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PCP sizing practices
To 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
- 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
- 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. 1). 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
- Actual fluid rates
- Volumetric efficiencies
- Hydraulic pressures
These reports should also include information on the pump components, including:
- Model number
- Unique rotor and stator serial numbers
- Elastomer type
- Threaded connections
In terms of the data reported for a pump test, the only parameters actually measured during the test are:
- Discharge pressure
- Fluid rate
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. 2. 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 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. 3). 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. 4, 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. 5 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. 6 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. 6).
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.
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. 7 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. 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 m3 /d/rpm) to as low as 10 to 15% for the larger models (e.g., > 0.8 m3 /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.
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