requirements, increasing pump intake pressure, or by implementing some combination of these changes. The individual pumps that satisfy the requirements are then evaluated on the basis of geometric design and fluid considerations to select the most appropriate pump model.
Once a specific pump model has been selected, rod loading, rod-string/tubing wear, and surface equipment requirements can be evaluated. If the calculated rod stresses exceed the allowable value, then either the rod-string strength must be increased through the use of a larger rod or higher-strength material, or the loading must be decreased through a reduction in the net lift requirements or the use of a smaller-displacement pump. Similarly, if the predicted rod-string/tubing wear rates are unacceptable, then steps must be taken to reduce axial loads (e.g., use of a smaller pump), or the rod string must be reconfigured so that it is less prone to wear. After the rod loading and wear considerations are satisfied, the final step in the design process is the selection of surface equipment. If the available surface equipment cannot meet the polished-rod power requirements, then the design process must be repeated to configure a downhole system or operating parameters that result in reduced system loads. For example, reduced power requirements can be achieved by lowering the pump speed (which will also likely lead to a lower differential pump pressure) or by selecting another pump with a smaller displacement. Once a final system design has been established, any areas of potential concern should be re-evaluated to confirm that the design satisfies the functional requirements of the application within acceptable operating guidelines.
It is quite apparent that the interdependency between the numerous equipment selection and well completion options, variations in operating conditions, and complex fluid flow and mechanical interactions that affect system loading and performance can make the assessment and design of PCP systems difficult and time consuming. In new applications, numerous iterations may be required just to establish a workable system. Because design optimization based on manual calculations is usually impractical, computer programs have been developed to help designers work faster and more effectively. The following sections provide further details on specific design parameters.
Pump SelectionFig. 15.19 summarizes the key technical considerations and decisions involved in selecting a PC pump for a particular application (note that other considerations, such as local vendor choice and economics, can also affect pump selection). As illustrated, the selection criteria include pump displacement, pressure capability, geometric design, elastomer type, and rotor coating characteristics.
Pump Displacement and Pressure Capability. When selecting a PC pump, the two most critical requirements are adequate displacement capacity and pressure capability to ensure that the pump can deliver the required fluid rate and net lift for the intended application.
It is typical to select pumps with a design (i.e., theoretical) flow rate that is somewhat higher than the expected fluid rate to reflect pump inefficiencies during production operations. Fluid slippage, inflow problems, and gas interference all contribute to reduced pump volumetric efficiency. Together, the design fluid rate and prescribed pump rotational speed define the minimum required pump displacement as
where smin = minimum required pump displacement (m3/d/rpm [B/D/rpm]), qa = required fluid rate (m3/d [B/D]), ω = pump rotational speed (rpm), and E = volumetric pumping efficiency in service.
Initially, an optimal pump speed should be assumed on the basis of the intended application conditions, with the primary considerations being the viscosity of the produced fluids and tubing-wear potential. Table 15.4 lists typical pump speeds recommended for the production of fluids in different viscosity ranges. Higher speeds may be considered if these suggested values do not deliver the required production rates or if a pump with the preferred displacement cannot be sourced. In most cases, it is preferable to pump at the lowest speed practical to increase the life of the pump, rod string, tubing, and surface equipment. However, consideration should also be given to the impact that the selection of larger-displacement pumps will have on the sizing of the rod string and surface drive.
In general, there has been a trend recently toward higher speeds because new pump models and better sizing practices have been developed that have led to improved pump lives. For example, pump speeds of 300 to 400 rpm remain typical for high-water-cut applications, but some operators now routinely pump at 500 rpm and higher in such applications. Higher speeds may also be practical in some high-viscosity applications in which sand production and tubing-wear problems are not an issue and reasonable pump efficiencies can be maintained. For example, the new large-capacity PC pumps used to produce the prolific heavy oil wells in several eastern Venezuela fields are being run successfully at speeds of 400 to 500 rpm.
The net pump lift requirement determines the minimum required pressure capability of the pump. In determining the net lift value for pump selection, the full service life conditions should be considered. Net lift is defined as the difference between discharge and intake pressures of the PC pump under the expected operating conditions and is estimated as follows:
where plift = net lift required (kPa [psi]), pd = pump discharge pressure (kPa [psi]), and pi = pump intake pressure (kPa [psi]).
Pump intake pressure is normally a function of the casing-head pressure plus the pressure caused by the gas and liquid column above the pump intake in the casing/tubing annulus. However, in systems in which tail joints or gas separators are used, the pressure drop that results from flow through these components must also be subtracted from the intake pressure. An estimate of the pump intake pressure can be calculated as follows:
where pi = pump intake pressure (kPa [psi]), pch = casing-head pressure (kPa [psi]), pg = annular gas-column pressure (kPa [psi]), pL = annular liquid-column pressure (kPa [psi]), and ptail = pressure loss associated with auxiliary components (kPa [psi]).
The pump discharge pressure can be calculated as the sum of the tubing head pressure, the liquid column pressure in the production tubing and the flow losses that occur in the tubing as follows:
where pth = tubing-head pressure (kPa [psi]) pL = tubing liquid-column pressure (kPa [psi]), and p losses = tubing flow losses (kPa [psi]).
For most existing applications, an accurate estimate of the tubing-head pressure will be available from previous measurements, but some additional calculations may be required to establish an appropriate value for the surface piping and related facilities in new installations. When the producing wells flow directly to a central gathering facility, consideration needs to be given to the fact that production from individual wells may be diverted to a test separator system that, in some cases, may impose above-normal backpressures on the pumping system.
Although the determination of static liquid- and gas-column pressures is routine, accurate calculation of flow losses and fluid densities can be much more difficult, especially in multiphase flow situations. As such, the use of analytical or empirical models is often necessary to determine these values.
Once the minimum pump displacement and net lift requirements are established, these values can be used to determine the range of pump models that will satisfy the requirements of a particular application. The main sources for obtaining pump specification information are product brochures and Websites of the various PC pump manufacturers and distributors, as well as design program databases. As noted, if there are no pumps that satisfy a particular set of requirements, then the system design or operating conditions must be changed. The relative cost and availability of particular pump models should also be taken into consideration during the pump selection process.
Torque Requirements. Rotation of the rotor within the stator forces fluid to move up the pump from cavity to cavity. A series of dynamic interference seals separate the cavities and provide a differential pressure capacity. The energy required to turn the rotor and move the fluid against this pressure gradient is provided in the form of torque. Pump torque is composed of hydraulic, viscous, and friction components. Hydraulic torque, the component used to overcome differential pressure, is directly proportional to pump displacement and differential pressure and can be calculated from
where Th = hydraulic pump torque (N•m [ft•lbf]), s = pump displacement (m3/d/rpm [B/D/rpm]), plift = differential pump pressure (kPa [psi]), and C = constant (0.111 [8.97 × 10 –2]).
Fig. 15.20 shows the variation in hydraulic torque as a function of differential pressure for a number of different pump displacement values.
"Friction torque" must be applied to overcome the mechanical friction associated with the interaction between the rotor and stator. The magnitude of the friction torque depends on the interference fit of the rotor and stator, the type of rotor coating and stator elastomer, the lubricating properties of the fluid, and the pump length. Because friction torque reduces the mechanical efficiency of a PC pump, use of rotor/stator pairs with excessive values should be avoided. Understanding the magnitude of the friction torque in a downhole application can be difficult because the torque value can only be established empirically from bench test results (see the Pump Sizing Practices section).
In wells producing highly viscous oil, PC pumps require some magnitude of additional input torque to overcome flow losses that occur within the pump itself. The magnitude of this torque requirement depends on the fluid properties (viscosity vs. shear rate), pump geometry, pump speed, and fluid rate. The additional torque requirements are typically quite small (i.e., can be ignored) in most low-rate wells (e.g., < 20 m3/d) but can be quite significant in heavy oil wells producing at high rates (e.g., > 150 m3/d). Unfortunately, little published information is available at this time to provide guidance or models to estimate these loads accurately. However, some proprietary empirical determinations have been made with data from several instrumented, high-rate, heavy oil wells in Venezuela and full-scale pump tests conducted with viscous oils. 
The total pump torque is thus equal to
where Tt = total pump torque (N•m [ft•lbs]), Tf = pump friction torque (N•m [ft•lbf]), Tv = viscous pump torque (N•m [ft•lbf]).
In the pump selection process, it is essential to make a proper allowance for the torque requirements associated with pump friction and viscous pump torque (i.e., especially in the case of highly viscous fluids) to ensure that the power limitations and load capacities of the surface-drive system and rod string are not exceeded. In some cases, the available torque or power may affect pump selection by limiting the maximum pump displacement. Also, note that the friction torque at startup can be considerably higher than the nominal operating torque due to swell or compression set of the stator elastomer or settling of produced sand above the pump after a shutdown.
Pump Geometric Design. In most cases, several different pumps will satisfy the minimum fluid rate and lift requirements. However, depending on the application, some pumps will likely be more suitable than others. As discussed, pumps with similar displacements can differ significantly in terms of design. These geometric variations cause pumps to perform differently under certain conditions. When selecting a specific pump, it is important to evaluate the nature of the application, the geometric design of the pump, and the compatibility between the performance characteristics inherent to the pump design and the anticipated operating conditions.
The first consideration is whether the casing size will impose a restriction on the pump diameter. Pump diameters currently range between 48 and 170 mm [1.89 and 6.75 in.], typically increasing with pump displacement, as illustrated in Fig. 15.7. Most vendors have pumps available in both standard diameters and slimhole configurations; i.e., the stator housing of many pump models can be machined down to facilitate use in smaller casing sizes. Reasonable clearances (e.g., > 6 mm [0.25 in.] diametrical clearance on casing drift) should be maintained to limit the annular fluid flow velocities to facilitate annular gas separation and to help prevent sand bridging. In the pump selection process, once the maximum allowable stator diameter has been determined, pumps that do not satisfy this requirement can be eliminated. Note also that the rotor major diameter for the selected pump model must be less than the drift diameter of the production tubing string.
For applications producing significant quantities of sand (i.e., > 2% sand by volume), the respective capabilities of different PC pump models to effectively transport the sand becomes an important selection criterion (see also High-Sand-Cut Wells). The sand-handling capabilities of a PC pump are strongly influenced by its geometric design, with shorter-pitch-length, wider-cavity pumps generally offering better performance than pumps with long, narrow cavities.
In applications producing high-viscosity fluids, pump inflow should be considered in the pump selection process. The rate at which fluids can flow into and along the narrow pump cavities is limited. The inflow rate declines with increasing fluid viscosity (because of viscous restrictions) and decreasing pump intake pressure (because of reduced driving force). Some vendors refer to a minimum net positive suction head. If the pumping rate exceeds the inflow rate, incomplete cavity filling occurs, resulting in a pressure drop at the pump inlet, possible cavitation, and reduced pump efficiency (see also High-Viscosity Oil Wells).
Suppliers should be consulted for assistance when choosing between different pump models to contend with sand or highly viscous fluid production.
Pump Elastomer Type and Rotor Coating. In many cases, the most important pump selection consideration is fluid compatibility. Even if the optimal pump geometry has been selected, reasonable pump service life can be achieved only if the stator elastomer is properly matched to the produced fluid conditions. Refer to the Elastomer Types, Properties, and Selection section for guidance on elastomer selection criteria.
Fluid properties should also be considered when it comes to rotor selection. In most cases, the standard chrome-plated rotor is the most suitable. However, if pumping corrosive or acidic fluids, a stainless steel rotor will be less susceptible to corrosion damage. Because the rotor is often the first component to wear when pumping abrasive solids,  the use of better wear-resistant coating materials should be considered. Most pump suppliers offer rotors with special coatings for improved wear resistance.
Pump Sizing PracticesTo contend with the wide range of application conditions, PC pump manufacturers typically fabricate rotors in a range of minor diameters for each pump model. The different rotor sizes are often categorized by standard (i.e., nominal), single or double oversized or undersized designations or by different temperature ratings. The minor rotor diameter typically changes by 0.25 mm [0.010 in.] per size increment. This allows individual pump models to be provided with various degrees of interference fit between the rotor and the stator. The task of selecting a "fit" that will result in optimal pump functionality under downhole conditions is often referred to as "pump sizing."
Through experience, operators and pump suppliers have developed sizing guidelines for many different field applications. These applications are usually classified in terms of fluid viscosity, temperature, and fluid composition (i.e., sand and water cut, aromatic and H2S content) at downhole conditions. Sizing guidelines take into account anticipated elastomer expansion and swell, clearances for abrasives, fluid slippage rates, and volumetric efficiency. For a given application, there is generally a relatively narrow range of acceptable volumetric efficiencies for the pump at rated pressure, as measured on a test bench under certain standard conditions. In some cases, the sizing guidelines may also contain limitations on maximum allowable friction torque.
When a new pump is sized, an initial pump bench test is completed with a particular rotor and stator. Depending on the results of this test, it may be necessary to conduct additional tests with different rotor sizes until a rotor/stator combination is found that meets the predetermined sizing criteria. It is essential to bench test a PC pump to establish its performance characteristics quantitatively given the numerous design, material, and fabrication parameters that can affect the results. The following section describes bench testing equipment, practices, and results in further detail.
Pump Testing Procedures. In a typical PC pump test, the pump is installed horizontally on a test bench (Fig. 15.21). Rotation and power are provided to the rotor through either a direct or hydraulic drive system. Fluid is pumped through a closed-loop system consisting of the pump, discharge lines, fluid reservoir, filtering system, and intake lines. In almost all cases, water with a small amount of oil added for lubrication is used as the test fluid. A choke on the discharge line is used to regulate the pump differential pressure. The test process normally consists of varying the discharge pressure while operating the pump at a constant speed. Various test parameters are monitored and recorded. The discharge pressure is usually set at zero at the start of the test and is then sequentially increased to the maximum test pressure that, in most cases, matches or exceeds the rated pressure of the pump. Depending on the manufacturer, this procedure is repeated at up to four different speeds. Some manufacturers also determine the maximum pressure that a pump can withstand. This is done by completely restricting the pump discharge and measuring the pressure under that condition.
Pump test reports usually contain such information as test speeds, pump discharge pressures, temperatures, actual fluid rates, volumetric efficiencies, hydraulic pressures, and torques. These reports should also include information on the pump components, including model number, unique rotor and stator serial numbers, dimensions, elastomer type, and threaded connections. In terms of the data reported for a pump test, the only parameters actually measured during the test are speed, discharge pressure, temperature, fluid rate, and torque. Speed is directly measured with any one of several mechanical, magnetic, or optical techniques, all of which generally provide quite accurate measurements. Discharge pressure is monitored with either a pressure gauge or pressure transducer. Depending on the type of instrument, the accuracy and resolution of the pressure measurements can vary substantially. Several different methods are commonly used to measure fluid rates. These include measuring the time required to fill a specific volume in a tank, use of a flowmeter or measuring mass changes in the discharge reservoir with time. Except for properly sized flowmeters, the reliability of measurements made with these techniques increases with sample size (volume or mass). Pump torques are determined either directly with the use of a load cell installed on the drive rod or indirectly by monitoring hydraulic pressure in a hydraulic drive system or by monitoring prime-mover current in an electric drive system. In general, the further removed the measurement point is from the pump rotor, the more the torque values will be influenced by frictional losses within the drive equipment.
In addition to differences in test equipment, there are currently no accepted industry standards for conducting bench tests, so test procedures differ among pump suppliers. This is particularly true for fluid additives and the lubrication of pump specimens. Although all suppliers typically use water for the test fluid, various amounts of oil are usually added to the water or applied directly to the pump rotor to provide lubrication. Differences in the type and quantity of oil in the test fluid can result in a large variation in fluid lubricity, which strongly affects the mechanical friction of the pump and thus the measured torque values.
Fluid temperature is also an important parameter that can have a large impact on the results of a pump test. Some manufacturers use temperature control systems to ensure that the test fluid temperature remains relatively close to the specified value throughout a pump test. The target fluid temperatures typically range between 15 and 50°C [59 and 122°F] among vendors. In other cases, no temperature control is used, and the test fluid is subject to temperature changes during individual tests (due to heat produced by the pump) or from one test to another, depending on the test setup and conditions (i.e., ambient temperature, duration, and frequency of tests). Whether regulated or not, a rise in temperature will generally cause the stator elastomer to expand, which can change the rotor/stator fit and pump performance. The duration of a pump test also varies between suppliers, depending on the equipment and procedures used, which also can lead to different test results.
In most pump test reports, the speed, pressure, fluid rate, and torque data are presented in a format similar to that shown in Fig. 15.22. Depending on the particular test, there may be data for more than one speed, or the test results may encompass a different pressure range. Nevertheless, the volumetric efficiency and torque-vs.-pressure curves contain the information used to evaluate characteristics of the pump that was tested.
Volumetric Efficiency. Volumetric efficiency is calculated as the ratio of the measured fluid rate to the theoretical fluid rate for the pump being tested. Theoretical fluid rates are determined based on the test speed and nominal displacement of the pump. At zero differential pressure, however, it is expected that a PC pump would operate at a volumetric efficiency of 100%. Invariably, because of manufacturing and sizing differences between pumps of a given model or variations in the bench test conditions and procedures, the actual efficiency of a PC pump at zero differential pressure can vary significantly from 100%.
In general, volumetric efficiency decreases with increasing differential pressure (Fig. 15.23). This decrease is caused by fluid slippage, or the leakage of fluid across the rotor/stator seal line from higher- to lower-pressure cavities. Accordingly, it is evident that higher pressure differentials cause the slippage rate to increase further once the pump efficiency drops below 100%.
In addition to being a function of differential pump pressure, volumetric efficiency and slippage also depend on the pump pressure capability, fluid viscosity, and interference fit. In Fig. 15.24, efficiency-vs.-pressure curves are shown for four pumps with the same displacement but different pressure ratings. At a particular pressure differential, the slippage rates decrease and efficiency values increase as the pressure capability of the pump increases. This trend can be attributed to the higher number of cavities and seal lines in the pumps with higher pressure ratings. For the same total differential pressure, the pumps with more cavities have a lower differential pressure across each cavity; as a result, they experience lower slippage rates.
Higher fluid viscosities may also contribute to decreased slippage rates and increased volumetric efficiencies. Although fluid viscosity variation is not typically an issue in pump testing because bench tests are usually conducted with water, it is an important consideration in the sizing of new pumps or in evaluating the potential reuse of used pumps in different heavy-oil applications.
At a given differential pump pressure, the slippage rate and volumetric efficiency depend primarily on the "interference fit" between the rotor and stator. The tighter the fit, the more difficult it is for fluid to leak across the seal lines and hence the lower the slippage rate and the higher the pump efficiency. These effects are illustrated in the pump test results in Fig. 15.25 for three similar pumps with loose (undersized), normal, and tight (oversized) fits.
Pump speed variations have a large effect on volumetric efficiency but generally are considered to have little effect on slippage rates. Fig. 15.26 shows efficiency-vs.-pressure data for a single pump tested at three different speeds. The notable improvement in pump efficiency with increased speed can be attributed to the fact that the fluid rate increases in direct proportion to speed, while slippage rates tend to vary predominantly as a function of pressure (see slippage rate curves in Fig. 15.26).
Under specific test conditions (speed, fluid, and temperature), bench test results provide the best indicator of the interference fit of a pump. However, when quantifying pump performance, most suppliers specify only the volumetric efficiency of a pump at its rated pressure and one speed. Although this parameter is commonly used for pump sizing and reuse criteria, the previous discussions illustrate the importance of paying close attention to other test parameters (e.g., test fluid temperature and test speed) that may have influenced the bench test results. This is especially important when pump sizing practices of different suppliers are compared.
Pump Torque. The torque values measured during pump tests can be used to diagnose certain pump characteristics. As discussed previously, pump torque consists of a combination of hydraulic, friction, and viscous components (viscous pump torque will be negligible for tests conducted with water). Hydraulic torque can be estimated accurately from pump displacement and differential pressure. Therefore, friction torque can be estimated by subtracting hydraulic torque from the measured pump torque. For example, Fig. 15.27 shows this breakdown for a typical pump test. In general, for a particular pump, friction torque remains relatively constant with changes in both differential pressure and speed.
Friction torque can vary substantially between different pumps and with variations in the factors that contribute to pump friction. Tighter rotor/stator fits are usually accompanied by larger elastomer displacements (and hence increased hysteretic heating) and higher energy losses, which lead to a corresponding increase in pump friction. Poor meshing or alignment between the rotor and stator also leads to increased friction torque. This "meshing" between the rotor and stator is closely related to the quality control on pitch specifications imposed during the manufacturing process. Material properties, surface finish, and test fluid lubricity control the magnitude of the friction developed because of the rolling/sliding surface interaction between the rotor and stator. The size and shape of the rotor and stator (i.e., the pump model design and fit) influence the seal surface geometry and have a direct influence on the friction torque values. Pump friction tends to increase as the number and length of the seal lines are increased. As a result, multilobe and higher-pressure-rated pumps tend to have higher friction torque magnitudes.
The input energy consumed by pump friction is largely converted into heat within the pump. Excessive heat generated as a result of pump friction and elastomer hysteresis can lead to thermal expansion and cracking of the rotor coating and to progressive damage to the stator elastomer.
It is important to recognize the friction torque values from pump test reports for a given pump model tend to correspond closely to the rotor/stator fit; therefore, they tend to be low for loose-fit pumps and quite high for normal-fit pumps. However, what matters in a system design is the friction torque that develops under the downhole operating conditions. Most pumps sized loosely on the basis of bench results will either swell up because of the fluid environment or expand because of increased temperature downhole, so their friction torque values will increase substantially relative to the bench test. In general, the friction torque of a properly fitted pump will range from 30 to 40% of its hydraulic torque at rated lift for smaller models (e.g., < 0.3 m 3 /d/rpm) to as low as 10 to 15% for the larger models (e.g., > 0.8 m 3 /d/rpm). If the geometric tolerances of a rotor/stator pair match poorly or the interference is overly tight, then the friction torque values can become much higher and may exceed the hydraulic torque.
Fluid Flow Considerations
In a PCP system, produced fluid flows from the pump to surface through the annular area between the rod string and tubing. High fluid viscosities, elevated flow rates, or restricted flow paths can result in large shear stresses developing in the fluid, which cause large frictional forces to act on the rod string. These effects can have the following implications on system loading:
- Fluid shear stresses produce flow losses along the tubing and across couplings, centralizers, and rod guides that contribute to increased pump pressure loading.
- Rotational frictional forces acting on the surfaces of the sucker rods, couplings, centralizers, and rod guides produce resistive rod string torque.
- Axial frictional forces acting on the rod-string body, couplings, centralizers, and rod guides and flow losses across couplings, centralizers, and rod guides produce upward forces that reduce rod-string tension.
Fluid-flow effects can range from having a minor to a dominant influence on PCP system design. This is illustrated in Fig. 15.28, which shows pressure losses for a range of flow rates and viscosities through a 100 m [328 ft] length of 76 mm [3.0 in.] ID tubing (typical of 89 mm [3.5 in.] tubing) without sucker rods present. Note that the pressure-drop values range from nearly zero to values that exceed the corresponding hydrostatic pressure. The change in slope in the curve of pressure loss vs. viscosity is a result of the transition from laminar to turbulent flow.
Unfortunately, depending on conditions, accurately quantifying fluid-flow effects can be extremely challenging. Difficulties arise when the calculations involve non-Newtonian fluid behavior, multiphase flow, or complicated flow patterns around couplings and rod guides. Designers typically resort to an appropriate computer model to perform these calculations. It is beyond the scope of this chapter to describe in detail the methods or formulations typically used to quantify the fluid-flow parameters (e.g., pressure-loss profile along tubing, fluid-column density profile) used in the design of a PCP system. However, the following sections briefly overview the general approach used and outline some special considerations required in these assessments.
Single-Phase Flow. When single-phase flow effects are assessed, the first step is to establish the type of flow regime. Normally, single-phase flow conditions can be classified as either laminar or turbulent. Laminar flow is smooth and steady and governed primarily by viscous forces (viscosity, velocity). Turbulent flow is fluctuating and agitated and depends mostly on inertial forces (density, velocity). The type of flow regime is determined by calculating the Reynolds number for the flow conditions in question.  Usually, the transition Reynolds number for annular pipe flow is assumed to be 2,100 for Newtonian fluids. Flow conditions with Reynolds numbers < 2,100 are considered laminar; conditions that have numbers > 2,100 are considered turbulent. The Reynolds number decreases as fluid viscosity increases or flow rate decreases. Thus, flow tends to be laminar in most heavy-oil applications.
Once the flow regime has been determined, appropriate annular pipe flow equations are used to evaluate the flow (pressure) losses within a surface-driven PCP system. These equations take into consideration the fluid properties, flow rate, and respective rod-string and tubing dimensions. In the case of standard rod strings, the reduced annular space associated with couplings, centralizers, and rod guides can lead to significant additional pressure losses, which should also be taken into consideration. In addition, the common flow-loss equations are typically based on a Newtonian fluid model in which the applied shear stress is proportional to the shear strain rate and the viscosity is the constant of proportionality (shear stress = viscosity × shear rate). However, most high-viscosity petroleum fluids (> 100 cp [100 mPa•s]) tend to be non-Newtonian, exhibiting pseudoplastic (shear thinning) behavior, which implies that the fluid effective viscosity decreases with increasing shear rate.  Fluid viscosities typically are strongly influenced by temperature and variations in fluid composition (water cut, solution gas content). Therefore, it is very important to obtain representative fluid-property information for the application in question and to pay attention to the temperature and shear rates associated with fluid viscosity tests.
Most annular flow correlations assume that the flow is through two concentric pipes.  In a rod-string and tubing system, however, wellbore curvature and gravity will position the rod string against one side of the tubing in most situations. As a result, the flow pattern that develops may deviate from the concentric case. The effect of offsetting the rod string is to create a larger, unrestricted area for flow, thus reducing the magnitude of the fluid shear rates and pressure losses.  The magnitude of this reduction depends on the amount that the rod string is offset from center (i.e., eccentricity) and the relative diameters of the tubing, rods, and couplings. Conservative reductions for laminar flow are 40% for coupling, centralizer, and rod-guide losses and 25% for rod-body losses. For turbulent flow, reductions of 10% for coupling, centralizer, and rod-guide losses and 5% for rod-body losses are reasonable.
The significance that flow losses have on system design depends on the application. In many instances, such as wells producing light oil or high-water-cut fluids at moderate rates, the flow losses are generally small, so they often are neglected in system design. However, in wells producing high-viscosity fluids, excessive flow losses may occur with certain rod-string and tubing combinations (i.e., large rods in small-diameter tubing). In such cases, flow losses are an extremely important consideration in system design that must be addressed through appropriate sizing of the rod-string and tubing components. For example, consider flow of a 2,500 cp [2500 mPa•s] fluid through a 760 m [2,493 ft] length of tubing with 25.4 mm [1 in.] rods and slimhole standard couplings. The corresponding flow losses are shown as a function of flow rate in Fig. 15.29 for 73 mm [2.875 in.] tubing (Case 1) and 88.9 mm [3.5 in.] tubing (Case 2). These flow losses have been "corrected" to account for non-concentric flow. The results show that excessive flow losses would render it impractical to use 73 mm [2.875 in.] tubing unless operating at very low flow rates (i.e., < 20 m 3 /d [126 B/D]). In contrast, use of 88.9 mm [3.5 in.] tubing leads to much lower flow losses because of the increased flow area. Fig. 15.29 also illustrates the effect that flow restrictions have on the magnitude of flow losses. With the 73 mm [2.875 in.] tubing, flow losses associated with the couplings comprised approximately 25% of the total losses even though the coupling flow length was a very small portion of the total rod length (10 of 760 m [33.3 of 2,493 ft]).
Multiphase Flow. Multiphase flow can be defined as the simultaneous flow of two or more phases of fluid, normally liquid and gas. In an oil well producing gas-saturated liquids, when the pressure drops below the bubblepoint, gas will evolve, resulting in multiphase gas/liquid flow. As this gas/liquid mixture flows through the production system, the two phases may commingle in a variety of flow patterns.  The particular pattern or "flow regime" that occurs has a significant effect on multiphase-flow behavior and pressure loss.  Flow-regime maps facilitate the determination of flow patterns from gas and liquid flow rates, fluid properties, and wellbore inclinations. Fluid properties are usually obtained from empirical correlations. Depending on the particular flow regime, different multiphase-flow algorithms are used to calculate the hydrostatic and frictional pressure gradients. The hydrostatic gradient is determined from both gas and liquid densities and takes into account the different velocities of the different phases. The frictional gradient is calculated from friction factors based on two-phase fluid properties. Fig. 15.30 illustrates the procedure used for multiphase-flow calculations, which generally are too complex to perform manually.
Most common empirical correlations for fluid properties have been developed for lighter oils,  and they may not apply to heavier crudes. In general, caution must be exercised when these empirical correlations are extrapolated out of the range for which they were developed. In addition, correlations developed for heavy oils from a particular field can differ considerably for heavy oils of the same API gravity in another region.
Rod LoadingIn 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.
Axial Load and Torque. The axial load and torque at any location along a rod string is made up of several different components (Fig. 15.31). 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]), and 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:
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.]), and 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]), and 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. 
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]), and 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. 15.32 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. 
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); therefore, 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 WearRod-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. Figs. 15.33 and 15.34 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 has shown that tubing wear rates correlate most strongly with sand cut, followed in decreasing order by contact load, centralizer type, rotational speed, and 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.
Power Transmission Equipment Design
The various surface-drive system components will generally have specified maximum load and speed limits. For example, drive-head manufacturers’ catalogs will typically specify a maximum torque, polished-rod speed, and power as well as give a thrust bearing rating for their equipment. Some may also provide a maximum axial load value for their drives. The maximum torque limits typically are set for structural purposes, whereas the power limits reflect the safe operating capacity of the power transmission system (belts and sheaves or gear set). There are also torque limits related to the braking system capacity, and in many cases, only the lower of the two is published. The structural load capacity of a drive head is typically specified from an allowable overhanging motor size or weight. Motor size specifications are also important with respect to functionality of the frame, doors, and other components. Hydraulic systems have maximum and minimum speeds and a maximum hydraulic pressure indicated by the manufacturer.
Note that the maximum axial load specification of a drive head is typically not the same as the thrust bearing load rating (i.e., the Ca-90 thrust bearing rating is the loading at which 90% of bearings will survive 90 million revolutions). At a speed of 200 rpm, this number of revolutions equates to only 312 days of life, so the actual axial load on the drive head should be kept significantly lower than the thrust bearing rating to ensure long service life. It is reasonable to expect the bearing life to increase by about 10 times if the load is reduced by half.
The prime mover should be able to provide sufficient power to the system without being overloaded. The prime-mover power can be calculated as follows:
where Ppmo = required prime-mover power output (kW [hp]), Tpr = polished-rod torque (N•m [ft•lbf]), ω = polished-rod rotational speed (rpm), Ept = power transmission system efficiency (%), and C = constant (1.047 × 10–2 [1.904 × 10–2]).
In calculating the prime mover power requirement, the efficiencies of all the power transmission equipment must be considered. Belts, gears, bearings, and hydraulic systems all have associated energy losses. When selecting an electric motor, it is important to ensure that the motor will be loaded reasonably close to its rating to facilitate efficient operation. The system torque capacity should be sufficient to handle the worst-case operating conditions in the application, including startup.
Drive-head manufacturers’ catalogs list maximum and minimum sheave sizes for the two sheaves required (for drive heads that use sheaves). The maximum sizes are usually determined by size restrictions; the minimum size of the motor sheave will typically be based on a belt curvature limitation and/or torque transfer performance. The sheave sizes and hydraulic equipment displacements will determine the speed at which the system operates, in conjunction with the gear reduction ratio in the drive head (if the drive head has a gearbox). They should be selected so that the prime mover operates as close as possible to its nameplate speed, even in systems in which it is possible to adjust the prime-mover speed (e.g., use of an ESC with an electric motor). When electric motors are operated at lower speeds, they are subject to reduced efficiency and overheating.
In most applications, a backspin brake is required to ensure safe operation of a PCP system. The brake system should have sufficient capacity to ensure that the maximum rated speed of the equipment is not exceeded during a worst-case backspin scenario. Again, both stuck pump and normal shutdown cases should be taken into consideration.
Specific Applications Considerations
Different PCP system applications have unique operational issues and challenges. Appropriate equipment configurations, installation procedures, sizing standards, and operating practices may be required, depending on the application characteristics.
This section discusses some specific application considerations, including (1) high-viscosity oil wells; (2) high-sand-cut wells; (3) low-productivity wells; (4) gassy wells; (5) directional- and horizontal-well applications; (6) hostile fluid conditions; (7) high-speed operations; (8) coalbed-methane and water-source wells; and (9) elevated-temperature applications.
High-Viscosity Oil ProductionOver the past decade, PCP systems have become a very popular artificial-lift method for producing heavy oil (API gravity < 18°) wells throughout the world.  Fluid viscosity under downhole conditions can range from a few hundred centipoise to > 100,000 cp in these applications, and the production rates also vary significantly although low rates are far more typical. In Canada, for example, the low-GOR, heavy oil wells generally have low productivities (< 10 m3/d [63 B/D]), whereas recent heavy oil field developments in eastern Venezuela using horizontal wells have demonstrated very high productivities (> 500 m3/d [2,000 B/D]). These latter applications have prompted revolutionary developments in large-volume PCP systems.
Production of high-viscosity fluids can result in significant flow losses through the production tubing and surface piping. In some instances, the pressure requirements generated because of flow losses can exceed the hydrostatic head on a well. As discussed previously, pressure losses in the system accumulate and are reacted at the pump, where they cause additional pump pressure loading, leading directly to increased rod-string axial loads and system torque. It is critical that system design account for the "worst-case" flow losses, particularly the selection of the pump (pressure rating), rod string (torque capacity), and prime mover (power output).
Fig. 15.35 shows a good example of the effects that viscous flow losses and water slugging can have on pump loads in a heavy oil well. The axial and torsional loads on the well were monitored in real time with a purpose-built PCP system dynamometer unit.  The data show that the axial load and torque values remained relatively constant at about 45 kN and 1100 N•m [10,050 lbf and 800 ft•lbf], respectively, over the first hour of the monitoring period. Over the next 2 hours, both loads declined significantly, with the torque dropping to less than one-half the initial value. The loads subsequently increased again but remained somewhat below the initial load levels. Fluid samples taken regularly during the monitoring period confirmed that the well had gone from initially producing heavy oil at a very low water cut to producing a large slug of water with relatively little oil during the period. Representative water-cut values are shown at different times in Fig. 15.35. Because the only significant difference during the operating period was the viscosity of the fluid being produced, these results clearly demonstrate the pronounced effect that flow losses can have on PCP system loads.
Several alternative methods are available to minimize flow losses. Because most of the pressure drop usually occurs in the production tubing, it is important to ensure that the rod/tubing annular flow area is not overly constricted. This is most easily accomplished through the use of large-diameter tubing. However, tubing sizing must also take into account casing limitations, economics, and sand transport considerations that favor small-diameter tubing. Streamlining of the rod string is another effective way to minimize tubing flow restrictions. Large-diameter centralizers and/or a number of sucker-rod guides can contribute to significant incremental flow losses and should be avoided when flow losses are an issue. Continuous rod provides the lowest-pressure-drop alternative.
Surface piping flow losses should also be considered. Use of small-diameter flowlines and 90° elbows and tees should be avoided. Because of the logarithmic effect that temperature typically has on viscosity, surface flow losses are usually quite temperature sensitive, so insulated systems or buried flowlines are a necessity in cold climates. These alternatives should also be considered in hot climates to preserve heat and to avoid daily temperature variations in long flowlines.
In certain situations, changing the equipment configuration is not an option; other methods must be implemented to reduce flow losses. This can be accomplished by reducing the viscosity of the produced fluid, typically by injecting diluent (light petroleum products or water) down the annulus (to reduce pressure losses in the tubing) or into the flowline near the wellhead (to reduce flowline losses). Note that if viscosity-reducing additives are injected down the annulus, special caution must be taken to ensure that they will not damage the stator elastomer.
Elastomer selection and pump sizing are important in heavy oil applications to achieve optimal performance and pump run lives. It is normally preferred to start with medium-NBR elastomers in these applications because of the superior mechanical properties of these materials. However, in heavy oil applications in which the pumps are prone to swelling (e.g., eastern Venezuela), consideration should be given to the use of high nitrile elastomers. Several vendors have recently introduced soft elastomers (i.e., < 65 shore A hardness) for heavy oil service to facilitate effective sealing while allowing high concentrations of sand to pass through the pump without causing damage. Because slippage rates decrease and pump efficiencies increase with higher fluid viscosities, PC pumps can typically be sized with bench-test efficiencies of 70 to 80% at speeds of 100 to 150 rpm (i.e., at rated pressure without consideration for swell or thermal expansion) without negatively affecting performance. In new applications, optimal sizing criteria can be determined only on a trial-and-error basis by varying pump sizing and subsequently tracking both short-term and long-term performance. There is a tradeoff between sizing pumps more tightly to permit a larger degree of wear to be tolerated before a significant loss in efficiency is incurred and relaxing the fit to reduce the elastomer stresses and prevent elastomer fatigue failures. As a result, it is preferable to start by sizing pumps in the middle and adjusting the sizing criteria based on the types of failures that occur.
Production from heavy oil wells can also be highly variable in nature. To respond to the changing operating conditions, it is important to have a flexible power transmission system. Hydraulic systems are quite common because they provide variable speed capability with a high turndown ratio that is often necessary to facilitate the low pump speeds typically required. Electronic systems (electric motors with speed control systems) can also be effective as long as they have the ability to operate within the lower speed ranges.
Sand production is frequently a byproduct of oil production, especially in some primary heavy oil operations (e.g., Canada) where it is an important part of the recovery process. In such operations, sand influx is usually most severe during the initial stage of production when the volumetric sand cuts can exceed 40%. Subsequently, the sand cuts often stabilize at ≤ 3%. In high-rate applications (e.g., Venezuela), even low sand cuts can equate to significant volumes of produced sand over time. Sand and other solids production can cause problems in PCP systems by accelerating equipment wear, increasing rod torque and power demand, or causing a flow restriction by accumulating around the pump intake, within the pump cavities, or above the pump in the tubing. Also, given its specific gravity of ≈ 2.7, even moderate volumes of sand can substantially increase the pressure gradient of the fluid column in the production tubing.
With proper system design and operation, PCP systems can effectively handle produced fluids with significant sand cuts under reasonably steady-state conditions. Severe operational problems (equipment failures, shutdowns requiring workovers) generally develop due to short periods of rapid sand influx (slugging). Although some slugging occurs naturally, sudden sand influx can also be initiated by operating practices that cause fairly rapid changes in bottomhole pressure. The pressure variations affect inflow rates and can disturb stable sand bridges that develop around perforations, causing the bridges to collapse and sand to flow into the wellbore. For example, experience has shown that large changes in pump speed can precipitate sand slugging. Therefore, large adjustments in pump speed should be made gradually over a few days to allow the well time to stabilize. If possible, other practices that produce sudden variations in bottomhole pressure, such as well loading or casing gas blowdown, should also be avoided. Workover operations that cause swabbing of a well (e.g., rapid pulling of the production tubing string within the perforated interval) are often followed by periods of high sand production. Changes in the produced-fluid conditions can also precipitate sand influx. For example, a sudden increase in water production or a slug of higher-viscosity fluid can lead to a breakdown of stable sand arches, causing a slug of sand to enter the wellbore.
Sand accumulation inside the tubing just above the pump is a common problem. It leads to increased pump discharge pressures, reduced fluid rates, and in severe cases, increased potential for sudden pump failure. Sand buildup occurs when the produced-fluid stream cannot carry all the sand up the tubing to surface. Therefore, it is very important to assess the sand-handling capabilities of a PCP system design for applications in which sand production is expected. Sand settling and fluid transport velocities (in vertical pipes) can be assessed by comparing the fluid drag forces calculated using well-established methods with the weight of the sand particles or particle conglomerates as appropriate.
Sand buildup in the pump intake area causes decreased production rates and, in severe cases, pump failure due to complete blockage of the intake. One effective way to minimize sand accumulation around the intake is to provide a sump below the pump where excess sand can settle. Deeper sumps provide a larger buffer, and therefore it will take longer before sand accumulates to the pump level. Certain pump intake designs also contribute to sanding problems. Restricted intakes tend to produce stagnant flow regions where the sand will settle out. For sandy applications, the pump intake should be configured so that fluids can readily flow (i.e., limited bends, channels) from the wellbore into the pump intake.
Operational problems associated with sand settlement and bridging, both above and below the pump, occur most commonly in directional and horizontal wells. The ability of the produced fluid to transport sand improves with increasing fluid viscosity and flow velocity. Initial system design should consider whether the lowest anticipated production rate will be capable of moving the sand up the tubing, and allowances should be made for slugs of sand entering the system. Decreasing the tubing size and increasing the flow rate are the easiest ways to improve sand transport capability. However, the use of smaller-diameter tubing must be evaluated in terms of its effect on flow losses. Injecting a fluid down the annulus and pumping at higher rates or introducing fluid into the tubing above the pump (recirculation system) are two possible ways to increase tubing flow rates. Because water has a low viscosity, it is often more effective (but more costly) to inject produced or blend oil.
Another recommended practice for operations prone to sand production is to build excess capacity into the equipment design to allow for the associated peak loading condition. If a system normally operates at full capacity in terms of torque, power, etc., any incremental loading will cause either a reduction in speed or a complete system shutdown, which may allow sand to settle out above the pump and necessitate a workover if the rotor cannot be freed.
Produced sands tend to be highly abrasive, causing accelerated wear of the pump, rod string, and tubing. Because abrasive wear is directly proportional to the number of revolutions, the use of larger-displacement pumps operated at lower speeds can help to extend equipment life. However, large-displacement pumps may not handle the sand as effectively as small-displacement pumps. Stator wear can be minimized by choosing an elastomer with good abrasion resistance. Although the standard chrome coating used on most rotors generally provides good wear resistance, double-thickness chrome coatings are commonly specified for abrasive applications; alternatively, special coatings designed to withstand abrasive wear are also available and have shown superior performance in service.  Note that chrome-coated rotors with visible wear can be repaired by replating as long as the underlying base metal has not been worn.
Low-Productivity or Pumped-Off WellsLow-productivity wells by definition deliver relatively low fluid rates; as a result, operators usually attempt to maximize recovery rates by producing them at low bottomhole pressures. If produced aggressively, the fluid column can be drawn down to very low levels even in some relatively high-productivity wells. These pumped-off conditions can cause pump inflow and gas interference problems that prevent the pump cavities from filling completely with liquid. This results in low volumetric pump efficiency, as illustrated by the field data in Fig. 15.36.
Pump inflow problems are common in wells producing viscous fluids under low submergence conditions. With highly viscous fluids, difficulties occur when the pump is operated at a speed that exceeds the rate at which the fluid can flow into and up the narrow pump cavities (cavity flow velocity of the PC pump). Fig. 15.37 shows, for example, a dramatic decline in pump operating efficiency with higher speed in a heavy oil well application. Although the trend evident in the data can be attributed in part to increased gas interference and reduced well inflow over time, the lower bottomhole pressures and pump inflow constraints definitely contributed to the large decline in efficiency.
Operating a PC pump at low volumetric efficiencies results in reduced heat removal rates, higher elastomer temperatures, and increased fluid slippage, which can substantially escalate wear rates (especially if sand is produced). As a result, continued operation at low volumetric efficiency (< 30%) can lead to significantly reduced pump life. Pump selection is a key consideration in low-productivity wells, given the potential for inflow problems to be mitigated to some degree through the use of a larger-displacement pump run at lower speed (i.e., the resultant higher torque requirements need to be considered). Pump intake designs with minimal flow restrictions are also desirable. In horizontal wells, pump submergence should be maximized by seating the pump intake as low as practical within the well.
The sensitivity of the dynamic fluid level to changes in the produced-fluid rate varies considerably between wells. Extra attention must be paid when implementing speed changes on low-productivity wells that can be pumped off rapidly to avoid damaging the pump. Caution should also be used when basing decisions on fluid-shot data in heavy oil and bitumen applications because it is common for a layer of foamy oil to exist in the annulus, which makes the acoustically measured fluid levels misleading.
Gassy Well ProductionIn most operations, dissolved gas begins to evolve as free gas when the pressure drops as the fluid moves toward and then enters the well. Depending on the fluid properties and gas volumes, the free gas may coalesce and flow as a separate phase, or, as in the case of many heavy oil wells, it may remain trapped as discrete bubbles within the liquid phase (foamy oil). Gas entering the pump causes an apparent decrease in pump efficiency because the gas occupying a portion of the pump cavities is normally not accounted for in the fluid volume calculations. The pump must then compress the gas until it either becomes solution gas again or it reaches the required pump discharge pressure.
The best way to reduce gas interference is to keep any free gas from entering the pump intake. When possible, the intake should be located below the perforations to facilitate natural gas separation. Even if the pump can be sumped below the perforations, small casing/tubing annuli can lead to high flow velocities that can "trap" free gas and carry it to the pump intake, thereby reducing the effectiveness of the natural gravity-based separation. Thus, seating of the stator, which typically has a larger diameter than the tubing, either within or above the perforation interval should be avoided if possible. Another option is the use of slimhole PC pumps in such circumstances.
In gassy wells in which the pump must be seated above the perforations, passive gas separators that divert free gas up the casing/tubing annulus can be effective. In such cases, assemblies that centralize the pump intake in the center of the casing should be avoided because free-gas bypass tends to be more efficient in a skewed annular space.  In directional or horizontal wells, it is best to have the pump intake positioned on the low side of the wellbore away from any free-gas flow, which naturally tends to be along the high side of the casing. With the gravity assistance available in such wells, a short tail joint can be used to locate the pipe intake on the low side of the well casing. Special intake devices are also available that incorporate a swivel assembly to ensure that the fluid intake port remains on the low side of the wellbore. Small-diameter or long tail joints should be avoided since flow losses within the tail joint can result in increased gas volumes entering the pump.
Gas production through the pump can lead to substantial fluctuations in rod-string loading, as illustrated by the field data shown in Fig. 15.38. Loading variations can be attributed to discharge pressure fluctuations associated with changes in the fluid-column density and to the lifting effects of the gas produced up the tubing. Pump friction may also vary because of changes in fluid lubricity. The load fluctuations can be significant, particularly when substantial percentages or slugs of gas enter the pump. Large, continuous changes in load may accelerate rod fatigue problems or damage surface power transmission equipment.
When attempts are made to maximize fluid rates in gassy wells, the pump speed should be increased in relatively small increments, with subsequent monitoring of the resulting effects on production rates in order to identify the onset of gas interference problems.
Directional- and Horizontal-Well ApplicationsBecause of the inherent curvature (angle build sections) and angled bottomhole segment of directional and horizontal wells, optimization of a PCP system design for such applications begins with the drilling program. The proposed well geometry, or directional plan, should take into consideration the design and operation attributes of a PCP system, including equipment selection, to contend with potential rod/tubing-wear and rod-string fatigue problems, the preferred pump seating location for achieving optimal production rates throughout the well life, and possible issues related to gas and solids production.
The first line of defense against rod/tubing-wear and sucker-rod fatigue problems in deviated and horizontal wells is a good wellbore profile (see previous sections on rod-string/tubing wear and rod loading). Ideally, the planned angle build rates should be kept as low as practical, and additional monitoring is typically required during drilling to ensure that the well closely follows the prescribed path. Note that slant wells (wells spud at an angle on surface), which typically have no planned curvature, often provide a good alternative to deviated wells for shallow reservoir developments as a means to avoid rod/tubing-wear problems. With slant wells, it is important to ensure that the well profile remains straight and does not "drop down" into the target bottomhole location. If it is not possible to avoid high wellbore curvature (> 5°/30 m [5°/100 ft]) in directional or horizontal wells, it becomes even more important to obtain the smoothest wellbore profile possible. Fluctuations in wellbore curvature and curvature reversals usually lead to severe wear. Therefore, drilling programs should include clauses that specify both maximum curvatures (i.e., dogleg severity) and allowable rates of change in curvature.
Experience has clearly demonstrated that closely spaced surveys (< 20 m [65 ft]) help to prevent large local curvature fluctuations and can typically be justified from an overall capital- and operating-cost perspective. Closely stationed directional surveys are also helpful in determining rod centralization requirements at a later stage. Caution should be exercised when specifying rod strings for directional and horizontal wells (i.e., where the pump is seated in the build section) based on directional surveys with long survey intervals (> 30 m [100 ft]) because the survey data may not reveal high-curvature segments that exist in the actual wellbore. This is illustrated in Fig. 15.39, which compares the dogleg severity established along a directional well based on the widely stationed openhole survey data recorded during drilling and a subsequent closely stationed gyro survey run in the cased wellbore. The gyro survey depicts significant variations and much higher curvatures. Therefore, if unexpected wear problems occur repeatedly at one or more locations along a directional or slant well, the survey may have provided a poor representation of the actual well curvature, and appropriate wear mitigation strategies must be taken to prevent additional failures.
In general, PCP installations that operate within the curved portions of directional or horizontal wells must be equipped to deal with potential wear and fatigue problems. To protect against rod and tubing-wear failures, options include the use of coated centralizers or rod guides with standard rod strings, use of continuous-rod strings, and use of coated and/or surface-hardened tubing joints. Use of tubing rotator systems has also grown considerably over the past decade because they have proved to be an effective preventive measure for severe wear problems in such applications. For example, a horizontal well that had experienced tubing failures monthly was subsequently on production for > 5 months without a failure after installation of a tubing rotator. From a rod-string fatigue perspective, slimhole coupling or centralizer designs offer the best performance because the inherent curvature localization adjacent to the connection is minimized. Keeping the stresses in the rod string at reasonable levels under all operating conditions is crucial, and undertaking detailed loading/fatigue analyses is highly recommended at the system design stage to facilitate proper equipment selection for the specific well conditions. Downhole-drive PCP systems, which remove any concerns about wear or fatigue problems, are another option.
Fortunately, PC pumps can operate effectively at high well angles, even beyond horizontal. However, attention is required when the pump seating interval is selected to avoid potential wear, pump inflow, and gas interference problems. This is illustrated by Fig. 15.40, which presents a vertical section plot of a horizontal well that was inadvertently drilled with a "trap" at the base of the build section. Because the severe sand plugging and gas slugging problems that occurred with the pump initially seated within the angle build section led to several workovers, the operator was forced to try seating the pump in the horizontal section beyond the trap at the location shown. Although the equipment options were quite limited and wear problems were still a concern for this well, it was successfully pumped in this configuration through the use of a continuous-rod string and a larger pump that could be run at low speeds.
Ideally, the pump should be seated as low as possible in directional and horizontal wells to maximize intake pressures. As mentioned, use of long, small-diameter tail joints should be avoided as a means to lower the intake position because of the inherent pressure losses. Depending on casing size, reducing the wellbore curvature over the planned pump seating interval may be important to prevent the pump from having to operate in a bent configuration. This condition would negatively affect pump life and increase the potential for wear and rod-string fatigue failures directly above the pump. Operating a PC pump while bent may also introduce the possibility for fatigue failures of the rotor within the stator. Close attention to the wellbore inclination and curvature is also important in the selection of an optimal pump intake location to ensure that the intake will not be positioned against the high side of the casing, thus increasing the potential for gas interference problems. This is especially crucial in horizontal wells, which are more prone to gas-slugging conditions as a result of elevation variations along the horizontal section. Sand production should also be taken into consideration in establishing the pump intake position. Given that sand transport capabilities are reduced in the casing relative to the smaller-diameter production tubing, seating the pump at nearly horizontal will reduce the potential for problems resulting from sand buildup.
Achieving proper rotor space out (i.e., positioning of the rotor within the stator) is also more difficult in directional and horizontal wells because rod weight is normally a key parameter used during rod-string installation to determine when the rotor enters the stator downhole. Because of friction and the non-vertical-well profile, the weight of the rod string is partially supported by the tubing in such wells. Experience and close attention to other details, such as recording accurate measurements of tubing/rod-string component lengths and monitoring for rotation, become more important in these applications.
Hostile Fluid Conditions
In many applications, the constituents of the produced fluids pose the greatest difficulty in the successful use of PC pumps.  In fact, the current use of PCP systems in many medium- and light-oil wells can be attributed to the recent development of new elastomers that can withstand the produced-fluid chemistry, allowing reasonable pump run lives to be achieved. However, further developments and improvements are required because there are still relatively few PCPs used in fields producing light oils with gravities > 40°API. The presence of different quantities of carbon dioxide, methane and hydrogen sulfide gases, aromatics, and paraffins in the produced fluids, as well as different downhole temperature conditions, requires that special consideration be given to elastomer selection, pump sizing, and well operation. Aromatics such as benzene and toluene typically induce swelling of the stator elastomer, which makes pump sizing more difficult, whereas H2S can cause extended vulcanization, which results in hardening and eventual breakdown of the elastomer material. Diffusion of a significant quantity of gas (in particular, CO2) into the stator elastomer can lead to blistering or fracturing of the rubber because of rapid decompression of the pump during shutdowns.
Pump selection should be based on geometry considerations and stator elastomer properties to minimize the swell potential, although some swelling of the elastomer is inevitable in most cases. Depending on the type of elastomer and the downhole conditions, total elastomer swelling can exceed 3 to 4 vol% in extreme cases, although much lower percentages are usually required for a pump to operate effectively and have a reasonable run life. Performing swell tests is highly recommended to assist in pump selection and sizing when fluid compatibility is expected to be an issue. Experience has shown that the swelling process can be quite gradual, with it sometimes taking up to 6 months for the stator to reach the maximum swell condition. To compensate for the substantial swelling expected in some challenging well applications, pumps may be sized so loosely that they cannot generate any flow at pressures below their rated capacity in a standard bench test. In such cases, the sizing process is usually a delicate balance because, if pumps are fit too loosely, they will not be able to generate sufficient head to produce fluid to surface for a long period of time. One approach used to avoid low initial pumping efficiency because of loose sizing requirements is to complete the initial pump installation with a tighter-fit rotor and then occasionally to replace the rotor with progressively smaller sizes as the stator swells. However, this approach obviously requires additional workovers, which must be justified by the economics of the operation and comparison to other practical options.
Given the many parameters that can influence pump life, it is highly recommended that operators maintain a detailed database of all pump testing and field performance records to establish optimal pump selection and sizing criteria. This information is also crucial in terms of monitoring failure causes and effectively guiding pump replacement decisions as well conditions change.
The most common problem associated with gas diffusion into a stator is the damage caused by expansion of the gas trapped within the elastomer as a result of the rapid decompression that may occur under shutdown conditions. Elastomer selection is obviously important under such conditions because some materials are much less prone to damage than others. Although the options available to prevent rapid decompression and potential damage to the pump are limited, use of drive systems with brakes that prevent rapid drainage of the tubing during shutdown events is highly recommended in these situations. There was also a unique check valve product available previously that prevented the fluid column in the tubing from draining through the pump in the event of a shutdown. Caution should be exercised when attempting to restart such wells immediately after a shutdown to avoid a high-torque-overload condition and potential pump damage. It is also very important to avoid multiple restart attempts in rapid succession because this may lead to reduced brake effectiveness, rod-string failures, or severe pump damage. If a high-torque condition can be attributed to stator swelling/expansion, the options are to load the tubing string to surface before attempting a restart or simply leaving the well shut down for several hours (perhaps a full day) to give the elastomer time to relax.
The fluids produced in light-oil applications often contain substantial quantities of paraffin. As fluid temperature declines through the production system, the waxes precipitate and accumulate on the inside of the tubing and flowlines. If the buildup becomes large enough to severely restrict flow, additional flow losses are generated that increase the operating torque and power requirements of the drive system. Because of the rotational nature of PCP systems, scrapers are not effective at cleaning wax from the tubing. Although chemical and hot-oil treatments are available to remove wax, operators must ensure these treatments will not damage the stator elastomer.
The combination of CO2 and high water cuts may accelerate corrosion of the rod and tubing strings, leading to failures of these components. The rotary interaction of the rod string against the tubing, even in "vertical" wells, results in a corrosion/erosion process whereby the material that would otherwise provide a protective film is constantly removed, leaving a fresh surface exposed for further corrosion attack. Given the mechanisms involved, in many cases the problems cannot be resolved by use of conventional rod guides or continuous-rod strings, although operators have successfully used standard rod strings equipped with spin-thru centralizers or rod guides to prevent additional failures in some wells. It is also important to instruct field personnel to handle and install the rod strings carefully in such wells because any surface damage will increase the potential for corrosion and corrosion/fatigue failures to occur. The use of rod strings made with special materials may help to mitigate these corrosion problems, but they are usually costlier. Some recently developed tubular products with liners or coatings have also proven to be successful in reducing corrosion-related failures. Corrosion inhibitors can also be used, but they must be compatible with the stator elastomer.
Different well stimulation treatments are commonly used by operators to improve production. When contemplating treatment of a well produced with a PCP system, particular attention must be paid to the chemistry of any fluids that may come into contact with the pump. For example, the fluids commonly used in acidizing jobs will remove the chrome from standard rotors. Other chemicals may be incompatible with the elastomer and cause stator failure.
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.
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.
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 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, and improper rotor space-out (i.e., substantial rotor stickup above the stator). The evidence points to tubing fatigue failure induced by vibration; therefore, consideration should be given to possible corrosion-enhanced fatigue. Possible remedies may include changes in pump speed or pump seating depth.
Coalbed-Methane and Water-Source Well Applications
PCPs have become one of the most common types of lift methods for dewatering coalbed-methane wells. Water rates are typically high during initial production and may exceed 400 m3/d [2,500 B/D] in some cases but normally decline to ≈ 25% of their original level after a few months. The produced water often contains high concentrations of suspended sand from hydraulic fracturing, coal particles, and dissolved solids. To facilitate maximum gas production, the wells are usually maintained in close to a pumped-off condition. This tends to exacerbate the problems associated with the handling of produced gas. Because coalbed-methane wells typically have quite modest gas flow rates, capital outlays and operating expenses must consequently be minimized for these operations to be economically viable.
Stator elastomer selection and pump sizing are critical in coalbed-methane applications. The many substances contained in the produced water, either naturally or as additives, can have a very detrimental effect on the performance of certain elastomers. Elastomer erosion characteristics are also important, given the typical presence of significant quantities of frac sand and coal particles in the produced water. In general, the best choice of elastomer for such abrasive pumping conditions is a medium NBR because it generally has the best mechanical properties and, with the inherently low ACN content (i.e., most nonpolar), can be expected to swell the least amount when producing water that is polar. However, one must use caution because some NBR compounds are prone to high water swell. This is not the result of the polymer itself but rather the presence of certain fillers or additives that have a tendency to draw in water. Since there is no oil in the fluid to provide lubrication in these applications, it is very important to ensure minimal elastomer swell because the tightening of the rotor/stator fit leads to high levels of friction, which in turn can cause operational problems and dramatically reduce pump life. As a result, some vendors offer elastomer products specifically formulated for water-production applications.
Solids production is usually most severe the first few weeks after a coalbed-methane well is brought on production. PC pumping systems usually can effectively handle the sand and coal particles contained in the produced water. However, some coal particles can reach diameters of up to 20 mm [0.8 in.]. Difficulties arise when these larger coal particles become lodged in the pump, resulting in a sharp escalation in operating torque, severe tearing of the stator, or complete pump seizure. To prevent these problems, slotted pump intake or tailpipe assemblies should be installed that are sized to prevent the entry of large coal particles but to allow passage of coal fines, sand, and water. Buildup of sand and coal particles around the pump intake can decrease production rates and may cause pump failure as a result of complete blockage of the pump intake. To minimize solids accumulation around the intake, it is common for the wells to have sumps that extend up to 50 m [160 ft] below the pump. When the tubing is pulled for a workover, the well must be flushed out to ensure that the maximum volume is available for solids deposition. To prevent solids from settling out in the tubing above the pump, the transport velocity of the water must exceed the settling velocity of the solids. Because the flow losses associated with water production are normally insignificant, relatively small-diameter tubing can be used to create high flow velocities and thus enhanced solids transport capability.
By nature, coalbed methane operations produce substantial quantities of gas. Ideally, the produced gas flows up the casing/tubing annulus to the gathering facilities. In practice, however, some gas usually enters the pump, causing a corresponding reduction in efficiency (see Gassy-Well Applications section). Maintaining reasonably high pump efficiencies is especially important in coalbed-dewatering and water-source well applications because more heat is generated by pump friction than in an oil well where the produced fluids provide more lubrication. This is reflected by the fact that burnt pumps are a most common mode of pump failure in dewatering applications. As a result, it is important to keep gas away from the pump intake and to carefully monitor for pumped-off conditions. The pump intake should always be located below the perforations or near the bottom of openhole well completions to encourage natural gas separation. It is not uncommon for pumps to be seated up to 100 m [325 ft] below the perforations in coalbed-methane wells. In some coalbed-methane operations, the produced gas may contain a fairly high percentage of CO2, which, as noted, can cause elastomer swelling and rapid decompression problems. In such cases, it becomes even more important to limit gas flow through the pump, although the elastomer selection and pump sizing should take potential swelling into consideration.
To achieve economic gas rates in most coalbed operations, the pressure (i.e., fluid level) at the coal seam must be maintained at a very low level. It is not uncommon for pressures to be as low as 140 kPa [20 psi], which equates to a fluid column above the perforations of only 14 m [45 ft]. The low fluid level requirements, combined with the natural fluctuations in water flow rates from the coalbed, make it critical to use some form of pumpoff control to prevent premature pump failures. The sophistication of these systems depends on the application and can vary from basic manual to fully automated control. Typically, more elaborate systems are required for wells that either have low water flow rates or need the fluid level to be maintained near the pump intake. The most basic pumpoff control systems use some form of apparatus that senses whether water is flowing at surface. Commonly used devices include differential pressure switches and hot-wire anemometers mounted in the flowline near the wellhead. Once a low-flow condition is detected, the control system will usually shut down the pumping system. Some systems will subsequently have to be manually restarted; other more sophisticated systems will automatically restart the well after a certain time delay.
Elevated-Temperature ApplicationsElevated-temperature applications can be divided into medium- and high-temperature categories. The medium-temperature category covers deeper-well applications with natural, higher-temperature reservoir conditions ranging from 40°C [104°F] to ≈ 100°C [212°F]. Field experience has proved that PC pumps can be used successfully in wells producing fluids within this temperature range if the fluid temperatures remain relatively constant. However, to achieve reasonable run lives in such wells, additional attention must be given to elastomer and pump model selection, pump sizing practices, and system operation. The importance of these considerations rises substantially as temperatures increase toward the higher end of this range. In such applications, some additional investigations should be undertaken to assess the effects that elevated temperatures may have on the compatibility of the selected elastomer and the produced fluids. Stator elastomer debonding problems may be encountered in wells producing high-water-cut fluids at bottomhole temperatures exceeding ≈ 85°C [185°F].
Applications that fall into the high-temperature category (temperatures > 100°C [212°F]) include many geothermal wells and most thermal recovery operations. Thermal operations include mature steamfloods in which the temperatures are also relatively constant but may be as high as 200°C [400°F]; cyclic steam operations in which the temperatures can be even higher and typically change substantially; and steam-assisted gravity-drainage wells, which may operate over a wide range of high-temperature and -pressure conditions. Currently, such high-temperature applications pose significant challenges to routine PCP system use, and most of the relevant experience to date has been acquired through various experimental projects. Although the results from high-temperature tests conducted recently by various PC pump manufacturers under controlled laboratory conditions have shown considerable improvement and promise, caution is warranted in translating such results to a field application because other factors besides temperature may affect performance under the downhole operating conditions. Nevertheless, given the potential market, both equipment manufacturers and operators continue to actively pursue alternative pump design and elastomer developments to effectively extend the service temperature range of PC pumps for such applications.
Although the tolerance that elastomers have for high temperatures varies significantly with formulation, the different elastomers used in PC pumps will all begin to experience permanent chemical and physical changes with continued exposure to temperatures above their respective limits. These changes may cause the elastomer to become hard, brittle, and cracked and in some cases to shrink, which typically results in rapid deterioration in pump performance. In addition, the susceptibility of elastomers to damaging chemical attack always increases with higher temperatures. A general assessment of the values in the product literature from several different PC pump vendors indicates that the temperature limit for NBR elastomers is typically 100°C [212°F]; the limits for HNBR elastomers are 125°C [265°F] (sulfur cured) and 150°C [318°F] (peroxide cured); and for FKM elastomers, 200°C [425°F]. High temperature resistance typically comes at the expense of other desirable attributes, such as good mechanical properties (e.g., abrasion resistance), and these requirements often limit elastomer selection.
Severe problems with the sizing and performance of PC pumps are most common when the producing temperatures in a well fluctuate substantially. Although different-sized rotors may be interchanged to compensate for gradual temperature changes over several months, installation of PC pumps in wells in which the bottomhole temperature varies regularly by > 15°C [27°F] is usually not recommended.
The thermal expansion coefficient of elastomers is approximately an order of magnitude higher than that of steel; therefore, temperature changes cause stator elastomers to expand and contract far more than the steel tube housing or the mating steel rotor. The stator housings are also much stiffer than the elastomeric sleeve, so the thermal expansion of the elastomer leads to inward deformation and distortion of the pump cavity. The magnitude of the distortion is proportional to the elastomer thickness at any given point on the pump cross section. Fig. 15.41 shows the change in stator cavity geometry with increasing thermal expansion of the elastomer. It is important to understand that thermal expansion changes are independent of any fluid-induced swell effects, which can exacerbate pump sizing problems. As a result, some vendors now offer high-temperature bench-testing capabilities as a means to eliminate elastomer thermal expansion as a parameter to be addressed indirectly in the sizing of PC pumps. Because pump performance and fit are highly dependent on temperature, caution should be exercised when bench-test results from different vendors are compared to ensure consistency among test parameters.
In certain situations, rod space-out procedures must take thermal expansion into consideration. If the tubing is anchored, temperature changes will cause the rod string to lengthen relative to the constrained tubing. For example, an average temperature rise of 50°C [106°F] will cause a 1000-m [3,280-ft] rod string to increase in length by > 0.5 m [1.6 ft]. However, temperature variations do not affect spaceout in wells with unanchored tubing because the resultant lengthening of the rod string and tubing is equal.
PCP System Installation, Automation, Troubleshooting, and Failure Diagnosis
Adherence to proper installation procedures for both downhole and surface equipment is key to the successful operation and performance of a PCP system. Given the many different types of equipment available and the number of system configuration alternatives, it is advisable to review the product manuals provided by PCP equipment vendors to obtain detailed installation instructions and system operating information for specific installations. The well-servicing guide books available from some service companies also provide useful information. Although the following list highlights a few key system installation and startup considerations, it is not intended to be comprehensive, and the appropriate equipment manuals should be consulted in all cases:
- Confirm that the equipment at the wellsite is configured properly for making the following connections: stator to tubing, tubing to drive head, rotor to sucker rods, and sucker rods to drive shaft or polished rod. Ensure that the stator OD is sufficiently under the casing drift diameter and that the rotor major diameter is less than the tubing-string drift diameter. Also, check to ensure that the size of any rod guides or centralizers is appropriate for the selected tubing size and weight.
- Visually inspect the various equipment components, new or used, for any signs of physical or chemical damage.
- Ensure that proper handling procedures are followed for all equipment components.
- Ensure that the tubing string is made up properly to API 5C1 specifications (i.e., makeup torque levels) to prevent backoff problems. This is especially important if a tubing anchor is not used. If the production tubing is of a smaller diameter than the pump stator, run at least one joint of larger-diameter tubing above the pump to allow for the eccentric motion of the rod string above the pump, and then swage down.
- Ensure that the rod-string connections are cleaned, undamaged, and made up to the proper API torque specifications (power tongs will likely be required for larger rod string sizes).  Proper makeup is essential to prevent failures during production operations, so it is recommended that every connection be validated by use of a makeup calibration card available from the rod manufacturers. Installation of at least two rod centralizers directly above the pump is recommended for directional-well applications. Record the type and position of all centralizers used.
- In hollow-shaft-drive installations, ensure proper spaceout of the rod string so that polished-rod stickup above the polished-rod clamp is minimal (≈ 30 cm [1 ft] maximum). Adequate spaceout allowance is also required for thermal expansion of the rod string in higher-temperature applications in which a tubing anchor is used.
- Give special attention to wellhead alignment, especially in cases in which hammer union connections are used. The use of flanged wellhead equipment is recommended.
- If possible, start the pump slowly and increase speed gradually after a minimum of 5 minutes. Note that after startup it is normal to hear some noise generated by the rods if rod guides are not used. The noise should subside once the produced fluid reaches surface. Continue to monitor the system operation until it is clear that the unit is functioning properly.
- If possible, record torque and speed with time during startup to obtain breakaway torque information.
PCP System Monitoring and Automation
Well monitoring typically refers to the periodic or continuous measurement of production parameters and evaluation of the pumping system operating conditions. Reasons for well monitoring include production optimization, failure detection, and production accounting. Production parameters include fluid rates, gas rates, water cuts, sand cuts, and fluid levels. Operating parameters include tubing-head pressure, casing-head pressure, rotational speed, hydraulic pressure, motor current, and polished-rod loads. Additional production performance parameters, such as pump efficiency, can be calculated from measured values of the production and operating parameters and installed equipment specifications.
Depending on equipment type and application, a variety of methods are available to obtain measurements of the production and operating parameters. The accuracy or frequency of the measurements required for production optimization varies considerably, depending on the parameter and application. The cost and accuracy of the various methods available to measure the individual parameters can also vary considerably.
Automated Monitoring and Control Systems. Relatively few PCP systems are operated with any sort of fully automated control system, although the use of ESC systems has grown considerably. In most cases, measurements of such key parameters as fluid level and polished-rod torque are taken infrequently. These data are generally used by the operator to make decisions regarding changing the pump speed on a particular well. In many cases, there may be periods between these assessments where either the pump runs too fast and the well becomes pumped off, which increases the potential for pump damage, or the pump runs too slow and the system does not produce fluid at the maximum rate possible. Therefore, from both workover and production perspectives, there is considerable incentive to optimize the production process by automating the measurement of a few key production and operation parameters and implementing a system that uses the data to control the pumping system. Potential benefits of implementing such a system include the following:
- Provide accurate, timely data for use in analysis of individual well production performance.
- Provide operators with a means to visually assess current well conditions and performance from remote locations.
- Provide immediate identification of existing or potential problems that could lead to downtime.
- Provide access to historical data for use with production optimization software tools.
- Increase the time available to operators and engineers for identifying and implementing production optimization programs.
The first and probably most beneficial step toward fully automated well monitoring and control is implementing a pumpoff control system. Most operators base their operating strategies on the bottomhole pressure they wish to maintain. The common practice is to try to pump the well at the rate which maintains the bottomhole pressure at the lowest level possible without running the pump dry or causing it to produce large quantities of gas. Usually, this strategy is implemented by periodically checking the annular fluid level and adjusting the pump speed according to the interpreted results. However, this approach suffers from inaccuracies in the methods used to measure fluid levels and the relatively long periods that are typical between actual measurements.
The preferred approach is to measure bottomhole pressure directly with a downhole pressure gauge or an automatically actuated acoustic device. The gauge can be suspended on wireline, strapped to the tubing string, or permanently installed on the well casing. The output from the downhole gauge can be displayed at surface for manual reading, or better yet, it can be processed and stored by a data logging system at a given time interval. The data acquired can be interpreted and used by the operator to adjust the pump speed. A more effective use of the data is in conjunction with a variable-speed controller and a feedback control system. The operating speed of the downhole pump can be adjusted automatically by a feedback control system, thereby ensuring that the bottomhole pressure in the well is maintained at the desired level. Other available systems measure pump temperature, fluid rate, or axial loads as a means to control pumpoff. 
Providing fluid rate, polished-rod torque, polished-rod axial load, and various other parameters as additional feedback to a control system is conceivable. Certain consistent decisions can be made automatically by software algorithms, and accurate data can be made available to the operator so that more complex optimization and diagnosis decisions can be made.
Often, motor line current is measured and used to estimate rod-string torque. However, the relationship between current and torque depends on the efficiency and power factor of the motor. When speed remains constant, the current draw will often vary linearly with changes in torque demand. This indicates that the motor efficiency–power factor product remains relatively constant over what is usually a small torque range. However, when an ESC system is introduced, speeds and loads usually change significantly over time. These changes can result in large variations in motor efficiency and power factor. This is illustrated in Fig. 15.42, which shows, for a single well, the variation in polished-rod torque, motor efficiency-power factor product, and motor output power with line current. At high currents, with the motor loaded near its rated power of 30 kW [40 hp], the motor efficiency-power factor product is ≈ 70%. This corresponds to a motor efficiency of 90% and a power factor of 0.8, which are close to nominal for full-load conditions. Unfortunately, as the current draw decreases, the motor efficiency-power factor product declines to ≈ 30%. Thus, when the motor was operating at low-load conditions, the efficiency and power factor were also very low. Consequently, torque values determined from nominal motor efficiencies and power factors may be artificially high. Depending on the conditions, this might result in a well operating at a lower speed than necessary on the basis of prescribed torque limits. Therefore, caution is required when polished-rod torque is determined from motor line current.
TroubleshootingMost PCP equipment vendors provide information describing troubleshooting procedures and suggestions for solving problems that may be encountered with their equipment. To assist in the diagnosis and correction of operational problems that may be encountered in PCP system installations, Table 15.5 outlines several problematic operating scenarios and provides some possible explanations and corresponding actions or strategies that may be taken to solve the problems. In some cases, the source of a particular operational problem may be easily addressed; in other situations, the problem may be quite difficult to diagnose and expensive to resolve, especially if a workover is required. It is important to consider all the information available because further problems can be caused if the diagnosis is incorrect and the wrong mitigation strategy is taken. Specific troubleshooting actions may be taken to determine the actual source of a problem if the system remains operational. For example, some additional backpressure can be applied to the system by partially closing the flowline valve to test the pressure integrity of the pump (e.g., if a worn or damaged pump condition is suspected). In such a case, the pump is likely okay if the flow rate remains constant and the system torque increases proportionally. Another technique is to implement speed changes to diagnose problems associated with well inflow or gas interference conditions.
Pump Failure AnalysesWhen a PC pump is pulled during a workover, it should be sent to a pump shop for a thorough examination and pump test. Usually, the pump components are first cleaned and visually inspected. Inspection of the rotor involves examining the condition of the threads and pin, assessing the amount and location of any wear, and identifying the presence of any heat checking. Although equipment is available to perform a full examination of the internals of a stator (e.g., bore-scope camera), not all vendors have these systems, and stator inspections are often limited to the visual checking of the long stator cavity for signs of damage or deterioration from the two ends. The elastomer surface typically is examined as carefully as possible to locate any areas of worn, hardened, cracked, torn, swollen, or missing rubber. If the rotor and stator components show no evidence of failure, the pump will subsequently be bench tested. If the test results show that the pump is within the accepted performance guidelines for the particular application, it will usually be sent back to the field for redeployment. Pumps that are tested but do not meet the guidelines may be retested with a new rotor if the stator appears to be in good condition. The stator will be scrapped if further testing provides evidence that it has sustained permanent damage (e.g., severe wear or loss of rubber).
Observations made during failed-pump inspections typically provide information that is crucial to the accurate determination of the root cause of failures. This knowledge is usually essential for establishing appropriate remedial actions to achieve improved pump run lives. The failure attributes provide clear indications of the physical mechanisms that resulted in damage to either the rotor or stator. The following sections provide descriptions of the unique damage characteristics associated with different types of pump failure mechanisms.
Stator Fatigue Failure. Fatigue failures are characterized by missing rubber primarily along the rotor/stator seal lines. The regions of torn or missing rubber are typically shiny and irregular (Fig. 15.43). Fatigue failures can be attributed to excessive cyclic deformation of the elastomer. As the material properties degrade, shear stresses can more readily generate cracks in the elastomer that subsequently propagate and eventually cause pieces of the rubber to separate from the pump. Excessive hysteretic heat buildup can accelerate material damage and associated crack growth. The loss of material along the rotor/stator seal lines leads to increased slip and a rapid decline in pump performance. Stators that have missing rubber as a result of fatigue damage are not suitable for reuse and must be scrapped.
Stator Wear. Stator wear usually can be attributed to the forced movement of abrasive solids along the stator cavities, although some wear can also occur because of the normal interaction of the rotor and stator during pump operation. Worn stators are characterized by the presence of roughened worn surfaces, usually along the minor diameter. The rate of abrasive wear is related most strongly to the quantity and abrasiveness (i.e., size, shape, and hardness) of the solid particles contained in the produced fluid. Wear rates are also influenced by elastomer type; soft stator materials are more likely to deform instead of tearing as solids pass through the pump. Stator wear is also proportional, but not necessarily linear, to the amount of interaction that occurs between the rotor and stator; consequently, stators tend to wear out more quickly at higher rotational speeds. Stator wear produces a gradual decline with time in volumetric efficiency and fluid rate. This effect is most pronounced when producing low-viscosity (< 100 cp [100 mPa•s]) fluids. Stators damaged by significant wear cannot be repaired and should be scrapped.
Rotor Wear. Rotor wear results from normal pumping action. Depending on the downhole conditions and exposure time, the severity of the wear rates can vary dramatically. Normal abrasive wear can be identified by the presence of erosion marks in the chrome plating along the major diameter of the rotor. Extreme abrasive wear is characterized by material loss through the surface coating and into the underlying base metal of the rotor. Examples of coating wear and severe base metal wear are shown in Fig. 15.44. Worn rotors can be rechromed and reused as long as the wear has not progressed through the chrome surface. Rotors that have sustained base-metal wear usually must be scrapped.
In some cases, base-metal wear is observed only on the top section of a rotor. This usually indicates contact between the upper portion of the rotor and the production tubing and can be attributed to the rotor being landed too high above the tag bar.
Stator Fluid Incompatibility. Fluid incompatibility and gas permeation can pose serious problems for stator elastomers. Signs of damage caused by fluid incompatibility include swelling, softening, or surface blistering of the stator elastomer. Visible swelling is the most common, occurring to some extent in many different applications. The compatibility between the elastomer and produced fluid determines the degree of swelling and the rate of any subsequent deterioration in mechanical properties. Badly swollen stators will often fail pump tests as a result of excessive torque or poor performance and must be scrapped. Stators that are only slightly swollen may be paired with a smaller-diameter rotor and reused.
Gas Permeation and Rapid Decompression. In gassy wells, stators are prone to severe damage under rapid decompression conditions (e.g., shutdown events) that facilitate the expansion of any gas that has diffused into the elastomer. The damage is caused when the force exerted by the pressurized gas trapped within the elastomer exceeds the tear strength, which leads to subsurface tearing of the material. These failures are characterized by a number of very soft, typically raised bubble areas or blisters on the stator cavity surface.
Rotor Fluid Incompatibility. Fluid incompatibility also occurs with rotors, but to a much lesser extent than with stators. Incompatibility can be identified by discoloration of the rotor and, in some cases, pitting of the base metal. It usually results from corrosive or acidic fluids attacking the chrome coating. Removing the outer chrome coating makes the rotor more susceptible to abrasive wear and may produce a noticeable increase in friction torque because of the loss of the smooth surface finish. Unless the rotor has extensive pitting, it usually can be rechromed and reused.
High-Temperature Stator Damage. Stators that have failed because of exposure to high temperatures typically exhibit elastomer surfaces that are hard, brittle, and extensively cracked. Fig. 15.45 shows an example of a stator damaged by high-temperature operation. Causes of excessive heat include running the pump dry, high produced-fluid temperatures, and heat generation within the pump. Heat damage usually produces a rapid decline in the pump’s volumetric efficiency. Stators that have failed because of high-temperature damage cannot be repaired and must be scrapped.
Rotor Heat-Cracking Damage. Heat cracking can be identified by fine cracks in the chrome plating of the rotor, primarily along the major diameter, although cracking may extend over the entire surface. Heat cracking is the result of differential expansion of the chrome and base metal in response to temperature changes. These cracks are considered normal, and minor heat cracking does not appear to affect PC pump performance negatively, although the slightly roughened surface may affect pump life. Most operators reuse rotors that have sustained minor heat cracking.
Stator Debris Damage. Occasionally, stators will exhibit damage in the form of large gouges or tears in the elastomer. This type of damage can be attributed to large foreign particles, such as pebbles, perforation plugs, or metallic debris, passing through the pump. In many cases, debris damage may go undetected unless an internal camera is used or caliper inspection is performed. Depending on the degree of damage, the pump may or may not be suitable for reuse.
Stator High-Pressure Wash. High-pressure wash or channeling is a common stator damage mechanism characterized by worm-like holes or groves cut in the elastomer (Fig. 15.46). These channels develop during production when a large sand particle or other debris becomes embedded in the elastomer material, creating a small orifice across the rotor/stator seal through which fluid passes at high velocity, eroding and cutting away the stator rubber. Because the channeling damages the pressure integrity of the pump, stators with extensive pressure-wash damage are not recommended for reuse.
System-Failure Analysis. A thorough analysis should be conducted after each downhole equipment failure incident to identify the circumstances during design, manufacturing, installation, and operation that likely resulted in the failure. Over time, this will lead to a valuable database of information that can be used to optimize PCP system design and operation for a particular well or field.
A vertical well is expected to produce 100 m3/d [629 B/D] of 12°API oil and no water, gas, or sand. The well is cased with 177.8 mm [7 in.] OD casing perforated at 1000 m [3,281 ft] from surface. At the desired flow rate, the fluid level is expected to be 600 m [1,968 ft] from surface. The casing is vented to atmosphere, while the flowline pressure is 1500 kPa [218 psi]. The oil viscosity is 1,000 cp [1000 mPa•s].
Design a PCP system to produce this well with the following constraints. The pump should be set below the perforations at 1010 m [3,312 ft]; its speed should not exceed 350 rpm; and the pump should not be loaded above its rated pressure. The rod stress should be < 80% of yield (assume API Grade D rods).
The following pumps are available. Assume that any of these pumps will operate at 85% volumetric efficiency under downhole conditions and that the friction torque will be 20% of the hydraulic torque at the pump’s rated pressure.
|Pump A||Pump B||Pump C||Pump D||Pump E|
|Pressure rating, kPa||12,000||12,000||18,000||15,000||12,000|
|Major diameter, mm||50||54||52||58||74|
|Minor diameter, mm||38||41||35||44||51|
Solution Using Eq. 15.4, we can determine the minimum displacement required to achieve the desired flow rate without exceeding the specified maximum pump speed:
The pump displacement must be > 0.336 m3/d/rpm. This eliminates Pumps A and B from further consideration.
The next step is to determine the differential pressure on the pump using Eqs. 15.5 through 15.7. The pump intake pressure is:
Casing-head pressure was defined in the problem statement to be atmospheric pressure, or 0 kPa (gauge pressure). The gas and liquid hydrostatic pressures can be calculated from the gas and liquid densities and the column heights. The pump intake is 1010 m from surface, and the fluid level is 600 m from surface. This means that there is 600 m of gas column and 410 m of liquid column. An average gas density can be estimated from the pressure at surface: 0.8 kg/m3.
This gives a gas column hydrostatic pressure of 5 kPa. (Note that this method is an approximation; the actual gas density will change as the pressure increases, but because the value is so small relative to the other pressures in the system, the error introduced by this approximation is small.) The density of 12°API oil is 984 kg/m3, so the liquid hydrostatic pressure is 3958 kPa:
In this case, the produced oil must flow from the perforations past the pump to reach the intake. Any flow losses here must also be considered in calculating the pump intake pressure. However, because the distance is small and there is a large clearance between the pump and casing, these losses are small and can be neglected. Note that if 139.7 mm OD casing had been used instead, there would be a very small annulus between the casing and the pump, and the flow losses between the perforations and the intake could be quite significant.
The pump discharge pressure is calculated from:
The tubing-head pressure is given as 1500 kPa. The liquid hydrostatic head will depend on the location of the top of the pump. The pump is seated at 1010 m (intake depth), but the three pump alternatives have different lengths, so the top will be at a different location in each case. Also, the flow loss will depend on the selection of tubing and rods. The solution process will be iterative; it is necessary to calculate these values for one set of equipment and then redo the calculation if it appears that the selected equipment may not be the best choice. If the pump length is 8 m, the top of the pump will be at 1002 m, and the hydrostatic head of the liquid in the tubing is 9673 kPa:
The calculation of flow losses was not described in detail in this chapter, but many different formulations are available in the literature, including this Handbook. For now, we will consider the use of 88.9 mm × 13.8 kg/m tubing, with 25.4 mm rods, 7.62 m in length, with standard couplings (55.6 mm diameter, 101.6 mm length). For the specified well depth, 131 couplings are needed, for a total length of 13.3 m; the remaining 988.7 m (assuming that the top of the pump is at 1002 m) is covered by rod segments. We can calculate the flow losses past 988.7 m of rod and 13.3 m of coupling separately and then add the two results together to obtain the total flow loss. This approximation neglects the flow effects at the ends of the couplings, but it should still provide adequate results. The ID of 88.9 mm × 13.8 kg/m tubing is 76.0 mm, and the drift diameter is 72.82 mm. For flow calculations, it is recommended that the ID instead of drift diameter be used. Assuming that the rods and couplings are concentric, the flow losses can be calculated (using one method) to be 5223 kPa past the rod body and 841 kPa past the couplings for a total of 6064 kPa. If, as normally expected, the rods and couplings are not concentric within the tubing, the flow losses would be somewhat reduced, but such a reduction will not be considered here, so the results are conservative.
We can now calculate the pump discharge pressure,
and the pump differential pressure,
The pump is required to work against a differential pressure of 13 274 kPa. Only Pumps C and D have a pressure rating exceeding this value. Also, note that Pump E cannot be used with this tubing because the major rotor diameter is larger than the drift diameter of the tubing. However, if a larger tubing size that would accommodate the large rotor diameter were used, the flow losses would be reduced, possibly to the point that the pressure rating of Pump E would not be exceeded. Therefore, Pump E will continue to be considered a potential candidate. All of the pumps have an OD that is less than the drift diameter of even the heaviest-wall 177.8 mm casing. Therefore, none of these pumps must be eliminated due to casing size.
The next task is to estimate the torque in the rods. The torque on the pump is given by:
The friction torque was estimated in the problem statement to be 20% of the hydraulic torque at the pump’s rated pressure. Hydraulic torque is calculated from Eq 15.8:
From this, we can estimate the friction torque for each pump. For example, for Pump C,
Accordingly, the values are: Pump C - 180 N•m; Pump D - 233 N•m; and Pump E - 266 N•m.
Next, the hydraulic torque for a differential pressure of 13 274 kPa is calculated for each of these pumps as
Thus, the hydraulic torque values are as follows: Pump C - 663 N•m; Pump D - 1026 N•m; and Pump E - 1470 N•m.
The torque on the rod string includes the pump torque plus torsional loading of the rod string resulting from mechanical interaction (friction) with the tubing and the resistance to rotation caused by the fluid viscosity. In a vertical well, the tubing friction loads can usually be considered negligible. The resistive torques for each of these pumps can be calculated at the speed at which they would run to produce the required amount of oil: Pump C - 69.4 N•m; Pump D - 44.4 N•m; and Pump E - 31.2 N•m. The total rod torque is then the sum of the respective pump friction, hydraulic torque and rod resistive torque values: Pump C - 912 N•m; Pump D - 1304 N•m; and Pump E - 1768 N•m.
When considering rod loading, we must calculate the axial load in the rods and the torque. Axial load can be found from Eq. 15.10:
Calculation of the uplift forces will be neglected for this example, providing a slightly conservative result. The rod weight is easily calculated from the specific weight of steel and the rod volume, neglecting the additional weight from the couplings and upsets. For a 25.4 mm rod that is 1002 m long (Pump C) with a steel specific weight of 77 kN/m3, the rod weight is
For pumps D and E, with their respective rod lengths, the rod weights are 38.9 kN and 39.0 kN.
Pump load is given by Eq. 15.11 as
where C = 7.9 × 10–4 when p is in Newtons, d and e are in millimeters, and pressures are in kPa.
To get the eccentricity values for the pumps for use in this equation, we must recognize that the major diameter is equal to the minor diameter plus twice the eccentricity. Therefore, the eccentricities for Pumps C, D, and E are 8.5, 7.0, and 11.5 mm, respectively. At a discharge pressure of 17 238 kPa and intake pressure of 3963 kPa, the axial load at the pump is as follows: Pump C - 38.2 kN; Pump D - 45.5 kN; and Pump E - 85.0 kN. So, neglecting the uplift forces, the total axial rod loads corresponding to the three pumps are: Pump C - 77.3 kN; Pump D - 84.4 kN; and Pump E - 124.1 kN.
The total stress of the rods can now be determined using Eq. 5.13. For Pump C, this gives:
The maximum stress is 514 MPa, which is 88% of the minimum yield for Grade D rods [586 MPa]. Note that the rod stresses exceed the yield capacity if the other two pumps are used. This condition would be in violation of the 80% loading criterion included in the problem statement.
To redesign the system to produce the well within the specified parameters, it appears that two viable options would be to decrease the differential pressure on the pump, or to increase the strength of the rods. There is nothing that can be done to reduce the hydrostatic head on the system while maintaining the same flow rate. However, a decrease in flow rate would reduce flow losses and would cause the fluid level in the casing to rise, thus increasing the pump intake pressure and decreasing the pump differential pressure. The tubing-head pressure can typically be reduced significantly only through changes in the gathering system to reduce the flowline pressure, through the addition of a transfer pump, or through the use of viscosity-reducing chemicals at surface.
Another way to decrease the pressure on the pump is to reduce the flow losses, which accounted for almost half the differential pump pressure. This can be achieved either through diluent injection or by increasing the flow area in the production tubing by using a larger-diameter pipe or a smaller-diameter rod string. Although using smaller rods would reduce flow losses, the load capacity would also be reduced (assuming the same material), so this does not appear to be a viable option, although the use of higher-strength rods may be an option in some cases. However, the use of a larger tubing string seems quite practical in this case.
The flow losses with 114.3 mm tubing with 25.4 mm rods would be ≈ 1338 kPa. This reduces the differential pressure to 8548 kPa, producing a corresponding reduction in the pump hydraulic torque values. The resistive torque is also reduced slightly. The total torque on the rod string for the three pump candidates can be recalculated to give the following values: Pump C - 671 N•m; Pump D - 935 N•m; and Pump E - 1241 N•m. The total axial load on the rod string can be recalculated as follows: Pump C - 63.0 kN; Pump D - 67.5 kN; and Pump E - 93.0 kN. With the lower torque and axial loads, the peak rod stress in the three cases is as follows: Pump C - 382 MPa (65%); Pump D - 520 MPa (89%), and Pump E - 693 MPa (118%). Pump C now gives a rod stress that is below 80% of yield, the criterion in the problem statement; the other two pumps will still cause the rod stress to exceed the specified criterion. Note that Pump C will operate at 261 rpm to produce 100 m 3 /d/rpm at a volumetric efficiency of 85%.
At this point in a typical system design, the pump, tubing, and rods have all been selected. The surface-drive system must now be established. The rod-string axial load at the surface is 63 kN, the torque is 671 N•m, and the operating speed of the polished rod is 261 rpm. A suitable drive can be selected from any manufacturer’s catalog by comparing these values to the published load and speed limits. The type of drive head (right angle or vertical, solid or hollow shaft, direct electric or hydraulic, etc.) normally is based on user preferences and field characteristics. For example, if electricity is not available, then an internal combustion engine must be used, which normally leads to the selection of a hydraulic system because otherwise the belts would typically have to be very long. If electricity is available but electronic speed control systems are not available or used in the area, hydraulic systems are often still preferred if regular speed adjustments are anticipated; otherwise, direct electric drives with a fixed selection of belts/sheaves or gears are typically used.
This example problem did not address wear and fatigue considerations because a vertical well was specified. In directional wells, however, wear- and fatigue-related problems can be significant. Estimating fatigue life and wear rates is quite difficult and is beyond the scope of this chapter. The example problem also did not consider the many issues that can arise when wells produce gas. The presence of gas affects both the frictional pressure losses and the hydrostatic gradient, and the corresponding calculations are much more complex. Pump efficiency is also significantly affected by any free gas that enters the pump intake. Most pump vendors have access to software tools that can be used to complete a system design evaluation for these more complex applications.
|d||=||rotor minor diameter, mm [in.]|
|dr||=||rod-string diameter, mm [in.]|
|e||=||rotor eccentricity, mm [in.]|
|E||=||volumetric pumping efficiency in service|
|Ept||=||power transmission system efficiency|
|Fp||=||axial load resulting from pump differential pressure, N [lbf]|
|Fr||=||rod-string axial load, N [lbf]|
|Fu||=||uplift forces on rods, N [lbf]|
|Fw||=||sum of rod-string weight below location, N [lbf]|
|Ls||=||stator pitch length, mm [in.]|
|pch||=||casing-head pressure, kPa [psi]|
|pd||=||pump discharge pressure, kPa [psi]|
|pg||=||gas-column pressure, kPa [psi]|
|pi||=||pump intake pressure, kPa [psi]|
|pL||=||liquid-column pressure, kPa [psi]|
|plift||=||differential pump pressure, kPa [psi]|
|plosses||=||tubing flow losses, kPa [psi]|
|Ppmo||=||required prime-mover power output, kW [hp]|
|pth||=||tubing-head pressure, kPa [psi]|
|ptail||=||pressure losses resulting from auxiliary components, kPa [psi]|
|qa||=||actual pump flow rate, m3/d [B/D]|
|qs||=||slippage rate, m3/d [B/D]|
|qth||=||theoretical pump flow rate, m3/d [B/D]|
|s||=||pump volumetric displacement, m3/d/rpm [B/D/rpm]|
|smin||=||minimum required pump displacement, m3/d/rpm [B/D/rpm]|
|Tf||=||pump friction torque, N•m [ft•lbf]|
|Th||=||hydraulic pump torque, N•m [ft•lbf]|
|Tpr||=||polished-rod torque, N•m [ft•lbf]|
|Tr||=||rod-string torque, N•m [ft•lbf]|
|TR||=||rod-string resistive torque, N•m [ft•lbf]|
|Tt||=||total pump torque, N•m [ft•lbf]|
|Tv||=||viscous pump torque, N•m [ft•lbf]|
|ρg||=||liquid density, kg/m3|
|ρL||=||liquid density, kg/m3|
|σe||=||Von Mises effective stress, MPa [ksi]|
|ω||=||pump rotational speed, rpm|
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SI Metric Conversion Factors
|°API||141.5/(131.5 + °API)||=||g/cm3|
|°F||(°F – 32)/1.8||=||°C|
|ft•lbf||×||1.355 818||E + 00||=||N•m|
|hp||×||0.7460*||E + 00||=||kW|
|in.||×||25.4*||E + 00||=||mm|
|lbf||×||4.448 222||E + 00||=||N|
|ft||×||0.3048||E + 00||=||m|
|psi||×||6.895 757||E + 00||=||kPa|
|scf/STB||×||0.178||E + 00||=||m3/m3|
Conversion factor is exact.