jp9504227 94-019 a simulation code treating all twelve

JAERI-Data Code 94-019

jAERI-Data/Code-94-019.

JP9504227

A SIMULATION CODE TREATING ALL TWELVE ISOTOPIC SPECIES OF HYDROGEN GAS AND WATER FOR MULTISTAGE

CHEMICAL EXCHANGE COLUMN

Dece roer 1 9 9 4

Toshihiko YAMANISHI and Kenji OKUNO

Japan Atomic Energy Research Institute

X319-11 «««»«;*

1x319-11

This repoit is issued irregularly.

Inquiries about availability of the reports should be addressed to Information Division.

Departmenl of Technical Information. Japan Atomic Energy Research Institute. Tokai-

mura. Naka-gun. Ibaraki-ken 319-11. Japan.

©•Japan Atomic Energy Research Institute, 1994

H * I 8 /•

JAERI-Data/Code 94-019

A Simulation Code Treating All Twelve Isotopic Species of Hydrogen Gas

and Water for Multistage Chemical Exchange Column

Toshihiko YAMANISHI and Kenji OKUNO

Department of Fusion Engineering Research

Naka Fusion Research Establishment

Japan Atomic Energy Research Institute

Naka-machi, Naka-gun, Ibaraki-ken

(Received November 14, 1994)

A simulation code of the multistage chemical exchange column has been

developed. The column has an electrolysis cell, a section for the liquid phase

catalytic exchange, and a recombiner. The sieve trays and the catalyst beds are

separated in the section for the liquid-vapor scrubbing steps and for the vapor-

hydrogen gas exchange steps. This type of column is a promising system for the

tritiated water processing.

The code can deal with all the twelve molecular species of the hydrogen gas

and the water. The equilibrium of atomic elements of H, D and T is also

considered in the liquid phase. The Murphree-type factors are introduced in the

code to evaluate the efficiencies for the sieve trays and catalyst beds. The

solution of basic equations can be found out by the Newton-Raphson method. The

atom fractions of D and T on the scrubbing trays are the independent variables

of the equations: The order of the Jacobian matrix is only twice the number of

sieve trays. The solution of the basic equations could be obtained for several

example cases; and no difficulty was observed for the convergence of the

calculations. Broyden's method was quite effective to reduce computation time

of the code.

Keywords: Fusion Reactor, Isotope Separation, Water Detritiation, Tritium,

Chemical Exchange, Multistage, Murphree Efficiency, Newton-raphson,

Convergence, Broyden Method

•JAhKI -Datu/Code 94-019

140SS)

ffiicfcIJ-5 3 00011^8, H, D,

: T311-01

.JAI~HI -[)はla!l、ode 94 -019

水素ガス及び水における12のすべての同位体成分を取り扱う

多段型化学交換塔のためのシミュレーションコード

日本原子力研究所那珂研究所核融合工学部

山西敏彦・奥野健二

(1994年11月14日受理)

多段型化学交換溶のためのシミュレーションコードを開発した。悠は.電解セル.液相化学交

換部，再結合器からなり.液相化学交換部は，気液平衡のための充域部と水素水蒸気化学交換

のための触媒層が分離されてしる。このタイプの塔は，核融合炉の水処理系システムとして 1つ

の有望なシステムである。

コードは，水素ガス及び水におけるすべての12の同位体成分を取り扱うことが可能である。液

相における 3つの原子種， H， 0， Tの平衡もまた考慮されてL、る。充填部と触媒層の効率を評

価するために，マーフリー型の段効率係数を導入した。導かれた基礎式の解は.ニュートンラフ

ソン法で求めることができる。式の独立変数は.充羽部各段のDとTの原子分率であり，ヤコビ

アン行列の階数は充填部段数の 2倍にすぎなL、。数列のシミュレーションに対し解を得ることが

でき，ニュートンラフソン法の収束図鑑性は認められなかった。ブロイデンの方法を試みたとこ

ろ，本コードの計算時間短縮に極めて有効であることが確認できた。

那珂研究所:〒31卜01茨城県那珂郡那珂町大字向山801-1

"

JAEHI- Data/Code 94-019

Contents

1. Introduction 1

2. Mathematical Simulation Procedure 3

2.1 Basic Equations for the Catalyst Bed 3

2.2 Basic Equations for the Scrubbing Trays 9

2.3 Basic Equations for the Electrolysis Cell 12

2.4 Bubble Point Calculation 13

2.5 Physical Properties 14

2.6 Simulation Procedure 14

3. Reduction of Computation Time 17

4. Numerical Examples 19

5. Owlusion 20

Acknowledgment 20

References 21

Nomenclature 23

1. £ m 1

2. *?W-> Sa U-i/ s y^m 3

2. i MKHidt-r-r s s & t 3

2.2 aaw&Kijtt-f**tts$ 9

2.3 £d?-tr;n::*f-f 5&K5*; 12

2.4 m&WK- 13 2. 5 ® 14 14

2. 6 i/la.U-i/3 y^m. 14

3. l t»BfF4©@^ 17

4. m «f m 19 5. *£ Ik 20 W » 20 ##£it 21

f 2 * £ 23

JAEH1- Data/Code 94-019

1. Introduction

In the fusion reactors, large amount of tritium-contaminated water is expected

to be produced: cooling water for plasma facing components; and waste water from the

tritium systems. The tritium concentration in the water is too high to discard directly to

the environment, so that it is required to recover tritium from the water!. For this

situation2~4, a chemical exchange column in liquid phase is one of the most attractive

process. The column is composed of an electrolysis cell, a liquid phase catalytic

exchange section, and a reactor* A The reactor is called as a recombiner. The hydrogen

gas produced by the electrolysis cell at the bottom of the column flows in the liquid

phase catalytic exchange section, and is oxidized to water by the recombiner. The water

drops to the electrolysis cell again. The multistage separation can thus be obtained by a

single column in contrast to vapor phase exchange process^. However, it has been

known that the catalysts that cause the water/hydrogen exchange reactions often lose the

activity; where the surface of the catalyst is covered with wate r^ . The multistage type

chemical exchange column has been proposed to overcome this problem. The liquid-

vapor scrubbing step proceeds in sieve trays; while vapor-hydrogen exchange step is

separately caused in hydrophobic catalyst beds (See Fig. 1)5.8. j n i s type of column is

expected to be promising process for the system of tritium recovery from the water for

the fusion reactors.

The multistage chemical exchange column has been designed and operated for

enrichment of D,0 for a fission reactor in Japan**. However, the characteristics of the

column have not yet been understood especially for the behavior of tritium in the column.

The atom fractions of tritium in the cooling and waste water of the fusion reactors are

expected to be 10"6 - 10~8'. The atom fractions of deuterium naturally contained in the

water is ~ 10"1. The concentrations of HDO, D,O, and DTO are ~ 10~\ ~ 1(T7, and

~ 10~"\ Hence, the effect of presence of deuterium in the water is not negligible. This

1 -

JAER]-Data/Code 94-019

means that at least ten-component system (H, - HD - HT - D, - DT - H2O - HDO

-HTO - D2O - DTO) must be considered to study the characteristics of the column. It

is also significant to study the dynamic behavior of the column for design of control

system. There are two approaches to simulate the chemical exchange column: the model

using the mass transfer coefficient 9~1 * and the stage model'2~15 The sieve trays for

the scrubbing step and the catalyst beds for the exchange step are completely separated

in the multistage chemical exchange column. It is reasonable to apply the stage model

for simulation. In addition, the stage model has great advantages: The model is

appropriate to apply for the multi-component system; and the dynamic behavior of the

column can easily be simulated in comparison with the other model. Kinoshita et al. has

developed the simulation code of the multistage chemical exchange coh.mn by the stage

mode|12~14 Their simulation code can deal with H-D system^, 14 n j s necessary to

develop the code for H-D-T system.

The purpose of the present study is to develop a simulation code dealing with all

the twelve molecular species of hydrogen gas and water for the multistage chemical

exchange column. The equilibrium of the atomic elements in the liquid phase is also

taken into account. The Murphree-type factors are also introduced in the code to

consider the efficiencies of scrubbing trays and catalysts beds. The code is applicable to

the simulation of the column in a wide range of operating conditions.

o

•JAERI- Data/Code 94-019

2. Mathematical simulation procedure

The model column is illustrated in Fig. 2. The column has the recombiner at the

top and the electrolysis cell at the bottom. The liquid phase catalytic exchange section is

composed of N sieve trays and (N-l) catalyst beds. The model can accept multiple feed

streams and multiple withdrawal streams of liquid water. All the feed streams are

assumed to be supplied in liquid state. Unlike the c.yogenic distillation columns within

which two phases exist, the three phases must be considered in this case.

The differences in latent heat of vaporization can be neglected for the isotopes of

water. An operating temperature is slightly higher than the room temperature, and a hot

water jacket is attached to the column. Hence, the heat transfer through the column wall

is expected to be negligible. As a consequence, the heat balance equations are not

required to taken into account, and flow rates of liquid and vapor are input variables '2.

The fusion reactors have a system composed of the cryogenic distillation columns

for the hydrogen isotope separation'. The bottom product of the chemical exchange

column in the fusion reactors is a hydrogen gas stream. The hydrogen gas stream is sent

to the system of the cryogenic distillation columns. The tritium in this stream is finally

recovered by the cryogenic distillation system.

2.1 Basic equations for the catalyst bed

There are twelve molecular species of hydrogen gas and water vapor. We can

describe the following 45 reactions between the water vapor and the hydrogen gas:

- 3

JAER1-Data/Code 94-019

H2(g):-T2(g)^-*2HT(g)

HDO(v) + D 2 ( g ) ^ ^ D 2 O ( v ) + HD(g)

HDO( v) + DT(g)« K" >DTO(v) + HD(g)

HTO(v) + D 2(g)*-^^D 2O(v) + HT(g)

HTO(v) + DT(g)< K" >DTO(v) + HT(g)

DTO(v) + T2(g)*-S«—T2O(v) + DT(g)

H2O( v) + D2O( v) <-Ju2-^2HDO( v)

H2O(v) + DT(g)< K?l »HDO(v) + HT(g)

H2O( v) + DT(g) < K^ > HTO( v) + HD(g)

- 4 -

JAEKI-Data/Code 94-019

D2O(v) + HT(g)« K?7 > HDO(v) + DT(g)

D2O(v) + HT(g) < K?s > DTO(v) + HD(g)

D2O( v) + T2 (g) «-*»-* DTO(v) + DT(g)

T2O(v) + H2(g) < - ^ ^ HTO(v) + HT(g)

T2O( v) + HD(g) ^ ^ HTO(v) + DT(g)

T2O(v) + HD(g)« Kff » DTO(v) + HT(g)

T2O(v) + D2(g) «-&»-* DTO(v) + DT(g)

HDO(v) + HT(g) < K" > DTO(v) + H2(g)

HDO( v) + DT(g) «H-5M-» H T O ( V ) + D2 (g)

HDO(v) + T2(g) «-S»-» DTO(v) + HT(g)

HDO(v) + T 2 ( g ) * - ^ ^ H T O ( v ) + DT(g)

HTO(v) + HD(g) < K" > DTO(v) + H2(g)

HTO(v) + D2 (g)< K" > DTO(v) + HD(g)

HD(g) + T2 (g) « - & ^ . DT(g) + HT(g)

H2(g) + DT(g) < - ^ - HD(g) + HT(g)

HD(g) + DT(g) ̂ ^ D2 (g) + HT(g)

HDO(v) + T2O(v)«^-^-^DTO(v) + HTO(v; (])

H2O(v) + DTO(v) < ^ > HDO(v) + HTO(v)

HDO(v) + DTO(v) < K '̂ > D2O(v) + HTO(v)

From the stoichiometric matrix of the reactions of (1), it can be shown that the rank of

the matrix is eight. In other words, among 45 reactions, only eight reactions are

independent. We choose the first eight reactions. For other reactions, the equilibrium

constants can be described by using those of the eight reactions.

- 5 -

JAERI- Data/Code 94-019

K9 = Ks K4 , K10 = K 6 /K 4 , K,, = K 7 /K 4 , K l 2 = K g / K 4 ,

K-,3 = K.6 K5, K14 = K 7 /K 5 , K1S = K 8 /K 5 , K ] 6 = K 7 / K 6 ,

KI7 = K8 K6 , K18 = K g /K 7 , K19 = K,K4 /K 6 , K2I) =K2K5 /K 8 ,

K2) = K3K7 (K6K8 j , K22 = K4K,, K2, = K3K2,

v K,K2., K 3 , K25 = K5 V ' K I K 2 / K , , K26 = K , K 4 / K 6 ,

K28 = K7AK6^/K2 /K,K3) , K29 = K3K7/K6

K 8 , K31 = KS-V/K2K3/K1 / K 8 , K32 = K7 V 'K 2 K 3 /K , , 'K8 ,

/K, /K 4 , K35 = K5^/^K2/K,K,/K4,

K-36 = K7 v K 2 K 3 / K, i K 4 , K37 = K5 A / ^ 2 K 3 / K , / K 4 ,

K-3S = K7 \ K 5 X ' K , K 2 / K 3 J , K,9 = K7J\KSV'K2/K1K3J, K4() = v iK2K3 , /K,,

K41 = V 'K ,K 2 /K 3 , K42 = V 'K 2 /K ,K 3 , K43 = K5K7 V; K 2 K 3 /K, / ( K , K g ) ,

K4J = K4 K5 v K, K2 / K, / K 7 , K45 = K5K6 v/ K2 /K , K3 / K7

• ( 2 )

Let us assume that compositions of the input streams, y""'+1 's and z l H ' s , are all

known. There are ten unknown variables for the output streams: yj^i = l,6,i * 2), and

zfj(i +1,6,i * 2). From the mass balances for atomic elements around the catalyst bed,

we can obtain

- 6 -


a, = 1

out

(3)

Thus, we obtain ten equations.

Here, we introduce the Murphree-type factors to consider the efficiency of the

catalyst bed.

in out J 1,1 J 1.1+1 / • -I f • rK\

Y - in.ee, 1 , ( 1 - 1 , 6 , 1 - 2 ) in.ee, { 4 )

It has been known that the rates of the first three reactions in Eq. (1) are very rapid '**.

We assume that the equilibrium for the three reactions is readily achieved at the outlet of

the catalyst bed. The bed performance is not a monotone increasing function of y ^ . It

may be better to introduce a factor for each hydrogen-water exchange reaction.

However, there has been no experimental data for the efficiency of catalyst bed; and it is

quite difficult to give a reasonable value for the factor of each reaction. For these

reasons, we introduce a factor for the efficiency of the catalyst bed.

From Eqs. (1), (3), and (4), we obtain

- 7 -


F. - z f J - K l 2 4 J ( 1 . 0 - 2 I i j - z 3 J - z 4 f j - > / K 3 Z 6 > j z 5 i j - z 6 J ) = 0

F2 = 2 ^ - K 2 z 5 J ( 1 . 0 - z K j - z 3 J - z 4 - J - ^ z ^ - z 6 J ) = 0

VY 2 5 OJ 2

xx = (K5 - l ) Z ] j + (K4 - l )z 3 j + (K6 - l)z4 f

( K 7 - l ) v < K j Z 4 j J z 6 j + ( K 8 - l ) z 6 J + 1 . 0 (5)

Consequently, for four unknown variables of z, r z 3 j , z 4 j , z 6 j , four equations are derived.

We can solve these equations by the Newton-Raphson method:

- 8 -


Azk = -JFlF,

'V z =

(6)

2.2 Basic equations for the scrubbing trays

The mass balance equations for atomic element of H can be derived as follows:

B, C, .

A2 B2 C2

A

A,

f -« ^nnt \ X out

rout

r -c \

(7)

where


Aj=-LH, Bj-Lj + Uj+^V, C J . -

E 1 - ( V + G-D)X-1+Vp I i l+O1ZFHtI ,

E-VP.y+OjZ,:,,,.,

bN = vYH N + ONZHHN, in _ cut in _ v o u t

H J l j l in out J 3,j J3.JV1 y + y 2 j + i ~ »

f v""1 V ° U t A •••/ X ° U t X ° U l

HJ ^ 2 J20 2 j , j 2 2j 2

-.in.out in.out in.out in.out

X in.out _ i.j in.out 3J v^in.out _ J l.j in.out J 3.j

H.j ,-. 2.j ^ ' H.j /̂ J 2.J ^ » - I ri ; — T V-3 ; i

2 J 2 2

(8)

Similar equations are derived for atomic elements of D and T also.

We introduce the Murphree-type factor for the efficiency of the scrubbing trays

also14:

? v ,q _ p oul.cq _ in ' Ji ,j ^rp • (9)

y i.j J i.j *

For the liquid water phase, the three equilibrium reactions are described by

H2O(1) + D2O(1) ^

D2O(1) + T2O(1)

The equilibrium compositions can be obtained by

- 1 0 -


+Q3X™12 + Q 4 < + Q, = 0,

Q

3 =2q,q3q6

+2q4q5q9+q42q10,

2

= 2 q q q +q 2 q 6 Q3 =2q,q3q6 +q22q

— K 4

— K 4

7 — K 4 6 K" K" 'kT n — K" V o u t n _ 48

^ V ^ 4 6 ^ 4 7 / K 4 8 ' q5~~K46AH.j' Qe ~ 2"

8 = V ' K 4 7 K 4 8 / K 4 6 -—r--> q9 = K ^ x ) out / « out . « °ul . « \ / / „ out . _ \

x5 j =(q1x l j +q2x1J +q3)/(q4x l i j +q s) , oul out v o u ' 2

out _ y o u t ^Xj_ _ *5.j out _ A5,j X 4 , j - ^ D . j " ~ ^ ' A 6 , j - „ out '

2 2 K-24X4,j

r xout ̂ -.out _ 'j v o u t v o u l 5'J v

o u t _ 1 v-o u t v o u t v o u t v o u l v o u 1 X3.j ~ Z AT.j ~X6.j ~ -, ' X2,j - 1 ~ X I , j ~X3.j ~X4,j ~X5,j ~ X6,j

• (ID

- 1 1 -


2.3 Basic equations for the electrolysis cell

We introduce two factors to consider the separation efficiency at the electrolysis

cell.

Tfa -{(1 -ZaN)/ZD,N};•••{(! -Y j N ) /Y j N } ,

T I T - { ( 1 - Z T , N ) / Z T . N } { ( 1 - Y ^ N ) / V J ? N } ,

7 -

From the mass balances of atomic elements of D and T around the electrolysis cell,

LNX°Dut

N=(G+W)ZD .N+vY'V

Substituting Eqs. (12) into (13), we obtain

o,2-4o2o3 - o, )/2o2 ,

o2 = v(l-Y]D), o3

O 5 -V(1 -TI T ) , O6 =

- 1 2 -

JAER1- Data/Code 94-019

In the liquid phase, the equilibrium reactions of (10) must be considered:

y^'/iytM = K22{(p;(Te))2/P;(Te)P;(Te)}

If the atom fractions of D and T in the water stream to the electrolysis cell are given,

y["N's and z,n 's can be calculated from Eqs. (14), (15) and (11).

2.4 Bubble point calculation

The tempe.atures of sieve trays, T.'s, can be calculated by the Newton method:

T jk + 1-T j

k+ATk

- 1 3 -


2.5 Physical properties

We need the vapor pressure of water and equilibrium constants of the reactions.

The vapor pressure of the six isotopic species of water can be calculated by the equations

reported by Van Hook'6.

pro}) = 1.013xl05exp[(t)u/^2 +4^/1 ; +^ i / (T j +4>4j) + <ki] • (17)

We describe the equilibrium constants as a function of temperature from the values at

several temperatures listed in Ref. 17.

The parameters of Eqs. (17) and (18) are presented in Tables 1 and 2, respectively.

2.6 Simulation procedure

The basic equations derived in preceding sections can be solved by the Newton-

Raphson method. The simulation procedure is as follows.

(i) Assume the atom fractions of D and T in liquid water streams leaving the sieve trays,

Xp1' s and X™J' s. A practical method is that all the atom fractions of D and T are equal

to the average values of all tb feed streams:

- \\ -


(19)

(ii) Assume the temperatures of the sieve trays. From Eq. (11), x™1' s are calculated,

(iii) By the bubble point calculation, Eq. (16), T/s and y"jlei"s become all known. If the

temperatures assumed in step (ii) are not equal to the values calculated by the bubble

point calculation, return to step (ii).

(iv) Since x " ' s are known, y,'nN's and zi N 's can be calculated from Eqs. (11), (14) and

(15).

(v) By accounting for the scrubbing efficiencies for the N'th tray, y|"JJ's are calculated

from Eq. (9).

(vi) Then, the catalyst beds are treated. From y™JJ's and ziiN's, y;nN_, and zlN_,'s can be

calculated with the efficiency of the catalyst bed by Eqs. (5) and (6).

(vii) Steps (v) and (vi) are sequentially carried out from j=N-l to 1. Thus, y™"s, y™'s,

and z 's for j=l to N become known.

(viii) Now we can evaluate all the values of Aj's, B;'s, Cj's, and E;'s in Eq. (8). The new

values of X'^'s, X^*'s, and X™J's are obtained by solving the tridiagonal equations of

Eq. (8) three times. Normarize the new atom fractions of H, D and T.

(ix) Denote the value of X ^ ' s and X ^ ' / s assumed at step (i) by ( X ^ / S J Q and

(X™;'s )0. The values of X™'/s and X™J's are not equal to (X^ 's )o and (X™J's )0 .

We define the functions of Sj' s by

(20) sJ + N=(x°Tu;) ( )-x-=o

- 1 5 -


The simulation can be understood to find out the solution of Eq. (21). This is carried out

by the 2N-variable Newton-Raphson method.

x =

A D,1

A D,N

T,l , s-

( -,C / '\{ V̂ ':

(21)

The partial derivatives are numerically calculated:

(22)

(x) Return to step (ii). If Sj's are equal to zero, the variables in steps (i) through (x)

satisfy all the basic equations derived. The simulation problem is considered solved once

- 1 6 -


2N •k-10

e-HT (23)

is satisfied. The simulation procedure is illustrated in Fig. 3.

3. Reduction of computation time

The order of Jacobian matrix is only twice the number of sieve trays in the present

simulation code. However, if the number of sieve trays is large, long computation time is

expected for evaluation of the Jacobian matrix and its inversion. To overcome this

problem, we introduce Broyden's method"*. The evaluation of the Jacobian matrix and

its inversion are needed only once in his method. In the present section, his method is

applied to the solution of Eq. (20).

The Jacobian matrix J s is given in Eq. (21). Expressing - / s " ' by H, the

simulation procedure can be summarized as follows:

(i) Obtain an initial estimate X".

(ii) Calculate Js and invert it. Thus H" is obtained. Also calculate S".

(iii) Compute &X° =H°S°.

(iv) Calculate X' = X" +xAX". In the case of <p' s«pu, x is set at unity. In the case of

cp1 a <p", T is calculated from

- 1 7 -

JAKKI-Data/Code 94-019

{(U6e) t2-i}/3e, e = cp7(p0, 2N . . 2 2N

2 j-1

Thus, X] and S] are calculated.

(v) If the convergence has not been achieved yet, calculate / / ' from

- (X , , ,X2N)

(25)

(vi) The values of A",S\Hx are substituted for X\S",H'\ and repeat from step (iii).

The Newton-Raphson method is replaced by this method.

The Newton-Raphson method sometimes fails to get convergence. If a set of

appropriate initial values is given, we can get the convergence even for this case. The

initial values of the present simulation code are atom fractions of D and T on sieve trays.

A possible method is that either top or bottom product composition is assumed'3. The

other product composition can be calculated from the overall mass balance of the column.

Then, the atom fractions of D and T on sieve trays are linearly set from top and bottom

atom fractions. However, it is not easy task to assume an appropriate product

composition. We propose the following procedure for setting the initial values for the

case where it is difficult to get the convergence:

(i) The initial values are calculated from Eq. (19).

(ii) Solve Eqs. (5), (6), (9), (11), (14), and (15). Evaluate all the values in Eq. (8).

(iii) Solve the tridiagonal equations of Eq. (7) three times. Normalize the new atom

fractions of H, D and T. These values are used for the initial values of the Newton-

Raphson iterations.

- 18 -


4. Numerical examples

A computer program was written in FORTRAN statements. Computations were

performed in the double precision. The system used was FACOM M-780 at the Japan

Atomic Energy Research Institute. For all the cases tested, no difficulty for the

convergence was observed. No technique for the setting the initial values was required.

An example case is presented in Table 3 and 4. The convergence is obtained by only

three iterations. The composition of the water supplied to the column is equal to that of

the waste water of ITER'. The tritium concentration can be reduced to -1/400 by the

column having only 35 sieve trays. If we get the same separation performance by the

water distillation column, about 200-300 stages are required'. The chemical exchange

column is thus attractive process.

Broyden's method was also tried to reduce the computation time. As shown in

Table 4, the method can reduce the computation time to half of that for the Newton-

Raphson method without increasing the number of iterations. Kinoshita reported that it

was required to evaluate the Jacobian matrix only once^; He obtained the convergence

by the Jacobian matrix which were calculated for the initial values for his code of H-D

system. Even Broyden's method was not necessary for his code. However, for the

present code of H-D-T system, we could not get the convergence by the Jacobian matrix

for the initial values; in spite of the setting method of initial values. The application of

Broyden's method is thus quite effective for the present simulation code.

- 19 -

JAER1-Data/Code 94-019

5. Conclusion

A simulation code for the multistage chemical exchange column has been

developed. Some significant features of this code are summarized here.

(1) The code can deal with all the twelve molecular species of hydrogen gas and w ter.

The equilibrium of atomic elements of H, D and T in the liquid phase is also considered

in the code. The separation factor between the isotopic species depends on the

temperature and composition. This dependency is fully taken into account.

(2) The Murphree-type factors are introduced in the code to evaluate the efficiencies for

both of the sieve trays and catalyst beds.

(3) The main calculation loop is based on the Newton-Raphson iteration. The order of

the Jacobian matrix is only twice the number of the sieve trays.

(4) The great stability and high converging speed were verified. It was also verified that

Broyden's method was effective for this code: The computation time was reduced to ~

1/2 without increasing the number of the iterations.

Acknowledgment

The authors wish to express their sincere thanks and appreciation to Assoc. Prof.

Dr. M. Kinoshita (Kyoto Univ.) for his guidance in developing the simulation code.

- 2 0 -


References

1. O. K. KVETON, "Water Detritiation and Isotope Separation System for ITER",

Private Communication, Joint Central Team of ITER at Naka Establishment of Japan

Atomic Energy Research Institute (1994).

2. T. E. HARRISON, "Design of a Demonstration Tntium Recovery Plant for Chalk

River," Proc. Tritium Technology in Fission, Fusion, and Isotopic Applications, Dayton,

Ohio, April 29-May 1, 1980, CONF-800427, p. 377 (1980).

3. R. E. ELLIS, T. K. MILLS, and M. L. ROGERS, "Catalytic Exchange Detritiation

Studies", MLM-2502, p. 6, Mound Laboratory (1978).

4. T. K. MILLS, R. E. ELLIS, and M. L. ROGERS, "Recovery of Tritium from

Aqueous Waste Using Combined Electrolysis Catalytic Exchange," Proc. Tritium

Technology in Fission, Fusion, and Isotopic Applications, Dayton, Ohio, April 29-May 1,

1980, CONF-800427, p. 422 (1980).

5. H. IZAWA, S ISOMURA, and R. NAKANE, "Gaseous Exchange Reaction of

Deuterium between Hydrogen and Water on Hydrophobic Catalyst Supporting

Platinum," J. Nucl. Sci. and Technol., 16, 741 (1979).

6. S. ISOMURA, H. KAETSU, and R. NAKANE, "Deuterium Separation by

Hydrogen-Water Exchange in Multistage Exchange Column," J. Nucl. Sci. and Technol.,

17,308(1980).

7. R. NAKANE, S. ISOMURA, and M. SHIMIZU, "Separation of Deuterium and

Tritium (in Japanese)," Gakkai Shuppan center, 1982, p. 13.

8. T. MORISHITA, S. ISOMURA, H. IZAWA, and R. NAKANE, "Tritium Removal by

Hydrogen Isotopic Exchange between Hydrogen Gas and Water on Hydrophobic

Catalyst," Proc. Tritium Technology in Fission, Fusion, and Isotopic Applications,

Dayton, Ohio, April 29-May 1, 1980, CONF-800427, p. 415 (1980).

9. M. SHIMIZU, T. DOI, A. KITAMOTO, and Y. TAKASHIMA, "Numerical Analysis

- 2 1 -

JAERI - Data/Code 94-019

on Heavy Water Separation Characteristics for a Pair of Dual Temperature ML. stage-

Type H2/H2O-Exchange Columns," J. Nucl. Sci. and Technol., 17, 448 (1980).

10. M. SHIMIZU, A. KITAMOTO, and Y. TAKASHIMA, "Numerical Analysis of

Pressure Effects on Heavy Water Separation Characteristics for a Pair of Dual

Temperature Multistage-Type H2/H2O-Exchange Columns," J. Nucl. Sci. and Technol.,

19,307(1982).

11. M. SHIMIZU, A. KITAMOTO, and Y. TAKASHIMA, "New Proposition on

Performance Evaluation of Hydrophobic Pt Catalyst Packed in Trickle Bed," J. Nucl. Sci.

and Technol., 20, 36(1983).

12. M. KINOSHITA and Y. NARUSE, "A Mathematical Simulation Procedure for a

Multistage-Type Water/Hydrogen Exchange Column in tritium System," Nuclear

Technol.,/Fusion 3, 112 (1983).

13. T. TAKAMATSU, I. HASHIMOTO, and M. KINOSHITA, "A New Simulation

Procedure for Multistage Water/ Hydrogen Exchange Column for Heavy Water

Enrichment," J. Chemical Engineering JAPAN, 17, 255 (1984).

14. M. KINOSHITA, "Simulation Procedure for Multistage Water/Hydrogen Exchange

Column for Heavy Water Enrichment Accounting for Catalytic and Scrubbing

Efficiencies," J. Nucl. Sci. and Technol., 22, 398 (1985).

15. M. Kinoshita, "Progress in Simulation Procedure for Multistage-Type

Water/Hydrogen Exchange Column," J. Nucl. Sci. and Technol., 23, 378 (1986).

16. W A. VAN HOOK, "Vapor Pressures of the Isotopic Waters and Ices," J. Physical

Chemistry, 72, 1234(1968).

17. Handbook of Chemistry (in Japanese), Nihon Kagakukai, 2nd eddition, p. 48 (1975).

- 2 2 -


Nomenclature

D : Flow rate of bottom product (mol/h)

G : Flow rate of hydrogen gas (mol/h)

J: Jacobian matrix (-)

K : Equilibrium constant of reaction (-)

L : Flow rate of liquid water (mol/h)

N : Total number of sieve trays (-)

No : Feed tray number (-)

O : Flow rate of feed stream (mol/h)

P : Total pressure (Pa)

p* : Vapor pressure of pure component for water (Pa)

R : Reflux ratio = (V+G-D)/D (-)

T : Temperature (K)

Tav : Temperature of hot-water bath (operating temperature) (K)

Te : Temperature at electrolysis cell (K)

U : Flow rate of side stream of water (mol/h)

V : Flow rate of water vapor stream (mol/h)

v : Flow rate of water vapor stream from electrolysis cell (mol/h)

X : Atomic fraction of element in liquid water (-)

x : mole fraction of component in liquid water (-)

Y : Atomic fraction of element in water vapor (-)

y : Mole fraction of component in water vapor (-)

Z : Atomic fraction of element in hydrogen gas (-)

z : Mole fraction of component in hydrogen gas (-)

ZF : Atomic fraction of element in feed water (-)

zF : Mole fraction of component in feed water (-)

a : Murphree-type scrubbing efficiency (-)

• 2 3 -

JAERI- Data/Code 94-019

y : Murphree-type catalytic efficiency (-)

Subscripts

i: Component or element index

1 : HD, HDO; 2 : H2, H2O; 3 : HT, HTO; 4 : D2 , D2O; 5 : DT, DTO; 6 ; T2, T2O

H : Hydrogen; D : Deuterium; T : Tritium

j : Tray index

Superscripts

eq : Equilibrium composition

k : Iteration number

in : Entering

out: Leaving

For Instance,

x™' : Mole fraction of HDO in liquid water stream leaving j-th tray

Yp"j : Atomic fraction of deuterium in water vapor stream entering j-th tray

z6j : Mole fraction of T2 in hydrogen gas leaving j-th catalyst bed and going through j-th

tray

In reaction equations, 1 means liquid phase, g means hydrogen gas phase, and v means

vapor phase.

- 2 4 -


Table 1 Parameters of Equation (17)

H2

HD HT

D 2

DT T?.

*1

0.0

-26398.8

-37813.2

-49314.9

-59313.4

-68702.3

*?.

0.0

89.6065

136.751

164.266

204.941

244.687

-3578.5

-3578.5

-3578.5

-3578.5

-3578.5

-3578.5

<t>4 -54.15

-54.15

-54.15

-54.15

-54.15

-54.15

11.20

11.124198

11.075904

11.059951

11.017314

10.975612

Table 2 Parameters of Equation (18)

Kl

K2

K3

K4

K5

K6

K7

K8

K46 K4 7

K4R

Xi

-77.5

-176.0

-20.2

472.0

673.0

923.0

1072.0

1189.0

-13.0

-71.7

-35.6

•h.

1.441

1.528

1.406

-0.297

-0.434

-0.667

-0.7354

-0.669

1.419

1.469

1.397

- 2 5 -


Table 3 Input specifications for an example case

N

N 0

0 D B

P

Pressure

per Tray

R

35 30

1111 mol/h

1000 mol/h

111 mol/h

101.3 kPa

Drop

66 Pa

1.0

TB 333.15K

Feed H2O:0.9996 HDO:4.0xlO"4

Composition HTO:6.0xlO"8 D2O:4.0xl0"8

DTO:1.2xlO-n T2O: l.OxlQ-15

R = (V + G - D)/D

The values of a and y are unity.

Table 4 Calculated results for an example case

Top Product

Composition

Bottom Product

Composition

Iteration Number

Computation Time

V

V

G

H2O:0.99995

HTO:1.6xlO-10

DTO:5.3xlO"15

H2:0.99647

HT:6.0xl0"7

DT:1.4xlO-9

3

3*

2.18

1.09*

51.66 mol/h

398.1 mol/h

1601.9 mol/h

HDO:5.3xl0"5

D2O:8.2xl0-10

HD:3.5xlO-3

D2:3.8xl0'6

T2:1.4xl0-13

* Broyden's method is used.

- 2 6 -


ooo ooo ooo I OOQ. OOCT OOO

W77A\

i n

ooo ooo ooo

Ji U ooo ooo ooo

Hydrophobic Catalyst

Sieve Tray

Liquid Water Stream —• Water Vapor Stream ••• Hydrogen Gas Stream

Figure 1 Structure of multistage watei/hydrogen exchange column.

- 2 7 -

F i 'zFi

F • , zF.

JU


i Recombiner

• C M ) — • 0 - • o

fyOUt

t — Sieve Tray

!• Liquid Water , iri •Water Vapor

' ij '.yij J-1'^J •Hydrogen Gas

- Sieve Tray

H" Catalyst Bed

Sieve Tray

Electrolysis Cell

Figure 2 Model column for simulation on digital computers.

- 2 8 -

JAKHI- Data/Code 94-019

Assume (Xgj 's)1 and

Assume (Tj 's)'

Calculate x°u t ' s by Eq. (11) by Newton method

Calculate y°^'eq 's and T- 's by Eq. (16) by Newton method \\J J

No

Calculate y1.1^ , z. XT by Eqs. (14), (15), and (11) 1'J-N l , J N

Calculate y?¥fc ,y\n. , z. . sequentially by Eqs. (9), (5), and (6)

T Calculate all the values of Eqs. (8). Solve Eqs. (7) three times

• Solution is obtained

Calculate all S. 's in Eq. (22) by Eqs. (11), (16), (14), (15), (11), (9) J

(5), (6), (8), and (7), and Calculate partial derivative by Eq. (22)

Modify (X°p Vs)' and (X^T's)1 by Eq. (21)

Figure 3 Flow chart of simulation procedure.

- 2 9 -

S 5 SI fgafiift

k

n B',

ft)

•r

111

ft

1(11

I*

lit 111]

A JIS

111 Iff

f'l

f)

+

T

-e

7

ft ft - r

u 7 7

y ^

/u t

y r

•y r

n.

u

y

y

y

y

m kg

s

A

K

mol cd

rad

sr

* 3 I SI Sll (f.tp

1.'.)

If. ! ,

1

Hi

y1; ,

• ' ! - * . (

4' . '4 111

vlitt. iliM

•«u

as

*

.»« tt «t «

Hi

y y ' / 7

*

s 9 1 tv y •?

I.

111

I'l Si

'ft til

'#; 1 -A

m •'i

a £• /*;

. .*>W

»l * Hi fit

!?Hj /J 111

til y x

* It

y x

(15 14

* Itt

m i.t

lit

. .

•y

'7

7

•t

7

t y

T

•Ir

/^

«.

7

>

ft

, -

-- ^

±

y

u y '

•>

7

.

ft

n

7

y

'1

y

• /

y

/!/

r

y

1-

i .

T;

/ -

•7

-

id y

*

/ i -

-f

r

Hz

N

Pa J

W C

V

K

n s

Wb

T

H

°C 1m Ix

Dq

Gy

Sv

(liic/) SI <IW

K '

m-kg/s1'

N/m1' N-m

J / s A s

W/A

C/V

V/A A/V

V s Wb/m'

Wb/A

cd • sr lm/m'

s '

J/kg

J/kg

',)

IS 'J 1-

iB

Wi

ft

. W y

f +' fTtfc

ft . 11 . f* h 11

y

hi sj-

min. h, d •

1. L t

eV

u

leV=1.602IBx 1 0 " J

I u=1.66054x 10"kg

t />

ft *

•7

ft

- j

y

ft

— y

— /u

h v y

A b

bar Gal Ci R

rad ren>

1 A- 0.1 nm-10'°m

1 b'lOOfm''- 10""m2

1 bar-0.1 MPa-lO'Pa

1 Gal- lcm/s'^10 'm/s '

I Ci-3.7xlO'"Bq

1 R 2.58x10 'C/kg

I rad = 1 cGy -10 'Gy

1 rem--lcSv' 10 ;Hv

10" 10" 10" 10" 10' 10' 10' 10'

10 ' 10 • 10 ' 10 • 10"* 10 " 10"" 10- "

t

T

if /

*

7"

T

•e

- ) •

f 7

r

</ It

•}

7

a a' a

t]

• y

y -f 'J

( t o

/

i A 1-1-

id V

E P T G M k h

da

d c m n n

P f

a

(it:)

1. k 1 5IJ rWRS'|t(4*J SB5 US. l«lffi

ISWSbl.j 1985^1-PJirlCct ,̂<, fctt. 1 eV

i> X U- 1 u ffldfili CODATA ffl 1986^(tSJ

2. / i 4 tc ciA>'i!,

3. barlJ.

r. barnfej:

N( -10'dyn)

1

9.80665

4 44822

Ibf

0.2?4809

2.20462

1

V, Itt 1 Pn-siN-s/m'!.- 10P(.f. r *><ff/<on-s>)

I m 7 s |O'St< * I- » "* )(cm-7s)

II

»

M P a t ' l O b a r )

1

0.0980665

0.101325

1.33322 x 10"'

6.89476 x 10 '

kgf/cm'

10.1972

1

1.03323

1.35951 x 10 '

7.03070 x 10 -'

a tm

9.86923

0.967841

1

1.31579 x 10 '

6.80460 x 10 •'

mmHg(Torr)

7.50062x10'

735.559

760

1

51.7149

Ibf/in'fpsi)

145.038

14.2233

14.6959

1.93368 x 10 '

1

t

1

(1

1.1

J( -10' erg 1

1

9 80665

:S6x )[)"

4 18605

1055 06

1 35582

1 fiO'.! 18* 10 '"

kgf-m

0 101972

1

:i 67098 x 10 •

0 426H58

107 586

0 iri825!>

1.63377" 10 '"

kW-

2.77778 x

272407 x

1

1.16279 x

2 93072 x

3 76616 »

•1 45051) x

I,

11) '

10 "

10 '

10 '

10 '

10 "

<-«K,iHit/A)

0.238889

2.34270

8.59999 x 10s

1

252.042

0.323890

3.82743x10 "

Btu

9.47813 x

9.29487 x

10 '

10 '

3412.13

3.96759 x

1

1.28506 x

10 '

10 '

1 51857 x 10 "

ft • Ibf

0.737562

7.23301

2.05522 x 10*

3.08747

778,172

1

1.18171 x 10""

eV

6.24150 x

6.12082 x

2.24694 x

2.612 u x

6.58515 x

8.46233 x

1

10"

10"

10"

10"

10"

10"

1 cal - 4.18605 J<al'liW;>

- 4.184 J (fflff?)

= 4.1855 J (15 "C 1

^ 4.1868 J (fK)PK.*xv/

( I ' l l * 1 PS <«..»„/J >

- 75 kgf-m/s

- 735.499 W

(k,

1

10'°

Ci

2.70270 x 10

I

Gy

1

0.01

rad

100

1

C/kg

2.58 x 10

3876

1

Sv

I

0.01

100

1

(86£f- 12 JI 26 nffifl-)

A SI

MUUT

ION

CODE

TRE

ATIN

G AL

L TW

ELVE

ISOT

OPIC

SPE

CIES

OF

HYDR

OGEN

GAS

AND

WAT

ER F

OR M

ULTIS

TAGE

CHE

MICA

L EX

CHAN

GE C

OLUM

N

jp9504227 94-019 a simulation code treating all twelve

Documents