steady state and dynamic simulation of the iter

STEADY STATE AND DYNAMIC SIMULATION OF THE ITER HYDROGEN ISOTOPE SEPARATION SYSTEM

A. Busigin NITEK Corporation 38 Longview CRT, London, ON, Canada N6K 411 (519) 657-4914

S.K. Sood Ontario Hydro 700 University A venue Toronto, ON, Canada MSG 1X6 (416) 592-5501

ABSTRACT

four column cryogenic distillation (CD) columns with equilibrators.

Steady state and dynamic simulation studies of the ITER Hydrogen Isotope Separation System (ISS) are presented. Ontario Hydro's FLOSHEET code has been used as the reference code for design studies of the ISS. Dynamic simulations were also carried out using Ontario Hydro's new DYNS IM code. Both codes have been verified against experimental and operating data from operating distillation systems. The DYNS IM code was used to model closed-loop control of the ISS under start-up conditions. The ITER ISS is expected to almost always operate under non-steady-state conditions. Start-up is of particular interest because it defines an upper bound of time to steady state for the system. Normal operation involves feed and product flow adjustments, which are much shorter term perturbations to the system. The simulated control scheme for ITER is similar to Princeton University's TFTR Tritium Purification System (TPS), which has recently been successfully commissioned.

The reference DW + VPCE + CD design option selected by the ITER-JCT is based on proven technologies. In addition, the design is based on permeation of 1000 Ci/h into the divertor coolant and production of 95% T 2 product from the last column of the ISS. The intent is to cascade about 100 to 120 kg/h of waste water at about 0.1 Ci/kg (produced from atmospheric detritiation, etc.) into the divertor and take an equivalent feed from the divertor at 1O Ci/kg into the water distillation column DWI. This enables effective detritiation of the divertor, while limiting the OW system to detritiation of a single feed. An enriched stream from the bottom of this column at about 300 Ci/kg is sent to a 2-stage VPCE where it is catalytically exchanged with recirculating H 2 gas whose sole function is to strip tritium from the water so that the DW overheads are suitable for discharge to the environment.

For the ITER ISS, dynamic simulation is important because it allows study of product quality control schemes and control system design. It also allows accurate assessment of tritium inventory variation in different operating modes. The cryogenic distillation model in the new DYNSIM code is described here in detail, including the underlying theory and numerical simulation approach. The discussion also addresses the suitability of different ISS design tools in terms of the design process, as well as HETP versus mass transfer modelling approaches. I. INTRODUCTION The design of the ITER Isotope Separation System has recently been described in detail 1• The reference design is based on steady state simulations using the FLO SHEET simulation code2 • The integrated process is composed of 2 water distillation (DW) colwp.ns, a twostage vapour phase catalytic exchange (VPCE) unit, and

544

3

In addition to the feed from the VPCE, the ISS has three more feeds, and an H 2 flow of 200 mol/h from the impurity purification system (e.g. using the HITEX process), a plasma exhaust feed and an NBI feed. The design considers two options - cycling 40% and 10% of the plasma exhaust through the ISS (32 mol/h and 8 mol/h, respectively). The NBI feed consists of 60 mol/h of contaminated D 2 recycled for tritium recovery. The CD system consists of a 4 column cascade, of a similar design to the Princeton TFTR TPS. A pure H 2 stream from the overhead of CDl is recycled to the VPCE, a pure D 2 stream is produced from CD3, and the T 2 product is withdrawn from the bottom of CD4. Two CD4s are included in the system, and are supposed to. be valved in for the 10% and 40% plasma recycle feeds, as required.

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II. FLOSHEET STEADY ST ATE SIMULATION Steady state simulations of the entire integrated ISS were performed using the FL0SHEET code. Specifically, using the ITER JCT reference design as a starting point, a large number of FL0SHEET runs were made to optimise the design for lower tritium inventory. The effects of sidestream equilibrators, nonidealities in the liquid hydrogen isotopes, and decay heat of tritium were taken into account. The optimisation was done using the same hold-up per stage assumptions as for the ITER JCT design. In the first series of optimisation runs, based on an earlier (May 1994) ITER JCT design, the tritium inventory was reduced from 180 g of tritium to about 130 g. This was achieved by adding more stages to CD3 and by increasing some of the side-stream equilibrator flows. This effectively pulled inventory from the larger CD2 into the smaller CD3 column, thus reducing overall inventory. The inventory in the last column CD3 of the JCT-I design was optimised by optimising side-stream equilibrator location, and adding an extra equilibrator to the column. Subsequently, the ITER JCT design was modified to meet new specifications. This revised design (February 1995) has about 130 g of tritium inventory. Further optimisation runs (more than 100) on this new configuration have identified methods to reduce the tritium inventory to near the I 00 g value. The net result is a large overall inventory reduction of tritium, which is quite significant in monetary as well as safety credits. A similar optimisation (OPT-III) for the current JCT reference design (JCT-II) has reduced the tritium inventory to near the I 00 g value. While the absolute magnitude of the tritium inventory still has to be verified, this optimisation, involving 100 or more rigorous FL0SHEET simulations, clearly illustrates the value of such an exercise. III. DYNSIM DYNAMIC SIMUtATION Dynamic simulation of the ITER ISS is useful because the system will almost never run under steady-state conditions. Dynamic. simulations require more computation time than steady-state simulations but they provide more information. Thus they complement the quicker but more limited steady-state simulations. The combination of steady state simulations for parametric design studies and dynamic simulations for more detailed analysis results in an effective set of design tools. There have been several other dynamic simulation codes developed for distillation columns 3'4 '5 , but few have been tailored like DYNS IM for the special requirements of hydrogen isotope separation. DYNSIM is unique in that it also includes a water distillation simulation model, feedback controller models, and integrated BASIC like

ITER HYDROGEN ISS SIMULATION

programming language for setting up simulations of arbitrary complexity. A VPCE model for DYNSIM is also largely complete, but has not yet been fully integrated with the rest of the code. The main features of the DYNS IM code distillation column model are described below, including underlying theory and numerical algorithms. The discussion focuses on the cryogenic distillation portion of the code, since this is of central importance to the ITER ISS. Specific ITER simulation results are presented. IV. DYNSIMCRYOGENIC DISTILLATION MODEL The usual approach for dynamic simulation of a distillation column is to adopt the theoretical plate model and carry out stage-by-stage calculations. This is the approach taken in DYNSIM. The alternative approach of developing a mass transfer model of the countercurrent liquid and vapour exchange within the column was considered in the initial development of DYNS IM. However, since in practice the theoretical plate model is very successful, it was concluded that there is little to be gained by alternative approaches. In any case, the models must be related to experimental data to enable them to be used as practical design tools. There is more published data available for theoretical plate models, making them the clear favourite. The DYNSIM distillation model is a fully rigorous distillation model. It does not use any short-cut approximations to speed up the calculations. In the limit where a dynamic model is simulated for long enough to reach steady state, the DYNSIM code gives the same results as the FLO SHEET steady-state simulation code. . The DYNSIM model equations are based on mass, species and energy balances around each stage. Each stage is a theoretical plate with stage l a partial condenser and stage N the reboiler. The vapour and liquid flowrates of component i leaving stage n are v n,, and / n.,. There are assumed to be T) components. (For hydrogen isotope distillation, the components i are usually numbered I through 6 corresponding to H2 • HD, HT, D 2, DT and T 2.) The vapour flow is to the previous stage n - l and the liquid flow is to the next stage n + 1 . The total liquid and vapour flows leaving stage n are l n and v n. The component flows are Vn., =_vn,,vn where Yn.i is the mole fraction of species i in the vapour leaving stage n, and l n.i = x n,;I,, where Xn,i is the mole fraction of species i in the liquid leaving stage n . The liquid and vapour feeds of component i to stage n are /,,,; and v'.:., . The total liquid and vapour feeds are

,;,; =}>/,; i=!

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anct

l=fr~,i=!

,

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ITER HYDROGEN ISS SIMULATION

The total liquid and vapour product withdrawal rates from stage n are /~ and v~. The liquid and vapour withdrawal rates for component i are /~,; and v~,;. Several simplifying assumptions are made in the development of the distillation column model: The column is adiabatic.

2.

The molar hold-up in each stage is constant throughout a given time interval. (Assuming constant liquid holdup by volume is not significantly more complicated and gives similar simulation results.)

3.

The HETP (height of packing equivalent to a theoretical plate) in the column is constant over time. HETP may be different in different sections of a column.

For a dynamic simulation, the time period in question is divided into a series of time intervals At m which are not necessarily equal. Calculations are carried out over each time interval one at a time and in order. For each time interval, everything about the column must be known at the beginning of the time interval t =Im, and then the operating variables for the end of the time interval t = t m + At m are calculated. For the first time interval Ato, information fort= to is assumed to be specified. Component material balance equations are developed by performing a component flow balance around general stage n as follows aq n,i I I .f f -ani, +Ln,·, +Vn-,·t =Vn+Ji, + n-Ji-Vn;, , ,

Id

d

ni-Vni• , ,

where q n,i is the hold-up of component i in stage n. Assuming that the total molar hold-up in each stage is fixed, the overall mass balance that must be satisfied is =Vn+J

+ln-1-Vn-ln+ln+ln-1~-v~=O.

It follows from these relations that

I: aqn,i =0. at i=I

Given the column pressure and the composition of the liquid phase of each stage, the temperature and composition of the vapour in equilibrium with the liquid can be determined by the vapor-liquid equilibrium relationship. The liquid mole fraction of component i on stage n is calculated from the liquid hold-ups qn,;according to

qn,i

The vapour mole fractions are then calculated from:

546

Sn,iP;

~ X n,i

=

K

[AG; +B;(p~ RTn

-PnJ] .

where AG; is the partial molal-excess Gibbs free energy of mixing with respect to component i at temperature T,,. B; is the second virial coefficient (m 3/mole) of component i, and R=8.31433 J/(mole K) is the universal gas constant. A heat balance for each stage is important since there is a significant difference in the heats of vaporisation for different hydrogen isotopic species. For systems containing a significant quantity of tritium, the radioactive decay heat of tritium is also significant and must be included in a heat balance. The decay heat of pure T 2 is l.954 W /mole. In a packed cryogenic distillation column producing very pure T 2 , the total radioactive decay heat may be comparable in magnitude to the reboiler and condenser duty of the column. The total radioactive decay heating rate for stage n is

E~

= 1. 954[ ½(qn,3 + qn,5) + qn,6].

Heat balance calculations adjust total liquid and vapour flowrates leaving each stage. Since the vapour inventory of a stage is negligible in comparison to the liquid inventory, the total enthalpy of stage n is approximately Hn =H~qn

where H~ is the specific liquid enthalpy (J/mole) for stage n. The rate of change of H n with time is aHn ,.,q,, aH~ =qnI: aH~ aqn,;. at at i=I aqn,i at

In this equation, the partial derivatives aq,,,;Jat are determined by the material balance. (The above equation has been derived assuming that the inventory qn of each stage is fixed.) The heat balance for the general stage in terms of material flows, heating or cooling, and tritium decay heat effects is aHn - HIn-1 I n-1- HIn(I n+ /dn)- If".( d Ttn Vn+Vni + H::+1 Vn+J + H} fn + H/J,; +En+ E~.

E~ is the radioactive decay heating rate in stage n, and En is the external heating/cooling rate in the stage.

Xn,i=~. "-i qn,i

Y n,i =

~ _

~n., - exp

1.

a:tn

where P~; is the pure component vapour pressure (Pa) of species i, P n is the total pressure (Pa), and Sn,, is the nonideality coefficient for species i. The nonideality coefficient Sn,; is estimated using the procedure6 •7

n,;X

n,i

The first stage in the column is the condenser, and the condenser duty E1 (negative since it corresponds to heat removal) is assumed to be known. The rate of liquid flow down from the condenser is calculated from the rate of condensation corresponding to the condenser duty. The

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Busigin and Sood feed and product rates are assumed to be under external control. The vapour flow up from stage 2 is calculated to satisfy the stage mass balance. For a condenser, n = I, v1 = 0 and/= 0 since there is no stage 0. Heat balance calculations are started at the condenser and progress downward. For an intennediate stage, all the flows are known except In and Vn+I • These two flows may be solved for by arranging the overall mass balance and heat balance equations into the fonn: Vn+J

-ln =-ln-1 +vn-fn-/n+!~ +v~

and

H;".+1vn+1-H~ln =-H1,,._ 11n-1 +H",,vn-H;/f,,_J/;,v✓,; + H~I~ + H",,v~ - En - E~. Since the right-hand-sides of these two simultaneous equations are known, one can solve for Vn+J and In. For a reboiler, n = N, Vn+1 = 0 and In= 0 since there is no stage N + l . Flow calculations are started at the condenser where all the variables are known except vn+1. The calculation proceeds by stepping down the column perfonning heat and mass balances. The reboiler duty is calculated from a heat balance around the last stage N.

V. NUMERICAL METHODS The numerical integration problem is best expressed in vector and matrix notation by defming an independent variable vector z which defines the state of the system. Each vector element Zn of z is itself a vector defined for stage n. The components z n,; are related to the species hold-ups on stage n according to Zn,i

= ln(q,,

~~n,,) = ln(i ::nJ.

Therefore, z is a vector of subvectors [z1 ,z2, • • •, ZN]T, where N is the number of stages in the distillation column. The model is formulated in terms of logarithmically transformed variables because the magnitude of the components may vary by many orders of magnitude, but is always greater than zero. By dealing with the logarithmically transformed variables, the magnitudes of all the components of the vector Zn are comparable, making the numerical algorithms for the simulation more well conditioned. From the definition of component i of vector follows that

azn,;

ar=

[ 1

I

Xn,i+l-xn,i

]axn,i [ ai=

1

l

Zn,

]aqn,;

qn,i+qn-qn,i

The vector z and its rate of change with time are:

Tt·

it

ITER HYDROGEN ISS SIMULATION ZJ

Z

=

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Z3

az2/at

and f=

az3/at

where

t~ =f(z, u(t)) and u(t) is the vector of independent control variables. Given z 0 =z(t = 0) and f, this non-linear system of differential equations can be integrated numerically. The simplest approach is to use an explicit algorithm with sufficiently small step size M such that the integration is stable. The approach that is used in DYNSIM is a semi-implicit method, which has much better stability and accuracy when employing larger step size 8•9 • In the notation adopted here, the value of z after time step m is denoted as zm . Initially m = 0. The value of z after the next time step (at tm+1 = tm +,Mm) is given by: zm+l

= zm + Mm[(l -

µ)fm(zm) + µfm+l (zm+l )] .

The adjustable parameter µ is chosen to provide an appropriate balance between explicit and implicit numerical integration. Ifµ = 1 then the integration is fully implicit (albeit for a linearized model of the system). If µ = 0 then the integration is fully explicit. For intennediate values of µ the numerical integration is semi-implicit. The value µ = 0.5 corresponds exactly to the trapezoidal rule for numerical integration. Generally, an implicit method(µ close to l) provides better stability than an explicit method (µ close to O) when taking a large step Mm. For moderate step sizes, choosing µ = 0.5 gives better accuracy. However, very large step sizes may sometimes be desirable when one is only interested in a steady-state solution (t • 00) and accuracy of the trajectory to the steady-state solution is unimportant. In this case only the stability of the method is important and it is best to set µ = I . Although 1he semi-implicit step described above is unconditionally stable for sufficiently small At, the calculation of

requires iterative solution of a system of non-linear equations. The value of rm-t-1 is not known at the beginning of the iteration, but is solved for by the Newton-Raphson (NR) method8 • To apply the NR method, the function to be zeroed after k iterations is defined as ek =z;+"

FUSION TECHNOLOGY

az1/at

z2

1

-

zm -Mm[ (1- µ)fffl +µf;+"

1

].

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Busigin and Sood

ITER HYDROGEN ISS SIMULATION

Now, given the k-th estimate zf+~ 1 for zm+I, the (k+ 1)-th estimate is calculated from m+l m+l J-1 Zk+I =zk k ek, where the Jacobian matrix is 1 af;+ aek Jk= a m+l =1-µh.tma m+l. zk

zk

and I is the identity matrix. The iteration continues until the error ek is sufficiently small such that llekll = Emaxllzmll, where the norm is Euclidean and the parameter Emax is the maximum allowable normalised error as discussed below. The step size fl.t is adjusted to maintain accuracy. The approach taken is to set µ = 0.5 for the balance between explicit and implicit integration, since this corresponds exactly to the trapezoidal rule. The trapezoidal rule has an error proportional to (M) 2. If the step size is reduced to M/2, then the error is reduced by a factor of 4. If we designate the value of zm+I calculated by a single step of Mas k1 and the value calculated by two half-steps M/2 as k 2 , then an improved estimate for zm+1 is given by the extrapolation zm+I ""k3 = ½[4k2 - ki]. This extrapolated value zm+ 1 has an error proportional to (fl.t)-1. The magnitude of the normalised error can therefore be estimated from

1 E"" 16

llk3 -kill llk3II

or E < O. lEmax then the step-size is increased or decreased to 0M where

r

4

The step-size is not increased past a specified value At max, which normally corresponds to the time interval during which there are no column control adjustments such as changes in feed or product flow rates. The numerical integration algorithm described above has been found to be simpler and more effective than Gear's general purpose algorithm9 • VI. ITER ISS STARTUP SIMULATION The ITER ISS start-up has been simulated to study the dynamics of the system. Initially, the cryogenic distillation system is assumed to be filled with pure D 2• This is a common practice to calibrate all the temperature diodes in the system. Feed and product flows are then

548

At start-up with pure D 2, there are no concentration profiles within the distillation columns. Therefore, buildup of hydrogen and tritium is required before the system can run in a steady manner. Start-up dynamics provide an upper bound estimate of the time for the ISS to stabilise. Process upsets due to starting and stopping of individual feed streams would be much shorter in duration. Figures 1, 2 and 3 show the H 2 , D 2 and T, product qualities as a function of time from start-up (t = 0). The simulation corresponds exactly to the design of the system described in Reference 1. Product quality is controlled by feedback control using proportional controllers which are assumed to measure tritium level in the product streams. CD1 H2 Product Composition

1 E-5 c 0

1 E-10

~

~

1E-15

• • • • • • - - - - - - • • · · · - - - - - - - - - - - - - - - - - - - - ·1

~ ...

:::E 1 E-20

-

--------------------------

---- -- --

1E-25 1 E-30

A practical error limit for most distillation simu1ations is Ema, < 1. 0 X 10-6 . lffor a given step-siz.e the error E > Emax

e = [ ½E~ax

started, with product rates on feedback proportional control. Feed and intercolumn flows are adjusted by flow controllers to maintain column inventories at design levels even though product rates vary. Flow control adjustments use the same strategy as successfully tested in operation of Princeton's TFTR TPS.

I 0

2

4

6

8

10

12

14

Time(h)

Figure 1. CD l hydrogen product composition during ITER ISS startup. It is interesting to note that the tritium product from column CD4 reaches steady state in less than two hours, whereas the hydrogen and deuterium products require approximately 12 hours to stabilise. This difference is due to the much smaller size of CD4 as compared to the other larger columns, and also due to the multiple equilibrators which effectively crack the DT species in CD4. The HT concentration in the CD 1 hydrogen product rises and then falls over the first fours hours. The decline only begins when the column CDl accumulates sufficient hydrogen to allow the HT species to come down to the equilibrator in CD 1. This suggests that it may be advantageous to preload CD 1 with hydrogen before feeding tritium to the system. The CD3 deuterium product has a slightly higher HT concentration than the FL0SHEET steady state simulation

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result. This is because the simulated feedback control is not exactly identical to the steady state simulation. The control algorithm can be easily adjusted to give identical flows and identical results. However, the results also suggest that it may be advantageous to modify the design to return the recycle stream from the top of CD4 to the bottom of CD l, instead of to CO2. The compositions are compatible, and this would eliminate the migration of HT back from CD4 through CO2 to CD l. This minor change may improve the CD3 D 2 product quality.

The cryogenic distillation portion of the DYNS IM code for hydrogen isotope separation is described in detail. Both the distillation column model and numerical integration technique are described. Criteria are also given for integration step-size control and for achieving desired simulation accuracy. The DYNS IM code is applied to simulating the startup of the ITER ISS. The results show that tritium product quality stabilises in less than two hours. Hydrogen and deuterium products require twelve hours to stabilise. The ITER ISS simulation also demonstrates that if CD 1 has too little hydrogen, then the HT species contaminates the hydrogen product. Preloading of the column with appropriate amounts of hydrogen and deuterium can therefore improve product quality during initial operation.

CD3 D2 Product Composition D2

0.01

ITER HYDROGEN ISS SIMULATION

· · - - - - - - - - - - - - - - - - . - - - - - - - - - .... _ ..... __ . ___ _

HD

C:

'5).0001

ACKNOWLEDGEMENTS

e!

u.

H2

This work was financially supported by Ontario Hydro, Canadian Fusion Fuels Technology Project, and NITEK Corporation.

~1E-06 ~

1E-08

1E-10

REFERENCES

.jl..LL-+--+---+--+--+----+---+----,-+--+-----, 12 14 10 2 4 6 8 Time (h)

0

1.

R. Haange, H. Yoshida, O.K. Kveton, J.E. Koonce, H. Horikiri, A. Busigin, S.K. Sood, C. Fong, and K.M. Kalyanam, "Design of the Water Detritiation and Isotope Separation Systems for ITER", Paper to be presented at the 5th Topical Meeting on Tritium Technology, Belgirate, Italy, May 28-June 3, 1995.

2.

A. Busigin and S.K. Sood, FLOSHEET -- A Computer Program for Simulating Hydrogen Isotope Separation Systems", Fusion Technol. 14, 529 (1988).

3.

J.F. Davis, "Dynamics and Control ofa Packed Distillation Column for the Isotopic Enrichment of Plasma Exhaust from Controlled Thermonuclear Reactors", M.Sc. Thesis, Northwestern University, Evanston, Illinois (1978).

4.

C.D. Holland, "Unsteady State Processes with Applications in Multicomponent Distillation", Prentice-Hall, New Jersey (1966).

5.

M. Kinoshita, "Drastic Reduction of Computing Time for Hydrogen Isotope Distillation Columns", Fusion Technol. 9, 492 (1986).

Figure 3. CD4 tritium product composition during ITER ISS startup.

6.

P.C. Souers, "Cryogenic Hydrogen Data Pertinent to Magnetic Fusion Energy", UCRL-52628 (1979).

VII. CONCLUSIONS

7.

P.C. Souers, "Hydrogen Properties for Fusion Energy", University of California Press (1986).

8.

W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, "Numerical Recipes", Cambridge University Press (1986).

9.

C.W. Gear, ''Numerical Initial Value Problems in Ordinary Differential Equations", Prentice-Hall (1971 ).

Figure 2. CD3 deuterium product composition during ITER ISS startup. CD4 T2 Product Composition

OT 0.01

5

D2

'§l,0001

e!

u. ~ 1E-06

-· -·-- --

~

1E-08

1 E-10 -+'------+----+---l"---+-----t----t----1 0

0.5

1

1.5

2

Time (h)

FLOSHEET optimisation studies to reduce the tritium inventory of the ITER ISS are described. Significant reductions in tritium inventory have been made. Total ISS tritium inventory of approximately 100 g now appears feasible. The value of optimisation studies is thus clearly demonstrated.

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