Engineering Encyclopedia: 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.
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File Reference: CHE10203 R. A. Al-Husseini on 874-2792
Engineering Encyclopedia Process
CONTENTS PAGE
COMPONENTS AND FUNCTIONS ......................................................................................................... 1

THERMODYNAMIC EQUATIONS FOR GAS COMPRESSION ............................................................ 4
Head Calculation .................................................................................................................................... 5
Centrifugal Compressors Are Polytropic ................................................................................................ 8
POLYTROPIC EFFICIENCY..................................................................................................................... 9
Compressor Discharge Temperature....................................................................................................... 9
Power Requirements............................................................................................................................. 10
MOLLIER DIAGRAM METHOD ........................................................................................................... 11
CASING ARRANGEMENTS................................................................................................................... 13
Intercooling .......................................................................................................................................... 13
Sidestreams........................................................................................................................................... 14
PERFORMANCE CURVES..................................................................................................................... 15
ACTUAL VOLUME.................................................................................................................................18
FAN LAWS .............................................................................................................................................. 19
SURGE ..................................................................................................................................................... 20
EFFECTS OF SURGE .............................................................................................................................. 20
STONEWALL .......................................................................................................................................... 20
EFFICIENCY OF AN OPERATING MACHINE..................................................................................... 21
Procedures ............................................................................................................................................ 21
Method A - Driver Output vs. Compressor Input............................................................................. 21
Method B - Temperature Rise .......................................................................................................... 22
Tracking Changes in Efficiency ....................................................................................................... 23
Method C - Mollier .......................................................................................................................... 23
Method D - Computer Program COMPRESS .................................................................................. 25
CONTROL SCHEMES FOR CENTRIFUGAL COMPRESSORS ........................................................... 26
Variable Speed...................................................................................................................................... 26
Suction Throttling.................................................................................................................................28
Discharge Throttling............................................................................................................................. 29
Antisurge Control .................................................................................................................................30
Antisurge Controls for Air Compressors .............................................................................................. 31
Combined Controls............................................................................................................................... 32
COMMON PROCESS PROBLEMS WITH CENTRIFUGAL COMPRESSORS .................................... 34
WORK AID 1: CENTRIFUGAL COMPRESSOR - CALCULATION FORM ....................................... 35
WORK AID 2: CALCULATION FORM - MOLLIER METHOD ........................................................... 37

WORK AID 3: COMMON OPERATING PROBLEMS FOR CENTRIFUGAL COMPRESSORS ........ 40

GLOSSARY.............................................................................................................................................. 41
REFERENCES.......................................................................................................................................... 44

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 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 vertical
split is called a barrel compressor.
Saudi Aramco DeskTop Standards 1

COMPONENTS AND FUNCTIONS (CONT’D)
Diaphragm Impeller
Radial Bearing
Casing Seal Ring
Thrust Bearing
Shaft
Suction
With Permission from Mitsui Engineering Discharge
FIGURE 1. BASIC COMPONENTS - CENTRIFUGAL COMPRESSOR

COMPONENTS AND FUNCTIONS (CONT’D)
Paste Figure
Horizontally Split Case

- vs -
Vertically Split Case
FIGURE 2. CASING DESIGNS FOR A CENTRIFUGAL COMPRESSOR

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.
Actual Compression Path

P Exp = I (Isothermal)
2
Exp = k (Isentropic)
Exp = n > k (Polytropic)
P
P
1
V1
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 which is added to the gas. The shape of the curve shown in Figure 3 is
determined by the relationship:
PVk = Constant (Isentropic Compression)

THERMODYNAMIC EQUATIONS FOR GAS COMPRESSION (CONT'D)
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 C v 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
excess heat input to the gas. 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:
PVn = constant
The exponent n is always larger than the isentropic exponent k.
The actual compression path is the path plotted by P 1T1, P2T2. The actual work can be expressed by:
Actual Work = Isothermal Work = Isentropic Work = Polytropic Work

Isothermal Eff. Isentropic Eff. Polytropic Eff.
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:
PVk = Constant
PV = ZRT
P
Work = 2 VdP
P1

Head Calculation (Cont'd)
If the proper substitution and integration are performed, the resulting equation for each stage of compression is:
 k −1

Z1RT1   P2  k
Work = − 1
(k − 1)   P  
MW
k 
1
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 which is equivalent to the head.
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.
P(2.31) Eqn. (2)

Head =
S.G. relative to water
where:
S.G. = Specific gravity

Head Calculation (Cont'd)
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,
specific gravities are 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 which occur during compression. Temperatures are higher
during polytropic compression, therefore Polytropic Head > Isentropic Head.
FIGURE 4. COMPRESSOR HEAD

Centrifugal Compressors Are Polytropic
Centrifugal compressors operate in a polytropic manner. The work input 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:
 n−1

Z1RT1  
P2 n
Head =
(n− 1)   P  − 1
MW
n  
1
Eqn. (3)
A fixed relationship exists between n and k as shown in the following equation:
k−1
n− 1 k
=
n Polytropic Efficiency

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 is between 60% and 85%.
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
 P2  n
T 2 = T1 
 P1  Eqn. (5)
where:
T1 = Suction Temperature, °R
T2 = Discharge Temperature, °R
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 weight flow and dividing by
efficiency to obtain the actual energy imparted to the gas. The proper conversion factor must also be included.
lbM
(Hpoly )
min
Gas Horsepower (ghp) = Poly. Eff. (33,000) Eqn. (6)
where:
FT − LBF
LBH
Hpoly = Polytropic Head
Poly Eff. = Polytropic Efficiency, decimal fraction
lbMASS
min = Gas flow rate, pounds per minute
FT − LBF
33,000 = Conversion Factor HORSEPOWER − MIN.
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.

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.
BTU FT − LBF
His = (h2 − h1) 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 13-37 for this purpose.
6. Calculate the gas horsepower.
His (lb/min.)
ghp = _________________ Eqn. (8)
Is. Eff. (33,000)
Is. Eff. = Isentropic efficiency, decimal fraction.
7. Calculate brake horsepower (bhp) by adding mechanical losses.
8. To calculate the discharge temperature, first calculate the actual enthalpy at discharge conditions.
h2 actual = (h2 -h1 )is + h1

______________ Eqn. (9)
Is. eff.
9. Read the actual discharge temperature from the Mollier diagram at actual discharge enthalpy and the
discharge pressure.

MOLLIER DIAGRAM METHOD (CONT'D)
Figure 5 illustrates this calculation method, using a pressure-enthalpy diagram available in the GPSA
Engineering Data Book, Section 24.
P = 20 psia
T = 100°F
P = 100 psia
Isentropic Efficiency = 0.68
1000
psia
²h actual = ²h = 133
____is ____ = 196 Btu/lb
Is Eff. 0.68
²h = (h - h ) = 133 Btu/lb
is 2 1
.0
2.7
6 V=5 0
0 6.
2.8 100 psia
S=
T 2=425
15.0
V=20.0
T=100
T=200
T=0
T=300
140
360
240
120
160
180
T=400
320
220
340
260
420
40
60
480
T=500
280
380
440
80
20
460
10 psia
-1540 -1510 -1480 -1450 -1420 -1390 -1360 -1330 -1300 -1270 -1240
Enthalpy, Btu/lb Methane
FIGURE 5. MOLLIER METHOD - EXAMPLE

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

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

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.
Manufacturer's performance curves are used for the following purposes.
• To determine whether a particular 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.
* This assumption is valid for gas density changes of 20%. Greater changes affect the head produced. In
these instances, a new performance must be supplied by the original equipment manufacturer (OEM).

PERFORMANCE CURVES (CONT’D)
Paste VG 18
FIGURE 8. GENERALIZED PERFORMANCE CURVE

PERFORMANCE CURVES (CONT’D)
Paste VG 21
With Permission from Exxon Company, U.S.A.
FIGURE 9. TYPICAL MANUFACTURER'S PERFORMANCE CURVE -

HEAD AND EFFICIENCY

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 x 14.7 x T1 x Z Eqn. (10)

P1 520
where:
SCFM = Standard cubic feet per minute (60°F, 1 Atm)
SCFM = lb mol x 379

minute
SCFM = lb/hr x 379

60(MW)
P1 = Suction pressure, psia

T1 = Suction temperature, °R
Z = Compressibility factor, at suction conditions. Z is calculated using GPSA Figures
23-3 or 23-8 to 23-10.

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 
Q 2 = Q1 2 
 N1  Eqn. (11)
2
N 
H2 = H1 2 
N  1 Eqn. (12)
3
N 
bhp2 = bhp1 2 
 N1  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 N 2, if the curve at speed N1 is
known. Start with any point on the head curve at speed N 1. 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 bhp 2 and Q2 to obtain equivalent operating points.
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.

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.
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. The greater the flow
rate, the faster the developed head decreases. At a certain point the head developed drops to zero. 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 head drops to zero.

EFFICIENCY OF AN OPERATING MACHINE
A process engineer is frequently asked to calculate the efficiency of an operating centrifugal compressor. This
actual efficiency can be compared with the predicted 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 = Theoretical 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 Æh to isentropic Æh.
Method D. A computer program, such as COMPRESS.
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.

Procedures (Cont’d)
Method A - Driver Output vs. Compressor Input (Cont'd)
3. Calculate the polytropic efficiency.
Poly. Eff. = 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.
m
T 2  P2  n− 1
=
T 1  P1  (Note that m = n )
 log T 2 
 T1 
 T1 
 
m=
 logP2 
 P1 
5. Calculate the polytropic efficiency.
k −1
k
Poly. Eff. = 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. 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.
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 Æh isentropic.
5. Plot the actual discharge pressure and temperature on the Mollier diagram.
6. Calculate the actual Æh.
7. Calculate the isentropic efficiency.
Isentropic Efficiency = Æh isentropic

Æh actual
8. 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.

Method C - Mollier (Cont’d)
FIGURE 10. EFFICIENCY FROM OPERATING DATA - MOLLIER METHOD

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 most accurate 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.

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 N 2, which is lower than the design speed N 1.

Variable Speed (Cont'd)
FIGURE 11. VARIABLE SPEED CONTROL

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

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.
P1 P2 P3
Q ²P
P2
System Head
²P
P3
Compressor Head
Head
ACFM
FIGURE 13. DISCHARGE THROTTLING

Antisurge Control
In addition to matching process flow to compressor capacity, the flow rate must be kept higher than the surge
point. 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.
Suction
Discharge
Recycle
FIGURE 14. ANTISURGE CONTROL
In many installations a small computer 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).

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.
Atmosphere Atmosphere
P1
P2
P* To Consumers
P*
Control
Valve
P2
“Blowoff”
QReq’d QCompressor
FIGURE 15. ANTISURGE CONTROL AIR COMPRESSOR

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.
PC PC
Recycle
Suction
Knockout Recycle
3 250 psig
psig Accumulator
Economizer
Cooling Load 30
psig
Cooling Load
FIGURE 16. COMBINED CONTROL SCHEME - REFRIGERATION CIRCUIT

Combined Controls (Cont'd)
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.

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.

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 °F, °R
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
T2 calculated

WORK AID 1: CENTRIFUGAL COMPRESSOR - CALCULATION FORM (CONT’D)
(Page 2 of 2)
Z1 (GPSA 23-3)
Polytropic Head:
Z1( 1544 ) T1  
n −1
Hpoly = ( r) n − 1
( n − 1)  
MW
n
[( ]
( )( 1544 )( )
Hpoly = (
)
)
− 1
( )( )
Hpoly = feet
Gas Horsepower:
Hpoly x lb/min
ghp = __________________
Poly Eff. x 33,000
ghp = _( ) ( )_
( )(33,000)
ghp =
Mechanical Losses (GPSA Figure 13-38) hp
ghp = ghp + Mechanical Losses
= +
= hp

WORK AID 2: CALCULATION FORM - MOLLIER METHOD
(Page 1 of 3)
Gas:
Suction Flow Rate: SCFM, lb/min, ACFM
P1 psia
T1 °F
P2 psia
h1 Btu/lb
h2 isentropic Btu/lb
ÆH isentropic = - ( )
= Btu/lb
Polytropic Efficiency:
From Manufacturer Spec
or: 0.0109 ln (Suction ACFM) + 0.643
= 0.0109 ln ( ) + 0.643
r = P2 = ____ = _____
P1 ____
k = ________
Isentropic Efficiency (from GPSA Figure 13-37):

WORK AID 2: CALCULATION FORM - MOLLIER METHOD (CONT’D)
(Page 2 of 3)
Gas Horsepower:
Isentropic Head = Isentropic Æh (778)
= ( )(778)
= feet
(Isentropic Head)(lb/min)
ghp = _______________________________
(Isentropic Efficiency)(33,000)
( )( )
= _______________
( )(33,000)
= hp
Mechanical Losses hp
(GPSA Figure 13-38)
bhp = ghp + Mechanical Losses
= +
= hp
Polytropic Efficiency
Polytropic Head = Isentropic Head x ___________________
Isentropic Efficiency
= ________ x ________
= feet

WORK AID 2: CALCULATION FORM - MOLLIER METHOD (CONT’D)
(Page 3 of 3)
Discharge Temperature:
Isentropic Æh
Actual Æh = _______________
Isentropic Eff.
= ________
= Btu/lb
Actual h2 = h1 + Actual Æh
= ________ + ________
= ________ Btu/lb
T2 = °F (from Mollier Diagram)

WORK AID 3: COMMON OPERATING PROBLEMS FOR CENTRIFUGAL

COMPRESSORS
Common Problems Possible Cause(s)
Surge • 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)
Driver Overload • High suction pressure

• High molecular weight of gas
• Low inlet temperature of gas
Vibration • Liquid in suction

• Deposits on rotor
• Rotor erosion/corrosion
• Mechanical problems (GPSA p. 13-39)
Tripout or • Liquid in suction knockout drum

Automatic Shutdown
• 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)

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 The point on the performance curve of a centrifugal compressor
(BEP) 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 The actual volume of a gas divided by the volume of the same
Factor, Z 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.
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, ÆS, is equal to ÆQ/T,
where ÆQ 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.
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.
Sidestream 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 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.

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 Standards
• AES-K-402 Centrifugal Compressors
• ADP-K-402 Centrifugal Compressors

Engineering Encyclopedia: Centrifugal Compressors

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What are the main components of a centrifugal compressor?

What are the main components of a centrifugal compressor?

What are some common control schemes used for centrifugal compressors?

What are some common control schemes used for centrifugal compressors?

Engineering Encyclopedia

Saudi Aramco DeskTop Standards

Chapter : Process For additional information on this subject, contact

COMPONENTS AND FUNCTIONS ......................................................................................................... 1

Saudi Aramco DeskTop Standards

WORK AID 3: COMMON OPERATING PROBLEMS FOR CENTRIFUGAL COMPRESSORS ........ 40

Saudi Aramco DeskTop Standards

COMPONENTS AND FUNCTIONS

Saudi Aramco DeskTop Standards 1

COMPONENTS AND FUNCTIONS (CONT’D)

FIGURE 1. BASIC COMPONENTS - CENTRIFUGAL COMPRESSOR

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COMPONENTS AND FUNCTIONS (CONT’D)

Horizontally Split Case

FIGURE 2. CASING DESIGNS FOR A CENTRIFUGAL COMPRESSOR

Saudi Aramco DeskTop Standards 3

THERMODYNAMIC EQUATIONS FOR GAS COMPRESSION

Actual Compression Path

FIGURE 3. COMPRESSION PATHS

PV = Constant (Isothermal Compression)

PVk = Constant (Isentropic Compression)

Saudi Aramco DeskTop Standards 4

THERMODYNAMIC EQUATIONS FOR GAS COMPRESSION (CONT'D)

The exponent k is equal to Cp/Cv, a common thermodynamic property of gases.

Polytropic compression follows a path described by:

The exponent n is always larger than the isentropic exponent k.

Actual Work = Isothermal Work = Isentropic Work = Polytropic Work

For isentropic compression:

Saudi Aramco DeskTop Standards 5

Head Calculation (Cont'd)

Z1 = Compressibility factor, at suction

P(2.31) Eqn. (2)

S.G. = Specific gravity

Saudi Aramco DeskTop Standards 6

Head Calculation (Cont'd)

• Head is Analogous to Pump Head

FIGURE 4. COMPRESSOR HEAD

Saudi Aramco DeskTop Standards 7

Centrifugal Compressors Are Polytropic

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

Saudi Aramco DeskTop Standards 8

Polytropic Efficiency = 0.0109 ln(ACFM) + 0.643 Eqn. (4)

ACFM = Actual cubic feet per minute at suction condition

Compressor Discharge Temperature

Saudi Aramco DeskTop Standards 9

Saudi Aramco DeskTop Standards 10

MOLLIER DIAGRAM METHOD

3. Calculate the isentropic head.

4. Obtain the polytropic efficiency from the manufacturer's data.

6. Calculate the gas horsepower.

Is. Eff. = Isentropic efficiency, decimal fraction.

7. Calculate brake horsepower (bhp) by adding mechanical losses.

h2 actual = (h2 -h1 )is + h1

Saudi Aramco DeskTop Standards 11