SIMULATING PRESSURE TRANSIENT EVENTS IN THE FUEL …...Pressure transient events in fuel gas pipelines are complex due to the finite speed of pressure waves that propagate throughout

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)


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.


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 _______________________________________


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) _________________________________


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


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


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.


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


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).


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.


[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

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SIMULATING PRESSURE TRANSIENT EVENTS IN THE FUEL …...Pressure transient events in fuel gas pipelines are complex due to the finite speed of pressure waves that propagate throughout