Pressure variations resulting from the oscillatory flow patterns found in positive-displacement machinery, especially reciprocating compressors, are referred to as “pulsations.” Found in both liquid- and gas-handling systems, pulsations are a common phenomenon in the chemical processing industries (CPI). Operational problems associated with pulsations include resonance conditions, high vibrations, degradation of support systems and increased risk for fatigue failures caused by dynamic forces. To avoid potential pulsation-related problems in reciprocating compressors and piping systems, there are two design considerations that must be taken into account. The first focuses on minimizing the magnitude of the harmonic forcing functions. The second method examines physical modifications to the piping support or piping layout to mitigate issues related to natural frequencies and harmonics. This article covers the first method in detail.
In systems that employ positive-displacement machinery, the pressure and flow of the gas or liquid are not steady. Instead, the fluid moves through the piping at varied conditions in a series of pressure pulses. These variations are superimposed upon the steady (average) and dynamic regimes in Figure 1. In addition, flow pulses act as excitations that create pressure and flow modulations, namely acoustic waves, which propagate at a speed equal to the speed of sound through the process fluid as it moves through the piping system. The frequencies of flow pulses are a function of the mechanical properties of the compressor, including the compressor’s piston-displacement and crank-rotation behavior. The piston-displacement function for reciprocating compressors is shown in Figure 2.
Flow variations, as plotted in Figure 3, appear as a saw-tooth flow function at both the suction and discharge sides of the compressor cylinder. The shape of the saw-tooth is determined by the rotational speed of the compressor, the single- or double-acting features of the compressor, the geometry of the cylinder-cylinder valve and the pressure ratio.
Actually, studying the crankshaft of a compressor allows for some predictability of the pulsation-producing behavior. Pulsations are produced at a rate equivalent to the compressor-crankshaft displacement, in revolutions per minute (rpm), and multiples thereof. Pulsation frequencies are generally expressed in cycles per second, or Hertz (Hz). For example, a 600-rpm compressor produces pulsations at 10, 20 and 30 Hz, as well as higher multiples. Compressors in natural-gas services are mostly double-acting, and compress gas on the head and crank ends of the cylinder. Double-acting cylinders produce more pulsation at the even multiples of crankshaft speed and less at the odd multiples. Therefore, a 600-rpm double-acting cylinder will produce its strongest pulsation at 20 Hz. When compressors have more than one cylinder, the crankshaft phasing of the cylinders will also cause certain multiples to be higher than the others. For example, if two double-acting cylinders are phased 90 deg apart, they will produce a significantly higher pulsation level at four times the crankshaft rpm level. In the case of a 600-rpm machine with two double-acting cylinders phased 90 deg apart, there will be a high fourth harmonic or 40 Hz. Generally, the higher multiples — sometimes called compressor harmonics or compressor orders — will contain less energy than the lower orders. When a discrete Fourier analysis is performed on the aforementioned saw-tooth function, the strength of the individual flow harmonics is determined. The discrete Fourier analysis of the flow’s saw-tooth function indicates which harmonics of the compressor running speed produce the largest pressure amplitude, as seen in Figure 4.
In most pulsation analyses, the pressure amplitudes for the first to tenth harmonics are usually used in the acoustic model to predict the pulsations and unbalanced forces. Any pulsations must be smaller than the limits given in API 618 , which defines the minimum suction and discharge surge volumes required for pulsation control. Additionally, unbalanced forces must not produce a fatigue failure on the piping system. Typically, the predominant pressure and flow modulations generated by a reciprocating compressor are at frequencies that can be modeled as generalized one-dimensional waves. However, in high-speed reciprocating compressors, such as those with speeds between 750 and 1,000 rpm, this assumption is not correct and a three-dimensional analysis should be conducted on both compressor suction and discharge manifolds.
Pulsation control in compressor piping systems can be accomplished by proper application of the basic filter elements, including pulsation dampeners, single- or double-volume bottles, choke tubes and orifices. These elements can be combined in various manners to achieve pulsation control ranging from attenuation of pulsations to true filtering.
Pulsation dampeners of any volume cause the dissipation of pulsative energy, preventing its transmission through a system. In most chemical plants, single-empty dampener volumes — usually spherical or cylindrical styles — are used. However, double-volume dampener filters with internal or external interconnection piping are also relatively common. The line between the two volume chambers in a two-volume dampener is referred to as the choke tube. Figures 5 and 6 illustrate single- and double-volume dampeners, respectively. The double-volume model is shown in both internal and external types, with choke-tube parameters as follows: choke-tube length (Lc), choke-tube area (Ac) and choke-tube internal diameter (dc).
In general, suction pulsation dampeners are mounted directly at the top of the cylinders, and discharge dampeners directly at the bottom. In fact, the API 618 standard requires a top-to-bottom gas flow to allow for proper liquid drainage. To gain insight into the effectiveness of the various configurations, the pulsation transmission factor (TF) is used. This factor is defined in Equation (1), in terms of a pulsation amplitude ratio, where Qin is the amplitude of pulsation at the dampener inlet and Qout is the amplitude of pulsation at the dampener outlet.
TF = Qou t / Q in (1)
The frequency at which Qout is equal to Qin is called the passband frequency. This frequency indicates a maximum in pulsations and is registered as resonance in the dampener. Thus, it is desirable to decrease TF by changing the dampener dimensions and area ratio to minimize pulsation amplitude downstream. By comparing the transmission factor of each pulsation dampener with other types of dampeners, it is possible to gain knowledge of the strengths and weaknesses in each configuration. This matter is explained in more detail in the following sections.
A single-volume (empty bottle) dampener, in either a cylindrical or spherical style, is attached to the suction or discharge of a compressor. This volume provides surge capacity and acts as a filter, which can effectively isolate the piping fluid from the flow modulations induced by the compressor. Based on the standards set in API 618, the surge volume is defined as 21 times the combined swept volume of the head and crank end of the compressor cylinder, corrected by a square root function for the speed of sound difference between a typical natural gas with a speed of sound of 600 m/s. However, in most applications, assuming 30 times the piston sweeping volume is considered an acceptable preliminary estimation.
The TF value of this type of bottle is reduced with increasing volume and a decrease in the piping cross-sectional area. In other words, the attenuation characteristics of the empty volume are a function of the volume enclosed by the bottle, as well as the expansion ratio of the attached pipe and bottle diameters. Moreover, according to API 618, for a single-cylinder empty volume bottle, the ratio of bottle length to inside diameter (L/D) shall not exceed four. However, in most practices, an L/D of approximately three is considered acceptable, with a general assumption that bottle diameter should be three to four times the compressor nozzle diameter. Bottle length should be minimized when comparing acoustic length response with the compressor excitation frequencies; in this regard, dampener length should be selected to be less than one-fourth of the compressor’s main harmonic wavelength. Also, passband frequencies are controlled by the bottle length, because they occur at half of the pulsation wavelength.
It is important to understand the differing characteristics of spherical and cylindrical dampeners. In general, a spherical single-volume type is much more efficient than the cylindrical type, but because of restrictions on fabrication costs, the cylindrical dampener type is much more commonly used. The transmission characteristics of spherical and cylindrical dampeners are illustrated in Figure 7. Here, it is seen that the cylindrical volume and the ideal volume are equal . The spherical volume transmission indicates excellent attenuation characteristics, making it a very effective choice for pulsation dampening, if not for the high associated costs.
Compressor manufacturers should provide pulsation bottles for both the suction and the discharge side of each cylinder, and cylinders operating in parallel configurations can be connected to a common suction or a common discharge bottle, if possible, and in accordance with API 618 requirements. However, suction-pulsation bottles should be designed to prevent liquid trappage and should not be equipped with internals for moisture removal. As such, suction piping is sloped back toward the knockout drum to prevent liquid accumulation in the machine suction bottles. Similarly, discharge bottles must be self-draining. Moreover, if suction bottles and piping are provided by the compressor vendor, they must have attachment features or facilities for installing insulation and heat tracing to maintain the metal temperature at least 6C above the rated gas temperature for the suction. It is recommended that welding-neck flange types be used in bottle fabrication, except for inspection or cleaning flanges, and that long-welding-neck type (LWN) flanges be used for instrument devices. All welds in bottle construction should be full-radiography afterwards; the root pass of welding should be gas-tungsten arc welding (GTAW) type and the next passes should be shielded-metal arc welding (SMAW) type .
Suction dampener supporting should be installed in a goalpost-type arrangement, and not on the compressor cylinder itself. It is recommended that tapping on the shell be minimized and pressure and temperature indicators be installed on the main nozzles or piping manifolds. One of the best practices for the design of volume bottles is to place the cylinder connections at the longitudinal center of both the suction and discharge bottles. In fact, the cylinder nozzle exit in the discharge bottle, or entrance, in the case of the suction side, can be the origin of the pressure pulsations in the bottle itself. If this origin is placed symmetrically with respect to the bottle ends, the pressure pulsations will hit the two opposite sides with the same phase, resulting in zero net pulsations.
In addition, the length of cylinder nozzle connections must be limited, because longer nozzle lengths result in more harmonic resonance in the section of pipe between the cylinder and the volume bottle. However, there is an exception with very light gases, such as pure hydrogen or helium, because high gas-sound velocity and wavelength produce no resonance in short lengths of pipe. In this case, the minimum bottle acoustical natural frequency that could be excited in resonance is above the tenth harmonic.
Due to restrictions on machine component layouts, including cylinder arrangement, interstitial spaces between cylinders or supporting structures for the bottles, there are some cylinders for which reaching the center of the cylinder is not possible from outside of the volume bottle. In these cases, a standard design practice is to insert a section of pipe directly into the bottle to balance the volume-bottle cylinder’s connection to the center of the volume bottle (Figure 8).
Another best practice is positioning a fixed orifice plate in the cylinder flanges. Actually, as illustrated in Figure 9, the standing wave pattern of the pressure pulsation is carried from the valves through the cylinder gas passages and the cylinder nozzle into the bottle, on each side of the cylinder. This pressure pulsation acts to produce varying positive and negative forces in the vertical direction. Dampening of this resonance is necessary to avoid excessive shaking forces inside the bottles and to prevent damage to the cylinder valves on the other side .
As a result, orifice plates in the throat of the flanged inlet or outlet nozzle connections are mandatory to reduce the pulsation amplitude, called nozzle-mode frequency, which is present between the cylinders and the volume bottles. These orifices must be located exactly at the outlet flange for the suction volume bottle and at the inlet flange for the discharge volume bottle. Orifice installation between cylinder flanges and pulsation dampener flanges has an advantage. When needed, the orifice plate can be easily changed during a plant overhaul or a redesign for new operating conditions. Furthermore, orifices in outlet connections for discharge bottles and in inlet connections for suction bottles can change piping cross-sectional area, increase TF and subsequently decrease the pulsation level prior to the dampener on both the suction and discharge sides.
The orifices’ recommended pressure drop is a maximum of 1% of the line’s mean pressure. They are typically large-bore orifice plates, and can provide equivalent pressure drop in the order of a valve or approximately 1/100 the diameter of the pipe. The normal orifice discharge coefficient (Cd) is 0.6, but orifices lose their efficiency at higher frequencies and in these cases, the user might consider multiple-bore orifice plates . The preferred material is stainless-steel type AISI 304 or 316 with 10-mm thickness. Most orifices have a clearly marked flow direction and should be installed carefully. The flow direction is always from the small-opening end to the large-opening end (Figure 10).
Two-volume dampeners are an extension of the single-volume variety, and there are significant differences in these two types of dampeners, with regard to low-frequency characteristics. The first bottle, which is directly connected to the compressor cylinder, is called the surge volume and the second bottle is the filter volume. Recall that a choke tube separates the two volume chambers in a double-volume dampener, hence the volume-choke-volume label. The single most important characteristic of a dampener’s volume-choke-volume configuration is its acoustic natural frequency — or Helmholtz frequency. This is a value at which a frequency pulsation is amplified, followed by a rapid drop-off in pulsation levels (Figure 11). Equations (2) and (3) are used to calculate the Helmholtz frequency (fH)  in terms of the speed-of-sound propagation through the process gas (C). L’c represents the corrected choke-tube length.
Figure 12 shows the realized response of double-volume dampeners, superimposed on the pulsation spectrum for a 300-rpm double-acting compressor. This figure exhibits a relatively high Helmholtz frequency compared to choke-tube passband and nozzle-mode response frequencies. The passbands, which amplify certain frequencies, are related to design considerations, such as the length of choke tubes and inlet nozzles. The frequency of passbands must be carefully considered to ensure low dynamic-pressure transmission and good compressor isolation. Actually, passband frequencies are controlled with dampening by adding pressure drop (orifices) or flow losses (choke tubes). However, adding dampening reduces compressor performance and increases power losses and operating costs. The minimum surge volume requirements and dampening are controlled by pressure drop in the choke tube. At frequencies below the Helmholtz frequency, there will be no attenuation of pulsations passing through the dampener.
Meanwhile, there will be a sharp reduction of pulsation at about 20–40% above the Helmholtz frequency and extending out to several Hertz before the passband frequency, due to choke-tube and cylinder-gas passage. In addition, it is very important to account for margins between the compressor pulsation and the Helmholtz frequency. This margin can be evaluated in two ways. For speeds above 500 rpm, the Helmholtz frequency should be placed 30% below the compressor pulsation (or rpm divided by 60). On the other hand, for compressor speeds below 500 rpm, the Helmholtz frequency should be placed 33% above the compressor pulsation. This 33% margin can also be applied in other cases, due to economical restrictions, physical impracticality, or when pressure drop is very critical in low suction pressures or when there is limitation in space for the compressor layout.
Double-volume dampeners can be used effectively to control pulsation with relatively high molecular-weight components and relatively low-speed systems with velocities less than 600 m/s. Each bottle volume (surge and filter) is approximately sized to be ten times the piston sweeping volume. The preferred arrangement is symmetric, with equal length between the bottles and the choke tube. It is worth noting that in symmetrical dampeners, passband frequencies are minimized. Besides this, the inside diameter of the choke tube should be so small that pressure-drop limits are minimized. Larger-diameter choke tubes create less pressure loss but require larger volumes. In most applications, a common procedure is to limit the gas velocity to 30 m/s for initial choke-tube sizing.
Double-volume dampeners with internal choke tubes and baffle plates are generally appropriate for speeds lower than 500 rpm and lighter gases. Conversely, dampeners with external choke tubes are generally appropriate for speeds higher than 500 rpm and heavier gases. The bottles’ diameter should be three to four times the compressor nozzle and outlet piping diameter. Bottle length will depend on the acoustic design technique. With regard to nozzle frequencies, dampening is controlled by the pressure drop in the nozzle, with the ideal location for pressure drop being the bottle’s connection. Design considerations for controlling the main amplified frequencies are summarized in Table 1.
|TABLE 1. CONTROLLING AMPLIFIED PULSATION FREQUENCIES|
|Helmholtz resonance||Choke tube passbands||Nozzle-mode response|
|Volume of 1st chamber
Volume of 2nd chamber
Length of choke tube Area of choke tube
|Length of choke tube
Chamber length (if not center-fed by nozzle)
Choke tube pressure drop
|Cylinder passage volume
Effective cylinder length
Length of nozzle
Volume of first chamber
Comparison of dampeners
The selection of a pulsation dampener depends on compressor speed, compressor construction, gas thermodynamic properties, sound velocity and the degree of pulsation control required. Figure 13 compares single-volume and double-volume dampener performance in terms of the transmission factor. The empty single-volume dampener provides adequate attenuation of pulsations between frequencies of 0 and 10 Hz. After that, the two-volume dampener has superior attenuation characteristics in the 10–120 Hz spectrum. In other words, for maximum attenuation over a wider frequency range, two-volume dampeners may be a more appropriate option. However, in two-volume pulsation dampeners, the transmission factor strongly depends on compressor gas composition and speed, whereas single-volume dampeners exhibit steady behavior under a variety of operating conditions — a single-volume dampener experiences very little efficiency decrease in a dynamic environment.
Actually, experience has shown that a single-volume dampener is effective and the preferred solution in pulsation dampening in most CPI plants. Moreover, pressure drop is lowest in this type, and there is much lower possibility for mechanical problems or failure of internals.
Conversely, in double-volume dampeners, internal component failure is a major weakness. Overall, operations are simpler and more flexible with single-volume dampeners. For example, double-volume dampeners must be synchronized according to the specified compressor operation; this process is not necessary for single-volume dampeners. For double-volume configurations, significant changes in operating conditions or gas composition may require the replacement of the volume bottles and internals, but pulsation control in single-volume dampeners can be adjusted by insertion of removable orifices or by additional volume located close to the existing bottle. Finally, due to the need for bottle internals in a two-bottle design, the cost of these devices is normally higher than that of a single empty-volume system.
Correct design of pulsation devices is an important step in ensuring safe and reliable operations by mitigating vibrations of compressors and piping-manifold systems. Usually, when designers adhere to the initial sizing procedures for pulsation dampeners, a final acoustic and vibration study will indicate the need for only minor equipment modifications, such as adding orifices or changing the support-piping type or layout.
1. Amer. Pet. Institute, Reciprocating Compressors for Petroleum, Chemical and Gas Service Industries, API 618 5th edition, Dec. 2007.
2. Blodgett, L.E., “Theoretical and Practical Design of Pulsation Design Damping”, Elsevier Ltd., 1992.
3. Giacomelli, E., others, “Pressure Vessel Design for Reciprocating Compressors Applied in Refinery and Petrochemical Plants”, ASME Pressure Vessel Division, 2005.
4. Howes, B.C. and Greenfield, S.D., “Guidelines in Pulsation Studies for Reciprocating Compressors”, 4th International Pipeline Conference, 2002.
5. Barta, M.L. and Bass, T.P., Gas piping design for high-speed reciprocating compressor units, Journal of Engineering for Industry, 1971.
6. Atkins, K.E., Pyle, A.S. and Tison, J.D., “Understanding the Pulsation & Vibration Control Concepts in the New API 618 Fifth Edition”, Gas Machinery Conference, 2004.
Ali Ghanbariannaeeni is a rotating equipment engineer currently working at Lloyd’s Register EMEA (Denburn House, 25 Union Terrace, Aberdeen, U.K., AB10 1NN, Phone: 0044 (0)1224 267413, Email: Ali.Ghanbariannaeeni@lr.org) specializing in reciprocating, centrifugal and screw compressors, gas and steam turbines, process pumps, engines and electric machines.. He is a chartered engineer and a member of the Institute of Mechanical Engineers (IMechE). He obtained a B.S. degree in mechanical engineering from Iran University of Science and Technology (Tehran, Iran).
Ghazalehsadat Ghazanfarihashemi is a rotating equipment engineer currently working at AMEC Group Ltd. (Pavilion 1, City View, Craigshaw Business Park, Craigshaw Drive, Aberdeen, U.K., AB12 3BE, Phone: 0044(0)1224 294189, Email: firstname.lastname@example.org) specializing in reciprocating and centrifugal compressors, process pumps, engines and electric machines. She obtained an M.S. and a B.S. degree in mechanical engineering from Sharif University of Technology in Tehran, Iran.
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