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Simulation of a steam generator leak detection experiment in the CCTL
Transactions of the International Association for MATHEMATICS AND COMPUTERS IN SIMULATION Trans. IMACS, Vol. XVII1 n3 2, April 1976
SIMULATION LEAK
DETECTION
OF
A
STEAM
EXBERIMEPJT
GENERATOR IN
THE
CCTL
by D. SAPHIER (*)
ABSTRACT. - A simulation study to predict the response of leak detectors in the CCTL (Core Components Test Loop) experiment at the Argonne National Laboratory was carried out. A mathematical model was developed for the sodium-water interaction and the subsequent distribution of the reaction products in a liquid metal steam generator loop. The detectors and the appropriate instrumentation were also modeled and their response to a series of designed experiments wrw calculated. The simulation progrum and the s,pecific CCTL leak detection experiment will be used to identify parameters of importance for leak detection in LMFBR. Preliminary experimental results show good agreement with the theoretical predictions.
RESUME. - Une btude de simulation a dte’ effectzke en vue de p&dire la rkponse des ditecteurs de fuites dans le CCTL (Core Component Test Loop) exphimental du Laboratoire Nationa,l &Argonne. On a dQvelopp6 un mod2le matbe’matique de l’interaction eau-sodium et de la distribution subskquente des produits de &action dans la boucle B mital liquide du ge’nkrateur de vapeur. Les de’tecteurs et leur instrumen-‘ tation adt!quate ont azzssi&te’ simz&s et leer r+onse 2 une szlite d’expkiences programme’es ont 6tte’ calcul&es. Le programme de simulation et les essais CCTL du systbme de de’tection de fuites ont &te’ utilish pour identifier les paramktres importants pour la de’tection de fuite dans un LMFBR. Des rdsultats exphimentaux pr6liminaires montrent une bonne concordance avec les p&visions tbdoriques.
1. INTRODUCTION
An experimental program is presently underway at the Argonne National Laboratory (ANL) in which the Core Components Test Loop (CCTL) will be used for small leak detection [I]. The purpose of this experimental program is to evaluate the most efficient means for detecting water to sodium leaks in the range of 1’O-7 - 10m3 lb/set and to gather enough experimental data on the leak detection methods so that they can be applied to the design of the Clinch River Breeder Reactor (CRBR).
The detection of water leaks into the sodium coolant of fast breeder reactors has become a major concern in the design of instrumentation for Liquid Metal Fast Breeder Reactors (LMFBR). The hazard to the LMFBR steam generator from small water leaks is presently well established [l-12] and subject to several experimental as well as theoretical studies. Large water leaks from the steam generator to the intermediate sodium loop will lead to a spontaneous violent reaction and to subsequent partial or. complete destruction of the steam generator. Small leaks if permitted to’ continue for a period sufficiently long will produce corrosive agents which cause destructive wastage of the steam generator tubing and finally large leaks with extensive damage. It is therefore of utmost importance to detect the small or primary leaks and their location so that the plant can be shut down before significant damage occurs. * Components Technology Division, boratory, 9700 South Cass Avenue,
Argonne Argonne,
National LaIL 60439.
In the present study a detailed mathematical model for the CCTL steam generator leak detection system was developed. This model is used to predict the responses of the hydrogen and oxygen detectors for a series of experiments to be performed. The detailed kinetic equations for the sodium-water interaction are presented as well as the assumptions made in assessing the various reaction rates and the rate of hydrogen gas migration toward a free surface in contact with cover gas. The dynamic model developed describes concentration changes as a result of primary and secondary sodium reactions, sodium flow through the system piping, mixing processes in the various plenum
D. Saphier
78
mental program is given in reference 1. Here only the salient features of the system will be described. The CCTL is a circulating sodium system and is shown schematically in figure 1. The sodium is drculated through the main loop by a mechanical pump having a capacity of 800 gpm (3.03 m3/min). The major component is a large sodium tank within which a simulated module of the CRBR superheater is placed. Instead of water and steam pipes, solid stainless steel rods of the same diameter are used. The water leak is represented by eight injectors located inside the superheater module. At several points in the system sample lines carry a small fraction of the flow to various types of hydrogen and oxygen detectors. A bypass line also goes to a purifying system, a cold trap, where the impurities are removed from the sodium by precipitation. The bypass flows are regulated by a series of valves and EM pumps, as shown in figure 1. A serie of experiments, as described in reference 1, to simulate water leaks in the CRBR heat exchangers is in progress. These experiments will be carried out at different coolant flow rates, sodium temperatures, water leak rates, and different leak positions. It is the purpose of the simulation program developed in this study to predict the detector readings under these varying experimental conditions. In figure 2 a different diagram of the CCTL leak detection experiment is shown. This is a schematic intended for the simulation and therefore only the features of importance to the mathematical modeling
elements, cold trap operation, cover gas pressure changes, the water leak, and the response of various detectors. A simulation program based on the dynamic model was developed to obtain the concentration of the different reaction products as functions of time for every segment of the CCTL system. The modeling and the program are set up in a general way so that the CCTL experiment is a particular case, the simulation of which is governed by the input data. The computer program is modular and with minor changes can be applied to the simulation of other systems with water leaks into a sodium loop. Several authors [I, 2, 3, 4, 51 have in the past established general relationships between the water leak size and the quantity of hydrogen to be found in sodium at equilibrium (after a long time). However, these relationships are strictly system dependent, and therefore a different approach to the modeling is suggested here. The mathematical mode! for the CCTL leak detection system is developed from basic principles of conservation and the kinetic equations for the chemical reactions. Even though some of the basic parameters, such as reaction rates and hydrogen gas disengagement rates, are not well known, they can be identified later by appropriate experiments. In the meantime an G intelligent guess D is made wherever unknown parameters are encountered. 2. THE EXPERIMENTAL
SETUP
A detailed description of the Core Components Test Loop (CCTL) as well as the leak detection experiI
._
_.
--1
I
L..-
Fig.
1. -
Schematic
Description
of the Core
Components
Test
Loop
and the Leak
Detection
System.
Simlnlation
of a steam generator -.___
leak detection
experiment
are shown in the diagram. The CCTL system is subdivided into segments, each segment being considered as a lumped parameter node in order to eliminate any partial differential equations. In the present version of the program up to 50 segments having sodium flow and sodium water reactions can be simulated. In addition LIP to seven detectors can be connected to any of the system nodes and a cover g,as plenum. There are two basic segment types in the system; mixing plenum segments in which ideal mixing is assumed In a pipe segment a pure delay and pipe segments. equivalent to the pipe transit time is assumed ; howchemical reactions are continuously ever, secondary simulated in the pipe.
I -INJECTOR @-DETECTOR w -FLOW CT - COLD TRAP
r----49
-----
---
1
-52
I
in the CCTL
79
Segment 42 in figure 2 is the cold trap. Here hydrogen and oxygen are removed from the system by cooling and precipitation, In the present configuration detectors are connected to nodes 25, 47, 49, and to the cover gas plenum. All the other nodes shown in the diagram are pipe nodes. The total flow through the system leaving the pump is designated as WS. A constant flow is assumed throughout the experiment. There is a small leak WEX from node 3 to node 23. The flow from node 7 to node 6 is equal to the flo’w WT1 leaving for the detectors connected to node 49. Other flows leaving the main flow are detector flows WT3 and WT4 and the cold trap flow WCT. All the detector flows return to the system through node 27 - the upper sodium node in the CCTL vessel. 3. THE CHEMICAL WATER-SODIUM
KINETICS REACTION
OF
THE
When physical contact is made between sodium and water with an excess of water, a spontaneous violent reaction producing sodium hydroxide and hydrogen occurs : Na
CCTL VESSEL -----i -_-.-._._ TO EXPANSION TANK
I
I46
H,O
+
-+ NaOH
Na
Fig.
2. -
CCTL
Schematics
for
the Simulation
Program.
The steam generator segments, nodes 6 to 22, are mixing plenum segments each having two baffle plates as a physical boundary. The flow between the segments is forced around the simulated tubes and the periphery of the baffle plate so that total mixing is a good assumption for these segments. Water injection points in the steam generator module are designated as II to I& in figure 2. Segments 25 to 27 comprise the CCTL vessel and contain large volumes of sodium. Two segments, namely, segment 1, the pump, and segment 27 are in contact with the cover gas and hydrogen can leave the sodium in these segments.
(1)
+
H,O
+
NaOH
+ NaH
(2)
4 Na +
H,O
+
2 NaH
+ Na,O
(3)
2 Na + H,O
EX -
+ H, (g)
However, under small leak conditions prevailing in heat exchangers the ratio of sodium to water is of the order of 10G and additional reactions take place. Several authors [I, 2, 3, 6, 7, 81 have shown that with excess of sodium the situation is much more co,mplex than given by equation (1). It is assumed that the following additional reactions take place under these conditions : 2
T
+
-+ Na,O
+ H,
(4)
The relative quantity of H,O participating in each of these reactions is prob’ably dependent on the amount of water introduced at the leak site, the sodium temperature, and the sodium flow rate. However, no numerical values were found in the literature as to the relative distribution of H,O among the above reactions. In the present study it was assumed that the above reactions are instantaneous and the split among them is I(, , K,, KS, and K,, respectively and K,
+ K,
+ I(,
+ K,
=
1
As a result, when Q-moles of water four reaction products are generated following distribution : Q (0.5 K,
Q (I& Q (K,
Q (Ks
+
(5)
leak into sodium, according to the
K4) mols of H,
(6)
+ J-G) + 2 KJ
mols
of NaOH
(7)
mols
of NaH
(8)
+
mols of Na,O
(9)
KJ
D. Saphier
80 These products enter the sodium and are predominantly dissolved and carried away by the rapid turbulent flow. The reaction products formed in the primary reactions are however not stable at the temperatures prevailing in a steam generator and the NaH and NaOH are decomposed according to the following equations : Na
+
NaOH
+
Na,O
NaH
+
Na
+ +
+ H,
5 H,
(10) (11)
It is apparent from these equations that the ultimate products of the sodium water-reaction are predominantly dissolved hydrogen gas and sodium oxide both of which can be detected by hydrogen and oxygen meters. In systems under equilibrium conditions some of the hydrogen diffuses into the cover gas and is found to have a partial pressure PH independent of the cover gas pressure (usually Argon). The equilibrium relation between the hydrogen in the cover gas and the hydrogen in the liquid phase (either as H, or as NaH) is governed by the Sieverts’ law [9] : c,
=
K,
PR1/Z
(12)
where C, is the hydrogen concentration in sodium given in mols/lb and KJ is the Sieverts’ constant given by : K,
= 2.255 X 1O-6 exp (1.9733
-
276.77/T,)
(13)
where K, is in mol/(lb-Torr1/2), T, is the temperature in ‘OK, and P, is the hydrogen partial pressure given in Torr (mm Hg). Hydrogen from the cover gas can also be absorb’ed by sodium if present in large quantities as was shown by Longton [6]. However this process can be neglected at the temperature prevailing in the heat exchanger b’ecause of the large dissociation pressure of sodium hyblride. In reactions 1 and 2 sodium hydroxide NaOH is formed. This product is unstable under the conditions prevailing in an operating reactor and decomposes according to equation (10) : Na
+
NaOH
-+ Na,O
+
3 H, (g)
From the experiments performed by A.K. Fischer [7] in 1972, by heating sodium with NaOD at 500 OC under vacuum it was found that the reaction is of the first order and follows the relation : Rt =I In Co/(Co
-
C)
present study it was therefore assumed that the reaction rate is independent of temperature. The partial pressure of H, over NaH has been well estabiished by several authors [7, 91 over a wide range of temperatures and is given by the following equation : P DIS =
exp (26.71
-
14046JT,)
(15)
where the dissociation pressure PDrs is given in Torr and T, is the temperature in degrees Kelvin. Banus, et al. [lo] have shown that equation (15) is correct even in dilute sodium solutions. Therefore in the present study this equation is used. G. Naud [2] of CEA has performed some experiments to find NaH dissociation rates. Large experimental errors are reported by the author; however, since these are the only rate constants available they are used in the present study. The values reported by Naud are given below : K(3lO’oC)
=
I~ (280 OC) =
0.05
[min-I]
0.035
[min-I]
By inserting the above values into the Arrhenius equation the following expression for the rate of NaH dissociation is obtained : R, I=: 0.597
exp (-3883/T,)
(16)
Longton [6] has shown that NaH dissociation and hydrogen absorption are governed by a parabolic law as shown below, and this equation will be used in the study : KNan
P R, ( ,Isp-
=
(17) DIS
In this section the various chemical reactions occurring when a small quantity of water is introduced into sodium are described. The dissociation equations of some of the products and their reaction rates are also given. It is now possible to’ write the kinetic equation for a volume of sodium into which a leak of Q lb/set of water has been injected. These equations give the change in concentration of the reaction products as a function of time :
ChTaH=I &
+ 2 K,) ;
-
Km
Ciw
(18)
(14
where Co is the initial concentration and C is the concentration at time t, and R is the rate constant. From the linear portion of the experimental curve Fischer [7] determined the rate constant to be R = .0045 min-I, or in other terms, the half life T~,~ of NaOH is 150 min. For the present study, therefore, &%OH = 7.5 . 1O-5 [set-I] is taken. Hydroxide decomposition in Na has been treated by several authors [7, 8, 41 but none have given temperature dependence of the reaction rate. In the
G,
=I (0.5 K, +
where
Kxaon
+
K4) 2
+
0.5 (K,,,
Gam)
C is the concentration
in mol/lb
CNaR
(21) of the different
Simulation
of d steam generator
leak detection
experiment
products, and c is the appropriate time derivative, M is the sodium mass in lb’ in the calculated segment, K Na” is given by equation (177, and KNaOH is a constant determined from equation (14).
GaH>GacH >Gall3>and C,.
are given
W,
the node in mol/sec.
IN
The development of the dynamic equations is based mainly on mass and concentration balance applied to each segment and each product in the system. The equations are written in a general way so that adaptation of the program to any other system requires mostly a change in the input data.
WH
The CCTL system is subdivided into several segmentsnodes as shown in figure 2. In a generalized node the following might take place :
f
‘2 = i
balance
equations
are given
below
dP, dt
f
T (Wij Cbij ~- W,j Cd) + C, -
Cd = i
:
.l
F (wij Gij -- Wxj C,) + Ci-g,,, J 1
(24) W,/‘M
(25) where j =
1 . . . including
all the inlet
of - concentration particular node of G - concentration particular node of G - concentration particular node of c4 - concentration particular node Wij - node inlet flow WXj - node exit flow M - total mass in lb
Cl
NaH NaOH Na,O
and outlet in mol/lb
at any
in mol/lb in molJlb
H, in mol/lb
flows
at any at any
at any
in lb/set at j-th inlet in lb,/sec at j-th outlet at the node.
by equa-
WE,
+
WHC
= W (554.5)
(26)
T,,/V,,,
(27)
where P, is in Torr, W, in mol/sec, T,,, is the absolute Rankin temperature, and V,, is the total plenum volume in ft3. The rate at which the hydrogen leaves for the cover gas is determined by the difference between hydrogen actual concentration and what it should be according to Sieverts’s law (equation 12) :
T (wij c2ij -- Wxj C,) + C~N~OH (23)
f ‘3 = k
=
__
a - primary chemical reactions resulting from water leak b - secondary chemical reactions c - sodium flow into and out of the segment d - hydrogen gas entering or leaving the node e - precipitation of reaction products. The appropriate
tions (18) to (21) - net hydrogen gas leaving
In the sodium loop of an LMFBR steam generator as well as in the CCTL leak detection experiment there might be several places where the sodium has a free surface with a cover gas through which some of the hydrogen might escape. In the CCTL experiment there are two places where the coolant makes contact with the cover gas - the pump and the CCTL vessel, and the amount of gas in mol/sec that can leave these nodes is W,, and W HC 2 respectively. All the cover gas plenums are connected through the expansion tank and it is assumed that equal pressure exists in all of them. The hydrogen partial gas pressure P, is calculated from the ideal gas law PV =I nRT
These equations are used in the next sections to develop the dynamic equations used in the simulation study.
4. THE DYNAMICS OF SODIUM-WATER REACTION PRODUCTS PROPAGATION A CLOSED SODIUM LOOP
81
in the CCTL
W,
=
R, (C,
-
CHS) M for C,
> C,H,
(28)
The rate constant R, , which governs the hydrogen disengagement, is assumed to ‘be such that if zero partial pressure of hydrogen exists in the cover gas it will take 71,2 min. for half of the hydrogen necessary to establish equilibrium to leave sodium node : R, =
In 2/,
C’ =
c (t -
=
O.693,/7,,,
(29) The dynamic equations for a pipe containing M lbs of sodium flowing at a rate of W IbJsec, are determined by the transit time 7 = M/W. The concentration of any of the reaction products at time t -. T is’ given by : T)
(30)
c’ is the concentration of a reaction product T seconds before it leaves the pipe exit. There are no leaks assumed in the pipe segments and therefore only secondary reactions take place. The change in C’, during the time 7, when the sodium flow is confined to the pipe segment, is obtained by a single step integration process given below : AC,
=
-KXaII
A C, =I -KNaOH
c’, T
(31)
c’, 7
A C, =’ KNaOH c’, T A C, =
0.5 (I&,
C’,
(32) (33)
+ I&iaoH C’,) T
(34)
82
D. Saphier
The concentration of any of the reaction the exit of the pipe at time t will be : c(t)
=
c’
5. COLD TRAP
+
products
at
A c
DYNAMICS
As shown in figures 1 and 2, a small bypass flow of sodium is passed through the cold trap. The sodium in this unit is cooled and come of the NaH and Na,O precipitates until saturation concentration is achieved. This process is used in all sodium loops to relmove impurities. Ideally the impurity concentration at the cold trap outlet stream should be equal to its solubility at the cold trap temperature. However the cold trap operation changes with time and flow and its static efficiency ,8 [5] given by equation (35) changes : i.J
=
ci -----ci
-cc,
(35) -
cL*T
Ci and C, are the impurity inlet and outlet concentrations and C,,, is the saturation concentration for the cold trap temperature. In a dynamic system the widely accepted concept of the static efficiency ,8 cannot be used. Instead, a dynamic efficiency is defined by equation :
dC -_ = WOT (Gin dt
C)/M -
/Id (Ci, -
tectors. The numerical results obtained from these instruments are different in their absolute values as well as in their transient b,ehavior from the actual concentrations because of the meters’ transfer functions. The hydrogen detectors yield readings proportional to the NaH and H, concentrations, and the oxygen detectors provide a reading proportional to the Na,O concentration. Both instruments are of the membrane diffusion type and details are given in reference 1. To predict the detector reading as the output of the simulation program, three parameters which characterize the detectors should be provided. The time lag 7, which is the time for the small flow of sodium to reach the detecting apparatus, the diffusion time constant, 8, in the detector, i.e., the time it takes the hydrogen or oxygen to diffuse through the membrane until equilibrium between the measured media and the detector interior is achieved, and finally the proportionality or the calibration constant of the detector. The detector transfer function is given by equation (40) : A -Z-I C
where A - is the detector reading, C - is the actual concentration, S - is the Laplace transform operator, and K, - is the proportionaiity constant.
7. THE SIlMULATION
,& - is the dynamic static efficiency
outlet
concentration
efficiency, related to the by equation (37) :
(3’) where the cold trap in gpm WCT - flow through M - cold trap sodium content in lb. The data available on the solub’ility of hydrogen and oxygen in sodium have been recently summarized by Rodgers and Dutina [lo]. Their recommended values as function of temperature were used in this study. For NaH : C 1EAT = For Na,O C 3SAT
exp (13.97
-
6631.4/T,)
(38)
: =
exp (16.131
-
6493.3/T”,)
The concentrations are given in ppm, temperature of the cold trap in OK.
(40)
CSAT) (36)
where C - is the average
K, e-87 --1 +se
and T,
(39) is the
6. THE DYNAMIC RESPONSE QF THE DETECTORS The results of the CCTL leak detection experiment are available through the hydrogen and oxygen de-
PROGRAM
CCTL-DYSP
A computer program CCTL-DYSP for the IBM 370/195, using the IBM 360/75 TSO system, was developed to solve the equations presented in the previous sections. Based on previous experience the FORTRAN languages rather than one of the available simulation language like CSMP was chosen. Using CSMP has large advantages when sirnnlation of simple models is considered. Whenever a complex or a large model has to be simulated CSMP reachs its limits in a way similar to how an analog computer reaches its limits - there is an insufficient number of elements to accomplish the simulation. Sometimes it is possible to overcome this difficulty in CSMP, but the complexity of programing that results, the time involved, and the inherent unflexibility of the final product, make FORTRAN a better choice for large scale simulations. FORTRAN is inherently more flexible and execution times are always better, sometimes by a significant factor. A simplified schematic diagram of the simulation program is shown in figure 3. The program is written in a modular form. It has 5 calculating subroutines, a coordinating main program, two service subroutines for printing and plotting results, and an integrating routine. The main coordinating program first calls the INIT routine in which data are read in, initial values are calculated and printed, and the pipe initial function is set up. The program then proceeds to the dynamic
Simzdlation
of a steam generator
I Calculate Reaction Products Concentrations
' <
leak detection
Subroutine LNTEGR
+
Subroutine
+
INTG
1
49
A
I
experifnent
Calculate Detector(
Subroutine
Response
-----+'
V
DETECT
7
53
in the CCTL
The main program then accesses the DETECT subroutine where the appropriate detector responses are computed. When the variables for a time step have been calculated by appropriate integration of the differential equations, the program updates the pipe segments inlet variabmle by caIling PIPE. The program then enters the PRIT routine, and if so required some data such as detector responses and concentrations at some of the nodes are printed. At predetermined intervals as determined by an input parameter - a complete (( map )> of the system which includes derivatives, sources, and actual concentration of the four reaction products at each segment and each pipe outlet is printed. The SPLOT routine is entered next, and user selected data are stored in a specific file for later plotting. Finally, the program checks the time, if it is less than the predetermined length of simulation it repeats the time step calculation. If the time is equal to the final simulation time the program will be terminated by printing a final <(map )) of the system and printplotting the results previously sto’red in a file. The CCTL-DYSP program is considered to be very efficient. There are some 200 differential equations to be integrated in addition to manv other non-linear relations. However, execution time is only 0.2 to 0.7 of the real time. The execution time is dependent on the type of transient to be calculated and the amount of requested output.
, Print
4
Results
f
8. REPRESENTATIVE
Subroutine PRIT
RESULTS
The results of the simulation as well as the detailed description of the program, its use and the appropriate description of the input data necessary to run the CCTL-DYSP, are given in ref. 12. Several experiments to be performed on the CCTL were simulated and analyzed and some of these are presented below.
T
Run # 100 to Simulate a Short Water Burst Pig.
3. - Simplified Loop Dynamic
Ihvchart Simulation
of the Core Components Progra.m (CCTL-DYSP)
Test
phase by increasing the time by a time step and increasing the time step counter by one. The first subroutine called in the dynamic section is SOURCE. In this routine the sources of reaction products resulting from any type of chemical reaction at each loop segment are calculated. The second routine called is INTEGR in which the derivatives of all the reaction product concentrations in the loop segments and pipe outlets are computed. This routine has access to the PIPE subroutine to compute pipe outlet concentrations and to the INTGI routine where the actual integration is performed.
The transient was initiated by a short leak of high pressure steam of 0.015 lb/set flow rate. It was started at 10 seconds and terminated at 15 seconds introducing a total of 0.075 lbs of water into the system. The sodium ;flow rate in the system was 800 gpm (3.03 m3) and the sodium temperature 9‘40 OF’ (504 “C). The injection point was I-4 (node 16) which is in the middle of the steam generator unit, as can be seen on figure 2. The simulation was continued for 100 set, a time sufficient for the major transients to be terminated. Figure 4 shows the resulting detectable hydrogen concentration at several nodes. The detectab’le hydrogen is in the form of hydride, NaH, and dissolved hydrogen, H, The hydrogen concentrations at the leak site (node 16) and at the steam generator outlet plenum (node 25) are shown in figure 4. In addition, the
D. Saphiev
84
20.0
0
60.0
40.0
*O
TIME(SECI Fig.
4. -
Run
#
100 to Simulate
a Short
Water
Burst
concentration at the end of the sampling line (node 42) through which 5 gpm flow prevails is also shown in the figure. It is seen that the transient is delayed by the pipe transit time. Finally, the hydrogen detector response is also shown for this experiment. The shape of the transient as seen by the detector differs signi-
0
120.0
of
0.075
lb.
Injected
at the
Middle
of
Superheater
Unit.
ficantly from the actual concentration in the pipe to which the detector is connected. The detector response is the result of an additional time lag which is clearly identified in the figure and the relatively slow diffusion process through the detector membrane that results in the lower rate of change as shown in figure 4.
240.0
360.0
I.0
480.0
TIMELSECI Fig.
5. -
Run
# 101,
Reaction
Product
Concentrations
at Segment 27 as a Result at Injector 14.
of
70
sec.
Water
Leak
of
0.001
lb/set.
Simulation Run
#
of
ti steam generator
101 Simulate
a Typical
leak detection
experiment
Experiment
This experiment was simulated under the same conditions as the previous run. The duration of the leak was increased to 70 set and the leak rate was reduced to 0.001 lb/set. The water leak was introduced at injector I-4, ten seconds after simulation startup. The simulation was continued for ten minutes. The cold trap was not included in this simulation. The concentration changes of the four reaction products in the upper part of the CCTL vessel (node 27) are shown in figure 5. A relatively fast decomposition of NaH at 940 OC can also be observed from the figure. The response of two hydrogen detectors, detector-l connected to sampling line-49 and detector-3 connetted to sampling line-47, are sho,wn in figure 6. It is seen that steady state conditions in detector-1 are achieved approximately after ten minutes while in detector-2 steady state conditions are achieved after approximately two minutes. Run
#
103 to Simulate
a Tightly
Coupled
Loop
The flexibility of the program is demonstrated by simulating a different type of loop. In this system the huge sodium vessel containing the steam generator is excluded. Instead three more segments are added to the steam generator unit. A short leak of 0.015 Ib/sec for 5 set period was simulated at 800’ GPM flow rate and 940 OF. The results are shown in figures 7 and 8. The oscillatory nature of the concentration changes is due to the elimination of the huge mixing volumes
0
120.0
in the CCTL
85
of the CCTL vessel which smooth out any type of transient. A short leak such as is simulated in this experiment will contaminate a lump of sodium. Whenever this lump passes through a segment of the loop or near a detector an increase in contamination wili be observed until finally after several passages the transients will die out because of the mixing process. The distance between the peaks is the loop transit time and as observed from the figure it is 14 set (calculated value 13.76). It is interesting to note that similar results were obtained by Berault, et al [13] in their experimental loop which included mainly piping segments, when a short b’urst of water was injected. The transit time in their loop was approximately 5 min and 13 peaks were observed before the hydrogen diffused through the system and a stable hydrogen concentration was established. In figure 7 the transients in hydrogen concentrations at nodes 23 and 29 are shown. It can be ob’served from the figure that segment 29 is at a <( 5 seconds distance >> from segment 23. The same transient results in both segments; however, because of mixing effects, the appropriate peaks at segment 29 are lower than those in segment 23. In figure 7 the response of the two hydrogen detectors connected to pipe segments 47 and 49 are shown. Run
#
103 to Simulate
hjection
22
Recently some experimental results from the CCTL leak detection experiment became available. On No-
240.0
360.0
400.0
TIHE[SECI Fig. G. -
Run # 101, Hydrogen Detector Response in CCTL Leak Experiment at Injector 14.
as a Result of a 70 sec. Leak of 0.0001 lb/set.
86
D. Saphier
I
I LEGEND NODE 23
o-AT
0
20.0
40.0
60.0
80.0
1
TIMEtSEC) Fig.
7. -
Run
102,
I
Simulation of Water
Injection
40.0
in Tightly
Coupled
Loop.
80.0
60’ 0
TIMEtSECl Fig.
8. -
Run
#
102,
Hydrogen
Detector
Response
vember 6, 1975 injection # 22 took place in which 2.54 grams/min of water were injected at injector I-4. The leak duration was 57.5 seconds, the sodium flow was 600 gpm and the sodium temperature was 940 OF. In figure 9 the experimental readings from
in Simulation
of
a Tightly
Coupled
Loop.
the hydrogen detector connected to segment 49 are superimposed on the detector response as predicted by the simulation. It is seen that except for the experimental random noise there is an excellent agreement between the
Simdation
of u steam generator
lea& detection
in the CCTL
experiment
results. For comparison purposes the simulated hydrogen concentrations at the exit of pipe segment 49 and
in the stagnant heat exchanger region segment 6 are also shown.
CCTLLEAKSIMULATIONOF INJECTION
120.0
87
240.0
22.
[2.54G/S)
480.0
360-O
f
0
TIME[SECl Fig. 9. -
Run
103 to Simulate
Injection
Experiment
# 22. Comparison
of Predicted
and Measured
CCTLLEAK SIMULATIONOF INJECTION
23
Hydrogen
Concentration
Changes.
L0.98G/M!
IENTAL RESULTS
I -0
360.0
TIDE Fig.
IO.
-
Run
104 to Simulate
Injection
Experiment
180-O
E 3.0
[SEC,,
# 23. Comparison
of Predicted
and Measured
Hydrogen
Concentrations.
D.
Run
#
104 to Simulate
Injection
23
On November 7, 1975 injection # 23 took place in which 0.98 gram/min of water were injected at injector I-4. The leak duration was 118.4 set, the sodium flow was 300 gpm, and the sodium temperature was 940 OF. In figure IO the experimental readings from the hydrogen detector are superimposed on the detector response as predicted by the simulation. Small differences between the experimental and the predicted curve can be seen. These seem to bse mainly due to the imperfect knowledge of the exact shape of the water injection curve, errors in the calculation of the delays in the sampling lines due to errors in the flowmeters, and random experimental noise which is clearly visible on the experimental curve. In this experiment there was apparently a large calibration error in the interpretntion of the detector readings and therefore the experimental results were normalized to the steady state result as obtained from the simulation. 9. CONCLUSIONS A model to account for the kinetic and dynamic processes resulting from a water leak into a circulating sodium loop was developed. A computer code, CCTLDYSP solving the model equations was prepared. The distribution and the concentration of the sodium water reaction products throughout the system was calculated and it is shown that qualitatively the results are in agreement with similar calculations or experiments pub’lished elsewhere [5, 131 and with the preliminary experiments performed at ANL. However, it should be noted that experimental and theoretical information on small leaks, sodium-water interaction, and its subsequent distribution in a system is scarce and of dubious validity. Most of the parameters governing hydrogen diffusion and transport throughout the system and its subsequent <( evaporation )> (or disengag,ement, if in bulk form) in the cover gas are not known. Some of the reaction parameters available, such as NaOH or NaH dissociation rates, are old data with large error limits obtained under laboratory conditions different from the actual operating conditions of the steam generator; and there is no quantitative information whatsoever on how the reaction proceeds at the leak site. As a result, several assumptions had to be made and the results presented are dependent on these assumptions. However since the mathematical model was developed from basic principles, it is believed to be correct and presently unknown parameters will be replaced when more experimental data become available. The program is system independent and can be apphed to predict hydrogen and oxygen distribution in any sodium loop having small water leaks and operating conditions similar to those in CCTL. To apply the CCTL-DYSP to a simulation of the CRBR steam generator some changes should be introduced into the program. The temperature variation from segment to segment should be calculated or supplied as
Saphier
input data. The program should account for hydrogen diffusion through the steam generator walls. Other sources and sinks of hydrogen and oxygen in the system might be found to be of some significance and should be inserted into the program. The above changes will not affect the program structure, they will only add some terms to the hydrogen and oxygen sources in the appropriate routine. ACKNOWLEDGEMENT The author extends his thanks to L.F. Epstein, R.A. Jaross, and J.M. McKee from the Argonne National Laboratory for their comments and useful discussions during this study. REFERENCES [I]
R.A. JAROSS, <(Work Plan for Steam Generator Leak Detector Test in CCTL )>, T0022-002~SA-00 (3, 1972). [2] G. NAUD, <, CEA Report 2583, also UKAEC TRG 552 (C). [ 31 D.D. ADAMS, G. J. BARENBORG, and W.W. KENDALL, (< Evaluation of the Sodium-Water Reaction in Heat Transfer Systems )>, Document No. KAPL-P-1512 (1956). [4] P. VILINSKAS, <
[6]
[7]
[S]
[9]
[lo] [ll]
[ 121
1131
(1968). H.C. PELLOW, Q A Model to Predict the Effect of Hydrogen Sources on an LMFBR Steam Generator Leak Detection System >>, GE NEDM-13992 (1973). P.B. Longton, <( Reactions with Alkali Metals with Gases - Part IV, The Reaction of Sodium with Hydrogen )) LJKAEC, IGR-TN/C435 (1957). A.K. Fischer, <( Studies of Oxygen-Hydrogen Interaction in Sodium - Isotope-Exchange Studies >>. In ANL-7944 (August 1972). P.B. LONGTON, B Reactions with Alkali Metals with Gases - Part VII, Reaction of Sodium with Water Vapor >>, UKAEC IGR-TN/C.418 (1956). D.R. VISSERS, J.T. HOLMES, and P.A. NELSON: <( A Hydrogen Activity Meter for LMFBRs >>, Trans. Am. Nucl. Sot., 14 (1971). M.D. BANUS, J.J. McSHARRY, and E.A. SULLIVAN ; J. Am. Chem. Sot. 77 (1955), 2007. D.N. RODGERS and D. DUTINA, ((Recommended Values for NaH Dissociation Pressure and the Solubilities of Oxygen and Hydrogen in Sodium )), NEDM12473, General Electric Company (Sunnyvale, Calif.) (1974). D. SAPHIER, (( A Kinetic Model of the Sodium Water Reaction Applied to the Dynamic Simulation of Leak Detection in the Core Component Test Loop >>, Argonne National Laboratory ANL-7522 (1975). (To be published), J. BERAULT, et al., <( Detection of Small Leaks by Hydrogen Measurements in a Sodium-Heated Steam Generator )>, Proc. of Conference on Sodium Technology and Large Fast Reactor Design, ANL 7520 (1968).
SIMULATION LEAK
DETECTION
OF
A
STEAM
EXBERIMEPJT
GENERATOR IN
THE
CCTL
by D. SAPHIER (*)
ABSTRACT. - A simulation study to predict the response of leak detectors in the CCTL (Core Components Test Loop) experiment at the Argonne National Laboratory was carried out. A mathematical model was developed for the sodium-water interaction and the subsequent distribution of the reaction products in a liquid metal steam generator loop. The detectors and the appropriate instrumentation were also modeled and their response to a series of designed experiments wrw calculated. The simulation progrum and the s,pecific CCTL leak detection experiment will be used to identify parameters of importance for leak detection in LMFBR. Preliminary experimental results show good agreement with the theoretical predictions.
RESUME. - Une btude de simulation a dte’ effectzke en vue de p&dire la rkponse des ditecteurs de fuites dans le CCTL (Core Component Test Loop) exphimental du Laboratoire Nationa,l &Argonne. On a dQvelopp6 un mod2le matbe’matique de l’interaction eau-sodium et de la distribution subskquente des produits de &action dans la boucle B mital liquide du ge’nkrateur de vapeur. Les de’tecteurs et leur instrumen-‘ tation adt!quate ont azzssi&te’ simz&s et leer r+onse 2 une szlite d’expkiences programme’es ont 6tte’ calcul&es. Le programme de simulation et les essais CCTL du systbme de de’tection de fuites ont &te’ utilish pour identifier les paramktres importants pour la de’tection de fuite dans un LMFBR. Des rdsultats exphimentaux pr6liminaires montrent une bonne concordance avec les p&visions tbdoriques.
1. INTRODUCTION
An experimental program is presently underway at the Argonne National Laboratory (ANL) in which the Core Components Test Loop (CCTL) will be used for small leak detection [I]. The purpose of this experimental program is to evaluate the most efficient means for detecting water to sodium leaks in the range of 1’O-7 - 10m3 lb/set and to gather enough experimental data on the leak detection methods so that they can be applied to the design of the Clinch River Breeder Reactor (CRBR).
The detection of water leaks into the sodium coolant of fast breeder reactors has become a major concern in the design of instrumentation for Liquid Metal Fast Breeder Reactors (LMFBR). The hazard to the LMFBR steam generator from small water leaks is presently well established [l-12] and subject to several experimental as well as theoretical studies. Large water leaks from the steam generator to the intermediate sodium loop will lead to a spontaneous violent reaction and to subsequent partial or. complete destruction of the steam generator. Small leaks if permitted to’ continue for a period sufficiently long will produce corrosive agents which cause destructive wastage of the steam generator tubing and finally
Argonne Argonne,
National LaIL 60439.
In the present study a detailed mathematical model for the CCTL steam generator leak detection system was developed. This model is used to predict the responses of the hydrogen and oxygen detectors for a series of experiments to be performed. The detailed kinetic equations for the sodium-water interaction are presented as well as the assumptions made in assessing the various reaction rates and the rate of hydrogen gas migration toward a free surface in contact with cover gas. The dynamic model developed describes concentration changes as a result of primary and secondary sodium reactions, sodium flow through the system piping, mixing processes in the various plenum
D. Saphier
78
mental program is given in reference 1. Here only the salient features of the system will be described. The CCTL is a circulating sodium system and is shown schematically in figure 1. The sodium is drculated through the main loop by a mechanical pump having a capacity of 800 gpm (3.03 m3/min). The major component is a large sodium tank within which a simulated module of the CRBR superheater is placed. Instead of water and steam pipes, solid stainless steel rods of the same diameter are used. The water leak is represented by eight injectors located inside the superheater module. At several points in the system sample lines carry a small fraction of the flow to various types of hydrogen and oxygen detectors. A bypass line also goes to a purifying system, a cold trap, where the impurities are removed from the sodium by precipitation. The bypass flows are regulated by a series of valves and EM pumps, as shown in figure 1. A serie of experiments, as described in reference 1, to simulate water leaks in the CRBR heat exchangers is in progress. These experiments will be carried out at different coolant flow rates, sodium temperatures, water leak rates, and different leak positions. It is the purpose of the simulation program developed in this study to predict the detector readings under these varying experimental conditions. In figure 2 a different diagram of the CCTL leak detection experiment is shown. This is a schematic intended for the simulation and therefore only the features of importance to the mathematical modeling
elements, cold trap operation, cover gas pressure changes, the water leak, and the response of various detectors. A simulation program based on the dynamic model was developed to obtain the concentration of the different reaction products as functions of time for every segment of the CCTL system. The modeling and the program are set up in a general way so that the CCTL experiment is a particular case, the simulation of which is governed by the input data. The computer program is modular and with minor changes can be applied to the simulation of other systems with water leaks into a sodium loop. Several authors [I, 2, 3, 4, 51 have in the past established general relationships between the water leak size and the quantity of hydrogen to be found in sodium at equilibrium (after a long time). However, these relationships are strictly system dependent, and therefore a different approach to the modeling is suggested here. The mathematical mode! for the CCTL leak detection system is developed from basic principles of conservation and the kinetic equations for the chemical reactions. Even though some of the basic parameters, such as reaction rates and hydrogen gas disengagement rates, are not well known, they can be identified later by appropriate experiments. In the meantime an G intelligent guess D is made wherever unknown parameters are encountered. 2. THE EXPERIMENTAL
SETUP
A detailed description of the Core Components Test Loop (CCTL) as well as the leak detection experiI
._
_.
--1
I
L..-
Fig.
1. -
Schematic
Description
of the Core
Components
Test
Loop
and the Leak
Detection
System.
Simlnlation
of a steam generator -.___
leak detection
experiment
are shown in the diagram. The CCTL system is subdivided into segments, each segment being considered as a lumped parameter node in order to eliminate any partial differential equations. In the present version of the program up to 50 segments having sodium flow and sodium water reactions can be simulated. In addition LIP to seven detectors can be connected to any of the system nodes and a cover g,as plenum. There are two basic segment types in the system; mixing plenum segments in which ideal mixing is assumed In a pipe segment a pure delay and pipe segments. equivalent to the pipe transit time is assumed ; howchemical reactions are continuously ever, secondary simulated in the pipe.
I -INJECTOR @-DETECTOR w -FLOW CT - COLD TRAP
r----49
-----
---
1
-52
I
in the CCTL
79
Segment 42 in figure 2 is the cold trap. Here hydrogen and oxygen are removed from the system by cooling and precipitation, In the present configuration detectors are connected to nodes 25, 47, 49, and to the cover gas plenum. All the other nodes shown in the diagram are pipe nodes. The total flow through the system leaving the pump is designated as WS. A constant flow is assumed throughout the experiment. There is a small leak WEX from node 3 to node 23. The flow from node 7 to node 6 is equal to the flo’w WT1 leaving for the detectors connected to node 49. Other flows leaving the main flow are detector flows WT3 and WT4 and the cold trap flow WCT. All the detector flows return to the system through node 27 - the upper sodium node in the CCTL vessel. 3. THE CHEMICAL WATER-SODIUM
KINETICS REACTION
OF
THE
When physical contact is made between sodium and water with an excess of water, a spontaneous violent reaction producing sodium hydroxide and hydrogen occurs : Na
CCTL VESSEL -----i -_-.-._._ TO EXPANSION TANK
I
I46
H,O
+
-+ NaOH
Na
Fig.
2. -
CCTL
Schematics
for
the Simulation
Program.
The steam generator segments, nodes 6 to 22, are mixing plenum segments each having two baffle plates as a physical boundary. The flow between the segments is forced around the simulated tubes and the periphery of the baffle plate so that total mixing is a good assumption for these segments. Water injection points in the steam generator module are designated as II to I& in figure 2. Segments 25 to 27 comprise the CCTL vessel and contain large volumes of sodium. Two segments, namely, segment 1, the pump, and segment 27 are in contact with the cover gas and hydrogen can leave the sodium in these segments.
(1)
+
H,O
+
NaOH
+ NaH
(2)
4 Na +
H,O
+
2 NaH
+ Na,O
(3)
2 Na + H,O
EX -
+ H, (g)
However, under small leak conditions prevailing in heat exchangers the ratio of sodium to water is of the order of 10G and additional reactions take place. Several authors [I, 2, 3, 6, 7, 81 have shown that with excess of sodium the situation is much more co,mplex than given by equation (1). It is assumed that the following additional reactions take place under these conditions : 2
T
+
-+ Na,O
+ H,
(4)
The relative quantity of H,O participating in each of these reactions is prob’ably dependent on the amount of water introduced at the leak site, the sodium temperature, and the sodium flow rate. However, no numerical values were found in the literature as to the relative distribution of H,O among the above reactions. In the present study it was assumed that the above reactions are instantaneous and the split among them is I(, , K,, KS, and K,, respectively and K,
+ K,
+ I(,
+ K,
=
1
As a result, when Q-moles of water four reaction products are generated following distribution : Q (0.5 K,
Q (I& Q (K,
Q (Ks
+
(5)
leak into sodium, according to the
K4) mols of H,
(6)
+ J-G) + 2 KJ
mols
of NaOH
(7)
mols
of NaH
(8)
+
mols of Na,O
(9)
KJ
D. Saphier
80 These products enter the sodium and are predominantly dissolved and carried away by the rapid turbulent flow. The reaction products formed in the primary reactions are however not stable at the temperatures prevailing in a steam generator and the NaH and NaOH are decomposed according to the following equations : Na
+
NaOH
+
Na,O
NaH
+
Na
+ +
+ H,
5 H,
(10) (11)
It is apparent from these equations that the ultimate products of the sodium water-reaction are predominantly dissolved hydrogen gas and sodium oxide both of which can be detected by hydrogen and oxygen meters. In systems under equilibrium conditions some of the hydrogen diffuses into the cover gas and is found to have a partial pressure PH independent of the cover gas pressure (usually Argon). The equilibrium relation between the hydrogen in the cover gas and the hydrogen in the liquid phase (either as H, or as NaH) is governed by the Sieverts’ law [9] : c,
=
K,
PR1/Z
(12)
where C, is the hydrogen concentration in sodium given in mols/lb and KJ is the Sieverts’ constant given by : K,
= 2.255 X 1O-6 exp (1.9733
-
276.77/T,)
(13)
where K, is in mol/(lb-Torr1/2), T, is the temperature in ‘OK, and P, is the hydrogen partial pressure given in Torr (mm Hg). Hydrogen from the cover gas can also be absorb’ed by sodium if present in large quantities as was shown by Longton [6]. However this process can be neglected at the temperature prevailing in the heat exchanger b’ecause of the large dissociation pressure of sodium hyblride. In reactions 1 and 2 sodium hydroxide NaOH is formed. This product is unstable under the conditions prevailing in an operating reactor and decomposes according to equation (10) : Na
+
NaOH
-+ Na,O
+
3 H, (g)
From the experiments performed by A.K. Fischer [7] in 1972, by heating sodium with NaOD at 500 OC under vacuum it was found that the reaction is of the first order and follows the relation : Rt =I In Co/(Co
-
C)
present study it was therefore assumed that the reaction rate is independent of temperature. The partial pressure of H, over NaH has been well estabiished by several authors [7, 91 over a wide range of temperatures and is given by the following equation : P DIS =
exp (26.71
-
14046JT,)
(15)
where the dissociation pressure PDrs is given in Torr and T, is the temperature in degrees Kelvin. Banus, et al. [lo] have shown that equation (15) is correct even in dilute sodium solutions. Therefore in the present study this equation is used. G. Naud [2] of CEA has performed some experiments to find NaH dissociation rates. Large experimental errors are reported by the author; however, since these are the only rate constants available they are used in the present study. The values reported by Naud are given below : K(3lO’oC)
=
I~ (280 OC) =
0.05
[min-I]
0.035
[min-I]
By inserting the above values into the Arrhenius equation the following expression for the rate of NaH dissociation is obtained : R, I=: 0.597
exp (-3883/T,)
(16)
Longton [6] has shown that NaH dissociation and hydrogen absorption are governed by a parabolic law as shown below, and this equation will be used in the study : KNan
P R, ( ,Isp-
=
(17) DIS
In this section the various chemical reactions occurring when a small quantity of water is introduced into sodium are described. The dissociation equations of some of the products and their reaction rates are also given. It is now possible to’ write the kinetic equation for a volume of sodium into which a leak of Q lb/set of water has been injected. These equations give the change in concentration of the reaction products as a function of time :
ChTaH=I &
+ 2 K,) ;
-
Km
Ciw
(18)
(14
where Co is the initial concentration and C is the concentration at time t, and R is the rate constant. From the linear portion of the experimental curve Fischer [7] determined the rate constant to be R = .0045 min-I, or in other terms, the half life T~,~ of NaOH is 150 min. For the present study, therefore, &%OH = 7.5 . 1O-5 [set-I] is taken. Hydroxide decomposition in Na has been treated by several authors [7, 8, 41 but none have given temperature dependence of the reaction rate. In the
G,
=I (0.5 K, +
where
Kxaon
+
K4) 2
+
0.5 (K,,,
Gam)
C is the concentration
in mol/lb
CNaR
(21) of the different
Simulation
of d steam generator
leak detection
experiment
products, and c is the appropriate time derivative, M is the sodium mass in lb’ in the calculated segment, K Na” is given by equation (177, and KNaOH is a constant determined from equation (14).
GaH>GacH >Gall3>and C,.
are given
W,
the node in mol/sec.
IN
The development of the dynamic equations is based mainly on mass and concentration balance applied to each segment and each product in the system. The equations are written in a general way so that adaptation of the program to any other system requires mostly a change in the input data.
WH
The CCTL system is subdivided into several segmentsnodes as shown in figure 2. In a generalized node the following might take place :
f
‘2 = i
balance
equations
are given
below
dP, dt
f
T (Wij Cbij ~- W,j Cd) + C, -
Cd = i
:
.l
F (wij Gij -- Wxj C,) + Ci-g,,, J 1
(24) W,/‘M
(25) where j =
1 . . . including
all the inlet
of - concentration particular node of G - concentration particular node of G - concentration particular node of c4 - concentration particular node Wij - node inlet flow WXj - node exit flow M - total mass in lb
Cl
NaH NaOH Na,O
and outlet in mol/lb
at any
in mol/lb in molJlb
H, in mol/lb
flows
at any at any
at any
in lb/set at j-th inlet in lb,/sec at j-th outlet at the node.
by equa-
WE,
+
WHC
= W (554.5)
(26)
T,,/V,,,
(27)
where P, is in Torr, W, in mol/sec, T,,, is the absolute Rankin temperature, and V,, is the total plenum volume in ft3. The rate at which the hydrogen leaves for the cover gas is determined by the difference between hydrogen actual concentration and what it should be according to Sieverts’s law (equation 12) :
T (wij c2ij -- Wxj C,) + C~N~OH (23)
f ‘3 = k
=
__
a - primary chemical reactions resulting from water leak b - secondary chemical reactions c - sodium flow into and out of the segment d - hydrogen gas entering or leaving the node e - precipitation of reaction products. The appropriate
tions (18) to (21) - net hydrogen gas leaving
In the sodium loop of an LMFBR steam generator as well as in the CCTL leak detection experiment there might be several places where the sodium has a free surface with a cover gas through which some of the hydrogen might escape. In the CCTL experiment there are two places where the coolant makes contact with the cover gas - the pump and the CCTL vessel, and the amount of gas in mol/sec that can leave these nodes is W,, and W HC 2 respectively. All the cover gas plenums are connected through the expansion tank and it is assumed that equal pressure exists in all of them. The hydrogen partial gas pressure P, is calculated from the ideal gas law PV =I nRT
These equations are used in the next sections to develop the dynamic equations used in the simulation study.
4. THE DYNAMICS OF SODIUM-WATER REACTION PRODUCTS PROPAGATION A CLOSED SODIUM LOOP
81
in the CCTL
W,
=
R, (C,
-
CHS) M for C,
> C,H,
(28)
The rate constant R, , which governs the hydrogen disengagement, is assumed to ‘be such that if zero partial pressure of hydrogen exists in the cover gas it will take 71,2 min. for half of the hydrogen necessary to establish equilibrium to leave sodium node : R, =
In 2/,
C’ =
c (t -
=
O.693,/7,,,
(29) The dynamic equations for a pipe containing M lbs of sodium flowing at a rate of W IbJsec, are determined by the transit time 7 = M/W. The concentration of any of the reaction products at time t -. T is’ given by : T)
(30)
c’ is the concentration of a reaction product T seconds before it leaves the pipe exit. There are no leaks assumed in the pipe segments and therefore only secondary reactions take place. The change in C’, during the time 7, when the sodium flow is confined to the pipe segment, is obtained by a single step integration process given below : AC,
=
-KXaII
A C, =I -KNaOH
c’, T
(31)
c’, 7
A C, =’ KNaOH c’, T A C, =
0.5 (I&,
C’,
(32) (33)
+ I&iaoH C’,) T
(34)
82
D. Saphier
The concentration of any of the reaction the exit of the pipe at time t will be : c(t)
=
c’
5. COLD TRAP
+
products
at
A c
DYNAMICS
As shown in figures 1 and 2, a small bypass flow of sodium is passed through the cold trap. The sodium in this unit is cooled and come of the NaH and Na,O precipitates until saturation concentration is achieved. This process is used in all sodium loops to relmove impurities. Ideally the impurity concentration at the cold trap outlet stream should be equal to its solubility at the cold trap temperature. However the cold trap operation changes with time and flow and its static efficiency ,8 [5] given by equation (35) changes : i.J
=
ci -----ci
-cc,
(35) -
cL*T
Ci and C, are the impurity inlet and outlet concentrations and C,,, is the saturation concentration for the cold trap temperature. In a dynamic system the widely accepted concept of the static efficiency ,8 cannot be used. Instead, a dynamic efficiency is defined by equation :
dC -_ = WOT (Gin dt
C)/M -
/Id (Ci, -
tectors. The numerical results obtained from these instruments are different in their absolute values as well as in their transient b,ehavior from the actual concentrations because of the meters’ transfer functions. The hydrogen detectors yield readings proportional to the NaH and H, concentrations, and the oxygen detectors provide a reading proportional to the Na,O concentration. Both instruments are of the membrane diffusion type and details are given in reference 1. To predict the detector reading as the output of the simulation program, three parameters which characterize the detectors should be provided. The time lag 7, which is the time for the small flow of sodium to reach the detecting apparatus, the diffusion time constant, 8, in the detector, i.e., the time it takes the hydrogen or oxygen to diffuse through the membrane until equilibrium between the measured media and the detector interior is achieved, and finally the proportionality or the calibration constant of the detector. The detector transfer function is given by equation (40) : A -Z-I C
where A - is the detector reading, C - is the actual concentration, S - is the Laplace transform operator, and K, - is the proportionaiity constant.
7. THE SIlMULATION
,& - is the dynamic static efficiency
outlet
concentration
efficiency, related to the by equation (37) :
(3’) where the cold trap in gpm WCT - flow through M - cold trap sodium content in lb. The data available on the solub’ility of hydrogen and oxygen in sodium have been recently summarized by Rodgers and Dutina [lo]. Their recommended values as function of temperature were used in this study. For NaH : C 1EAT = For Na,O C 3SAT
exp (13.97
-
6631.4/T,)
(38)
: =
exp (16.131
-
6493.3/T”,)
The concentrations are given in ppm, temperature of the cold trap in OK.
(40)
CSAT) (36)
where C - is the average
K, e-87 --1 +se
and T,
(39) is the
6. THE DYNAMIC RESPONSE QF THE DETECTORS The results of the CCTL leak detection experiment are available through the hydrogen and oxygen de-
PROGRAM
CCTL-DYSP
A computer program CCTL-DYSP for the IBM 370/195, using the IBM 360/75 TSO system, was developed to solve the equations presented in the previous sections. Based on previous experience the FORTRAN languages rather than one of the available simulation language like CSMP was chosen. Using CSMP has large advantages when sirnnlation of simple models is considered. Whenever a complex or a large model has to be simulated CSMP reachs its limits in a way similar to how an analog computer reaches its limits - there is an insufficient number of elements to accomplish the simulation. Sometimes it is possible to overcome this difficulty in CSMP, but the complexity of programing that results, the time involved, and the inherent unflexibility of the final product, make FORTRAN a better choice for large scale simulations. FORTRAN is inherently more flexible and execution times are always better, sometimes by a significant factor. A simplified schematic diagram of the simulation program is shown in figure 3. The program is written in a modular form. It has 5 calculating subroutines, a coordinating main program, two service subroutines for printing and plotting results, and an integrating routine. The main coordinating program first calls the INIT routine in which data are read in, initial values are calculated and printed, and the pipe initial function is set up. The program then proceeds to the dynamic
Simzdlation
of a steam generator
I Calculate Reaction Products Concentrations
' <
leak detection
Subroutine LNTEGR
+
Subroutine
+
INTG
1
49
A
I
experifnent
Calculate Detector(
Subroutine
Response
-----+'
V
DETECT
7
53
in the CCTL
The main program then accesses the DETECT subroutine where the appropriate detector responses are computed. When the variables for a time step have been calculated by appropriate integration of the differential equations, the program updates the pipe segments inlet variabmle by caIling PIPE. The program then enters the PRIT routine, and if so required some data such as detector responses and concentrations at some of the nodes are printed. At predetermined intervals as determined by an input parameter - a complete (( map )> of the system which includes derivatives, sources, and actual concentration of the four reaction products at each segment and each pipe outlet is printed. The SPLOT routine is entered next, and user selected data are stored in a specific file for later plotting. Finally, the program checks the time, if it is less than the predetermined length of simulation it repeats the time step calculation. If the time is equal to the final simulation time the program will be terminated by printing a final <(map )) of the system and printplotting the results previously sto’red in a file. The CCTL-DYSP program is considered to be very efficient. There are some 200 differential equations to be integrated in addition to manv other non-linear relations. However, execution time is only 0.2 to 0.7 of the real time. The execution time is dependent on the type of transient to be calculated and the amount of requested output.
4
Results
f
8. REPRESENTATIVE
Subroutine PRIT
RESULTS
The results of the simulation as well as the detailed description of the program, its use and the appropriate description of the input data necessary to run the CCTL-DYSP, are given in ref. 12. Several experiments to be performed on the CCTL were simulated and analyzed and some of these are presented below.
T
Run # 100 to Simulate a Short Water Burst Pig.
3. - Simplified Loop Dynamic
Ihvchart Simulation
of the Core Components Progra.m (CCTL-DYSP)
Test
phase by increasing the time by a time step and increasing the time step counter by one. The first subroutine called in the dynamic section is SOURCE. In this routine the sources of reaction products resulting from any type of chemical reaction at each loop segment are calculated. The second routine called is INTEGR in which the derivatives of all the reaction product concentrations in the loop segments and pipe outlets are computed. This routine has access to the PIPE subroutine to compute pipe outlet concentrations and to the INTGI routine where the actual integration is performed.
The transient was initiated by a short leak of high pressure steam of 0.015 lb/set flow rate. It was started at 10 seconds and terminated at 15 seconds introducing a total of 0.075 lbs of water into the system. The sodium ;flow rate in the system was 800 gpm (3.03 m3) and the sodium temperature 9‘40 OF’ (504 “C). The injection point was I-4 (node 16) which is in the middle of the steam generator unit, as can be seen on figure 2. The simulation was continued for 100 set, a time sufficient for the major transients to be terminated. Figure 4 shows the resulting detectable hydrogen concentration at several nodes. The detectab’le hydrogen is in the form of hydride, NaH, and dissolved hydrogen, H, The hydrogen concentrations at the leak site (node 16) and at the steam generator outlet plenum (node 25) are shown in figure 4. In addition, the
D. Saphiev
84
20.0
0
60.0
40.0
*O
TIME(SECI Fig.
4. -
Run
#
100 to Simulate
a Short
Water
Burst
concentration at the end of the sampling line (node 42) through which 5 gpm flow prevails is also shown in the figure. It is seen that the transient is delayed by the pipe transit time. Finally, the hydrogen detector response is also shown for this experiment. The shape of the transient as seen by the detector differs signi-
0
120.0
of
0.075
lb.
Injected
at the
Middle
of
Superheater
Unit.
ficantly from the actual concentration in the pipe to which the detector is connected. The detector response is the result of an additional time lag which is clearly identified in the figure and the relatively slow diffusion process through the detector membrane that results in the lower rate of change as shown in figure 4.
240.0
360.0
I.0
480.0
TIMELSECI Fig.
5. -
Run
# 101,
Reaction
Product
Concentrations
at Segment 27 as a Result at Injector 14.
of
70
sec.
Water
Leak
of
0.001
lb/set.
Simulation Run
#
of
ti steam generator
101 Simulate
a Typical
leak detection
experiment
Experiment
This experiment was simulated under the same conditions as the previous run. The duration of the leak was increased to 70 set and the leak rate was reduced to 0.001 lb/set. The water leak was introduced at injector I-4, ten seconds after simulation startup. The simulation was continued for ten minutes. The cold trap was not included in this simulation. The concentration changes of the four reaction products in the upper part of the CCTL vessel (node 27) are shown in figure 5. A relatively fast decomposition of NaH at 940 OC can also be observed from the figure. The response of two hydrogen detectors, detector-l connected to sampling line-49 and detector-3 connetted to sampling line-47, are sho,wn in figure 6. It is seen that steady state conditions in detector-1 are achieved approximately after ten minutes while in detector-2 steady state conditions are achieved after approximately two minutes. Run
#
103 to Simulate
a Tightly
Coupled
Loop
The flexibility of the program is demonstrated by simulating a different type of loop. In this system the huge sodium vessel containing the steam generator is excluded. Instead three more segments are added to the steam generator unit. A short leak of 0.015 Ib/sec for 5 set period was simulated at 800’ GPM flow rate and 940 OF. The results are shown in figures 7 and 8. The oscillatory nature of the concentration changes is due to the elimination of the huge mixing volumes
0
120.0
in the CCTL
85
of the CCTL vessel which smooth out any type of transient. A short leak such as is simulated in this experiment will contaminate a lump of sodium. Whenever this lump passes through a segment of the loop or near a detector an increase in contamination wili be observed until finally after several passages the transients will die out because of the mixing process. The distance between the peaks is the loop transit time and as observed from the figure it is 14 set (calculated value 13.76). It is interesting to note that similar results were obtained by Berault, et al [13] in their experimental loop which included mainly piping segments, when a short b’urst of water was injected. The transit time in their loop was approximately 5 min and 13 peaks were observed before the hydrogen diffused through the system and a stable hydrogen concentration was established. In figure 7 the transients in hydrogen concentrations at nodes 23 and 29 are shown. It can be ob’served from the figure that segment 29 is at a <( 5 seconds distance >> from segment 23. The same transient results in both segments; however, because of mixing effects, the appropriate peaks at segment 29 are lower than those in segment 23. In figure 7 the response of the two hydrogen detectors connected to pipe segments 47 and 49 are shown. Run
#
103 to Simulate
hjection
22
Recently some experimental results from the CCTL leak detection experiment became available. On No-
240.0
360.0
400.0
TIHE[SECI Fig. G. -
Run # 101, Hydrogen Detector Response in CCTL Leak Experiment at Injector 14.
as a Result of a 70 sec. Leak of 0.0001 lb/set.
86
D. Saphier
I
I LEGEND NODE 23
o-AT
0
20.0
40.0
60.0
80.0
1
TIMEtSEC) Fig.
7. -
Run
102,
I
Simulation of Water
Injection
40.0
in Tightly
Coupled
Loop.
80.0
60’ 0
TIMEtSECl Fig.
8. -
Run
#
102,
Hydrogen
Detector
Response
vember 6, 1975 injection # 22 took place in which 2.54 grams/min of water were injected at injector I-4. The leak duration was 57.5 seconds, the sodium flow was 600 gpm and the sodium temperature was 940 OF. In figure 9 the experimental readings from
in Simulation
of
a Tightly
Coupled
Loop.
the hydrogen detector connected to segment 49 are superimposed on the detector response as predicted by the simulation. It is seen that except for the experimental random noise there is an excellent agreement between the
Simdation
of u steam generator
lea& detection
in the CCTL
experiment
results. For comparison purposes the simulated hydrogen concentrations at the exit of pipe segment 49 and
in the stagnant heat exchanger region segment 6 are also shown.
CCTLLEAKSIMULATIONOF INJECTION
120.0
87
240.0
22.
[2.54G/S)
480.0
360-O
f
0
TIME[SECl Fig. 9. -
Run
103 to Simulate
Injection
Experiment
# 22. Comparison
of Predicted
and Measured
CCTLLEAK SIMULATIONOF INJECTION
23
Hydrogen
Concentration
Changes.
L0.98G/M!
IENTAL RESULTS
I -0
360.0
TIDE Fig.
IO.
-
Run
104 to Simulate
Injection
Experiment
180-O
E 3.0
[SEC,,
# 23. Comparison
of Predicted
and Measured
Hydrogen
Concentrations.
D.
Run
#
104 to Simulate
Injection
23
On November 7, 1975 injection # 23 took place in which 0.98 gram/min of water were injected at injector I-4. The leak duration was 118.4 set, the sodium flow was 300 gpm, and the sodium temperature was 940 OF. In figure IO the experimental readings from the hydrogen detector are superimposed on the detector response as predicted by the simulation. Small differences between the experimental and the predicted curve can be seen. These seem to bse mainly due to the imperfect knowledge of the exact shape of the water injection curve, errors in the calculation of the delays in the sampling lines due to errors in the flowmeters, and random experimental noise which is clearly visible on the experimental curve. In this experiment there was apparently a large calibration error in the interpretntion of the detector readings and therefore the experimental results were normalized to the steady state result as obtained from the simulation. 9. CONCLUSIONS A model to account for the kinetic and dynamic processes resulting from a water leak into a circulating sodium loop was developed. A computer code, CCTLDYSP solving the model equations was prepared. The distribution and the concentration of the sodium water reaction products throughout the system was calculated and it is shown that qualitatively the results are in agreement with similar calculations or experiments pub’lished elsewhere [5, 131 and with the preliminary experiments performed at ANL. However, it should be noted that experimental and theoretical information on small leaks, sodium-water interaction, and its subsequent distribution in a system is scarce and of dubious validity. Most of the parameters governing hydrogen diffusion and transport throughout the system and its subsequent <( evaporation )> (or disengag,ement, if in bulk form) in the cover gas are not known. Some of the reaction parameters available, such as NaOH or NaH dissociation rates, are old data with large error limits obtained under laboratory conditions different from the actual operating conditions of the steam generator; and there is no quantitative information whatsoever on how the reaction proceeds at the leak site. As a result, several assumptions had to be made and the results presented are dependent on these assumptions. However since the mathematical model was developed from basic principles, it is believed to be correct and presently unknown parameters will be replaced when more experimental data become available. The program is system independent and can be apphed to predict hydrogen and oxygen distribution in any sodium loop having small water leaks and operating conditions similar to those in CCTL. To apply the CCTL-DYSP to a simulation of the CRBR steam generator some changes should be introduced into the program. The temperature variation from segment to segment should be calculated or supplied as
Saphier
input data. The program should account for hydrogen diffusion through the steam generator walls. Other sources and sinks of hydrogen and oxygen in the system might be found to be of some significance and should be inserted into the program. The above changes will not affect the program structure, they will only add some terms to the hydrogen and oxygen sources in the appropriate routine. ACKNOWLEDGEMENT The author extends his thanks to L.F. Epstein, R.A. Jaross, and J.M. McKee from the Argonne National Laboratory for their comments and useful discussions during this study. REFERENCES [I]
R.A. JAROSS, <(Work Plan for Steam Generator Leak Detector Test in CCTL )>, T0022-002~SA-00 (3, 1972). [2] G. NAUD, <
[6]
[7]
[S]
[9]
[lo] [ll]
[ 121
1131
(1968). H.C. PELLOW, Q A Model to Predict the Effect of Hydrogen Sources on an LMFBR Steam Generator Leak Detection System >>, GE NEDM-13992 (1973). P.B. Longton, <( Reactions with Alkali Metals with Gases - Part IV, The Reaction of Sodium with Hydrogen )) LJKAEC, IGR-TN/C435 (1957). A.K. Fischer, <( Studies of Oxygen-Hydrogen Interaction in Sodium - Isotope-Exchange Studies >>. In ANL-7944 (August 1972). P.B. LONGTON, B Reactions with Alkali Metals with Gases - Part VII, Reaction of Sodium with Water Vapor >>, UKAEC IGR-TN/C.418 (1956). D.R. VISSERS, J.T. HOLMES, and P.A. NELSON: <( A Hydrogen Activity Meter for LMFBRs >>, Trans. Am. Nucl. Sot., 14 (1971). M.D. BANUS, J.J. McSHARRY, and E.A. SULLIVAN ; J. Am. Chem. Sot. 77 (1955), 2007. D.N. RODGERS and D. DUTINA, ((Recommended Values for NaH Dissociation Pressure and the Solubilities of Oxygen and Hydrogen in Sodium )), NEDM12473, General Electric Company (Sunnyvale, Calif.) (1974). D. SAPHIER, (( A Kinetic Model of the Sodium Water Reaction Applied to the Dynamic Simulation of Leak Detection in the Core Component Test Loop >>, Argonne National Laboratory ANL-7522 (1975). (To be published), J. BERAULT, et al., <( Detection of Small Leaks by Hydrogen Measurements in a Sodium-Heated Steam Generator )>, Proc. of Conference on Sodium Technology and Large Fast Reactor Design, ANL 7520 (1968).