1. Subject: Report for Wheatstone PTC10 Type 2 compressor performance test on Apache (D14) bundle
Date: 6‐August‐2012
Time: 9:00 a.m. till 6:30 p.m.
Venue: Dresser‐Rand test department (Le Havre)
Author: CangTo Cheah (Rotating equipment engineer, Technip Malaysia)
Author’s email contact: ctcheah@technip.com
Review of test procedure with D‐R’s test engineer
The test was kicked off by D‐R test engineer Mathieu Hebert with a brief introduction to D‐R’s test procedure WS2‐
1230‐QAC‐PCD‐DME‐GCP‐00001‐000. The guaranteed point (i.e. Apache minimum turndown) is normalized to the
following dimensionless parameters:‐
a) Flow coefficient: 0.0148 per PTC10’s definition (see note # 2 below) or 0.6768 per D‐R’s definition (Q/N)
b) Work input factor: 0.6604
c) Polytropic efficiency: 0.8130
d) Polytropic head coefficient: 0.5368
Notes:
1. work input factor = polytropic head coefficient / polytropic efficiency
2. Flow coefficient = Q/(2 x pi x N x (d2/12)^3), where N = rpm; Q = acfm; d2 = inches. Q/N is used by D‐R
omitting impeller diameter (i.e. d2) to ease calculate step during and after test, as impeller diameter is a
fixed number. Q/N can be related to PTC’s 10 definition with specific conversion factor provided by D‐R (see
table provided below).
Using pure CO2 as test gas, the anticipated test speed matching the Apache minimum turndown’s dimensionless
parameter is 3530 rpm (actual operating speed for Apache minimum turndown compression duty is 5345 rpm per D‐
R’s API 617 data sheet) with the following test conditions:‐
a) Suction pressure = 8 barA
b) Suction temperature = 20 deg. C
c) Molecular weight = 44.01 kg/kmol
As advised by D‐R, actual test speed may vary from the predicted test speed (i.e. 3530 rpm in this case) due to actual
as‐measured temperature at compressor suction flange. The actual test speed can be evaluated by the following
equation (extracted from D‐R’s test procedure):‐
The background of speed correction factor with respect to temperature is derived by the author as follows (note:
Theories stipulated below are based on author’s fundamental understanding of thermodynamics and physics,
suggestions and comments from readers are welcome):
CangTo
Cheah

2. From thermodynamics perspective, energy can be related to temperature; Energy = Cp x temperature. Assuming
constant Cp due to small change from Tpredicted to Tactual, energy is therefore directly proportional to temperature, i.e.
Energy ∝ T.
And in term of Newtonian physics: Kinetic energy added to the gas at impeller exit channel can be related by
Energykinetic = 0.5 x mass x velocity2
. (0.5 can be omitted as it is a numerical constant, mass can also be eliminated
from the equation since mass flow within the test loop shall consider constant, i.e. conservation of mass).
Rotational speed N (in rpm) can be related to impeller tip velocity by the following formula, N = 60 x velocity / (pi x
diameter); 60, pi and diameter can be omitted from the equation since these are mere numerical constants, then
Energykinetic ∝ N2
.
By equating equations of thermodynamics and physics, temperature change is therefore directly proportional to the
squared of rotational speed, i.e. T ∝ N2
. And T1/T2 = (N1/N2)2
.
For example, if the actual temperature at compressor suction flange is measured at 23 deg. C, then actual test speed
shall be adjusted to: Nactual = square root ((273.15+23)/(273.15+20)) x 3530 rpm = 3548 rpm.
There will be 5 (five) test points covering from the Stonewall to Surge limit of compressor at test speed (or 100%
similarity speed per D‐R’s terminology), please refer to snap shot (extract from D‐R’s test agenda) provided below.
For 100% similarity speed, first point will be started at the Stonewall limit (i.e. point at the right of performance
curve), gradually progress towards the guaranteed point on the left by reducing inlet volume flow rate (manually
closing of suction throttling valve), and finally reaching the surge limit at point 5.

3. After completion of 100% similarity speed, next test speeds will be 110% speed (note: do not confuse 110% test
speed with actual MCOS of turbo‐compressor. 110% is 1.1 x 3530 rpm = 3883 rpm in this case) and 95% speed at
surge limit, point 6 and 7 respectively. Intent is to derive actual compressor surge limit (defined by the peak of
polytropic head or polytropic head coefficient, Mu).
Client has specifically requested an additional test point of Apache maximum power compression duty to be
included, which was not planned per D‐R’s test agenda. This additional point is agreed by D‐R to be added to the test
and associated test report. The test speed of additional point (Apache maximum power) is calculated at 3810 rpm,
which is slightly below the 110% test speed. D‐R advised that Apache maximum power test point will be tested prior
to point 6 as its speed lies between 100% and 110% test speed.
Prior to the start of performance test, the gas analyser is calibrated with pure CO2.

4. After the calibration with pure CO2, the gas analyser is disconnected from CO2 bottle and connected to test loop.
Commencement of test
For first test point, polytropic efficiency (Nh) is recorded at 85% (represents by red dot and circle) vs. predicted value
of 76%. This is anticipated since the steady state has not been reached, as indicated by “temperature variation”
module of the test program. It measures the difference of discharge temperature (at same location) at 5 seconds
interval.

5. Steady state is declared once the temperature variation (of 5 seconds interval) is less than or equal to 0.2 deg. C (or
Kelvin), per D‐R’s experience.
Test points 2, 3, 4, 5, 6, 7 and Apache maximum power are continued.

6. The test points (1 to 5) of 100% similarity speed are plotted adjacent to the predicted curves (Nh, Wi and Mu for
polytropic efficiency, work input factor and polytropic head coefficient, respectively).
Special note: flow coefficients appear on the x‐axis are in accordance with D‐R’s definition (i.e. Q/N = ft^3/rev),
conversion factor of 0.0116 shall be applied if D‐R’s flow coefficient is translated to PTC10’s definition (Q/[2 x pi x N x
(d2/12)^3], where N = rpm; Q = acfm; d2 = inches).
From the plot compiled during the test, it appears that as‐tested polytropic efficiency is in good alignment with
predicted data. However, polytropic head coefficient is low when predicted curve compared with tested data set.

7. Post‐test data review on polytropic head, polytropic efficiency, rotational speed and associated gas power
As‐tested discharge pressure for point 3 (guaranteed point) is 0.17 barA below the predicted pressure of 15.50 barA,
this is due to lower head coefficient value: predicted Mu is 0.5368 and tested Mu is 0.5220.
Test curves (both Nh and Mu) are reproduced below with curve fitting method using second order polynomial (i.e.
quadratic) equations (note: dotted lines are predicted curves prior to the performance test):‐

8. Polytropic head (or discharge pressure) requirement: Discharge pressure of 15.50 barA can be achieved by increasing
compressor speed from 3530 rpm to 3569 rpm. Derivation as follows:‐
Ntest is numerically solved using Newton’s method:‐
Equating Mu: 0.48793 + 0.55623 (Qtest / Ntest) – 0.74771 (Qtest / Ntest)^2 = 38418 / (3.142 x Ntest x Deq / 60)^2 [where:
Qtest = 2389 ft^3/minute and Deq = 1.4474 meters], which is further simplified to: 0 = 0.48793 + (1328.833 / Ntest) –
(10956408 / Ntest ^2)
Note: Deq (equivalent impeller diameter) is defined as square root (D1
2
+ D2
2
+ D3
2
+ D4
2
+ D5
2
+ D6
2
+ …), it is used to
calculate equivalent tip speed in order to evaluate overall polytropic head required for a compression duty.
To solve the equation, Newton’s method proceeds as follows.
1. Consider the following equation in one unknown: 0 = 0.48793 + (1328.833/Ntest) – (10956408/Ntest^2)
2. To apply Newton’s method to the solution of this equation, it is best to re‐write the equation in terms of
residual, e, where: e = 0.48793 + (1328.833/Ntest) – (10956408/Ntest^2)
3. Newton’s method requires an estimate of the total derivative of the residual, J. For this equation, the
derivative is: J = de/dNtest = 2 x 10956408/(Ntest^3) – 1328.833/(Ntest^2)
4. An initial guess is made for Ntest, e.g. Ntest = 3000.
5. The value of e is evaluated using the guess value for Ntest. With Ntest = 3000, e = ‐0.286504333.
6. The derivate of J is evaluated. With Ntest = 3000, J = 0.000663938.
7. The change to the guess value for Ntest, i.e. delta Ntest is calculated by solving J x delta Ntest = e. In this
example, delta Ntest is ‐431.522939151.
8. A better value for Ntest is then obtained as Ntest – delta Ntest. In this case, the improved value for Ntest is
3431.522939 (which results in e = ‐0.055279947).
Number of
iteration
1 2 3 4 5 6
Ntest 3000 3431.522939 3560.246012 3568.690074 3568.723019 3568.723019839
e ‐0.286504333 ‐0.055279947 ‐0.003215001 ‐0.000012447 0.000000000 0.000000000
J 0.000663938 0.000429449 0.000380741 0.000377798 0.000377786 0.000377786
delta Ntest ‐431.52293915 ‐128.72307249 ‐8.444062559 ‐0.032945134 ‐0.000000498 0.000000000

9. Results from the above calculation for test point # 3 are transferred into Nh and Mu curves:‐
Note that:‐
a) Q/N is decreased from 0.6735 to 0.6694,
b) Polytropic efficiency is increased from 0.8175 to 0.8191, and
c) Polytropic head coefficient is increased from 0.5220 to 0.5251

10. For Apache minimum turndown; the predicted operating speed is 5345 rpm and adjusted speed according to test
curves is calculated at 5405 rpm:‐
Equating Mu: 0.48793 + 0.55623 (Qtest / Ntest) – 0.74771 (Qtest / Ntest)^2 = 88081 / (3.142 x Ntest x Deq / 60)^2 [where:
Qtest = 3617 ft^3/minute and Deq = 1.4474 meters], which is further simplified to: 0 = 0.48793 + (2011.88391 / Ntest) –
(25117907.5109 / Ntest ^2)
To solve the equation, Newton’s method proceeds as follows.
1. Consider the following equation in one unknown: 0 = 0.48793 + (2011.88391/Ntest) – (25117907.5109/Ntest^2)
2. To apply Newton’s method to the solution of this equation, it is best to re‐write the equation in terms of
residual, e, where: e = (2011.88391/Ntest) – (25117907.5109/Ntest^2)
3. Newton’s method requires an estimate of the total derivative of the residual, J. For this equation, the
derivative is: J = de/dNtest = 2 x 25117907.5109/(Ntest^3) – 2011.88391/(Ntest^2)
4. An initial guess is made for Ntest, e.g. Ntest = 4000.
5. The value of e is evaluated using the guess value for Ntest. With Ntest = 4000, e = ‐0.578968242.
6. The derivate of J is evaluated. With Ntest = 4000, J = 0.000659192.
7. The change to the guess value for Ntest, i.e. delta Ntest is calculated by solving J x delta Ntest = e. In this
example, delta Ntest is ‐878.3000404.
8. A better value for Ntest is then obtained as Ntest – delta Ntest. In this case, the improved value for Ntest is
4878.30004 (which results in e = ‐0.155126371).
Number of
iteration
1 2 3 4 5 6
Ntest 4000 4878.30004 5323.834711 5401.616779 5403.526933 5403.52804
e ‐0.578968242 ‐0.155126371 ‐0.020374001 ‐0.000477139 0.000000276 0.000000000
J 0.000659192 0.00034818 0.000261937 0.000249791 0.000249502 0.000249501
delta Ntest ‐878.3000404 ‐445.5346709 ‐77.78206763 ‐1.91015418 ‐0.001107191 0.000000000

11. Results from the above calculation for Apache minimum turndown are transferred into Nh and Mu curves:‐
Shaft power requirement: Power = mass flow rate x polytropic head / polytropic efficiency; per D‐R’s API 617 data
sheet, the predicted gas power for Apache minimum turndown is 11340 kW. The gas power calculation based on as‐
tested Mu and Nh curves as follow: 104.6333 kg/s x 88081 J/kg / 0.8191 = 11251 kW (at: Mu = 0.5251, Q/N = 0.6693
and Nh = 0.8191), i.e. calculated gas power based on test curves is 88 kW (0.7793%) less than predicted gas power,
the reduction of gas power is due to improved polytropic efficiency (with test curves) at required polytropic head.
Conclusion
The reduction of polytropic head coefficient causes the following:‐
a) Power (energy) saving of 88 kW due to improved efficiency (i.e. from 0.8120 to 0.8191) occurs at lower flow
coefficient (or Q/N).
b) Increased operating speed (rpm) of 60 rpm (or 1.12%), i.e. from 5345 rpm to 5404 rpm. This is deemed
acceptable as the design speed of high speed power turbine (of PGT25+G4) is rated at 6100 rpm (and
maximum continuous operating speed of PGT25+G4 is 6405 rpm).
Based on dimensionless parameters obtained from the test (i.e. Nh, Wi and Mu), D‐R will then develop as‐tested
compressor performance curves, namely polytropic head vs. actual inlet volume flow rate, discharge pressure vs.
inlet volume flow rate, polytropic efficiency vs. actual inlet volume flow rate.

12. Picture of Datum compressor D16 casing with D14 bundle
Discussion of technical issues with D‐R on 7‐August‐2012
1) D‐R advised that flow induction vibration on anti‐surge piping is not within D‐R’s bailiwick. Anyhow, D‐R is
willing to check with their valve specialist (instrument engineer) and revert to Wheatstone Project.
2) Maintenance data sheet. The latest mineral lube oil console general arrangement drawing doesn’t reflect
the individual weight (and dimension) of mechanical items that require maintenance (e.g. pump, motor,
filter, valve, electric heater, etc). D‐R is asked to provide the weight data to Wheatstone Project as soon as
the revised GA drawing is submitted by D‐R’s sub‐vendor.
3) Mineral lube oil bypass from rundown tank to power turbine bearing. D‐R proposed to implement
accumulator (bladder type) on the mineral lube oil line to GE’s power turbine (and delete bypass line from
RDT to PT). Technical and commercial proposal will be submitted.
End of report