AECL6543

ATOMIC ENERGY » S H L'ENERGIE ATOMIQUEOF CANADA UMITED V ^ & J T DU CANADA LIMITÉE

DEAERATOR DYNAMICS

Dynamique des désaerateurs

C M . TSENG

Chalk River Nuclear Laboratories Laboratoires nucléaires de Chalk River

Chalk River, Ontario

June 1979 juin

ATOMIC ENERGY OF CANADA LIMITED

DEAERATOR DYNAMICS

by

C.M. Tseng

Chalk River Nuclear LaboratoriesChalk River, Ontario KOJ 1JO

June 19 79

AECL-654 3

Dynamique des désaërateurs

par

C M . Tseng

Résumé

Un modèle mathématique décrivant la dynamique d'un désaérateur dans unecentrale nucléaire CANDlf a été établi. Ce modèle peut simuler une variétéde conditions de fonctionnement thermodynamiques, â savoir:

- le fluide d'entrée se dirigeant vers le désaérateur peut être de l'eau

sous-refroidie, un mélange d'eau et de vapeur ou de la vapeur surchauf-

fée;

- dans le dësaérateur la vapeur peut être surchauffée ou saturée;

- l'eau dans le dësaérateur peut être saturée ou sous-refroidie.

Des équations linéaires concernant les petites perturbations d'une condi-

tion de référence donnée ont été développées et mises en oeuvre sur un ordi-

nateur hybride à Chalk River. Des données provenant d'un dësaérateur de la

centrale nucléaire Pickering ont été employées pour valider le modèle et les

paramètres du désaërateur de la centrale nucléaire Gentilly-1 ont servi à

illustrer sous forme graphique le comportement dynamique de la simulation.

Les fonctions de transfert du modèle ont été mesurées et comparées aux valeurs

théoriques.

L'Energie Atomique du Canada, Limitée

Laboratoires nucléaires de Chalk River

Chalk River, Ontario KOJ 1J0

Juin 1979

*CANDU - CANada Deuterium Uranium

AECL-6543

ATOMIC ENERGY OF CANADA LIMITED

DEAERATOR DYNAMICS

by

CM. Tseng

ABSTRACT

A mathematical model, describing the dynamics of a deaera-

tor in a CANDU nuclear power plant, has been derived. The

model can simulate a variety of thermodynamic operating condi-

tions, viz., the

- input fluid to the deaerator can be subcooled water, a

saturated steam/water mixture, or superheated steam,

- steam in the deaerator can be superheated or saturated,

and

- water in the deaerator can be saturated, or subcooled.

Linearized equations, dealing with small disturbances about a

given reference condition, were developed and implemented on a

hybrid computer at the Chalk River Nuclear Laboratories.

Field data from one deaerator at the Pickering Nuclear Genera-

ting Station (NGS) were used to validate the model, and para-

meters from the Gentilly-1 NGS deaerator are used to illustrate,

in graphic form, the dynamic behaviour of the simulation.

Transfer functions of the model were measured and compared with

theoretical values.

Chalk River Nuclear LaboratoriesChalk River, Ontario KOJ 1JO

June 1979AECL-6543

(i)

TABLE OF CONTENTS

Page

LIST OF FIGURES

LIST OF TABLES (Hi)

NOMENCLATURE dv)

1. INTRODUCTION 1

2. ASSUMPTIONS 2

3. GOVERNING EQUATIONS 5

3.1 Input Mixture 53.2 Condensation Due to Direct-Contact Mixing 6

3.3 Steam/Water Thermodynamics 6

4. DEAERATOR MODEI 8

5. REFERENCE CONDITIONS AND MODEL LINEARIZATION 12

6. MODEL IMPLEMENTATION ON THE HYBRID COMPUTER 14

7. COMPARISON OF DEAERATOR SIMULATION WITH 16PICKERING DATA

8. TEST CASE: GENTILLY-1 STEAM SUPPLY TO THE 22LA PRADE HEAVY WATER PLANT

9. FREQUENCY RESPONSE 26

10. CONCLUSIONS 29

11. REFERENCES 31

(ii)

LIST OF FIGURES

Figure No. Title Page

1 Schematic of Deaerator 3

2 Block Diagram of Deaerator Simulation 15

3 Pickering Deaerator Pressure During 17Poison-Prevent Operation

4 Schematic of Pickering Deaerator 19Pressure Control

5 Simulation of Pickering Deaerator 21Pressure Control During the Poison-Prevent Incident

6 The Effect of Mixing Time Constant on 23Pickering Deaerator Pressure Oscil-lations During Poison-Prevent Operation

7 Gentilly-1 Deaerator Response to a 10% 24Increase in Steam Inflow, Using a 10 sMixing Time Constant

8 Gentilly-1 Deaerator Response to a 10% 25Step Decrease in Steam Inflow, Using a10 s Mixing Time Constant

9 Gentilly-1 Deaerator Response to a 27Periodic Change in Steam Inflow, Usinga 10 s Mixing Time Constant

10 Frequency Response of the Gentilly-1 28Deaerator Simulation, Assuming SubcooledWater, Saturated Steam, T = 10 sand h = h.

m f

(Hi)

LIST OF TABLES

r.vible No. Title

1 Thermodynamic Conditions for the 8Deaerator and its Input Fluid

2 Unknowns and Governing Equations for 9Various Conditions in the Deaerator

3 Main Equations for Deaerator Model 10

4 Values of DEN for Various Conditions 14in the Deaerator

5 Controller and Valve Parameters Used 20in the Pickering Deaerator Simulation

6 Transfer Functions for the Gentilly-1 30Deaerator Simulation

(iv)

NOMENCLATURE

functions defined in Table 3

functions defined in Tables 3, 4

thermodynamic functions defined inTable 3

h specific enthalpy J-kg"1

K normalized gain for pressure lift'Pa"1

controller

L normalized valve lift

L normalized control signal topressure-control valve

M

P

S

TI

Tm

v

x

W

W2

Greek

mass

pressure

Laplace transform variable

reset time for pressure controller

mixing time constant

specific volume

quality

mass flow

live steam inflow

kg

Pa

s-1

s

s

m'-kg-

kg-s-1

kg'S-1

e pressure difference between set- Papoint and actual value

£ damping factor of pressure controlvalve

u) natural frequency of pressure s-1

control valve

Y isentropic expansion exponent

Symbol

Subscripts

c

ce

f

fg

g

h

i

m

ms

mw

o

P

r

s

V

w

Superscripts

(v)

NOMENCLATURE (continued)

Item

condensation

condensation due to direct-contact mixing

saturated liquid

property difference between saturated steam andsaturated water

saturated steam

constant enthalpy

i component of input flow to the deaerator

input mixture

steam component of input mixture

water component of input mixture

output to feedwater pump

constant pressure

output to relief valve

steam (not necessarily saturated)

vapourization

water (not necessarily saturated)

dt

steady-state value of the input fluid

1. INTRODUCTION

In a CANDU-PHW* plant, the deaerator is located in

the secondary heat-transport circuit, and its main function

is to remove dissolved, corrosive gases from the feedwater

system. The deaerator consists basically of two main parts;

an upper deaerating section, containing perforated trays,

and a lower section, which is a water storage tank. Condensate

and extraction steam from various sources are piped into the

upper section where they mix and reach a common temperature.

Feed pumps circulate the water from the storage tank to the

steam generators.

The design and analysis of deaerators in power plants

is discussed in [1,2] where it is pointed out that two-stage

vacuum deaerators give considerable improvement in performance

characteristics over the single-stage designs.

Deaerator behaviour in the operation of power plants

is discussed in [3,4] where it is shown that leakage of air

into the steam space of the turbine and the discharge of

fluids from the separator into the deaerator during the startup

had an important effect on the deaerator performance.

Liao [5,6] analyzed power plant deaerators under

transient turbine loads. He presented a mathematical analysis

showing that, under a rapid load reduction of the turbine, the

differential pressure across the tray stack of the deaerator

would increase by a factor of 10 to 20 over the normal maximum

load. This might damage the deaerator. To protect it, he

recommended an on-off type deaerator bypass system [6].

Recently, Chen and Chou [7] reported on a simulation

study of deaerator control at the Pickering Nuclear Generating

Station (NGS-A). Two mathematical models, based on thermo-

dynamic equilibrium and non-equilibrium,describe the deaerator

*CANDU-PHW = CANada Deuterium Uranium reactor, Pressurized Heavy-Watercooled

- 2 -

behaviour and are programmed on a digital computer. The

simulation predicts deaerator pressure which, in the Pickering

case, is controlled by regulating the live steam input to the

deaerator. Model predictions seem to agree with field data

taken during a poison-prevent incident.

One of the objectives of the Reactor Control Branch

at the Chalk River Nuclear Laboratories (CRNL) is to develop

a detailed, real-time simulation of a CANDU-PHW power plant,

and to implement it on a hybrid computer. This simulation

will be used to test advanced, multivariable controller

designs. A deaerator model is one subsystem of this large

simulation. The model can also provide insight into opera-

tional difficulties such as those experienced at the Pickering

NGS-A during start-up and poison-prevent operation, when

deaerator-pressure control was found to be inadequate.

The deaerator model is based on the continuity and

energy equations for steam and water, equations of state and

the constraint of a fixed overall volume. The individual

equations are linearized about steady-state operating condi-

tions, but the overall model is non-linear because different

equation sets describe various thermodynamic conditions, viz.

saturation, subcooling or superheat. No empirical relations

or constants are required to obtain solutions. The model is

shown to provide reasonable agreement with observed pressure

fluctuations in the deareator of Unit 4 of the Pickering

NGS-A.

2. ASSUMPTIONS

The deaerator is shown schematically in Figure 1.

All inlet fluids from various sources such as the main

condenser, high-pressure heaters, low-pressure heaters,

reheaters, live steam, etc. meet in the deaerating section

DEAERATINGSECTION

STORAGETANK

i

FIG. t SCHEMATIC OF DEAERATOR

- 4 -

where they mix and produce water which drains into the storage

tank. Steam from the storage tank is admitted to the

deaerating section through equalizers.

The following assumptions are made to obtain a

mathematical model that is reasonably simple and manageable:

(i) The enthalpy of the mixture is assumed to propagate

through the deaerating section with a time constant

proportional to the water mass on the trays.

(ii) The water mass on the trays of the deaerating

section is assumed to remain constant, and to be

small relative to the water mass in the storage

tank.

(iii) Heat transfer between phases through conduction is

neglected.

(iv) Heat transfer through the deaerator walls is also

neglected.

(v) The whole deaerator is treated as a point mass of

water and a point mass of steam at a common pressure.

(vi) Water entering the deaerating section mixes with

steam and becomes saturated before reaching the

storage tank, i.e. the water reaching the storage

tank is always saturated.

(vii) Neither steam nor water can exist in a metastable

form.

- 5 -

3. GOVERNING EQUATIONS

3.1 Input Mixture

From the conservation of mass and energy, the theo-

retical flow and enthalpy of the mixture are

v -1 wi (1)

I w. h.V - -vn^ (2)

m

The actual mixture flow, W , that enters the storage

tank is the same as the steady-state value, W *, because we

assume that the amount of water held by the trays in the

deaerating section remains constant, i.e.

Wm = Wm* (3)

The relationship between the actual enthalpy of the

mixture, h , and the steady-state value, h *, is dependent on

the design of the trays and their operating efficiency. We

assume a first-order lag, i.e.

where the mixing time constant, T , is proportional to the

liquid mass holdup on the trays.

The quality of the mixture, x, can be determined

from

h -hcx = -S—Ê (5)

- 6 -

The liquid and steam flow components of the inputmixture can be calculated from

Wmw

Wms " V Wmw

3.2 Condensation Due to Direct-Contact Mixing

When the input mixture to the deaerator is subcooled

water, part of the steam existing in the deaerating section

will be condensed as the water cascades down through the

stack of perforated trays. This direct-contact mixing will

ensure that the water is always saturated when it reaches

the storage tank. This contact condensation, as opposed to

the spontaneous condensation due to falling pressure, is

denoted by W and can be calculated from

w _ < h f - y WmwW (8w yWcc hfg+(hs-hg)

(8'

Note that W exists only if h < hf, i.e. the input mixture

is subcooled water, so that

Wms = °-

3.3 Steam/Water Thermodynamics

The conservation of mass and energy equations for

the point masses of steam and water are

Ms »

M = W -W -W +W +W (10)w mw v o c cc

- 7 -

A . w V V c c c f v g

and the boundary condition is

The equations of state are

3v \ /3v(3

( Vdv \

• (

*•

vg = l^W ± iP (15)

(16)

(17)

(18)

dhf \ •- / P (19)

4. DEAERATOR MODEL

The possible thermodynamic conditions in the deaerator

are summarized in Table 1,

TABLE 1

THERMODYNAMIC CONDITIONS FOR THE DEAERATORAND ITS INPUT FLUID

Input Fluid

subcooled water

saturated mixture

superheated steam

Steam inDeaerator

saturated

superheated

Water inStorage Tank

saturated

subcooled

During a transient, each component may change from one state

into another; thus twelve combinations of thermodynamic

conditions are possible.

There are 14 unknowns, M , M , v_, h,, v , h , v ,S W t II CJ CJ S

h , v , h , W , W , W and P, but only 12 governing equationsS W Vr C CC V

(8) to (19), are available. Apparently, two additional

restraint conditions are required to obtain solutions. This

is provided by imposing the appropriate thermodynamic condi-

tions in the deaerator. Table 2 summarizes the proper

equations and unknowns for various conditions in the deaerator.

Based on these conditions» the final forms of sub-sets

of the governing equations can be obtained. These are given in

Table 3, where the input fluid conditions have also been applied,

i.e.

Input Fluid

subcooled water

Restraint

w m s = 0

saturated'mixture Wcc=0 ' hmw=hf hms=hç

superheated steam W =W =0cc mw

TABLE 2

UNKNOWNS AND GOVERNING EQUATIONS FOR VARIOUSCONDITIONS IN THE DEAERATOR

common unknowns : M ,

common equations: (8),

Conditions in Deaerator

Steam

saturated

saturated

superheated

superheated

Water

saturated

subcooled

saturated

subcooled

M , W ,w ccp

(9), (10), (11)

Additional

Unknowns

Vvf,

V

VVWv

vf,

hf,

VV

Wc

vg

hg

Wc

vg

hg

vs

hs

Vs

hs

r (12), (13

Additional

Equations

(15)

(16)

(18)

(19)

(15)

(17)

(18)

(14)

(16)

(19)

(14)

(17)

)

Restraints

vw = vf

Vs=Vg

Vhf

Vhg

v°Vs=Vg

Vhg

wc=o

Vw = Vf

Vhf

wc=o

wv=o

- 10 -

TABLE 3

MAIN EQUATIONS FOR DEAERATOR MODEL

InputFluid

subcooled

saturated

superheatedsteam

InputFluid

subcooledwater

saturatedmixture

superheatedsteam

Deaerator Conditions: Water -Steam -

P

WrV(Wmw-Vvf-WccvfaDEN

( Wms-W r !V I Wmw-V v fDEN

ms r g o f ^fn \ "^ 9/ '"^DEN

V, /dh, \ dv ,DEN = Msf2 + Hwf,. f, = ^[âp1 " vf/ " 3fT.

Deaerator Condi t ions : Water -

Steam -

p

1 d V " ! /DEN

Î(W -W ) v +(W -W ) v| ms r g mw o w

d v w 1+ ( V W aT^j/DEN

| ( Wms-Wr l vg-Vw

+ —j!l§ a_ | (v +v,-V ) - ( h , - h )ôû^|W >/DEN Al

DEN = HsEî +^-(^a-v g ) [<v f -vw ) - lh f-

SaturatedSaturated

Wv

Mu /dhf \ .

h f g d p

„

•••fcfr-SubcooledSaturated

wc

Al

Al

(h -h )- ms g w

M

h f g

M

h f g

w

h

\ dv

(h

A2 •

W

A 2 - - v_

fc.AVdP g,/P

/ d h \

\dP g /

^ h -hfg m s «

fiw

f -h w )

(h -h )

- 11 -

TABLE 3 (con t inued)

InputFluid

subcooledwater

; saturatedI mixture

superheatedsteam

InputFluid

subcooledwater

saturatedmixture

superheatedsteam

i

DEN =

Dcaerator Conditions :

•} _w v + (W -W ) v vDEN

-W )vf-(h -h )1—- ) W [/\ s/p »

fg ̂ P L S

Deaerator Conditions:

P

mw-Mo ) v

W

M = v«* + k

Water

Stean

JEN

A3

Water -

Steam -

<Vhw

- Saturated

- Superheated

Wv

"w /dhf

" ̂ w 'v

»

••

Subcooled

Superheated

K

A4 + pr^V

A4

. ) •

1 + ~PY~"

w1

*.

A3

W

A3 • JSlh -h )M ins s

If p

s

- 12 -

5. REFERENCE CONDITIONS AND MODEL LINEARIZATION

The main equations of the deac^ator model may be

implemented on a hybrid computer by using the technique

of linearizing the equations individually, around reference

conditions, and switching from one set to another as the

thermodynamic state of the steam and water changes [8,9].

A non-linear, small-signal simulation is thus obtained.

The reference condition used here is the steady-

state operating condition of the deaerator; both the water and

steam in the deaerator are saturated, and the input fluid to

the deaerator is saturated water only, i.e.

"a " K = fig ° fif = *g = *f = * = °

V = V , V = V,s g w f

h = h , h = h.es g w f

and Wms = Wr = o, h m w - hm - hf

Given the above conditions, equations (1) to (10) can be

linearized to obtain

AWm = I AW± (20)

A hm* = W- I |"(hi-hf)AWi + W± AhJ (21)

m i L J

= (Ahm* - Ahm)/Tm (22)

AWmw = AWm + K ^ (Ahf " A V (23)

— 13 —

JLhfg

-V

AM = AW - AW + AW - AW - AW (26)s ms r v c cc

A Mw = AWmw - AWv - AWo + A Wc + AWcc (27)

The equations of Table 3 can also be linearized. It can be

seen that for all the possible cases, AP is a function of as

many as 11 independent variables. This can be reduced to

6 if the reference conditions are applied. By using DEN to

represent different values for different situations, as

given in Table 4, AP can be expressed in a single equation to

cover all cases,

(28>

The values of DEN in equation (28) depend on the conditions

in the deaerator, as summarized in Table 4. When linearized,

the other equations of Table 3 are

= V*

Ahg = vsAP (30)

MAWc = ÏT~ l ̂ " v~ / AP (31)

- 14 -

M / dh, \

"r • - h £ { d T "Vf ) ̂ (32)

Equation (31) exists only when the steam in the deaerator is

saturated, while equation (32) exists only when the water in

the deaerator is saturated.

TABLE 4

VALUES OF DEN FOR THE LINEARIZED DEAERATOR EQUATIONS

Deaerator

Steam

saturated

saturated

superheated

superheated

Conditions

Water

saturated

subcooled

saturated

subcooled

Msf2

V1

M vs sPy

DEN

+ M f,w '

- M Vw w

M v... s s

PY

- M VW W

dvwdhw

dvwdhw

6. MODEL IMPLEMENTATION ON THE HYBRID COMPUTER

The non-linear, small-signal disturbance model,

described above, was implemented on one AD-5 analog console

and the PDP-11/55 digital processor of the Dynamic Analysis

Facility at CRNL. The equations were patched essentially as

given, but they were organized in three major groups, as

shown in Figure 2.

INPUTS—>

-s.

SINPUT

MIXER

[â»,][4t0] r

[AWm«,J ^ l — 1 * * ^^—i

[AWCC]

MAIN

EQUATIONS

\ f \ f \ (

[Ah s

[ A h f

[AP]

-Ah

-Ah wl LOGICCONTFOL

OUTPUTS

FIG. 2 BLOCK DIAGRAM OF DEAERATOR SIMULATION

- 16 -

The input mixer (Figure 2) calculates the mixture

enthalpy and flows from equations (20) to (25). The re-

sultant mixture enthalpy is compared with the saturated

value, calculated from the current deaerator pressure. The

main equations, (26) to (32), describe the steam/water thermo-

dynamics. The logic control selects the appropriate set of

equations from those given in Table 3. The variables affected

are

- AW and AW , according to Table 2

- AP (or DEN), according to Table 4

- AW , according to the thermodynamic state of thecc

input mixture.

The criteria used to determine i \e state of the steam

and water in the deaerator are as follows:

The steam is superheated if

- the pressure is rising (AP > 0), or

- the pressure is falling but the steam is super-

heated (A(hg-h ) > 0).

Similarly, the water is subcooled if

- the pressure is rising (AP > 0), or

- the pressure is falling but the water is

subcooled (A(hf-hw) > 0).

7. COMPARISON OF DEAERATOR SIMULATION WITH PICKERING

DATA

During early operation of the Pickering NGS-A, some

difficulties in controlling the deaerator pressure were en-

countered during the start-up and poison-prevent operation.

The data shown in Figure 3 were reconstructed from the

records of the poison-prevent operation of Unit 4 in

400

TO

o.

CO

a.

ceUJ

LU

• ACTUAL READINGSLINE THROUGH READINGS

ASSUMED VALUES

2028 30

22 24 26

MINUTES SINCE TURBINE TftIP

FIG. 3 PICKERING DEAERATOR PRESSURE DURING POISON PREVENT OPERATION [71

-4

I

- 18 -

1974 April [7]. Only the magnitude of pressure oscillations is

significant; the reconstructed frequency shown could be lower

than the actual values because of the coarse readings during

this rapidly changing transient.

To obtain a meaningful comparison, the actual Pickering

operating conditions, plus the deaerator pressure control

scheme, i.e. the PI controller algorithm and the valves with

an assumed second-order characteristic, were incorporated into

the simulation. Figure 4 shows the block diagram of the whole

Pickering deaerator pressure-control loop. It is assumed that

the mass flow of live steam is proportional to the lift of

the pressure control valve.

The PI controller algorithm was described by

: (33)

The second-order characteristic of the control valve

was expressed as

LL = — (34)

CO 9

N a,/

The numerical values of the controller and valve

parameters are given in Table 5.

set

rPI

CONTROLLER

Lo PRESSURECONTROLVALVES

AW2 DEAERATORMODEL

AP

FIG. 4 SCHEMATIC OF PICKERING DEAERATOR PRESSURE CONTROL

- 20 -

Linearized forms of equations (33) and (34), used for

describing small signal disturbances, are given below.

ALD = K

AL = AL

(35)

(36)

TABLE 5

CONTROLLER AND VALVE PARAMETERS USED IN THEPICKERING DEAERATOR SIMULATION

Symbol

K

TI

eWN

-

Description

normalized gain

reset time

damping factor

natural frequency

valve stroking time

5.

12

0.

0.

20

Value

80xl0~6

8

9044

Units

lift/Pa

s

-

S"1

s

Figure 5 shows the results of the simulation, using

a mixing time constant* of 10 s and all coefficients calcu-

lated at reference (steady-state) conditions, with a

deaerator pressure of 206.8 kPa. The results indicate that

the deaerator pressure (uppermost trace in Figure 5) oscillates

over the range from (172-32) kPa to (172+170) kPa, which

agrees with the field data shown in Figure 3. The period of

36 s falls between the simulation results of Chou and Chen

(20 s) [7], and the reconstructed field data (̂ 60 s). The

results also show that the pressure in the deaerator lags the

valve lift by % 90°.

*The trays in the deaerating section hold 5.66 m3 of water, which takes•v» 10 s to fill under poison-prevent operating conditions.

- 21

a.

og onj= -se«3 \

«9 CO

-2.5

H20s(-FIGURE 5 SIMULATION OF PICKERING DEAERATOR

PRESSURE CONTROL DURING THE POISONPREVENT INCIDENT

- 22 -

It should be noted that the simulation presented here

is based on a more general model than that of Chou and Chen [7].

For example, it allows the steam in the deaerator to stay

saturated while the water is subcooled, or the water to be

saturated while the steam is superheated, neither of which are

considered by Chou and Chen. On the other hand, as implemented

on the Dynamic Analysis Facility, the simulation is based on

linear equations and is thus accurate only for small distur-

bances. The pressure oscillations observed during the Pickering

poison-prevent incident were more than just small disturbances,

but even under these conditions, the simulation results agree

well with the field data.

Different values of the mixing times constant, T ,

were used to run the simulation to determine the effect of T

on system behaviour. The results are summarized in Figure 6,

which indicates that

- a mixing time constant of ^ 8 s produces deaerator

pressure oscillations of maximum amplitude,

- the oscillation frequency remains about the same for

time constants greater than ^ 10 s, but increases

rapidly for T < 7 s.r m

8. TEST CASE: GENTILLY-1 STEAM SUPPLY TO THE LA PRADE

HEAVY WATER PLANT

A test case had been set up using the data of the

Gentilly-1 (G-l) nuclear Generating Station with its proposed

steam supply to the La Prade Heavy Water Plant. All coefficients

needed for the deaerator simulation were calculated by the

PDP-11/45 computer, using the steady-state reference condition

with a deaerator pressure of 413.7 kPa.

Figures 7 and 8 show G-l deaerator responses to ±10%

step changes in steam inflow, respectively. Figure 7 shows

COQ_

400

FREQUENCY

AMPLITUDE

5 10

MIXING TIME CONSTANT (s)

20

0.08

0.06

0.04

0.02

0.0

>-o

FIG. 6 THE EFFECT OF MIXING TIME CONSTANT ON PICKERING DEAERAT0R PRESSUREOSCILLATIONS DURING POISON-PREVENT OPERATION

10

0

<a ro

FIGURE 7

2.5

WATER - SU3C00LED

STEM - SUPERHEATED

{-100 s -IGENTILLY-1 DEAERATOR RESPONSE TO A IGINCREASE IN STEAM INFLOW, USING A 10MIXING TIME CONSTANT

10

0

-10

0.25

<n

-0.25

5

CO' O-

-5

2.5

-2 .5

2.5

•„ - o

- 2 . 5

WATEÎ1 - SATURATEDTFAw - SOTURATED

I—100s - IFIGURE 8 GENTILLY-1 DEAERATOR RESPONSE TO A 10% STEP

DECREASE IN STEAM INFLOW, USING A 10 s MIXINGTIME CONSTANT

- 26 -

that the step increase in AW2 instantly puts the water and

steam into the subcooled and superheated states, respectively.

A short time constant (3.3 s) dominates the response of AP,

(Ahf-Ah ) and (Ah -Ah ). The slow decrease of (Ahf-Ah ),

after the initial sharp rise, indicates that the water in the

deaerator gradually approaches a new saturated state, corres-

ponding to the higher pressure, by the process of displacement

of the existing water in the deaerator by the input flows.

Figure 8 shows that the water and steam in the

deaerator remain saturated when a -10% step in AW2 is applied.

A long time constant (183 s) prevails in the response of AP and

AP.

Figure 9 shows the results obtained by using a periodic

input of AW2. During the first half cycle, where AW2 is

negative, i.e. the input live steam is less than its normal

value, the input fluid is subcooled water. Consequently, the

pressure in the deaerator decreases and the water in the

deaerator becomes saturated, with a time lag of about 8 s.

Both the pressure and enthalpy of the superheated steam in the

deaerator decrease slowly, with a response typical of the

long time constant (183 s). In the second half cycle, where

AW2 is positive, the input fluid changes from subcooled water

into a two-phase saturated mixture, resulting in an increase of

deaerator pressure and consequent subcooling of the water in

the deaerator. The short time constant (3.3 s) prevails through-

out this half cycle, as can be seen from the close correspondence

of the AP, (Ah -Ah ) and (Ah--Ah ) curves.S CX 11 W

9. FREQUENCY RESPONSE

The frequency response of the Gentilly-1 deaerator

model, implemented on the Dynamic Analysis Facility, was

measured using the PRBS/FFT technique [10]. A typical set of

results is shown in Figure 10. Theoretical transfer functions,

- 27 -

<3 O

FIGURE 9 GENTILLY-1 DEAERATOR RESPONSE TO A PERIODICCHANGE IN STEAM INFLOW, USING A 10 s MIXINGTIME CONSTANT

GAIN (dB) GAIN (dB)<D

co co -n—i — ajm s m

—t — n

3D10 s A

o3"

II3"«1

ASSUMI

CD

tnUBC00I

•pna

ESPONSE

o-n

THE Gl

ill

H

oco m—i m<= =o=O toX» —I-H Om soa

en

O1

ai

-

-

**.

ro1

/cA

SEN/

|

CO

a

\

/

/

1

I I

A

sGA

IN

1

en

-

-

-

en

cocoo

K)03

PHASE (degrees) PHASE (degrees)

- 29 -

obtained from equations (1) to (13), are given in Table 6.

Good agreement between calculated responses and those

measured on the simulation has been obtained, thus verifying

the correct implementation of the equations.

The results summarized in Table 6 show that

- the gain constants of the transfer functions are

not affected by the thermodynamic states of the

deaerator fluids;

- the time constant in the AP/AW2 transfer function

increases by a factor of about 50 when the water

changes from the subcooled to the saturated state,

but the time constant is only slightly affected

(̂ 15%) when steam changes from the superheated

to the saturated state.

10. CONCLUSIONS

The mathematical model of deaerator dynamics, derived

in this paper, accounts for all combinations of the thermo-

dynamic conditions of the water (saturated or subcooled) and

steam (saturated or superheated) in the deaerator. The

governing equations are linearized and implemented on a hybrid

computer, but the overall simulation is non-linear because

different equation sets generate specific segments of the

transient solution, depending on the thermodynamic status of

water and steam. The simulation predicts the correct amplitude

and a compatible frequency for the pressure oscillations

observed in the deaerator of the Pickering Nuclear Generating

Station during poison-prevent operation in the early life of the

plant.

The simulation was also used to predict the frequency

response of the deaerator in the feedwater train of the

Gentilly-1 Nuclear Generating Station with the proposed steam

APAWa

(Pa-s-kg-1)

Ah -Ah

TABLE 6

TRANSFER FUNCTIONS FOR THE GENTILLY-1 DEAERATOR SIMULATION

steam

water

saturated

saturated

saturated

subcooled

superheated

saturated

superheated

subcooled

1.34x10* 1.34x10" 1.34x10*(1+183.0s)(1+T s)

TO

(l+3.8s)(l+Tms) (1+182.6s)(1+Tffls)1.34x10"

s)

9.07xl05s(l+3.8s)(l+180s)(l+T s)

9.07x105s(l+3.3s)(l+180s)(l+T

I

o

5.05X103

(1+183.0s)(l+Tms)5.05x103

(1+182.6s)(1+T s)IB

(J'S-kg-2)

- 31 -

supply to the La Prade Heavy Water Plant. The results show

that the gain constants of the transfer functions are not

affected by the thermodynamic states of the water and steam

in the deaerator, but one of the dominant time constants

increases by a large factor (*v 50) when the water in the

deaerator changes from the subcooled to the saturated state.

The deaerator model is based on physical principles,

without the need for empirical correlations or constants,

and should thus be applicable to deaerators other than those

discussed in this paper.

11. REFERENCES

[1] I.I. Oliker, T.I. Teplyakova, A.S. Gimme1'berg ,

G.A. Ziskand, V.Z. Potochkin and N.A. Zelenov,

"Testing the Prototype of the TsKTl DSV-400 Vacuum

Deaerator", Thermal Eng., V. 18, N 12, p.61-65,

December 1971.

[2] I.I. Oliker, V.E. Ivanov, P.E. Sivko, V.V. Graubart,

V.B. Gribov and V.I. Dlugosel'skii, "New System for

Deaerating Water at H3at and Power Stations with the

TsKTl Two-Stage Vacuum Deaerators", Thermal Eng. V.19,

N 4, p.64-67, April 1972.

[3] A.K. Kirsh, G.M. Knovalov and V.D. Kanaev, "Deaeration

in Steam Turbine Condensers", Thermal Eng. V.10, N 9,

p.87-90, September 1972.

[4] L.V. Golyshev, A.V. Misyuk, A.G. Prokopenko and

L.I. Lyashenko, "Transferring Discharge of the Medium

from the Integral Separator into the Deaerators in

Starting a 300 MW Boiler/Turbine Unit", Thermal Eng. V.23,

N 2, p.11-14, February 1976.

- 32 -

[5] G.S. Liao, "Analysis of Power Plant Deaerator Under

Transient Turbine Loads", Trans. ASME, J. Eng. for Power,

95, p.171-179, July 1973.

[6] G.S. Liao, "Protection of Boiler Feed Pump Against

Transient Suction Pressure Decay", Trans. ASME, J. of Eng.

for Power, Vol. 96, p.247-255, July 1974.

[7] S.N. Chen and Q.B. Chou, "A Simulation Study of Deaerator

Control for CANDU Nuclear Power Plants", Paper

presented at the IEEE 1977 Power Industry Computer

Applications Conference, Toronto, May 1977.

[8] E.O. Moeck and H.W. Hinds, "A Mathematical Model of

Steam-Drum Dynamics", Proc. 1975 Summer Computer

Simulation Conference, Publ. Sci., Vol. 1, pp.694-704,

July 1975.

19] E.O. Moeck and P.D. McMorran, "Dynamic Simulation of a

Reboiler", Proc. 4th IFAC Symposium on Multivariable

Technological Systems, pp.513-522, Predericton,

July 1977.

[10] C.B. Lawrence and A. Pearson, "Measurement Techniques

Using a Pseudo Random Binary Sequence and Fourier

Transformation for Determining a System's Transfer

Function", Atomic Energy of Canada Limited, report

AECL-3601, Chalk River, April 1970.

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