Theory Basic Thermodynamics of Reciprocating Compression

Basic Thermodynamics of Recip Compression October 2011

Greg Phillippi Ariel Corporation 1

Greg PhillippiAriel Corporation

Phone: [email protected]

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Basic Thermodynamicsof Reciprocating

Compression

This short course will provide the attendee an opportunity to learn the very basic and fundamental concepts governing compression with areciprocating compressor. This will include discussions of pressure versus time (or crank angle) and pressure versus volume diagrams, volumetric efficiency, capacity, horsepower and compression efficiency. In addition, the effects of changing conditions, gas analysis, temperature, and gas pulsation will be discussed. Many of these topics are presented through the explanation of the underlying thermodynamic theory.



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Course Outline

• Pressure - time diagram animation• Pressure - volume diagram• Capacity

• Fixed clearance• Volumetric efficiency• ACFM, ACF, SCF, MMSCFD

• Ideal and real gas laws

The short 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

• Horsepower• Adiabatic• Valve loss• Resistance factor• Valve equivalent area• Deactivated end• IHP, BHP, friction• Compression efficiency

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Course Outline

• Varying conditions• Pressure• Speed

• Gas analysis effects• Adiabatic exponent (k-value)• Compressibility factor (Z)



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Course Outline

• Temperature• Adiabatic discharge temperature• Actual discharge temperature• Suction temperature preheat

• Multi-stage compression• What• Why• How• Capacity balance



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Course Outline

• Rod load• Tension• Compression• Gas + inertia• Non-reversing

• Pulsation



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Pressure versus TimeDiagram Animation

The P-T diagram (pressure versus time diagram) is a plot of the pressure inside the compression chamber (inside the bore) versustime or crank angle – time and crank angle being directly related.

IDC is inner dead center.ODC is outer dead center.

PD is discharge pressure (typically said to be the pressure that exists at the cylinder flange).PS is suction pressure - at the cylinder flange.



Suction

Discharge

Crank Angle

Ps

Pd

Pres

sure

ODC IDC ODC

HeadEnd

CrankEnd

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EXPANSION

EXPANSIONCO

MRE

SSIO

N

COM

RESS

ION



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Volume

Pres

sure

PS

PD

Pressure-Volume Diagram

VMIN VMAX

The P-V diagram (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 circuit around the diagram represents one revolution of the crankshaft.

This is an “ideal” diagram in that it does not show any valve pressure drop and therefore no valve loss horsepower (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 - at the cylinder flange.



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Volume

Pres

sure

PS

PD

Compression

Compression

Suction valve is closed

Discharge valve opens

This depicts the compression event.

It starts at the point where the suction valve closes. When thesuction 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 is decreasing, the pressure increasing and the temperature increasing.

Compression stops when the discharge valve opens.

The shape of the curve 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

Pres

sure

PS

PD

Discharge

Discharge


Discharge valve 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.



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.

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Volume

Pres

sure

PS

PD

Expansion

Expansion

Suction valve opens

%ntdisplacemepistonin

clearancefixedinClearanceFixed% 1003

3×=



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Volume

Pres

sure

PS

PD

Suction

Suction

Suction valve opens

Suction valve closes

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

Pres

sure

PS

PD

Four Events

Suction

Suction valve opens

Suction valve closes

Expansion

Discharge


Discharge valve closes

Compression

All four events representing the compression cycle are shown on this chart - Compression, Discharge, Expansion, and Suction.



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Fixed Clearance

Head End Clearance

There are many pockets of volume in the compression chamber thatcombine to form the fixed clearance volume: around the piston between the piston and the bore, between the piston and the head, around the head between the head and bore, between the end of the valve and the head, and in the valve itself.

The fixed clearance volume is the gas that needs to expand from discharge to suction pressure inside the cylinder.



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Crank End Clearance

Fixed Clearance



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Fixed Clearance

This shows the fixed clearance volume that is between the valve and the bore and inside the valve.

It can then be imagined that the fixed clearance volume changes with the diameter and thickness of the valve.



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Fixed Clearance

100%ntDisplacemein

ClearanceinClearanceFixed% 3

3

×=

Fixed clearance is typically expressed as a percent – the ratio of the fixed clearance volume to the piston displacement in volume units.



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Volume

Pres

sure

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. The piston displacement of the head end and crank end of a double-acting cylinder are different due to the existence of the piston rod in the crank end.



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ntDisplacemevolumeInletVE =

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 (V.E.) is the percentage of stroke that can (or will) fill with suction gas and is the cylinder end’s capacity.

• V.E. is NOT suction valve open time.• A higher number for V.E. does not mean it is

“better”.• The influence of V.E. on compression (energy)

efficiency is through the relationship of V.E. to average piston velocity (avg velocity of gas thru valves)



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Volumetric EfficiencyNot Valve Open Time

VALVE OPEN TIME

Here, “X” represents how much the volumetric efficiency is “distorted” by pulsation. This shows that valve open time and volumetric are not always necessarily the same thing.



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⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−= 1

K1

sPdP

dZsZ

%CL100SVE

Suction pressure, psia=PS

Discharge pressure, psia=PD

Adiabatic exponent, k-value=K

Compressibility factor @ PS & TS=ZSCompressibility factor @ PD & TD=ZD

Fixed clearance, %=%CLVolumetric efficiency, %=VES

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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⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−= 1

K1

sPdP

dZsZ

%CL-CR100SVE



Adiabatic exponent, k-value=K

Compressibility factor @ PS & TS=ZSCompressibility factor @ PD & TD=ZD

Fixed clearance, %=%CLVolumetric efficiency, %=VES

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.



This a pressure-volume diagram showing low volumetric efficiency.

The concern with low volumetric efficiency is the time required for the discharge valve to open and close properly. With low VE the discharge valve will close late causing the seal element to slam against the seat with excessive closing impact velocity.The seal element will then fail.

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Low Volumetric Efficiency

Ps

PdPr

essu

re

Volume



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Change in Capacity forAdded 10% Clearance

0

10

20

30

40

50

60

70

80

90

1.0 1.5 2.0 2.5 3.0 3.5

20%40%60%80%

Compression Ratio

Cha

nge

i n C

a pac

it y, %

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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ACFM

( ) ( )SVEPDACFM ×=

Volumetric efficiency, decimal=VES

Piston displacement, cubic feet per minute=PDActual 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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What is ACF & SCF?

• When capacity is provided in volume terms the density must be specified or known.

• ACF = “actual” cubic feet• Density is PS and TS

• SCF - “standard” cubic feet• Density is PSTD and TSTD• Typically PSTD = 14.7 psia & TSTD = 60 ºF

This shows how much volume one pound (mass) of gas occupies at two different pressures (14.7 psia and 500 psia) at the same temperature (60 deg F)

SCF (standard cubic foot) is volume measured at a standard pressure and temperature of 14.6 psia and 60 deg F (typically).

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 United States 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.

ACF (actual cubic foot) is volume measured at the actual pressure and temperature conditions.



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MMSCFD

( )( )( )( )( )( )SS

STDSZT

ZPACFM0.0509MMSCFD =

Actual cubic feet per minute=ACFM

Compressibility factor @ standard conditions=ZSTDSuction temperature, ºR=TSCompressibility factor @ suction conditions=ZS


Million standard cubic feet per day=MMSCFDWhere:

This equation converts ACFM (actual cubic feet per minute) to MMSCFD (million standard cubic feet per day).



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MMSCFD to LB per HR

1909.8HRLB

R5201

LB-1545.33FTRLB

24HRDAY

LB29)LB(.6

MMSCFCF1,000,000S

DAY1.0MMSCF

FT144IN

IN14.7LB

HRLB

O

OMOL

MOL2

2

2

=

×−

×××

××××=

This equation shows the conversion from MMSCFD to LB per HOUR.

This equation converts million standard cubic feet per day capacity (MMSCFD) into pounds-mass per hour (LBm/HR).



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Ideal Gas Law

RTPVm,

PmRTVmRT,PV ===

Volume, cubic feet=VMass, pounds mass=mUniversal gas constant, 1545.3/MW (FT-LB)/(LBmol-ºR)=RTemperature, ºR (ºF + 459.6)=T

Pressure, psia=PWhere:

This is the ideal gas law. This is the simplest gas equation ofstate in that it relates pressure, mass and volume.



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Real Gas Law

ZRTPVm,

PZmRTVZmRT,PV ===

Volume, cubic feet=V

Mass, pounds mass=mUniversal gas constant, 1545.3/MW (FT-LB)/(LBmol-ºR)=RTemperature, ºR (ºF + 459.6)=T

Compressibility factor @ P & T=Z

Pressure, psia=PWhere:

This is the real gas law. It is a slightly more complicated form of the ideal gas law as it adds the compressibility factor parameter.

Good to remember this relationship. Knowing pressure temperature and compressibility factor and either volume or mass, the unknown of volume or mass can be calculated.



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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 isthe majority of the horsepower.



This a real life pressure-volume diagram with the adiabatic horsepower region highlighted.

Remember the following from thermodynamics classes?

This means that the area enclosed by the P-V diagram is directly related to work or horsepower.

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Volume

Pres

sure

Ps

Pd

Adiabatic Horsepower

AdiabaticHorsepower

∫= PdVW

∫= PdVWork



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Adiabatic Horsepower

( )( )( )( )( )( )( )( )( )

( )

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛×−

+=

−

1PP

Z21K33000ZZVEPDPK144AHP

K1K

S

D

S

DSSS

Compressibility factor, discharge=ZD


Compressibility factor, suction=ZS


Piston displacement, cfm=PDVolumetric efficiency, suction, decimal=VES

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 the product of piston displacement and volumetric efficiency (PDxVE) is capacity.



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Adiabatic HP per MMSCFD

( )( )( )( )( )

( )

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−⎟⎟⎠

⎞⎜⎜⎝

⎛−

+=

−

1PP

1KTZZK0.04283

MMAHP K

1K

S

DSDS


Compressibility factor=Z


Suction temperature, ºR=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

Pres

sure

Ps

PdDischarge valve loss horsepower

Suction valve loss horsepower

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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( )( )( )( ) ( ) ( )

( )( )( )2

pkt vlvANsTsZ1910

3RPMS3boreApRsVEsPSG28.977.045

VLHP

⎟⎠⎞⎜

⎝⎛

×⎟⎠⎞⎜

⎝⎛

=

This is the equation for valve loss horsepower.



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( )( )( )RPMSVEAΔPVLHP BORE ×≈

Pressure drop=ΔP

Volumetric efficiency, suction, fraction=VESpeed, revolutions per minute=RPM

Stroke=SCylinder main bore cross-sectional area=ABORE

Valve loss horsepower=VLHPWhere:

This is a relationship between pressure drop, bore area, volumetric efficiency, stroke, and speed.

Stroke multiplied by speed is known as “piston speed”. Piston speed is the average linear speed at which the piston moves through one revolution of the crankshaft (two stroke lengths).

Piston speed is:

rpmSpeedinchesStroke

fpm,6

SpeedStroke12

SpeedStroke2SpeedPiston

==

×=

××=



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Valve Pressure Drop

2ρVΔP ≈

Pressure drop=ΔP

Velocity=VDensity=ρ

Where:

This is the general relationship for any calculation of pressuredrop. Pressure drop is related to density times velocity squared.



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Gas Density

( )( )TZSGPρ ≈

Gas specific gravity=SGPressure=P

Compressibility factor=ZTemperature=T

Density=ρWhere:

This is an equation for density.

This is derived by rearranging the ideal gas law:

ZTP(SG)ρ

VMρ

)(SG)(28.961545.35R

ZRTP

VM

ZMRTPV

≈

=

=

=

=



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Gas Velocity

( )( )( )( )

( ) ( )( )( )2PKTVLV

2BORE

PKTVLV

BORE

DNRPMSD

ANRPMSAV ×

≈×

≈

Number of S or D valve pockets feeding end=N

Cylinder main bore diameter=DBORE

Speed, revolutions per minute=RPM

Valve pocket area=AVLV PKT

Stroke=SCylinder main bore cross-sectional area=ABORE

Valve pocket diameter=DVLV PKT

Average gas velocity through the valve pocket=VWhere:

This is an equation for the relationship of the velocity of the gas through the valve pocket area.

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 valvediameter).



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Typical Valve Pocket

FrontHead

Liner

ValveCap

ValveCage

Body

Valve

This is a drawing of a typical valve pocket in a compressor cylinder.

The section is taken parallel to the piston rod.



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Valve Pocket Diameter

ValvePocket

Diameter

This slide defines “valve pocket diameter” for a typical valve pocket.



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Valve Pressure Drop

( )( )( ) ( )( )( )( )2PKTVLV

22BOREP

ANTZRPMSARSGPΔP ×

≈

Number of S or D valve pockets feeding end=NValve resistance factor=RP

Compressibility factor=ZTemperature=T

Cylinder main bore area=ABORE

Speed, rev per minute=RPMStroke=S



Pressure drop=ΔPWhere:

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 (area squared), and inversely related to the diameter of the valve to the fourth power (valve pocket area squared).

2. Pressure drop is directly related to stroke squared and speedsquared, or piston speed squared.



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Valve Resistance Factor -Definition

Ratio of measured pressure drop across the suction or discharge side of a cylinder to the pressure drop that would be predicted in flowing the same quantity of the same gas at identical upstream pressure and temperature conditions through a round hole having a discharge coefficient equal to one and an area equal to the valve pocket opening.

Typical resistance factors range from 50 (poppet valve) to 200 (low lift plate valve).

Ref: Hartwick, “Efficiency Characteristics of Reciprocating Compressors”, December 1968, ASME technical paper 68-WA/DGP-3.



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Valve Resistance Factor

ΔPOrificeΔPValveCompressorRP =

Valve resistance factor=RP

Pressure drop, psi=ΔPWhere:

This is the definition of resistance factor in equation form.



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Valve Equivalent Area - Definition

Orifice area required to generate the same pressure drop as thatthrough a compressor valve when flowing the same quantity of thesame gas at the same conditions.



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Valve Equivalent Area

P

PKT

RAVEA =

Valve pocket area=APKT


Valve equivalent area=VEAWhere:

This equation shows the relationship between valve equivalent area and resistance factor.

So, knowing one allows the other to be calculated.



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( )( )( ) ( ) ( )( )( )( )2PKTVLV

33BOREP

ANTZVERPMSARSGPVLHP ×

≈

Number of S or D valve pockets feeding end=N


Temperature=T



Volumetric efficiency, decimal=VECompressibility factor=Z


Stroke=SCylinder main bore area=ABORE

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 (or area) and valve diameter (or area) to VLHP.

2. The relationship of stroke and speed to VLHP. Another way to look at this relationship is to say that stroke times speed is piston speed and that VLHP is directly related to piston speed cubed.



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Valve Pocket Area as% of Bore Area

30%

40%

50%

60%

70%

5 7 9 11 13 15 17 19 21 23 25 27

Cylinder Diameter

% V

alve

Pkt

Are

a of

Bor

e Ar

ea

This is a plot of valve pocket area as a percentage of cylinder bore area.

Note that as the cylinder gets larger the amount of valve pocket area decreases significantly. Large cylinders are never as efficient as small ones.



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Why Large CylindersAre Not Efficient

4πDAreaBore

2=

πDnceCircumfere =

This simple drawing explains why as cylinders get larger they get less efficient. The space available to fit valves in the cylinder (the circumference) grows by diameter to the first power, but the gas flow through the valves grows by diameter squared.



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Deactivated End Horsepower

( ) ( )( ) ( ) ( )( )( )( )( )2PKTVLV

15

33BORE

3PoutPin

ANTZ10RPMSARRSGP9.59DHP ×+

=

Number of valve pockets feeding deactivated end=N

Valve resistance factor, out-stroke=RPout

Valve resistance factor, in-stroke=RPin

Temperature=T


Gas specific gravity=SGPressure, psia=P

Compressibility factor=Z

Valve pocket area, sq. in.=AVLV PKT

Stroke, in.=SCylinder main bore cross-sectional area, sq. in.=ABORE

Deactivated end horsepower=DHPWhere:

Ref: Hartwick, “Power Requirements and Associated Effects of Reciprocating Compressor Ends Deactivated by Internal Bypassing”, December 1974 , ASME Technical Paper 75-DGP-9

This is the equation for deactivated end horsepower (parasitic horsepower).

Note the following:

1. DHP is directly related to pressure and specific gravity.

2. Pressure is most typically suction pressure.

3. DHP has the effect of creating heat and raising the temperature.



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Deactivated EndP-V Diagram

This is a sample P-V diagram of a deactivated end.



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Deactivated End Temperature

Photo courtesy of Energy Imaging 580-388-4385

123

This is an infrared photo of three compressor cylinders on one side of a six throw compressor. Each cylinder is unloaded differently.

Cylinder #1 is not unloaded.

Cylinder #2 has a head end fixed clearance pocket open.

Cylinder #3 has the head end deactivated using finger type suction valve unloaders.



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Indicated Horsepower

HPIndicatedHPLossValveDischarge

HPLossValveSuctionHPAdiabatic

++

This is the “definition” of indicated horsepower.

It is the sum of the horsepower developed directly from the pressure-volume diagram.



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Brake Horsepower

HPBrakeHPFrictionHPIndicated

+

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.MIHPBHP

.=

Mechanical efficiencyTypically 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 the cylinders only, typically 0.95

=M.E.

Frame friction HP, constant number to account for 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 separate 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 toaccount 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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Compression Efficiency

DVLHP)SVLHP(AHPM.E.AHP

BHPAHPEFF

++×

==

Suction valve loss horsepower=SVLHP

Brake horsepower=BHPMechanical efficiency=M.E.

Discharge valve loss horsepower=DVLHP

Adiabatic horsepower=AHPCompression efficiency=EFF

Where:

This is an expression for compression efficiency.



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Hig

h R

C

Lo R

C


This compares compression efficiency between high and low compression ratio P-V diagrams.

Which is more efficient? Why?



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203040

50607080

90100

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Compression ratio

Com

pres

sion

Effi

cien

cy, %

Std

Standard design 12.5 inch bore, 1100 fpm

This is a very typical plot of compression efficiency versus compression ratio.

Note how compression efficiency drops off with decreasing compression ratio.



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203040

50607080

90100

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Compression ratio

Com

pres

sion

Effi

cien

cy, %

Low Rc

Low ratio design 12.5 inch bore, 1100 fpm

This is a very typical plot of compression efficiency versus compression ratio for a cylinder designed for low compression ratio applications.



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203040

50607080

90100

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Compression ratio

Com

pres

sion

Effi

cien

cy, %

Large

Standard design 26.5 inch bore, 1100 fpm

This is a very typical plot of compression efficiency versus compression ratio for a large (26.5 inches) bore cylinder.



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203040

50607080

90100

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Compression ratio

Com

pres

sion

Effi

cien

cy, %

LargeStdLow Rc

This chart plots all three of the previous slides on one chart.

Note the differences.



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203040

50607080

90100

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Compression ratio

Com

pres

sion

Effi

cien

cy, %

Std H2Std Nat Gas

This is a plot of compression efficiency versus compression ratio for a cylinder compressing natural gas and another hydrogen. Shows the effect of gas composition on efficiency.

If the gas is very “light” (very low mole weight - like hydrogen) - forget about efficiency!



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Compression Efficiency:BHP per MMSCFD

0

10

20

30

40

50

60

70

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Compression ratio

BH

P/M

M

StdLow RcLarge

This plot shows how BHP per MMSCFD changes with compression ratio for three different cylinder designs - “standard”, “low ratio” and “large”.

Notice how the numeric difference stays approximately the same over the complete range of compression ratio.

Also notice how the “large” cylinder has the highest BHP/MM and the “low ratio” the lowest.



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Compression Efficiency:BHP per MMSCFD

-40

-20

0

20

40

60

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Compression ratio

% In

crea

se in

BH

P pe

r MM

Low RcLargeStd

This plot shows the percentage difference in BHP per MMSCFD using the “standard” cylinder design as the base.

Notice that on a percentage basis the “large” cylinder is significantly worse and the “low ratio” better.



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Increased Discharge Pressure

Increased PDwith 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 PDwith PS constant

This shows the effect of decreasing the discharge pressure.

Note that volumetric efficiency increases.



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Increased Suction Pressure

Increased PSwith PD constant

This shows the effect of increasing suction pressure with discharge pressure remaining constant.



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Increased Suction Pressure

Increased PSwith PD constant

CAPACITY INCREASE

This shows the effect of increasing suction pressure with discharge pressure remaining constant.

Capacity increases! Always!



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HP vs. Suction Pressure

Suction Pressure

Pow

erPd is constant

Each line represents additional fixed clearance added.

This plot shows how compressor horsepower varies as suction pressure varies with a constant discharge pressure.



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Capacity vs.Suction Pressure

PD is fixed.

Suction Pressure

Cap

acity

Pd is constant

This plot shows how compressor horsepower varies as suction pressure varies with a constant discharge pressure.



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HP per MMSCFD vs.Suction Pressure

Suction Pressure

Pow

er p

er C

apac

ityPd is constant

This plot shows how compressor horsepower per MMSCFD varies as suction pressure varies with a constant discharge pressure.



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Effect of Speed

Pressure drop varies with RPM2 70% Speed

49% ΔP

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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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 assuming that they are adiabatic (or isentropic or entropy is a constant).



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Entropy

Tem

pera

ture

Temperature-EntropyDiagram

K1-K

S

D

S

D

PP

TT

⎟⎟⎠

⎞⎜⎜⎝

⎛=

PS

PD

Isentropic or adiabatic compression

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 isexchanged (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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K-value

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛

−

=

⎟⎟⎠

⎞⎜⎜⎝

⎛=

S

D

S

D

K1-K

S

D

S

D

PPlog

TTlog

1

1K

orPP

TT

K-value is determined from the adiabatic temperature pressure relationship as shown. Knowing the pressures and temperatures allow the calculation of K.



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K-value for an Ideal Gas

1.986CMWCMWor,

CCK

P

P

V

P

−××

=

Specific heat at constant pressure=CPSpecific heat at constant volume=CP

Mole weight=MWK-value=K

Where:

If it is assumed that the compressed gas is an ideal gas this expression can be used to calculate the adiabatic exponent.

For many gases at low pressures this will suffice and be accurate. For other gases, carbon dioxide and propane being two examples, using this expression may result in errors in K-value and therefore errors in the calculation of capacity and horsepower.



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Effect of K-value

K = 1.4Air, nitrogenor hydrogen

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)

gas real for ZMRTPVgasidealforMRTPV

==

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

K1K

S

DSAdiabatic-D P

PTT

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=



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

( )sT

EfficiencyTTT 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 suction event• Heat transfer in the suction gas passage

There can be an effect during the compression process where the suction gas temperature is pre-heated. In other words the temperature of the gas at the instant the compression event 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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Multi-stage:What?

• Cylinders piped in series to reduce the compression ratio across each cylinder

Stage 1 Stage 2



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Multi-stage:What?

• An intercooler is installed between stages to cool the gas prior to compressing it in the next stage:

Stage 1 Stage 2



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Multi-stage:Why?

• Assume PS = 50 psia, PD = 500 psia, TS = 60 °F, one stage of compression• Compression ratio = 10• Adiabatic TD = 425 °F, too high!!

A gas discharge temperature of 425 deg F is much too high for the sealing materials that are commonly used in today’s reciprocating compressors. A typical discharge temperature limit is about 300 deg F.



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Multi-stage:Why?

• Assume PS = 50 psia, PD = 500 psia, TS = 60 °F, two stages of compression• Compression ratio per stage = 3.16• Adiabatic TD = 218 °F

Breaking the compression ratio across two stages significantly reduces the discharge temperature.



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Capacity Balance

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

160 180 200 220 240 260Interstage Pressure, psig

Cap

acity

, MM

SCFD

11” 1ST Stage, 6.25” 2ND Stage

0%

38%

75%

0%

38%

75%

Ps=55, Pd=650

The next couple of charts show how the pressure between compression stages is determined.



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Capacity Balance

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5


Cap

acity

, MM

SCFD

0%

38%

75%

0%

38%

75%

199

16,20015,600CRL258254Tdis2nd1stQ=3.6

11” 1ST Stage, 6.25” 2ND Stage Ps=55, Pd=650



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Capacity Balance

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5


Cap

acity

, MM

SCFD

0%

38%

75%

0%

38%

75%

170

16,90012,700CRL279232Tdis2nd1stQ=2.4




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Capacity Balance

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5


Cap

acity

, MM

SCFD

0%

38%

75%

0%

38%

75%

212

15,90016,900CRL248262Tdis2nd1stQ=2.4




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Rod Load

• Reciprocating compressor frames are limited in operating range by rod load• Rod load is a force that generates a stress in

many parts of the compressor frame assembly

• Results from differential pressure across the compressor piston



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Tension Rod Load

PD

PS

PD

A tension rod load is created when discharge pressure is acting on the crank end of the piston and suction pressure on the head end.



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Tension Rod Load

RODDHESD A)(PA)P(PTRL ×−×−=

Suction pressure, psig=PSArea, head end, in2=AHEArea, rod, in2=AROD

Discharge pressure, psig=PD

Tension rod load, lbf=TRLWhere:

This is the equation used to calculate tension rod load (TRL).



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Compression Rod Load

PS

PD

PS

A compression rod load is created when suction pressure is acting on the crank end of the piston and discharge pressure on the head end.



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Compression Rod Load

RODSHESD A)(PA)P(PCRL ×+×−=

Suction pressure, psig=PSArea, head end, in2=AHEArea, rod, in2=AROD

Discharge pressure, psig=PD

Compression rod load, lbf=CRLWhere:

This is the equation used to calculate compression rod load (CRL).



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Inertia Rod Load

• Inertia rod load is a force developed from the acceleration and deceleration of a mass, typically the crosshead + crosshead nut + piston/rod assembly

onAcceleratiMassForce ×=



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Gas + Inertia Rod Load

Inertia Rod Load

GasRod Load

Gas + InertiaRod Load

Image courtesy of ACI Services, Inc.

This is a plot of three different rod loads of a typical double-acting compressor cylinder.

The three are:

1. Gas rod load – the load generated from just the gas pressure acting on the piston.

2. Inertia rod load – the load generated by inertia (F = ma). Note that inertia is maximum at the ends of the stroke (180 and 360) whereacceleration is maximum.

3. Gas + inertia rod load – a summation of gas rod load and inertia rod load.



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Crosshead Guide AssemblyCrosshead

Guide

Piston Rod

Crosshead Balance

NutCrosshead

CrossheadPin

Connecting Rod



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Crosshead Assembly

Piston Rod

Crosshead Balance

Nut

Crosshead Bushing

Crosshead Pin

Connecting Rod

Crosshead



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Non-Reversing Rod Load

Image courtesy of ACI Services, Inc.

No Reversal!

This chart shows a non-reversing rod load. Note how the gas + inertia rod load never moves into tension – it remains in compression during the full 360 degrees of crankshaft rotation.



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This is a photo of a crosshead that failed due to non-reversing rod load. Typically the crosshead heats up relative to the slide bore which causes the running clearance to disappear and the crosshead to stick and fail.



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This photo shows a crosshead pin with the crosshead and connecting rod bushings stuck to it.



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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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PulsationP-V Diagram Distortion

Average flange

pressure during valve

open time

RC for capacity

RC for HP/MM

Suction pressure

for capacity


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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Effect of ΔP 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

Cha

nge

in V

.E.,

%

K = 1.3ZS = ZD = 1.0Clearance = 40%

70% V.E.

50% V.E.

30% V.E.

3% ΔP

2% ΔP

1% ΔP

This graph shows how much pulsation can affect volumetric efficiency.

Pulsation is represented by percentages of pressure drop.

Documents

Theory Basic Thermodynamics of Reciprocating Compression