Fundamentals of Centrifugal Compressor - Head (revised)

Impact of Molecular Weight and Other
Parameters on
Centrifugal Compressor Head
IMPACT OF MW AND OTHER PARAMETERS ON CENTRIFUGAL COMPRESSOR’S HEAD - SUDHINDRA TIWARI MAR 2018

What and Why of Presentation
Why this presentation?
◦ These questions arise in many engineers’ minds
◦ Information is not available in structured form
What this presentation is about?
◦ What is compressor head, how different from pressure
◦ Effects of various parameters on compressor head
◦ Presentation is limited to centrifugal machines
◦ Supported by real life examples
Slide 1

Operating Characteristics
Centrifugal compressors rarely work at
single operating point.
They work within an operating envelope
(Fig 1):
◦ Attached envelope is for variable speed
operation.
◦ Operation limited by surge and stonewall
lines and minimum and maximum speeds.
(Centrifugal Compressor Operation – Tony Barletta and Scott W. Golden. www.digitalrefining.com)
Figure 1
Slide 2

Head
Head: Energy required to move unit mass of fluid from one point to another, generally
expressed in feet (or lbf-ft/lbM). For compressor it is the work of compressor performed on
a unit mass of the gas or vapor.
Fig 2: Head, produced by compressor impeller, is proportional to impeller tip velocity (U)
and gas tangential velocity (V) at impeller exit:
Head α U*V
Figure 2
(Forsthopper’s Best Practice Handbook For Rotating Machinery)
IMPACT OF MW AND OTHER PARAMETERS ON CENTRIFUGAL COMPRESSOR’S HEAD - SUDHINDRA TIWARI MAR 2018Slide 3

Compressor Characteristics: Head
vs. Capacity
Fig 3 depicts shape of compressor’s characteristic performance curve. Increase in head is
caused at reduced flow rates. Because, in accordance with Fig 2, a lower flow rate reduces
relative gas velocity from Vrel1 to Vrel2, which in turn increases gas tangential velocity from V1
to V2 hence the head.
Figure 3
(www.compressedairducation.com)
Slide 4

Compressor Head – Why Polytropic?
In real life some heat transfer takes place during
compression, resulting in a polytropic process:
Polytropic: falls between the above two processes,
pvn = constant, where (n-1)/n = (k-1)/(k*effpol)
Note: polytropic exponent “n” and polytropic efficiency
“effpol” are provided by compressor manufacturer derived
from actual tests.
Work of compression, being the area under p-v curve, is
minimum for isothermal and maximum for isentropic
compression (Fig 4).
Figure 4
https://en.wikipedia.org/wiki/Compressor
Two types of theoretical compression processes (two extremes, See Fig 4):
Isothermal: compression at constant temp - all heat generated during
compression is removed, represented by the equation:
pv = constant
Isentropic (reversible adiabatic): no heat transfer during compression,
pvk = constant, where k = cp/cv oor isentropic exponent
Slide 5

Head and Pressure
Head and Pressure are inter-related as follows,
For liquids – via specific gravity (density)
For gases/vapors - via pr, temp, MW,
compressibility, sp. heat ratio
Figure 5: the same differential pressure of 100
psi (or the same pressure ratio of 7.8) produced
by a machine (pump or compressor), generates
water head of 231 ft and N2 head of 86,359 ft
(which is equivalent to a N2 column of 86,359 ft
compared to a water column of 231 ft).
Typically the gas / vapor head is much higher
than liquid heads for the same pressure (note
the same 114.7 psia pressure at the bottom of
both columns).
Figure 5
Slide 6

Head, Pressure Ratio – Impact of MW
Impact of MW: Equation 1 (isentropic head in
this case) shows, if all other parameters on right
are kept constant, increase in MW will require a
lower head to produce the same discharge
pressure P2.
This is why less number of impellers / stages are
required to compress a heavy gas (Fig 6).
However, in real life the compressibility of gases
and changes in other parameters with change in
MW affect compressor’s characteristics. We will
see this later.
Equation 1
Compressor head is given by:
Figure 6
Compression Ratio vs. Number of Impellers
(A Practical Guide to Compressor Technology, 2nd Edition – Heinz P Bloch)
Slide 7

Compressor Downstream
Requirements and Impact of MW
Constant discharge head: Such as
pipelines where required head
depends on static and friction head,
thus remains more or less constant,
irrespective of change in gas MW
According to equation the
compressor discharge pressure P2
will increase for the same head for a
heavy gas (as shown in next slide).
Constant discharge pressure or
pressure ratio: Such as feed to a
reactor where the process requires
supply of gas at constant pressure,
irrespective of change in gas MW.
Here, the compressor has to speed
down to produce the same
discharge pressure (to reduce the
head per the equation), when
compressing a higher MW gas.
There are other compressor applications requiring constant mass flow rates.
Both the cases below (representing compressor’s downstream requirements),
where a constant inlet flow through compressor is assumed, can be explained using
equation 1:
Slide 8

Head, Pressure and MW
Figure 7 shows a constant head
requirement of 20,714 ft., where
the compressor discharge pressure
is higher for Oxygen (25.3 psig ,
MW 32) compared to 22.4 psig for
Nitrogen (MW 28).
The next slide presents a real life
case with constant discharge
pressure requirement.
Figure 7
Slide 9

Real Life Example – Impact of MW on
Polytropic Head
Compressor performance in Fig 8 is a real life
example depicting the impact of change in
MW from 20.83 to 18.72.
Changes in MW, polytropic head, speed and
power are highlighted in yellow.
Inlet volume (orange highlight) is almost
constant. Compressor suction and discharge
pressures are also constant.
Compressor power, being product of
polytropic head and weight flow rate, does
not change significantly due to decrease in
weight flow rate with MW.
The k value (=Cp/Cv) in fact increases with
reduced MW, which works in the reverse
direction i.e. to reduce the polytropic head
by about 4.8%. Also, the impact of change in
Z value causes only 0.37% increase in the
polytropic head.
Figure 8
Slide 10

Head, Pressure Ratio – Impact of
Other Parameters
Impact of inlet and discharge pr., and inlet temp (constant pressure ratio
application)
The same impact (as that of MW) is produced if compressor suction pressure
(P1) increases while other parameters remain unchanged. Means an increased
compressor suction pressure (P1) requires compressor to produce a lower head
to maintain the same pressure ratio (typically by reducing compressor speed).
An opposite impact is produced if inlet temp (T1) increases, while other
parameters remain unchanged. Means an increased suction temp requires
compressor to produce a higher head to maintain the same pressure ratio
(typically by increasing compressor speed).
The above explains compressor’s behavior, next slide explains system’s behavior.
Slide 11

System Head and Impact of MW
Equation 2 provides pipeline / system
head (generic) required to push a given
gas through a given pipeline of length L:
P2 = pipeline upstream pressure, psia
P3 = pipeline downstream pressure, psia
S = specific gravity of gas,
Q = gas flow rate, MMscf/D
Z = compressibility factor for gas
T = flowing temperature, °R,
f = Moody friction factor
d = pipe ID, in.,
L = pipe length, ft
http://petrowiki.org/Pressure_drop_evaluation_along_pipelines
Figure 9
Equation 2
Pipeline of length L
Compressor
Note from equation 2 that an increase in specific
gravity ‘S’ (or MW) will require a higher upstream
pipeline pressure (P2) to push the gas to the same
length L of pipeline.
This also jibes with what is explained in Slide 9
already.
Slide 12

MW and Performance Curve’s Shape
Gases and vapors being compressible in nature produce the
following impact upon change in MW:
From equation 1, for a constant downstream head, a heavy gas
shall develop higher discharge pressure P2 or shall be compressed
more compared to a light gas. Meaning a heavy gas shall have a
higher volume ratio (or a lower discharge volume) according to the
following relation for volume ratio:
Volume Ratio: V1/V2 = (P2/P1)1/n [Note uppercase V for volume]
In accordance with Slide 3, for a given acfm of gas entering a given
impeller at given speed the magnitude vrel is less for heavy gas than
for a light gas; causing magnitude vt to be greater.
Since head output is proportional to vt , a given impeller running at a given speed will produce more head
while compressing a heavy gas than when compressing a like acfm of light gas. The magnitude of
difference increases with increased acfm, so the basic slope of a given impeller is less steep for heavy gas
than for a light gas
Slide 13

MW and Performance Curve’s Shape
(Real Life Example)
This is an example from constant
pressure ratio application. All curves
are at 8000 rpm compressor speed.
Notice the change in slope and
reduction in surge margin (Fig 11)
Figure 11
Slide 14

Thanks for your review and comments
Sudhindra Tiwari
Lead Design Engineer – Rotating Equipment

Fundamentals of Centrifugal Compressor - Head (revised)

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