Patent Publication Number: US-2019178239-A1

Title: Apparatuses, Systems, and Methods for Improved Performance of a Pressurized System

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation of U.S. patent application Ser. No. 14/176,015, filed Feb. 7, 2014, which is a continuation of U.S. patent application Ser. No. 12/686,017, filed Jan. 12, 2010. application Ser. No. 12/686,017 claims priority to U.S. provisional patent application Ser. No. 61/143,974, filed Jan. 12, 2009, and is a continuation-in-part of U.S. patent application Ser. No. 12/189,630, filed Aug. 11, 2008, now U.S. Pat. No. 9,567,996. All of the above referenced applications are incorporated herein in their entireties. 
    
    
     FIELD OF THE INVENTION 
     The present invention is concerned with reducing pulsations in fluid systems. 
     Embodiments of the invention also increase fluid flow, reduces power consumption, or both over traditional systems, resulting in smoother, more efficient fluid flow in a closed system. 
     BACKGROUND OF THE INVENTION 
     The theory of cyclical finite amplitude pressure wave propagation in pipes is discussed, for example, in Professor Gordon P. Blair&#39;s book “Design and Simulation of Two-Stroke Engines” and will not be repeated in detail in this application. Rather, the following is a summary of some of the underlying principals of physics that this invention exploits: 
     1. There are always two waves propagating in opposite directions within a pipe that has flow. 
     2. The convention is to call one wave the right wave and the other wave the left wave. 
     3. The two waves superimpose upon each other and create the pressure that can be measured by a pressure transducer. 
     4. It is not possible to measure the right or left wave separately, however they can be tracked, for example, by a one-dimensional gas flow simulation software developed by OPTIMUM Power Technology. 
     5. Both waves propagate without reflection if the cross sectional area of the pipe stays the same. 
     6. When the cross sectional area of the pipe changes, part of the wave continues to propagate and the remainder of the wave reflects in the opposite direction. 
     7. When pipes branch or terminate, part of the wave continues to propagate and the remainder of the wave reflects in the opposite direction. 
     As a result of these phenomena, a compressor creates pulsations that propagate away from it and piping that attaches to both the suction and discharge sides of the compressor create pulsations that propagate back to the compressor, affecting compressor performance. 
     By properly phasing the cylinders of the compressor and/or properly choosing the lengths and diameters of pipes in fluid communication with the compressor, outward bound pulsations can be attenuated and inward bound pulsations can used to improve the performance of the compressor. 
     A fluid, whether gaseous or liquid, may flow through a conduit or duct. The fluid may be propelled by a pressure creating device, such as a compressor or other type of pump. One type of compressor used to propel fluid, particularly gas, is a reciprocating compressor. The pressure and flow delivered by reciprocating compressors varies throughout the stroke of each compressor cylinder piston, thus creating pressure waves or pulses that propagate at acoustic velocity throughout the attached piping system. Effective control of the pressure pulsations generated by reciprocating compressors is desirable for various reasons, including to prevent damaging forces and stresses in system piping, vessels, and mechanical equipment and structures, and to prevent detrimental time-variant suction and discharge pressures at or near the compressor cylinder flanges. 
     A reciprocating compressor may have a piston that is moved alternately toward one end of a cylinder and then to an opposing end of the cylinder and fluid may be propelled from the cylinder by the piston in either one or both directions of piston movement. A piston that propels fluid when moving in only one direction may be referred to as single-acting piston, while a piston that propels fluid when moving in both directions may be referred to as a double-acting piston. Double-acting pistons compress gas at the discharge of the compressor using both strokes of the piston, while single acting pistons compress gas at the discharge of the compressor using only one stroke of the piston. Exemplary double-acting compressors are those manufactured by Ariel Corporation of Mount Vernon, Ohio. 
     The pumping action of each single-acting or double-acting piston creates complex cyclic pressure waves. The pressure waves of a double-acting piston generally have a primary frequency at twice the compressor operating speed with many harmonics. Variations in pressure within conduits and ducts created by such pumping actions are commonly referred to as pulsations. 
     In a typical fluid pumping system (e.g., a natural gas pumping station), wherein the pumping is performed by one or more reciprocating compressors, pressure pulsations are controlled with a system of primary and/or secondary volume bottles, often with complex internal choke tubes, baffles, and chambers, as well as various orifice plates installed at various locations in the system piping. Those pressure pulsation control devices are thought to accomplish pulsation control by adding resistance, or damping, to the system, and their use results in pressure losses that typically exist both upstream (or in a direction away from the compressor cylinders) and downstream (or in a direction toward the compressor cylinders) of the compressor cylinders. For common pipeline transmission applications, particularly those having low pressure ratios between their inlets and outlets, such as natural gas pipeline systems, pressure losses can noticeably degrade system operating efficiency. As larger high-speed compressors have been increasingly applied to pipeline transmission applications, the influences of existing pressure wave or pulsation control devices are thought to have become more detrimental to performance, because of the higher frequency pulsations that must be damped in such high-speed compressors. In certain cases, installed systems using traditional methods of pulsation control have been reported to add 20 percent or more to the driver horsepower requirements for high-speed, low-ratio compressors. 
     Commonly, in systems such as natural gas pipeline systems, bottles are employed near the outlets of their compressors to dampen pulsations close to the fluid source. In addition to the drawbacks of using bottles to control pulsation as described above, bottles are commonly very bulky. A natural gas pipeline or other system that eliminated, decreased, or did not rely exclusively on bottles to address pulsation may overcome certain drawbacks. Thus, a natural gas pipeline or other system that addressed pulsation by attenuating pulses at various positions along the pipeline without significantly affecting efficiency of the system may be desirable. 
     Study has been made as to the effect of the use of differing length parallel tubes to cancel sounds of a particular wavelength. Acoustic wave interference in pipes was studied in  1833  by Herschel, who predicted that sound could be canceled by dividing two waves from the same source and recombining them out of phase after they followed paths of different lengths. Experiments by Quincke in 1866 verified that Herschel&#39;s system did suppress sound. 
     Variations on the Herschel-Quincke solutions have been proposed including a method for controlling exhaust noise from an internal combustion engine by using bypass pipes such as shown in U.S. Pat. No. 6,633,646 to Hwang (hereinafter “Hwang”). See  FIG. 1  and  FIG. 5  of Hwang. In such an apparatus, a main exhaust pipe is provided with two U-shaped bypass pipes through which the exhaust passage of the main pipe is partially diverted before being reintegrated. With such a construction, the phase difference between the main noise components of the exhaust gas passing through the fixed pipe and the noise components of the exhaust gas passing through the first bypass pipe is adjusted 180 degrees, thus suppressing the main noise component and its odd harmonics. The length of the second bypass pipe is adjusted so that the noise component having a frequency of two times the frequency of the main noise component is suppressed. However, the above method does not effectively attenuate the 4th harmonic, i.e., the noise component having a frequency four times the main noise component, nor any other harmonics divisible by  4 . Such an arrangement furthermore operates on a single primary frequency and certain of its harmonics and so is unlikely to provide effective noise attenuation over a range of noise frequencies. Furthermore, Herschel, Quincke, and Hwang directed their efforts toward sound attenuation, not improvement of system integrity and performance. While attenuation of sound and pulsations may be achieved by similar means, they operate differently by degrees to achieve different results. For example, reduction of sound is frequently directed to human comfort and reduction of high frequency wavelengths that are bothersome to human beings. Conversely, pulsation reduction frequently focuses on reducing low frequency wavelengths that may cause damage to mechanical systems, such as pipes, conduits, ducts, mechanical equipment and structures, sometimes in critical safety applications such as natural gas pipelines. 
     U.S. Pat. No. 5,762,479 to Baars et al. (hereinafter “Baars”) is directed to a discharge arrangement for a reciprocating hermetic compressor of the type used in small refrigeration systems. That arrangement includes a gas discharge tube through which gas flows from a gas discharge chamber. To attenuate a pulse at a certain frequency, part of the gas flow from the gas discharge chamber is displaced through a gas discharge auxiliary tube. The lengths of the gas discharge tube and gas discharge auxiliary tube differ by a fraction, preferably half, of the length of a wave at that frequency. As such, when the gas flow in the gas discharge tube and gas discharge auxiliary tube join, the pulse is attenuated. 
     Baars does not, however, address system performance such as gas flow rate or efficiency. Additionally, Baars only addresses attenuation of a pulse at a single frequency, and does not attenuate pulses at any other fundamental or harmonic frequencies. Additionally, there may be a need for a pulsation attenuation apparatus, system, and method that attenuates pulses at multiple frequencies and, unlike Baars, is directed to natural gas pipeline systems. 
     U.S. Pat. No. 3,820,921 to Thayer (hereinafter “Thayer”) is directed to a hermetic refrigerator compressor with radially-configured cylinders. Thayer discloses a six-cylinder discharge arrangement in which the first three cylinders have discharge tubes that connect side-by-side at a joint to one common discharge line, and the other three cylinders have discharge tubes that connect side-by-side at a joint to a second common discharge line. The discharge tubes may be of unequal length to reduce noise including that caused by vibration and resonance at certain frequencies. That configuration may minimize the need for mufflers, and may increase compressor efficiency. The side-by-side relationship at the connection point at the joint is said to create an aspiration effect in the joint by which gas being discharged from one of the cylinders helps to withdraw the discharge pulses from the opposing cylinder. 
     Thayer is directed to noise reduction in a hermetic refrigerator compressor with radially-configured cylinders and does not go to improving performance of a compressor with in-line cylinders, such as those sometimes used in natural gas pumping. Thayer is further directed to an apparatus having a single joint in which flows are combined and arranged to create an aspiration effect, not a system that combines flows at two or more locations in series to improve compressor performance by attenuating various pressure variations. Accordingly, there may be a need for a pulsation attenuation that improves the performance of a compressor in a system such as a natural gas system. 
     Furthermore, the Thayer system does not recognize the wave reflection issue created by its joint. At discontinuities in the pipe flow conditions and geometry, such as at junctions of multiple routes of fluid flow and with respect to diameter changes, wave reflection normally occurs. Where the discontinuity is introduced close to the outlet of a compressor, such as in Thayer, the reflected portion of a wave may significantly affect the pressure at the outlet of the compressor. Thayer fails to address that issue. Additionally, there may be a need for a pulsation attenuation apparatus, system, and method that addresses that issue and further is, unlike the hermetic refrigerator compressor in Thayer, directed to natural gas pipeline systems. 
     Thus, certain embodiments of the present pulsation attenuation apparatuses, systems, and methods may account for those reflected portions of waves when determining, e.g., pipe length and positioning of certain junctions. Other embodiments of the present pulsation attenuation systems, apparatuses, and methods may account for those reflected portions of waves propagating through natural gas pipelines. 
     Embodiments of the present pulsation attenuation apparatuses, systems, and methods including reciprocating compressors with multiple sources, such as multiple cylinders, may reduce the pressure wave propagating through the fluid when combined from the multiplicity of sources while employing other means to improve system performance. 
     Certain embodiments of the present apparatuses, systems, and methods for improved performance of a pressurized system attenuate pulsations in a conduit or duct. While sound wave propagation cancellation and pulse propagation cancellation may be based on some of the same principles, it should be recognized by one skilled in the art of wave dynamics that reduction of sound wave propagation has a different goal and operates differently from reduction of pulse propagation to improve performance of a pumping system. 
     Certain embodiments of the present apparatuses, systems, and methods for improved performance of a pressurized system may further preserve the integrity of piping and vessel systems subjected to pulsations. 
     Embodiments of the apparatuses, systems, and methods for improved performance of a pressurized system described herein reduce pulsations in pumping systems, including pumping systems utilizing reciprocating compressors and rotary pumps (collectively referred to herein as “pumps”). 
     Embodiments of the present apparatuses, systems, and methods for improved performance of a pressurized system described herein reduce energy consumption as compared with existing systems. 
     Embodiments of the present apparatuses, systems, and methods for improved performance of a pressurized system described herein increase flow in pumping systems as compared to existing systems. 
     Embodiments of the present apparatuses, systems, and methods for improved performance of a pressurized system described herein reduce the pressure differential against which pumps operate as compared to existing systems. 
     Embodiments of the apparatuses, systems, and methods for improved performance of a pressurized system described herein may employ multiple means to reduce or cancel primary and harmonic frequencies of waves propagating through the pumped fluids, such as natural gas, and may improve system performance such as flow rate or efficiency. 
     SUMMARY OF THE INVENTION 
     Embodiments of apparatuses, systems, and methods for improved performance of a pressurized system are directed to systems, methods and apparatuses for reducing pressure waves in a fluid pumping system and to systems, methods and apparatuses for increasing flow or efficiency in a fluid pumping system. 
     In accordance with one embodiment of the present invention, a natural gas pumping system is provided. The natural gas pumping system includes a reciprocating compressor with two cylinders where each cylinder has an inlet through which natural gas is received and an outlet through which natural gas is discharged. The natural gas pumping system further includes a first conduit having a first end in fluid communication with the outlet of the first cylinder and a second end in fluid communication with a junction and a second conduit having a first end in fluid communication with the outlet of the second cylinder and a second end in fluid communication with the junction. 
     In accordance with another embodiment of the present invention, a natural gas pumping system that includes a reciprocating compressor is provided. The reciprocating compressor includes a first cylinder having an inlet through which natural gas is received and an outlet through which natural gas is discharged and a second cylinder having an inlet through which natural gas is received and an outlet through which natural gas is discharged. The natural gas compressor also includes a first conduit having a first end in fluid communication with the inlet of the first cylinder and a second end in fluid communication with a junction and a second conduit having a first end in fluid communication with the inlet of the second cylinder and a second end in fluid communication with the junction. 
     A pressure wave attenuation system is provided in another embodiment of the present invention. The pressure wave attenuation system includes one or more reciprocating compressors together comprising a first cylinder, a second cylinder, and a third cylinder, a first header coupled to the first cylinder and a first junction, a second header coupled to the second cylinder and the first junction such that a pressure wave propagating in the fluid flowing through the first header is out of phase with fluid flowing through the second header when the fluid flowing from the first and second headers combine at the first junction, a third header coupled to the third cylinder and a second junction; and a first branch line extending from the first junction to the second junction. 
     In yet another embodiment, a pressure wave attenuation system is provided that includes one or more reciprocating compressors together comprising a first cylinder, a second cylinder, a third cylinder, and a fourth cylinder; a first header in fluid communication with the first cylinder and a first junction; a second header in fluid communication with the second cylinder and the first junction such that a pressure wave propagating in the fluid flowing through the first header and a pressure wave propagating in the fluid flowing through the second header are attenuated when the fluid flowing from the first header and the fluid flowing through the second header combine at the first junction; a third header in fluid communication with the third cylinder and a second junction; a fourth header in fluid communication with the fourth cylinder and the second junction such that a pressure wave propagating in the fluid flowing through the third header and a pressure wave propagating in the fluid flowing through the fourth header are attenuated when the fluid flowing from the third header and the fluid flowing through the fourth header combine at the second junction; a first branch line in fluid communication with the first junction and a third junction; and a second branch line in fluid communication with the second junction and the third junction, the length of the second branch line differing from the length of the first branch line such that a pressure wave propagating in the fluid in the first branch line and a pressure wave propagating in the fluid in the second branch line are attenuated when the fluid flows from the first and second branch lines combine at the third junction. 
     In another embodiment, a method of reducing pressure variations in a natural gas pumping system is provided. That method includes combining natural gas flowing from a first reciprocating cylinder having a first periodic pressure fluctuation characteristic operating in a first phase with natural gas flowing from a second reciprocating cylinder having a second periodic pressure fluctuation characteristic operating in a second phase when the first periodic pressure fluctuation characteristic is out of phase with the second periodic pressure fluctuation characteristic. 
     The present invention also includes a method of attenuating pressure waves in a natural gas pumping system, comprising combining gas flowing from a first cylinder in which propagates a first periodic wave with gas flowing from a second cylinder in which propagates a second periodic wave such that the first periodic wave and the second periodic wave are out of phase. 
     Accordingly, the present invention provides solutions to the shortcomings of prior fluid pumping systems, apparatuses, and methods. Those of ordinary skill in the art will readily appreciate, therefore, that those and other details, features, and advantages of the present invention will become further apparent in the following detailed description of the preferred embodiments of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated herein and constitute part of this specification, include one or more embodiments of the invention, and together with a general description given above and a detailed description given below, serve to disclose principles of embodiments of pulsation attenuation devices and networks. 
         FIG. 1  illustrates an embodiment of a pulsation attenuation device; 
         FIG. 2  illustrates a schematic diagram of an embodiment of a six cylinder reciprocating compressor type pump; 
         FIG. 3  illustrates a schematic diagram of an embodiment of a six cylinder reciprocating compressor type pump; 
         FIG. 4  illustrates an embodiment of a fluid pumping system; 
         FIG. 5  illustrates an embodiment of an inlet piping system; 
         FIG. 6  illustrates an embodiment of a six-cylinder reciprocating compressor type pump system. 
         FIG. 7  illustrates an embodiment of a tuned loop network including two tuned loops; 
         FIG. 8  illustrates an embodiment of a tuned loop network including two tuned loops respectively in fluid communication with the inlet and outlet of a pump; 
         FIG. 9  illustrates an embodiment of a network including a suction tuned loop network and a discharge tuned loop network; 
         FIG. 10  is a flow chart of an embodiment of a method for attenuating pulsations, vibrations, or other undesirable waves in a fluid; 
         FIG. 11  is a flow chart of an embodiment of a method of attenuating pressure waves or pulsations created by a pump; and 
         FIG. 12  illustrates an embodiment of a fluid pumping system employing aspects of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Reference will now be made to embodiments of apparatuses, systems, and methods for improved performance of a pressurized system, examples of which are illustrated in the accompanying drawings. Details, features, and advantages of those apparatuses, systems, and methods for improved performance of a pressurized system will become further apparent in the following detailed description of embodiments thereof. It is to be understood that the figures and descriptions included herein illustrate and describe elements that are of particular relevance to apparatuses, systems, and methods for improved performance of a pressurized system, while eliminating, for purposes of clarity, other elements found in typical fluid pumping systems. 
     Any reference in the specification to “one embodiment,” “a certain embodiment,” or any other reference to an embodiment is intended to indicate that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment and may be utilized in other embodiments as well. Moreover, the appearances of such terms in various places in the specification are not necessarily all referring to the same embodiment. References to “or” are furthermore intended as inclusive so “or” may indicate one or another of the ored terms or more than one ored term. 
       FIG. 1  illustrates an embodiment of a pressure wave attenuation device  100 , also referred to as a pulsation attenuation device, having one tuned loop  102 . The tuned loop  102  includes an inlet conduit  104  coupled to an inlet junction  106 . The inlet junction  106  has an inlet  108  coupled to the inlet conduit  104 , a first outlet  110  and a second outlet  112 . The first outlet  110  of the inlet junction  106  is coupled to a first end  114  of a first branch line  116 , also referred to as a first attenuating conduit, and the second outlet  112  of the inlet junction  106  is coupled to a first end  120  of a second branch line  122 , also referred to as a second attenuating conduit. 
     The inlet conduit  104  illustrated in  FIG. 1  is a pipe having a length, an internal diameter, and an internal area. Similarly, the first branch line  116  and the second branch line  122  illustrated in  FIG. 1  are pipes and each has a length, an internal diameter, and an internal area. Other conduits discussed herein may have various shapes (e.g., round or rectangular), but those conduits generally also have a length and an internal area. The dimensions (e.g., length and area) of those conduits (e.g.,  104 ,  116 , and  122 ) furthermore affect various aspects of system operation as discussed herein. 
     It should be noted that the term “junction” as used herein includes any connecting device to which three or more conduits may be coupled, including, for example, a wye-, a tee- or an x-shaped junction, or a junction formed on or with a conduit. In an embodiment, the inlet junction, outlet junction, first branch line, and second branch line are formed as a single entity. In another embodiment, the inlet junction, outlet junction, first branch line, and second branch line are formed of more than one component wherein at least one junction is formed with at least one branch line. 
     In certain embodiments, the branch lines and attenuating conduits  116  and  122  are formed straight, angled, curved, or otherwise to meet the desires or constraints of an application, such as to minimize the size of the pulsation attenuation device  100 . 
     An outlet junction  124  includes a first inlet  126  coupled to a second end  118  of the first attenuating conduit  116  and a second inlet  134  coupled to a second end  128  of the second attenuating conduit  122 . The outlet junction  124  also has an outlet  130 , which may be coupled to an outlet conduit  132  as illustrated in the embodiment shown in  FIG. 1 . 
     The pulsation attenuation device  100  may carry a pressurized fluid, such as, for example, natural gas. The inlet conduit  104  may be arranged in fluid communication with a pump, such as for example the pump  450  illustrated in  FIG. 4 , pump  806  illustrated in  FIG. 8 , or pump  906  illustrated in  FIG. 9 , applying pressure to the fluid. The outlet conduit  132  may be in fluid communication with a system (not shown) to which the pressurized fluid is carried. Fluid communication with either the pump (e.g.,  450 ,  806 ,  906 ) or the system may, for example, be accomplished by direct coupling or through additional conduits. The tuned loop  102  may attenuate pressure fluctuations, variations, or waves in a primary pressure wavelength propagated in the fluid and odd harmonics of that primary pressure wavelength. 
     The term “pressure wave” as used herein describes a periodic, repeating variation or fluctuation in pressure. The term “pulsation” as used herein refers to the difference between a highest pressure point or portion of the pressure wave and the lowest pressure point of portion in a periodic pressure wave. The term “peak pressure” generally refers to the higher pressure portion of the periodic pressure wave, but may also refer to the lower pressure portion of the periodic pressure wave. The pressure wave may repeat for any length of time. In a reciprocating compressor example, the pressure wave will generally repeat periodically at a frequency that is constant while the reciprocating compressor operates at a constant speed. When the speed of the reciprocating compressor changes, the frequency of the periodic pressure wave generally changes to a different frequency. 
     Regarding conduit sizes, the inlet conduit  104  and the outlet conduit  132  may have approximately the same cross-sectional area. The first attenuating conduit  116  may have approximately half the cross-sectional area of the inlet conduit  104  and the outlet conduit  132 , and the second attenuating conduit  122  may have approximately half the cross-sectional area of the inlet conduit  104  and the outlet conduit  132 . For example, where a fourteen inch, schedule  80 , round, steel inlet conduit  104  and a fourteen inch, schedule  80 , round, steel outlet conduit  132  having cross-sectional areas of 122.72 square inches are used, the first and second attenuating conduits  116  and  122  may be ten inch, schedule  80 , round, steel conduits having cross-sectional areas of 71.84 square inches each. 
     Dividing fluid flow into different length conduits of appropriate lengths and areas, and then recombining those flows may reduce or cancel certain pressure waves emanating from a pump (such as pump  450 ,  806 , or  906 ) thereby smoothing the pressure of the fluid flow leaving the pulsation attenuation device  100 . For example, where one or more properly designed tuned loops  102 ,  802 ,  910 , and  912  are located downstream of the discharge of a pump, such as pump  806  shown in  FIG. 8  or pump  906  shown in  FIG. 9 , certain pressure waves in the fluid flowing downstream of the tuned loop  102 ,  802 ,  910 , and  912  should be attenuated. 
     Locating a tuned loop  102  or an inlet junction  106  of a tuned loop  102  at an optimum location with respect to a pump (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ) can partially reflect waves or pulsations so as to increase flow or increase pump (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ) efficiency. For example, where a properly designed tuned loop  102  is located at an appropriate location downstream of a pump (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ) waves partially reflected upstream may have a phase relationship with cylinder cycles (not shown in  FIGS. 8 and 9 ) of the pump (e.g.,  806  and  906 ) reducing pressure at the pump (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ) cylinder outlets discharge (e.g., near the pump outlet  808  and  908  as shown in  FIGS. 8 and 9 ). That phase relationship may determine, at least in part, the flow capacity and efficiency and can be varied by, for example, varying the lengths of the first branch  116  and second branch  122  of the tuned loop  102 . 
     Thus, while previous fluid pumping systems dissipated a significant amount of energy by various apparatuses and methods including use of bottles and by muffling fluid flow, embodiments of pressure wave and pulsation attenuation cancel or reduce undesirable pressure waves and pulses, thereby dissipating less energy than muffling. Furthermore, embodiments of pressure wave and pulsation attenuation improve pump (e.g.,  450 ,  806 , and  906 ) efficiency or system flow capacity by addressing reflected waves at the cylinder outlets (e.g.  441 ,  442 ,  443 , and  444  for pump  450 , near the outlets  808  and  908  for pumps  806  and  906 ). Embodiments of pressure wave and pulsation attenuation may improve pressure conditions at a pump inlet (e.g.,  804  and  904  as shown in  FIGS. 8 and 9 ) as well. 
     The pulsation attenuation devices, networks, and methods described herein are based in part on the following principles: 
     1) Repeating pulses with frequency F and period P are made up of the sum of a series of sine waves with frequencies F, 2*F, 3*F, . . . periods P/1, P/2, P/3, . . . and amplitudes A1, A2, A3, . . . . These sine waves may be referred to as the primary frequency, F, the first harmonic frequency, 2*F, second harmonic frequency, 3*F, and so on. This infinite series of sine waves may be referred to as a Fourier series. 
     2) The sum of two sine waves of equal amplitude but 180 degrees out of phase is zero (i.e. the waves cancel each other [sin(X+180 deg)=−sin(X)]). 
     3) A pressure wave propagating down a pipe can be divided into two roughly equal parts with a Y branch. 
     4) If the two divided pressure waves travel different distances and are recombined at a later point, the different distances will time shift and may phase shift, the two pressure wave parts. 
     5) The time/phase shift caused by such a separation and recombination will cancel frequency components that have periods of 2, 6, 10, 14, . . . times the time shift if they are present in the repeating pressure wave. 
     6) The delay loop created by dividing pressure waves, causing the pressure waves to travel different distances, and recombining the pressure waves should also attenuate, that is partially cancel, frequencies components of the pulse in between the canceled frequencies except for the frequencies that are half way between two consecutive canceled frequencies. 
     7) The difference in length of two paths of different distances can be “tuned” to one or more frequencies present in a pressure wave to dramatically reduce the pressure waves in a conduit or duct. 
     8) If the lengths of the two paths are tuned to the speed at which a pump is running, the pressure waves will generally be substantially reduced without a significant pressure loss. 
       FIG. 2  illustrates a schematic diagram depicting a six cylinder reciprocating compressor  200  type pump. The reciprocating compressor  200  includes a motor  202  that turns a crankshaft  204 . The reciprocating compressor  200  may be of any desired type, including an electrically powered or natural gas powered compressor  200 . 
     The crankshaft  204  illustrated in  FIG. 2  is coupled to a first connecting rod  210 , a second connecting rod  212 , a third connecting rod  214 , a fourth connecting rod  216 , a fifth connecting rod  218 , and a sixth connecting rod  220 . In various embodiments, the crankshaft  204  may be coupled to any number of connecting rods or other piston operating apparatuses. 
     The first connecting rod  210  is coupled to a first piston  230  in a first cylinder  250 . The second connecting rod  212  is coupled to a second piston  232  in a second cylinder  252 . The third connecting rod  214  is coupled to a third piston  234  in a third cylinder  254 . The fourth connecting rod  216  is coupled to a fourth piston  236  in a fourth cylinder  256 . The fifth connecting rod  218  is coupled to a fifth piston  238  in a fifth cylinder  258 . The sixth connecting rod  220  is coupled to a sixth piston  240  in a sixth cylinder  260 . 
     For simplicity,  FIG. 2  shows a single simplified disc-like crank throw  222 ,  224 , and  226  for each pair of opposed cylinders  250  and  256 ,  252  and  258 , and  254  and  260 . Alternatively, the crank shaft  204  may have an individual crank throw for each cylinder  250 ,  256 ,  252 ,  258 ,  254 , and  260  or any other crankshaft  204  configuration desired. 
     The frequency of the reciprocating compressor  200  is the frequency at which the reciprocating compressor  200  applies its propelling force. For example,  FIG. 2  illustrates a double acting reciprocating compressor  200  with double acting cylinders  250 ,  252 ,  254 ,  256 ,  258 , and  260 . The pistons  230 ,  232 ,  234 ,  236 ,  238 , and  240  of those cylinders  250 ,  252 ,  254 ,  256 ,  258 , and  260  propel fluid with each motion in both directions in a cylinder  250 ,  252 ,  254 ,  256 ,  258 , and  260 . Thus, the frequency of the pressure waves or pulsations for each of the cylinders  250 ,  252 ,  254 ,  256 ,  258 , and  260  will be twice the frequency of the rotating speed of the compressor (one pulsation or high pressure peak for each motion of the cylinders  250 ,  252 ,  254 ,  256 ,  258 , and  260  during each cycle of the motor  202 ). 
     A wavelength, for purposes of an embodiment, is the period of the pressure wave times the acoustic velocity of the fluid in which the pressure wave is propagating. Thus, in the embodiment of  FIG. 2 , wherein fluid is being pumped by the reciprocating compressor  200 , the primary wavelength of a pressure wave for one cylinder  250 ,  252 ,  254 ,  256 ,  258 , and  260  is the period from one fluid propelling motion of the cylinder  250 ,  252 ,  254 ,  256 ,  258 , and  260  to the next fluid propelling motion of the cylinder  250 ,  252 ,  254 ,  256 ,  258 , and  260  multiplied by the acoustic velocity of the fluid. 
     Pumps (e.g.,  200 ,  450 ,  806 , and  906 ) furthermore frequently operate at various speeds. The ratio of the fastest speed to the slowest speed of operation in pumping system embodiments may be a narrow, but significant range, such as a  25 % turndown rate. Moreover, in a natural gas pumping station, the pump (e.g.,  200 ,  450 ,  806 , and  906 ) speed may vary to meet a varying demand on the gas pumping system. A primary wavelength may, therefore, be established for the pump (e.g.,  200 ,  450 ,  806 , and  906 ) at a selected speed. The primary wavelength, however, will vary when the speed of the pump (e.g.,  200 ,  450 ,  806 , and  906 ) is varied. Accordingly, embodiments of the present pressure wave attenuation apparatuses, systems, networks, and methods operate to minimize pressure waves created by the pump (e.g.,  200 ,  450 ,  806 , and  906 ) operating over a range of speeds. 
     Different speed and load conditions under which the pump (e.g.,  200 ,  450 ,  806 , and  906 ) operates may create different repeating pressure waves and different Fourier series. Embodiments of pulsation attenuation use one or more tuned loops or other systems, apparatuses, or methods described herein to effectively attenuate the critical frequencies present in the Fourier series that characterize the speed and load range of the pump (e.g.,  200 ,  450 ,  806 , and  906 ). 
     It should be recognized that, in embodiments, full cancellation may occur for sinusoidal pressure waves when the fluid stream carrying those sinusoidal pressure waves is divided into equal parts and recombined at 180 degrees out of phase. For sinusoidal pressure waves that are recombined at a relative phase shift of 360 degrees, effectively no cancellation may occur and for sinusoidal pressure waves that are recombined at other degrees out of phase, partial cancellation of those sinusoidal pressure waves may occur. A tuned loop  102 , also referred to as a delay loop herein, and other flow combining systems, apparatuses, and methods described herein, may thus cancel a series of pressure wave frequency components propagating in a fluid (i.e., a primary frequency and its odd harmonics) and provide partial cancellation or attenuation of one or more ranges of pressure wave frequencies, while leaving certain pressure wave frequencies, such as even frequencies divisible by four, not effectively attenuated. 
     In certain embodiments where pressure wave attenuation is desired in a pumped fluid, it may be less necessary, or simply unnecessary, to attenuate higher harmonics. Higher harmonics tend to be lower amplitude in certain fluid flow applications and so those higher harmonics may not be as important to attenuate, or may create pressure waves that are not necessary to attenuate. 
     Referring again to  FIG. 1 , in pressure wave attenuation, a first tuned loop  102  or other flow combining system, apparatus, or method described herein may be selected to recombine waves at 180 degrees out of phase of a primary frequency in the range of operation of the pump (e.g.,  200 ,  450 ,  806 , and  906 ) to cancel or attenuate pressure waves at that frequency. It should be recognized that certain harmonics of that frequency will also be attenuated by that tuned loop  102  or the other flow combining systems, apparatuses, and methods described herein. 
     A second tuned loop  102  may be selected to recombine waves at 180 degrees out of phase of a different primary frequency in the range of operation of the pump (e.g.,  200 ,  450 ,  806 , and  906 ) to attenuate that frequency and certain harmonics of that frequency. 
     Because a selected number of tuned loops  102  tuned to primary frequencies in the pump (e.g.,  200 ,  450 ,  806 , and  906 ) operating range will cancel frequencies for which they are tuned and certain harmonics of those frequencies and will also attenuate frequencies near the tuned frequencies, a small number of tuned loops  102 , in many cases from two to four tuned loops  102 , may be sufficient to attenuate a range of primary frequencies that may be created by a pump that operates at varying speeds to a desired level. 
     Frequently in fluid pumping applications, the speed range of a pump (e.g.,  200 ,  450 ,  806 , and  906 ) may be significant enough to justify the use of two or three tuned loops  102  tuned to primary frequencies in the pump (e.g.,  200 ,  450 ,  806 , and  906 ) operating range, but not so large as to merit more than two or three tuned loops  102 . A defined range of primary frequencies within which attenuation is desired may, therefore, be determined and a desired level of pressure wave attenuation for that range may be designed using a finite number of tuned loops  102 . 
     Additional tuned loops  102  may be employed to cancel problematic or undesirable non-primary frequencies. Accordingly, networks of two, three, or four tuned loops  102  or networks that combine one or more tuned loops  102  with other flow combining systems, apparatuses, and methods described herein are believed to be effective to minimize a wide range of undesirable frequencies in a fluid pumping application. Furthermore, other pressure wave attenuation devices, such as bottles, and methods, such as those previously used or those developed in the future, may be used in combination with one or more tuned loops  102  to attenuate pressure waves. 
     Referring again to the embodiment illustrated in  FIG. 2 , the cycles of the three cylinders  250 ,  252 , and  254  on the first side  246  of the reciprocating compressor  200  may be offset by 60 degrees (noting this figure depicts a double acting compressor configuration) one from another. The three cylinders  256 ,  258 , and  260  on the second side  248  of the reciprocating compressor  200  may also be offset by 60 degrees (noting this figure depicts a double acting compressor configuration) one from another. In addition, the cylinders on the second side  248  may be offset from the cylinders on the first side  246  by 30 degrees such that pressure peaks or pulsations propagating from the second side  248  cylinders  256 ,  258 , and  260  occur at or near a midpoint in time between pressure peaks or pulsations propagating from the first side  246  cylinders  250 ,  252 , and  254 . In that way, there can be twelve pressure peaks or pulsations leaving the reciprocating compressor  200  at equally spaced time intervals per rotation of the shaft  204 . For example, the first cylinder  250  may reach peak discharge pressure on a first of its two strokes per cycle at 0 degrees of shaft  204  rotation, the fourth cylinder  256  may reach peak discharge pressure on a first of its two strokes per cycle at 30 degrees of shaft  204  rotation, the second cylinder  252  may reach peak discharge pressure on a first of its two strokes per cycle at 60 degrees of shaft  204  rotation, the fifth cylinder  258  may reach peak discharge pressure on a first of its two strokes per cycle at 90 degrees of shaft  204  rotation, the third cylinder  254  may reach peak discharge pressure on a first of its two strokes per cycle at 120 degrees of shaft  204  rotation, and the sixth cylinder  260  may reach peak discharge pressure on a first of its two strokes per cycle at 150 degrees of shaft  204  rotation. The first cylinder  250  may reach peak discharge pressure on a second of its two strokes per cycle at 180 degrees of shaft  204  rotation, the fourth cylinder  256  may reach peak discharge pressure on a second of its two strokes per cycle at 210 degrees of shaft  204  rotation, the second cylinder  252  may reach peak discharge pressure on a second of its two strokes per cycle at 240 degrees of shaft  204  rotation, the fifth cylinder  258  may reach peak discharge pressure on a second of its two strokes per cycle at 270 degrees of shaft  204  rotation, the third cylinder  254  may reach peak discharge pressure on a second of its two strokes per cycle at 300 degrees of shaft  204  rotation, and the sixth cylinder  260  may reach peak discharge pressure on a second of its two strokes per cycle at 330 degrees of shaft  204  rotation. 
       FIG. 3  illustrates a schematic diagram depicting another embodiment of a six cylinder reciprocating compressor  300  type pump having an offset cylinder operation. The compressor  300  includes a motor  302  that turns a crankshaft  304 . The compressor  300  may be of any desired type, including an electrically powered or natural gas powered compressor  300 . 
     The crankshaft  304  illustrated in  FIG. 3  is coupled to a first connecting rod  310 , a second connecting rod  312 , a third connecting rod  314 , a fourth connecting rod  316 , a fifth connecting rod  318 , and a sixth connecting rod  320 . In various embodiments, the crankshaft  304  may be coupled to any number of connecting rods or other piston operating apparatuses. 
     The first connecting rod  310  is coupled to a first piston  330  in a first cylinder  350 . The second connecting rod  312  is coupled to a second piston  332  in a second cylinder  352 . The third connecting rod  314  is coupled to a third piston  334  in a third cylinder  354 . The fourth connecting rod  316  is coupled to a fourth piston  336  in a fourth cylinder  356 . The fifth connecting rod  318  is coupled to a fifth piston  338  in a fifth cylinder  358 . The sixth connecting rod  320  is coupled to a sixth piston  340  in a sixth cylinder  360 . 
     For simplicity,  FIG. 3  shows a single simplified disc-like crank throw  322 ,  324 , and  326  for each pair of opposed cylinders  350  and  356 ,  352  and  358 ,  354  and  360 . Alternatively, the crank shaft  304  may have an individual crank throw for each cylinder  350 ,  356 ,  352 ,  358 ,  354 , and  360  or any other crankshaft  304  configuration desired. 
     The reciprocating compressor  300  embodiment illustrated in  FIG. 3  may provide better balanced inertia than the reciprocating compressor  200  illustrated in  FIG. 3  and other arrangements may be used that further improve inertial balance. Any arrangement of cylinders may be used to meet any number of constraints or consideration. Moreover, the reciprocating compressors  200  and  300  illustrate only certain components of a reciprocating compressor and additional components may be used as desired. For example, counterweights may be used to balance the rotational momentum of a reciprocating compressor (e.g.,  200  or  300 ). 
     The cycles of the three cylinders  350 ,  352 , and  354  on the first side  346  of the reciprocating compressor  300  may be offset by 120 degrees (noting this figure depicts a double acting compressor configuration) one from another. The three cylinders  356 ,  358 , and  360  on the second side  348  of the pump  300  may also be offset by 120 degrees (noting this figure depicts a double acting compressor configuration) one from another. In addition, the cylinders on the second side  348  may be offset from the cylinders on the first side  346  by 30 degrees such that pressure peaks or pulsations propagating from the second side  348  cylinders  356 ,  358 , and  360  occur at or near a midpoint in time between pressure peaks or pulsations propagating from the first side  346  cylinders  350 ,  352 , and  354 . In that way, there can be twelve pressure peaks or pulsations leaving the reciprocating compressor  300  at equally spaced time intervals per rotation of the shaft  304 . For example, the fourth cylinder  356  may reach a peak discharge pressure on its stroke away from the crankshaft  304  at 0 degrees of shaft  304  rotation, the first cylinder  358  may reach a peak discharge pressure on its stroke away from the crankshaft  304  at 30 degrees of shaft  304  rotation, the fifth cylinder  358  may reach peak discharge pressure on its stroke toward the crankshaft  304  at 60 degrees of shaft  304  rotation, the second cylinder  352  may reach peak discharge pressure on its stroke toward the crankshaft  304  at 90 degrees of shaft  304  rotation, the sixth cylinder  360  may reach peak discharge pressure on its stroke away from the crankshaft  304  at 120 degrees of shaft  304  rotation, and the third cylinder  354  may reach peak discharge pressure on its stroke away from the crankshaft  304  at 150 degrees of shaft  304  rotation. The fourth cylinder  350  may reach peak discharge pressure on its stroke toward the crankshaft at 180 degrees of shaft  304  rotation, the first cylinder  350  may reach peak discharge pressure on its stroke toward the crankshaft  304  at 210 degrees of shaft  304  rotation, the fifth cylinder  358  may reach peak discharge pressure on its stroke away from the crankshaft  304  at 240 degrees of shaft  304  rotation, the second cylinder  252  may reach peak discharge pressure on its stroke away from at 270 degrees of shaft  304  rotation, the sixth cylinder  360  may reach peak discharge pressure on its stroke toward at 300 degrees of shaft  304  rotation, and the third cylinder  354  may reach peak discharge pressure on its stroke toward the crankshaft  304  at 330 degrees of shaft  304  rotation. 
       FIG. 4  illustrates an embodiment of an outlet or discharge fluid piping system  440 . The piping system includes a reciprocating pump  450 , a flow combination system  494 , and a tuned loop  480 . The reciprocating pump  450  includes four cylinders  452 ,  454 ,  456 , and  458 , having outlets  441 ,  442 ,  443 , and  444  respectively. A first header  460  carries fluid flowing from the first outlet  441  to a first side junction  474  and a second header  462  carries fluid flowing from the second outlet  442  to the first side junction  474 . A third header  464  carries fluid flowing from the third outlet  443  to a second side junction  476  and a fourth header  466  carries fluid flowing from the fourth outlet  444  to the second side junction  476 . The first header  460  and second header  462  are attached to a first branch line  470  at a first side junction  474  and the third header  464  and fourth header  466  are attached to a second branch line  472  at a second side junction  476 . The first inlet branch line  470  and second inlet branch line  472  are attached to an inlet of the tuned loop  480  at a branch junction  478 . 
     A connecting conduit  490  leads from the branch junction  478  to an inlet of a tuned loop inlet junction  486 . The tuned loop inlet junction  486  also has two outlets, the first outlet being attached to a first end a first attenuating conduit  482  of the tuned loop  480  and the second outlet being attached to a first end of a second attenuating conduit  484  of the tuned loop  480 . A second end of the first attenuating conduit  482  is attached to a first inlet of a tuned loop outlet junction  488  and a second end of the second attenuating conduit  482  is attached to a second inlet of the tuned loop outlet junction  488 . An outlet of the tuned loop outlet junction is attached to a discharge conduit  492 . 
     In an embodiment of the reciprocating pump system  440  the reciprocating pump  450  includes four double-acting cylinders  452 ,  454 ,  456 , and  458 . Each double-acting cylinder  452 ,  454 ,  456 , and  458  causes fluid to flow twice during each rotation of a shaft  496  turned by a motor  498  and driving the reciprocating pump  450 , thus creating pressure variations in the form of waves in the fluid propagating through the flow combination system  494  and the tuned loop  480  at twice the frequency of the shaft  496  rotation. In one embodiment, pairs of those cylinders  452  and  456 ,  454  and  458  create flow simultaneously (one on the upstroke and the other on the down-stroke) and the pairs of cylinders  452  and  454 ,  456  and  458  operate at 90.degree. out of phase. In such an arrangement, the outlets  441  and  442  of two cylinders  452  and  454  operating at 90.degree. of shaft  496  rotation out of phase (and creating fluid pressure waves which, at twice the shaft  496  rotation frequency, are 180.degree. out of phase) are coupled using short, equal length header pipes  460  and  462  to quickly interleave the primary wavelength pressure waves existing in the fluid flow created by those cylinders  452  and  454 . The outlets  443  and  444  of the other two cylinders  456  and  458  operating at 90.degree. out of phase are similarly coupled using short, equal length header pipes  464  and  466  to quickly interleave the primary wavelength pressure wave existing in the fluid flow created by those cylinders  456  and  458 . 
     In the embodiment illustrated in  FIG. 4 , cylinders,  452  and  454 , contain double acting pistons which produce pressure waves that have two peaks 180.degree. apart for every complete rotation of the crankshaft. The troughs on the pump crankshaft for cylinders  452  and  454  are offset by 90 crank angle degrees. The first header  460 , carrying the fluid flow and pressure wave from the first cylinder  452 , and the second header  462 , carrying the fluid flow pressure wave from the second cylinder  454 , are of equal length and join at a first side junction  474 . In that way, the flows and pressure waves of the first cylinder  452  and second cylinder  454  are combined at 90.degree. out of phase, thus interleaving, and significantly attenuating, pressure waves propagating from the first and second cylinders  452  and  454  and through the first and second headers  460  and  462  as the flow and pressure waves proceed down stream of junction  474  in conduit  470 . 
     Pressure waves emanating from the third cylinder  456  and the fourth cylinder  458  on a second side  448  of the pump  450  are also 180.degree. out of phase. The third header  464 , carrying fluid flow from the third cylinder  456 , and the fourth header  466 , carrying fluid flow from the fourth cylinder  458 , are of equal length and the flows through those headers  464  and  466  join at a second side junction  476 . In that way, the flows of the third cylinder  456  and fourth cylinder  458  are combined at 180.degree. out of phase, thus interleaving, and thereby cancelling or at least significantly attenuating, pressure waves flowing from the third and fourth cylinders  456  and  458  and through the third and fourth headers  464  and  466 . 
     In the embodiment illustrated in  FIG. 4 , pistons in the first cylinder  452  and the third cylinder  456  operate in phase and pistons in the second cylinder  454  and the fourth cylinder  458  operate in phase such that pressures at the outlets  441  and  443  of the first and third cylinders  452  and  456  follow similar cycles and pressures at the discharges  442  and  444  of the second and fourth cylinders  454  and  458  follow similar cycles. 
     In another embodiment, the cycles of the first cylinder  452  and the third cylinder  456  are offset 45 degrees of shaft  496  rotation from one another and the cycles of the second cylinder  454  and the fourth cylinder  458  are offset 45 degrees of shaft  496  rotation from one another. In that way, pressure peaks from the first cylinder  452  to the second cylinder  454  are offset by 90 degrees of shaft rotation, which corresponds to a 180 degree wave phase offset, such that peak high pressure from the first cylinder  452  coincides with low pressure from the second cylinder  454 . Pressure peaks from the second cylinder  454  to the third cylinder  456  are also offset by 90 degrees of shaft rotation and 180 degrees of wave phase such that peak high pressure from the second cylinder  454  coincides with low pressure from the third cylinder  456 . Pressure peaks from the third cylinder  456  to the fourth cylinder  458  are also offset by 90 degrees of shaft rotation and 180 degrees of wave phase such that peak high pressure from the third cylinder  456  coincides with low pressure from the fourth cylinder  458 . Pressure peaks from the fourth cylinder  458  to the first cylinder  452  are also offset by 90 degrees of shaft rotation and 180 degrees of wave phase such that peak high pressure from the fourth cylinder  458  coincides with low pressure from the first cylinder  452 . 
     In an embodiment headers leading from the first cylinder  452 , second cylinder  454 , third cylinder  456 , and fourth cylinder  458  may be combined directly, for example at the first side junction  474  by equal length headers  460 ,  462 ,  464 , and  466  in certain embodiments, or in another way designed to attenuate pressure waves in the fluid flowing through those headers  460 ,  462 ,  464 , and  466  and the second side junction  476  may not be used. 
     A first branch line  470  extends from the first side junction  474  where the first header  460  from the first cylinder  452  is coupled to the second header  462  from the second cylinder  454 . A second branch line  472  extends from the second side junction  476  where the third header  464  from the third cylinder  456  is coupled to the fourth header  466  from the fourth cylinder  458 . Those first and second branch lines  472  and  474  are further coupled at a branch line junction  478 . 
     The lengths of the first branch line  470  and second branch line  472  are arranged such that the fluid flow in the first branch line  470  is coupled to the fluid flow from the second branch line  472  at the branch line junction  478  at 45.degree. out of phase for a desired frequency. 
     Thus, the lengths of branch line  470  and branch line  472  in that embodiment are different. Moreover, the difference in the lengths of branch lines  470  and  472  is arranged so that a pulsation frequency experienced in the fluid flowing through the first branch line  470  and/or the second branch line  472  is interleaved and attenuated at the branch line junction  474 . 
     Another consideration in determining the length of headers  460 ,  462 ,  464 , and  466  and branch lines  470  and  472  is the effect of pressure waves traveling upstream to one or more cylinders  452 ,  454 ,  456 , and  458 . Wave peaks may, for example, be created when a piston is moving toward or when a piston reaches either end of a cylinder (for example cylinder  452 ) in a double-acting cylinder. Those wave peaks may affect the operation of one or more other cylinders (for example, cylinders  454 ,  456 , or  458 ) as they propagate through the piping system  440  and reach those cylinders (for example, cylinders  454 ,  456 , or  458 ). It should be recognized that each cylinder  452 ,  454 ,  456 , and  458  will create pressure waves that may include pulses or wave peaks when they operate and those pressure waves will affect the other operating cylinders  452 ,  454 ,  456 , and  458 . Those pressure waves, furthermore, move along the piping system  440  at a regular frequency when the cylinders  452 ,  454 ,  456 , and  458  operate at a constant speed. Thus, the time between wave peaks can be determined for a cylinder  452 ,  454 ,  456 , and  458  operating at a constant speed, the time it takes for pressure waves to move along a length of pipe may be determined, and the times and regularity at which pressure peaks will arrive at a cylinder  452 ,  454 ,  456 , and  458  can be determined. 
     Accordingly, header  460 ,  462 ,  464 , and  466  and/or branch line  470  and  472  length can affect the efficiency at which the cylinders  452 ,  454 ,  456 , and  458  operate and header  460 ,  462 ,  464 , and  466  and/or branch line  470  and  472  length can be selected to optimize efficiency or other operating conditions existing at cylinders  452 ,  454 ,  456 , and  458 . 
     Pressure waves created by operation of the cylinders  452 ,  454 ,  456 , and  458  propagate upstream and downstream in the headers  460 ,  462 ,  464 , and  466  and branch lines  470  and  472  illustrated in  FIG. 4 . Accordingly, pressure waves from the first cylinder  452  partially impinge or come into contact with other cylinders  454 ,  456 , and  458  in the piping system  440  and can affect the operation of those cylinders  454 ,  456 , and  458 . Likewise, pulse waves emanating from the other cylinders  454 ,  456 , and  458  will partially impinge or come into contact with other cylinders  452 ,  454 ,  456 , and  458  connected to the piping system  440  and can affect the operation of those cylinders  452 ,  454 ,  456 , and  458 . 
     For example, pressure waves created by the motion of a piston (e.g.,  230  in  FIG. 2 ) in the first cylinder  452  may propagate along the first header  460  and at least partially upstream along the second header  462  to the second cylinder  454 . Those pressure waves may also propagate at least partially through the first side junction  474 , along first branch line  470 , through the branch line junction  478 , upstream along the second branch line  472 , through the second side junction  476  and along both the third header  464  and the fourth header  466  to contact or impinge upon the third cylinder  456  and the fourth cylinder  458 . 
     Thus, in an embodiment, first and second headers  460  and  462  can have lengths selected to optimize the effect on the second cylinder  454  from pulses or pressure waves propagating from the first cylinder  452  and to optimize the effect on the first cylinder  452  from pulses or pressure waves propagating from the second cylinder  454 . Similarly, the third and fourth headers  464  and  466  can have lengths selected to optimize the effect on the fourth cylinder  458  from pulses or pressure waves propagating from the third cylinder  456  and to optimize the effect on the third cylinder  456  from pulses or pressure waves propagating from the fourth cylinder  458 . 
     The lengths of the first and second headers  460  and  462  can be maintained equal in an embodiment, while the total length of the first and second headers  460  and  462  combined is determined to optimize the effect of the pressure waves propagating from the first cylinder  452  on the second cylinder  454  and to optimize the effect of the pressure waves propagating from the second cylinder  454  on the first cylinder  452 . 
     Similarly, the lengths of the third and fourth headers  464  and  466  can be maintained equal in that embodiment, while the total length of the third and fourth headers  464  and  466  combined is determined to optimize or reduce the effect of the pressure waves propagating from the third cylinder  456  on the fourth cylinder  458  and to optimize the effect of the pressure waves propagating from the fourth cylinder  458  on the third cylinder  456 . 
     Thus, the length of each of the first and second branch lines  470  and  472  may be determined to attenuate pressure waves or pulsations propagating through those lines  470  and  472  by combining the flow passing through those lines  470  and  472  at branch line junction  478  when the flows passing through those lines will cancel or attenuate undesired pressure waves or pulsations. Alternately or in addition, the lengths of branch lines  470  and  472  may be arranged to optimize the effect of pulse waves propagating from the first side junction  474  at least partially to the third and fourth cylinders  456  and  458  and to optimize the effect of pulse waves propagating from the second side junction  476  at least partially to the first and second cylinders  452  and  454 . 
     In a system where first, second, third, and fourth cylinders  452 ,  454 ,  456 , and  458  are driven by a common shaft  496  and motor  498 , as is depicted in  FIG. 4 , and where opposing cylinders, such as the first cylinder  452  and third cylinder  456  (and the second cylinder  454  and fourth cylinder  458 ) are operating in phase (the pistons in the in phase cylinders  452  and  456 ,  454  and  458  reach one of the two ends of their strokes simultaneously or nearly simultaneously), the total branch line length (length of the first branch line  470  plus length of the second branch line  472  and, possibly, plus a length associated with the branch line junction  478 ) may be selected to optimize the effect of pulse waves on both the cylinders on the first side  446  and second side  448  of the pump  450 . 
     For example, the combined length of the first header  460 , the first branch line  470 , the second branch line  472  and the third header  464  (plus junctions  474 ,  478 , and  476  if applicable) may be selected such that pulsations or undesirable portions of a pressure wave emanating or propagating from the first cylinder  452  arrive at the third cylinder  456  at a time in the third cylinder  456  cycle when those pulsations or undesirable portions of a pressure wave have a less detrimental effect on the operation of the third cylinder  456 . The combined length of the first header  460 , the first branch line  470 , the second branch line  472  and the fourth header  466  may also be selected to minimize or reduce any detrimental effect of the operation of the first cylinder  452  on the fourth cylinder  458 . 
     Because the cycles of the third and fourth cylinders  456  and  458  may be offset one from the other and the lengths of the third and fourth headers  464  and  466  may be equal or otherwise arranged such that it is not practical or possible to have pulsations or undesirable portions of a pressure wave arrive at both the third and fourth cylinders  456  and  458  at an optimal time, a compromise in combined line (e.g.,  460 ,  470 ,  472 ,  464 , or  460 ,  470 ,  472 ,  466 , or  462 ,  470 ,  472 ,  464 , or  462 ,  470 ,  472 ,  466 ) length may be made such that combined operation of the third and fourth cylinders  456  and  458  is improved or optimized, rather than optimization of one or the other cylinder  456  and  458 . Thus, for example, where the pressure waves of the third cylinder  456  are offset from the pressure waves of the fourth cylinder  458  by 90 degrees of shaft rotation and the third header  464  and the fourth header  466  are of equal length, the combined lengths of the lines  460 ,  470 ,  472 ,  464 , and  460 ,  470 ,  472 ,  466  leading from the first cylinder  452  to the third and fourth cylinders  456  and  458  may be arranged such that pulsations or undesirable portions of a pressure wave emanating from the first cylinder  452  arrive at the third and fourth cylinders  456  and  458  at mid-cycle for both the third and fourth cylinders  456  and  458  or another desirable time in the cycles of the third and fourth cylinders  456  and  458 . 
     Because the cycles of the first and second cylinders  452  and  454  may be offset one from the other and the lengths of the first and second headers  460  and  462  may be equal or otherwise arranged such that it is not practical or possible to have pulsations or undesirable portions of a pressure wave emanating or propagating from the first and second cylinders  452  and  454  arrive at the third or fourth cylinders  456  and  458  at an optimal time, a compromise in combined line  460 ,  470 ,  472 ,  464 , or  460 ,  470 ,  472 ,  466 , or  462 ,  470 ,  472 ,  464 , or  462 ,  470 ,  472 ,  466  length may be made such that combined operation of the cylinders  452 ,  454 ,  456  and  458  is improved or optimized, rather than optimization of any subset of those cylinders  452 ,  454 ,  456  and  458 . Thus, for example, where the pressure waves of the first cylinder  452  are offset from the pressure waves of the second cylinder  454  by 90 degrees of shaft rotation the pressure waves of the third cylinder  456  are offset from the pressure waves of the fourth cylinder  458  by 90 degrees, the first header  460  and the second header  462  are of equal length and the third header  464  and the fourth header  466  are of equal length, the combined lengths of the lines leading from one cylinder (e.g.,  452 ,  454 ,  456 , or  458 ) to one or more other cylinders (e.g.,  452 ,  454 ,  456 , or  458 ) may be arranged such that pulsations or undesirable portions of a pressure waves emanating from each cylinder (e.g.,  452 ,  454 ,  456 , or  458 ) arrive at each other cylinder (e.g.,  452 ,  454 ,  456 , or  458 ) at a desirable time in the cycles of those other cylinders (e.g.,  452 ,  454 ,  456 , or  458 ). 
     In one embodiment of the outlet (discharge) piping system  440 , the length of the first and second headers  460  and  462  is selected such that a low pressure point of a wave created by a piston (e.g.,  230  in  FIG. 2 ) in the first cylinder  452  moves along the first header  460 , the first side junction  474 , and the second header  462  and arrives at the second cylinder  454  at a time when a piston in the second cylinder  454  is at or near an end of its stroke (i.e. either end for a double-acting piston) and thus near either end of the cylinder and thus not near the center of its stroke. Such an arrangement may increase gas flow capacity. In another embodiment, the lengths of the first and second headers  460  and  462  may be selected such that a low pressure point of a wave created by a piston (e.g.,  230  in  FIG. 2 ) in the first cylinder  452  moves along the first header  460 , the first side junction  474 , and the second header  462  and arrives at the second cylinder  454  at a time when a piston in the second cylinder  454  is at or near the middle of its stroke (in a double-acting piston). Such an arrangement may improve compressor efficiency. 
     Note that in an embodiment in which the piston is a single-acting piston in an outlet or discharge piping system  440 , the above regarding a double-acting cylinder may apply, except that for increased gas flow capacity, the low pressure point of the wave may arrive at the second cylinder  454  when the piston in the second cylinder  454  is at or near the end of its stroke, and thus the end of the second cylinder  454  where the piston is finishing or has just finished expelling gas from the second cylinder  454 . For increased efficiency, the above regarding a double-acting cylinder may apply, except that the low pressure point of the wave may arrive at the second cylinder  454  when the piston in the second cylinder  454  is at or near the middle of its stroke moving in a direction in which it is pushing gas out of the second cylinder  454 . 
     As used herein in relation to a piston stroke on the outlet or discharge side of a piping system, “at or near an end” or a similar term regarding a piston stroke refers to (for a double-acting piston) a position of the piston closer to either end of the cylinder than the middle of the cylinder, and refers to (for a single-acting piston) a position of the piston closer to the end of the cylinder where the piston is finishing or has just finished expelling gas. That term or a similar term thus encompasses both a single-acting and double-acting cylinder and piston unless otherwise specified. 
     As used herein in relation to a piston stroke on the outlet or discharge side of a piping system, “at or near the middle” or a similar term regarding a piston stroke refers to (for a double-acting piston) a position of the piston closer to the middle of the cylinder than either end of the cylinder, and refers to (for a single-acting piston) a position of the piston closer to the middle of the cylinder when the piston is moving in a direction in which it is pushing gas out of the cylinder. That term or a similar term thus encompasses both a single-acting and double-acting cylinder and piston unless otherwise specified. 
     It may be recognized that pressure waves and pulses may propagate along all the pipes  460 ,  462 ,  464 ,  466 ,  470 ,  472 ,  482 ,  484 ,  490 , and  492  in the system  440  and to all apparatuses connected to the piping system  440  including any cylinders of additional pumps (not shown) that are connected to the piping system  440 . The lengths of the headers  460 ,  462 ,  464 , and  466  and various pipes  470 ,  472 ,  482 ,  484 ,  490 , and  492  may, therefore, be selected such that pressure waves or pulses passing through the piping system  440  arrive at cylinders  452 ,  454 ,  456 , and  458  and any other cylinders present in the piping system  440  at times that are beneficial or at least minimally detrimental to operation of the cylinders  452 ,  454 ,  456 , and  458  and any other cylinders present in the piping system  440 . Such an arrangement may improve efficiency, fluid flow, power consumption, or other operational aspects of cylinders (such as cylinders  454 ,  456 , or  458 ) based on pulse waves propagating from another cylinder (such as cylinder  452 ). The lengths of the headers  460 ,  462 ,  464 , and  466  and various pipes  470 ,  472 ,  482 ,  484 ,  490 , and  492  may, therefore, be selected such that pressure waves and pulses passing through the piping system  440  arrive at any selected portion of the piping system  440  or anything connected to the piping system  440  at a desired time. 
     It should be recognized that headers  460 ,  462 ,  464 ,  466  and branch lines  470  and  472  may be devised in various lengths and sizes to combine fluid flow from multiple cylinders (including cylinders  452 ,  454 ,  456 , and  458 ) or multiple pumping devices (including pump  450 ) to cancel and attenuate undesirable frequencies created by those cylinders (including cylinders  452 ,  454 ,  456 , and  458 ) and pumps (including pump  450 ) having various arrangements. Thus, headers (including headers  460 ,  462 ,  464 ,  466 ) may have unequal lengths to combine flows that do not have frequencies of 180.degree. out of phase. Branch lines  470  and  472  may also have varied lengths and sizes to cancel and attenuate pressure waves or frequencies other than those that are 180.degree. out of phase. 
     For example, in the embodiment illustrated in  FIG. 4 , the first and second headers  460  and  462  may be the same length to combine the pressure waves propagating from the first and second cylinders  452  and  454  at 180 degrees out of phase. Similarly, the third and fourth headers  464  and  466  may be the same length to combine the pressure waves propagating from the third and fourth cylinders  456  and  458  at 180 degrees out of phase. While pulsations or pressure waves in a primary wavelength created by the first and second cylinders  452  and  454  and odd harmonics of that primary wavelength may be cancelled or attenuated by such a combination of the flows propagating from the first and second cylinders  452  and  454 , pulsations or pressure waves in other undesirable wavelengths may still exist in the combined flow leaving the first side junction  474 . Similarly, pulsations or pressure waves in a primary wavelength created by the third and fourth cylinders  456  and  458  and odd harmonics of that primary wavelength may be cancelled or attenuated by a similar combination of the flows propagating from the third and fourth cylinders  456  and  458  at 180 degrees out of phase. Nonetheless, pressure waves or pulsations in other undesirable wavelengths may still exist in the combined flow leaving second side junction  476 . The pulsations or pressure waves may, furthermore, exist in various undesirable wavelengths because, for example, the pump  450  may be a reciprocating compressor that operates at various speeds or with certain cylinders  452 ,  454 ,  456 , and  458  unloaded and configurations where flow or pressure waves is not smooth or similar but opposite on opposites sides of a pressure peak because, for example, of the operation of pistons (e.g.,  230 ,  232 ,  234 ,  236 ,  238 ,  240 ,  330 ,  332 ,  334 ,  336 ,  338 , and  340 ) working in conjunction with inlets and outlets at various pressures. Accordingly, the difference in the lengths of the first and second branch lines  470  and  472  may be selected to cancel or attenuate a primary wavelength remaining after the combination of the flows at the first side junction  474  and the second side junction  476 . In an embodiment, such as that depicted in  FIG. 4 , where the pump  450  may operate at various speeds or with certain cylinders  452 ,  454 ,  456 , and  458  unloaded, the wavelength selected to be cancelled or attenuated at branch line junction  478  may be selected to attenuate pressure waves or pulsations created at a mid-portion of the range of operation of the pump  450 . 
     Junctions  474 ,  476 ,  478 ,  486 , and  488 , terminations, restrictions, certain bends, changes in pipe cross-sectional area, atmospheric discharge points and other piping system  440  components or features may reflect pressure waves and pulses upstream, for example back to the pump  450 . Thus, the downstream waves, or waves propagating in the direction of fluid flow out of the pump  450 , may, at those components and features, be partially reflected or otherwise travel back, or upstream, toward the discharge side of the pump  450 . The downstream waves and reflected or otherwise formed upstream waves superimpose and may be measured together by a pressure transducer, while neither may be separately measurable by a pressure transducer. However, those waves may be otherwise tracked, such as by gas flow simulation software in one embodiment. That software may be, for example, the one dimensional gas flow simulation software developed by OPTIMUM Power Technology. A designer can use the gas flow simulation software to observe the effect of positioning the junctions and other piping components that may reflect pressure waves and thus determine the pipe lengths extending to those components that cause the upstream waves so as to affect the performance of the pump  450  and piping system  440 . Depending upon the positioning of the junctions and reflective components and the pipe lengths used to attach those reflective components to the system, system performance criteria, such as flow rate or efficiency, may be improved. 
     In one embodiment, for example, the fluid pumping system  440  may be made more efficient by locating junctions  474 ,  476 ,  478 ,  486 , and  488  at appropriate positions in relation to the pump  450  or other components of the piping system  440 . For example, the side junctions  474 ,  476  may be located at an appropriate distance from the pump  450  to reflect pressure waves back to the pump  450  outlet of one or more cylinders  452 ,  454 ,  456 , and  458  of the pump  450  such that those waves are at a low or lower pressure point at the cylinder outlets  441 ,  442 ,  443 , and  444  when the pistons of the cylinders  452 ,  454 ,  456 , and  458  are at a higher velocity or at or near the middle of the piston stroke. Such a phase arrangement may decrease the energy needed to cause the piston to move the same amount of fluid flow out of the pump, and thus increase pump and system efficiency. 
     Alternatively, in another embodiment, the fluid pumping system  440  may increase flow capacity by locating junctions  474 ,  476 ,  478 ,  486 , and  488  at appropriate positions in relation to the pump  450  or other components of the piping system  440 . For example, the side junctions  474 ,  476  may be located at an appropriate distance from the pump  450  to reflect pressure waves back to the pump  450  outlet of one or more cylinders  452 ,  454 ,  456 , and  458  of the pump  450  such that those waves are at a low or lower pressure point at the cylinder outlets  441 ,  442 ,  443 , and  444  when the pistons of the cylinders  452 ,  454 ,  456 , and  458  are at a lower velocity, for example the pistons in those cylinders  452 ,  454 ,  456 , and  458  may be at or near the ends of their strokes. Such a phase arrangement may increase flow rate. 
     In embodiments, the location of any combination of the junctions  474 ,  476 ,  478 ,  486 , and  488  can be adjusted to increase flow capacity or improve pump  450  efficiency. Note that, as described above, various components and features of the piping system  440  may each cause wave reflections. Those components and features may be thus be adjusted such that the total, superimposed reflected or otherwise upstream-moving wave is at a low or lower pressure point at the cylinder outlets  441 ,  442 ,  443 , and  444  when the cycles of the cylinders  452 ,  454 ,  456 , and  458  are at a higher velocity at or near the middle of the piston strokes (for efficiency) or a lower velocity at or near the ends of the piston strokes (for increased flow capacity) or at any desired point in the cycles of the cylinders  452 ,  454 ,  456 , and  458  or stroke of the pistons in the cylinders  452 ,  454 ,  456 , and  458 . 
     The time it takes for a reflected wave to reach a destination varies dependent upon the lengths of conduits extending between a reflective component and the destination and the acoustic velocity of the fluid. Thus, for example, the time required for a wave reflected from the first side junction  474  to the first cylinder outlet  452  outlet  441  will depend on the length of the first header  460  and the acoustic velocity of the fluid flowing through the first header  460  and carrying the wave. 
     In embodiments, gas flow simulation software, for example, may be used to specify the location of one or more other junctions (e.g.,  478 ,  488 ) to reduce or otherwise affect pressure at the outlet of one or more cylinders  452 ,  454 ,  456 , and  458  of the pump  450 , recognizing that waves partially reflected back upstream (e.g. at junction  488 ) may themselves be partially reflected back downstream as they encounter junctions (e.g.  478 ,  474 ,  476 ) on their way upstream toward the pump  450 . Such additional reflections may be simulated by, for example, the one dimensional gas flow simulation software developed by OPTIMUM Power Technology or other software. 
     In one embodiment, the length of pipe (e.g., headers  460 ,  462 ,  464 , and  466 ) extending from a cylinder outlet (e.g.,  441 ,  442 ,  443 , and  444 ) to a first junction (e.g.,  474  and  476 ) may be determined to produce the desired operation of the pump  450  (e.g., high flow, low power consumption, a desired flow at a desired power consumption, or other desired combination operating characteristics). Next, the length of a pipe (e.g., branch lines  470  and  472 ) extending from the first junction (e.g.,  474  and  476 ) to a second junction (e.g.,  478 ) may be determined to produce the desired operation of the pump  450 . 
     Additionally, the aforementioned positioning of junctions and specification of pipe lengths and other specifications that may affect pressure at a pump based on reflected waves may be applied to systems other than the piping system  440  of  FIG. 4 . Thus, for example, in an embodiment the piping system  540  of  FIG. 5  may be designed using the one dimensional gas flow simulation software developed by OPTIMUM Power Technology or other software to specify locations of junctions  574 ,  576 ,  578 ,  586 , and/or  588  to reduce or otherwise affect pressure at the pump  550  based, at least in part, on reflected waves. Similarly, in the embodiment of the six-cylinder reciprocating compressor type pump  694  system  600 , that software may be used to specify locations of junctions  660 ,  662 , and/or  678  to reduce or otherwise affect pressure at the pump  550  based, at least in part, on reflected waves. 
     Further attenuation may be accomplished by adding one or more tuned loops, such as tuned loop  480  illustrated in  FIG. 4 , to the piping system  440  to attenuate one or more additional frequencies of pressure waves or pulsations in the fluid flowing through the piping system  440 . The tuned loops  480  may be located anywhere desired in the piping system  440 , such that the tuned loop  480  may, for example, be located in or between the headers  460 ,  462 ,  464 , and  466  and in or between the branch lines  470  and  472 . 
     The tuned loop  480  illustrated in  FIG. 4  includes or is attached to the connecting conduit  490  leading from the branch line junction  478  and coupled at its discharge to the tuned loop inlet junction  486 . It is noted that the branch line junction  478  may be attached directly to the inlet junction  486  and the inlet conduit  490  may not be used in an embodiment. The inlet junction  486  is coupled to a first or inlet end of a first attenuating conduit  482  and a first or inlet end of a second attenuating conduit  484 . The first and second attenuating conduits  482  and  484  are coupled to an outlet junction  488  at their second or discharge ends and the outlet junction  488  discharges into the discharge conduit  492 . 
     A pressure wave or pulsation attenuation system, such as the piping system  440  illustrated on the outlet side of the pump  450  in  FIG. 4  may alternately or in addition be used on the inlet (e.g.,  804  and  904  as shown in  FIGS. 8 and 9 ) side of a pump such as the pump  450  in  FIG. 4 . Thus, all or any part of the piping system  440  illustrated on the outlet side of the pump  450  in  FIG. 4  may be applied to the pump  450  inlet (e.g.,  804  and  904  as shown in  FIGS. 8 and 9 ), the pump  450  outlet (e.g.,  808  and  908  as shown in  FIGS. 8 and 9 ), or both the inlet and the outlet of the pump  450 . Moreover, a piping system  440  may combine flow from cylinders  452 ,  454 ,  456 , and  458  of more than one pump  450  so that, for example, headers may combine flows from different pumps (including pump  450  and one or more other pumps not illustrated) or different cylinders (including cylinders  452 ,  454 ,  456 , and  458  and one or more other cylinders not illustrated) of different pumps (e.g., pump  450  and one or more other pumps not illustrated) and branch lines (e.g.,  470  and  472 ) may combine flows from different pumps (including pump  450  and one or more other pumps not illustrated) or different cylinders (including cylinders  452 ,  454 ,  456 , and  458  and one or more other cylinders not illustrated) of different pumps (including pump  450  and one or more other pumps not illustrated). 
     It should also be recognized that traditional pulsation dampening devices, such as bottles, may be incorporated into the fluid pumping system  440  if desired. 
       FIG. 5  illustrates an inlet piping system  540  that may operate on inlet fluids similar to way the outlet piping system  540  illustrated in  FIG. 4  operates on outlet fluids and may be used on the same pump  450  with which the outlet piping system operates. 
     The inlet piping system  540  is connected to inlets  541 ,  542 ,  543 , and  544  of the cylinders  552 ,  554 ,  556 , and  558  of the pump  550  illustrated in  FIG. 5 . Thus, the pump  550  cylinders  552 ,  554 ,  556 , and  558  include inlets  541 ,  542 ,  543 , and  544 , respectively. The cylinder inlets  541 ,  542 ,  543 , and  544  are attached to a first inlet header  562 , a second header  560 , a third inlet header  566 , and a fourth inlet header  564 , respectively. The first inlet header  562  and second inlet header  560  are attached to a first inlet branch line  570  at a first side inlet junction  574  and the third inlet header  566  and fourth inlet header  564  are attached to a second inlet branch line  572  at a second side inlet junction  576 . The first inlet branch line  570  and second inlet branch line  572  are attached to an inlet tuned loop  580  at a branch junction  578 . 
     A connecting conduit  590  leads to the inlet branch line junction  578  from an outlet of a tuned loop inlet junction  586 . The tuned loop inlet junction  586  also has two inlets, the first inlet being attached to a first end a first attenuating conduit  582  of the tuned loop  580  and the second inlet being attached to a first end of a second attenuating conduit  584  of the tuned loop  580 . A second end of the first attenuating conduit  582  is attached to a first outlet of a tuned loop inlet junction  588  and a second end of the second attenuating conduit  582  is attached to a second outlet of the tuned loop inlet junction  588 . An inlet of the tuned loop inlet junction is attached to a supply conduit  592 . 
     The tuned loop  580  may operate to cancel or attenuate pressure waves or pulsations propagating through the fluid flowing toward the pump  550 . Those pressure waves or pulsations propagating through the fluid may be created by the pump  550  or by one or more other system features (not shown) acting on the fluid flow either upstream or downstream of the tuned loop  580 . The inlet branch lines  570  and  572  can similarly operate to cancel or attenuate pressure waves or pulsations propagating through the fluid flowing toward the pump  550  and the inlet headers  560 ,  562 , and  564 ,  566  may operate to cancel or attenuate pressure waves or pulsations propagating through the fluid flowing toward the pump  550 . 
     In an embodiment, the inlet (suction) piping system  540  may be configured to increase gas flow capacity. Thus, for a double-acting piston arrangement, the resultant pressure wave propagating toward one or more of the cylinders  552 ,  554 ,  556 , and  558  is at a higher or high pressure point at one or more of the inlets  541 ,  542 ,  543 , and  544  when the piston of its corresponding cylinder  552 ,  554 ,  556 , or  558  is at or near the end of its stroke. For a single-acting piston arrangement, the resultant pressure wave propagating toward one or more of the cylinders  552 ,  554 ,  556 , and  558  is at a higher or high pressure point at one or more of the inlets  541 ,  542 ,  543 , and  544  when the piston of its corresponding cylinder  552 ,  554 ,  556 , or  558  is at or near the end of its stroke moving in the direction in which it is suctioning gas into the cylinder. 
     In an embodiment, the inlet (suction) piping system  540  may be configured to increase efficiency. Thus, for a double-acting piston arrangement, the resultant pressure wave propagating toward one or more of the cylinders  552 ,  554 ,  556 , and  558  is at a higher or high pressure point at one or more of the inlets  541 ,  542 ,  543 , and  544  when the piston of its corresponding cylinder  552 ,  554 ,  556 , or  558  is at or near the middle of its stroke. For a single-acting piston arrangement, the resultant pressure wave propagating toward one or more of the cylinders  552 ,  554 ,  556 , and  558  is at a higher or high pressure point at one or more of the inlets  541 ,  542 ,  543 , and  544  when the piston of its corresponding cylinder  552 ,  554 ,  556 , or  558  is at or near the middle of its stroke moving in the direction in which it is suctioning gas into the cylinder. 
     As used herein in relation to a piston stroke on the inlet (suction) side of a piping system, “at or near an end” or a similar term regarding a piston stroke refers to (for a double-acting piston) a position of the piston closer to either end of the cylinder than the middle of the cylinder, and refers to (for a single-acting piston) a position of the piston closer to the end of the cylinder where the piston is finishing or has just finished suctioning gas. That term or a similar term thus encompasses both a single-acting and double-acting cylinder and piston unless otherwise specified. 
     As used herein in relation to a piston stroke on the outlet side of a piping system, “at or near the middle” or a similar term regarding a piston stroke refers to (for a double-acting piston) a position of the piston closer to the middle of the cylinder than either end of the cylinder, and refers to (for a single-acting piston) a position of the piston closer to the middle of the cylinder when the piston is moving in a direction in which it is suctioning gas into the cylinder. That term or a similar term thus encompasses both a single-acting and double-acting cylinder and piston unless otherwise specified. 
       FIG. 6  illustrates an embodiment of a six-cylinder reciprocating compressor type pump  694  system  600 . A first cylinder  602  has a first outlet  622  connected to a first header  642 , a second cylinder  604  has a second outlet  624  connected to a second header  644 , a third cylinder  606  has a third outlet  626  connected to a third header  64 , a fourth cylinder  608  has a fourth outlet  628  connected to a fourth header  648 , a fifth cylinder  610  has a fifth outlet  630  connected to a fifth header  650 , and a sixth cylinder  612  has a sixth outlet  632  connected to a sixth header  652 . 
     The pump  694  is operated by a motor  698  driving a shaft  696  that causes pistons (e.g.,  230 ,  232 ,  234 ,  236 ,  238 ,  240 ,  330 ,  332 ,  334 ,  336 ,  338 , and  340  illustrated in  FIGS. 2 and 3 ) to reciprocate in each of the cylinders  602 ,  604 ,  606 ,  608 ,  610 , and  612 . While the cylinders  602 ,  604 ,  606 ,  608 ,  610 , and  612  may be arranged in any way desired, the cylinders  602 ,  604 ,  606 ,  608 ,  610 , and  612  in the embodiment illustrated in  FIG. 6  are arranged with three cylinders  602 ,  604 , and  606  on a first side  616  of the pump  694  and three other cylinders  608 ,  610 , and  612  on a second side  618  of the pump  694 . 
     The first, second and third headers  642 ,  644 , and  646 , respectively, are attached to inlets of a first side junction  660  in  FIG. 6 , but the fluid flowing through the first, second and third headers  642 ,  644 , and  646  could otherwise be combined by placing those fluid flows in fluid communication through multiple junctions or otherwise as desired. Similarly, The fourth, fifth and sixth headers  648 ,  650 , and  652  are attached to inlets of a second side junction  662  in  FIG. 6 , but the fluid flowing through the fourth, fifth and sixth headers  648 ,  650 , and  652  could also otherwise be combined by placing those fluid flows in fluid communication as desired. A first branch line  670  carries the fluid flow from the first side junction  660  to a branch line junction  678  and a second branch line  672  carries the fluid flow from the second side junction  662  to the branch line junction  678 . The fluid then flows from the branch line junction  678  to an outlet conduit  680  or, alternately, to a desired system (not shown). 
     In an embodiment where peak pressure waves, also referred to as a type of pulsation, are offset, the lengths of the branch lines  670  and  672  may be equal. When such equal length branch lines  670  and  672  used in conjunction with cylinders  602 ,  604 ,  606 ,  608 ,  610 , and  612  having offset operation (such as the offset cylinder operation illustrated and discussed in connection with  FIGS. 2 and 3 ), the branch lines  670  and  672  may be effective to cancel or attenuate pressure waves at varying pump  694  speeds. 
     For example, in the embodiment depicted in  FIG. 6 , the cycles of the three cylinders  602 ,  604 , and  606  on the first side  616  of the pump  694  may be offset by 60 degrees of shaft rotation (in a double acting compressor configuration) one from another. The three cylinders  608 ,  610 , and  612  on the second side  618  of the pump  694  may also be offset by 60 degrees of shaft rotation (in a double acting compressor configuration) one from another. In addition, the cylinders  602 ,  604 , and  606  on the first side  616  may be offset from the cylinders  608 ,  610 , and  612  on the second side  618  by 30 degrees such that pressure peaks or pulsations from the second side  618  cylinders  608 ,  610 , and  612  occur at or near a midpoint in time between pressure peaks or pulsations from the first side  616  cylinders  602 ,  604 , and  606 . In that way, there can be twelve pressure peaks or pulsations leaving the pump  694  at equally spaced time intervals per rotation of the shaft  696 . For example, the first cylinder  602  may reach peak discharge pressure on a first of its two strokes per cycle at 0 degrees of shaft  696  rotation, the fourth cylinder  608  may reach peak discharge pressure on a first of its two strokes per cycle at 30 degrees of shaft  696  rotation, the second cylinder  604  may reach peak discharge pressure on a first of its two strokes per cycle at 60 degrees of shaft  696  rotation, the fifth cylinder  610  may reach peak discharge pressure on a first of its two strokes per cycle at 90 degrees of shaft  696  rotation, the third cylinder  606  may reach peak discharge pressure on a first of its two strokes per cycle at 120 degrees of shaft  696  rotation, and the sixth cylinder  612  may reach peak discharge pressure on a first of its two strokes per cycle at 150 degrees of shaft  696  rotation. The first cylinder  602  may reach peak discharge pressure on a second of its two strokes per cycle at 180 degrees of shaft  696  rotation, the fourth cylinder  608  may reach peak discharge pressure on a second of its two strokes per cycle at 210 degrees of shaft  696  rotation, the second cylinder  604  may reach peak discharge pressure on a second of its two strokes per cycle at 240 degrees of shaft  696  rotation, the fifth cylinder  610  may reach peak discharge pressure on a second of its two strokes per cycle at 270 degrees of shaft  696  rotation, the third cylinder  606  may reach peak discharge pressure on a second of its two strokes per cycle at 300 degrees of shaft  696  rotation, and the sixth cylinder  612  may reach peak discharge pressure on a second of its two strokes per cycle at 330 degrees of shaft  696  rotation. 
     Accordingly, combining the pump  200  embodiment illustrated in  FIG. 2  with the partial system  600  embodiment illustrated in  FIG. 6 , where six cylinders create 12 peak pressure points or pulsations per shaft  204  rotation with each peak pressure point or pulsation occurring at 30 degree intervals, fluid flowing from three cylinders  250 ,  252 , and  254  having six peak pressure points or pulsations occurring at 60 degree intervals may be combined at a first junction (e.g., junction  660  in  FIG. 6 ) and fluid flowing from three other cylinders  256 ,  258 , and  260  having six peak pressure points or pulsations occurring at 60 degree intervals may be combined at a second junction (e.g., junction  662  in  FIG. 6 ). By so combining fluid flow using equal length headers (e.g., headers  642 ,  644 ,  646  and  648 ,  650 ,  652  in  FIG. 6 ) pressure waves are combined out of phase such that the pressure of the combined flow leaving the side junctions  660  and  662  has lower amplitude pressure waves with lower pressure peaks or pulsations. 
     When flow from a first set of cylinders (first, second, and third cylinders  602 ,  604 , and  606  in the embodiment depicted in  FIG. 6 ) is combined with flow from a second set of cylinders (fourth, fifth, and sixth cylinders  608 ,  610 , and  612  in the embodiment depicted in  FIG. 6 ) where pressure peaks or pulsations created by the first set of cylinders (first, second, and third cylinders  602 ,  604 , and  606  in the embodiment depicted in  FIG. 6 ) are offset from pressure peaks or pulsations created by the second set of cylinders (fourth, fifth, and sixth cylinders  608 ,  610 , and  612  in the embodiment depicted in  FIG. 6 ) the headers  642 ,  644 ,  646 ,  648 ,  650 , and  652  may all be of equal length and the branch lines  670  and  672  that combine the flow from the first set of cylinders and the second set of cylinders 
     The embodiment illustrated in  FIG. 6  is one example of combining fluid flow from cylinders at least some of which operate out of phase. It should be recognized, however, that various systems, methods, and apparatuses may be used to combine fluid flowing from multiple cylinders operating in or out of phase to cancel or attenuate pressure waves or pulsations propagating through the fluid. Thus, any number of cylinders may be combined out of phase in one or more sets of cylinders and any number of sets of cylinders may be combined out of phase by branch lines. 
     In the embodiment illustrated in  FIG. 6 , the pressure peaks or pulses created by the first set of cylinders  602 ,  604 , and  606  are approximately 180 degrees out of phase from the pressure peaks or pulses created by the second set of cylinders  608 ,  610 , and  612 . Accordingly, if the headers  642 ,  644 ,  646 ,  648 ,  650 , and  652  connected to all six cylinders  602 ,  604 ,  606 ,  608 ,  610 , and  612  are of equal length and the branch lines  670  and  672  connecting the flow from the first side  616  to the flow from the second side  618  are of equal length, then the combined pressure waves emanating from the first side junction  660  will be 180 degrees out of phase with the combined pressure waves emanating from the second side junction  662  and the flows passing through the branch lines  670  and  672  will combine at the branch junction  678  180 degrees out of phase, thereby further reducing pressure waves or pulsations propagating through the branch lines  670  and  672 . 
       FIG. 7  illustrates a tuned loop network  700  that includes two tuned loops  702  and  752 . Those two tuned loops  702  and  752  may each be similar to the tuned loop  102  illustrated in  FIG. 1 . Those two tuned loops  702  and  752  may furthermore be incorporated into any portion of a fluid pumping system such as the fluid pumping system  440  illustrated in  FIG. 4  (e.g., in one or more headers  460 ,  462 ,  464 , and  466 , one or more branch lines  470  and  472 , or in place of or in addition to the tuned loop  480 ). 
     A fluid, such as a gas or liquid may be pumped through the tuned loop network  700  by, for example, a pump, such as the pump  450  illustrated in  FIG. 4 , the pump  550  illustrated in  FIG. 5 , the pump  694  illustrated in  FIG. 6 , the pump  806  illustrated in  FIG. 8 , the pump  906  illustrated in  FIG. 9 , or any other pump described herein or other than as described herein and the pump may be a reciprocating compressor. The lengths of the various conduits (e.g.,  716 ,  722 ,  766 ,  772 ) may be adjusted to cancel primary pulsations and harmonics over a range of the pump (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ) operating speeds or conditions. 
     The first tuned loop  702  illustrated in  FIG. 7  includes an inlet conduit  704  coupled to a first inlet junction  706 . The first inlet junction  706  includes an inlet  708 , a first outlet  710  and a second outlet  713 . The first tuned loop  702  illustrated in  FIG. 7  also includes a first attenuating conduit  716  having a first end  714  coupled to the first outlet  710  of the inlet junction  706 , having a first length, and having a second end  718  opposite the first end  714 . 
     The first tuned loop  702  illustrated in  FIG. 7  also includes a second attenuating conduit  722  having a first end  720  coupled to the second outlet  713  of the inlet junction  706 , having a length that is approximately equal to the length of the first attenuating conduit  716  plus half a first primary wavelength of a pressure wave or pulsations or vibrations propagating in a fluid flowing through the tuned loop network  700 . The first primary wavelength may be selected from a range of wavelengths that may be imparted on the fluid by the pump (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ). 
     The term “wavelength,” as used in this section, may indicate the distance over which a wave&#39;s shape repeats, wherein the wave is formed by the repeating pressure variations or pulsations of the pump (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ) which may be caused by the motion of a piston (e.g.,  230 ,  232 ,  234 ,  236 ,  238 ,  240   330 ,  332 ,  334 ,  336 ,  338 , and  340  illustrated in  FIGS. 2 and 3 ) in a cylinder (e.g.,  452 ,  454 ,  456 ,  458 ,  552 ,  554 ,  556 ,  558 ,  602 ,  604 ,  606 ,  608 ,  610 , and  612  illustrated in  FIGS. 4, 5, and 6 ) compressing a gaseous fluid. The term “wavelength,” as used in this section, may also indicate the distance between consecutive corresponding points of a repeating wave, such as a pressure oscillation wave, wherein the corresponding points of the wave may correspond to one or more positions of the piston in the cylinder (e.g.,  452 ,  454 ,  456 ,  458 ,  552 ,  554 ,  556 ,  558 ,  602 ,  604 ,  606 ,  608 ,  610 , and  612  illustrated in  FIGS. 4, 5, and 6 ). That distance may furthermore be measured in length of pipe, such that the difference in length between the first attenuating conduit  716  and the second attenuating conduit  722  may be selected such that fluid flowing through those conduits is combined at a first outlet  730  such that pressure waves or pulsations in the fluid are attenuated. 
     The first tuned loop  702  illustrated in  FIG. 7  further includes the first outlet junction  724  having a first inlet  726  coupled to the second end  718  of the first attenuating conduit  716 , a second inlet  734  coupled to the second end  728  of the second attenuating conduit  722 , and an outlet  730 . The outlet  730  of the first outlet junction  724  may be attached to a discharge conduit  732  coupling the first tuned loop  702  to the second tuned loop  752 . 
     The second tuned loop  752  illustrated in  FIG. 7  includes a second inlet junction  756  in fluid communication with the first outlet junction  724 . The outlet junction  724  of the first tuned loop  702  may be coupled directly to the inlet junction  756  of the second tuned loop  752  without the use of the connecting conduit  732  or the connecting conduit  732  may interconnect the outlet junction  724  to the inlet junction  756 . The second inlet junction  756  includes an inlet  758 , a first outlet  760  and a second outlet  763 . The second tuned loop  752  illustrated in  FIG. 7  also includes a third attenuating conduit  766  having a first end  764  coupled to the first outlet  760  of the inlet junction  756 , the third attenuating conduit  766  having a first length and having a second end  768  opposite the first end  764 . 
     The second tuned loop  752  illustrated in  FIG. 7  also includes a fourth attenuating conduit  772  having a first end  770  coupled to the second outlet  763  of the second tuned loop  752  inlet junction  756 , the fourth attenuating conduit  772  having a length that is approximately equal to the length of the third attenuating conduit  766  plus half a second primary wavelength of pressure variations or vibrations propagating in the fluid flowing through the tuned loop network  700 , and having a second end  778 . 
     The second primary wavelength is also selected from a range of wavelengths that may be imparted on the fluid by the pump (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ). The second primary wavelength will not be the same as the first primary wavelength since the first tuned loop  702  and the second tuned loop  752  are tuned to attenuate different wavelengths in this embodiment. The second primary wavelength will also typically not be offset from the first primary wavelength by half the first primary wavelength since the purpose of the second tuned loop  752  in this embodiment is not to cancel certain even harmonics of the first tuned loop  702 . Rather, the first and second tuned loops  702  and  752  are arranged to provide good attenuation over a range of pressure wave or pulsation frequencies that may be produced, for example, by adjusting the speed of a pump (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ). 
     The second tuned loop  752  illustrated in  FIG. 7  further includes a second outlet junction  774  having a first inlet  776  coupled to the second end  768  of the third attenuating conduit  766 , a second inlet  784  coupled to the second end  778  of the fourth attenuating conduit  772 , and an outlet  780 . The outlet  780  of the second outlet junction  774  may be attached to a system through which the fluid is being pumped through, for example, a system coupling conduit  782 . 
     Each of the tuned loops  702  and  752  of the pulsation attenuation network  700  may include two conduits  716 ,  722  or  766 ,  772 , such as pipes of approximately equal area and different lengths, that extend from a header  704  at a junction  706  or  756  and that are recombined at a pipe  732  or  782  or vessel  786 . When the areas of the two conduits  716 ,  722  or  766 ,  772  are equal the two pressure waves or pulses carried therein can have equal energy to effectuate attenuation of the pressure waves or pulses when the fluid flow carrying the pressure waves and pulses are recombined. 
     In alternate embodiments, the conduits  716 ,  722  and  766 ,  772  of the tuned loops  702  and  752  may be of unequal cross-sectional size and the lengths of those conduits  716 ,  722  and  766 ,  772  may be varied by other than half of a wavelength of the pressure wave or pulse stream carried in the fluid flowing through the conduits  716 ,  722  and  766 ,  772  to be attenuated, so as to effectuate pressure wave or pulsation attenuation. 
     Multiple tuned loops, such as the tuned loops  702  and  752  illustrated in  FIG. 7  may be combined with the header cancellation system  460 - 478  illustrated in  FIG. 4 . For example, tuned loops  702  and  752  may be coupled to branch line junction  478  in place of or in addition to the tuned loop  480  illustrated in  FIG. 4 . In another embodiment, one or more tuned loops, such as the tuned loops  702  and  752  illustrated in  FIG. 7  may be connected to the inlet (e.g.,  804  and  904  as shown in  FIGS. 8 and 9 ) side of the pump (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ), with or without additional attenuation conduits, such as conduits  460 ,  462 ,  464 ,  466 ,  468 ,  470 , and  472  shown on the outlet (e.g.,  808  and  908  as shown in  FIGS. 8 and 9 ) side of the pump  450  illustrated in  FIG. 4 . 
     The inlet junctions (e.g.,  706  and  756 ) may divide the fluid stream into two equal parts using two half-round or D-shaped ports that become round and have a substantially constant area. A similarly configured outlet junction (e.g.,  724  and  774 ) may be used to recombine the divided streams at the end of the tuned loop (e.g.,  702  and  752 ). 
     Using the tuned loops of  FIG. 7  as an example, wherein the various configurations described in connection with  FIG. 7  may be incorporated into various configurations including those illustrated and described in connection with  FIGS. 4, 5, 6, 8, and 9 , the shorter of the two conduits  716  and  766  in the tuned loops  702  and  752  may be of a selected length and the longer of the conduits  722  and  772  may be equal to the length of the shorter of the conduits  716  and  766  plus half of a wavelength of pulsations, vibrations, or pressure waves propagating in the fluid of a primary frequency to be canceled or attenuated. 
       FIG. 8  illustrates an embodiment of a tuned loop network  800  having a first tuned loop  802  in fluid communication with the inlet  804  of a pump  806  and a second tuned loop  852  in fluid communication with the outlet  808  of the pump  806 . In the embodiment illustrated in  FIG. 8 , the inlet  804  may also be referred to as a suction side of the pump  806  and the outlet  808  may also be referred to as a discharge side of the pump  806 . Those tuned loops  802  and  852  may be configured as shown in  FIG. 1, 4 , or  7  and as described in connection with  FIG. 1, 4 , or  7 . Either or both of those tuned loops  802  and  852  may furthermore be used in connection with the piping system  440  illustrated and discussed in connection with  FIG. 4 , for example, or another piping system. 
     Pressure waves and pulsations generally exist in both the inlet  804  and outlet  808  of a pump  806 . Therefore, attenuating pressure waves and pulsations in both the inlet  804  and outlet  808  of the pump  806  by applying at least one tuned loop  802  and  852  at each of the inlet  804  and outlet  808  of the pump  806  may be beneficial to reduce pressure waves and pulsations existing prior to the inlet  804  and propagating from the outlet  808 . 
       FIG. 9  illustrates yet another embodiment wherein a suction tuned loop network  902  is placed at the suction  904  side of a pump  906  and a discharge tuned loop network  952  is placed at the discharge side  908  of the pump  906 . The suction tuned loop network  902  may include any desired number of tuned loops such as, for example the two tuned loops  910  and  912  illustrated in  FIG. 9 . Similarly, the discharge tuned loop network  952  may include any desired number of tuned loops such as, for example, the two tuned loops  960  and  962  illustrated in  FIG. 9 . The suction tuned loop network  902  and discharge tuned loop network  952  may furthermore be constructed as illustrated in and described in connection with  FIGS. 1, 4, 5, and 7 . 
     It should be noted that the acoustic velocity of a gas being pumped may vary from the inlet  904  to the outlet  908  of a pump  906  and, for at least that reason, the tuned loop configurations on the inlet  904  side and outlet  908  sides of the pump  906  may not be identical. It should also be recognized that a tuned loop network of two or more tuned loops  910 ,  912 , and  960 ,  962  may be used on the inlet  904 , the outlet  908 , or both the inlet  904  and the outlet  908  of the pump  906 . 
     Simulations have shown that tuned loop networks having three tuned loops are likely to provide substantial benefit over networks having two tuned loops in certain applications and that tuned loop networks having four tuned loops are likely to provide substantial benefit over networks having three tuned loops in certain applications. Thus, it is contemplated that three, four, or more tuned loops  910 ,  912 , and  960 ,  962  may be placed on either or each side of the pump  906  as required or desired to attenuate pulsations, vibrations, or other waves present in fluid received at or discharged from the pump  906 . 
     Other configurations having two or more tuned loops  910 ,  912  and  960 ,  962  placed on one or both sides  904  and  908  of the pump  906  are also possible to attenuate one or more primary frequencies or an entire range of frequencies. As has been discussed, a range of frequencies may exist where, for example, the speed of the pump  906  is varied. 
     Tuned loops networks such as those illustrated in  FIGS. 9  ( 902  and  952 ) can create relatively steady pressure upstream or downstream of the pump  906  in comparison to the wide pressure variations that may exist in fluid flow created by the pump  906 . When tuned loop networks (e.g.,  902  and  952 ) are properly positioned, the pump  906  may require less power to create a desired pressure downstream in a pipe or vessel, may provide a greater differential pressure created by the pump  906 , or both. 
     Using  FIG. 9  as an example, a wavelength may be determined using the speed of the pump  906 , the number of compression volumes (per rotation of the pump  906 , for example), and the acoustic velocity of the fluid being pumped by the pump  906 . Thus, a single-acting reciprocating compressor type pump  906  having a single cylinder may be used to compress a gas and propel the gas through the inlet  904  once per engine cycle, as an example. 
     Pumps (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ) including reciprocating compressors frequently operate over a range of speeds. In this example, a single acting reciprocating compressor  906  operates at 600 rpm, which is equal to a primary frequency of 10 revolutions per second. A single compression occurs in each cylinder during each rotation of this single-acting reciprocating compressor  906 . If the velocity of the gas is 1000 ft/sec., the gas moves 100 feet per revolution of the reciprocating compressor  906  and its half wavelength would be 50 feet. In a double-acting reciprocating compressor, which compresses the gas and propels the gas through the inlet  904  on both strokes, the wavelength is half the wavelength of a single-acting reciprocating compressor so that, in the example provided, half a wavelength would be 25 feet. 
     In a two-stage pressure wave or pulsation attenuation network (e.g., the tuned loop network  700  illustrated in  FIG. 7  or the suction tuned loop network  902  or the discharge tuned loop network  952  illustrated in  FIG. 9 ), the first pressure wave or pulsation attenuation device  702 ,  912 , and  962  in the series may be designed to eliminate the most prevalent primary frequency expected to be present in the fluid passing through the pressure wave or pulsation attenuation network  700 ,  902 , and  952 . That primary frequency eliminating pulsation attenuation device  702 ,  912 , and  962  may furthermore be the longest of the pressure wave or pulsation attenuation devices  702 ,  752 ,  912 ,  910 ,  962 , and  960  in the series of pressure wave or pulsation attenuation devices  702 ,  752 ,  912 ,  910 ,  962 , and  960  placed in series to form the pulsation attenuation network  700 ,  902 , and  952 . 
       FIG. 10  illustrates an embodiment of a method for attenuating pulsations, vibrations, or other undesirable waves in a fluid  1000 . The method for attenuating pulsations  1000  begins with a first wave, such as a pulse wave, entering a first pipe, duct, or conduit at  1010  and a second wave, such as a pulse wave, entering a second pipe, duct, or conduit at  1020 . Each of the first wave and the second wave will propagate in a fluid, such as a liquid or gas, which is being pumped. At  1030 , the first wave and the second wave are combined, for example, by conducting the first and second waves into a junction coupled to first and second branch conduits carrying fluid in which the first and second waves are propagating. The first and second waves may be attenuated by such a combination of waves where, for example, the waves are combined at a time when a pulse peak in the first wave joins near a pulse valley in the second wave. 
     To further attenuate pulses, vibrations, or other undesirable waves in a fluid, at  1040  the fluid that was combined at  1030  may be combined with another fluid in such a way as to attenuate waves existing in the combined fluid and the other fluid. 
     Such combinations of fluid as described at  1030  and  1040 , wherein waves propagating in the fluid are combined out of phase, may result in a differential phase shift in the combined fluids, thereby attenuating the pulsations, vibrations, and other undesirable waves. 
     For example, in the method illustrated and described in connection with  FIG. 10 , fluid flows from two or more cylinders (e.g.,  460 ,  462 ,  464 ,  466 ,  560 ,  562 ,  564 ,  566 ,  602 ,  604 ,  606 ,  608 ,  610 , and  612 ) are combined at a junction (e.g.,  474 ,  476 ,  574 ,  576 ,  660 , and  662 ) to reduce variations or fluctuations in pressure waves propagating from those cylinders (e.g.,  460 ,  462 ,  464 ,  466 ,  560 ,  562 ,  564 ,  566 ,  602 ,  604 ,  606 ,  608 ,  610 , and  612 ) at  1030 . The fluid flowing from the cylinders (e.g.,  460 ,  462 ,  464 ,  466 ,  560 ,  562 ,  564 ,  566 ,  602 ,  604 ,  606 ,  608 ,  610 , and  612 ) is combined such that pressure waves caused by operation of the cylinders (e.g.,  460 ,  462 ,  464 ,  466 ,  560 ,  562 ,  564 ,  566 ,  602 ,  604 ,  606 ,  608 ,  610 , and  612 ) join out of phase at  1030 . In one embodiment, the flows are a gaseous fluid, such as natural gas. In an embodiment, periodic pressure waves exist in the flow propagating from each cylinder (e.g.,  460 ,  462 ,  464 ,  466 ,  560 ,  562 ,  564 ,  566 ,  602 ,  604 ,  606 ,  608 ,  610 , and  612 ) and the flows from two cylinders (e.g.,  460 ,  462 ,  464 ,  466 ,  560 ,  562 ,  564 ,  566 ,  602 ,  604 ,  606 ,  608 ,  610 , and  612 ) are combined 180 degrees out of phase at  1030 . In another embodiment, the flows propagating from three or more cylinders are combined at  1030  such that pressure peaks or pulsations in the flows arrive at the place where the flows are combined at regular intervals, such as 60 degrees out of phase when combining flow from three cylinders (e.g.,  602 ,  604 , and  606  or  608 ,  610 , and  612 ) or 45 degrees out of phase when combining flow from four cylinders. 
     The pressure waves in the fluid streams combined at  1030  may not be symmetrical such that a first wave near its peak pressure may be joined with a second wave near its low pressure so as to attenuate both waves, but not necessarily cancel both waves. 
     At  1040 , a further reduction in the amplitude of pressure waves may be achieved by combining two or more flows of fluid that carry combined flows from two or more headers (for example, flow from side junctions  474 ,  476 ,  574 ,  576 ,  660 , and  662 ) out of phase in a branch line junction for example, branch line junction  478 ,  578 , or  678 . In an embodiment, the combined header flows may be combined directly by, for example, connecting side junctions  660  and  662  directly in another junction such as branch line junction  678  without the use of branch lines  670  and  672 . In another embodiment, as illustrated in  FIGS. 4 and 6 , combined header flow may be combined at side junctions (e.g.,  474 ,  476  and  660 ,  662 ) and branch lines (e.g.,  470 ,  472 ,  670 , and  672 ) may carry flow from the side junctions (e.g.,  474 ,  476  and  660 ,  662 ) to the branch line junction (e.g.,  478  and  678 ). 
     Cylinders (e.g.,  452 ,  454 ,  456 ,  458 ,  552 ,  554 ,  556 ,  558 ,  602 ,  604 ,  606 ,  608 ,  610 , and  612 ) may be of varying capacity such that flows from the cylinders may be combined out of phase at intervals other than 360 degrees divided by the number of cylinders being combined. Moreover, the total flow traveling along two or more branch lines (e.g.,  470 ,  472 ,  570 ,  572 ,  670 , and  672 ) that are to be combined may vary, for example, in quantity or amplitude of pressure waves, such that flows through the branch lines may be combined out of phase at intervals other than 360 degrees divided by the number of branch lines to be combined. 
     In accordance with one embodiment of pressure wave or pulsation attenuation, and depicted in the flow chart of  FIG. 11 , a method of attenuating pressure waves or pulsations created by a pump  1100  includes: discharging a first fluid stream from a first cylinder into a first conduit at  1112 , discharging a second fluid stream from a second cylinder into a second conduit at  1114 , discharging a third fluid stream from a third cylinder into a third conduit at  1116 , discharging a fourth fluid stream from a fourth cylinder into a fourth conduit at  1122 , discharging a fifth fluid stream from a fifth cylinder into a fifth conduit at  1124 , discharging a sixth fluid stream from a sixth cylinder into a sixth conduit  1126 , the first, second, third, fourth, fifth, and sixth conduits having equal lengths, and the pressure waves in the first, second, third, fourth, fifth, and sixth fluid streams having relative phases that vary by approximately 60 degrees at the points of discharge from the first, second, third, fourth, fifth, and sixth cylinders respectively. 
     In an embodiment, the fluid streams from the first, second, and third conduits are combined at  1130  and the fluid streams from the fourth, fifth, and sixth conduits are combined at  1140 . Such a combination may occur to minimize the lengths of the conduits when, for example, a first set of cylinders are in close proximity to one another (for example, on one side of a compressor) while a second set of cylinders are close to one another, but further from the first set of cylinders. In that way proximate flows can be joined and used to reduce pressure waves or pulsations quickly and close to the cylinders. The flows may furthermore be joined in one or more junctions such as side junctions  474 ,  476 ,  574 ,  576 ,  660 , and  662 . 
     Further in that embodiment, the fluid streams discharged from the first, second and third conduits may be directed into a seventh conduit of a second length at  1130  and the fluid streams discharged from the fourth, fifth and sixth conduits may be directed into an eighth conduit of a length equal to the second length at  1140 . The gas discharged from the seventh and eighth conduits is then combined at  1150  and that combination may occur in a branch line junction such as one of branch line junctions  478 ,  578 , and  678 . 
     In various embodiments, the first and second lengths may be chosen to optimize or improve flow or power consumption or to improve both flow and power consumption. 
       FIG. 12  illustrates a fluid pumping system  1210 , such as may be used in a natural gas pumping application. The fluid pumping system  1210  has a suction side  1222  and a discharge side  1224 . Fluid is supplied to the suction side  1222  of the pump  1216  from a source system  1212 , such as another pumping station in a natural gas pumping system. The fluid supplied to the pump  1216  passes through one or more suction side tuned loops  1214 , such as the tuned loop  100  illustrated in  FIG. 1  or the tuned loops  702  and  752  illustrated in  FIG. 7  before reaching the pump  1216 . The first pipe  1232  carries fluid from the source  1212  to the suction side tuned loop  1214  and the second pipe  1234  carries fluid from the suction side tuned loop  1214  to the pump  1216 . 
     The fluid discharged from the pump  1216  also passes through one or more discharge side tuned loops  1218  (such as the tuned loop  100  illustrated in  FIG. 1  or the tuned loops  702  and  752  illustrated in  FIG. 7 ) after being discharged from the pump  1216  and before reaching its destination. That destination may, for example, be a home or another pumping station in a natural gas pumping system. Third pipe  1236  carries fluid from the pump  1216  to the discharge side tuned loop  1218  and fourth pipe  1238  carries fluid from the discharge side tuned loop  1218  to the destination  1220 . 
     It should be recognized that the fluid pumping system  1210  illustrated in  FIG. 12  is simple and that many more components may be situated between the source  1212  and the pump  1216  or between the pump  1216  and the destination  1220 . 
     A first consideration in designing a tuned loop  1214  or  1218  may be to select appropriate dimensions for the first branch line (e.g., first branch line  116  illustrated in  FIG. 1 ) and the second branch line (e.g., second branch line  122  illustrated in  FIG. 1 ) to attenuate pulsations or pressure waves emanating from the pump  1216 . 
     A second consideration in designing a tuned loop  1214  or  1218  may be to select appropriate length and area dimensions for the pipes  1232 ,  1234 ,  1236 , and  1238 . For example, the dimension of second pipe  1234  may be selected such that waves reflected from the suction side tuned loop  1214  back upstream toward the pump  1216  reach the pump  1216  at a time in the pump  1216  operation that causes the pump  1216  to be more efficient, to create more flow, or a combination of both. The dimension of third pipe  1236  may also be selected such that waves reflected from the discharge side tuned loop  1218  back toward the pump  1216  reach the pump  1216  at a time in the pump  1216  operation that causes the pump  1216  to be more efficient, to create more flow, or a combination of both. 
     Thus, the location of a pressure wave or pulsation attenuation network (e.g.,  100 ,  440 ,  540 ,  600 ,  700 ,  800 , and  900 ), components thereof, or another source of reflected waves in relation to the pump (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ) or another source of pulsations, vibrations, or waves in fluid flowing through a system (e.g.,  100 ,  440 ,  540 ,  600 ,  700 ,  800 , and  900 ) may affect the quantity or efficiency of flow through the system (e.g.,  100 ,  440 ,  540 ,  600 ,  700 ,  800 , and  900 ). In an embodiment where the source of the pulsation is a reciprocating compressor (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ) pumping natural gas through a natural gas piping system (e.g.,  100 ,  440 ,  540 ,  600 ,  700 ,  800 , and  900 ), a header pipe (e.g., headers  460 ,  462 ,  464 ,  466 ,  560 ,  562 ,  564 ,  566 ,  642 ,  644 ,  646 ,  648 ,  650 , and  652  in  FIGS. 4, 5, and 6 ) may be employed to carry the compressed gas from the compressor (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ) to the system (e.g.,  100 ,  440 ,  540 ,  600 ,  700 ,  800 , and  900 ) and that header (e.g., headers  460 ,  462 ,  464 ,  466 ,  560 ,  562 ,  564 ,  566 ,  642 ,  644 ,  646 ,  648 ,  650 , and  652 ) may have a particular length that may promote quantity or efficiency of fluid flow through the system (e.g.,  100 ,  440 ,  540 ,  600 ,  700 ,  800 , and  900 ). 
     Lengths and areas of piping on the intake side of the pump (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ) or other source of pulsations, vibrations, or waves in fluid flowing through a system (e.g.,  100 ,  440 ,  540 ,  600 ,  700 ,  800 , and  900 ) may affect the efficiency of flow through the system (e.g.,  100 ,  440 ,  540 ,  600 ,  700 ,  800 , and  900 ) as well. In an embodiment where the source of a pressure wave that includes pressure peaks or pulsations is a reciprocating compressor (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ) pumping natural gas through a natural gas piping system (e.g.,  100 ,  440 ,  540 ,  600 ,  700 ,  800 , and  900 ), an intake pipe (e.g.,  590 ) may be employed to carry the compressed gas from the tuned loop (e.g.,  100  and  580 ) to the compressor (e.g.,  450 ,  550 ,  694 ,  806 , and  906 ). That intake pipe (e.g.,  590 ) may furthermore have a particular length that may promote quantity or efficiency of fluid flow through the system (e.g.,  100 ,  440 ,  540 ,  600 ,  700 ,  800 , and  900 ). 
     While the present invention has been disclosed with reference to certain embodiments, numerous modifications, alterations, and changes to the described embodiments are possible without departing from the scope of the present invention, as defined in the appended claims. Accordingly, it is intended that the present invention not be limited to the described embodiments, but that it have the full scope defined by the language of the following claims, and equivalents thereof.