Intro to Recips

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1

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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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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−

−= 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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( )

−

−−= 1R

Z

Z%CLR100VE K

1

CD

SC

Compression ratio, Pd/Ps=RC





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


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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( )K

1

CD

S

SD

RZ

Z

VEVE

=

Compression ratio, Pd/Ps=RC





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



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


Compressibility factor, suction=ZS


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


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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( )( )( )( )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



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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( )( ) ( ) ( ) ( )

( )( )4VALVE

336PISTON

DTZ

V.E.RPMSDSGPVLHP ≈

Temperature=T

Speed, revolutions per minute=RPM


Volumetric efficiency, decimal=V.E.

Compressibility factor =Z


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

−

=



K-value, adiabatic exponent=K


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.



9/14/01

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.

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Intro to Recips