Determining Compressor Acceptability

Engineering Encyclopedia Saudi Aramco DeskTop Standards

DETERMINING COMPRESSOR ACCEPTABILITY

Note: The source of the technical material in this volume is the Professional Engineering Development Program (PEDP) of Engineering Services. Warning: The material contained in this document was developed for Saudi Aramco and is intended for the exclusive use o f Saudi Aramco’s employees. employees . Any material contained in this document which is not already in the public p ublic domain may not be copied, reproduced, sold, given, or disclosed to third parties, or otherwise used in whole, or in part, without the written permission of the Vice President, Engineering Services, Saudi Aramco.

Chapter : Mechanical File Reference: MEX-212.04

For additional information on this subject, contact PEDD Coordinator on 874-6556

Engineering Encyclopedia

Compressors Determining Compressor Acceptability

Section

Page

INFORMATION INFORMATION ...................................................... ................................................................................. ...................................................... .............................. ... 4 INTRODUCTION..................... INTRODUCTION................................................ ...................................................... ...................................................... .................................. ....... 4 TEST METHODOLOGIES FOR ACCEPTABILITY OF DYNAMIC AND POSITIVEDISPLACEMENT DISPLACEMENT COMPRESSORS COMPRESSORS .................................................. ........................................................................... ............................. .... 5 Hydrostatic Hydrostatic Test............................................ Test...................................................................... .................................................... .............................. .... 5 Helium Leak Test.................................................................... Test.............................................................................................. .............................. .... 6 Mechanical Mechanical Running Test (Including (Including Rotor Dynamics) Dynamics) ......................................... ......................................... 7 Gas Leakage Leakage Test .................................................. ........................................................................... ............................................ ................... 18 Performance Performance Test ................................................ ......................................................................... ............................................... ...................... 19 String Test Test ................................................. ........................................................................... .................................................... ............................... ..... 21 Post-Test Post-Test Inspection Inspection ................................................... ............................................................................. ........................................ .............. 22 DETERMINING DETERMINING DYNAMIC COMPRESSOR COMPRESSOR ACCEPTABILITY ACCEPTABILITY .................................... .................................... 23 Acceptability Acceptability Criteria Criteria (31-SAMSS-001 (31-SAMSS-001)................................... )........................................................... ............................ .... 26 Calculating Calculating Inlet Inlet Flow Flow ................................................. ........................................................................... ........................................ .............. 26 Polytropic Polytropic Calculations Calculations ................................................ ......................................................................... ....................................... .............. 28 Calculating Calculating Pressure Pressure Ratio from Head .................................................... ............................................................... ........... 30 Calculating Calculating Horsepower Horsepower and Efficiency Efficiency ............................................... .............................................................. ............... 31 Use of Fan Laws to Find the Operating Point at Difference Difference Tip Speeds ................................................ .......................................................................... ........................................ .............. 35 DETERMINING DETERMINING POSITIVE-DISPLACEM POSITIVE-DISPLACEMENT ENT COMPRESSOR ACCEPTABILITY ACCEPTABILITY ....... 38 Acceptability Acceptability Criteria Criteria (31-SAMSS-00 (31-SAMSS-002/31-SAMS 2/31-SAMSS-003).................................... S-003)...................................... 38 Calculating Calculating Capacity................................. Capacity........................................................... .................................................... ................................ ...... 39 Volumetric Volumetric Efficiency..................... Efficiency................................................ ...................................................... ................................ ..... 40 Cylinder Displacement Displacement........................ ................................................. .................................................. ............................ ... 43 Percent Clearance .................................................. ........................................................................... ................................. ........ 44 Calculating Calculating Discharge Discharge Temperature Temperature .................................................... ................................................................... ............... 44 Calculating Calculating Power............................................. Power...................................................................... .................................................. ......................... 45 WORK AIDS.................................................. AIDS............................................................................ .................................................... ...................................... ............ 47

Saudi Aramco DeskTop Standards

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Section

Page

INFORMATION INFORMATION ...................................................... ................................................................................. ...................................................... .............................. ... 4 INTRODUCTION..................... INTRODUCTION................................................ ...................................................... ...................................................... .................................. ....... 4 TEST METHODOLOGIES FOR ACCEPTABILITY OF DYNAMIC AND POSITIVEDISPLACEMENT DISPLACEMENT COMPRESSORS COMPRESSORS .................................................. ........................................................................... ............................. .... 5 Hydrostatic Hydrostatic Test............................................ Test...................................................................... .................................................... .............................. .... 5 Helium Leak Test.................................................................... Test.............................................................................................. .............................. .... 6 Mechanical Mechanical Running Test (Including (Including Rotor Dynamics) Dynamics) ......................................... ......................................... 7 Gas Leakage Leakage Test .................................................. ........................................................................... ............................................ ................... 18 Performance Performance Test ................................................ ......................................................................... ............................................... ...................... 19 String Test Test ................................................. ........................................................................... .................................................... ............................... ..... 21 Post-Test Post-Test Inspection Inspection ................................................... ............................................................................. ........................................ .............. 22 DETERMINING DETERMINING DYNAMIC COMPRESSOR COMPRESSOR ACCEPTABILITY ACCEPTABILITY .................................... .................................... 23 Acceptability Acceptability Criteria Criteria (31-SAMSS-001 (31-SAMSS-001)................................... )........................................................... ............................ .... 26 Calculating Calculating Inlet Inlet Flow Flow ................................................. ........................................................................... ........................................ .............. 26 Polytropic Polytropic Calculations Calculations ................................................ ......................................................................... ....................................... .............. 28 Calculating Calculating Pressure Pressure Ratio from Head .................................................... ............................................................... ........... 30 Calculating Calculating Horsepower Horsepower and Efficiency Efficiency ............................................... .............................................................. ............... 31 Use of Fan Laws to Find the Operating Point at Difference Difference Tip Speeds ................................................ .......................................................................... ........................................ .............. 35 DETERMINING DETERMINING POSITIVE-DISPLACEM POSITIVE-DISPLACEMENT ENT COMPRESSOR ACCEPTABILITY ACCEPTABILITY ....... 38 Acceptability Acceptability Criteria Criteria (31-SAMSS-00 (31-SAMSS-002/31-SAMS 2/31-SAMSS-003).................................... S-003)...................................... 38 Calculating Calculating Capacity................................. Capacity........................................................... .................................................... ................................ ...... 39 Volumetric Volumetric Efficiency..................... Efficiency................................................ ...................................................... ................................ ..... 40 Cylinder Displacement Displacement........................ ................................................. .................................................. ............................ ... 43 Percent Clearance .................................................. ........................................................................... ................................. ........ 44 Calculating Calculating Discharge Discharge Temperature Temperature .................................................... ................................................................... ............... 44 Calculating Calculating Power............................................. Power...................................................................... .................................................. ......................... 45 WORK AIDS.................................................. AIDS............................................................................ .................................................... ...................................... ............ 47


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WORK AID 1: RESOURCES USED TO DETERMINE DYNAMIC COMPRESSOR ACCEPTABILITY ACCEPTABILITY .................................................. ............................................................................ .................................................... .............................. .... 47 Work Aid 1A: Calculation Calculation Procedures............... Procedures....................................... ................................................ .......................... 47 Work Aid 1B: Pertinent Pertinent Data......................... Data .................................................. ................................................... ............................ .. 52 Nomenclature Nomenclature ................................................ .......................................................................... .......................................... ................ 52 Charts for Determining Determining Compressor Compressor Performance Performance Characteristics Characteristics .......... 53 WORK AID 2: RESOURCES USED TO DETERMINE POSITIVE-DISPLACEMENT COMPRESSOR COMPRESSOR ACCEPTABILITY ACCEPTABILITY......................... ................................................... ..................................................... ............................. .. 55 Work Aid 2A: Calculation Calculation Procedures............................................................. Procedures................................................................ ... 55 Work Aid 2B: Pertinent Pertinent Data......................... Data .................................................. ................................................... ............................ .. 58 Nomenclature Nomenclature ................................................ .......................................................................... .......................................... ................ 58 GLOSSARY GLOSSARY .................................................... .............................................................................. .................................................... .................................... .......... 60


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LIST OF FIGURES

Figure 1. Typical Rotor Response Plot......................................................................... 12 Figure 2. Typical, Multi-Stage, Centrifugal Compressor Characteristic Curve.............. 24 Figure 3. Typical Axial Compressor Characteristic Curve ............................................ 25 Figure 4. Adiabatic Versus Polytropic Process............................................................. 34 Figure 5. Head Curve................................................................................................... 37 Figure 6. Horsepower Curve ........................................................................................ 37 Figure 8. Compressibility Factors at Low Reduced Pressure....................................... 54 Figure 9. Loss Correction Factor for Reciprocating Compressor ................................. 59

LIST OF TABLES

Table 1. Critical Constants of Gases............................................................................ 53


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INFORMATION INTRODUCTION Gas compressor inspection and testing for acceptability are performed as indicated on the compressor data sheets and the referenced Saudi Aramco Form 175 based on the compressor type and the associated auxiliary equipment. The inspection requirements for gas compressors will vary with the compressor type and application. The Engineer must become familiar with the requirements and criteria used for the acceptance of a gas compressor. This module provides background information on the testing and the inspection requirements, the methods, and the Gas compressor inspection and testing for acceptability criteria for dynamic and positive-displacement compressors.


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TEST METHODOLOGIES FOR ACCEPTABILITY OF DYNAMIC AND POSITIVE-DISPLACEMENT COMPRESSORS All compressor inspections and tests are to be within the guidelines and conditions that are set forth in the applicable Saudi Aramco Engineering Standard (SAES-K-402 for centrifugal compressors and SAES-K-403 for reciprocating compressors). These tests and inspections include the following:

• Hydrostatic Test • Helium Leak Test • Mechanical Running Test • Gas Leakage Test • Performance Test • String Test • Post-Test Inspection Before the above tests are conducted, a visual inspection of the compressor is performed in accordance with the applicable Saudi Aramco Engineering Standards and API Standards for the compressor to be tested.

Hydrostatic Test Hydrostatic tests are performed by the vendor, and they do not require visual inspection or witnessing by a Saudi Aramco representative. The vendor is required to provide Saudi Aramco with certificates and data for the hydrostatic test results for evaluation. Pressure-containing parts (including auxiliaries) must be hydrostatically tested with liquid at a minimum of 1-1/2 (150%) times the maximum allowable working pressure but at not less than 20 psig for all components of a reciprocating compressor. The only exceptions to the minimum hydrostatic test pressure are the cylinder cooling jackets and packing cases, which have a minimum pressure of 115 psig. The test liquid must be at a higher temperature than the nil-ductility transition temperature of


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the material that is being tested. The tests must be maintained for a sufficient period to allow a complete examination of the parts that are under pressure. The hydrostatic test will be considered satisfactory when neither leaks nor seepage through the casing or casing joint is observed for a minimum of 30 minutes. Large, heavy castings may require a longer testing period. For example, SAES-K-403 (for reciprocating compressors) requires that test pressure for critical items, such as large cast cylinders, must be maintained for four hours. Seepage past internal closures that are required for testing of segmented cases and the operation of a test pump to maintain pressure are acceptable. The chloride content of the liquids that are used to test austenitic stainless steel materials in centrifugal compressors must not exceed 50 parts per million. To prevent the deposition of chlorides that is caused by evaporative drying, all residual liquid must be removed from the tested parts at the conclusion of the test. If the part to be tested is to operate at a temperature at which the strength of a material is below the strength of that material at room temperature, the hydrostatic test pressure will be multiplied by a factor. The factor is obtained through division of the allowable working stress for the material at room temperature by the allowable working stress for the material at operating temperatures. The stress values that are used will conform to those values that are given in ASME B31.3 for piping. For compressor casings and pressure vessels, the stress values must conform to those values that are given in Section VIII, Division 1 or 2, as applicable, of the ASME Code. The pressure that is obtained will then be the minimum pressure at which the hydrostatic test must be performed. The data sheets must list the actual hydrostatic test pressures.

Helium Leak Test Helium leak tests are performed by the vendor on rotary and centrifugal compressors that are used for hydrogen service. The helium leak test must be witnessed by a Saudi Aramco representative. Test documentation and data must be submitted to Saudi Aramco for review. SAES-K-402 requires a helium leak test to be performed on the compressor casing of any centrifugal compressor that is in hydrogen service. API


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Standard 618 (for reciprocating compressors) requires a helium leak test to be performed on all pressure-retaining parts, such as cylinders and volume pockets, for all compressors that handle gases with a molecular weight of 12 or less, or for gases that contain more than 0.1 mol percent hydrogen sulfide. The helium leak test is to be performed after the hydrostatic test. The compressor casing for centrifugal compressors and the pressure-retaining parts for reciprocating compressors are tested for gas leakage with helium at the maximum allowable working pressure. The test can be conducted in the following two ways: The casing or pressure-retaining parts are pressurized with helium to the maximum allowable working pressure. The components are then submerged in water. The maximum allowable working pressure must be maintained for a minimum of 30 minutes; no bubbles are permitted (zero leakage). The casing or pressure-retaining parts are pressurized with helium to the maximum allowable working pressure. The pressure is maintained for a minimum of 30 minutes. A nonsubmerged soap-bubble test is performed on the casing of a centrifugal compressor. Leak detection is accomplished through use of a helium probe for the pressure-retaining parts of a reciprocating compressor. Zero leakage is required.

Mechanical Running Test (Including Rotor Dynamics) The following discussion of test methods and requirements is derived from applicable sections of API Standard 617 and API Standard 618. Test procedures and acceptance criteria will be based on the applicable API standard for centrifugal compressors (API Standard 617) and reciprocating compressors (API Standard 618) and must be mutually agreed upon by the vendor, the buyer, and the Saudi Aramco Engineer. A mechanical running test is an operational test of the compressor that is conducted at the vendor’s facilities. The mechanical running test must be of four hours in duration for both centrifugal and reciprocating compressors. The four-hour mechanical running test allows compressor components, such as bearings and rotors, to become thermally stable. SAES-K403 requires that a mechanical running test must be performed on all reciprocating compressors and that this test must be witnessed for reciprocating process gas compressors. SAES-KSaudi Aramco DeskTop Standards

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402 requires that a mechanical running test must be performed and witnessed on all centrifugal compressors. When a spare rotor is purchased, the rotor must be installed and run in a separate test prior to the job rotor test. For reciprocating compressors, the mechanical running test proves the mechanical operation of all of the auxiliary equipment as well as the compressor, reduction gears (if applicable), and the driver. The compressor does not have to be pressure-loaded for this test. The test is not acceptable if any repair or replacement is required to correct mechanical or performance deficiencies that are identified during the mechanical running test. The test must be rerun after the repairs or corrections are completed. For centrifugal compressors, the following requirements must be satisfied prior to the performance of the mechanical running test:

• The shaft seals and bearings that were specified with the compressor must be installed and used in the machine for the mechanical running test.

• The oil pressures, the oil viscosities, and the oil temperatures must be at the same operating values as the operating values that are recommended in the manufacturer’s operating instructions for the specific unit under test. The oil filtration must be ten microns nominal or better.

• All joints and connections must be checked for tightness. Any leaks must be corrected prior to the mechanical running test.

• Facilities must be installed to prevent the entrance of oil into the compressor during the test. These facilities must be in operation throughout the test.

• All warning, protection, and control devices must be calibrated to the their alarm, shutdown, or relief set points.

• Any auxiliary gear units that are supplied with the compressor must be included in the mechanical running test. The mechanical test should include the coupling that is to be installed on the compressor. If the inclusion of the job coupling is not practical, the mechanical running test must be performed with coupling-hub moment simulators in place. When all of the tests are complete, the moment simulators


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must be furnished as part of the special tools for the compressor.

• The radial vibration and axial position transducer sensors, signal conditioners, and connecting cables that are to be supplied with the compressor must be used in the test. If the vendor does not furnish the vibration monitoring equipment or if the equipment is not compatible with the test shop readout equipment, shop equipment and readouts that meet the accuracy and calibration requirements of the applicable API Standard must be used. The compressor should be started and operated at speed increments of approximately 10% from zero to the maximum continuous speed. The compressor is run at the maximum continuous speed until the bearing and lube oil temperatures and the shaft vibrations have stabilized. Once the bearing and lube oil temperatures and the shaft vibrations have stabilized, the speed is increased to the trip speed, and the compressor is operated for a minimum of 15 minutes. After 15 minutes, the speed of the compressor is adjusted to the maximum continuous speed, and the equipment is run for a minimum duration of the test (four hours) at the maximum continuous speed. The mechanical operation of all equipment being tested and the operation of the test instrumentation must be satisfactory during the test. During the four-hour test, radial shaft vibration, bearing pad temperature, lubrication supply, and return temperatures and flow must be measured. The inner seal-oil leakage rate must be measured at each seal. The lube oil and seal oil inlet pressures and temperatures should be varied through the range that is permitted by the compressor’s operating manual. Processed from unfiltered transducer output signals, measurements of radial shaft vibration and axial position must be recorded, and they must not exceed the applicable vibration limits throughout the test. While the mechanical test is being conducted, vibration sweep readings must be recorded for vibration amplitudes at frequencies other than synchronous. As a minimum, these sweep readings must cover a frequency range from 0.25 to 8 times the maximum continuous speed, but they must not exceed 90,000 cycles per minute (1500 Hertz). Polar plots that show the synchronous vibration amplitude (in terms of radial shaft vibration), phase angle, and phase shift versus rotational speed must be made before and after the four-


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hour test. The speed range that is covered by the plots must be from zero to the specified driver trip speed. The critical speeds of the compressor must be verified during the mechanical running test. Taped recordings of all real-time vibration data should be made during the mechanical running test. These recordings provide the initial data for vibration analysis. An inspection that includes the dismantling, the inspection, and the reassembly of the compressor, the gear, and the driver must be made after satisfactory completion of the mechanical running test. A bearing inspection must be completed. All bearings must be removed, inspected, and reassembled after completion of the mechanical running test. Shaft seals should be removed for inspection. If minor scuffs or scratches occur on bearings or on shaft seal surfaces, minor cosmetic repairs are not a cause for rerunning the test. The rotor dynamics of a compressor include the following different areas and considerations:

• The performance of a lateral analysis. • The performance of a torsional analysis. • The performance of assembly vibration testing and balancing. When an exciting frequency is applied to a rotor-bearing support system that corresponds to the natural frequency of the rotorbearing support system, the system may be in a state of resonance. A resonating rotor-bearing support system will have its normal vibration displacement amplified. The magnitude of amplification and the rate of phase shift (phase-angle change) are related to the amount of damping in the rotor-bearing support system and the mode shape that is taken by the rotor as it deflects. The mode shapes for deflection are commonly referred to as the first rigid (translatory or bouncing) mode, the second rigid (conical or rocking) mode, the first bending mode, the second bending mode, and the third bending mode. An exciting frequency may be less than, equal to, or greater than the rotational speed of the rotor. The following are some of the sources of exciting frequencies that must be considered:

• Unbalance in the rotor system.


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• Oil-film instabilities (whirl). • Internal rubs. • Blade, vane, nozzle, and diffuser passing frequencies. • Gear-tooth meshing and side bands. • Coupling misalignment. • Loose rotor-system components. • Friction whirl. • Boundary-layer flow separation. • Acoustic and aerodynamic cross-coupling forces. • Asynchronous whirl. The magnitude of the amplification is called the rotor amplification factor. The rotor amplification factor (AF) is determined through use of the following formula and the bode plot that is shown in Figure 1: AF =

Nc1 N2

− N1

The bode plot is a graph of amplitude versus the rotor speed (in revolutions per minute) and phase (between the shaft reference mark and peak vibration) versus rotor speed (in revolutions per minute. The polar plot is a graph of amplitude versus phase for a range of compressor speeds Figure 1 represents an actual centrifugal compressor rotor response. The specific points of interest on the bode and polar plots are identified. A rotor response plot provides the following information:

• The rotor’s first critical speed in revolutions per minute (N c1). • The rotor’s initial (or lesser) speed (N 1). The initial speed occurs at the first peak-to-peak amplitude that is equal to 0.707 times the peak-to-peak amplitude at the critical speed (Ac1).

• The rotor’s final or greater rotational speed (N 2) occurs after the displacement at the first critical speed. The value of peak-to-peak displacement at N 2 is equal to 0.707 of peakto-peak displacement at N 1.

• The peak-to-peak amplitude (A c1) at the rotor’s first critical speed (Nc1).


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Figure 1. Typical Rotor Response Plot


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If the rotor amplification factor is greater than or equal to 2.5, the vibration frequency at which resonance occurs is called critical. The rotational speed at which the resonance occurred is called a critical speed. A critically damped system is a system that has an amplification factor of less than 2.5. Critical speeds for compressors must be determined analytically through use of a damped, unbalanced, rotor response analysis, which must be confirmed by test-stand data. Resonances that occur within the specified operating speed range of the compressor must be critically damped. Any operating speed that should be avoided as a critical speed must be included in the operating and maintenance instructions for the compressor. The critical speeds of the driver must be compatible with the critical speeds of the compressor, and the combination must be suitable for the operating speed range. It is the vendor’s responsibility to provide a damped, unbalanced-response, lateral analysis for the compressor in order to ensure acceptable amplitudes of vibration at any speed from zero to trip. The effects of other equipment in the train should be included in the damped, unbalanced-response analysis. The following considerations should be included in the damped, unbalanced-response analysis:

• Support stiffness (base, frame, and bearing housing), mass, and damping characteristics. These characteristics must include the effects of rotational speed variations.

• Bearing lubricant-film stiffness and any damping changes that are due to speed, load, preload, oil temperatures, accumulated assembly tolerances, and maximum to minimum bearing clearances.

• Rotational speeds (starting speeds, operating speed and load ranges, trip speed, and coast-down speeds). (Any special speeds, such as test condition speeds, should also be included.)

• Rotor masses, which include the mass moment, the stiffness, and the damping effects of the coupling halves. (Examples of the damping effects are accumulated fit tolerances, fluid stiffening and damping, and frame and casing effects.)

• Asymmetrical loading. (Examples of asymmetrical loading are partial arc admission, gear forces, side streams, and eccentric clearances.) Saudi Aramco DeskTop Standards

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As a minimum, the damped, unbalanced-response analysis must include the following:

• A plot and identification of the mode shape at each resonant speed (critically damped or not) from zero to trip. The next mode that occurs above the trip speed must also be included in the plot.

• The frequency, phase, and response amplitude data that were based on measurements processed from the vibration probe locations over the range of each critical speed.

• For each response, diagrams that indicate the phase and the major-axis amplitude at each coupling engagement plane, the centerlines of the bearings, the locations of the vibration probes, and each seal area throughout the machine. The minimum design diametral running clearance of the seals must also be indicated.

• An additional plot of the unbalance and location (usually the coupling) that will be used for shop testing. This additional, unbalanced-response plot must include the effects of any test stand conditions or test seals that may be used to perform the shop verification test.

• A stiffness map of the undamped rotor response from which the damped unbalanced response analysis was derived. This plot should show frequency versus support system stiffness. The calculated support system stiffness curves are superimposed. The damped unbalanced response analysis must indicate that the compressor, in the unbalanced condition, will meet the following acceptance criteria:

• If the amplification factor is less than 2.5, the response is considered critically damped, and no separation margin is required.

• If the amplification factor is between 2.5 and 3.55, a separation margin of 15% above the maximum continuous speed and 5% below the minimum operating speed is required.

• If the amplification factor is greater than 3.55 and if the critical response peak is below the minimum operating speed, the required separation margin as a percentage of


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minimum speed is determined by the following equation:

 

SM = 100 −  84 +

  AF − 3  6

Where: SM = Separation Margin AF = Amplification Factor

• If the amplification factor is greater than 3.55 and if the critical response peak is above the trip speed, the required separation margin, as a percentage of maximum continuous speed, is determined by the following equation:

 

SM =  126 −

 − 100  AF − 3  6

Where: SM = Separation Margin AF = Amplification Factor A shop verification of the unbalanced-response analysis must be performed. The actual responses are the criteria used to confirm the validity of the damped unbalanced response analysis. The shop verification is performed on a test stand with a rotor unbalanced magnitude of at least two times and no more than eight times the specific unbalanced limit, typically placed at the coupling. The actual critical speed responses are recorded on the test stand. The dynamic response of the machine on the test stand is a function of the test conditions. The test results should be obtained at the conditions of pressure, temperature, speed, and load that are the expected in the field; otherwise, the test stand results may not be comparable with what occurs during actual operation in the field. The performance of a torsional analysis includes a determination of the excitations of torsional resonances of the compressor. Excitations of torsional resonances should be considered in the dynamics analysis. These excitations may be produced from any of the following partial list of sources:

• Gear problems, such as unbalanced gears and pitch line runout. Saudi Aramco DeskTop Standards

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• Gas pressure forces or unbalanced mass in connecting rod of reciprocating compressors.

• Start-up conditions that include speed detents that are under the inertial impedances as well as other torsional oscillations.

• Torsional transient, such as startups of synchronous and/or variable frequency electric motors. Any greater torsional resonances, including the natural frequencies, that are a product of the complete train must be at least 10% above or 10% below any possible excitation frequency that exists within the speed range of minimum to maximum continuous speed. Torsional resonances are called torsional criticals if they occur at frequencies that are twice the compressor’s running speeds or greater, and they should be avoided. If the compressor’s torsional resonances are calculated to be a multiple of the running speed and if all efforts to remove the critical from within the limiting frequency range have been exhausted, a stress analysis must be performed to demonstrate that the resonances have no adverse effect on the complete compressor train. The major components of the rotating element of a compressor (the shaft, balancing drum, and impellers) must be vibrationtested and dynamically-balanced. When a bare shaft with a single keyway is dynamically-balanced, the keyway must be filled with a fully crowned half-key for an initial balance. This initial balance correction to the shaft must be recorded. The rotating element (rotor) must be multi-plane, dynamically balanced during the assembly of the compressor. Two of the major components that make up the rotating element may be added to the rotating element prior to completion of the dynamic balancing. Any corrections that must be made to the rotating element to correct an unbalance condition must be applied to the components that were added to the rotating element. After the compressor is completely assembled, minor corrections of other components that were added to the assembly may be required. These minor corrections will be determined during the final trim balancing of the completely assembled element. Residual unbalance is the amount of unbalance that remains in a rotor after the rotor has been balanced. For dynamic compressors, API Standard 617, Appendix D provides the


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specific procedures and calculations for determining the residual unbalance of a dynamic compressor. The following equation is used to calculate the maximum allowable residual unbalance per plane for a compressor: Umax = 4W/N Where: Umax =

Amount of residual unbalance, in ounce-inches (gram-millimeters).

W

=

The journal static weight load, in pounds (kilograms).

N

=

The maximum continuous speed, in revolutions per minute.

After the balancing machine readings indicate that the rotor has been balanced to within the specified tolerances, a residual unbalance check should be performed before the rotor is removed from the machine. To perform a residual unbalance check (multiplane balancing), a known trial weight is attached to one of the balance planes of the rotor, and a balance check is performed. The weight is moved around the rotor in six or twelve equal increments and a balance check is performed. The trial weight is moved to the next balance plane, and the test is repeated until all of the balance planes have been tested. The balance check readings are plotted on a polar plot, and the amount of residual unbalance is calculated. If the specified maximum allowable residual unbalance has been exceeded in any balance plane, the rotor must be balanced more precisely, and the residual-unbalance check must be repeated. The peak-to-peak amplitude of unfiltered vibration in any specific plane is tested during the testing of the balanced rotor. With a balanced rotor operating at its maximum continuous speed, the peak-to-peak amplitude of unfiltered vibration that is measured on the shaft adjacent and relative to each radial bearing must not exceed its calculated limitation or 2.0 mils (50 micrometers) on any plane, whichever is less. The peak-to-peak amplitude of unfiltered vibration limitation is calculated through use of the following formula (for U.S. customary units): A =

12,000 N

Where:


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A

=

N

=

The amplitude of unfiltered vibration, in mils (micrometers) peak-to-peak.

The maximum continuous speed, in revolutions per minute. For any speed that is greater than the maximum continuous speed, the vibration limit is a comparison to the maximum vibration value that is recorded at the maximum continuous speed. The vibration for any speed that is greater than the maximum continuous speed must not exceed 150% of the vibration value that is recorded at the maximum continuous speed. If the vendor can demonstrate that electrical runout or mechanical runout is present in the rotor system, a maximum of 25% of the peak-to-peak amplitude of unfiltered vibration that was calculated from the above formula or 0.25 mil (6.4 micrometers), whichever is greater, may be subtracted from the vibration signal that is measured during the factory testing. The electrical and mechanical runout are determined by rotation of the rotor in V-blocks at the journal centerline while measuring the runout. The runout measurement is measured with a noncontact proximity probe (for electrical runout) and with a dial indicator (for mechanical runout). The runout measurement is taken for the full 360 degrees of rotation. The noncontact proximity probe is located at the normal probe location, and the dial indicator is located one probe tip diameter on either side of the noncontact proximity probe. The electrical runout and mechanical runout readings are recorded. The electrical runout and mechanical runout readings must be supplied by the vendor in the mechanical test report.

Gas Leakage Test After the mechanical running test is completed, each completely assembled, centrifugal compressor casing that is intended for toxic or flammable gas service must have a gas leakage test as specified in API 617. The gas leakage test must be witnessed. The requirements of API 617 may require two separate tests as described in the following text to accomplish the gas leakage test. The casing (including the end seals) is pressurized with an inert


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gas to the maximum sealing pressure or the maximum seal design pressure. The test is considered satisfactory when no casing or casing-joint leaks are observed or detected. When specified, the casing (with or without the end seals installed) is pressurized to the rated discharge pressure and is held at this pressure for a minimum of 30 minutes. After 30 minutes, a soap-bubble test (or another approved test) is performed to check for gas leaks. The test is considered satisfactory when no casing or casing-joint leaks are observed or detected.

Performance Test In accordance with SAES-K-402 for centrifugal compressors, as a minimum, a performance test must be specified and witnessed for each centrifugal compressor duty. For a series of identical units, only one unit needs to be performance tested. Tests must be in accordance with ASME Power Test Code 101965 (compressors and exhausters), Class I, II, or III. Tests must be to Class III specifications unless otherwise specified. Class I or Class II tests must be considered for medium to high discharge pressures (500 psia) where rotor instability that is due to high gas densities could be encountered or where compressors are located on an offshore platform. In these circumstances, Saudi Aramco’s Engineer must be consulted concerning advisability of Class I or II full load, full pressure tests. The extra costs of such tests, as compared to a Class III test, must be weighed against the cost (and delay) to correct any malperformance after the compressors are installed. ASME Power Test Code (PTC10-1965) has defined the following three classes of performance tests:

• Class I, which is a test run on the design gas at near design conditions. This test generally applies to air compressors.

• Class II, which covers tests when using the design gas is not practical. Both test and design gas must closely follow perfect gas laws.

• Class III, which is similar to test 2 in that a different gas is used for the test; however, in this test, the gas does not follow the perfect gas law.


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When a performance test is conducted through use of a substitute gas, the test must be performed at an equivalent speed. In accordance with ASME PTC-10, when operating at the equivalent speed, the test parameters must agree with the corresponding field parameters. ASME PTC-10 includes the required tables, the procedures, and the calculations that are necessary to determine the equivalent speed and to correct the test results to actual field conditions. A minimum of five points that include surge and overload must be taken at normal speed. For variable-speed machines, additional points may be specified. Head and capacity should have zero negative tolerance at the normal operating point (or other points as specified). The horsepower at this point should not exceed 104% of the specified value. The compressor test must show that the compressor is suitable for continuous operation at any capacity at least 10% greater than the predicted approximate surge capacity that is designated on the data sheets. For constant-speed compressors, the head should be within the range of 100% to 105% of the normal head. The horsepower will be based on the required normal head and capacity. Unless otherwise specified, the performance test should be conducted through use of only one contract rotor. Field test procedures should be in accordance with ASME PTC10-1965, Compressors and Exhausters, within practical limits. Tests should not be conducted until it is certain that the compressor has reached equilibrium, with all parameters as close as possible to those parameters that are anticipated in actual service. All pressure and temperature instrumentation must be properly calibrated. The ASME code provides guidelines for instrumentation of the external flanges of the compressor and the flow measuring sections. This instrumentation will provide adequate readings at the compressor flanges and flowmeasuring devices. Temperatures should be measured through use of a thermocouple or an RTD system. The sensitivity and readability of the temperature measuring device should be .5 °F and should have an accuracy within 1 °F. Pressure readings during testing should be at approximately mid scale. The pressure gage sensitivity should be about .25% with a .5%


20



maximum error of full scale when reading pressures that are greater than 20 psig. When pressures are less than 20 psig, a vertical manometer should be used unless disallowed for safety reasons. A gas sample sample should should be taken taken at the top of the suction and and the discharge of the compressor at the beginning and the end of the test. To avoid condensation in the sample, the gas sample must be analyzed at a temperature that is equal to or greater than the expected field conditions. The gas sample should be analyzed by a gas chromatograph. The equipment speed should be determined through use of two independent phase reference transducers. Mass flow rates are measured through use of the process flow indicator but should be verified through calculations; therefore, metering device upstream temperature, upstream pressure, and differential pressure must also be recorded. If field tests are conducted to confirm that the guaranteed conditions on new equipment are met, the acceptance tolerances are the same as noted for the performance tests. When field tests are conducted on existing equipment to determine whether inspection is required, a reduction of polytropic head and/or efficiency of 10% or greater from the performance test results (at rated flow) is a sound basis for recommending internal compressor inspection.

String Test As specified specified in SAES-K-4 SAES-K-402, 02, a string string test is used for long equipment trains, for off-shore installations, and in situations where early detection of equipment malfunction is necessary. The following system components are tested as a unit:

• • • •

Driver Gear Compressor(s) Oil Systems (Lube Oil and Seal Oil Systems)

String tests require prior agreement by Saudi Aramco’s Engineer, and they must be witnessed. String tests are performed in addition to separate tests of individual components. Torsional vibration measurements are to be performed to verify data sheets.


21



Post-Test Inspection In accordance with SAES-K-402 for centrifugal compressors, all bearings and seals (except labyrinth types) must be removed and inspected after the completion of the mechanical running test. Additional dismantling, inspection, and re-assembly of the compressor should be considered an optional extra for application only in special circumstances. The merits of a posttest inspection of the casing internal should be evaluated against the benefits of shipping a unit with proven mechanical assembly and casing joint integrity. In accordance with SAES-K-403 for reciprocating compressors, dismantling of the compressor after the mechanical running test should be requested only on a compressor that is not of a proven design. This dismantling and inspection is other than any dismantling and inspection that is required by evidence of a malfunction during the mechanical running test.


22



DETERMINING DYNAMIC COMPRESSOR ACCEPTABILITY ACCEPTABILITY When determining a dynamic compressor’s acceptability, several characteristics of the compressor must be considered. The relationships between the inlet volume flow, head, speed, efficiency, and power of a dynamic compressor are often referred to as the compressor’s characteristics. The actual compressor characteristics are compared to the compressor’s vendor-guaranteed characteristics. The compressor must perform within the specified tolerances of the guaranteed characteristics. Figure 2 is a typical multi-stage centrifugal compressor characteristic curve. The curve is a plot of the inlet volume in percent versus the head in percent and the horsepower in percent. Speed and efficiency lines are plotted on the curve to provide the compressor’s characteristics. The speed that is shown on the curve ranges from 70% to 110%. The efficiency that is shown on the curve ranges from 83% to 100% of the peak efficiency, with the approximate surge line drawn in at a low volume and efficiency. As an example, example, if a compressor compressor has a rated efficiency efficiency of of 75%, the efficiency will be 75% of the 100% line and 62.25% on the 83% line.


23



Figure 2. Typical, Multi-Stage, Centrifugal Compressor Characteristic Curve


24



Figure 3 is a typical axial compressor characteristic curve. The curve is a plot of the design volume in percent versus the design compression ratio in percent. Speed and efficiency lines are plotted on the curve to provide the compressor’s characteristics. The speed that is shown on the curve ranges from 75% to 105%. The efficiency that is shown on the curve ranges from 80% to a maximum efficiency of 100% of peak efficiency.

Figure 3. Typical Axial Compressor Characteristic Curve

Once the decision has been made as to which type of compressor is to be used in a given application, each compressor is tested against its vendor-guaranteed characteristics to determine compressor acceptability. This remainder of this section of the Module will examine the following areas that Saudi Aramco Engineers must consider when determining the acceptance of dynamic compressors:

• • • • • •

Acceptability Criteria (31-SAMSS-001) Calculating Inlet Flow Volume Polytropic Calculations Calculating Pressure Ratio from Head Calculating Horsepower and Efficiency Use of Fan Laws to Find Operating Point at Different Speeds


25



Acceptability Criteria (31-SAMSS-001) The following account is cited from 31-SAMSS-001 (for centrifugal compressors), which adopts and specifies exceptions to API Standard 617. Centrifugal compressor systems must be supplied by vendors who are qualified by experience in manufacturing the proposed units. To qualify, the vendor must have manufactured, at the proposed location of manufacture, at least two compressors of comparable speed, power rating, and discharge pressure for a gas of comparable characteristics. These compressors must have been in operation for at least one year, and they must be performing satisfactorily.

Calculating Inlet Flow The performance curves that are supplied by the manufacturer and the machine’s performance are usually based on the actual volume flow at the suction of the compressor. The calculations to determine these performance curves have been discussed in the Volumetric Flow and Mollier Method sections of Module 212.02. It is important that the Mechanical Engineer understand that the process data are usually given in SCFM or lb./hr and that the process data must be converted to ACFM in order to determine compressor performance. For the purpose of performance calculations, compressor capacity is expressed as the actual volumetric quantity of a gas at the inlet to each stage of compression on a per minute basis (ICFM). All centrifugal compressors are based on actual flow, which is converted to inlet or actual cubic feet per minute. This conversion is done because a dynamic compressor’s (axial and centrifugal) produced head is a function of inlet gas velocity. The inlet velocity is derived by the division of volume flow by blade area. The following equation is used to determine inlet flow (Q1) in actual or inlet cubic feet per minute (ICFM) if the inlet flow is known in standard cubic feet per minute (SCFM): 14.7 T ICFM = SCFM× × 1 ×Z1 P1 520°R Where: P1 = Inlet pressure (psia)


26



T1 = Inlet temperature ( °R) (°R = °F = 460) Z1 = Inlet compressibility factor The following example will determine the actual ICFM of a compressor that has suction of 60,000 SCFM at an inlet pressure (P1) of 100 psia, an inlet temperature (T 1) of 100°F, and an inlet compressibility factor (Z 1) of 1.0. 14.7 T ICFM = SCFM× × 1 ×Z1 P1 520°R

= 60,000×

14.7

×

560°R

100psia 520°R

×1.0

= 60,000×.147×1.08×1.0 = 9525 ft 3 /min The following equation is used to determine inlet flow (Q 1) in actual or inlet cubic feet per minute (ICFM) if the inlet flow is known in weight flow (mass flow) in lb/min: ICFM =

W ρ

Where: w = Mass flow (lb./min)

ρ = Density (lb./ft 3) The following equation is used to determine density ( ρ): ρ =

2.7 x

MW 28.95

x

P1 T1 x Z1

Where:


MW =

Molecular weight

P1

Inlet pressure (psia)

=

27



T1

=

Inlet temperature ( °R) (°R = °F = 460)

Z1

=

Inlet compressibility factor

The following example will determine the actual ICFM of a compressor that has weight flow ( ω) of 3600 lb./min at an inlet pressure (P 1) of 100 psia, an inlet temperature (T1) of 100°F, a molecular weight (MW) of five, and a compressibility factor (Z 1) of 0.98. ρ

= 2.7 ×

= 2.7 ×

MW 28.95

×

P1 T1 × Z1

5 100 × 28.95 560 × 0.98

= 2.7 × 0.172 × 0.182 = 0.085 Q=

=

ϖ

p 3600 lb/min 0.085 lb/ft 3

= 42,353 ft 3 /min Polytropic Calculations The actual compression path does not follow any reversible process (isothermal, isentropic, or polytropic). The actual compression path is most closely approximated by the polytropic process in which PVn = a constant. In such cases, polytropic calculations must be used. The polytropic head is obtained through use of the following equation:

 P2 (n−1)/n  Polytropic Head= − 1  MW (n − 1)/n  P1  Zavg Runiv T1


28



Where: T1

=

Inlet temperature

P1

=

Inlet pressure

P2

=

Discharge pressure

n

=

Polytropic exponent

MW =

Molecular weight

Zavg =

Average compressibility factor

Runiv =

Universal gas constant (1545.32 ft-lbf/lbm-Mol°R)

The polytropic exponent ( η) factor may be found from the equation: n −1

k − 1  1 =    n  k  ηP

Where: k

=

Isentropic exponent

ηP =

Polytropic efficiency

Also, the relationship between discharge pressure and temperature for an ideal gas polytropic process is useful during field testing when polytropic efficiency is not known. This relationship can be stated as the following equation:

 P2  (n−1)/n =  T1  P1 

T2

Where: T2 =

Discharge temperature

This equation can be rewritten as follows:


29



 T2   T n −1 =  1  n  P  Ln 2   P1  Ln

For real gases, n can be found from the following relationship:

 ρ2   ρ n =  1   ρ  ln 2   ρ1  ln

Where: ρ 1

= Inlet density

ρ 2

= Outlet density

Calculating Pressure Ratio from Head The primary variable in calculating head required is pressure, P 2 and P1. The plot of pressure ratio versus flow rate will be similar to head versus flow rate. Pressure ratio is calculated through use of the following equation: r P

=

P2 P1

Where: r P

=

Pressure ratio

P1 =

Inlet pressure

P2 =

Discharge pressure

The pressure ratio can be calculated from the head through use of the following equation:

r P


 H xMW  n − 1    =  p  + 1  Z R T n  avg univ 1   

n n −1

30



Where: Hp

=

Polytropic head

MW =

Molecular weight

Zavg =


Runiv =

Universal gas constant

T1

Inlet temperature

=

n = Polytropic exponent For the same compressor that is operating at the same flow and speed, r P will change if MW, Z, η-1/η, or η/η-1 changes.

Calculating Horsepower and Efficiency The efficiency of a thermodynamic system is stated as the ratio of the work output of the system (head) to the work input to the system (shaft power). The difference between head and work is the amount of losses that are internal to the machine due to such conditions as friction and windage. These losses show up as heat, and they add to the discharge temperature. These losses include losses that are external and internal to the main flow path. Losses that are external to the main flow path include losses such as windage losses, disk friction losses, and leakage losses. Losses that are internal to the main flowpath are actual losses of blade input energy, and they include the following:

• Skin friction • Blade loading and diffusion • Incidence angle • Exit mixing losses • Clearance losses Horsepower is the rate of doing work. If a compressor is lifting a weight of gas to a given head (H) at a specific rate (M), horsepower would be calculated as follows:


31



GHP =

HxM ηx 33,000

Where: GHP = Gas horsepower H

= Head (ft-lbf/lbm)

M

= Weight flow (lb./min)

η

= Efficiency

If polytropic head (H poly) is used in the equation, polytropic efficiency ( ηpoly) must also be used. If isentropic head (H isen) is used in the equation, isentropic efficiency ( ηisen) must also be used. Gas horsepower is not the true input horsepower to the compressor. Mechanical and hydraulic losses must be considered in order to determine the true input horsepower or brake horsepower (bhp). Typical losses to be considered are as follows:

• Bearing losses • Seal losses • Friction losses Other losses, such as radiation losses, labyrinth seal losses, and recirculation due to balancing devices, may typically be ignored in calculating bhp. Bhp can be calculated as follows: bhp = GHP + mechanical losses The mechanical losses are typically noted on the compressor data sheets. If the mechanical losses are not available, an estimate of 20 hp may be used for seal losses, and an estimate of 50 hp may be used for bearing horsepower. The estimated horsepower values may vary greatly due to bearing load, speed, and oil temperature. As the following equation shows, adiabatic or isentropic efficiency uses isentropic relationships to define head (useful work) and total work input.


32



ηad

=

 

T1 (P2 /P1 )

(k −1)/k

− 1 

T2 − T1

Where:

ηad =

Adiabatic efficiency

T1

=

Inlet temperature

T2

=

Discharge temperature

P1

=

Inlet pressure

P2

=

Discharge pressure

k

=

Isentropic exponent

The overall adiabatic efficiency is useful as a measure of the overall performance of a compressor in the determination of power; however, adiabatic efficiency is not always a true indication of efficiency in reference to internal losses. Figure 4 illustrates this point. Because isentropic work is proportional to temperature rise (W ad = cpDT), the distance from point 1 to point 2ad is proportional to the adiabatic work that is required to compress the gas from P 1 to P2 . The actual work, however, is proportional to the vertical distance from point 1 to point 2.


33



Figure 4. Adiabatic Versus Polytropic Process

The polytropic equation represents the true aerodynamic efficiency of a compressor for compression of an ideal gas. There are, however, limitations to this equation. Real gases do not always have a constant k value. The value of k for some gases at discharge conditions can vary significantly from the k value at suction conditions. The enthalpy (or Mollier) equation is the most accurate method to calculate the aerodynamic efficiency for any condition. In some cases, the enthalpy (or Mollier) is the only equation that can provide accurate results. If the average value of k is known and, if η is determined by calculation, ηp can be determined by the following:


34



ηP

=

=

(k avg − 1)/k avg (n − 1)/n Head Work Input Hp (ft − lbf/lbm)

=

778(ft − lbf/BTU) h2 (BTU/lbm) − h1(BTU/lbm)

Where:

ηP

=


Hp

=

Polytropic head (BTU/lb.)

h2

=

Discharge enthalpy (BTU/lb.)

h1

=

Inlet enthalpy (BTU/lb.)

kavg

=

Average isentropic coefficient

n

=

Polytropic coefficient

Use of Fan Laws to Find the Operating Point at Difference Tip Speeds The fan laws for centrifugal compressors are similar to the affinity laws for centrifugal pumps. The following equations show the relationship between the volume flow rate (Q), the head (H), the horsepower (bhp), and compressor speed (N): Equation 1 Q2

 N  = Q1 2   N1 

Equation 2

 N  H2 = H1 2   N1 

2

Equation 3


35



 N  bhp2 = bhp1 2   N1 

3

Where: Q

=

Suction flow, actual

H

=

Polytropic head

bhp =

Brake horsepower

N

Speed, rpm

=

As indicated in Equation 1, the performance of a centrifugal compressor at speeds other than design speed is such that the capacity or flow rate will vary directly as the speed varies. As indicated in Equation 2, the head that is developed will vary as the square of the speed varies. As indicated in Equation 3, the horsepower will vary as the cube of the speed varies. As the speed of the compressor deviates from the design speed, the error of these laws increases. The fan laws only accurately apply to single-stages with very low compression ratios. These laws can be used to estimate the performance at one speed if the performance at another speed is already known. The accuracy of the fan laws decreases with increasing compressor stages and gas density; therefore, the actual performance prediction at off-design speeds must be obtained from the compressor’s vendor. If the curve at speed N 1 is known, these relationships are used to draw the head and horsepower curves at speed N 2, as shown in Figure 5. Starting with any point on the head curve at speed N1 (point A1), both the head (H 2) and the flow (Q 2) are calculated by equations 1 and 2. This calculation gives an equivalent operating point on the curve for speed N 2 (point A2). A series of these points defines the curve for N 2. Similarly, for the horsepower curve that is shown in Figure 6, the horsepower (bhp2) and the flow (Q 2) are calculated to obtain the equivalent operating points.


36



Figure 5. Head Curve

Figure 6. Horsepower Curve


37



DETERMINING POSITIVE-DISPLACEMENT COMPRESSOR ACCEPTABILITY This section of the Module will examine the following areas that Saudi Aramco Engineers must consider when determining the acceptance of positive-displacement compressors:

• • • •

Acceptability Criteria Calculating Capacity Calculating Discharge Temperature Calculating Power

Acceptability Criteria (31-SAMSS-002/31-SAMSS-003) The following account is in accordance with 31-SAMSS-002 (for packaged reciprocating plant and instrument air compressors), which adopts and specifies exceptions to API Standard 680. Reciprocating compressors must be supplied by vendors who are qualified in manufacturing the proposed units. To qualify, the vendor must have manufactured, at the proposed point of manufacture, at least two compressors of identical frame size. These compressors must have been in service in desert environment conditions (as specified in Section 2.1.13 of 31SAMSS-002 and in SAES-A-112) for at least one year, and they must be performing satisfactorily. In addition to the design criteria of 20 years of service life, compressors must be suitable for a minimum period of 10,000 hours of uninterrupted operation between planned maintenance shutdowns. The vendor must advise Saudi Aramco’s Engineers of the flow rate, the outlet temperature, and the inlet pressure that are required at design conditions for Saudi Aramco’s specified coolant inlet temperature (specified on the data sheet). The proposal and the operating instructions must specify maximum and minimum operating conditions of the unit as limited by pressure, temperature, and other conditions that could shorten the life of the machine. The vendor must furnish any required protective devices that are used to prevent damage to the equipment. In accordance with 31-SAMSS-003, reciprocating compressors


38



for process air or gas service must be supplied by vendors who are qualified in manufacturing the proposed units (31-SAMSS003 adopts and specifies exceptions to API Standard 618). To qualify, the vendor must have manufactured, at the proposed point of manufacture, at least two compressors of identical frame size, speed, power rating, and discharge pressure for a gas of comparable characteristics. These compressors must have been proven in service in a desert environment for at least one year, and they must be performing satisfactorily.

Calculating Capacity The value for the capacity of a positive-displacement compressor is used to determine other pertinent compressor operating characteristics. The theoretical capacity of the positive-displacement compressor is used to compare against the actual measured capacity of a compressor that is installed in a system. A large difference between the calculated theoretical compressor capacity and the measured compressor capacity indicates that there may be compressor component degradation. The following equation is used to calculate the theoretical maximum capacity of a reciprocating compressor cylinder: Q = 0.0509 x

Ps Zstd x xDISP x VE Ts Zs

Where: Q

=

Theoretical maximum capacity in million standard cu ft per day (mmscfd) at 14.7 psia and 520°R

PS

=

Suction pressure in psia

TS

=

Suction temperature in °R

Zstd

=

Compressibility factor at standard conditions

ZS

=

Compressibility factor at suction conditions

DISP =

Cylinder displacement in cu ft per minute (cfm)

VE

Volumetric efficiency

=

To determine the capacity of a single stage that has more than one cylinder, the capacity value should be multiplied by the number of cylinders in the stage.


39



Volumetric Efficiency

The critical portion of the theoretical capacity equation is the theoretical volumetric efficiency, as defined as: VE = 1 - C(R 1/k - 1) Where: C

=

Percent clearance as a decimal fraction of displaced volume

R

=

Pressure ratio across the cylinder (discharge pressure divided by suction pressure, psia)

k

=

Isentropic volume exponent at operating conditions (the specific heat ratio for ideal gas, Cp/Cv)

An alternate equation for determining the theoretical volumetric efficiency is: VE = 100 -

R -

 Z s

C 

 Z d

R 1/k

 − 1 

Where: Pd =

Discharge pressure in psia

Ps =


Zd =

Compressibility factor at discharge conditions

Zs =


R

=


k

=


C

=

Cylinder clearance as a percentage

Volumetric efficiency is the suction volume flow rate divided by the displacement. For a reciprocating compressor, the theoretical volumetric efficiency is considerably less than 100% because of clearance volume, valve losses, piston ring leakage, and packing losses. Clearance volume is that portion of the cylinder that is not swept by the piston. At the end of a


40



discharge stroke, the clearance volume is filled with a gas at discharge pressure. During the subsequent suction stroke, this gas begins to expand. The suction valve does not open until the gas in the clearance volume expands from the discharge pressure to the suction pressure. After this expansion, the gas is admitted to the cylinder until the end of the suction stroke; however, the gas is admitted during only 70% to 80% of the total suction stroke. The amount of lost suction volume depends on the compression ratio, the properties of the gas, and the amount of clearance volume. The volumetric efficiency of an operating compressor is calculated to determine whether the valves, pistons, and packing are properly operating. An actual volumetric efficiency that is significantly less than the theoretical value indicates that the valves, the piston rings, and/or the packing are leaking and that maintenance is required. The actual volumetric efficiency can be determined by the following equation: VE = 1 - L - C ( R 1/k - 1) Where: C

=

Percent clearance as a decimal fraction of displaced volume

R

=


k

=


L

=

Loss correction factor as a decimal fraction

or VE = 100 -

R -

 Z s

L - C 

 Zd

R1/k

 − 1 

Where: C

=

Cylinder clearance as a percentage

L

=

Loss correction factor as a percentage

The loss correction factor (L), which accounts for the valve packing losses and the piston ring losses, can be obtained from Figure 7. The loss correction factor is determined by locating


41



the compression ratio value on the x axis. The compression ratio is followed vertically up the graph until it intersects with a line that corresponds to the inlet pressure. The y axis value for the point of intersection is the value for the loss correction factor. For nonlubricated reciprocating compressors, the loss correction factor should be multiplied by two. If the alternate volumetric efficiency equation is used, the loss correction factor from Figure 7 must be multiplied by 100.

Figure 7. Loss Correction Factor for Reciprocating Compressors

The volumetric efficiency equations can be used during a project’s estimating phase to approximate the actual volumetric efficiency that is quoted by the vendor.


42



Cylinder Displacement

Calculation of cylinder displacement can be used with the measurement of actual cylinder volume to determine the volumetric efficiency of any positive-displacement compressor in the field. The actual capacity that is measured in the field is equal to the product of the displacement and the volumetric efficiency. The cylinder displacement of a reciprocating compressor is calculated through use of the following equations: Single-acting compressor: D=

A × m × Ls × n 1728

Double-acting compressor (without tail rod): D=

(2A − a ) × m × Ls × n 1728

Where: D

=

Displacement, ACFM (actual cubic feet/minute)

A

=

Cross-sectional area of cylinder, sq. in.

a

=

Cross-sectional area of piston rod, sq. in.

m

=

Number of cylinders (for each stage)

Ls

=

Length of stroke, in.

n

=

Speed, strokes/minute, or rpm of crankshaft

The calculated displacement can be used to determine the actual volumetric efficiency as follows: VE =

actual measured capacity (ACFMor m3 /hr) displaceme nt (ACFMm3 /hr)

When the actual volumetric efficiency equation is used, both volumetric flow rates must be in the same units (ACFM or m3/hr).


43



Percent Clearance

The percent clearance for each stage is typically provided by the compressor’s manufacturer. The percent clearance for a stage can be determined through use of the following equation: C=

clearance volume, in3 piston displaceme nt, in3

(100 )

Calculating Discharge Temperature The effects of discharge temperature on a reciprocating compressor encompass deterioration of packing, carbonization of oils, and combustibility of gases. Packing life may be significantly shortened by the dual requirement to seal both high pressure and high temperature gases. To reduce carbonization of the oil and the danger of fires, a safe operating limit for discharge temperatures may be considered to be approximately 300°F. When handling gases containing oxygen, which could support combustion, there is a possibility of fire and explosion because of the oil vapors that are present. There are limiting factors when considering discharge temperature. The maximum ratio of compression that is permissible in one stage is usually limited by the discharge temperature, particularly in the first stage. There are certain processes that require a controlled discharge temperature. For example, the compression of gases, such as oxygen, chlorine, and acetylene, requires that the temperature be maintained below 200°F, but for most field applications, the use of 300 °F maximum is a good average, and this maximum is recommended by the API for nonlubricated compressors; however, in accordance with 31-SAMSS-002, compressor vendors are to determine the safe maximum discharge temperature. In accordance with SAES-K-403, the following guidelines apply: When compressors supply an air dryer, the maximum allowable discharge temperature downstream of the after cooler is 50 °C (120°F) for silica gel desiccant, and 60 °C (140°F) for activated alumina desiccant. Compressors that are equipped with refrigerated dryers are limited to a 40 °C (100°F) air discharge temperature. Compressors in hydrogen service are limited to


44



135°C (275°F) discharge temperature. Calculation of compressor discharge temperature may be estimated as the adiabatic temperature at the end of the compression process, which is given by the following equation: Td = Where:

Ts x (R (k-1)/k)

Td =

Discharge temperature, °R

Ts =

Suction temperature, °R

R

=

Pressure ratio cylinder (discharge pressure divided by suction pressure, psia)

k

=


The actual discharge temperature will differ from the calculated value because the equation does not include the effects of cylinder cooling and efficiency.

Calculating Power The manufacturer’s performance predictions should always be used as a first choice in the calculation of the power of a compressor. If the performance predictions are not available, the equations that are provided below can be used to make reasonable approximations. The equations to calculate isentropic horsepower are as follows: HP = 43.67 × Q ×

k k −1

(R (k-1)/k-1)

Where: HP = Isentropic horsepower


Q

= Compressor capacity in million standard cubic feet per day (mmscfd) at 14.7 psia and 520 °R

R

= Pressure ratio cylinder (discharge pressure divided by suction pressure, psia)

k

= Isentropic volume exponent at operating

45



conditions (the specific heat ratio for ideal gas, Cp/Cv) The isentropic horsepower equation indicates that the major effects on isentropic power are the capacity (Q) and the pressure ratio ( R ). Any factors that affect capacity - for example, valve losses and leakage - increase the horsepower that is actually consumed by a compressor. To compensate for these factors, the isentropic horsepower equation can be modified by factoring the compressor’s efficiency and its mechanical efficiency. The following equation provides a more accurate calculation of a compressor’s brake horsepower: bhp = 43.67 x Q x

k k −1

(R (k-1)/k-1) x

Where: bhp =

Brake horsepower

Q

=

Compressor capacity in million standard cubic feet per day (mmscfd) at 14.7 psia and 520 °R

R

=

Pressure ratio cylinder (discharge pressure divided by suction pressure, psia)

k

=


ηc

=

Compression efficiency

ηm

=

Mechanical efficiency

The compression and mechanical efficiencies can be supplied by the compressor’s manufacturer. Compression efficiency varies with many factors, but the typical industry standard is 0.85 (85%) for lubricated double-acting reciprocating compressors and 0.80 (80%) for nonlubricated and/or singleacting reciprocating compressors. The typical industry standard for mechanical efficiency is 0.95 (95%). Screw compressor compression efficiency is typically 80% for lubricated compressors and 75% for nonlubricated compressors.


46



WORK AIDS WORK AID 1:

RESOURCES USED TO DETERMINE DYNAMIC COMPRESSOR ACCEPTABILITY

Work Aid 1A:

Calculation Procedures

Convert the inlet and discharge pressure to psia.

P1 = (

)+(

)=(

) psia

P2 = (

)+(

)=(

) psia

Convert the inlet and discharge temperature to °R.

T1 = (

)+(

)=(

)°R

T2 = (

)+(

)=(

) °R

The polytropic head is given by: (n -1)/n   n    P2  -1      Hp = Zavg RT1   n - 1    P1  


47



To calculate Z avg: From Table 1in Work Aid 1B . Pc = (

) psia

Tc = (

) °R

At the inlet

P r =

P 1

=

P c

Tr =

T1 Tc

=

(

)

(

)

(

)

(

)

=(

)

=(

)

) from Figure 9 in Work Aid 1B

Z1 = (

At the outlet

Pr =

Tr =

P2 Pc

T2 Tc

=

=

(

)

(

)

(

)

(

)

=(

)

=(

)


48



) from Figure 9 in Work Aid 1B

Z2 = (

Zavg =

Z1 + Z2 ( = 2

)+(

)

2

=(

)

To calculate (n-1)/n

(n -1)/n

 T 2   P2    =    T1   P1 

  

  ) 

(

)

(

(n - 1) n

=

=

  

ln (

)

ln (

)

( (

=(


  )  )

(n-1)/ n

)

49



To calculate gas constant (R)

R=

Runiv ( = MW (

) )

=(

)

Refer to Table 1 for the molecular weight of ethane.

The polytropic head equation becomes (n −1)/n  n  P2     Hp = Zavg RT − 1   n − 1  P1  

=(

)(

)(

=(

) ft

)    (

 ( )   (

(

) 

 )    ( 

 ) 

)



-1 



To calculate the inlet flow (ACFM)

 14.7   T1     Z1 520   P  1 

ACFM = SCFM 



=(

) 

=(

)

 (


14.7

  (   )  

)  520

( 

)

50



To calculate polytropic efficiency

ηp =

(k - 1)/k (n - 1)/n

=

(

- 1)/(

)

(

)

=(

)

To calculate the gas horsepower GHP =

=

(Hp)xFlow Rate(lb/min ) η(33000)

(

)( (

) )(33000)

=(

) hp

To calculate the brake horsepower bhp = ghp = =(

(

+ mechanical losses

)+ (

) ) bhp


51



Work Aid 1B:

Pertinent Data

Nomenclature

Hp

=

Polytropic head

Zavg

=


R

=

Gas constant

T1

=

Inlet temperature

n

=

Polytropic exponent

P1

=

Inlet pressure

P2

=

Discharge pressure

Runiv

=

Universal gas constant

MWgas

=

Molecular weight of a gas

p

=


k

=

Isotropic exponent

Cp

=

Specific heat at constant pressure

Cv

=

Specific heat at constant volume

r

=

Compression ratio

ACFM

=

Actual cubic feet per minute

SCFM

=

Standard cubic feet per minute

Z

=

Compressibility factor

MCp

=

Molar specific heat at constant pressure

MCv

=

Molar specific heat at constant volume


52



Charts for Determining Compressor Performance Characteristics

Table 1. Critical Constants of Gases

Compound Acetylene Air Ammonia Benzene 1,2-Butadiene 1,3-Butadiene N-Butane Isobutane N-Butene Isobutene Butylene Carbon dioxide Carbon monoxide Chlorine Ethane Ethyl alcohol Ethylene N-Hexane Helium Hydrogen Hydrogen sulfide Methane Methyl alcohol Nitrogen N-Octane Oxygen N-Pentane Isopentane Propane Propylene Sulfur dioxide Toulene Water Hydrogen chloride

Formula

Critical Constants Mol. Wt. Pressure Temp. M psia Pc R Tc

C2H2 N+O2 NH3 C6H6 C4H6 C4H6 C4H10 C4H10 C4H6 C4H6 C4H6 CO2 CO Cl2 C2H4 C2H5OH C2H4 C6H14 He H2 H2S CH4 CH3OH N2 C8H18 O2 C5H12 C5H12 C3H8 C3H6 SO2 C7H8 H2O HCl

26.036 28.966 17.032 78.108 54.088 54.088 58.120 58.120 56.104 56.104 56.104 44.010 28.010 70.914 30.068 46.069 28.052 86.172 4.003 2.016 34.076 16.042 32.042 28.016 114.224 32.00 72.146 72.146 44.094 42.078 64.060 92.134 18.016 36.465


905.0 547.0 1,657.0 714.0 653.0 628.0 550.7 529.1 583.0 579.8 583.0 1,073.0 510.0 1,120.0 708.3 927.0 742.1 439.7 480.0 188.0 1,306 673.1 1,157.0 492.0 362.1 730 489.5 483.0 617.4 667 1.142 611 3,206 1,199.2

557.4 238.7 731.4 1,013.0 799.0 766.0 765.6 734.9 755.6 752.5 755.6 548.0 242.0 751.0 550.1 629.6 509.8 914.5 510.0 60.2 672.7 343.5 924.0 227.2 1,025.2 278.2 845.9 830.0 666.2 657.4 775.0 1,069.5 1,165.4 584.5

53



Figure 8. Compressibility Factors at Low Reduced Pressure


54



WORK AID 2:

RESOURCES USED TO DETERMINE POSITIVEDISPLACEMENT COMPRESSOR ACCEPTABILITY

Work Aid 2A:

Calculation Procedures

Convert the suction and discharge pressure to psia.

P1 = (

)+(

)=(

) psia

P2 = (

)+(

)=(

) psia

Calculate the compression ratio:

R=

P2 P1

R =

( ) =( ) ( )

Convert the inlet temperature to °R.

T1 = (

)+(

)=(


)°R

55



Calculate the volumetric efficiency, using Figure 9 in Work Aid 2B. VE = 100 -

R -

 Z s

L - C 

 Z d

VE = 100 − (

VE = (

R1/k

 − 1 

)− (

)− (

 (

)

 (

) ( )

)× (

)

)

1

(

)

)

Calculate the compressor displacement. DISP

=

(2A − a ) × m × Ls × n

DISP

=

(2(

DISP

=(

1728

)− (

)) × (

)× (

1728

)


56

 − 1 



Calculate the compressor capacity. Q = 0.0509 ×

Ps Ts

Q = 0.0509 ×

( (

Q

=(

×

Zstd × DISP × VE Zs

) ( × ) (

) ×( )

)× (

)

)

Calculate the compressor brake horsepower. bhp = 43.67 x Q x

= 43.67 × (

=(

k k −1

)×

(R −

k 1/k

( (

− 1) x

1

x

ηc

)  ( ) − 1

1 ηm

((

)

)−1)

(

)

 − 1 ×  (

1

×

1

) (

)

)


57



Work Aid 2B:

Pertinent Data Hydrogen Sulfide Zs ........................ 1.015 Zstd ...................... 0.99 Zd........................ 1.022 k........................ 1.320

Nomenclature

A

=

Cross-sectional area of cylinder, sq. in.

a

=

Cross-sectional area of piston rod, sq. in.

bhp

=

Brake horsepower

C

=

percent clearance as a decimal fraction of displaced volume

D

=

Displacement, ACFM (actual cubic feet/minute)

DISP

=

Cylinder displacement in cubic feet per minute (cfm)

HP

=

Isentropic horsepower

k

=

Isentropic volume exponent at operating conditions (the specific heat ratio for ideal gas, C p/Cv)

L

=

Loss correction factor

Ls

=

Length of stroke, in.

m

=

Number of cylinders (for each stage)

n

=

Speed, strokes/minute, or rpm of crankshaft

ηc ηm

=

Compression efficiency

=

Mechanical efficiency

Pd

=

Discharge pressure in psia

Ps

=


Q

=

Capacity in million standard cubic feet per day (mmscfd) at 14.7 psia and 520°R

R

=


Td

=

Discharge temperature, °R

Ts

=

Suction temperature in °R

VE

=

Volumetric efficiency


58



Zd

=

Compressibility factor at discharge conditions

Zs

=


Zstd

=

Compressibility factor at standard conditions

Figure 9. Loss Correction Factor for Reciprocating Compressor


59



GLOSSARY adiabatic compression

A compression process in which no heat is added or removed.

best efficiency point (BEP)

The point on the performance curve of a centrifugal compressor at which the efficiency is at a maximum.

brake horsepower (bhp)

The total horsepower that is required to drive a compressor. Brake horsepower is equal to the sum of the gas horsepower and the mechanical losses.

compressibility factor, Z

The actual volume of a gas divided by the volume of the same weight of ideal gas at the same molecular weight, temperature, and pressure. Also, Z =

PV RT

displacement

The volume of the space swept by the pistons(s). The theoretical maximum capacity of a reciprocating compressor.

dynamic compression

The compression of a gas with continuous flow due to the interaction between a vane and a gas.

efficiency, isentropic

For a compression process, the ideal work that is required divided by the actual work that is imparted to the gas.

efficiency, polytropic

For a compression process, the minimum work along a polytropic path divided by the actual work imparted to the gas.

enthalpy

A thermodynamic quantity that is the sum of the internal energy of a body (U) and the product of its volume (V) multiplied by the pressure (P). Also called heat content.

entropy

A quantity that is the measure of the amount of energy in a system that is not available for doing work. A small change in entropy (DS) is equal to DQ/T, where DQ is a small increment of heat added or removed and where T is the absolute temperature.

gas horsepower

The total energy that is imparted to the gas in a compressor and that includes the losses due to gas friction but that does not include mechanical friction losses.

head, isentropic

The energy per unit weight of gas that is applied during an ideal compression process in which no heat is lost.

head, polytropic

The ideal energy per unit weight of gas that is applied during polytropic compression.

isentropic compression

Ideal compression along a path of constant entropy under adiabatic conditions (no heat lost).


60

Determining Compressor Acceptability

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