053-563 1 Copyright © 2017 by ASME
Proceedings of the ASME 2017 Power and Energy Conference PowerEnergy2017
June 26-30, 2017, Charlotte, North Carolina, USA
PowerEnergy2017-3431
SIMULATING PRESSURE TRANSIENT EVENTS IN THE FUEL GAS SUPPLY TO A MULTI-BLOCK COMBINED CYCLE PLANT
Robert Schroeder Sargent & Lundy Chicago, IL, USA
Matthew Zitkus Sargent & Lundy Chicago, IL, USA
Michael Czyszczewski Sargent & Lundy Chicago, IL, USA
Beniamino Rovagnati Sargent & Lundy Chicago, IL, USA
ABSTRACT As power plant combustion turbines (CTs) are pushed
towards higher thermal efficiencies, increased attention is being
given to operating requirements for their fuel gas supply such
as the maximum allowable rate-of-change in pressure. It is
important to perform detailed analyses for multi-unit plants to
ascertain whether pressure transient events, such as those
caused by initial trip of one or two combustion turbines, will
cause additional combustion turbines to trip off. In this paper,
single and dual CT trips were postulated in a near-realistic
combined cycle power plant. Predictions of the gas flow
behavior, along with propagation and superposition of pressure
waves, was carried out using the method of characteristics
(MOC) for compressible flows. Specifically, the rate of change
in fuel gas supply pressure to each CT was monitored and
compared against a typical manufacturer limit of 0.8 bar/s.
Instances where simulations showed this threshold exceeded
were noted, since such events correspond to automatic valve
closure that would shut down one more CT and thereby further
reduce plant electrical output.
The overall goal of fuel gas transient analyses is to
improve pipeline designs, iteratively when necessary, such that
those additional trips are avoided. To that end, this paper
presents several simulation cases to illustrate pressure transient
phenomena and to show the impact of various pipeline design
alterations, some of which caused 40% reductions in the worst
pressure rate-of-change during simulations.
INTRODUCTION Combustion turbines have become a technology of choice
for new power projects due to the affordability of natural gas,
the prevalence of existing gas pipelines, and the versatility of
these machines. Combustion turbines operate at high efficiency
and have low emissions, making them desirable for base-load
operations. Yet, depending on the model, combustion turbines ___________________________________
also have fast-start, high ramp rate, and cycling capabilities –
making them also ideal for peaking power applications. In both
services, high reliability is a must and situations that could trip
(shut down) the operating CTs at a plant must be anticipated
and avoided.
Fuel gas transient events are one such situation. The
original equipment manufacturers (OEMs) of combustion
turbines issue strict guidelines for the allowable composition,
temperature, and pressure of fuel gas supplied to combustion
turbines [1]. If the stated requirements are not met at a location
where fuel gas enters the OEM-scope equipment, the automatic
control system usually will shut down the combustion turbine
to prevent damage. During fuel gas transient events, pressure
waves transmitted through the pipelines have potential to
exceed the OEM pressure requirements.
In project-specific literature [2], combustion turbine OEMs
typically establish at least three guidelines for the fuel gas
pressure. First, in the long-term, fuel gas pressure is only
allowed to vary from nominal by a certain pressure range,
typically a few bar in pressure. Second, the fuel gas pressure
must not feature significant high-frequency fluctuations. High-
frequency fluctuations can sometimes be a concern when
dynamic machines, such as centrifugal compressors [3] or
combustion turbines, share the same pipeline with reciprocating
compressors.
Most relevant to this paper is the third OEM guideline,
which focuses on the rate of change in pressure for time scales
on the order of a second. Combustion turbine OEMs set forth a
“threshold” maximum allowable rate of change in pressure,
typically a value in the range of 0.1 to 1.0 bar/second. Rate of
change is calculated using Equation 1:
𝑑𝑃
𝑑𝑡|mean
=Δ𝑃
Δ𝑡=𝑃(𝑡) − 𝑃(𝑡 − Δ𝑡)
Δ𝑡 (1)
053-563 2 Copyright © 2017 by ASME
The prose of this paper refers to the above calculation as
“dP/dt” for shorthand. Notice that dP/dt can be positive or
negative, but it is the absolute value |dP/dt| that is evaluated
against the OEM threshold. Notice that Equation 1 features an
implied time scale “Δt” (a “sampling rate” or “averaging
interval”) which is dependent on sensitivity of the OEM’s
instrumentation and equipment. To highlight the importance of
this time scale, two averaging intervals are used in this paper,
namely, Δt = 0.01s and Δt = 1.0s.
PRESSURE TRANSIENTS AND PREVIOUS STUDIES Pressure transient events in fuel gas pipelines are complex
due to the finite speed of pressure waves that propagate
throughout the system. Flow at each location in a pipeline
network only begins to change once pressure waves from the
transient event reach that location. Moreover, gases take time to
compress or expand, and therefore pressure transient events
with gases can be more complex than seen with incompressible
flows. The method of characteristics (MOC) is one of several
computational methods that can model the rate of pressure
change in gases for both fast and slow fluid transient events
[4, 5]. Very briefly stated, MOC applies the potential flow
equation along “characteristic” lines that run in two dimensions
(in our case, time and space, where space is axial distance along
pipelines). The flow geometry is discretized (all pipelines are
represented as 1-dimensional flow paths with nodes along their
length). The characteristic lines are then calculated for the
forward and reverse spatial directions from each node, for each
time step as the solution marches forward in time. The
calculation yields three fluid variables (in our case the primary
variables were velocity, density, and pressure), from which
other fluid variables may be calculated using additional
equations such as the ideal gas state equation for methane.
While many studies have focused on the method of
characteristics, to the authors’ knowledge there are relatively
few papers that apply MOC to determine tripping behavior
expected for a multi-unit combustion turbine plant. Perhaps
closest is the study by Afzali et al. [6] which used MOC to
investigate pressure transient events (including emergency
shutdown) in the piping immediately upstream of a heavy duty
combustion turbine. This present paper complements that work.
Whereas Afzali et al. focused on piping components typically
within the combustion turbine OEM scope, this paper focuses
on pressure transient phenomena in the “balance of plant”
pipelines upstream of that OEM scope, for a large, near-realistic
power plant composed of different users of the fuel gas,
including two separate blocks of combustion turbines. Rates of
pressure change (dP/dt) are evaluated to show which events –
and which equipment configurations – lead to more or less
severe rates of pressure change.
APPLICATION OF THE METHOD OF CHARACTERISTICS The power plant pipeline network that was simulated for
combined cycle operation is shown in Figure 1. The pipeline
network was for a power plant featuring two power blocks of
three combustion turbines each (referred to as “Block 123” and
“Block 456” in this paper). Between the blocks was a pipeline
supplying small amounts of fuel gas to other users (such as
auxiliary boilers, CO2 generators, etc.). Upstream of the power
blocks was a pipeline supplying fuel gas to duct burners of the
heat recovery steam generators (HRSGs). While Figure 1 does
not show pipeline lengths to scale, the figure does convey name
of each individual pipeline along with pipe inside diameters
(indicated by symbol φ).
The simulated pipeline network corresponded to a power
plant featuring frame-type combustion turbines. Each CT would
nominally produce 300 MW electricity in simple cycle mode
and potentially would feature three HRSGs and two steam
turbines (STs) for each of the two power blocks, a 3 x 3 x 2
configuration (CTs x HRSGs x STs). In combined cycle mode,
maximum plant electrical output would be around 2700 MW.
This operating point of maximum combined cycle output is the
initial state for the baseline “Case 10” referenced throughout
the results of this paper. For simplicity, the pressure transient
cases in this paper all began with combustion turbines running
at full load (except for CTs that were turned off). Cases
featuring throttled combustion turbine output were not
simulated for this paper.
As depicted in Figure 1, simulations of this paper modeled
the valves, major components, and area changes of the piping.
In implementing the method of characteristics, each component
was modeled as a length of pipe (referred to in this paper as a
pipeline “leg”) or as a junction at the end of one or more legs
or as a combination of such legs and junctions. Three
examples: 1) Valves were each modeled as a junction having a
minor loss coefficient “K” based on its open area relative to
area of the adjoining pipes; 2) Performance heaters were each
modeled as a leg having specified length, internal diameter, and
friction factor; and 3) Filters (and filter-separators) were
modeled by a leg/junction combination—a dead end leg teeing
off the main line (to credit the “accumulator-like” reserve
volume of the filter), and an in-line junction with a minor loss
“K” to represent pressure drop across the filter. In each
instance, the specified attributes of legs and/or junctions were
matched to dimensions and pressure drops of real components
at power plants comparable to the multi-block plant featured in
this paper.
Table 1 provides general information on the simulations,
such as properties of the fuel gas and attributes of gas
conditioning components. Note that fluid velocities in the duct
burner lines (up to 36 m/s) and in dead-end pipes (0 m/s) were
omitted from the ranges stated for velocity and Mach number
and Reynolds number, in order to better communicate pipeline
conditions at the locations nearest to the CTs. Also, simulations
were performed with one stagnation temperature (62.5 °C) for
the pipeline network, even though temperature would be higher
in pipelines downstream of heaters such as the performance
heaters (combined cycle mode) and the water bath heaters
(simple cycle mode, not shown in Figure 1). To ensure that a
single stagnation temperature was appropriate, a few
simulations were also performed with higher stagnation
temperature and were seen to have similar dP/dt to simulations
presented in this paper.
053-563 3 Copyright © 2017 by ASME
Figure 1. Fuel gas pipeline network model used for implementation of MOC for the combined cycle cases.
Also included in Table 1 is information about the inflow
and outflow boundary conditions used. At the inlet to leg L1 a
constant stagnation pressure of 33 bar absolute (barA) was
applied. This resulted in delivery pressure of 30 barA to the
combustion turbines (CTs were not assumed to be G- or H-class
units, which typically require even higher supply pressures).
Outflows were modeled to mimic a non-reflective wave
boundary while also obtaining the correct mass flow rates. For
each case in this study, mass flow rate during the initial steady
state was 19 kg/s to each operating combustion turbine. Mass
flow rate was negligible to the “other users”. Mass flow rate to
HRSG duct burners was zero for simple cycle operation and
was 3.6 kg/s per operating CT for combined cycle operation.
In this paper, all pressure transients were assumed to be
caused by one combustion turbine (or two) tripping off for
unspecified reason. MOC simulations were run a long time to
first establish the initial steady state conditions. Then the
transient was initiated by 0.3s-duration closure of shutoff
valves for the combustion turbines assumed to have tripped.
During valve closure, the open area of a shutoff valve varied
linearly in time from full-port open to fully closed. Pressure
waves originating at shutoff valves propagated around the
pipeline network and pressure fluctuation (dP/dt) values were
monitored for the remaining combustion turbines.
To partially validate MOC simulations, initial steady-state
conditions of the baseline combined cycle “Case 10” were
compared to the solution obtained with a compressible flow
solver, AFT Arrow [7]. As shown in Figure 2, results compared
favorably. Good agreement was obtained for pressure
distributions along various flow paths such as the one shown.
RESULTS AND DISCUSSION The results are organized into four sections. The first
section presents behavior in cases where the plant was running
in combined cycle mode and one of the combustion turbines
tripped. The second section presents analogous cases for simple
cycle operation. The third section presents combined cycle
cases where two combustion turbines tripped in quick _______________________________________
053-563 4 Copyright © 2017 by ASME
Table 1. MOC Simulation Details
Figure 2. Comparison of steady state pressures calculated by MOC to those calculated by a steady state flow solver [7] for the flow path from the fuel gas source to combustion turbine CT6. Components that imposed major pressure drops are noted.
Table 2. Status of the Six Combustion Turbines for Each Simulation Case
succession. The fourth section investigates the implications of
having the combustion turbine blocks (Blocks 123 and 456)
connected by more than one large pipeline. All cases discussed
in this paper are summarized in Table 2.
COMBINED CYCLE BASELINE CASES This section presents investigation of the baseline
combined cycle cases, Cases 10, 20, and 30. However only
Case 10 is discussed in detail, both to orient the reader to the
phenomena and to lend credence to MOC simulations. The
validation of Case 10 includes examination of the uncertainty
due discretization step sizes in time and distance.
Pressure Wave Behavior in Baseline Case 10
Traces of pressure as a function of time are shown in
Figure 3 at inlets to shutoff valves for the combustion turbines
(for instance, downstream end of leg L30 for CT1), and also for
a pipeline position near the fuel gas source (leg L1). Since the
trip criteria for operating CTs is concerned with pressure
changes, and not pressure magnitude, it was fitting to stagger
the pressure traces vertically such that each could be seen.
The traces are plotted out to 10 seconds after beginning of
the CT1 shutoff valve closure, as t = 10s was the minimum time
to which each simulation in this paper was computed. This
length of time was deemed appropriate for observing the
maximum rates of pressure change (either positive or negative) _________________________________
053-563 5 Copyright © 2017 by ASME
Figure 3. Traces of pressure vs. time for Case 10, for the six combustion turbines and also a node shortly downstream of the fuel gas source. Symbols on each trace indicate times of maximum dP/dt: crosshair symbols (+) for the 0.01 second basis and diamond symbols (◊) for the 1.0 second basis. The dashed red line on the CT3 trace illustrates dP/dt calculation on the 1.0 second basis.
from the transient event. Note that in Figure 3 the times of
maximum |dP/dt| for each operating CT were during the initial
“pressure upswing”, well within the 10 second window.
Figure 3 shows the expected propagation of pressure waves
during the transient event. The transient event was initiated by
closure of the CT1 shutoff valve. For just this CT1 line,
pressure abruptly increased by more than 2 bar (which is off the
scale of the chart). Pressure waves first propagated to Block
123, then reached the upstream end of the pipeline network
(leg L1), and finally arrived at Block 456 around t = 2 seconds.
Overall, pressures at combustion turbines CT2 through CT6
increased no more than 0.4 bar. Also in Figure 3, note the
temporary pressure rise of 0.06 bar for the leg L1 trace. This
pressure rise was much less than pressure rises near CTs, due to
how pressure waves at leg L1 had travelled a long distance and
had experienced attenuation both from pipe friction and from
wave reflection at components such as pipe tees.
Since overall pressure changes at operational CTs were less
than 1 bar (safely within the first “OEM requirement” in the
Introduction), it was pressure rates of change that mattered in
the context of ensuring combustion turbines would remain
operational. Pressure rates of change, dP/dt, are shown in
Figures 4 and 5 for the two averaging intervals of Δt = 0.01s
and 1.0s. The traces had similar shape for the two averaging
intervals: pressure fluctuation magnitudes at CT2 and CT3 first
rose, and then fell. Then pressure fluctuation magnitudes rose
and fell for the Block 456 combustion turbines. Within the
same block, the operational combustion turbines exhibited
similar pressure fluctuations in time. Pressure rates of change
Figure 4. Traces of dP/dt on the 0.01 second basis for Case 10, for the five operational combustion turbines.
Figure 5. Traces of dP/dt on the 1.0 second basis for Case 10, for the five operational combustion turbines. To show detail, the vertical axis scale is made finer than in Figure 4.
were not similarly plotted for the CT1 shutoff valve which
started the transient event, as CT1 was thereby out of operation.
The similarities between Figures 4 and 5 did not extend
much past the general shape of dP/dt traces. Especially different
between the two averaging intervals was the dP/dt magnitude.
With the 0.01s interval used for Figure 4, CT2 and CT3
registered pressure fluctuation values of 0.46 and 0.55 bar/s,
which were significantly higher than pressure fluctuation values
for Block 456. Conversely, Figure 5 shows that when pressure
fluctuations were calculated on the 1.0s basis, dP/dt magnitudes
were similar between the Block 123 and Block 456 combustion
turbines, all being in the range 0.23 – 0.26 bar/s. It is striking
that these dP/dt values were less than half the 0.55 bar/s seen
with the 0.01s averaging interval. These differences underscore
053-563 6 Copyright © 2017 by ASME
the strong sensitivity of pressure transient analyses to the value
selected for the Δt averaging interval.
Mass flow rates at outflow junctions to the combustion
turbines were next examined and are plotted in Figure 6. Note
that these outflow junctions are at ends of the flow network,
positions slightly downstream of the OEM scope boundary
where pressures were reported. The flow rate results help verify
that each outflow boundary condition appropriately modeled
the combustion turbine consumption of fuel gas. During a
transient event, it might be expected that controllers and
throttling valves in the combustion turbine OEM scope (dashed
boxes in Figure 1) would actuate to help maintain steady flow
rate. For the cases simulated in this paper, such actuation was
deemed negligible, as Figure 6 shows that flow rates to the
operating combustion turbines in Case 10 only changed 1%
from their initial steady state values. Among the other cases
presented in this paper, the maximum change in flow rate to
operating combustion turbines was 2.2%. These small changes
in flow rate indicate that the analytical representation of the
OEM scope was acceptable.
Discretization Uncertainty
Also examined were simulation uncertainties due to the
time and distance discretization step size. The maximum step
sizes for simulations presented in this paper were 0.25
milliseconds in time and 0.305 meters in axial distance along
pipeline legs. To check that these step sizes were small enough,
maximum dP/dt values with the Case 10 configuration were
compared for three step sizes in time and three in axial
distance. Results on the 1.0s averaging interval are shown in
Figures 7a-b. For each pipeline location considered, the change
in maximum dP/dt between step sizes indicated a sufficiently-
fine step size, yielding “grid convergence.” Uncertainties due to
discretization were quantified based on the values in _________________________________________
Figure 6. Traces of change in flow rate vs. time for Case 10. Symbol legend is the same as that in Figure 3.
Figures 7a-b. Using the Richardson method as described by
Celik et al. [8], the effective order of convergence and
“approximate discretization error” were calculated and are
presented in Table 3. Using the worst percent errors in time and
distance of 1.3% and 1.6%, a conservative uncertainty for dP/dt
on the 1.0s averaging interval would be √(1.3%)2 + (1.6%)2
= 2.1%. For a dP/dt value typical of Figures 7a-b, such as
0.25 bar/s, the corresponding uncertainty would be 0.0052 bar/s.
Note the small ΔP difference that this uncertainty corresponds
to, per Equation 1: a difference of only 5.2 x 10-3
bar.
Discretization uncertainty on the 0.01s averaging interval
was more difficult to quantify than for the 1.0s interval. As
noted by Celik et al. [8], the Richardson method can give
ambiguous results when results differ only by small amounts
that are comparable to roundoff error. This situation was the
case with the 0.01s averaging interval: between the different
step sizes, the ΔP values used to calculate dP/dt only differed by
up to 0.55 x 10-3
bar – a miniscule 0.002% of the Case 10
absolute pressures shown in Figure 2. Lacking a discretization
______________________
Figure 7. Convergence of Case 10 maximum dP/dt with (a) time discretization and (b) distance discretization. These dP/dt were for the 1.0s averaging interval. The smallest discretization sizes (rightmost data) represent step sizes of time and distance used in simulations of this paper.
Table 3. Discretization Error Estimation
Based on dP/dt Values in Figure 7
053-563 7 Copyright © 2017 by ASME
uncertainty, the dP/dt uncertainty was estimated for the 0.01s
averaging interval by applying that small 0.55 x 10-3
bar as the
ΔP in Equation 1. Combined with Δt = 0.01s, this yielded an
estimated uncertainty of 0.055 bar/s. Henceforth in this paper,
when dP/dt on the 0.01s basis was within 0.055 bar/s of the
0.8 bar/s threshold, the corresponding CT was assumed to be at
risk of tripping.
Single-Block Combined Cycle Cases
The two other combined cycle cases relevant to this first
results section were Cases 20 and 30. These cases differed from
Case 10 in that only one of the two blocks was operating in
each case, Block 123 for Case 20 and Block 456 for Case 30. In
both cases the pressure and dP/dt traces were similar to CT2
and CT3 of Case 10, and therefore additional plots are omitted.
Table 4 summarizes the maximum magnitudes of dP/dt
observed for Cases 10, 20, and 30, for both 0.01s and 1.0s
averaging. All the values are positive as the maximum
magnitudes occurred during initial pressure upswings. Table 4
highlights the strong influence of the “averaging interval”
parameter. In each row, the cell with highest dP/dt for the row is
highlighted orange. When the longer averaging interval (1.0s)
was used instead of the shorter interval (0.01s), dP/dt calculated
was often lower by a factor of two. Also note that the chosen
averaging interval affected which combustion turbine had the
highest calculated dP/dt: in Case 10, the 1.0s averaging interval
resulted in combustion turbine CT6 appearing to have the most
severe pressure fluctuation, which disagreed with how the 0.01s
averaging interval indicated CT3 had the most severe pressure
fluctuation. The different results obtained with different
averaging intervals shows that it is critical to use the
appropriate averaging interval. Since more-severe dP/dt values
are obtained with the shorter averaging interval of 0.01s,
henceforth in this paper the data is primarily presented on this
0.01s averaging basis.
Lastly for these baseline combined cycle cases, note that
none of the maximum values in the highlighted cells exceeded
the 0.8 bar/s threshold, even if the respective uncertainties of
0.005 and 0.055 bar/s were added in. As will be shown, other
cases in this paper did not always have such low dP/dt values.
Table 4. Maximum Pressure Fluctuations of
Baseline Combined Cycle Cases
SIMPLE CYCLE BASELINE CASES This section presents investigation of the three baseline
simple cycle simulations, Cases 40, 50, and 60. These cases
only differed from the combined cycle cases in that flow to duct
burners was zero, and in that flow was bypassed around the
performance heaters shown in Figure 1 and instead proceeded
through two parallel water bath heaters. Each water bath heater
handled 50% of the fuel gas flow to combustion turbines. The
two water bath heaters were located where the “WBH bypass
valve” is shown in Figure 1.
Figure 8 presents the pressure traces for Case 40. Pressures
are plotted out farther in time than in Figure 3 to illustrate the
nature of the pressure fluctuations. After the initial propagation
of pressure waves around the pipeline network, accompanied
with high rates of pressure change, pressures gradually
approached the new steady state in an oscillatory “ringing”
manner. This observation again makes clear that the focus in
this study on the first 10 seconds of transient events was
appropriate, as the magnitude of pressure rates of change was
highest during that initial period. The observation also shows
that the simulations were reasonable – pressure transients in the
piping asymptotically decayed, as expected due to pipe friction.
However, the rates of change in pressure were more severe
for simple cycle cases than for combined cycle cases.
Illustrating this is Figure 9, which shows much higher dP/dt
calculated on the 0.01s basis for Case 40 than was seen in
Figure 4 for the analogous combined cycle case, Case 10. The
maximum value for dP/dt is nearly three times higher than that
seen for Case 10. However, like Case 10, the more severe dP/dt
values on the 0.01s basis were experienced by combustion
turbines in the same block as the tripped combustion turbine
(Block 123), rather than the block farther away (Block 456). ___________________________________________
Figure 8. Traces of pressure vs. time for Case 40, for the six combustion turbines and also a node shortly downstream of the fuel gas source. Pressures are staggered along the vertical axis; symbol legend is the same as that in Figure 3.
053-563 8 Copyright © 2017 by ASME
The cause of more-severe pressure fluctuations for simple
cycle cases, as compared to combined cycle cases, was the lack
of performance heaters. In simple cycle cases the performance
heaters were bypassed since steam was unavailable. However,
in the combined cycle cases these performance heaters played
an important role in dampening pressure waves that propagated
between combustion turbines. Pressure traces for Cases 40
and 10 were compared at locations throughout the pipeline
network (not shown). Significant pressure-trace differences
between cases were found at times as early as t = 0.32s, well
before pressure waves had even reached the water bath heaters.
Table 5 summarizes the maximum pressure fluctuations for
these simple cycle cases. As in Table 4, highest dP/dt for each
row are in highlighted cells. However for these cases many
cells with the 0.01s averaging interval are highlighted red
because they were within 0.055 bar/s uncertainty of the
0.8 bar/s threshold, and thus corresponded to risk of these CTs __________________________________
Figure 9. Traces of dP/dt on the 0.01 second basis for Case 40, for the five operational combustion turbines. The simple cycle cases exhibited more oscillation of pressure than did the combined cycle cases; note that the horizontal and vertical axes have the same scales as in Figure 4.
Table 5. Maximum Pressure Fluctuations
of Baseline Simple Cycle Cases
tripping. Table 5 also presents dP/dt calculated on the 1.0s
basis. Note that if only the 1.0s averaging basis had been used,
the additional trips for these cases could have been overlooked.
One possible solution for dP/dt values exceeding the 0.8
bar/s threshold would be to add additional internal volume to
the pipeline network. Internal volume can be augmented by
increasing the diameter of select pipeline legs, or by adding tee
connections at strategic locations which connect to new,
additional “accumulator” pressure vessels. (Strategic locations
may be directly upstream of combustion turbines, near the
“final filters”, or may be farther upstream.) Since augmentation
of internal volume is subject to optimization, it is beyond the
scope of the present paper and the authors plan to address such
optimization in a later paper dedicated to the topic.
DUAL UNIT TRIP CASES Since the combined and simple cycle cases exhibited
similar patterns of pressure fluctuation behavior, the effect was
analyzed of two combustion turbines tripping in close
succession, a “dual trip.” Would pressure traces be qualitatively
similar but lead to twice the magnitude for pressure rates of
change? To investigate, six modified versions of Case 10 were
simulated. Cases 11 and 12 featured two combustion turbines
tripping at exactly the same time (shutoff valves began
actuating at t = 0 seconds, and were fully closed at t = 0.3
seconds). Cases 13 and 14 featured one of the combustion
turbine shutoff valves beginning closure at 0.3 seconds, just as
the first shutoff valve became fully closed. And Cases 15 and
16 had double the time delay, 0.6 s (the latter shutoff valve
began closing at 0.6 s and finished at 0.9 s).
The resulting maximum values of pressure fluctuation are
shown for each case in Table 6. For convenience, relevant
shutoff valve statues are repeated from Table 2. Maximum
dP/dt in each row are highlighted red or orange, depending on
whether the 0.8 bar/s threshold was reached. Cases are
presented in order of decreasing maximum dP/dt value, except
for Case 11 which was the only case where combustion turbine
CT3 was tripped instead of CT2.
The six simulations corroborated the hypothesis. While not
shown for brevity, pressure traces for the operating combustion
turbines showed similar (not identical) pressure wave arrival
times to that seen for Case 10 in Figure 3. More importantly,
the pressure rate-of-change magnitudes were around twice that _________________________________________
Table 6. Maximum Pressure Fluctuations of Dual Trip Cases
053-563 9 Copyright © 2017 by ASME
observed for Case 10 on the 0.01s averaging interval. For Cases
11, 12, and 13 the one remaining operational CT in Block 123
would not remain operational very long, as the 0.8 bar/s
threshold was exceeded in these cases. The most severe
pressure fluctuation was 0.93 bar/s for CT3 in Case 12.
In comparing the six “dual trip” cases, the dominant
pattern that emerged was that severity of pressure fluctuations
decreased as delay time between trips was increased. For
instance, in Table 6 the maximum dP/dt values were 0.63 bar/s
for both cases that featured the longest delay time, 0.6 seconds.
This dP/dt magnitude is less than that observed for either of the
cases with 0.3 second delay time. While increased delay time
contributed to reduced dP/dt in these specific simulations, this
trend is not expected to be universal for all multi-unit power
plants. Propagation and reflection of the many pressure waves
in pipeline networks is complex and should be evaluated on a
case-by-case basis.
WAVE PROPAGATION BETWEEN POWER BLOCKS This final results section presents investigation of the
propagation of pressure waves from one combustion turbine
block (Block 123) to another (Block 456) for the baseline
combined cycle Case 10. To show the influence of the shorter
pipeline connection between the two blocks (Legs 43–43A–
61A–61, totaling 130 meters long), one additional case was
simulated with modification of just this shorter pipeline. The
diameter of legs L43A and L61A was increased to 620 mm to
match that of the “header” pipelines to which they connected.
Also, for simplicity, leg L46 with negligible mass flow to
“Other Users” was removed. In comparison to the shorter
pipeline, the longer interconnecting pipeline (legs L25 and L7)
totaled 740 meters long.
The resulting pressure rates of change on the 0.01s
averaging interval are shown in Table 7. With larger diameter
for the short interconnecting line between power blocks, the
rates of pressure change were made 40% less severe than in the
baseline Case 10 (0.33 vs. 0.55 bar/s). For combustion turbine
CT3, which had the most severe dP/dt in Case 10, the pressure
rate of change reduced by nearly a factor of two.
An instructive figure for determining why dP/dt values
were made less severe is Figure 10, which shows pressure
traces for Case 10b and also shows, in dashed gray lines,
pressure traces for the baseline Case 10. In Figure 10 several
aspects of the pressure behavior are evident: magnitude of
pressure increases; the times at which initial pressure waves
arrived at each CT; and even relative magnitudes of dP/dt
between traces (evident by comparing the slope of pressure
traces). While traces of dP/dt itself could also be plotted for
both cases, such traces are omitted for brevity.
Table 7. Maximum Pressure Fluctuations of Baseline Case 10 and Modified Case 10b
Two main differences between Cases 10 and 10b are
evident in Figure 10. First, the effective arrival time for
pressure waves to Block 456 was over 1 second sooner for
Case 10b than for Case 10, due to the increased diameter of the
short interconnecting pipeline. This result is interesting because
it is slightly non-intuitive – by making it easier for pressure
waves to propagate to the Block 456 combustion turbines, the
worst dP/dt values of Case 10 (shown in Table 7) were avoided.
The second difference evident in Figure 10 is that shape of
the pressure traces for combustion turbines CT2 and CT3 were
initially similar, but then diverged such that pressures
temporarily plateaued for Case 10b during the times which
gave maximum dP/dt for Case 10 (see earlier figures). The
divergence between cases, and the earlier plateauing of
Case 10b pressures, was due to different propagation of
pressure waves down the shorter interconnecting pipeline as
this pipeline was the only difference between the Case 10 and
10b configurations.
Finally, note in Figure 10 how the increase in diameter of
the shorter interconnecting pipeline generally caused shallower
slope for pressure traces of Case 10b as compared to Case 10.
The shallower slope is especially evident for CT4. By
increasing diameter of the interconnecting pipeline, the internal
volume of the pipeline network was increased, which generally
contributed to attenuation of pressure waves. Pressure traces for
CT4 additionally show that enlarging of the shorter pipeline
resulted in “staggered” arrival of pressure waves at the
Block 456 combustion turbines. Pressure waves took different
amounts of time to propagate down the short and the long
interconnecting pipelines. For CT4, the staggered arrival times
resulted in a smooth, nearly monotonically-increasing pressure
________________________________________
Figure 10. Traces of pressure vs. time for Case 10b, for the six combustion turbines and also a node near the fuel gas source. Pressures are staggered along the vertical axis; symbol legend is the same as that in Figure 3. For comparison, dashed gray traces show corresponding pressures in Case 10 (identical to Figure 3).
053-563 10 Copyright © 2017 by ASME
trace. Using disparate-length parallel pipelines is a possible
design strategy for reducing pressure fluctuations in large,
interconnected pipeline networks.
CONCLUSIONS Simulations were performed for various transient events in
the fuel gas pipeline network feeding multiple combustion
turbines in an example power plant configuration. Each
transient event was assumed to start with trip of one or more
combustion turbines. The goal was to determine whether the
pressure waves transmitted from the initial trip would have the
undesirable effect of causing additional units to also trip.
Simulations were performed using the method of
characteristics, a computational method often applied for
simulation of water lines. This method has less often been
applied for simulation of pipeline networks feeding multi-unit
combustion turbine plants. Note that the results of this paper
only apply to the specific power plant configuration simulated.
Complexity of pressure transient phenomena necessitates the
evaluation of pipeline networks on a case-by-case basis.
In trip analyses such as those performed in this paper, a
parameter of primary importance is the sampling time over
which pressure rate-of-change is calculated. Manufacturers
specify a threshold rate-of-change (“dP/dt”) that will cause
their combustion turbine to trip off, and therefore correct
evaluation of dP/dt is critical for determining whether this
threshold is exceeded by pressure waves reaching each
combustion turbine. Results in this paper for the simple and
combined cycle baseline cases showed that longer sampling
times can lead to non-conservative values of dP/dt, sometimes
differing by a factor of two or more from the dP/dt calculated
with a conservatively-short “sampling period” of 0.01s.
Working from the conservative sampling period of 0.01s,
simulations of other cases highlighted dP/dt trends encountered
at combustion turbines during transient events:
Rates of change in pressure can vary drastically when only
a few pipeline components are bypassed/not bypassed.
With the pipeline network simulated, bypassing of the
performance heaters caused dP/dt as high as 1.6 bar/s,
which far exceeded the threshold of 0.8 bar/s.
Rates of change in pressure can nearly double when two
combustion turbine units trip in quick succession, as
compared to just one unit tripping. In severe cases,
pressure rates of change exceeded the 0.8 bar/s threshold.
However, as the delay time between trips of the first and
second units was increased, maximum dP/dt approached
that seen for just a single unit trip.
Rates of change in pressure can be decreased by increasing
pipeline diameters, even when doing so shortens the
effective distance (and thereby wave transit time) between
combustion turbines.
The last observation was just one example of the non-intuitive
nature of wave propagation and reflection in pipeline networks.
Finally, the conclusions lead to a few guidelines for the
design of fuel gas supply pipelines:
If given the option, items that impose pressure drop
(dampening) should be preferred in the lines feeding
individual combustion turbines rather than overall supply
pipelines farther upstream. Such “isolation by dampening”
of the combustion turbines minimizes wave propagation
between units.
Designers should sometimes incorporate two or more flow
paths of differing length between the same pipeline
junctions. Pressure waves will propagate down both paths
but arrive at the latter junction at different times, thus
helping attenuate pressure fluctuations propagating beyond
this latter junction.
To prevent rework or costly modifications, accurate
transient simulations should be performed prior to detailed
design and construction. A key aspect of these simulations
is using a dP/dt sampling time consistent with the pressure
rate of change threshold given by the manufacturer.
ACKNOWLEDGEMENTS The authors are thankful for helpful technical discussions
with colleagues David Rice, Ed Giermak, and Raj Gaikwad.
A portion of the results of this paper also were presented at the
19th
Annual Electric Power Conference.
NOMENCLATURE CT combustion turbine
dP/dt rate of change in pressure [bar/s]
f Darcy friction factor [-]
HRSG heat recovery steam generator
K minor loss coefficient [-]
MOC method of characteristics
OEM original equipment manufacturer
P pressure [bar, or barA for absolute pressure]
ΔP change in pressure [bar]
ReD Reynolds number based on pipe diameter [-]
Rgas ideal gas constant for methane [J/kg∙K]
ST steam turbine
t time elapsed from beginning of transient event [seconds]
Δt averaging interval [seconds]
WBH water bath heater
Greek
φ symbol for pipe inside diameter
γ ratio of gas specific heats [-]
REFERENCES [1] Wilkes, C., 1996, “Gas Fuel Clean-Up System Design
Considerations for GE Heavy-Duty Gas Turbines,” GE
Power Systems, Schenectady, NY, GER-3942.
[2] Private communications from multiple combustion turbine
manufacturers (OEMs), 2015-2016.
[3] Brun, K., Simons, S., and Kurz, R., 2016, “The Impact of
Reciprocating Compressor Pulsations on the Surge Margin
of Centrifugal Compressors,” Proc. ASME Turbo Expo,
GT2016-56025.
053-563 11 Copyright © 2017 by ASME
[4] Wylie, E. B., and Streeter, V. L., 1983, Fluid Transients,
corrected version, FEB Press, Ann Arbor, Michigan.
[5] Moody F. J., 1990, Introduction to Unsteady Thermofluid
Mechanics, Wiley Interscience, New York, NY.
[6] Afzali, B., Karimi, H., and Tahmasebi, E., 2010, “Dynamic
Simulation of Gas Turbine Fuel Gas Supply System During
Transient Operations,” Proc. ASME Turbo Expo, GT2010-
23097.
[7] Applied Flow Technology, AFT Arrow Version 5.0,
released October 2014.
[8] Celik, I. B., Ghia, U., Roache, P. J., and Freitas, C. J.,
2006, “Procedure for Estimation and Reporting of
Uncertainty Due to Discretization in CFD Applications,”
Journal of Fluids Engineering Editorial Policy Statement
on the Control of Numerical Accuracy, ASME Author
Resources.