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Downhole PC pumps
Progressing cavity 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.
Types of downhole PC pumps
The PC pump products currently on the market generally fall into two different categories based on their geometric design:
- Single lobe
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 page. Other variations of these basic configurations include semi-elliptical rotor/stator geometries and uniform-thickness elastomer pumps.
Single lobe PC pump
The geometric design of a single-lobe PC pump is illustrated in Fig. 1. The longitudinal cross-section in Fig. 1 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. 2 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. 3 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. 3.
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:
- 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, so 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. 4 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:
- 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
- Higher frequency of stator flexing, which increases hysteretic heat generation and may impact pump life
- Greater potential for inflow problems to develop when high-viscosity fluids are pumped
- More prone to cause vibration problems because of the larger rotor mass and increased nutation speeds
- 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. 5. 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.
PC pump models and specifications
A wide variety of progressive cavity (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. 6 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.
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. 1.
It is apparent from Eq. 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]),
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]),
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.
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. 1 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.
- Karassik, I.J., Krutzsch, W.C., Fraser, W.H. et al. 1986. Pump Handbook, second edition. New York City: McGraw-Hill Book Co. Inc.
- Saveth, K.J. and Klein, S.T. 1989. The Progressing Cavity Pump: Principle and Capabilities. Presented at the SPE Production Operations Symposium, Oklahoma City, Oklahoma, 13-14 March 1989. SPE-18873-MS. http://dx.doi.org/10.2118/18873-MS.
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