Method and apparatus for assessing and quantifying pulsation induced error in gas turbine flow meters

A method and apparatus for identifying, quantifying and correcting turbine meter errors related to pulsation effects in a gas stream being measured. A turbine meter pulse rate output signal is monitored and abnormal pulse rate modulations in the signal are detected and used to indicate turbine meter measurement errors. The equation used to determine turbine error requires measurements of pulsation intensity over a desired frequency range. Because of the difficulty in measuring pulsation intensity at field sites, meter error is determined directly from rotor speed modulation data. Rotor speed modulation data is obtained and then quantitatively related to pulsation intensity using a rotor response model. Thus, meter error is determined directly from rotor speed modulation data, allowing on-site quantification and correction of errors.

FIELD OF THE INVENTION 
The present invention relates generally to systems for testing the 
operation of flow meters. More specifically, the present invention 
comprises an improved method for detecting, quantifying and correcting 
pulsation-induced errors in gas turbine flow meters using measured rotor 
response data. 
BACKGROUND OF THE INVENTION 
Turbine meters are commonly used for large volume gas flow measurement 
applications where accuracy and rangeability are essential. When 
calibrated, properly maintained, and used in steady flow conditions, 
turbine meters can provide reliable and accurate fluid metering. However, 
at many gas metering stations flow is not steady. Pulsations from 
operating compressors can be present and unsteady flow can result from 
control valves or natural resonant lengths within the piping system. These 
pulsations and unsteady flow conditions can cause errors in turbine meter 
registration. 
U.S. patent application Ser. No. 07/708,357 filed on May 31, 1991 titled 
"DETECTION OF ERRORS IN TURBINE METERS" and assigned to the same assignee 
as the present application discloses a method and apparatus for monitoring 
the torsional oscillation of gas turbine meters which are induced by 
pulsating flow. The above-referenced application discloses how these 
torsional oscillation can be used to predict when meter errors are likely 
to occur. However, there is currently no method available for 
quantitatively assessing the magnitude of pulsation-induced errors at 
field turbine metering sites. There is also no available method for 
correcting meter readings to compensate for such errors. 
Because of the growing use of turbine meters, there is a need for a method 
and apparatus for quantitatively assessing and correcting turbine meter 
errors due to unsteady flow. Ideally, the parameters used for determining 
pulsation-induced errors should not involve extra measurements such as 
velocity modulation or differential pressures, but should result from a 
signal already available to the user. Heretofore, there has not been a 
practical field method for diagnosing, quantifying, and correcting 
pulsation-induced turbine meter errors. 
SUMMARY OF THE INVENTION 
The present invention comprises a method and apparatus for identifying, 
quantifying, and correcting pulsation-induced flow measurement errors in 
gas turbine meters at field installations. The system of the present 
invention determines the existence of a turbine error and quantifies the 
error directly from the pulse signal output of the meter and does not 
require the measurement of additional flow parameters. The equation used 
to determine turbine error has heretofore required measurements of 
pulsation intensity over a relevant frequency range. Because of the 
difficulty in measuring pulsation intensity at field sites, meter error is 
determined directly from rotor speed modulation data according to the 
present invention. 
The preferred embodiment of the invention detects an output signal produced 
by a turbine meter in response to the flow of a gas stream through the 
meter and monitors the torsional oscillation of the gas turbine meter 
rotors which are caused by the pulsating flow. The output signal produced 
by the turbine meter is normally in the form of a series of pulses 
produced by a transducer system in the turbine. A turbine meter pulse rate 
modulation signal is determined from the pulse-to-pulse time period of the 
pulse signals produced by the turbine. This pulse rate modulation signal 
is processed to remove any inherent modulation effects which are produced 
by imperfections in the pulse generating system of the turbine. Rotor 
oscillation data is then obtained using this pulse rate modulation signal. 
The method then determines turbine meter error from a relationship which 
depends on pulsation velocity modulation amplitude and frequency. The 
obtained rotor speed modulation data is quantitatively related to 
pulsation intensity using a rotor response model. Thus, meter error is 
determined directly from rotor speed modulation data, allowing on-site 
quantification and correction of errors.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring to FIG. 1, a turbine meter 10 is shown in fluid communication 
with a section of pipe 12 for transporting gas. A properly calibrated 
meter 10 provides an accurate indication of the gas flow volume, assuming 
that the flow of gas in the pipe 12 is steady and uniform. A number of 
factors, however, can create pulsations in the flow which cause 
significant inaccuracies in the measurement provided by the meter 10. For 
example, compressors operating in the gas stream can create pulsations. 
Pulsating or unsteady flow can also be created by control valves within 
the gas stream or by natural resonant lengths within the piping system. 
The aggregate result of the aforementioned pulsation effects can be 
described as "modulation" of the otherwise steady flow of the gas within 
the pipeline. The waveform 14 shown in FIG. 1 is a general illustration of 
a velocity modulation waveform within the gas stream carried by the pipe 
12. For purposes of illustration, the waveform 14 is shown as a sinusoid 
extending outside the boundaries of the pipe 12. The effects of the 
waveform 14, however, will be a series of wavefronts 16 within the 
pipeline 12, which cause unsteady flow of the gas and inaccuracies in 
turbine meter flow measurement. 
FIG. 2 illustrates a system for using a turbine meter 10 to measure gas 
flow in a pipe 12. The turbine meter 10 comprises a system of transducers, 
known to those skilled in the art, for converting rotation of the turbine 
into a series of pulses. It is customary for turbine meter registration to 
be reported in terms of the number of pulses per unit volume of gas flow. 
The unit volume of gas flow at a particular pressure and temperature can 
be determined from the turbine pulse signal output by the pulse counter 
18. 
However, as discussed above, modulation of the gas flow creates errors in 
the measured flow rate of the turbine meter. These errors can be detected 
in the form of pulse rate modulation of the pulse output signal produced 
by the meter 10. The variation in pulse rate output can be detected as 
modulation in the period from one pulse to the next. Pulse rate modulation 
is defined as: 
##EQU1## 
Each turbine meter has a unique characteristic pulse rate modulation 
pattern at steady flow which is related to the meter's transducer system 
for producing pulses. Therefore in the preferred embodiment, the pulse 
count determined by the pulse counter 18 is provided to a programmable 
computer 20 which processes the pulse count signal from the pulse counter 
18 and generates a pulse rate modulation signal based on the 
pulse-to-pulse spacing. 
FIG. 3a is a graphical illustration of the pulse rate modulation signal 
produced by a turbine meter measuring the flow of gas under uniform, 
steady flow conditions. In the preferred embodiment, this signal is 
obtained by measuring the pulse signal output while the turbine is spun at 
a constant rotational rate. Because of the inherent "signature" of this 
signal, however, it is possible to isolate and remove this signal from the 
composite pulse output signal by using signal processing techniques known 
to those skilled in the art. FIG. 3b is a graphical illustration of a 
pulse rate modulation signal produced by a turbine meter measuring the 
flow of an unsteady, pulsating gas stream. The effects of pulsation can be 
seen in the somewhat sinusoidal waveform impressed on the waveform of FIG. 
3a. 
The pulse rate modulation signals effectively measure the torsional 
oscillations of the rotor of the gas turbine meter. These oscillations are 
caused by pulsations in the gas stream, i.e., by flow velocity modulations 
which are one manifestation of pulsations. For more information on a 
method and apparatus for obtaining rotor speed modulation data, please see 
U.S. patent application Ser. No. 07/708,357 filed May 31, 1991, which is 
hereby incorporated by reference. 
The computer 20 implements a method or program 22 according to the present 
invention which quantifies the amount of pulsation-induced turbine error 
using the obtained rotor torsional oscillation measurements. This method 
is discussed further below. The amount of error can be output or indicated 
as a message on the display 24, which can be in the form of a cathode ray 
tube or the like. Alternatively, the turbine meter error can be displayed 
directly on the display 24. 
Determining Pulsation-Induced Error 
The pulsation-induced error in turbine meters can be described as a 
function of pulsation intensity (I), physical characteristics of the meter 
[rotor inertia (J), slip factor (.eta.), and mean effective rotor radius 
(r)], flowing gas density (.rho.), and volume flow rate (Q). The 
theoretical equations which describe pulsation error are quite complex and 
require solution by numerical methods. An approximate solution to these 
equations is described in Haalman, A. "Pulsation Errors in Turbine 
Flowmeters," Control Engineering, pp. 89-91, 1965, which is hereby 
incorporated by reference. The approximate solution to these equations 
described by Haalman provides a reasonable match to the complex numerical 
solutions when flow pulsations are sinusoidal. The Haalman's equation is: 
##EQU2## 
where: .DELTA.W.sub.o =shift in average rotor speed due to pulsations; 
i.e., the difference between the average speed without pulsations and the 
average speed with pulsations; 
V.sub.o =average pipe flow velocity; 
##EQU3## 
.DELTA.V=peak-to-peak modulation amplitude of flow velocity; w=pulsation 
frequency (rad/sec); 
.tau.=rotor time constant; 
##EQU4## 
The rotor time constant T is defined in Lee, W. F. Z., Kirik, M. J. and 
Bonner, J. A. "Gas Turbine Flowmeter Measurements of Pulsating Flow," 
Journal of Engineering for Power, Paper No. 74-WA/FM-1, 1974, which is 
hereby incorporated by reference. This reference describes the rotor time 
constant .tau. as follows: 
##EQU5## 
where: J=rotor moment of inertia (supplied by manufacturer); 
.eta.=rotor slip factor (supplied by manufacturer); 
.rho.=flowing gas density (available at site); 
Q=volume flow rate (approximate turbine speed); 
r=mean effective radius of rotor blading center of action 
FIG. 4 illustrates the results of turbine meter error computations using 
Equation (1) for a range of w.tau. (rotor response) and I (pulsation 
intensity) values. Computations performed by the authors of the Lee 
Reference show that these curves compare well with numerical solutions of 
the basic turbine meter equation. As such, they validate the use of 
Haalman's equation as a basis for calculating turbine meter error as a 
function of measured field conditions (I, .rho., Q) so long as properties 
of the rotor (J,.eta.,r) are known. For more information on these 
properties, please see McKee, R. J., "Pulsation Effects on Gas Turbine 
Meters," Gas Research Institute Topical Report GRI-92/0220 (1993) which is 
hereby incorporated by reference. 
However, prior art methods are inadequate as a practical basis for 
identifying pulsation problems and assessing their magnitudes at field 
metering sites. For example, measurement of pulsation intensity (I) at the 
meter location requires the use of hot wire or laser doppler anemometry 
systems which are too complex for routine diagnostic purposes, especially 
if diagnoses are to be performed by gas measurement technicians. On the 
other hand, the dynamic response of Pitot tubes is not sufficient to 
accurately reproduce pulsating flow conditions over the required frequency 
range. 
Rotor speed modulation data, however, provides a convenient source of data 
for diagnosing pulsation effects on turbine meter rotor speed and 
registration, if rotor response can be quantitatively related to pulsation 
intensity. A rotor response model is described below which defines rotor 
speed modulation as a function of pulsation intensity, and this equation 
is combined with Haalman's approximate equation (Equation 1) to relate 
meter registration error directly to rotor speed modulation data. 
Rotor Torsional Response Model 
In commercial gas turbine meters, rotor speed is linearly related to volume 
flow rate under steady flow conditions. Any modulation of flow rate 
(.DELTA.V) is therefore linearly related to rotor speed modulation 
amplitude (.DELTA.W) so long as these modulations are at low frequencies 
(i.e., below the torsional cutoff frequency of the turbine meter rotor). 
At low frequencies, therefore, the rotor speed modulation ratio is 
numerically equal to the flow velocity modulation ratio; i.e., 
##EQU6## 
The turbine meter transfer function G (output response divided by input 
flow) is defined as 
##EQU7## 
When pulsation frequencies are above rotor cutoff, (i.e., when w&gt;1/.tau.) 
rotor speed modulations no longer track velocity modulations, and rotor 
modulation amplitude decreases with increasing pulsation frequency at a 
rate of 6 dB/octave. The generalized transfer function for rotor response 
is of the form: 
##EQU8## 
where: 
##EQU9## 
and denotes a quadrature vector direction. 
If the expression for .tau. (Equation 2) is substituted into Equation 3, 
then: 
##EQU10## 
The transfer functions given in Equations 3 and 4 are complex terms 
containing real and imaginary components which define rotor response 
amplitude and phase. Since only error magnitude information is desired, 
the amplitude of the transfer function can be defined as follows: 
##EQU11## 
Equations 4 and 5 show that rotor torsional response (like pulsation error) 
can be defined in terms of Pulsation Intensity (I), frequency (w), and 
rotor time constant, .tau.. It can be seen from Equation 5, for example, 
that for very small values of w.tau. (i.e., w.tau.&lt;&lt;1) that 
.vertline.G.vertline.=1, whereas when w.tau.&gt;&gt;1, then 
EQU .vertline.G.vertline.=(1/w.tau.). 
FIG. 5 is a plot of Equation 4 for a typical 4" single rotor gas turbine 
meter, showing rotor speed modulation ratio as a function of the rotor 
response parameter (w.tau.) for several values of pulsation intensity. If 
we define intensity as in the Haalman reference: 
##EQU12## 
where: .DELTA.V=peak-to-peak amplitude of the velocity modulation waveform 
V.sub.o =average velocity 
Then rotor modulation ratio must also be defined as the zero peak value; 
i.e., 
##EQU13## 
CORRELATION 
FIG. 6 superimposes the plot of rotor speed response (FIG. 5) and rotor 
error (FIG. 4) versus w.tau. for several intensity values (I=0.10, 0.20, 
and 0.40). It can be seen that both rotor response and meter error vary 
with I and w.tau., but that the form of these variations is substantially 
different. If field measurements of .DELTA.W/2W are to be used to predict 
error, a correlation equation is required to reconcile the two data sets. 
Mathematically, the process of developing this correlation (i.e., of 
analytically defining rotor response as a function of I and w.tau.) now 
becomes quite simple. Remembering that 
##EQU14## 
Equation 5 can be solved in terms of I: 
##EQU15## 
Substituting this expression for I into Haalman's approximate equation 
(Equation 1), we have meter error in terms of rotor modulation ratio: 
This equation provides a basis for defining meter error directly from rotor 
speed modulation data taken with the 
##EQU16## 
instrumentation system described hereinabove. As such, it provides a 
convenient basis for identifying and quantifying meter error using data 
which is easily accessible from the turbine meter itself; i.e., without 
additional complex sensors or intrusion into the gas stream. While some 
additional rotor design information is required to define rotor time 
constant .tau., such information is readily available from the meter 
manufacturer. Similarly, Q and .rho. data are available in the normal 
turbine meter measurement process (i.e., from rotor speed and system 
pressure and temperature). No additional information regarding pulsation 
amplitude or frequency is required (dynamic pressure, flow velocity, 
pulsation intensity, etc). 
FIG. 7 is a flowchart diagram illustrating the processing steps implemented 
by the computer 20 to gather rotor speed modulation data and 
quantitatively relate this data to pulsation intensity. Using these 
techniques, meter error can be determined directly from rotor speed 
modulation data. In step 100, the counter 18, shown in FIG. 2, is 
initiated. In step 102, the time of arrival of the pulses is determined. 
This can be accomplished through the use of a "time-stamping" algorithm 
known to those skilled in the art. In step 104, the pulse-to-pulse spacing 
is calculated and a turbine meter pulse modulation signal is constructed 
therefrom. In step 106, the characteristic pulse rate modulation related 
to the turbine meter is removed, using signal processing techniques known 
in the art, to provide a filtered turbine meter response signal. This was 
discussed previously with regard to FIGS. 3a and 3b. Also, as previously 
discussed, the filtered pulse rate modulation signal is essentially 
equivalent to the rotor torsional or modulation data. In step 108, the 
filtered turbine meter response signal is tested for the existence of 
modulation. If this test indicates the existence of pulse rate modulation, 
then a "meter error" is indicated. However, if the test in step 108 
indicates that there is no modulation, a "no error" indication is provided 
in step 112. 
If meter error is indicated in step 108, then in step 120 the method 
determines the pulsation intensity using the obtained rotor modulation 
data as previously described. In step 122 the method determines the 
predicted registration or meter reading error using the pulsation 
intensity determined in step 122. This can be illustrated by the graph of 
FIG. 6 whereby, knowing the rotor modulation ratio, the pulsation 
intensity I and hence the amount of meter error can be determined. This 
error can then be used in adjusting the meter reading to ascertain a more 
correct reading. 
As noted previously, the technique is based on sinusoidal wave forms. This 
however, is not a serious limitation for most field applications of 
practical concern for the following reasons: 
1) Most serious pulsation problems at field measurement sites involve 
pulsation waveforms which are predominantly pure tone (single frequency). 
When multiple frequencies do exist, it is rare that the amplitude of more 
than one frequency is strong enough to contribute significant error 
components. In many cases, an acoustic resonance within the piping is the 
basic cause for high pulsation levels, although unfiltered compressors 
(typical in gas gathering systems) can produce strong pulsations at one or 
two times crankshaft speed (depending upon whether they are single or 
double acting. Such large amplitude single pulsation frequencies are 
dominately sinusoidal. 
2) Complex pulsation wave forms can be described as a series of harmonic 
components using spectral analyzers or FFT routines. It may be possible, 
therefore, to simply combine the error contribution from each frequency 
component. This is the technique used for defining pulsation-induced error 
at orifice meters, where it can be shown analytically and experimentally 
that total pulsation error is the linear summation of error contributions 
from each frequency component. 
Therefore, the method according to the present invention utilizes the 
magnitude of the torsional oscillations to quantitatively assess 
pulsation-induced error in turbine meter registration (reading). 
Although the method and apparatus of the present invention has been 
described in connection with the preferred embodiment, it is not intended 
to be limited to the specific form set forth herein, but on the contrary, 
it is intended to cover such alternatives, modifications, and equivalents, 
as can be reasonably included within the spirit and scope of the invention 
as defined by the appended claims.