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Basic Compression
Short Course
by Greg Ph i l l ippi , ACI Services, Inc.
and Manny An gulo, El Paso Energy
for 2001 Gas Machin ery Conference, Aus tin, TX
This short course will cover the fundamental principles of reciprocating compressors
and engines. For the compressor, this will include discussions of PV diagrams,
capacity, volumetric efficiency, and horsepower. In addition, it will cover the effects of
changing conditions, gas analysis, temperature, and pulsation on compressors. For
the engine, discussions of the sequence of events for two stroke and four stroke
engines that include pressure and vibration patterns with respect to volume and time
will be presented. Finally, it will briefly cover engine combustion characteristics for afew common cases.
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Course Outline
®Pressure –volume diagrams
®Capacity
®Volumetric efficiency
®Horsepower
®Adiabatic
®Valve loss
®Friction
The course will cover the basic thermodynamic theory supporting a reciprocating
compressor. Mechanical design details will not be covered. An understanding of the
basic thermodynamics is vital and forms a good foundation for a deeper understanding
of the mechanical aspects.
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Course Outline
®Vary ing cond i t ions
®Pressure
®Speed
®Gas analysis effects
®Adiabatic exponent (k-value)
®Compressibility (Z)
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Course Outline
®Temperature
®Pulsat ion
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P-V Diagram
Volume
P r e s s u r e
PS
PD
The P-V diagram (or pressure-volume diagram) is a plot of the pressure inside the
compression chamber (inside the bore) versus the volume of gas inside the chamber.
A complete trip around the diagram represents one revolution of the crankshaft.
This is an “ideal” diagram in that it does not show any valve losses (which will be
explained later in the course).
PD is discharge pressure (typically said to be the pressure that exists at the cylinder
flange).
PS is suction pressure.
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Compression
C o m
p r e s s i o n
Suction valvecloses
Dischargevalve opens
Volume
P r e s s u r e
PS
PD
This depicts the compression event.
It starts at the point where the suction valve closes. When the suction valve closes,
gas is trapped inside the compression chamber at suction pressure and suction
temperature.
As the piston moves towards the other end of the compression chamber, the volume isdecreasing, the pressure increasing and the temperature increasing.
Compression stops when the discharge valve opens.
The shape of the compression event is determined by the adiabatic exponent (k-value
or n-value). This is a thermodynamic property of the gas and will be discussed later in
the course.
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Volume
P r e s s u r e
PS
PD
Discharge
Dischar ge
Dischargevalve opens
Dischargevalve closes
When the discharge valve opens, compression stops, and gas at discharge pressure
and discharge temperature is pushed out of the compression chamber through the
discharge valve, into the discharge gas passage and out into the discharge piping.
The discharge event continues until the piston reaches the end of the stroke, where
the discharge valve closes and the next event, expansion, begins.
The compression and discharge events together represent one-half of one revolution
of the crankshaft and one stroke length.
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When the discharge valve closes at the end of the discharge event, there is still some
gas left in the compression chamber. This volume of gas is referred to as the “fixed
clearance volume” and is usually expressed as a percentage:
As the piston moves away from the head, the volume inside the compression chamber
increases with all of the valves (suction and discharge) closed. The gas in the fixed
clearance volume expands, decreasing in pressure and temperature, until the
pressure inside the compression chamber reaches suction pressure, where the
suction valve opens and the expansion event ceases.
Expansion
E x
p a n s i o n
Dischargevalve closes
Volume
P r e s s u r e
PS
PD
%
ntdisplacemepistonin
clearancefixedinClearanceFixed% 100
3
3
×=
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Suction
Suction
Suction valveopens
Suction valvecloses
Volume
P r e s s u r e
PS
PD
At the end of the expansion event, the suction valve opens opening the compression
chamber to the suction gas passage and suction piping system. As the piston moves,
the volume in the compression chamber is increasing and the compression chamber
fills with gas at suction pressure and suction temperature.
The suction event ceases when the piston reaches the other end of the stroke, the
suction valves closes and the piston turns around and goes the other direction.
The end of the suction event marks the end of one complete cycle. One complete
cycle requires one complete revolution of the crankshaft and two stroke lengths.
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Volume
P r e s s u r e
PS
PD
Volumetric Efficiency
Inlet volume
Displacement
The inlet volume is the amount of gas brought into the compression chamber during
the suction event. The amount of gas brought into the compression chamber out of
the suction piping system IS the capacity!
The displacement represents the volume displaced during one complete stroke length
of the piston.
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Volumetric Efficiency
ntDisplaceme
volumeInletefficiencyVolumetric =
Volumetric efficiency (VE) is the ratio of inlet volume to displacement, usually
expressed as a percent.
It should be noted that VE has nothing to do with when the suction valve opens. It has
everything to do with how much of the compression chamber fills with gas at suction
pressure and suction temperature.
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Volumetric Efficiency
−
−= 1
P
P
Z
Z%CL100VE
K1
S
D
D
S
Suction pressure, psia=PS
Discharge pressure, psia=PD
Adiabatic exponent, k-value=K
Compressibility factor @ suction conditions=ZS
Compressibility factor @ discharge conditions=ZD
Fixed clearance, %=%CLVolumetric efficiency, %=VE
Where:
This is the equation for volumetric efficiency.
Note the influence of the thermodynamic gas properties K and Z. The higher the K-
value the higher the volumetric efficiency, everything else equal. The influence of Z is
not so straight forward because it is actually a ratio of Z and the ratio for most typical
applications is around 1.0 (meaning ZS = ZD).
Also, note the influence of clearance. The higher the %CL (percent fixed clearance)
the lower the volumetric efficiency.
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Volumetric Efficiency
( )
−
−−= 1R
Z
Z%CLR100VE K
1
CD
SC
Compression ratio, Pd/Ps=RC
Adiabatic exponent, k-value=K
Compressibility factor @ suction conditions=ZS
Compressibility factor @ discharge conditions=ZD
Fixed clearance, %=%CLVolumetric efficiency, %=VE
Where:
This equation shows a common “fudge factor”, - RC (compression ratio), added to the
equation to account for piston ring leakage and any other leakage.
Compressor OEM’s have many ways to account for the difference between “real
world” volumetric efficiency and volumetric efficiency by pure theory.
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Change in Capacity for
+10% Clearance
0
10
20
30
40
50
60
70
80
90
1.0 1.5 2.0 2.5 3.0 3.5
Compression Ratio
C h a n g e i n C a p a c i t y ,
20%
40%
60%
80%
This chart shows the effect of fixed clearance on volumetric efficiency.
Specifically, the chart shows the effect of adding 10% clearance to four different base
fixed clearances over a range of compression ratio.
The chart also shows the effect of compression ratio on volumetric efficiency.
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Volume
P r e s s u r e
Discharge
Volumetric Efficiency
Outletvolume
Displacement
Ps
Pd
There is also discharge volumetric efficiency.
It is the ratio of the outlet volume to the piston displacement.
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Volumetric Efficiency
( )K
1
CD
S
SD
RZ
Z
VEVE
=
Compression ratio, Pd/Ps=RC
Adiabatic exponent, k-value=K
Compressibility factor @ suction conditions=ZS
Compressibility factor @ discharge conditions=ZD
Fixed clearance, %=%CLVolumetric efficiency, %=VE
Where:
This is the equation for discharge volumetric efficiency.
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ACFM
( ) ( )V.E.P.D.ACFM ×=
Volumetric efficiency, decimal=V.E.Piston displacement, cubic feet per minute=P.D.Actual cubic feet per minute=ACFM
Where:
This is the equation used to calculate ACFM or actual cubic feet per minute of volume
flow, knowing volumetric efficiency.
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MMSCFD
( )( )( )( )( )SS
STDS
ZT
ZPACFM0.0509MMSCFD =
Actual cubic feet per minute=ACFM
Compressibility factor @ standard conditions=ZSTD
Suction temperature, deg R=TS
Compressibility factor @ suction conditions=ZS
Suction pressure, psia=PS
Million standard cubic feet per day=MMSCFDWhere:
This equation converts ACFM to MMSCFD or million standard cubic feet per day.
The standard pressure and temperature in the United States is usually 14.7 psia and
60 degrees F. The MMS (Minerals Management Service in the Department of the
Interior) in the past has used 15.025 psia as the standard pressure for natural gas
measurement. Believe the rules have been changed to 14.696 psia. 15.025 psia
works out to 10 ounces per square inch above the average barometric pressure of 14.4 psia.
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Horsepower Breakdown
Valve Loss
Friction
Adiabatic
This pie chart shows how total horsepower might breakdown for an “average” (say
moderate to high compression ratio) application. In this type of application adiabatic
horsepower is the majority of the horsepower.
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This a real life pressure-volume diagram with the adiabatic horsepower region
highlighted.
Remember from college thermodynamics:
This means that the area enclosed by the P-V diagram is directly related to work or
horsepower.
Adiabatic Horsepower
Volume
P r e s s u r e
Ps
Pd
AdiabaticHorsepower
∫ = PdVWork
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Adiabatic Horsepower
( )( )( )( )( )( )( )
( )
−
×−
+=
−
1P
P
Z21K33000
ZZV.E.P.D.PK144AHP
K
1K
S
D
S
DSS
Compressibility factor, discharge=ZD
Suction pressure, psia=PS
Compressibility factor, suction=ZS
Discharge pressure, psia=PD
Piston displacement, cfm=P.D.Volumetric efficiency, decimal=V.E.
Adiabatic exponent (k-value)=KAdiabatic horsepower =AHP
Where:
This is an equation for adiabatic horsepower.
Note the influence of the gas thermodynamic data, K and Z’s.
Remember that (P.D.)(V.E.) is capacity.
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Adiabatic HP per MMSCFD
( )( )( )( )
( )
−
−
+=
−
1P
P
1K
TZZK0.04283
MM
AHP K
1K
S
DSDS
Compressibility factor =ZPressure, psia=P
Suction temperature, deg R=TS
Adiabatic exponent (k-value)=KAdiabatic horsepower per MMSCFD=AHP/MM
Where:
This is an equation for adiabatic horsepower per million standard cubic feet per day
(MMSCFD or MM).
Note the data required: pressures, suction temperature and gas thermodynamic data
(K and Z’s).
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Valve Loss Horsepower
Volume
P r e s s u r e
Ps
PdDischarge valveloss horsepower
Suction valve losshorsepower
This P-V diagram highlights suction and discharge valve loss horsepower (VLHP).
VLHP is created by the pressure drop encountered as gas flows through the valve(s).
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Valve Loss Horsepower
( )( )( )( )RPMV.E.SAÄPVLHP PISTON≈
Pressure drop=ÄP
Volumetric efficiency, decimal=V.E.Speed, revolutions per minute=RPM
Stroke=SArea of the piston=APISTON
Valve loss horsepower =VLHPWhere:
This is an equation that shows the relationship between pressure drop, piston (or bore)
area, stroke, volumetric efficiency and speed.
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Valve Pressure Drop
2ñVÄP ≈
Pressure drop=ÄP
Velocity=VDensity=ñ
Where:
This is the general relationship for any calculation of pressure drop. Pressure drop is
related to density times velocity squared.
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Gas Density
( )( )TZ
SGPñ ≈
Gas specific gravity=SGPressure=P
Compressibility factor =ZTemperature=T
Density=ñWhere:
This is an equation for density.
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Gas Velocity
( )( )( )( )
( ) ( )( )
( )2VALVE
2PISTON
VALVE
PISTON
D
RPMSD
A
RPMSAV ≈≈
Piston diameter =DPISTON
Speed, revolutions per minute=RPMValve area=AVALVE
Stroke=SPiston area=APISTON
Valve diameter =DVALVE
Velocity=VWhere:
This is an equation for gas velocity.
Note the ratio of the area of the piston to the area of the valve (this is not valve flow
area, this is the area of the full valve diameter).
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Valve Pressure Drop
( )( ) ( ) ( )
( )( )4VALVE
224PISTON
DTZ
RPMSDSGPÄP ≈
Compressibility factor =Z Temperature=T
Piston diameter =DPISTON
Speed, rev per minute=RPMStroke=S
Gas specific gravity=SGPressure=P
Valve diameter =DVALVE
Pressure drop=ÄPWhere:
Combining the density and velocity relationships into the pressure drop equation yields
this relationship.
Note the following:
1. Pressure drop is directly related to the ratio of the diameter of the piston to the
fourth power, and inversely related to the diameter of the valve to the fourth power.
2. Pressure drop is directly related to stroke squared and speed squared, or piston
speed squared.
As an aside, the equation for piston speed is:
Where:
Piston speed = average piston velocity, feet per minute
Stroke = inches
Speed = rpm
6
speedstroke
12
speedstroke2speedPiston
×=
××=
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Valve Loss Horsepower
( )( ) ( ) ( ) ( )
( )( )4VALVE
336PISTON
DTZ
V.E.RPMSDSGPVLHP ≈
Temperature=T
Speed, revolutions per minute=RPM
Gas specific gravity=SGPressure=P
Volumetric efficiency, decimal=V.E.
Compressibility factor =Z
Valve diameter =DVALVE
Stroke=SPiston diameter =DPISTON
Valve loss horsepower =VLHPWhere:
This is the equation for VLHP with substitutions for pressure drop.
Note the following:
1. The relationship of the piston diameter and valve diameter to VLHP.
2. The relationship of stroke and speed to VLHP. Another way to look at thisrelationship is to say that stroke times speed is piston speed and that VLHP is directly
related to piston speed cubed.
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Indicated Horsepower
HPIndicated
HPLossValveDischarge
HPLossValveSuction
HPAdiabatic
++
This is the “definition” of indicated horsepower.
It is the sum of the horsepower developed from the pressure-volume diagram.
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Brake Horsepower
HPBrake
HPFriction
HPIndicated
+
This is the “definition” of brake horsepower.
Brake horsepower is the horsepower required at the face of the crosshead, in the case
of an integral-engine compressor, or at the driver coupling connection, in the case of a
separable compressor (provided the “friction HP” component includes allowance for
the friction losses inside the crankcase).
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Brake Horsepower
E.M
IHPBHP
.=
Mechanical efficiency
Typically 92% to 97%
=M.E.Indicated horsepower =IHPBrake horsepower =BHP
Where:
This is another way to express brake horsepower, or BHP.
The numbers used for mechanical efficiency vary with the OEM.
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Brake Horsepower
FFHPM.E.
IHPBHP +=
Mechanical efficiency, associated with thecylinders only, typically 0.95
=M.E.
Frame friction HP, constant number to accountfor friction in the frame
=FFHP
Indicated horsepower =IHPBrake horsepower =BHP
Where:
This is yet another way to express brake horsepower (BHP).
The friction component has been divided into cylinder and frame (or crankcase)
components.
The mechanical efficiency factor is intended to cover the friction in the cylinders.
The frame friction factor is typically a constant number used to account for the friction
in the frame or crankcase. OEM’s may vary FFHP with speed or speed squared.
This is an approach most typically associated with separable compressors.
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Increased Discharge Pressure
Increased PD
with PS constant
This shows the effect on the P-V diagram of increasing discharge pressure with
everything else remaining constant.
Note that volumetric efficiency decreases and discharge VLHP decreases.
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Decreased Discharge Pressure
Decreased PD
with PS constant
This shows the effect of decreasing the discharge pressure.
Note that volumetric efficiency increases.
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Increased Suction Pressure
Increased PS
with PD constant
This shows the effect of increasing suction pressure with discharge pressure
remaining constant.
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Effect of SpeedPressure drop
varies with RPM2 70% Speed49% ÄP
This depicts the effect of a speed change on the P-V diagram.
Note that the width of the diagram does not change - in other words the basic shape of
the diagram does not change.
The only change is in the valve pressure drop or the valve loss horsepower.
Remember that the pressure drop changes with the square of the speed.
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Effect of K-value
This is a temperature-entropy diagram for carbon dioxide.
Entropy is a thermodynamic term used to measure the unavailability of energy.
Entropy increases as a system loses heat but remains constant when there is no gain
or loss of heat.
The compression and expansion segments of the P-V diagram are modeled assumingthat they are adiabatic (or isentropic or entropy is a constant).
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T-S Diagram
Entropy
T e m p e r a t u r e
PS
PD
K
1-K
S
D
S
D
P
P
T
T
=
Isentropic or adiabaticcompression
TS
TD
K-value is the adiabatic exponent and defines an adiabatic (or constant entropy) path
from one state point to another. For a recip compressor this is from suction pressure
and temperature to discharge pressure.
Note that k-value is a path function and not a point function - in other words k-value
cannot be determined at a point or at a specific pressure and temperature. K-value
defines a path.
The equations calculates adiabatic discharge temperature and essentially defines k-
value.
Adiabatic or isentropic (constant entropy) means that no heat is exchanged (goes into
or out of the process) during the process - here the process being the compression of
a gas from P1 and T1 to P2.
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Effect of K-value
K = 1.4Air, nitrogen
K = 1.12Propane
These two different P-V diagrams depict the effect of k-value. The greater the k-value,
the “fatter” the P-V diagram.
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Compressibility (Z)
gasidealfor MRTPV =gasrealfor ZMRTPV =
Universal gas constant=RMass=M
Temperature=TCompressibility factor =Z
Volume=VPressure=P
Where:
PV = MRT is the perfect gas law.
PV = ZMRT uses “Z”, or compressibility factor, to correct the perfect gas law for real
gases. This defines compressibility factor.
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Effect of ZS
ZS = 0.8
ZS = 1.0
Shows how suction compressibility factor affects the P-V diagram.
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Effect of ZD
ZD = 1.0
ZD = 0.8
Shows how discharge compressibility factor affects the P-V diagram.
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Adiabatic Discharge
Temperature
K
1K
S
DSAdiabatic-D P
PTT
−
=
Suction pressure, psia=PS
Discharge pressure, psia=PD
K-value, adiabatic exponent=K
Suction temperature, deg R=TS
Adiabatic discharge temperature, deg R=TD-Adiabatic
Where:
The equation for adiabatic discharge temperature.
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Actual Discharge
Temperature
( )Efficiency
TTT SAdiabatic-D
Actual-D−
=
Compression efficiency=EfficiencySuction temperature=TS
Actual discharge temperature=TD-Actual
Where:
This shows that the inefficiency of the compression process adds to the discharge
temperature - in other words all of the energy that goes into the compression process
goes into the compressed gas stream. Of course, there is heat removed by the
cooling water jackets and heat is rejected to the surrounding environment, so the
actual discharge temperature will most likely be somewhere between adiabatic and the
actual given by the above.
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Suction Temperature Pre-heat
®Mixing effect during the suctionevent
®Heat transfer in the suction gaspassage
There can be an effect during the compression process where the suction gas
temperature in pre-heated. In other words the temperature of the gas at the instant
that the compression leg of the P-V diagram begins is greater than that measured in
the suction pulsation bottle or even than that measured in the suction gas passage. It
is the temperature (and pressure) of the gas when compression starts that determines
the capacity and has an effect on horsepower.
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Pulsation
Pulsation is a multi-day short course all unto itself!
Here we will just touch on how pulsation might affect the P-V diagram and therefore
the compression process.
The slide shows a P-V diagram distorted by pulsation.
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Pulsation
Suction pressure for capacity=Z
Compression ration for HP/MM= Y
Compression ratio for capacity=X
Average pressure during valve open time=
“Z” represents the suction “toe” pressure.
“X” represents the compression ratio based on suction and discharge toe pressures.
“Y” represents the compression ratio based upon volume averaged pressures during
the valve open time (the dashed lines across suction and discharge).
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Pulsation
Here, “X” represents how much the volumetric efficiency is distorted by pulsation.
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Effect of ÄP on V.E.
0
5
10
15
20
25
1.0 1.5 2.0 2.5 3.0 3.5 4.0
Compression Ratio
C h a n g e i n V . E . , %
K = 1.3ZS = ZD = 1.0Clearance = 40%
70% V.E.
50% V.E.
30% V.E.
3 % Ä P
2 % Ä P
1 % Ä P
This graph shows how much pulsation can affect volumetric efficiency.
Pulsation is represented by percentages of pressure drop.