ROTORDYNAMIC STABILITY OF A 9500 PSI REINJECTION ... · rotordynamic stability problems of the compressors have caused tremendous losses in revenues in the past. In low and medium

Yves Bidaut is Manager of theMechanical Development department ofMAN Turbo, in Zürich, Switzerland. His jobfunction includes the development andanalysis of the components of centrifugalcompressors for oil and gas application. Heis responsible for providing technicalsupport in rotordynamics and stressanalysis. Before joining the site inSwitzerland in 2003, he was employed for

six years in MAN Turbo, Berlin, where he was involved in thedesign, finite element analysis, rotordynamic analysis, testing, anddevelopment of centrifugal compressors.Mr. Bidaut received his diploma (Mechanical Engineering,

1995) from the University of Valenciennes (France).

Urs Baumann is the Manager ofthe Calculation and Developmentdepartment of MAN Turbo AG, in Zürich,Switzerland. His responsibilities include theaerodynamic and mechanical improvementof turbocompressors and associatedcomponents, as well as the implementationand maintenance of test stands andanalytical tools needed to perform this task.Before joining MAN Turbo in 1996, Mr.

Baumann worked for Sulzer Innotec, the Corporate Research andDevelopment Center of Sulzer Ltd. For several years he was incharge of the machinery dynamics group that is responsible for thedevelopment, design improvement, and troubleshooting on a widerange of Sulzer products.Mr. Baumann has a diploma (Mechanical Engineering, 1987)

from the Swiss Federal Institute of Technology in Zurich.

Salim M. H. Al Harthy is Technical Consultancy Manager andCorporate Functional Discipline Head of Petroleum DevelopmentOman (PDO), in Muscat, Sultanate of Oman. He has been workingfor PDO since 1975.Mr. Al Harthy received his B.S. degree (Mechanical and Production

Engineering) from the University of Liverpool (England).

ABSTRACT

Extensive stability measurements were performed during thefull-load, full-pressure factory testing of a five-stage inlinecentrifugal compressor. The compressor, tested up to a maximumdischarge pressure of 655 bar (9,500 psi), is equipped with ahole-pattern balance piston seal. The purpose of the tests wasthe validation of the predicted rotordynamic stability with theconsideration of all available boundary conditions (including theanalytical determination of the correct seal geometry). In order tovalidate the prediction of the internal pressure distribution, thecompressor thrust force and the balance piston leakage flow weremeasured and compared to the analytical results. The test arrangementincluded a magnetic exciter attached to the free end of thecompressor shaft. An asynchronously rotating force was injectedinto the rotor to excite the first forward and backward precessionmodes. The measurement results demonstrated the good stabilitybehavior of the compressor throughout the complete performancecurve, a large rise of the first natural frequency even at very lowpressure levels, and the insensitivity of the stability characteristicsto the pressure ratio or level. Generally, a good correlation isobtained between the test results and the analytical predictions eventhough the predicted damping ratio is underestimated in most cases.

INTRODUCTION

In the last years enhanced oil recovery (EOR) methods have createdan increasing demand for high pressure injection compressors. Thefirst compressors in the design pressure range of 8,700 to 11,600 psi(600 to 800 bars) have all been built for oil production facilities inthe Caspian region and in Venezuela. Areas currently underdevelopment include southwestern Africa and Oman, to where thetested compressor described in this paper has been shipped.In the turbomachinery business for the oil and gas industry,

rotordynamic stability problems of the compressors have causedtremendous losses in revenues in the past. In low and mediumpressure applications this issue could—to a good extent—besolved. The physical mechanisms that can drive a compressor rotorinto instability are known. Modern computer codes are used tosafely layout these compressors and a variety of design features areused to positively influence the stability of the machines.Unfortunately more than 99 percent of all the experiences are inapplications at low and medium pressures, with dischargepressures below 4,300 psi (300 bars) and average densities below

251

ROTORDYNAMIC STABILITY OF A 9500 PSI REINJECTION CENTRIFUGAL COMPRESSOREQUIPPED WITH A HOLE PATTERN SEAL—MEASUREMENT VERSUS PREDICTION

TAKING INTO ACCOUNT THE OPERATIONAL BOUNDARY CONDITIONS

byYves Bidaut

Manager Mechanical Development

Urs BaumannHead of Calculation and Development

MAN Turbo AG Schweiz

Zürich, Switzerland

andSalim Mohamed Hamed Al-Harthy

Head Mechanical Services

Petroleum Development Oman LLC

Muscat, Sultanate of Oman

approximately 200 kg/m3. Worldwide only a small number ofcompressors are running at pressures above 5,800 psi (400 bars)and average densities above 250 kg/m3. Figure 1 shows a referencechart containing the highest pressure applications built to date onthe Fulton diagram (Fulton, 1984).

Figure 1. API 617 Level I Diagram with Fulton Line Showing theHighest Pressure Compressor References to Date.

In recent years hole pattern and honeycomb balance piston sealshave evolved from revamping and trouble shooting solutions(Zeidan, et al., 1993; Gelin, et al., 1997) to a specific middleand high pressure design feature. Numerous compressors in anintermediate pressure range have been built and are now successfullyin operation. There are even measurements available (Memmott,1994, 1999; Moore, et al., 2002) where the damping of acompressor with a discharge pressure of approximately 400 bar,equipped with a hole pattern seal, was determined.

THE ZALZALA PROJECT

The Zalzala/Harweel oil field is located approximately 100 km tothe northeast of Salalah, a large port in the south of Oman. An aerialview of the facility is shown in Figure 2. It is the largest fielddevelopment project ever undertaken by PDO, the government ownedOmani Oil Company. The different reservoirs are spread out over anarea of more than 250 km2 and the wells are linked via an extensivenetwork of pipelines to a central processing facility. In this facility amiscible-gas injection capacity of 5 million m3 per day is provided bythe compressor described in this paper. By the application of thismiscible-gas injection, the percentage of oil recovered can beincreased from about 10 percent to more than 33 percent.

Figure 2. View of the Zalzala/Harweel Plant Facility.

The injection compressor was successfully tested in spring 2008.After arriving in Oman, it was installed and commissioned earlyin 2009. First oil produced with this facility is expected by theend of 2009.

SCOPE OF INVESTIGATION

The stability behavior of a compressor equipped with a holepattern balance piston seal is dominated by the forces producedby this element. Therefore it is of utmost importance to knowthe parameters influencing the boundary conditions of the sealcalculations. Figure 3 shows a schematic of the extent of theinvestigations with the dependencies between the differentanalyses and measurements. The heart of the calculations consistsof the casing finite element analysis (FEA), which produces thegeometrical boundary conditions. The thrust calculation and theleakage calculation serve as additional input for the casing FEAand the seal calculation itself. The focus is set on the correctdetermination of the pressure distribution within the machine, i.e.,along the flow path. The thrust and leakage measurements are usedto calibrate and tune the respective calculations.

Figure 3. Schematic of the Analyses.

HIGH PRESSURE COMPRESSOR DESIGN

General Arrangement

The train tested in the original equipment manufacturer’s (OEM’s)test bed consists of a synchronous motor driving, via a speedincreasing gear, the high-pressure (HP) compressor. The compressordoes not have its own thrust bearing because the thrust is transferredvia a solid coupling and a thrust collar gearbox to the bull gear wherethe thrust is taken by a low speed axial bearing. Figure 4 shows thedescribed train arrangement. Its main advantages are:

• Very high thrust bearing capacity.• No coupling overhung mode near speed range.• High basic damping (at no load).

Figure 4. Schematic of the Compressor Train Arrangement.

PROCEEDINGS OF THE THIRTY-EIGHTH TURBOMACHINERY SYMPOSIUM • 2009252

The disadvantages for this train arrangement are as follows:

• Dynamically coupled system• Thrust collar capacity limited• Sensitivity to misalignment

Since the OEM has an extensive experience with the shown trainarrangement the advantages were rated higher and consequentlythis configuration was chosen.The tested compressor consists of five radial stages in an inline

design. The machine has a pressure rating of 10,100 psi (700 bars)and a maximum power consumption of 9.5 MW. The layoutaccounts for two different gear sets, a main 100 percent gear ratiofor all specified operating conditions and a spare 105 percent gearset as a provision for lower molecular weights or higher requiredpressure ratios. Table 1 shows the main operating conditions of thecompressor for site operation as well as for the shop tests.

Table 1. Compressor Operating and Test Conditions.

Compressor Design

Figure 5 shows a cross-sectional drawing of the compressor. Foraerodynamic stability and enhanced pressure ratio all diffusers areof a bladed design. In high pressure compressors this has anotherhighly important advantage since these blades allow for the axialforce transmission between consecutive statoric parts and thereforereduce considerably the deformations at the stage seals in operation.

Figure 5. Cross Sectional Drawing of the Compressor.

The stages 2 to 5 are equipped with so-called thrust brakes.These devices take out the circumferential speed component of thegas in the shroud side room and consequently change the pressurewithin this cavity. Figure 6 shows the pressure distribution in theside rooms with and without thrust brakes. The shown effect leadsto a smaller stage thrust and to a smaller thrust variation fordifferent operating and seal conditions. As a second effect thrustbrakes reduce the inlet swirl to the shroud labyrinths and aretherefore considered a stability increasing feature. The stages areequipped with stationary see-through labyrinth seals. Previousstability measurements in high-pressure compressors equippedwith comb-grooved labyrinth seals had shown that these labyrinths

produce negative direct stiffness and are therefore not suitable forhigh-pressure application (Baumann, 1999). For the balance pistona hole pattern design is used. The casing was specificallydeveloped for this type of balance piston seal and is optimized forminimum deformations of the hole pattern sleeve in operation. Thesleeve consists of a single circular piece with a convergent taperedbore. Figure 7 shows a picture of the installed hole pattern sleeve.It can be seen that at the entrance to the seal the inlet swirl isreduced by a swirl brake.

Figure 6. Pressure Distribution on the Impeller Disks with/withoutThrust Brake.

Figure 7. Photo of the Hole Pattern Seal.

TEST SET-UP

General Test Arrangement

The tests were performed on the job skid with the originalcomponents consisting of the synchronous motor, the gear, bothcouplings and the dry gas seal device. The mechanical andthermodynamic measurements were performed in the same testsetup in accordance with the API 617 (2003) and ASME PTC-10(1997) Class II specifications. All tests were carried out in a closedloop. Prior to these tests the full-load, full-density test was performedon the compressor for both gear ratio configurations correspondingto specified rotating speeds of 12,068 rpm (100 percent) and 12,643rpm (105 percent). During the high-pressure test the vibrations,damping ratio, thrust, and the leakage at the balance piston seal weremeasured. Furthermore, a frequency analysis was carried out to

253ROTORDYNAMIC STABILITY OF A 9500 PSI REINJECTION CENTRIFUGAL COMPRESSOREQUIPPED WITH A HOLE PATTERN SEAL—MEASUREMENT VERSUS PREDICTION


verify the absence of subsynchronous shaft vibration. Figure 8 showsthe compressor on the test stand. Pure nitrogen (N2) was used for thetest at 105 percent speed. At 100 percent speed carbon dioxide (CO2)was supplied to the loop in order to obtain a gas composition of 17percent carbon dioxide and 83 percent nitrogen and thereby, reach asimilar gas discharge density as on site.

Figure 8. Photo of the Compressor in the Test Facility.

Additional Test Equipment

To measure the frequency and damping ratio of the lowestbending mode at full speed, the first natural frequency was excitedasynchronously. For this purpose an electromagnetic exciter wasattached to the shaft end of the suction side (nondriven-end). Theshaft end with the exciter is shown in Figure 9. An asynchronouslyrotating force was injected into the rotor to excite the firstforward and backward precession modes. The force was appliedsimultaneously on two axes to excite the rotor in circular orbits.The shaft response was measured while running the magnetic forceexcitation frequency through the natural frequency of the rotor.Furthermore the effect of the exciter on the lateral modes of theoriginal system was analyzed. The calculated natural frequency ofthe model with the shaker device shows an increase of the naturalfrequency less than 1 Hz in comparison to the original model.

Figure 9. Cross Sectional Drawing of the Compressor Shaft Endwith Shaker.

In addition, the thrust bearing was equipped with loadmeasurement cells to measure the thrust forces. Figure 10 showsthe arrangement of the load cells in the thrust bearing.

Figure 10. Cross Sectional Drawing of the Thrust Measuring Device.

Test Procedure

After starting the train up to the maximum rotating speed(12,643 rpm), the compressor was throttled to reach themaximum discharge pressure of 650 bar at a suction pressure of310 bar. Holding the suction pressure constant at 310 bar theflow was then varied to measure the damping ratio and thethrust along the performance curve from near surge (pressureratio 2.2) down to near choke (pressure ratio 1.6). The suctionpressure was then reduced to 250 bar, and the equivalentmeasurements were performed for this performance curve.Afterwards the operating point was adjusted near the ratedpoint, and the suction pressure was reduced in steps of 50 bardown to 50 bar. Additional measurements were performed witha suction pressure of 25 bar and 10 bar. At a rotating speedof 12,068 rpm the measurements were performed along theperformance curve for suction pressures of 300 bar and 250 bar.The measured operating points are represented in Figure 11. Ithas to be noted that the pressure ratio is greater at lowerpressures due to real gas effects. As shown in Figure 12 thedamping ratio measurements were carried out by applying aharmonic force with a sweep over a frequency range from 50Hz to 300 Hz. To avoid any distortion of the measuredresonance curves a frequency increase rate of 1 Hz/sec wasdefined. The level of the excitation force was adjusted in orderto ensure high quality responses.

Figure 11. Measured Performance Curves.


Figure 12. Power Signal of the Magnetic Bearing Exciter.

TEST RESULTS

Stability Measurement: Signal Processing

Figure 13 shows two waterfall plots of the loaded compressorwhile exciting the forward and backward precession mode,respectively. It can clearly be seen that each type of asynchronousrotating force (forward and backward) excited mainly itscorresponding forward or backward precession mode. Theextracted orbits at the critical speeds (Figure 13, below eachwaterfall diagram) indicate the precessional direction.

Figure 13. Waterfall Plot While Exciting the Forward andBackward Precession Mode.

The recorded averaged time series of the measured shaftvibrations were transformed into the electromagnet axes (V and Win Figure 12) and then fast Fourier transformed (FFT) and thereby,resonance peaks—if existent—could be recognized. The dampingratio was evaluated by the circle fit method. This method is based onthe same background as the well-known half power method;however, the bandwidth is determined by using phase information.The high rate of phase change in the region ofthe resonance can beused to facilitate a more robust modedetermination. In the vectordiagram the amplitude and phase information is presented as asingle curve by plotting the real part of the frequency responsefunction versus the imaginary part (Nyquist plot). The damping ratio

is determined by fitting the best circle through the plotted points foreach resonance with the half power point band being represented bydrawing the diameter normal to the resonance diameter.The results of the evaluation are visualized in Bode plots. Figure

14 shows a typical Bode plot for a forward and backwardasynchronous excitation together with the originally measured dataand the curve fit superimposed. The best evaluation of responseswas obtained at the nondrive-end sensors. Generally it can be saidthat the responses to excitations of the forward and backwardmodes indicate similar results. The forward and backward modesare very close to each other.

Figure 14. Bode and Nyquist Plots of a Measured Transfer Function.

Due to the compressor design the natural frequency correspondingto the first conical mode is much higher than the operationalfrequency. Therefore it can be stated that the natural frequency,excited by the shaker within the frequency range from 50 Hz to300 Hz, can only be attributed to the first whirling mode.

Thrust and Leakage Measurement

The correct determination of the thrust is essential to ensure thereliability of a high-pressure-compressor. Therefore the thrust wasmeasured at the same test points as the stability measurements. Figure15 shows the measured thrust. It can be seen that the thrust is mainlyinfluenced by the position of the operating point within the compressorcharacteristic: Near the surge limit the thrust is nearly twice as high asnear the optimum point. Furthermore the thrust decreases withincreasing flow and reaches values near zero when approaching choke.It should be mentioned that the absolute level of the thrust curve isdefined by the layout of the balance piston. The rotating speed and thecomposition of the gas have no influence on the thrust. To facilitate thecomprehension of the diagram the corresponding performance curveswere reproduced in the same picture. The balance piston leakage wasmeasured via an orifice meter installed in the balance return line. Themeasurements, as expected, showed a strong dependency of theleakage flow to discharge pressures.

Figure 15. Measured Axial Thrust.



Stability Measurement: Results

The results of the stability measurements, Figure 16, show that thecompressor is very stable throughout the entire performance map. Themost remarkable result on the stability curves is the large rise of thenatural frequency at low pressure. At a discharge pressure of only 25bar the natural frequency already increases from 100 Hz (unloadedcompressor) up to 140 Hz! The natural frequency then increasessteadily with increasing pressure up to 180 Hz at 300 bar. Beyond thispressure the natural frequency did not increase. The same observationcan be made for the damping ratio: The damping ratio alreadyincreases at very low pressures reaching a constant value of about 120percent log dec at 300 bar. In opposition to the observations made byMoore, et al. (2002), the damping does not increase steadily with thedischarge pressure. It should be mentioned that Moore, et al. (2002),made measurements on a back-to-back compressor where the holepattern seal was at the center, which is the point of maximumamplitude. The modeshape in Figure 17 shows the hole pattern seal isdriving a nodal point in the rotor, which places a practical limit on theamount of damping it can provide. The stability behavior of thecompressor is more or less independent of the suction pressure atconstant discharge pressure. As expected the damping ratio decreaseswith increased rotational speed. The comparison of these test resultswith the measurements performed on high-pressure compressorsequipped with a labyrinth balance piston reveals the major influence ofthe hole pattern seal on the natural frequency. Measurements of acompressor with labyrinth piston carried out by Baumann (1999)indicated that the natural frequency decreases with increasing pressure,deteriorating the stability behavior of the compressor. Thus the damperseal, which increases the natural frequency with increasing dischargepressure, ensures a constant high stability of the compressor.

Figure 16. Measured Natural Frequency and Damping.

Figure 17. Modeshapes of the Lowest Bending Modes for theUnloaded and Loaded Compressor.

The shapes of the first bending modes are shown in Figure 17for the unloaded and the loaded compressor. The comparisonbetween both shapes confirms the influence of the damper sealacting on the compressor like an additional bearing.

CALCULATIONS

The accurate determination of the compressor’s stability isnecessary for a correct layout. This implies a profound knowledge ofthe parameters that influence the rotordynamics. In the past a lot ofmeasurements and analyses were carried out on labyrinths and holepattern seals, in seal test rig (albeit often at middle pressure levels) orin compressor test bed (Picardo and Childs, 2004; Childs and Wade,2004; Holt and Childs, 2002; Wagner, et al., 2000; Wyssmann, 1988).The most dominant component affecting the rotor stability is the holepattern seal. An adaptation of the hole pattern parameters wasperformed in order to achieve a good match with the measurements (asexplained in the next sections). According to the scheme, Figure 3,the calculations accounted for the results of the measurements andconsidered all the parameters that could possibly influence the analyses.

FE Calculations

The first parameter to take into consideration is the deformation ofthe casing at operating conditions. Special attention must be paid tothe clearance of the hole pattern that must be kept convergent at alloperating conditions. It is desired to have a convergent (inlet largerthan exit) conical clearance for the hole pattern seals to prevent thestrong negative direct stiffness that occurs in the hole pattern sealwith diverging clearance. Many investigators (Camatti, et al., 2003;Eldridge and Soulas, 2005; Moore, et al., 2006) described a clearancedivergence of the damper seal leading to a rotordynamic instabilityof the compressor. For that purpose finite element (FE) analyseswere carried out considering the operating pressures. Due to largedifferential pressures across the balance piston seal the manufacturedclearances are expected to change in operation. Figure 18 shows thetotal deformation of the casing parts due to pressure only. It turnsout that increasing pressures lead to a growing tendency towarddivergence at the hole pattern seal. Similarly the thermal influencewas analyzed taking into account the thermal distribution in thecasing as shown in Figure 19. Furthermore the reduction of theclearance due to the centrifugal forces of the rotor was considered.All these influences were then adapted at each operating point havingdifferent pressures, temperatures and speed. Hence the slope ofdeformation with respect to pressure and temperature difference isused later to calibrate the predicted hole pattern rotordynamiccoefficients. Figure 20 shows the modification of the clearancedistribution along the hole pattern length between the manufacturedand the operating (high pressure) state.

Figure 18. Total Deformation of the Casing Due to Pressure Loading.

Figure 19. Temperature Distribution in the Casing.


Figure 20. Balance Piston Clearance Distribution.

Labyrinth Seal and Hole Pattern Coefficients

To predict the frequency dependent stiffness and dampingcoefficients the code developed by Kleynhans and Childs (1997)was used. The exact distribution of the clearance along the lengthof the hole pattern was integrated in the code. Thus the clearancedistribution is no longer assumed to be linear. Furthermore thepressure drop inside the piston at this high pressure level isconsiderable and can exceed 300 bar. Therefore the variation of thereal gas properties of the gas (among others the viscosity) along thelength of the seal was included in the analyses.Besides the damping and stiffness coefficients, the code

predicts the amount of leakage through the balance piston. For thiscalculation the friction of the seal and rotor surfaces is modeled viaa Blasius (function of Reynolds number, only) friction factor. Forthe calculation of the leakage (as well as the stiffness and dampingcoefficients of the hole pattern seal) the measured manufacturedclearances were considered and then adapted taking into accountthe calculated deformations in operation. Therefore the calculatedleakage was adapted to the measured values by modifying thefriction coefficients of the stator only.The coefficients of all labyrinth seals were calculated using a

combination of bulk-flow and computational fluid dynamics(CFD) software.

Thrust Analysis

The calculation of the rotordynamic stability takes into accountthe thermodynamic properties of the gas at each labyrinth of thecompressor. To ensure the reliability of the stability analysis as wellas the thrust calculation, the pressure and the swirl of the gas at theentrance of each labyrinth have to be predicted with the highestaccuracy. Therefore these pressures were calibrated on the basis ofthe measured thrusts. The thrust acting on an impeller is brokendown into the momentum force in the impeller eye, the static eyeforce, the shroud force and the hub force and—if applicable—thebalance piston force. The overall thrust of the compressor is thecumulative thrust of all impellers resulting from these four (or five)components. Whereas the values of three components (momentum,static eye and piston) are well defined and fairly accurate, the huband shroud thrusts are difficult to determine because they aredependent on the pressure distributions in the hub and shroud sideroom. Among others these distributions depend on the hub andshroud side room, on the thermodynamic conditions of the gasleakage (viscosity, circumferential speed, and swirl) and on thenature of the leakage (centripetal or centrifugal). The staticpressure distribution must account for the core rotation factor (ratioof the angular gas velocity in the side room to the angular velocityof the disk).

Lüdtke (2004) shows typical measured core factors along thedisk at optimum, overloaded and partloaded flow. He found that thecore factor at the shroud varies approximately 20 percent betweenpart- and overloaded conditions. Unfortunately these measurementswere performed at ambient pressure. At high pressure the densityand viscosity and thus the leakage properties through the secondaryleakage passages change considerably. In the past the pressuredistribution acting on the side room could be determined quiteaccurately by systematic measurements on the stages. In order toachieve a better match with the measurements, some decisiveparameters like entrance swirl and core rotation factor wereoptimized. Figure 21 shows an example of the thrust distributionfor each impeller at three different operating points (near surge,optimum, near choke). What strikes the eye is that the overall thruston the compressor of 35 kN results from the sum of impeller thruststhat reach levels around 500 kN. However it should be mentionedthat a large part of this high thrust on the first stage is due to staticforces: the values of the hub and shroud forces correspond toapproximately 10 percent of the resulting thrust. For the other fourstages the resulting thrust is mainly influenced by the hub andshroud forces. As shown in Figure 21 the stage thrust depends onthe presence of thrust brakes. Therefore it can be stated that with anet thrust of only about 35 kN it is essential that even the smallcontributions are calculated with the highest accuracy. The parameterswere adapted only as function of the position of the operating pointon the performance curve. Table 2 shows a good correlationbetween the calculated thrust and the test measurements.

Figure 21. Thrust on Impellers at Operating Condition.

Table 2. Measured and Calculated Thrust.

Stability

On the basis of the thrust force analyses, the aerodynamic forcesthat act on each labyrinth and the hole pattern seal were calculated.Thereafter, the stability (natural frequencies and damping) wascalculated for each operating point. Figure 22 shows the measureddata together with the analytical prediction. Generally the goodcorrelation of the natural frequency allows the conclusion that the



seal forces in radial direction are calculated with a high level ofreliability. The measured natural frequency shows a higherascending gradient than the prediction. At low discharge pressures(i.e., lower than 100 bar) the frequency is higher than expected,whereas at high discharge pressures the calculated naturalfrequency is approximately 10 Hz higher than the measured value.Regarding the damping ratio, it can clearly be seen that all thepredictions give a conservative result.

Figure 22. Natural Frequency and Damping: Comparison ofMeasurement and Calculation.

To find out if the difference between the prediction and the testresults could be attributed to the assembly and manufacturingtolerance of the seal/cartridge assembly, additional calculationswere carried out with varying clearances and taper values at thehole pattern seal.Figure 23 documents the lowest logarithmic decrement value

for any mode with a whirl frequency below 300 Hz as functionof assumed taper amounts. The figure clearly shows that thecompressor operates in a stable regime at nominal clearances.Taking into account the manufacturing tolerances and all thedeformations listed above, the logarithmic decrement remains constantat this range of high convergent taper values. The considerablemargin between the “seal taper stability threshold” and the actualtaper values demonstrates the robustness of the design.

Figure 23. Sensitivity to Hole Pattern Seal Taper.

Moreover the pressure at the labyrinth inlets was varied in order todetermine the sensitivity to the pressure (resulting from the thrustcalculation). The whole results of the analyses reveal that thevariation of the natural frequency and damping is negligible. Thisallows the conclusion that the stability behavior of the compressor ispractically insensitive to manufacturing tolerances. At this high levelof convergent tapering of the hole pattern seal, the consideration ofthe pressure distribution in the casing for the calculation of thetaper at operating conditions is enough to ensure a satisfactoryprediction of the stability of the compressor.

CONCLUSIONS

The measurement of the first bending frequency, the dampingratio, and the thrust under loaded conditions supports thefollowing conclusions:

• The compressor is well damped (above 100 percent logarithmicdecrement) over the complete tested discharge pressure range up to655 bar (corresponding to 384 kg/m3).

• The first bending frequency rises significantly at a very low pressurelevel and stays nearly constant over the entire operating range.

• The range of the residual axial thrust is well within the thrustcapacity. The level of thrust is strongly dependent on the operatingpoints within the compressor characteristic.

The comparison of predictions versus measurements supportsthe following conclusions:

• The damping is well predicted even though somewhatunderestimated for discharge pressures above 300 bar.

• The first bending frequency is well predicted for dischargepressures above 100 bar.

• A very good correlation between measured and calculated thrustwas achieved. The accurate prediction of thrust is only possible ifthe pressure distribution in the side rooms is correctly determined.

• Due to the high level of damper seal convergent taper, themanufacturing tolerances and the thermodynamic uncertainties arenegligible for the stability prediction of the compressor.

The measured robust compressor behavior as well as the goodquality of the prediction will allow for a further increase of thedischarge pressures with this compressor design.

REFERENCES

API Standard 617, 2003, “Axial and Centrifugal Compressors andExpander-Compressors for Petroleum, Chemical and GasIndustry Services,” Seventh Edition, American PetroleumInstitute, Washington, D.C.

ASME PTC-10, 1997, “Performance Test Code on Compressorsand Exhausters,” American Society of Mechanical Engineers,New York, New York.

Baumann, U., 1999, “Rotordynamic Stability Tests on High-PressureRadial Compressors,” Proceedings of the Twenty-EighthTurbomachinery Symposium, Turbomachinery Laboratory,Texas A&M University, College Station, Texas, pp. 115-122.

Camatti, M., Vannini, G., Fulton, J., and Hopenwasser, F.,2003, “Instability of a High Pressure CompressorEquipped with Honeycomb Seals,” Proceedings of theThirty-Second Turbomachinery Symposium, TurbomachineryLaboratory, Texas A&M University, College Station, Texas,pp. 39-48

Childs, D. W. and Wade, J., 2004, “Rotordynamic-Coefficient andLeakage Characteristics for Hole-Pattern-Stator Annular GasSeals—Measurements Versus Predictions,” ASME Journal ofTribology, 126, pp. 326-333.


Eldridge, T. M. and Soulas, T. A., 2005, “Mechanism and Impact ofDamper Seal Clearance Divergence on the Rotordynamicsof Centrifugal Compressors,” Proceedings of GT2005Symposium, ASME Turbo Expo 2005: Power for Land, Sea andAir, Reno-Tahoe, Nevada.

Fulton, J. W., 1984, “The Decision to Full Load Test a HighPressure Centrifugal Compressor in its Module Prior toTow-Out,” ImechE Second European Congress, FluidMachinery for the Oil, Petrochemical and Related Industries,The Hague, The Netherlands.

Gelin, A., Pugnet, J.-M., Bolusset, D., and Friez, P., 1997,“Experience in Full-Load Testing of Natural Gas CentrifugalCompressors for Rotordynamics Improvements,” ASMEJournal of Engineering for Gas Turbines and Power, 119,pp. 934-941.

Holt, C. G. and Childs, D. W., 2002, “Theory Versus Experimentfor the Rotordynamic Impedances of Two Hole-Pattern-StatorGas Annular Seals,” ASME Journal of Tribology, 124,pp. 137-143.

Kleynhans, G. F. and Childs, D. W., 1997, “The Acoustic Influenceof Cell Depth on the Rotordynamic Characteristics ofSmooth-Rotor/Honeycomb-Stator Annular Gas Seals,” ASMEJournal of Engineering for Gas Turbines and Power, 119,pp. 949-957.

Lüdtke, K. H., 2004, Process Centrifugal Compressors, Basics,Function, Operation, Design, Application, Berlin, Germany:Springer-Verlag.

Memmott, E. A., 1994, “Stability of a High Pressure CentrifugalCompressor Through Application of Shunt Holes and aHoneycomb Labyrinth,” Proceedings of the 13th MachineryDynamics Seminar, Toronto, Canada, CMVA, pp. 211-233.

Memmott, E. A., 1999, “Stability Analysis and Testing of a Train ofCentrifugal Compressors for High Pressure Gas Injection,”ASME Journal of Engineering for Gas Turbines and Power,121, pp. 509-514.

Moore, J. J., Walker, S. T., and Kuzdzal, M. J., 2002,“Rotordynamic Stability Measurement During Full-Load,Full-Pressure Testing of a 6000 PSI Reinjection CentrifugalCompressor,” Proceedings of the Thirty-First TurbomachinerySymposium, Turbomachinery Laboratory, Texas A&MUniversity, College Station, Texas, pp. 29-38.

Moore, J. J., Camatti, M., Smalley, A. J., Vannini, G., and Vermin,L. L., 2006, “Investigation of a Rotordynamic Instability in aHigh Pressure Centrifugal Compressor Due to Damper SealClearance Divergence,” 7th IFToMM-Conference on RotorDynamics, Vienna, Austria.

Picardo, A. and Childs, D. W., 2004, “Rotordynamic Coefficientsfor a Tooth-on-Stator Labyrinth Seal at 70 bar SupplyPressures—Measurements Versus Theory and Comparisons toa Hole Pattern Stator Seal,” Proceedings of GT2004Symposium, ASME Turbo Expo 2004: Power for Land, Sea andAir, Vienna, Austria.

Wagner, N. G., de Jongh, F. M., and Moffat, R., 2000, “Design,Testing and Field Experience of a High-Pressure Natural GasReinjection Compressor,” Proceedings of the Twenty-NinthTurbomachinery Symposium, Turbomachinery Laboratory,Texas A&M University, College Station, Texas, pp. 39-53.

Wyssmann, H. R., 1988, “Rotor Stability of High PressureMultistage Centrifugal Compressors,” ASME Journal ofVibration, Acoustics, Stress and Reliability in Design, 110,pp. 185-192.

Zeidan, F. Y., Perez, R. X., and Stephenson, E. M., 1993, “The Useof Honeycomb Seals in Stabilizing Two CentrifugalCompressors,” Proceedings of the Twenty-Second TurbomachinerySymposium, Turbomachinery Laboratory, Texas A&M University,College Station, Texas, pp. 3-15.

ACKNOWLEDGEMENT

The authors would like to thank all those who made it possibleto carry out these tests. Special thanks are expressed to PDO whoallowed us to modify and test the machine. The authors are alsograteful to Sulzer Innotec for their support in measurement anddata evaluation.




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ROTORDYNAMIC STABILITY OF A 9500 PSI REINJECTION ... · rotordynamic stability problems of the compressors have caused tremendous losses in revenues in the past. In low and medium