compressibility, ratio of specific heats, and

7/28/2019 Compressibility, Ratio of Specific Heats, And

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Compressibility,Compressibility,

Ratio of Specific Heats,Ratio of Specific Heats,andand PolytropicPolytropic ExponentsExponents

Presented by Warren Laible


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IntroductionIntroduction

Compressibility (Z dis, Z suc, Z std),

K, N ratio and Polytropic values arepresented in the compressorperformance report, but do we knowhow they affect our calculations?

This presentation will define thesevalues in simple terms and explainwhat effect they have on theperformance calculations.


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Compressibility (Z)Compressibility (Z)

The term "compressibility" is used to

describe the deviance in theproperties of a real gas from thoseexpected from an ideal gas.

It is a volume ratio which indicates thedeviation of the actual volume fromthat determined by perfect gas laws.

Usually calculated at suction (Zs),discharge (Zd) and standard (Zstd)conditions.


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Using the Z factor, we are accounting

for the existence of intermolecularforces. When we have a Z factor of less than

1, the actual density of the gas isgreater than would be predicted by theideal gas law.

When we have a Z factor greater than1, the actual density of the gas is lessthan would be predicted by the idealgas law.


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When we have more than one gasinvolved, we assume the overall Z isthe sum of the fractional Zs for eachcomponent in the gas mixture.

mmscfd = (dv*VE*rpm*prcorrection*temp correction) / Z A compressibility (Z) of less than 1.00

increases the flow calculation


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Things That Affect CompressibilityThings That Affect Compressibility

Gas composition

Are all components in a gaseous state? Gas pressure

Is atmospheric pressure entered correctly? Is pressure transducer calibrated accurately?

Gas temperature Is the suction temperature reflective of the

actual gas temperature that entered thecylinder bore?

Is the discharge temperature reflective of theactual gas temperature leaving the cylinderbore?


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What Methods Do We Use toWhat Methods Do We Use to

Calculate Compressibility?Calculate Compressibility?

Benedict-Webb-Rubin

Redlich-Kwong Beattie-Bridgeman


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Where Is Compressibility Used InWhere Is Compressibility Used InThe Calculations?The Calculations?

All Flow Rate Calculations

Suction Discharge

Average Flow (Indirectly)

Flow Balance (Indirectly) Leak Index

Theoretical Flow in Economics Report

Ideal Capacity Clearance Calculations

K Temperature Theoretical PV model


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Average CompressibilityAverage Compressibility

When the suction and discharge

compressibility values are both close to theaverage compressibility then the K based(isentropic) theoretical PV model workswell

When the suction and dischargecompressibility values are both farther from

the average compressibility then theEquation of State model K temperaturetheoretical PV model works better.


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Large Difference in CompressibilityLarge Difference in Compressibility

K Temperature

modified K


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Ratio of Specific Heats (K)Ratio of Specific Heats (K) Heat capacity of a gas in a constant

pressure process - to heat capacity ina constant volume process.

Affected by the temperature of thegas.

For equal compression ratios andsuction temperatures, the higher the Kvalue, the higher the predicted and

actual discharge temperatures. The following K value calculations are

based on 14.7 psia:


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K @K @ 50 deg F 150 deg F50 deg F 150 deg F

Methane 1.31 1.29 Ethane 1.20 1.18 Propane 1.13 1.11

Air 1.40 1.40 Hydrogen 1.41 1.40 CO2 1.30 1.27

Nitrogen 1.40 1.40 Ammonia 1.30 1.30


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Where Is K Used In TheWhere Is K Used In The

Calculations?Calculations? Clearance calculations

For equal conditions, the calculated clearances will be higher

with a higher K value Theoretical discharge temperature

For equal compression ratios and suction temperatures, thehigher the K value, the higher the predicted and actualdischarge temperatures.

Theoretical IHP For equal conditions, the calculated theoretical IHP

will be higher with a higher K value (measured IHPwill not be affected)

Compressor efficiency (indirectly) Higher K will result in higher calculated efficiency

Theoretical PV (K-based models) Higher K will predict more vertical compression and

expansion lines


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PolytropicPolytropic N ValueN Value The N value is calculated from the toe pressures

and the beginning, and end of, the expansion or

compression slope of the PV card

The set clearances must be accurate for a propercalculation of N

The N ratio is calculated by dividing theexpansion N value by the compression N value

When both N values are very near to K then the

process is adiabatic acting When N values are not near K then the process

is a polytropic process or there are leakages(rings, packing, valves)


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K and N ComparisonK and N Comparison


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QUESTIONS?QUESTIONS?

compressibility, ratio of specific heats, and

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