the impact of reciprocating compressor pulsations...

The Impact of Reciprocating Compressor Pulsations on the Surge Margin of Centrifugal Compressors

ByDr. Klaus Brun – Southwest Research Institute

Ms. Sarah Simons – Southwest Research InstituteDr. Rainer Kurz – Solar Turbines, Inc.Mr. Joseph Thorp – Aramco Services

Objective

• Many compressor stations have both recip and centrifugal compressors installed.

• There is still limited understanding of how pulsations, piping resonance, and impedance impact centrifugal compressor performance and surge.

• Analytical and computational predictions exist but no test data is available.

• Current design practices are limited because of lack of knowledge and data.

• Fundamental questions:– Can pulsations drive a centrifugal compressor into surge?– If so, what amplitudes and frequencies are required?

Unexpected periodic surge has been observed in the compressors when pulsations were present

Pulsations: What are They?

• A traveling compression wave in a fluid • Fluid particles (molecules) force interaction • Waves are composed of two components: Pressure and Velocity• Waves move at the speed of sound. (Flow does not.)

xx

y

y

A

y

A

Speed of sound, c, is function of fluid bulk modulus of fluid, B

c2 = 𝑩𝑩𝝆𝝆

Centrifugal Compressor Map and Surge

-6-4-202468

1012

0 1 2 3 4 5 6 7 8 9

Time [s]

CC

In

let

Flo

w [

m/s

]

Compressor Map

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Flow*10 (kg/s)

Pres

sure

Rat

io (P

2/P1

)

8000 RPM

14300 RPM

10000 RPM

12000 RPM

Flow pulsations can cause periodic surge in centrifugal compressor

Surge

Brun et al. 2010

Surge

Sources of Excitation in Compressor Piping System

• Strouhal excitation or vortex-shedding • Blade passing and blade vane interactions • Turbulence induced radial or other 3-D acoustic responses in large

vessels • External pulsation from reciprocating compressors or other positive

displacement machines • Unstable flow control valve control cycling (process valve dynamics)• Check valve or relief valve chatter• Surge cycles• Diffuser rotating stall and other stalls • Mismatch between the operating points of the compressors resulting

in periodic “hunting” for a stable operating point.• Other process and aero flow instabilities

All periodic excitations can be amplified by piping system acoustic resonances

Pulsation Decay

0 5 10 15 20 25 30Distance - Miles

Pres

sure

Dis

turb

ance

-ps

i

16141210

86420

Decay of a 33Hz pulsation in a pipeline.Pulsation amplitude at inlet was 1% inletpressure of 1500 psi. [Kurz et al., 2003]

Pulsations can propagate over long distances

What is Piping Acoustic Impedance?

Z = pU

= puA

= ρuA

~ ρcA

Z – Acoustic impedanceA – Pipe cross section areap – sound pressureU – acoustic volume flowρ – densityu – molecule particle bulk velocityc – local speed of sound

• Different than pipe friction or flow resistance• Applies only to transient flows/pulses (frequency typically > 1 hz)• Results in different behavior for steady-state and transient flows

Pressure rise perparticle velocity

Classic Compressor Dynamic Response Theory

(Sparks et al., 1983)

Provided explanation and analysis on how pulsations behave in centrifugal compressor systems

Numerical Analysis of Pulsations in Compressors (Brun et al., 2010/2014)

Pressure to Pipe Impedance for Steady Flow: Pipe Flow

Converging Nozzle

Flow

Pipe Impedance

Flow Velocity

Pressure

Z

V ~ Z2

P ~ 1/Z4

Z ~ 𝑷𝑷𝑷𝑷𝑷𝑷𝑷𝑷 𝑹𝑹𝑷𝑷𝑹𝑹𝑷𝑷𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑷𝑷 (𝐑𝐑)

Pressure to Pipe Impedance for Short Pulse: Pipe Flow

Converging Nozzle

Pressure Pulse(travels at speed of sound)

Pipe Impedance

Pulse Velocity

Pressure of Pulse

Z

V ~ c

P ~ Z

c c c

Piping Impedance for Short Pulses: Centrifugal Compressor

c c

Pressure Pulse

MostlyClosed Valve

Open Valve

∞

c

Pressure Pulse

∞c c

c

High Impedance

Low Impedance

Pulse can be amplified or attenuated(Is this the same if the through flow velocity is high or low?)

DischargePressure (Pd)

Volume Flow (V)

Ps Pd

SurgeLine

Constant Suction PressureLines

Ps1

Ps2

Ps3

Compressor Map: Resistance versus Impedance


(Slow Transients)


Volume Flow (V)

Ps Pd

SurgeLine


Ps1

Ps2

Ps3

Resistance ~ V2


Volume Flow (V)

Ps Pd

SurgeLine


Ps1

Ps2

Ps3

Low Impedance p ~ Z∙V

Valve Open


(Fast Transients)


Volume Flow (V)

Ps Pd

SurgeLine


Ps1

Ps2

Ps3

High Impedance p ~ Z∙VValve Closed


(Fast Transients)


Volume Flow (V)

Ps Pd

SurgeLine


Ps1

Ps2

Ps3

Low Impedance p ~ Z∙V

Valve Open

Surge

Compressor Map: Resistanceversus Impedance

(Fast Transients)

What affects piping impedance?

• Pipe friction• Flow constrictions (valves, orifices)• Flow area changes (bottles, transition pieces)• Speed of sound changes (coolers)• Gas composition changes (side streams,

coalescers, scrubbers)• Pressure drops (hard elbows, leaks, leaking

valves)

What is Piping Acoustic Resonance?

Nodes

• A standing wave occurs there is coherence between a wave and its reflection.• Resonance occurs when the standing wave frequency coincides with a periodic excitation frequency.

Half-wave Acoustic Response Frequency

Closed-closed configuration Open-open configuration

Pressure minimum at midpoint

Pressure maximum at midpoint

L2cnf =

f = Response frequency (Hz)c = Velocity of sound (ft/sec)L = Acoustic length of pipe span (ft)n = 1,2,3,…

Quarter-wave Acoustic Response

Open-closed configuration

Pressure minimum at open end

f = Response frequency (Hz)c = Velocity of sound (ft/sec)L = Acoustic length of pipe span (ft)n = 1,2,3,…

( )L4c1n2f −=

What Causes Piping Resonance?

(What can cause a pressure wave to reflect?)

• Open and closed ends• Rapid area changes (bottles, T’s, transitions)• Speed of sound changes (coolers)• Hard walls in the flow path (orifices, valves)• Rapid flow direction change (elbows)• Any surface projected normal into the flow path.• A rapid change of impedance.

Significant amplification of periodic excitation is possible

The theory is good. Numerical analysis and lots of anecdotal field evidence agrees with it.

But there was absolutely no test data available to validate it…

Surge Testing Project

Surge Testing Project

• Determine whether pulsations from reciprocating compressors (RC), vortex-shedding or other sources can cause surge in centrifugal compressors (CC) when operating at low surge margin.

• Develop understanding of the physical process that causes pulsation induced CC surge.

• Determine the amplitude and frequency of pulsations required to cause CC surge. (Develop simple physical relationship or rules for pulsation induced surge avoidance.)

• Determine impact of pulsations on performance.• Evaluate the impact and interaction of acoustic pipe resonances on

pulsation induced CC surge.• Evaluate the impact and interaction of pipe impedance on pulsation

induced CC surge.• Validate Compressor Dynamic Theory (Sparks et al., 1983) predictions

for pulsation amplification in centrifugal compressors.

Surge Testing ProjectTest Setup

Recip mounted upstream of centrifugal:- 700 Hp Clark 2 stage CC with VFD (0-

14,000 rpm)- 50 Hp Ariel single stage RC with VFD

(50 -1000 rpm)- Dynamic pressures, temperatures, and

flow measurements throughout piping and machinery flanges

Actual Test P&ID

HWXXXHot Wire

Anemometer

Spool PieceSuction

Spool PieceDischarge Flow Control

CoarseFlow ControlFine

Key Measurements

- Pressure and temperature measurements per ASME PTC-10- Transient flow measurement using high speed hot wire

anemometer near centrifugal suction flange- Steady flow measurement from orifice plate meter and PV

card mass balance- Dynamic pressure measurements from recip discharge and

centrifugal suction and discharge- Centrifugal power from shaft torque meter- Uncertainties (% from operating point):

Surge Line Validationand Surge Identification

(No Recip)

Discharge & Suction Pulsations(7,000 RPM, No Surge, No Stall)

No peaks at ~1/3 running speed

Pressure pulsation at ~ 1/3 running speed, indicates onset of stall

Discharge & Suction Pulsations(7,000 RPM, Stall, No Surge)

4 Hz pressure pulsation indicating onset of surge

Discharge & Suction Pulsations(7,000 RPM, Surge)

No 4 Hz Peak

Axial Vibration(7,000 RPM, No Surge, No Stall)

4 Hz Peak

Axial Vibration(7,000 RPM, Surge)

Surge at 4 hz axial vibrations and pulsations is consistent with previous measurements (McKee 2003)

Axial Vibration(7,000 RPM)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Mils

acfm

4 Hz Axial Vibration vs. Flow (no Recip)

Surge Line (at 100.5 acfm)

Discharge Pulsations and Flow(7,000 RPM)

70.00

75.00

80.00

85.00

90.00

95.00

100.00

105.00

110.00

115.00

120.00

0

0.05

0.1

0.15

0.2

0.25

0.3

acfm

PSI P

k-Pk

Time

4 Hz Discharge Volute Pulsation and Flow vs. Time (no Recip) Surge Line

4 hz axial vibrations and discharge pulsation provide best indication of onset of surge

Surge Line(based on 4hz axial vibrations & discharge pulsations)

1.04

1.06

1.08

1.1

1.12

1.14

1.16

1.18

1.2

1.22

0 50 100 150 200 250 300

Pres

sure

Rat

io

Flow (acfm)

7000 RPM

6000 RPM

5000 RPM

4000 RPM

Testing on 7,000 rpm Speed Line

Surge (at 100.5 acfm)

Surge Line Testing with RecipRunning to Determine Impact of Pulsations

• Flow through centrifugal compressor is controlled using recycle line to near surge line

• Recip compressor is then swept to decrease speed until surge

Discharge Pulsation(7,000 RPM, Recip Running, No Surge, No Stall)

4 Hz pressure pulsation. Less than 0.01 psi.

Discharge Pulsation(7,000 RPM, Recip Running, Approaching Surge Line)

4 Hz pressure pulsation. Above 0.12 psi.

4 Hz pressure pulsations. Above 0.2 psi, indicating full surge.

Discharge Pulsation(7,000 RPM, Recip Running, Full Surge)

Discharge Pulsations and Flow(7,000 RPM, Recip Running)

70.00

75.00

80.00

85.00

90.00

95.00

100.00

105.00

110.00

115.00

120.00

0.00

0.05

0.10

0.15

0.20

0.25

1:55

:44

PM1:

55:5

9 PM

1:56

:19

PM1:

57:1

0 PM

1:57

:26

PM1:

57:4

9 PM

1:58

:11

PM1:

58:1

5 PM

1:59

:01

PM1:

59:3

0 PM

2:00

:18

PM2:

00:2

9 PM

2:00

:36

PM2:

00:4

4 PM

2:00

:53

PM2:

01:1

1 PM

2:01

:27

PM2:

01:4

8 PM

2:01

:59

PM2:

02:2

4 PM

2:03

:12

PM2:

03:1

7 PM

2:03

:24

PM2:

03:2

8 PM

2:04

:05

PM2:

04:3

1 PM

2:05

:21

PM2:

05:4

4 PM

2:05

:50

PM2:

06:2

6 PM

2:07

:01

PM2:

07:5

2 PM

2:08

:00

PM2:

08:1

4 PM

acfmPS

I P-P

Time

4 Hz Discharge Volute Pulsation and Flow Vs. Time (Recip)

4 Hz Discharge VolutePulsationFlow

Surge Onset

SurgeLine

100.5 acfm

106.5 acfm

Recip Impact on Surge Margin:Overlay Comparisons of

no Recip versus Recip Runs

Axial Vibrations and Flow(7,000 RPM, Recip Running, Recip Not Running)

1

2

3

Surge Onset(106.5 acfm)

Surge Line(100.5 acfm)

Full Surge(95 acfm)

Pulsations from the recip reduce the surge margin by 6%(Pulsation Induced Surge Margin Differential)


AQ BQ

CQ%6

58.10615.10058.106100(%) =

−=⋅

−=

A

BA

QQQSM

%600332.

00312.00332.100(%) =−

=⋅Φ

Φ−Φ=

A

BASM

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

mils

Flow Coefficient

Axial Vibration vs. Flow Coefficient4 Hz Axial Vibration (withRecip)

AΦ BΦ

CΦ


Surge MarginDifferential

1.04

1.06

1.08

1.1

1.12

1.14

1.16

1.18

1.2

1.22

70 100 130 160 190 220 250 280

Pres

sure

Rat

io

7000 RPM6 acfm

44 acfm

0.058 psi

Operating Map Ellipse: Pulsationsand Flow Fluctuations

(7,000 RPM, Recip Running)

Operating MapEllipse

1.14

1.16

1.18

1.2

1.22

6 acfm

44 acfm

0.058 ps

Operating Map Ellipse:Surge Margin Differential and

Area Across Surge Line

Surge MarginDifferential

Area AcrossSurge Line

Surge Line Testing with RecipRunning to Determine

Impact of Acoustic Resonances

• Suction piping acoustic resonance frequencies are identified

• Recip is run fixed speed on a resonance • Flow through centrifugal compressor is

controlled using recycle line to near surge line

Suction Line Resonance Pulsations

(at Volute)

DoubleActing

615rpm(10.25 Hz)

480rpm(8 Hz)

405rpm(6.75 Hz)

At RecipDischarge

Impact of Acoustic Resonance: Pulsations and Flow Fluctuations


Condition 1 2 3 4Recip Speed (RPM) 310 (5.17 Hz) 405 (6.75

Hz) 480 (8 Hz) 615 (10.25 Hz)

Excitation pulsations (psi pk-pk)

0.37 0.65 0.55 0.88

Excitation Pulsations (psi pk-pk) [normalized]

0.15[0.0298]

0.11[0.0158]

0.13[0.02252]

0.38[0.10699]

Flow fluctuations (p-p acfm) [normalized]

44.9[0.0014]

90[0.0028]

110[0.0034]

250[0.0078]

At CentrifugalSuction

615 (10.25 Hz) rpm -1st Order Pulsations

1.18

1.185

1.19

1.195

1.2

1.205

1.21

1.215

1.22

70 100 130 160 190 220 250 280

Pres

sure

Rat

io

Flow (acfm)

7000 RPM

54 acfm

0.002

13 acfm

Impedance Line

615 (10.25 Hz) rpm - 1st and 2nd

Order Pulsations

1.18

1.185

1.19

1.195

1.2

1.205

1.21

1.215

1.22

70 100 130 160 190 220 250 280

Pres

sure

Rat

io

Flow (acfm)

7000 RPM

54 acfm

0.01987

158 acfm

Impedance Line

615 (10.25 Hz) rpm -1st, 2nd, and 3rd Order Pulsations

1.18

1.185

1.19

1.195

1.2

1.205

1.21

1.215

1.22

60 90 120 150 180 210 240 270

Pres

sure

Rat

io

Flow (acfm)

7000 RPM

54 acfm

0.02235

177 acfm

Impedance Line

615 (10.25 Hz) rpm - 1st, 2nd, and 3rd Order Pulsations

Impedance Line Slope Locally Relates Acoustic Transient Flows and Pressures

Effect of Pressure and Flow Fluctuations on Surge


Recip Speed (RPM) 405 (6.75 Hz) 480 (8 Hz) 615 (10.25 Hz)

Excitation Pulsations (psi pk-pk)[Pressure ratio fluctuations]

0.11[0.0091]

0.13[0.0108]

0.38[0.0315]

Flow fluctuations (p-p acfm) [normalized]

90[0.0028]

110[0.0034]

250[0.0078]

Flow at Surge (acfm) 102.5 121.0 150.8

Pressure Ratio at Surge 1.201 1.204 1.204

Surge Margin Differential % 7.9 24.3 41.2

% Area Across Surge Line 31 29 31

Pulsation Flow Coefficient (Baseline Impedance)

vs. Surge Margin Reduction

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

40.0%

45.0%

0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

Surg

e M

argi

n D

fiife

rent

ial

Pulsation Flow Coefficient

4

3

21

3tipDN

Q⋅

∆=∆ϕ

Surge Line Testingwith Recip Running to

Determine Impact of Piping Impedance Changes

• Suction piping acoustic resonance frequencies are identified

• Recip is run fixed speed on a resonance • Flow through centrifugal compressor is

controlled using recycle line to near surge line

Impact of Piping Impedance:Operating Geometries Tested

SPEED5.17 Hz 6.75 Hz 8.00 HZ 10.25 Hz

Suct

ion/

Dis

char

ge

Pipi

ng6 inch / 6

inch 1 2 3 4

6 inch / 4 inch - 5 6 7

6 inch / 3 inch - 8 9 10

4 inch / 6 inch - 11 12 13

3 inch / 6 inch - 14 15 16

Pipe Diameter6/6 inch 6/4 inch 6/3 inch

Suction 0.0001 0.0003 0.0006Discharge 0.0001 0.0002 0.0005

Impedance line slope [psi/acfm]:

Test Points:

Results from Tests 1-16

Test No

RecipSpeed(RPM)

Excitation Pulsations

(psi pk-pk) at Recip

Discharge

Excitation Pulsations

(psi pk-pk) at Centrifugal

Suction(0-75 Hz)

Flow Fluctuation

s at Centrifugal

Suction(p-p acfm)

Surge Margin Differential %

Compressor Pulsation

Amplification or

Attenuation Factor

6/6

Suct

ion/

D

isch

arge

1 310 (5.17 Hz) 0.37 0.152 44.9 6.1 0.56644

2 405 (6.75 Hz) 0.65 0.166 209 7.9 0.93785

3 480 (8 Hz) 0.55 0.183 153 24.3 1.40769

4 615 (10.25 Hz) 0.88 0.325 376 41.2 3.69318

6/4

Suct

ion/

D

isch

arge 5 405 (6.75 Hz) 1 0.17 213 6.8 0.69388

6 480 (8 Hz) 0.66 0.175 174 17.8 1.75000

7 615 (10.25 Hz) 2.04 0.415 407 39.8 5.12346

6/3

Suct

ion/

D

isch

arge 8 405 (6.75 Hz) 1.1 0.195 203 8.2 1.30000

9 480 (8 Hz) 0.55 0.195 182 8.2 1.95000

10 615 (10.25 Hz) 2.25 0.405 391 27.3 2.48466

4/6

Suct

ion

Dis

char

ge 11 405 (6.75 Hz) 1.03 0.151 297 19.6 0.61633

12 480 (8 Hz) 0.575 0.21 294 26.2 1.11702

13 615 (10.25 Hz) 2.2 0.7 394 40.1 1.07692

3/6

Suct

ion/

D

isch

arge 14 405 (6.75 Hz) 1.13 0.158 336 35.7 0.74528

15 480 (8 Hz) 1.03 0.21 371 42.9 0.80769

16 615 (10.25 Hz) 2.35 0.33 396 42.9 2.55814

Pulsation Amplification vs. Discharge Piping Impedance Slope

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006

Puls

atio

nAm

plifi

catio

n

Discharge Piping Impedance Slope [psi/acfm]

6/6

6/4

6/3

Surge Margin Reduction vs. Suction Piping Impedance Slope

20

25

30

35

40

45

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007

Surg

e M

argi

n D

iffer

entia

l [%

]

Suction Piping Impedance Slope [psi/acfm]

6/6

4/6

3/6

Impact of Piping ImpedanceGeneral Trends

Increasing (“Steeper”)

Impedance Slope

Decreasing (“Flatter”)

Impedance Slope

Suction Piping

↓↓↓ Surge Margin Differential ↑↑↑Surge Margin Differential

↑ Pulse Amplification ↓ Pulse Amplification

Discharge Piping

↓↓ Surge Margin Differential ↑↑ Surge Margin Differential

↑↑↑ Pulse Amplification ↓↓↓ Pulse Amplification

Consistent with Compressor Dynamic Response Theory

Comparison of Transient Analysis to Test Results 8 Hz recip

TAPS Model of the System

Pulsation Analysis can accurately predict suction/discharge pulsation into a centrifugal compressor and thus define the

operating map ellipse of the compressor

Approx. 30% of time spent across surge line

Portion of Pulse from Recip that Takes the Flow Across the Surge Line

Surge was consistently identified when 30% of the area of the operating map ellipse crosses the surge lines for all suction/

discharge pulsation frequency orders below 75 Hz

Conclusions

• External pulsations applied to the suction or discharge flange of a centrifugal compressor reduce its surge margin significantly.

• The geometry of the piping system immediately upstream and downstream of a centrifugal compressor can have significant impact on the surge margin reduction (surge margin differential).

• The reduction of surge margin due to external pulsations is a function of the pulsation’s amplitudes and frequencies at the compressor suction and discharge flange. High suction flange amplitudes at low frequencies significantly increase the risk of surge. Surge margin reductions (differentials) over 40% were observed during testing.

• Utilizing the transient operating map ellipse of the centrifugal compressor to identify whether induced pulsations can result in the operating point temporarily crossing the surge line is a useful tool to identify the potential onset of surge. From the operating map ellipse surge margin differential can be calculated for various orders of pulsations.

Conclusions – cont.• If the upstream piping system impedance curve is flat, pressure pulses are

converted to high volume flow pulses which increase the centrifugal compressor pulsation induced surge margin differential. On the other hand, steep piping impedance curves of the downstream piping reduce the surge margin differentials.

• Surge was consistently identified when approximately 30% of the area of the operating map ellipse had crossed the surge lines for all suction/ discharge pulsation frequencies orders under 75 Hz.

• Test result and trends were consistent with predictions from CDR (Spark, 1983) and numerical predictions (Brun, 2014) for pulsation amplification and attenuation across a centrifugal compressor.

• A transient time domain 1-D Navier-Stokes pipe network analysis model was able to accurately predict suction/ discharge pulsations into a centrifugal compressor and thus, its operating map ellipse. Using the above described basic design rule (30% of the operating map area across the surge line for all pulsations below 75 Hz), these pressure/ flow pulsation amplitude predictions can be related to surge margin differential.

Thanks!Any Questions?

Dr. Klaus BrunContact info:Southwest Research InstituteTel: [email protected]

The 2nd Law of Thermodynamics Does Not Violate the 1st Law!

mailto:[email protected]

the impact of reciprocating compressor pulsations...

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