STUDY OF PULSATION DAMPENER DESIGNS FOR PLUNGER PUMPS
Kelly Eberle, PEng Principal Consultant Wood Calgary, Alberta, Canada Mathieu Barabe Senior Engineer Wood Calgary, Alberta, Canada
Michelle Witkowski, PE Team Lead Wood Houston, Texas, United States David Zhou Engineer and Software Developer Wood Calgary, Alberta, Canada
Kelly is a principal consultant and has been with Wood since 1988. He graduated from the University of Saskatchewan with a Bachelor of Science in Mechanical Engineering in 1986. He has accumulated a wide range of design and field experience, particularly in the area of pressure pulsation analysis and mechanical analysis of reciprocating compressor and pump installations. His experience also includes field vibration analysis, flexibility studies, structural analysis and foundation analysis. Michelle graduated from Texas A&M University with a Bachelor of Science in Mechanical Engineering in 2008. She has been a team lead with Wood since 2012, and her experience includes acoustical simulations, dynamic finite element analysis and torsional analysis. Prior to her time at Wood, Michelle worked as a technical analysis engineer with a compressor packager, where she provided technical solutions for performance, pulsation, vibration and torsional issues surrounding reciprocating equipment. During this time, Michelle also gained experience in application engineering, field troubleshooting and package design. Mathieu is a senior engineer and has been with Wood since 2007. Mathieu is a graduate of the University of Laval with a Bachelor of Science, Mechanical Engineering 2005. His work experience includes seven years of pulsation and mechanical analysis of reciprocating compressors, pumps and screw compressors. He has worked for more than five years as a field engineer troubleshooting rotating machinery. In his current role, he provides engineering support for Wood’s anti-vibration products development. Dave is an engineer and software developer and has been with Wood since 2013. He graduated from the University of British Columbia with a Ph.D. degree, Chemical and Biomedical Engineering 2010. His experience includes pulsation and mechanical analysis of reciprocating compressors and pumps. His current role also includes the development of Wood’s pulsation analysis software.
ABSTRACT Pressure pulsations from reciprocating pumps can generate high shaking forces that put the pump systems at risk of high vibration and fatigue failures. Pressure pulsations can also cause cavitation in the pump suction system that can damage the pump fluid end and power end. API 674 Positive Displacement Pumps—Reciprocating, 3rd Edition, includes two design approaches for reducing the effects of pressure pulsations. Design Approach 1 describes best practices for the design of the pulsation and vibration control, including pulsation control devices. Design Approach 2 includes pulsation control design using acoustic simulations and mechanical analysis. However, API 674 does not give adequate guidance on when either design approach should be used. The sizing of pulsation control devices using best practices is often insufficient in the author’s experience. Pulsation control devices may be selected early in the project by the equipment vendors or engineering company, well before the acoustical (pulsation) simulation has been conducted. Changes in the pulsation control device that are required from the pulsation simulation can be difficult to implement, as they are often issued late in the project schedule. Consequences of receiving pulsation control recommendations late in the project schedule can be a compromised design or significant redesign of the pump package. A better approach for selecting and designing pulsation control devices is required. This paper presents results from a parametric pulsation simulation study done to evaluate a range of pulsation control strategies for reciprocating pump systems. Equipment vendors have an empirically based approach for sizing pulsation dampeners. Sizing of pulsation dampeners using this empirical approach is compared to pulsation simulation results of the same designs. A range of pump sizes from 10 HP to 400 HP (7.5 kW to 30 kW) are investigated considering different fluid types such as water, propane and oil. Different pump configurations including triplex and quintuplex pumps are evaluated, as these are the most common reciprocating pump configurations in the authors’ experience. Different pulsation control device designs are evaluated, including gas-charged dampeners, surge volumes and pulsation filters. The goal of this paper is to provide better guidance for pump package designers to select the appropriate pulsation control devices and specify the correct API 674 design approach study for reciprocating pump applications. INTRODUCTION Plunger pumps are used in many applications where it is necessary to deliver liquids from low pressure to high discharge pressures of 1,000 psi or more. The mechanism that delivers the liquids is a slider-crank mechanism that converts the rotational motion of a motor or engine shaft to reciprocating motion of a plunger or piston. The reciprocating motion of the plunger along with the check valves at the inlet and discharge of the plunger pumping chamber cause a non-uniform, fluctuating or pulsating flow and pressure in the pump suction and discharge systems. These fluctuating flows and pressure pulsations can lead to reliability problems in the pump and piping system, particularly when these pulsations interact with acoustic responses. An example of an acoustic resonance is the tone generated when air is blown over the top of an empty bottle. The acoustic resonance in the bottle is excited by flow fluctuations at the neck of the bottle, causing a loud sound. The suction and discharge piping systems are like the bottle, and the plunger pump is sending out flow and pressure pulsations. If the frequency of the pulsations coming from the pump matches the frequency of the piping system, a significant amplification of the existing pressure pulsation occurs. This condition is known as a pulsation or acoustical resonance. These pressure pulsations can cause cavitation, create high dynamic shaking forces that lead to vibration and fatigue failures of the piping or cause relief valves to prematurely lift-off, leading to an unexpected release of liquids. Such events pose a serious risk to the safety of operating personnel and reliability of the pump system. Industry best practices have been developed to help control the damaging effects of pressure pulsation. API 674 is the main reference for plunger pump pulsation control. Many different devices have been designed to help control pressure pulsation in plunger pump systems. This paper primarily focuses on one device called a gas-charged dampener, as shown in Figure 1. This device goes by other names such as accumulator, stabilizer, surge suppressor or snubber but for the purposes of this paper, the name “gas-charged dampener” or “dampener” will be used. The paper focuses on gas-charged dampeners, as they are the most commonly used pulsation control device in plunger pump systems. A typical gas-charged dampener is installed on a branch connection from the main suction or discharge piping, as shown in Figure 1. The dampener includes a bladder made of an elastomeric or metal bellows element that physically separates the gas charge from the fluid. A nitrogen gas charge is typically used in the dampener, as nitrogen is not reactive with most fluids in the case of a bladder
failure. The gas charge is typically set to 60 to 80 percent of the system operating pressure. Charging the dampener to a lower pressure will compress the bladder slightly when it is at the system operating pressure. A properly sized gas-charged dampener will reduce pressure and flow fluctuations in the pump system as the bladder and gas charge will expand and contract as flow fluctuations from the pump enter the dampener.
Figure 1: Gas-charged dampener
GAS-CHARGED DAMPENER SIZING The approach for gas-charged dampener sizing varies somewhat from manufacturer to manufacturer. Generally, the dampener size is based on a simple formula that is a function of the line pressure, the desired level of pulsation, properties of the gas used to charge the dampener and a pump characteristic or pump constant derived from testing. An example formula for determining the nominal dampener volume, 𝐷𝐷𝐷𝐷, is given by Griffco(1) using the following expression:
𝐷𝐷𝐷𝐷 =𝑃𝑃𝐷𝐷 × 𝐶𝐶𝑝𝑝 × �𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚� �
𝑚𝑚
1 − �𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚� �𝑚𝑚 (1)
Where
𝑃𝑃𝐷𝐷 is the pump displacement per stroke (in3) 𝐶𝐶𝑝𝑝 is a pump constant 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 is mean line pressure (psi) 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 and 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 are the minimum and maximum pressure due to pulsation (psi) 𝑃𝑃 is the polytropic expansion coefficient of charge gas
The theoretical basis for the numerous gas charge dampener formulae used by industry is not always well documented. The general concept behind the sizing formulae appears to be similar to that used for accumulators that are essentially reservoirs for storing fluid as a temporary energy or fluid source. The process of energy storage in an accumulator is somewhat different from that of controlling pressure pulsations. The pressure pulsations in a pump system can occur quickly with frequencies of 10 Hz to 200 Hz. The pump generates pulsations that travel much faster than when using accumulators for fluid storage. A second assumption built into the formulae is that the gas-charged dampener is intended to absorb the pressure fluctuations created by the pump. The assumption is the complete volume of the pulsation is absorbed by the dampener. This will not be the case for appendage-type gas-charged dampeners like the one shown in Figure 1. Some pressure pulsations created by the pump will travel into the gas-charged dampener, but some will pass by the dampener and continue into the piping system. The gas charge in the dampener is assumed to undergo isentropic compression of the gas inside the dampener; hence the polytropic
coefficient used in the formula. A final factor in the formulae that results in uncertainty in the calculated volume is the pump constant. Typically, the pump constant is based on a laboratory or test stand run. The configuration of the pump system and fluid type may be much different from the actual system where the pump is to be installed, resulting in pressure pulsations in the pump test system that may be much different than the actual system. The sizing of the gas-charged dampener will be evaluated in an example setting aside these uncertainties. Consider an example quintuplex pump with 2.75” (70 mm) bore, 4” (102 mm) stroke. The pump constant for a quintuplex pump is 0.06. If the dampener is charged with nitrogen to 80 percent of line pressure, what size of dampener is required for a line pressure of 350 psig (2413 kPag), assuming the criterion is for 5 percent (peak) pressure pulsation? Using the example formula given in Equation 1,
𝐷𝐷𝐷𝐷 =𝑝𝑝𝑝𝑝4 2.752 × 4 × 5 × .06 × �350
332.5� �0.714
1 − �350367.5� �
0.714
𝐷𝐷𝐷𝐷 = 216 𝑝𝑝𝑃𝑃3 (3540 𝑐𝑐𝑃𝑃3)
The dampener is supplied in standard sizes of 150 in3 (2458 cm3) and 300 in3 (4916 cm3), so a 300 in3 (4916 cm3) dampener is selected. This process is relatively easy for selecting a dampener. Based on this approach, a range of dampener sizes can be determined for a range of desired pulsation control. Figure 2 shows the relationship between the dampener size and pressure pulsation based on Equation 1. Intuitively the results shown in the chart make sense, as one would expect that a larger dampener volume will result in further pulsation control. Note that the y-axis of Figure 2 is the overall pressure pulsation, that is, the sum of pressure pulsations at all frequencies. The overall pulsation is shown in Figure 2 as well as all following charts unless otherwise noted.
Figure 2: Overall pressure pulsation versus dampener size
Further evaluation of this dampener selection was done with a pulsation model of the pump system. A pulsation model was created and evaluated using Wood’s pulsation simulation software for reciprocating pump and compressor systems. The software uses
equations of the conservation of mass, momentum and non-linear pressure loss to simulate the time vary pressure and flow in a piping system. The pulsation software has been verified by laboratory and field measurements as well as through its use as a design tool for pump installations since the 1970s. Using the pulsation software and model is a reliable method for evaluating the dampener size in this example as well as other aspects of the dampener and pump system in the remainder of the paper. A pulsation model of the quintuplex pump used in the dampener volume calculation above was created, including a section of the suction piping and the dampener as shown in Figure 3. This pump is a produced water application with a specific gravity of 1.2 operating between 140 and 350 rpm.
Arrangement of pump, suction line and dampener
Pulsation model of pump, suction line and dampener
Figure 3: Pump arrangement and pulsation model
Pulsation simulations were run with this model for different dampener sizes. The dampener sizing formula given in Equation 1 calculates the dampener volume to achieve a specified pulsation amplitude. The pulsation amplitude in Equation 1, that is, the peak-to-peak pressure fluctuation that would be transmitted to the rest of the piping system, is the same parameter as the overall pressure pulsation at the termination of the pulsation model as shown in Figure 3. The overall pressure pulsation as calculated by the pulsation model is shown as the blue trace in Figure 4. The results show that the reduction in pressure pulsation is relatively insensitive to the size of the dampener. The results also show that a small amount of gas volume has a significant impact on the pressure pulsations. Increasing the gas volume has virtually no impact on the pulsations that are transmitted to the rest of the suction system. Based upon these results, the simple dampener sizing equation is not a reliable approach for determining a dampener size for all applications. Note: This paper assumes the fluid does not contain any air or vapor. Fluid with even a small amount of gas present will behave very differently to a single, 100% liquid phase, and is outside the scope of this paper.
Figure 4: Pressure pulsations versus dampener size using different calculation methods
As was demonstrated in this example, a small amount of gas charge in the dampener has a significant impact on the pressure pulsations in the piping system of a reciprocating pump application. A gas-charged dampener is an absorptive device. An absorptive device uses the gas volume as a large spring to absorb the pulsation energy being generated by the pump. A dampener could be filled with liquid rather than gas, however, the volume of the dampener would need to be much larger. The following expression is referenced by McKee and Broerman(2) to relate the volume of a gas to the equivalent volume of liquid.
𝐷𝐷𝑔𝑔 = 𝐷𝐷𝑙𝑙 × �𝜌𝜌𝑔𝑔 × 𝑐𝑐𝑔𝑔2�(𝜌𝜌𝑙𝑙 × 𝑐𝑐𝑙𝑙2)� (2)
Where
V is volume (in3), ρ is density (lb/in3), c is acoustic velocity (ft/s), g and l are subscripts for gas and liquid
Consider the example of 300 in3 (~5 L) of nitrogen gas. The density and acoustic velocity at 60oF (15.6 oC) and 350 psia (2414 kPa) 1.775 lbm/ft3 (28.433 kg/m3) and 1147 ft/s (349.6 m/s). The density and acoustic velocity of water is 62.4 lbm/ft3 (999.6 kg/m3) and 4830 ft/s (1472 m/s). The equivalent volume of water is approximately 108 ft3 (~3064 L) or a ratio of about 1:625. A small amount of gas charge in the dampener will have a large absorptive effect. Adding more gas volume has no significant change in the absorptive effect of the dampener. Aside from its absorptive effect, the dampener also changes or creates different pulsation resonances in the piping system. Pulsation or acoustic resonances occur where there are components in a system that create an acoustical boundary. One type of acoustical boundary is a closed end. A closed end will cause a perfect reflection of pulsation traveling toward it. In the case of a pump system, the non-flow or dead end of the manifold is considered a closed end. The other type of acoustical boundary is an open end. An open end is where there is little or no reflection of incoming pressure pulses. The interface of the gas and liquid in the dampener is an acoustical open end. The combination of a closed end at the pump manifold non-flow end and the open end at the gas interface in the dampener creates a quarter (¼)-wave resonance in the piping system. A quarter-wave resonance means that the distance between the closed at the end of the pump manifold and open end at the gas interface in the dampener is equal to ¼ of a full wavelength at the same frequency as the excitation frequency. The classic example of a quarter-wave resonance is the tone generated when blowing air past the neck of a bottle. The bottle generates a tone at a frequency equal to a ¼ wave length based on the acoustic velocity of air. The same effect occurs for the plunger pump. Pulsation generated by the pump are amplified by the quarter-wave resonance between the pump manifold and dampener based on the acoustic velocity of the fluid being pumped. Figure 5 demonstrates the quarter-wave
resonance in the pulsation model with a maximum pulsation at the end of the pump and a minimum pulsation at the dampener. This quarter-wave resonance is a combination of the pulsation energy generated by the pump and the physical geometry of the system (pipe lengths and diameters).
Figure 5: Pump system quarter-wave resonance
PIPING SYSTEM EFFECTS The previous section compared the results of sizing a gas-charged dampener using empirical formulae versus the performance of the dampener considering pulsations generated by the pump and the pulsation resonance between the pump and dampener. Consider that, the extent of the suction piping as shown in Figure 3 includes only the pump and a short section of piping that is within the pump packager’s responsibility. There will be additional suction and discharge piping, other process vessels, dead legs of piping for recycle or bypass lines and perhaps other pump packages that will connect to the piping systems. These additional components could introduce additional pulsation resonances that will impact the dampener effectiveness. The example quintuplex pump described previously is part of a somewhat complicated piping system, as shown in Figure 6. The image on the left is the CAD model of the pump system. The image on the right is the pulsation model of the same CAD model. Note that the colors shown in the pulsation model only represent the pipe nominal size and schedule and do not indicate pulsation results. The CAD model on the left shows produced water is pumped from a large tank as shown by the green vessel, which creates an open-end boundary condition for pulsation resonances. There are numerous pipe spans with dead legs at normally closed valves for recycle, blowdown and relief as well as liquid that may be supplied from other sources. These closed valves create closed-end boundary conditions. Figure 7 shows the calculated pressure pulsation at the pump skid edge when only the pump package model is included (blue trace) versus the pulsation at the same location when the complete system model is simulated (orange trace). The 300 in3 (4916 cm3) gas-charged dampener was used in these model results. The orange trace of Figure 7 shows that the pressure pulsations are much higher when the complete pump suction system is included in the simulation. There are also several peaks in the pulsation response with the complete system included in the simulation. These peaks represent pulsation resonances that occur due to the complete system piping as the pump speed varies. The maximum skid edge pulsation is calculated at approximately 295 rpm. This result indicates there is a particular pulsation resonance at 295 rpm that results in the highest pulsation at the skid edge. Other locations in
the suction system could have higher pressure pulsations at this same speed. There could be other pulsation resonances that result in higher pressure pulsations than the skid edge pulsation at other locations. The pulsation analysis of the complete system shows the potential for cavitation and vibration problems due to high pressure pulsations. Selecting a gas-charged dampener without considering the complete piping system poses risks to the reliability and safety of the pump system. It is also important to note that at some speeds, the simple model of the pump package piping and dampener gives the same results as calculated with the full piping system. The gas-charged dampener selected from the simple sizing formula may be acceptable if the pump is only operated at one speed or over a small speed range.
Piping arrangement
Pulsation model
Figure 6: suction system arrangement
Figure 7: Skid edge pulsation
EVALUATING GAS-CHARGED DAMPENER DESIGN PARAMETERS Questions often arise during the selection of a gas-charged dampener as to where the best location for the dampener is, how close it
should be located to the main process pipe, and what influence the variations in fluid have. There are some industry rules of thumb regarding these parameters. A parametric study was conducted to quantify some of these effects using the pump from the previous example. To simplify the model, the pipe and dampener arrangement shown in Figure 8 was used.
Figure 8: Pump model used for parametric study
Location of the Dampener The typical recommendation for the location of a gas-charged dampener is to locate it within 10 main line pipe diameters from the pump flange (Blacoh (3)). Several pulsation models were run with the dampener location varied from 1 diameter to 20 diameters from the pump flange. Figure 9 summarizes the maximum pressure pulsation at the termination of the pulsation model for different locations of the dampener. The general trend is that the pressure pulsation transmitted in the suction piping system increases in amplitude as the dampener is moved farther from the pump. This result is somewhat intuitive. What is not intuitive is that the pressure pulsation trend does not constantly increase with distance from the pump. The pulsations with the dampener at 6 diameters and 16 diameters away from the pump are lower than the pulsations when the dampener is 10 diameters away. The main reason for this result is that pressure pulsations are the consequence of pulsation generated by the pump exciting a quarter-wave resonance between the dampener and the non-flow end of the pump. As the dampener moves farther away from the pump, the frequency of the quarter-wave resonance is reduced. Generally, the pressure pulsation excitation created by the pump increases as the frequency decreases. However, the pressure pulsation excitation also increases with the pump speed or stated another way the pulsation excitation reduces with lower pump speed. As the dampener moves farther from the pump, the quarter-wave resonant frequency shifts from a high pump speed to a lower pump speed resulting in lower pressure pulsations. The combination of increasing pump pulsation excitation at lower frequencies, decreasing pump excitation at lower speeds and the quarter-wave resonant frequency results in the variation of the pressure pulsations as the dampener moves farther from the pump as shown in Figure 9. The pump pulsation excitation and quarter-wave resonant frequency will change for each pump application and fluid type. It is not possible to state a best dampener location for all application other than to say the dampener should be located as close to the pump as practical. Note one data point is shown in Figure 9 for the dampener on the non-flow end of the manifold. Typically, the pump fluid end is designed so that the pipe may be connected on either end. Figure 10 is an image of the pulsation model showing the dampener on the non-flow end of the pump. The pulsations resulting from this dampener location are lower than at all locations on the inlet piping. This is due to the dampener on the non-flow end acting primarily as an absorptive component. There are no pulsation resonances created in this limited suction system model with the dampener on the non-flow end. The pulsations will increase when the complete suction system is added, similar to the results shown in Figure 7. A dampener on the non-flow end should be investigated in the pulsation study as it can be an effective solution for controlling pulsations.
Neck Geometry The neck of a gas-charged dampener is the pipe connections between the main line pipe and the larger diameter of the dampener, as shown in Figure 1. The geometry of the neck, that is the length and diameter, impacts the performance of the dampener. A parametric study was done to evaluate its effect on pressure pulsation. The model shown in Figure 8 was used in this analysis. The length of the neck, L, and diameter of the neck, Dn, was varied. The results for a range of geometry are presented in Figure 11 as a ratio of the diameter of the neck to the diameter of the main line, Dn/Dm.
Figure 11: Pressure pulsations for different neck parameters
The results show that pulsations are lowest when the length of the neck is short, and the diameter of the neck is the largest. This result is reasonable, as s shorter, larger diameter neck means that the gas volume in the dampener is more exposed to the pressure pulsations generated by the pump and are therefore reduced to lower levels. However, there are practical limits to the neck dimensions. The neck often includes a set of flanges to allow for easy maintenance, which increased the neck length. Also, dampeners that are commercially available have limits on the neck diameter. Regardless of these limitations, it is recommended to minimize the neck length and maximize the neck diameter as much as practical when selecting a dampener to maximize its pulsation control. As shown by this parametric analysis, even when the neck length is very short and the neck diameter is equal to the main line pipe diameter, significant pulsations remain in the system. This result is due to the quarter-wave resonance that is always created between the non-flow end of the pump and the gas-charged dampener. Some gas-charged dampeners include a special diverter element at the T-junction, claiming to direct flow into the dampener to better interact with the gas charge and improve the dampener pulsation control. It must be noted that the wavelengths of the pressure pulsations are at least 50 times greater than the geometry of the diverter. The pressure pulsations will not be significantly impacted by these diverter elements other than perhaps a bit of additional pressure drop due to the change in direction of the flow. For most applications, the benefits of special diverter elements do not justify the extra costs. Type of Liquid The type of liquid in a pump system can have a significant impact on the pulsations in the system. The most important parameter in describing pressure pulsations in a liquid is the compressibility or stiffness of the fluid as this describes how fast pressure waves travel in the fluid. The bulk modulus is the name of the fluid property that describes its stiffness or resistance to being compressed. The bulk modulus for water is quite high, typically near 350,000 psi (2413 MPa) whereas propane may be as low as 16,000 psi (110 MPa). The
speed at which pressure waves will travel in water and propane, or speed of sound, will be much different. The speed of sound in a fluid, cf, is defined by the following expression
𝑐𝑐𝑓𝑓 = �𝑘𝑘𝑏𝑏𝜌𝜌�12�
(3)
Where 𝑘𝑘𝑏𝑏 is the fluid isentropic bulk modulus and 𝜌𝜌 is the fluid density As previously noted, the bulk modulus for some fluids such as water is quite high. The stiffness of the water is in the same order of magnitude as the stiffness of the pipe in these cases. Therefore, the stiffness of the pipe must also be considered in the pulsation analysis. The calculation of the speed of sound is a combination of the pipe and fluid stiffness. The following relationship derived by Wylie and Streeter (4) calculates the speed of sound including the pipe flexibility, c,
𝑐𝑐 =𝑐𝑐𝑓𝑓
�1 + 𝑘𝑘𝑏𝑏𝑑𝑑𝐸𝐸𝐸𝐸
(4)
Where 𝑑𝑑 is pipe diameter 𝐸𝐸 is elastic modulus of the pipe and 𝐸𝐸 is pipe thickness The speed of sound is important to understand, as it is used in calculating pulsation wavelengths and possible resonances in a piping system. The variation in the bulk modulus and speed of sound is important to evaluate when selecting a gas-charged dampener, particularly for a pump system that may operate with different fluids or over a range of pressures and temperatures where the bulk modulus varies. A parametric study was done using the same piping system as is shown in Figure 8 with a variation in fluids. The same pump and operating speed were used, however, a range of suction pressure and temperatures were evaluated for some fluids to demonstrate the influence of these input parameters. Figure 12 shows the pulsation model results for different fluids. The highest pressure pulsations were calculated with water and the lowest with propane at 104 oF (40 oC). These cases represent a significant variation in the liquid bulk modulus as described in the opening paragraph for this section. The other interesting result is the large variation in pressure pulsations for propane. Propane applications often include a storage vessel or “bullet” where the temperature of the propane will vary with ambient conditions. The simplified analysis done here shows a variation in pressure pulsations of 3x when the full range of ambient temperatures is considered. This result is typical for liquified hydrocarbon gases in that the bulk modulus is sensitive to temperature. This result emphasizes the importance of simulating a full range of pressures and temperatures when selecting a dampener.
Figure 12: Maximum pressure pulsation transmitted to the suction system for different fluids
One approach to normalize these results is to view the pressure pulsations versus the speed of sound (or acoustic velocity) as shown in Figure 13. Figure 13 shows that as the speed of sound increases, pressure pulsations increase. Selection of the appropriate dampener must consider the speed of sound of the fluid.
Figure 13: Pressure pulsations for different acoustic velocities
Note that the acoustic velocity in the previous discussion is the acoustic velocity for a 100% liquid phase fluid. The acoustic velocity will be much lower if the fluid includes a small amount of air or other gas. As was noted in the discussion of Equation 2, a small amount of gas has a significant impact of the pulsation characteristics of a liquid system. EFFECT OF NUMBER OF PLUNGERS The number of plungers is one of the key inputs for sizing the gas-charged dampener, as shown in Equation 1 with the pump constant. The pump constant for the quintuplex pump in this example is 0.06. A triplex pump will have a pump constant of 0.13. This means the dampener size for a triplex pump application should be about 2x larger than a quintuplex pump, all other things being equal. The rationale for this difference is that with fewer plungers, the flow from the pump has larger amplitude fluctuations, so a larger
dampener is required. This concept of high flow fluctuations with fewer plungers is often demonstrated by charts, as shown in Figure 14. The individual plungers for quintuplex pumps are spaced 72 degrees of crankshaft revolution apart as shown by the overlapping sine-waves. The net or average flow from the quintuplex pump has a relatively low amplitude ripple or fluctuation over one crankshaft revolution, as represented by the red trace in the left chart. The phasing between plungers on the triplex pump is 120 degrees, resulting in a larger amplitude fluctuation, as shown the red trace in the right chart.
Quintuplex pump
Triplex pump
Figure 14: Flow versus crank angle for quintuplex and triplex pumps
The flow in Figure 14 is a simplified representation of the actual flow into the suction of the pump and each plunger pumping chamber. The suction valve will not open at exactly dead center. There will be some delay in the valve opening, typically opening 10o to 30o after dead center depending on the bulk modulus of the fluid and the stiffness of the pump fluid end. The closing of the suction valve will also be delayed slightly past dead center. A valve that is operating properly should close no more than 7o to 10o after dead center. Figure 15 is a more accurate representation of the flow for each plunger for one crankshaft revolution.
Figure 15: Suction flow for one plunger versus crank angle
This complex flow-versus-time signature is the sum of many different frequencies with different amplitudes. A Fourier transform is a mathematical function used to determine these individual frequency components. Considering only the plunger-passing frequencies for the quintuplex pump used in the example in Figure 8 gives the individual frequency components shown by the blue bars in Figure 16. Figure 16 also shows the flow components for a triplex pump that provides the same flow for the same pressure and fluid as the quintuplex pump. The results in Figure 16 are similar to those in Figure 14 in that the flow excitation from the plungers that cause pulsations will be higher for a triplex pump as compared to a quintuplex pump operating at the same conditions.
Figure 16: Flow fluctuations for a quintuplex and triplex pumps
The pulsation model of the quintuplex pump, as shown in Figure 8, was modified to simulate a triplex pump, as shown in Figure 17. The flow rate, pressures, fluid, piping and dampener for the model with the quintuplex and triplex pumps are identical. The diameter of the plungers for the triplex pump was increased so the flow was the same as the quintuplex pump. The overall pulsations at the model termination for the quintuplex pump are calculated to be 45.5 psi pk-pk (314 kPa pk-pk) versus 26.1 psi pk-pk (180 kPa pk-pk) for the triplex pump. This result indicates pulsations from the triplex pump are lower than those from the quintuplex pump, which is counter to what is expected from the previous discussion regarding the flow fluctuations that create the pressure pulsations. A closer examination of the pulsation results is required.
Figure 17: Triplex pump pulsation model
The pulsation spectrum at the model termination is shown in Figure 18. The quintuplex pump shows a maximum pulsation of about 18 psi pk-pk at 130 Hz. This frequency corresponds to the quarter-wave resonance between the pump non-flow end and the gas volume in the dampener. The frequency of the highest pulsation corresponds to 4x plunger pass frequency (PPF). The triplex pump spectrum shows that the quarter-wave resonance is at a higher frequency, approximately 185 Hz. The quarter-wave resonance is at a higher frequency for the triplex pump since the fluid manifold of the pump is much shorter for the triplex arrangement. The quarter-wave resonant frequency corresponds to 10x PPF. The difference in the quarter wave resonant frequency for the two pump systems means that the order of the pump flow excitation will be much different. Figure 16 shows that the quintuplex flow excitation at 4x PPF is about 0.012, while the triplex excitation at 10x PPF is about 0.005, about 2.5 times smaller. The difference in the flow excitation
amplitude at the different resonant frequencies explains the difference in the pulsation results. This example highlights that sizing of the gas-charged dampener based solely on the pump characteristics is not a reliable method. The system characteristics considering pulsation resonances must be evaluated to determine the appropriate pulsation controls.
Quintuplex pump results
Triplex pump results
Figure 18: Pulsation spectrum
OTHER PULSATION CONTROL DEVICES The focus of this paper has been on gas-charged dampener. Other devices and approaches can be used. A common approach for pulsation control is the use of a pulsation filter. The analogy of a pulsation filter is a low-pass filter used in electrical circuit design. The low-pass filter design allows low frequencies to pass through the device, but blocks or attenuates high frequencies as they pass through the filter. The lowest frequencies of interest generated by a quintuplex are 1x PPF. The approach when designing a low-pass filter is to design its frequency to 30 percent below 1x PPF. The filter frequency is a key consideration in the sizing of the filter. Two common designs for a low-pass filter are shown in Figure 19. The traditional design for a pulsation filter is the volume-choke-volume, as shown in the left image, which includes a baffle plate inside the volume to create two different chambers and a pipe or choke tube between the volumes to create the pulsation filter.
Where 𝑑𝑑𝑐𝑐=diameter of choke tube 𝑐𝑐=acoustic velocity 𝜋𝜋=choke length 𝐷𝐷1, 𝐷𝐷2=volume of the two chambers
The goal is to design the Helmholtz frequency to be 30 percent below 1x PPF, as previously noted. Equation 5 shows there are several parameters that can be varied to achieve the desired Helmholtz frequency. Other factors must also be considered in the design. Inspection of Eq 5 shows that a small diameter choke tube would minimize the Helmholtz frequency, all other factors being fixed. However, a small diameter choke tube will result in high flow velocity in the choke tube. A high flow velocity could result in excessive pressure drop or erosion of the choke tube when flow velocities are greater than 10-15 ft/s (3-5m/s). If the minimum choke diameter is selected, and the Helmholtz frequency is not low enough, the length of the choke tube could be increased. The drawback to increasing the choke tube length is that the pressure drop will increase. Also, the length of the vessel may need to increase if the choke tube length will not fit within the vessel. Another option to lower the Helmholtz frequency if the choke tube diameter and length is fixed is to increase the diameter of the shell. A drawback to increasing the shell diameter is the shell wall thickness must be increased to meet the pressure containment criterion. A larger diameter shell will be heavier and more costly to purchase materials and fabricate as well as take up more space as the ideal location for a pulsation filter is as close to the pump as possible. Selecting the proper combination of choke tube and shell requires balancing the requirements for pulsation control as well as pressure drop, erosion, material costs, fabrication costs and space considerations. An alternate pulsation filter design is a volume-choke as shown in the right-hand side of Figure 19. The Helmholtz frequency for the volume-choke design is described in Equation 6.
𝑓𝑓𝐻𝐻 =𝑑𝑑𝑐𝑐𝑐𝑐24
�1
4𝜋𝜋𝜋𝜋𝐷𝐷�12
(6) The advantage of a volume-choke filter is that the Helmholtz frequency is lower than that of a volume-choke-volume filter for the same choke and volume components. The disadvantage of a volume-choke design is that it is not as effective as a volume-choke-volume filter. A volume-choke filter may not be an effective pulsation filter for applications where very high pulsations are generated by the pump. The typical steps in sizing a pulsation filter include:
1. Determine minimum choke diameter based on erosion and pressure drop 2. Determine the required Helmholtz frequency 3. Assess size, spacing and operating constraints 4. Check response with pulsation simulation
The example pump described in Figure 8 will be used in the pulsation filter sizing. Recall that the application is produced water with an SG=1.2. The suction pressure is 350 psig (2413 kPag) with the pump delivering 5900 BPD (170 GPM, 30 m3/hr) for a speed range of 140 to 350 rpm. The first step in the sizing of the pulsation filter is selecting the choke tube diameter. A 3” S160 pipe will have a flow velocity of 10 ft/s (3 m/s), a typical limit to minimize erosion. The pressure drop in the choke tube will be about 3 psi (21 kPa). Given the suction line pressure is 350 psig (2413 kPag), this pressure drop is not a concern for the NPSH. The next step is determining the Helmholtz frequency. The pump is a quintuplex operating over a range of 140 rpm to 350 rpm. The goal is to design the Helmholtz to be 30 percent below 1x PPF, which is 140/60*5*.7 = 8.2 Hz. Assuming a maximum shell length of 84 inches (2133 mm) and a 3” (75 mm) S160 choke tube, Equation 5 can be used to develop a relationship between the Helmholtz frequency and vessel diameter as shown in Figure 20. A Helmholtz frequency of 8.2 Hz will require a vessel diameter of about 40 inches (1016 mm). A 40-inch (1016 mm) vessel is quite large and is often difficult to accommodate in a package design. If a 30-inch (762 mm) diameter shell is used, the Helmholtz will be 11.3 Hz which corresponds to a minimum speed of 192 rpm. Pulsations at low speed would not be filtered, however, pulsations at 200 to 350 rpm will be filtered. A 30-inch (762 mm) diameter shell is a reasonable compromise between the vessel size and operating speed range that owners and operators are willing to accept. A 30-inch (762 mm) shell will be used in this example.
As a final check of the pulsation filter design, the pulsation simulation is completed using the pump and pump package piping, as shown in Figure 3. The volume-choke-volume design is checked as well as a volume-choke and simple volume design to assess the pulsation control, as shown in Figure 21. All models used the same volume of 30” (762 mm) diameter x 84” (2133 mm) s/s with a 3” (75 mm) S160 choke tube.
Volume-choke-volume filter Volume-choke filter Volume only
Figure 21: Pulsation model to assess different filter designs
The overall pressure pulsations at the skid edge termination for the gas-charged dampener model, as shown in Figure 3, and the different pulsation filter designs are shown in Figure 22 for the pump speed range. The pressure pulsations are highest for the gas-charged dampener, except for speeds around the Helmholtz frequency of the volume-choke-volume, about 190 rpm. The volume-choke-volume is the most effective option for controlling pulsations for speeds above 245 rpm. Surprisingly, the empty volume is quite effective as compared to the two pulsation filter designs.
Figure 22: Overall pressure pulsation at the skid edge for different pulsation controls
The previous work showed that the pulsation simulation results for the gas-charged dampener model with only the pump package piping were much different from the results when the complete piping system was included in the simulations. Similar comparisons were made with the volume-choke-volume, volume-choke and volume-only pulsation filter designs. Figure 23 shows the overall pulsation results for each of the four pulsation control devices with the complete piping system modeled. The pressure pulsation results with the complete system model included in the simulation are much lower for the pulsation filter designs as compared to the gas-charged dampener. The gas-charged dampener results were removed in the results shown in Figure 24 to better illustrate differences. The results with the complete system model are similar to the results with only the pump package piping. The volume-choke-volume filter has the lowest response for frequency above 240 rpm. The empty volume is quite effective over a wide speed range. The results from the simulation with the full system model divided by the pump package model are shown in Figure 25 as a method of demonstrating the sensitivity of the different pulsation control devices to the piping model included in the simulations. Ideally, the ratio of the full system to the package model over the speed range should be close to 1, indicating that a simple model of the pump package will be sufficient for selecting the pulsation control design before the complete system design is known. It is clear that selecting a gas-charged dampener with only the pump package piping poses risks to unacceptable pulsation that can result in cavitation, vibration and other negative consequences. The pulsation could be 5x to 10x higher than expected. The volume-choke-volume and simple-volume designs are relatively insensitive to the suction system arrangement. A volume-choke-volume or empty volume could be determined using a pulsation model of the pump package. It may be prudent to apply a design factor of 1.5 or 2.0 to the pressure pulsation if the vessel sizes are selected and ordered before the complete system can be evaluated.
Figure 25: Sensitivity of skid edge pulsation to pulsation control devices
GENERAL GUIDANCE FOR SPECIFYING PULSATION CONTROL DEVICES The sizing formula for gas-charged dampeners, Eq 1, is a simple step to allow for selecting a pulsation control device early in the design process. The dampener size and location can be determined, and the rest of the pump package design can progress. However, as is shown in this paper, the gas-charged dampener determined from this approach may not be appropriate. A surge volume or pulsation filter may be required in some cases. The difficulty arises that when the requirement for a large vessel is found to be necessary and the design of the pump package has progressed to a point where installing the vessel is very difficult. As shown in the example, the vessels tend to be relatively large. Locating the vessel near the pump is difficult if the arrangement of the pump package and piping did not consider the requirements for such a vessel. Also, the vessel is a custom-built component, so time for delivery of material and fabrication must be added to the schedule. A simple approach is required that would aid designers early in a project to determine when a particular pulsation control device is required for a specific application. One tactic is to consider the basics of acoustic theory used in pulsation studies of plunger pump systems. The characteristic acoustic impedance, z, for a plane wave such as a pressure pulsation traveling down a pipe is described by the following equation (Munjal (5))
𝑧𝑧 = 𝜌𝜌𝑐𝑐𝐴𝐴� (7)
Where 𝜌𝜌 is the density of the fluid 𝑐𝑐 is the speed of sound or acoustic velocity 𝐴𝐴 is the cross-section area
The acoustic impedance is more generally described by the following relationship (UNSW(6))
𝑧𝑧 = 𝑝𝑝𝑄𝑄� (8)
Where 𝑝𝑝 is the acoustic pressure or pressure pulsation Q is the acoustic volume flow rate
The acoustic pressure, or pressure pulsation, is a dynamic pressure described with a unit of peak-to-peak to indicate the pressure is time-varying from a minimum to a maximum. The same is true for the acoustic volume flow rate. The fluid flow has a mean or steady-state flow component, but it also has a dynamic flow component superimposed over the mean flow. The quantity Q describes the amplitude of this dynamic flow component. Rearranging Equations 7 and 9 gives the following relationship
𝑝𝑝 = 𝜌𝜌𝑐𝑐𝑄𝑄𝐴𝐴� (9)
Consider the numerator of Eq 9. The units of the term 𝜌𝜌𝑐𝑐𝑄𝑄 are force. The numerator can be thought of as the magnitude of the dynamic force that is driving or creating pressure pulsations. Calculating the numerator of Eq 9 should give an indication of the relative strength of pressure pulsations created by a pump that must be controlled by the pulsation control device. The numerator of Eq 9 has been called the source strength coefficient. The source strength coefficient can be calculated from the pump performance, so it can be determined early in the design process. A pulsation model or pulsation analysis of the system is not required. The values 𝜌𝜌𝑐𝑐 are relatively available from the fluid properties. The value of Q requires calculation of the pump flow-versus-time curve as shown in Figure 15. A Fourier transform is then done on the flow-versus-time curve to calculate the spectrum or flow harmonics as is shown in Figure 16. All these calculations can be done with a spreadsheet, so this approach is relatively easy to implement early in the design stage. A benchmark for the source strength coefficient must be established to aid in making decisions about the type of pulsation control that will likely be required. The 1x PPF harmonic of the flow, as shown in Figure 16, will be the highest magnitude, so a calculation of the source strength coefficient at 1x PPF should be the focus of the calculation. As there are multiple plungers in a pump application and the pulsations from all plungers will sum at 1x PPF, the source strength coefficient should be the sum from all plungers. A range of pump performance calculations were done for pump powers from 10 HP to 400 HP (7.5 kW to 30 kW). A review of past design and field projects was also done. The results from this review were correlated to determine typical ranges for the source strength coefficient for different pulsation control designs. The results are summarized in Table 1. Note that the source strength coefficient numbers are in units of lbf (pounds force) peak-peak based on the density in slug/ft3, speed of sound in ft/s and acoustic volume flow is ft3/s pk-pk.
Table 1: Pulsation control selection based on source strength coefficient
Pulsation control selection Source strength coefficient
Pump required power
lbf N HP kW Traditional dampener sizing is appropriate <120 <535 <25 to 50 <18 to 37 API 674 pulsation study recommended >120 >535 25 to 50 18 to 37 Surge volume or volume-choke filter is likely required >220 >980 >50 to 100 >37 to 75 Volume-choke-volume is likely required >400 >1780 >100 to 200 >75 to 150
The source strength coefficients and approach for selecting pulsation control devices for plunger pump systems does apply a level of engineering rigor to the process. Additional work is recommended to refine the range of source strength coefficients further, however, this table provides a starting point. An alternative to using the source strength coefficient for evaluating a pulsation control strategy early in the design process is the pump-required power. The power that the pump requires is an indicator of the energy that the pump puts into the flow and is, therefore, an indirect indicator of the relative level of pulsations in the system. The limitation in evaluating only the pump-required power is that the effect of the fluid type is ignored. Generally, a fluid that is more dense and less compressible, such as water, has high pressure pulsation as compared to propane at an elevated temperature, which is less dense and quite compressible, and will have pressure pulsations that are lower and easier to control. The third column in Table 1 summarizes the typical range of pump-required power for the different pulsation control approaches. The lower power numbers should be considered for dense, relatively incompressible fluids while the higher power numbers are for lighter, compressible fluids.
CONCLUSIONS Conclusions from this parametric analysis of pulsation models for a gas-charged dampener in a plunger pump application are: • The traditional formula used for sizing gas-charged dampeners will not be suitable to reliably reduce pressure pulsations to
acceptable levels • Increasing the volume of a gas-charged dampener does not have a significant impact on the pressure pulsations for the pump
package model evaluated in this study. It is the authors’ experience that changes in only the gas-charged dampener volume will have a small impact on pump system pulsations.
• The dampener should be installed as close to the pump flange as possible. The dampener should be less than five main line diameters from the pump, ideally right at the pump flange.
• A gas-charged dampener on the non-flow end of the pump fluid end will be effective in reducing pressure pulsations. • The neck of the gas-charged dampener should be as large a diameter and as short as possible. • A plunger pump with more plungers will not necessarily result in lower pressure pulsations as compared to a pump with fewer
plungers. The acoustical (pulsation) resonances in the piping system and their coincidence with the pump operating speed are an important factor in the resulting pulsations.
• A variable-speed pump is more likely to have excessive pressure pulsations at some speeds due to acoustic resonances than a fixed-speed pump.
• The variation in the fluid bulk modulus and speed of sound (acoustic velocity) must be considered in the selection of the pulsation control devices — generally, the lower the bulk modulus, the lower the pressure pulsations.
• A pulsation model of only the pump package system with a gas-charged dampener will not give a reliable estimate of the pressure pulsations when the full piping system is included. A pulsation filter or simple surge volume designed with the pump package model will give representative results of pressure pulsation when the full piping system model is added.
• A source strength coefficient can indicate the type of pulsation control device that will be required for a pump application. A range of pump power has been suggested as an alternative approach.
NOMENCLATURE 𝐴𝐴 = the cross-section area (L2) 𝐶𝐶𝑝𝑝 = pump constant (-) 𝑐𝑐 = acoustic velocity (L/T) cg = acoustic velocity of gas (ft/s) (L/T) cl = acoustic velocity of liquid (L/T) 𝑑𝑑 = pipe diameter (L) 𝑑𝑑𝑐𝑐 = diameter of choke tube (L) 𝐸𝐸 = elastic modulus of the pipe (F/L2) 𝑘𝑘𝑏𝑏 = fluid isentropic bulk modulus (F/L2) 𝜋𝜋 = choke length (L) 𝑃𝑃𝐷𝐷 = pump displacement per revolution (L3/rev) 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚= mean line pressure (F/L2) 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 = minimum pressure due to pulsation (F/L2) 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 = maximum pressure due to pulsation (F/L2) 𝑃𝑃 = polytropic expansion coefficient of charge gas (-) 𝜌𝜌 = fluid density (F/L3) ρg = density of gas (F/L3) ρl = density of liquid (F/L3) 𝐸𝐸 = pipe thickness (L) V = volume (L3) 𝐷𝐷1, 𝐷𝐷2=volume of the acoustic filter chambers (L3) REFERENCES
1. Griffco Valve Inc, 2019, https://griffcovalve.com/griffco-pulsation-dampeners-calculator 2. McKee, R. and Broerman, E., 2009, Acoustics in Pumping Systems, Proceedings of the Twenty-Fifth International Pump
https://www.walchem.com/literature/Accessories/PD/SENTRY%20Pulsation%20Dampener%20FAQs.pdf 4. Wylie, E.B., Streeter, V.L., Fluid Transients in Systems, Prentice Hall, 1993, 5. Munjal, M.L., Acoustics of Ducts and Mufflers, Acoustic Impedance, John Wiley and Sons, 1987 6. Acoustic impedance, intensity and power, University of New South Wales, 2019,
http://www.animations.physics.unsw.edu.au/jw/sound-impedance-intensity.htm ACKNOWLEDGMENTS The authors acknowledge the contribution of Brian Howes, Jordan Grose and Shelley Greenfield in preparation of this paper and their support in this field of study.
