Centrifugal Compressors

Engineering Encyclopedia Saudi Aramco DeskTop Standards

CENTRIFUGAL COMPRESSORS

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 of Saudi Aramco’s employees. Any material contained in this document which is not already in the public 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 : General Engineering File Reference: AGE-102.03

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

Engineering Encyclopedia

Rotating Equipment Centrifugal Compressors

Section

Page

INTRODUCTION------------------------------------------------------------------------------------------ 3 COMPONENTS AND FUNCTIONS ------------------------------------------------------------------ 4 THERMODYNAMIC EQUATIONS FOR GAS COMPRESSION ------------------------------ 7 Head Calculation ---------------------------------------------------------------------------- 9 Centrifugal Compressors Are Polytropic--------------------------------------------- 11 POLYTROPIC EFFICIENCY ------------------------------------------------------------------------- 12 Compressor Discharge Temperature------------------------------------------------- 12 Power Requirements --------------------------------------------------------------------- 13 MOLLIER DIAGRAM METHOD --------------------------------------------------------------------- 15 CASING ARRANGEMENTS ------------------------------------------------------------------------- 17 Intercooling---------------------------------------------------------------------------------- 17 Sidestreams--------------------------------------------------------------------------------- 18 PERFORMANCE CURVES -------------------------------------------------------------------------- 19 ACTUAL VOLUME ------------------------------------------------------------------------------------- 23 FAN LAWS ----------------------------------------------------------------------------------------------- 24 SURGE ---------------------------------------------------------------------------------------------------- 26 Effects Of Surge --------------------------------------------------------------------------- 26 Stonewall ------------------------------------------------------------------------------------ 27 EFFICIENCY OF AN OPERATING MACHINE -------------------------------------------------Procedures ---------------------------------------------------------------------------------Method A - Driver Output vs. Compressor Input -----------------------------Method B - Temperature Rise ----------------------------------------------------Tracking Changes in Efficiency---------------------------------------------------Method C - Mollier -------------------------------------------------------------------Method D - Computer Program COMPRESS----------------------------------

28 28 29 29 30 30 33

CONTROL SCHEMES FOR CENTRIFUGAL COMPRESSORS --------------------------Variable Speed----------------------------------------------------------------------------Suction Throttling -------------------------------------------------------------------------Discharge Throttling ---------------------------------------------------------------------Antisurge Control -------------------------------------------------------------------------Antisurge Controls for Air Compressors --------------------------------------------Combined Controls------------------------------------------------------------------------

34 34 35 36 37 38 39

COMMON PROCESS PROBLEMS WITH CENTRIFUGAL COMPRESSORS --------- 41 WORK AID 1: CENTRIFUGAL COMPRESSOR - CALCULATION FORM -------------- 42 WORK AID 2: CALCULATION FORM - MOLLIER METHOD------------------------------- 44

Saudi Aramco DeskTop Standards

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WORK AID 3: COMMON OPERATING PROBLEMS FOR CENTRIFUGAL COMPRESSORS --------------------------------------------------------------------------------------- 47 GLOSSARY ---------------------------------------------------------------------------------------------- 48 REFERENCES ------------------------------------------------------------------------------------------ 51

LIST OF FIGURES

Figure 1. Basic Components - Centrifugal Compressor ---------------------------------------- 5 Figure 2. Casing Designs for a Centrifugal Compressor --------------------------------------- 6 Figure 3. Compression Paths ------------------------------------------------------------------------- 7 Figure 4. Compressor Head ------------------------------------------------------------------------- 10 Figure 5. Mollier Method - Example --------------------------------------------------------------- 16 Figure 6. Casing Arrangements - Intercoolers -------------------------------------------------- 17 Figure 7. Casing Arrangements - Sidestreams ------------------------------------------------- 18 Figure 8. Generalized Performance Curve ------------------------------------------------------ 21 Figure 9. Typical Manufacturer's Performance Curve - Head And Efficiency ----------- 22 Figure 10. Efficiency From Operating Data - Mollier Method-------------------------------- 32 Figure 11. Variable Speed Control----------------------------------------------------------------- 34 Figure 12. Suction Throttling ------------------------------------------------------------------------ 35 Figure 13. Discharge Throttling--------------------------------------------------------------------- 36 Figure 14. Antisurge Control ------------------------------------------------------------------------ 37 Figure 15. Antisurge Control Air Compressor --------------------------------------------------- 38 Figure 16. Combined Control Scheme - Refrigeration Circuit------------------------------- 39


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INTRODUCTION Centrifugal compressors are the basic compressor type used in Saudi Aramco. They cover a wide of range of capacity and head requirements. They can run for long periods of time between shutdowns for maintenance. Typical average run times are ten years of operation between overhauls, with some machines reaching fifteen years.


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COMPONENTS AND FUNCTIONS Figure 1 shows the basic components of a centrifugal compressor. Impellers are mounted on a horizontal shaft. They are the primary rotating elements that impart velocity to the gas. Impellers are also called wheels. Diffusers are stationary elements mounted in the compressor casing. There is one diffuser downstream of each impeller. The diffuser converts velocity to pressure. Each diffuser is contained in a removable section of the casing called a diaphragm. Each diaphragm also has a passage that directs the gas to the suction of the next impeller. Each impeller and diffuser assembly is a stage of compression. The shaft is supported at both ends by journal bearings. These are normally tilt-pad type bearings. Another bearing mounted on the shaft is a thrust bearing. The thrust bearing absorbs the axial or horizontal force generated by unequal gas pressures on the impellers. A balance piston mounted on the shaft neutralizes as much thrust as possible. This neutralization is accomplished by connecting a high pressure zone to one side of the piston and a low pressure zone to the other side of the piston. The residual thrust is absorbed by the thrust bearing on the end of the shaft. This value changes as a function of compressor differential pressure (Discharge-Suction). Case seals are located at each place where a shaft enters the casing. Normally there are two seals for each casing. These seals usually contain pressurized oil to prevent the leakage of any gas from the inside of the compressor to the atmosphere. However, gas seals can also be used. These seals direct small amounts of leakage gas to flare (1 SCFM or less). Internally, labyrinth seals minimize recirculation of gas from high pressure zones to lower pressure zones. The casing of a centrifugal compressor is divided, or split, into halves that are held together by bolts. See Figure 2. This division permits access to the internal parts without disconnecting the suction or discharge piping if the nozzles are mounted on the lower half of the casing. The casing may be split horizontally into an upper and lower half or it may be split vertically so that one end of the compressor is removable. The Saudi Aramco DeskTop Standards

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vertical split type is called a barrel compressor.

Figure 1. Basic Components - Centrifugal Compressor


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Figure 2. Casing Designs for a Centrifugal Compressor


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THERMODYNAMIC EQUATIONS FOR GAS COMPRESSION Gas compression can take place in one of three separate paths. See Figure 3. The first such mode is isothermal compression, compression taking place at constant temperature.

Figure 3. Compression Paths Isothermal compression is not common in actual machinery because large amounts of heat transfer area must be supplied to keep the temperature constant. However, one can see that if the temperature were maintained constant, then pressure times volume would be a constant value at all points along the compression path. PV = Constant (Isothermal Compression) A second compression path is isentropic. This path is sometimes also called adiabatic, but its proper name is isentropic. As the name isentropic implies, this compression follows a path of constant entropy. It is, therefore, an ideal thermodynamic process. In this case, temperature is not constant. It increases as the pressure increases because of the work of compression that is added to the gas. The shape of the curve shown in Figure 3 is determined by the relationship: PVk = Constant (Isentropic Compression)


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The exponent k is equal to Cp/Cv, a common thermodynamic property of gases. Cp is the heat capacity of the gas at constant pressure and Cv is the heat capacity of the gas at constant volume. Figure 3 shows that the isentropic path results in a larger volume as compression proceeds, compared to the isothermal path. This is because the rise in temperature causes an increase in volume. Therefore, the exponent k is always larger than 1. Polytropic compression is the compression path that occurs in a real centrifugal compressor. Centrifugal compression is not an ideal thermodynamic process. The inefficiency of the compression process results in some conversion of the kinetic energy of the gas into heat energy.. Therefore, temperature rises faster than it does in isentropic compression. The volume at the end of compression is again higher than it was at the end of an isentropic path, due to the increased temperature of the gas. Polytropic compression follows a path described by: n

PV = constant The exponent n is always larger than the isentropic exponent k. The actual compression path is the path plotted by P1T1, P2T2. The actual work can be expressed by: Actual Work =


Isothermal Work Isothermal Eff .

=

Isentropic Work Isentropic Eff .

=

Polytropic Work

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Head Calculation The primary variable to be calculated for a compression service is the work or power requirement of the compressor. The equation for work is developed from three fundamental thermodynamic relationships. For isentropic compression: PV k = Constant PV = ZRT P Work = 2 VdP P1 If the proper substitution and integration are performed, the resulting equation for each stage of compression is: Z1RT1 Work = (k − 1) MW k

k −1     P2  k − 1     P1   

Eqn. (1)

where: Z1

= Compressibility factor, at suction

R

= Gas constant, 1545 ft-lb/lb mol -°F

T1

= Suction temperature, °R

MW = Gas molecular weight P1

= Suction absolute pressure

P2

= Discharge absolute pressure

k

= Cp/Cv, average

The units of work in this equation are foot-pounds (force) per pound (mass). These units are commonly simplified. The pound terms are implied and the resulting unit is feet. This work term is then called head. Head is energy, even though the common units for it are feet. Head is work per unit of mass. It is the work, or energy, needed to lift a unit of mass to a height that is equivalent to the head.


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The head developed by a centrifugal compressor is analogous to the head developed by a pump. It can be compared to a column of fluid at the discharge of the compressor. Refer to Figure 4. Visualize a column of gas with the discharge pressure P2 at the bottom and the suction pressure P1 at the top. The height of this column corresponds to the head required to generate this differential pressure. The following relationship applies, which is the same as for pump head. Head =

where:

P(2.31) S.G. relative to water

Eqn. (2)

S.G. = Specific gravity

The temperature and specific gravity vary along the height of the theoretical column, matching the temperatures along the compression path from suction to discharge. This is the reason why polytropic head is greater than isentropic head for the same terminal pressures. Since temperatures are higher during polytropic compression, the gas density is lower and a higher column is required to achieve the same differential pressure. •

Head is Analogous to Pump Head − Column of Fluid at Discharge

Note:

Temperatures along the theoretical column are those that occur during compression. Temperatures are higher during polytropic compression, therefore Polytropic Head > Isentropic Head.

Figure 4. Compressor Head


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Centrifugal Compressors Are Polytropic Centrifugal compressors operate in a polytropic manner. The work input to the gas is greater than the ideal amount. The temperature rise occurs at a faster rate than it does during isentropic compression. This is accounted for mathematically by substituting the polytropic exponent n for the isentropic exponent k. The following equation results:

Z1RT1 Head = (n − 1) MW n

n−1    P2  n  − 1    P1    

Eqn. (3)

A fixed relationship exists between n and k as shown in the following equation:

k −1 n −1 k = Polytropic Efficiency n


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POLYTROPIC EFFICIENCY Polytropic efficiency is a characteristic of each compressor. Polytropic efficiency is equal to reversible work divided by total work applied to the gas. Reversible work and total work are different because of the friction losses caused by the gas passing through the impellers and the diffusers at high velocity. For a centrifugal compressor, the polytropic efficiency typically ranges between 60% and 85%. Thus, approximately 25% of the energy supplied through the compressor shaft is lost as heat, with a 75% polytropic efficiency compressor. Polytropic efficiency is shown on the manufacturer's performance curve. It varies with volume flow rate and compressor speed. The manufacturer's curve is the best place to find the polytropic efficiency to make calculations. If this is not possible, a reasonable approximation can be made using the following formula. Polytropic Efficiency = 0.0109 ln(ACFM) + 0.643

Eqn. (4)

where: ACFM = Actual cubic feet per minute at suction condition Note that Eqn. (4) will give the efficiency at the machine's Best Efficiency Point (BEP). At speeds and flow rates above or below BEP, the efficiency will be lower.

Compressor Discharge Temperature The discharge temperature of a centrifugal compressor can be estimated using the following equation. n−1

P  n T2 = T1 2   P1 


Eqn. (5)

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where: T1 = Suction Temperature, ºR T2 = Discharge Temperature, ºR This calculation of discharge temperature is approximate unless the compressibility factor is 1.0, because gas compressibility has an effect on temperature rise. If the compressibility is less than 1.0, the temperature calculated will be lower than the actual temperature.

Power Requirements The energy that is imparted to the gas is called gas horsepower. Head is energy per unit of mass flow assuming 100% efficiency. Horsepower is obtained by multiplying head times the mass flow and dividing by efficiency to obtain the actual energy imparted to the gas. The proper conversion factor must also be included. lbM min Gas Horsepower (ghp ) = Poly. Eff. (33,000) (Hpoly )

Eqn. (6)

where: Hpoly

= Polytropic Head

FT − LBF LBH

Poly Eff. = Polytropic Efficiency, decimal fraction lb MASS min

= Gas Flow Rate, pounds per min ute

33,000

= Conversion Factor


FT − LBF HORSEPOWER − MIN

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Brake horsepower is the total horsepower required at the shaft of the compressor. This is equal to gas horsepower plus mechanical losses. Mechanical losses are caused by friction between the rotating surfaces. To estimate mechanical losses see GPSA Engineering Data Book Figure 13-38. To estimate total mechanical losses, add bearing friction losses to oil seal friction losses. Work Aid 1 is a calculation form to facilitate the calculation of head, discharge temperature, and brake horsepower.


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MOLLIER DIAGRAM METHOD Mollier diagrams are another way to calculate head and horsepower. Mollier diagrams show thermodynamic properties with various quantities, such as temperature and pressure constants, especially in terms of entropy and enthalpy as coordinates. This method is useful only for pure gases. Mollier diagrams are published for all of the common gases. The procedure for calculating head and horsepower using Mollier diagrams is as follows: 1. Locate the suction temperature and pressure on the Mollier diagram. At this point, read the initial gas enthalpy, h, in Btu/lb. 2. Follow a constant entropy line on the diagram to the discharge pressure. At the discharge pressure, read the enthalpy h2. This will be the isentropic enthalpy. 3. Calculate the isentropic head. His = (h2 − h1)

BTU FT − LBF x 778 LBM BTU

Eqn. (7)

4. Obtain the polytropic efficiency from the manufacturer's data. 5. Because Mollier diagrams are based on isentropic calculations, it is necessary to convert the polytropic efficiency to an isentropic efficiency. Use GPSA Figure 1337 for this purpose. 6. Calculate the gas horsepower. ghp =

His (lb min .) Is. Eff .(33,000 )

Eqn. (8)

Is. Eff. = Isentropic efficiency, decimal fraction. 7. Calculate brake horsepower (bhp) by adding mechanical losses.


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8. To calculate the discharge temperature, first calculate the actual enthalpy at discharge conditions. h2 actual =

(h2 − h1)is + h1 Is. Eff .

Eqn. (9)

9. Read the actual discharge temperature from the Mollier diagram at actual discharge enthalpy and the discharge pressure. Figure 5 illustrates this calculation method, using a pressureenthalpy diagram available in the GPSA Engineering Data Book, Section 24.

Figure 5. Mollier Method - Example


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CASING ARRANGEMENTS Intercooling Frequently, a compressor service requires two or more casings. The gas is cooled in between casings. The reasons for intercooling can be any of the following: •

To avoid exceeding a maximum temperature limit set by the mechanical parts or by the seal oil.

•

To reduce power requirements.

•

The additional casings are necessary because many impellers are required. Intercooling is then convenient.

For calculations, each casing is treated as a separate compressor. Each casing is often referred to as a stage. This stage is a process stage and should not be confused with the impeller/diffuser assembly discussed earlier. See Figure 6.

Figure 6. Casing Arrangements - Intercoolers


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Sidestreams Sometimes additional gas is added to a compressor casing between wheels (impellers). This is common practice with refrigeration compressors, where some gas is available at higher pressure. This gas is called a sidestream. Sidestreams may also be taken out before discharge pressure is reached. These sidestreams divide the compressor into sections. Each section must be calculated as a separate compressor and has its own performance curve. See Figure 7.

Figure 7. Casing Arrangements - Sidestreams


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PERFORMANCE CURVES Figure 8 shows a generalized performance curve. Performance curves contain the following information: •

Head versus flow characteristic at several speeds

•

Horsepower versus flow rate and speed

•

The surge limit

Manufacturers plot performance curves in several ways. The x axis may show actual cubic feet per minute or volume flow at standard conditions. The y axis may show polytropic head, pressure ratio for a particular gas, or discharge pressure for a particular gas and a particular suction pressure. The most useful parameters on a performance curve are head and efficiency vs. actual flow since they are relatively unaffected by gas composition or inlet temperature changes. Figure 9 shows a typical manufacturer's performance curve for a specific compressor. Remember that the compressor always produces the same polytropic head at a given speed and actual volume flow.* If the gas composition or the suction temperature changes, then the pressure ratio and the discharge pressure will change. If the molecular weight of the gas increases, the pressure ratio will increase. The horsepower required will also increase. The polytropic efficiency for a machine is also constant at a given actual volume flow rate and speed.

________________ * This assumption is valid for gas density changes of 20%. Greater changes affect the head produced. In these instances, a new performance curve must be supplied by the original equipment manufacturer (OEM).


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Manufacturer's performance curves are used for the following purposes. •

To determine whether a particular process operation will be within the limits of the machine. The curve will tell you if an operating condition such as flow, gas composition, suction pressure or discharge pressure is feasible.

•

To determine the correct speed for a set of process conditions such as suction ACFM and head.

•

To determine the brake horsepower required for an operation, so that you can see if the driver will have enough power.

•

To compare actual operating head and efficiency with the predicted values. This determines whether the machine is performing normally or whether it needs maintenance.


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Figure 8. Generalized Performance Curve


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With Permission from Exxon Company, U.S.A.

Figure 9. Typical Manufacturer's Performance Curve Head And Efficiency


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ACTUAL VOLUME Manufacturer's curves and the machine's performance are based on actual volume flow at the suction of the compressor. The units are actual cubic feet per minute. Process data is given in standard cubic feet per minute. To convert from standard cubic feet per minute to actual cubic feet per minute, use the following equation: ACFM = SCFM ×

14.7 T1 × ×Z P1 520

Eqn. (10)

where: SCFM = Standard cubic feet per minute (60ºF, 1 Atm) SCFM = lb mol x 379 SCFM =

lb mol × 379 min ute

SCFM =

lb hr × 379 60(MW )

P1

= Suction pressure, psia

T1

= Suction temperature, ºR

Z

= Compressibility factor, at suction conditions. Z is calculated using GPSA Figures 23-3 or 23-8 to 23-10.


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FAN LAWS Fan laws for centrifugal compressors are similar to those for centrifugal pumps. The equations show the relationship between volume flow rate, head, horsepower, and compressor speed. They can be used to predict performance at one speed if the performance at another speed is already known. The equations are as follows: N  Q2 = Q1 2   N1 

N  H2 = H1 2   N1 

Eqn. (11)

2

N  bhp2 = bhp1 2   N1 

Eqn. (12) 3

Eqn. (13)

where: Q

= Suction flow, actual

H

= Polytropic head

bhp = Brake horsepower N

= Speed, rpm

These relationships are used to draw head and horsepower curves at speed N2, if the curve at speed N1 is known. Start with any point on the head curve at speed N1. Calculate both H2 and Q2 by Eqns. (11) and (12). This gives an equivalent operating point on the curve for speed N2. A series of these points defines the curve for N2. Similarly, for the horsepower curve, calculate bhp2 and Q2 to obtain equivalent operating points.


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Similar relationships exist for impellers of different diameters. However, compressor impeller diameters are very seldom changed in the field. Speed changes are much more common for compressors. It should be noted that the fan laws are reasonable approximations and do not include the effects of gas density and multistage compressor performance. They can be used for estimating purposes only.


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SURGE One important characteristic of a centrifugal compressor is its surge point. Surge is a condition at which flow through the compressor becomes unstable. This condition must be avoided to prevent damage to the machine. Surge occurs as follows: As the system resistance increases, a centrifugal compressor reacts by backing up on its curve. That is, the flow decreases so that the head produced can rise to match the system demand. When the highest point on the compressor curve is reached, the compressor cannot increase the discharge pressure further. At this point, the system discharge pressure is higher than the maximum possible discharge pressure of the compressor. The flow in the impellers becomes unstable and reverses, causing the discharge pressure to collapse. After a few seconds forward flow resumes. The discharge pressure rises again and the cycle repeats every few seconds. Surge occurs at a predictable flow rate. This flow rate is shown on the manufacturer's curve. In practice, controls are provided to keep the actual flow rate above this minimum value.

Effects Of Surge It is normal practice to take careful precautions to prevent surge. Surge disrupts the process and it can damage the compressor. As a result of the reversing flow, the direction of shaft thrust reverses. The temperature rises because the gas is internally recycled and recompressed. Compressor vibration and speed fluctuations are quite common. The reversing axial motion, high temperatures and fluctuating pressure can also damage the compressor seals. In a severe case, failure of the seal or the thrust bearing, or even the impellers, can occur. External piping can also be damaged. A check valve is normally installed at the discharge of a centrifugal compressor. During surge, this check valve can slam shut many times. This causes loud noise, pipe vibrations, and possible leaks at piping flanges.


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Stonewall Another phenomenon encountered in centrifugal compressors is stonewall. As the flow rate through the compressor increases beyond the design value, the amount of head developed decreases, as per the compressor curve. At a certain flowrate, the velocity of the gas will reach Mach 1. This is called the stonewall condition. Stonewall is the result of reaching sonic velocity in some part of the compression path, often in an impeller or a diffuser. Once sonic velocity is reached, the velocity cannot increase further and the flowrate cannot increase beyond this point..


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EFFICIENCY OF AN OPERATING MACHINE A process engineer is frequently asked to calculate the efficiency of an operating centrifugal compressor in the field. This actual efficiency can be compared with the original design efficiency. If the actual efficiency is deficient, compressor maintenance is required to remove deposits in the compressor or to replace damaged impellers, labyrinth seals or diffusers. The definitions of efficiency are as follows: Efficiency =

Theoretica l ghp Actual ghp

Note that gas horsepower (ghp) is used, not brake horsepower (bhp). Mechanical losses are not included in efficiency, by convention. Isentropic Efficiency =

Minimum adiabatic work Actual work, excluding mechanical losses

Polytropic Efficiency =

Minimum work along polytropic path Actual work, excluding mechanical losses

Procedures There are four different ways to calculate operating efficiency. Method A.

Compare driver power output to compressor power input.

Method B.

Compare compressor's actual temperature rise to isentropic temperature rise.

Method C.

Using a Mollier chart, compare actual ∆h to isentropic ∆h.

Method D.

A computer program, such as COMPRESS.


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Method A - Driver Output vs. Compressor Input

1. Calculate the gas horsepower using the process data and compressor equations. If the gas is a pure compound, the Mollier method can be used. 2. Calculate the actual work delivered to the gas by the driver. After the driver horsepower is determined, subtract an allowance for mechanical friction losses in the compressor. 3. Calculate the polytropic efficiency. Polytropic Efficiency =

ghp Driver bhp − Mechanical Losses

Note: It is not always possible to calculate the brake horsepower of the driver accurately. If this is the case, use method B. Method B Temperature Rise

It is possible to calculate the efficiency of a centrifugal compressor from compressor data only. The method is as follows. 1. Analyze the gas compositions. 2. Calculate the value k for the gas. 3. Obtain temperatures and pressures at the suction and discharge of the compressor from field data. Use calibrated gauges. 4. Calculate the value m. T 2  P2  = T 1  P1 


m

n − 1   Note that m =  n  

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 log T 2  T1    T1    m=  logP2   P1  5. Calculate the polytropic efficiency.

k −1 Polytropic Efficiency = k m Note: If the compressibility factor is not equal to 1.0, some inaccuracy will result from this method. However, the method is suitable for tracking changes in efficiency over time. Tracking Changes in Efficiency

The usual reason for calculating compressor efficiency is to track changes in performance. The process engineer wants to know whether the compressor is fouling, or if there is mechanical deterioration due to erosion or corrosion. Method A is not the best method for this purpose. Errors in data from the driver will cause fluctuations in the calculated compressor efficiency. For this purpose method, B is better because it uses data only from the compressor. Note that accurate gas analysis methods and gauge calibration are very important. All suction/discharge temperature and pressure gauges should be renewed or calibrated before any readings are taken. A small inaccuracy in these values can lead to large inaccuracies in efficiency. Gas samples should always be obtained from the top of pipes and analyzed at the same temperature at which they were taken. Method C - Mollier

The efficiency of an operating compressor can also be calculated using the Mollier method, if the gas is a pure compound. The procedure is as follows.


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1. Measure the temperature and pressure at the suction and discharge of the machine. 2. Plot the suction condition on the Mollier diagram. See Figure 10. 3. Follow an isentropic line to the discharge pressure. 4. Calculate ∆h isentropic. 5. Plot the actual discharge pressure and temperature on the Mollier diagram. 6. Calculate the actual ∆h. 7. Calculate the isentropic efficiency. Isentropic Efficiency =

8.

∆h isentropic ∆h actual

Convert the isentropic efficiency to polytropic efficiency using GPSA chart Figure 13-37. It is necessary to track the polytropic efficiency of the compressor to draw meaningful conclusions about its performance. The isentropic efficiency can change as process conditions change, even though the condition of the compressor remains the same.


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Figure 10. Efficiency From Operating Data - Mollier Method


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Method D - Computer Program COMPRESS

The fourth method for calculating compressor efficiency is by using a computer program such as COMPRESS. The input data are •

Compressor T1, T2, P1, P2

•

Gas composition

•

Gas flow rate information

The program calculates •

Polytropic efficiency

•

Gas horsepower

•

Polytropic exponent n

•

Polytropic head

The program uses an equation of state to calculate enthalpies and entropies at inlet and outlet. The COMPRESS program is the mosttaccurate of the four methods. It is also the most convenient, when a PC is available. Other computer programs such as PRO-II may also be used. The greatest source of potential error with a computer program is in the accuracy of input data. For critical calculations, calculate the power output of the driver (Method A) as a check on the COMPRESS calculation. After accounting for mechanical losses in the compressor and for gear efficiency, the power output of the driver should match the power input of the compressor.


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CONTROL SCHEMES FOR CENTRIFUGAL COMPRESSORS Variable Speed A control system must match the performance curve of the compressor to the system requirements. One way to match the compressor performance and system requirements is to use a variable speed driver. Steam turbines and gas turbines are usually capable of speed control. The range of control is normally from 80% to 105% of rated speed. Motors normally have a fixed speed, but they can be converted into variable speed devices by changing their electrical input frequency. Figure 11 illustrates the principle of speed control. The solid line shows the head capacity curve at design speed. The design point is on this curve. The desired operating point is at a lower flow rate and a lower head. The objective is to find the operating curve shown by the dashed line which passes through that operating point. This operating curve will be at a new speed N2, which is lower than the design speed N1.

Figure 11. Variable Speed Control


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Suction Throttling If a fixed speed driver is used, suction throttling is an alternative method to control compressor flow. Throttling the suction increases the actual volume of the gas and moves the operating point away from the surge point. Suction throttling utilizes a butterfly control valve in the suction line upstream of the compressor. Figure 12 shows the principle of suction throttling control. The speed of the compressor is constant; therefore, there is only one operating curve, shown by the solid line in the diagram. The operating point is matched to the operating curve by a different method. As the throttle valve in the suction closes, the pressure downstream of the valve decreases. As the pressure decreases, the volume of suction gas increases. At the same time, the compression ratio required by the machine is increasing because the discharge pressure remains constant while the suction pressure is dropping. This causes the actual operating point to move from point A to point B.

Figure 12. Suction Throttling


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Discharge Throttling Discharge throttling of a centrifugal compressor is not used as the primary control because it increases the horsepower required from the driver and moves the compressor towards the surge point. However, discharge throttling is often used as a secondary control to prevent stonewall. See Figure 13.

Figure 13. Discharge Throttling


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Antisurge Control In addition to matching process flow to compressor capacity, the flow rate must be kept higher than the surge point minimum flow limit. This higher flow rate is accomplished by recycling a portion of the compressor discharge flow back to the suction vessel. This practice keeps the flow through the compressor above the minimum flow required to keep the compressor out of surge. Refer to Figure 14. A flow transmitter is located in the discharge line from the compressor. A signal from this flow transmitter controls the control valve in the compressor recycle line. If the discharge flow falls below the minimum safe value, the recycle valve opens and maintains the minimum flow rate. The circuit must be arranged so that the recycle flow always flows through a cooler. Otherwise, the recycling gas would continue to be heated and exceed the temperature limits of the compressor.

Figure 14. Antisurge Control

In many installations a microprocessor is added to the controls. The computer calculates the actual surge flow at any moment. This flow rate is not a constant value, but can change with process conditions and gas composition. Another requirement is that the recycle controller must respond quickly when the flow drops below the minimum. Normal flow controllers experience reset windup. With reset windup, it can take up to one minute before the control valve opens. A compressor recycle controller must have special features to eliminate reset windup. In addition, the instrumentation used must have adequate accuracy and the control valve must open quickly (1-2 seconds).


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Antisurge Controls for Air Compressors Figure 15 shows an alternative antisurge control for centrifugal compressors in compressed air service. Instead of recycling air to the suction of the machine, the air is discharged to the atmosphere. In this case, the composition of the gas is fixed and the suction pressure is fixed at atmospheric pressure. Therefore, it is common to use discharge pressure as the control variable rather than flow rate. A pressure controller in the discharge line opens the control valve to atmosphere whenever the discharge pressure rises above a preset safe value. It is important to note that this scheme assumes all intercoolers function as designed. If they become fouled, the compressor will surge at a lower discharge pressure.

Figure 15. Antisurge Control Air Compressor


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Combined Controls Figure 16 shows a combined control scheme for a typical refrigeration circuit. The controls are shown in a simplified manner, but they illustrate all of the principles mentioned so far. This compressor has a side inlet or a second suction nozzle operating at a pressure higher than the first suction pressure. This is a common feature of refrigeration machines and divides the compressor into two sections. The first section is between the first suction and the sidestream inlet. The second section is between the sidestream inlet and the discharge. The flow rate for the second section is different from the flow rate for the first section. Both flow rates must be controlled to keep the two sections out of surge. Therefore, two flow sensors and two recycle loops are used. This compressor is assumed to have a constant speed driver. Therefore, a pressure controller in the suction line is the primary flow control device. This pressure controller matches the compressor head to the head required by the system.

Figure 16. Combined Control Scheme - Refrigeration Circuit


39



In the circuit shown, a second pressure controller is included in the discharge line. This is sometimes necessary with multisuction machines. If this pressure controller is not included, the discharge pressure will drop during cold weather, a condition that might be undesirable for the compressor or the process. If the pressure drops very far, it may not be possible to keep all of the compressor wheels out of surge. Secondly, the operation of the external circuit (for example, the economizer) would be affected when the discharge pressure drops. All the pressures in the machine drop, including all the pressure at the sidestream inlet. This could have an adverse effect on the process. Note that discharge pressure control is a secondary control. The primary control for matching compressor and process is suction throttling.


40



COMMON PROCESS PROBLEMS WITH CENTRIFUGAL COMPRESSORS Work Aid 3 lists the most common problems encountered with centrifugal compressors. The possible causes of these problems are also listed.


41



WORK AID 1:

CENTRIFUGAL COMPRESSOR - CALCULATION FORM (Page 1 of 2)

Gas MW Suction Flow Rate:

SCFM,

lb/min,

ACFM

P1 psia P2 psia r =P2/P1 =

=

T1

ºF,

ºR

Polytropic Efficiency: From Manufacturer's Specification or:

0.0109 ln (Suction ACFM) + 0.643 = 0.0109 ln (

) + 0.643

= lst Trial

2nd Trial

3rd Trial

T2, °K assumed k1 (GPSA Figure 13-8 or 13-6) k2 k avg (k-1)/k (n-1)/n =

(k − 1) k Poly. Eff .

T2 = T1(r)(n-1)/n


42



T2 calculated (Page 2 of 2) Z1 (GPSA 23-3) Polytropic Head:  n−1  Z1(1544 )T1  n (r ) − 1 Hpoly =  (n − 1)  MW    n

[

]

Hpoly =

( )(1544 )( ) ( )( ) − 1 ( )( )

Hpoly =

feet

Gas Horsepower: ghp = ghp =

Hpoly × lb / min Poly Eff . × 33,000

(

(

)( ) )(33,000 )

ghp =

Mechanical Losses (GPSA Figure 13-38) ghp

hp

= ghp + Mechanical Losses

=

+

=

hp


43



WORK AID 2:

CALCULATION FORM - MOLLIER METHOD (Page 1 of 3)

Gas: Suction Flow Rate:

SCFM,

lb/min,

ACFM

P1 psia T1 ºF P2 psia h1

Btu/lb

h2 isentropic

Btu/lb

∆H isentropic

=

-

=

Btu/lb

(

)

Polytropic Efficiency: From Manufacturer Spec or: 0.0109 ln (Suction ACFM) + 0.643 = 0.0109 ln (

) + 0.643

= P r= 2 P1

= _____ = _____

k

=

Isentropic Efficiency (from GPSA Figure 13-37):


44



(Page 2 of 3) Gas Horsepower: Isentropic Head

= Isentropic ∆h (778) = ( )(778) feet

= ghp

=

(Isentropic Head)(lb min ) (Isentropic Efficiency )(33,000 )

( =

Polytropic Head


)(

) )(33,000 )

hp hp

Mechanical Losses (GPSA Figure 13-38) bhp

(

= ghp + Mechanical Losses =

+

=

hp

= Isentropic Head × =

x

=

feet

Polytropic Efficiency Isentropic Efficiency

45



(Page 3 of 3) Discharge Temperature: Actual ∆h

=

Isentropic ∆h Isentropic Efficiency

= = Actual h2

T2


Btu/lb

= h1 + Actual ∆h =

+

=

Btu/lb

=

ºF (from Mollier Diagram)

46



WORK AID 3:

COMMON OPERATING PROBLEMS FOR CENTRIFUGAL COMPRESSORS

Common Problems

Surge

Driver Overload

Vibration

Tripout or Automatic Shutdown

Possible Cause(s)

•

Improper setting of recycle flow control

•

Slow response of recycle controller and/or valve

•

Deposits in rotor or diffuser

•

Blockage in discharge line or recycle line

•

Low gas density (Low MW or high suction temperature)

•

High suction pressure

•

High molecular weight of gas

•

Low inlet temperature of gas

•

Liquid in suction

•

Deposits on rotor

•

Rotor erosion/corrosion

•

Mechanical problems (GPSA p. 13-39)

•

Liquid in suction knockout drum

•

High discharge temperature

•

Loss of lube or seal oil

•

Loss of buffer gas

•

High axial displacement

•

Instrument malfunction, false trip

•

High thrust bearing pad temperature

•

Overspeed of driver (steam or gas turbine)


47



GLOSSARY Adiabatic Compression

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

Balance Piston

A device installed on the shaft of a centrifugal compressor. It balances the thrust forces of the impellers.

Best Efficiency Point (BEP)

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

Brake Horsepower

The total horsepower required to drive a centrifugal compressor. The power on the shaft between the compressor and the driver.

Casing

The outer containment vessel of a centrifugal compressor.

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

Diaphragm

A removable section inside of a casing. It contains the diffuser and a return passage, which directs the gas to the suction of the next impeller.

Diffuser

A component of centrifugal compressors located after an impeller. The diffuser converts velocity head to pressure head and directs the flow to the next impeller.

Efficiency, Isentropic

For a compression process, the ideal work required divided by the actual work 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.


48



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. It is also called Heat Content.

Entropy

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

Erosion

Damage to the internal parts of a compressor caused by abrasion by solid particles.

Fouling

The deposition of solid material on the internal passages of a compressor.

Gas Horsepower

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

Head, Isentropic

The energy per unit weight of gas applied during an ideal compression process.

Head, Polytropic

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

Impeller

The rotating element of a centrifugal compressor that develops velocity head. Also called a Wheel.

Intercooler

A gas cooler located between two casings of a compressor.

Isentropic Compression

Ideal compression along a path of constant entropy under adiabatic conditions.

Isothermal Compression

Compression at constant temperature. Heat must be removed during the compression process.

Journal Bearing

A bearing that supports the weight of the shaft of a centrifugal compressor.

Labyrinth Seal

A seal made of several rings in series that fit very closely to a shaft and impeller eye. A labyrinth seal minimizes leakage but cannot stop it completely.


49



Mollier Diagram

A diagram that shows the relationship between enthalpy, entropy, temperature, and pressure for a particular gas.

Oil Seal

A seal at the end of a shaft. It is lubricated with oil which positively prevents leakage of gas from the casing of a compressor.

Performance Curve

A curve supplied by the manufacturer which shows the relationship between capacity, head, horsepower, and efficiency.

Polytropic Compression

The type of compression which takes place in a real centrifugal compressor as compared to ideal isentropic compression.

Side stream

A stream of gas that is introduced into a casing after one or more wheels. It can also be removed from a casing before the final discharge nozzle.

Stonewall

The maximum flow condition for a centrifugal compressor. Stonewall is reached when the gas velocity becomes sonic at some point in the compression path.

Surge

An unstable operating condition in a centrifugal compressor. It is caused by process conditions that result in flow rate being too low or the required discharge pressure being too high.

Throttling

Restricting the flow of a fluid, usually by means of a control valve in the suction or discharge process system.

Thrust

An axial force on the shaft of a compressor. It is caused by unequal pressures on the sides of the impellers.

Thrust Bearing

A bearing located on the shaft of a centrifugal compressor that absorbs the axial force on the shaft.

Wheel

Another name for impeller.


50



REFERENCES Vendors Bulletin

•

Elliot Bulletin P-25C, Multistage Centrifugal Compressors

Supplementary Text

•

Gas Processors Suppliers Association Engineering Data Book, Section 13

Industry Standard

•

API 617 - Centrifugal Compressors for General Refinery Service

Saudi Aramco Engineering Standards

•

SAES-K-402 - Centrifugal Compressors


51

Centrifugal Compressors

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