COMPUTER SIMULATION OF THE WATER AND HYDROGEN DISTILLATION AND CECE PROCESS AND ITS EXPERIMENTAL VERIFICATION

COMPUTER SIMULATION OF THE WATER AND HYDROGEN DISTILLATION AND CECE PROCESS AND ITS EXPERIMENTAL VERIFICATION Oleg A. Fedorchenko Ivan A. Alekseev Veniamin D. Trenin Vadim V. Uborski Petersburg Nuclear Physics Petersburg Nuclear Physics Petersburg Nuclear Physics JSV "DOL" Institute Institute Institute Gatchina, Leningrad district, 188350 Gatchina, Leningrad district, 188350 Gatchina, Leningrad district, 188350 OMIKRON Box 1, Troitsk, Moscow district, 142092 RUSSIA RUSSIA RUSSIA RUSSIA +7-812 -7131985 +7-812 -7130275 +7-812 -7131985 +7-095 - 9166860 ABSTRACT Mathematical simulation procedures have been developed for three processes of hydrogen isotopes separation: 1) a non steady-state water distillation; 2) a cryogenic distillation; 3) combine electrolysis and multistage water/hydrogen catalytic exchange (CECE) process. The simulation procedures possess some special features. Thus, the comparatively large step of integration and as a result of this high fast-acting is the peculiarity of the model for the dynamic behaviour of water distillation column operating at total reflux. The simulation procedure for CECE process considers six components and three phases (liquid water, water vapour, and hydrogen gas) and allows to carry out computations for any mole fraction stock. This procedure, as the one for cryogenic distillation process, is not based on the Newton- Raphson method, and, in spite of this, convergence is reached by a small number of iterations (4-11). I. INTRODUCTION The Detritiation Plant design was developed at Petersburg Nuclear Physics Institute for the tritium and protium extraction from heavy water of reactor PIK. Now the design of the Plant for Reprocessing contaminated tritium light and heavy water wastes is being developed. Both rigorous calculations and project initial data experimental control are necessary for successful fulfilment of this work. The non steady-state water distillation is comparatively simple method of heavy water enrichment especially for reprocessing of small amount of definite mole fraction stock. The usual approach for calculating of the process requires the step of integration less 1 second and hence - considerable computer's time. The present report suggests the idea allowing to calculate the process much more rapidly. There are a number of reports describing computer simulation procedures for cryogenic distillation 1,2 and CECE process 3,4. These procedures are based either on the successive iteration method, which does not always present adequate stability in achieving convergence, or on the Newton-Raphson method, which needs large computation efforts for the numerical evaluation of the elements of the Jacobian matrix and calculation of its inverse matrix. Another way of looking at these equilibrium stage processes is proposed in the present paper. It provides stable and relatively rapid solutions of the basic equations for both above-mentioned processes. For example, approximately 10 seconds are required for computation of a seventy tray catalytic exchange column with six components on an IBM PC 486DX 33. II. A NON STEADY-STATE WATER DISTILLATION The column operating at total reflux is studied. The column is assumed to be composed of N theoretical stages. The N+1-th stage is the condenser and the 0-th stage is the reboiler. At the beginning the column is loaded by water with deuterium concentration -- Xo. At first let's consider the case when the liquid holdup in the packed section (Vp) is small in comparison with the liquid holdup in the reboiler (Vr) and condenser (Vc) and hence is neglected. It is along this pathway that at every instant there is no accumulation of a component in the packed section and flux of isotope (J) through any section of the column is constant: where J = L (X j+1 - Y j ) = Vr dx r / dt (1) L = flow rate of liquid stream, mol/h; X j = atomic fraction of element in the liquid stream leaving the j-th stage; Fedorchenko 1

Y j = atomic fraction of element in the vapour stream leaving the j-th stage; X r = atomic fraction of element in the reboiler. It is obviously X r t = Vr dx r / J (2) Xo The relation between J and X r is readily available by numerically method: for each J out of the range [Jo.. 0] the composition distributions within the column is found by (1) calculating from stage to stage in such a way that material balance of column is held. When the function J(X r ) is determined, the time of achievement of this or that concentration in the reboiler is easily calculated using (2). The computer code "Prosto" has been developed on the base of this procedure. In the case when one must not neglect the holdup in the packet section the following equations take place: J j+1 - J j = Vs dx j / dt (3) J j+1 = L (X j+1 - Y j ) (4) where J j = the flux of isotope leaving the j-th stage, mol/h; Fig. 1 Concentration profile within the column at time 155.0 h. (See conditions in Fig. 2) Vs = liquid holdup in a theoretical stage, mol. At each instant of time such composition distribution within the column is found calculating from stage to stage by (3) and (4) that material balance of column is held like just considered procedure for the case when the Vp is neglected. Such calculations are repeated from the beginning of the process consecutively with some step t. The time derivative in the equation (3) is replaced by ratio of the concentration increase in the j-th stage to the time step. The computer code "NestRect," that uses just mentioned procedure, allows to work with time step about 1 hour, whereas the step of integration less 1 second is required in the ordinary way, in which no special efforts for the holding of material balance are applied. Graphic possibilities of the Turbo - Pascal are widely used in the code "NestRect". The diagram of concentrations in the reboiler and condenser in relation to the time and also the concentration profile within the column are displayed during the calculation. The print of the screen at the moment the simulation was close to steady state is shown in Fig. 2. It is interesting that the profile of concentrations in the column is altered in time in such a way that the point of inversion -- section of the column with the concentration equal Xo -- moves across the column (Fig. 1 and Fig. 2). This fact is often overlooked whereas it holds significance because disproves the Theory of Geometrical Resemblance of Concentration Profile 5,6, which sometimes 6 is wrong used for the calculation of rate of the attainment of a steady state in the case when the condition Xo << 1 is not met. Dynamic behaviour of the water distillation column (80 mm inner diameter, 10 m height, stainless steel spiral prismatic packing) has been studied. Good coincidence computer simulation with the experiment is clearly seen from diagram in Fig. 2 on which the experimental points are plotted. In addition to this, points calculated by code "Prosto" are plotted too. III. STEADY-STATE PROCEDURE FOR CRYOGENIC DISTILLATION COLUMN WITH A FEEDBACK STREAM AND CATALYTIC EQUILIBRATOR The mathematical simulation procedure has been developed for a single cryogenic distillation column with a feedback stream and catalytic equilibrator used for hydrogen isotope separation. The computer programme "Cry_En" has been created on its base. Nonidealities of the hydrogen isotope solutions and heat balance are incorporated. The model column for mathematical simulation is shown in figure 3. The initial data for the computation: N - the number of theoretical stages; P - pressure in the top of the column [kpa]; P - pressure drop across the column [kpa]; Fedorchenko 2

Bot - flow rate of bottom product [kmol/h]; Top - flow rate of top product [kmol/h]; W = Bot + Top - flow rate of the gas external feed stream [kmol/h]; Aw1, Aw2, Aw3 - composition (atomic fractions of protium, deuterium and tritium) in the external feed stream; Tw - temperature of the external feed stream [K]; Nw - feed stage number for the external feed stream; Ns - side stream stage number; Ws - flow rate of the gas side stream [kmol/h]; Nws - feed stage number for the equilibrated stream; Tws - temperature of the equilibrated stream [K]; R - reboiler load [kw]; Q - heat subtraction rate per stage [W]. The steady-state simulation procedure for cryogenic column is composed of the following components: 1) Catalytic Equilibrator model; 2) BeComp procedure allowing to determine profile of concentration of a component when separation factor and flow rates of all streams are given for each stage; 3) Temp procedure which defines the temperature in a stage taking into account vapour and liquid nonidealities when pressure and composition are known; 4) Heat Balance procedure for a more precise definition of flow rates of liquid and vapour streams. Fig. 3 The model column for mathematical simulation. Fedorchenko 3

The simulation procedure is realised in the following way. STEP 1. Input of all initial data and determination equilibrium composition in external feed stream. STEP 2. The definition of the temperature in the feed stage and the calculation of the separation factor for each of six components. These values are given to all stages. STEP 3. The determination of the flow rates of liquid and vapour streams from the heat balance for the reboiler and material balance for the column. STEP 4. The concentration profiles within the column are calculated using BeComp for each of six components. STEP 5. The calculation for each stage, reboiler and condenser: 6 Sj = X[j,i], i=1 where X[j,i] - mole fraction of i-th component in the liquid stream living j-th stage. STEP 6. If N+1 Sj / (N+2) - 1 ε, 0 < ε << 1 j = 0 then go to STEP 8. STEP 7. The normalisation: X[j,i] = X[j,i] / Sj. The calculation of composition after the equilibrator. The calculation for each stage of: the temperature, new separation factors and new flow rates for liquid and vapour streams. Go to STEP 4. STEP 8. Convergence is achieved. Output of: calculated composition in the top product and bottom product; composition distribution within the column; temperature profile; composition of the equilibrated stream. A few words about the procedure BeComp. It is stage-to-stage procedure like the one for water distillation. The calculations are carried out in the direction to feed stage from bottom and top in order to reduce the truncation error. The calculation conditions and the results for two examples are given in Table 1, Table 2 and Table 3. The case 1 shows the possibility of cryogenic column for tritium removal from heavy water used as moderator for nuclear fission reactor. Thus in this case the decontamination factor is equal 424. The case 2 may be considered as the example of the first stage of the heavy water waste contained tritium reprocessing. It is observed from Table 3 that tritium decontamination factor is equal 2.8 10 4 whereas the deuterium atomic fraction in the Top is sufficiently high due to HD. Table 1 Calculation conditions for two cases. Case 1 2 N 80 80 Nw 40 40 Ns 75 - Nws 40 - R, kw 2.0 2.0 Q, W 7.5 5.0 P, kpa 150 150 P, kpa 6.0 5.0 Bot, mol/h 10 200 Top, mol/h 200 200 Ws, mol/h 100 - Tws, K 25.2 - Tw, K 25.2 23.5 Aw1, Aw2, Aw3 0.002, 0.99798, 2e-5 0.499999, 0.5, 1e-6 The number of iteration 8 8 The time of calc. * 2 m 36 s 2 m 39 s Case 1 Table 2 Results of calculation in the case 1. Feed Composition Before Equilibrator After Equilibrator Bottom Top H2 4.89e-6 2.63e-7 1.40e-7 2.6e-21 5.08e-6 HD 3.99e-3 6.75e-4 6.75e-4 1.0e-10 4.19e-3 HT 7.28e-8 2.50e-8 3.2e-11 7.6e-12 6.39e-8 D2 0.9956 0.9993 0.9993 0.9992 0.9958 DT 3.99e-5 7.84e-8 1.03e-7 8.38e-4 3.05e-8 T2 4.2e-10 1.5e-15 2.8e-15 8.82e-9 2.3e-16 ah 0.0020 3.38e-4 3.38e-4 5.4e-11 0.0021 ad 0.9980 0.9997 0.9997 0.9996 0.9979 at 2.00e-5 5.17e-8 5.17e-8 4.19e-4 4.72e-8 Table 3 Results of calculations in the case 2. Case 2 Feed Composition Bottom Top H2 0.2626407 7.60e-10 0.5252815 HD 0.4747156 0.4747127 0.4747185 HT 9.02e-7 1.805e-6 7.22e-11 D2 0.2626416 0.5252833 1.420e-8 DT 1.098e-6 2.195e-6 2.47e-17 T2 1.20e-12 2.41e-12 1.74e-26 ah 0.4999990 0.2373573 0.7626407 ad 0.5000000 0.7626407 0.2373593 at 1.00e-6 2.00e-6 3.61e-11 * The IBM PC 486 DX 33 time Fedorchenko 4

A number of calculations were made under experimental conditions that are presented in Reference 7. The results obtained by "Cry_En" are in a good agreement with experimental observation. The conclusion is that although the proposed simulation procedure needs further enhance (to make shorter computation time), it allows to carry-out calculation of a single cryogenic column in a wide range of conditions. IV. SIMULATION PROCEDURE FOR CECE PROCESS The mathematical simulation procedure has been developed for multistage water/hydrogen exchange column (CECE process). The algorithm of this procedure is very much alike to the one of the procedure for cryogenic distillation column just considered. But it has its own specific features, such as: 1) presence of three streams (liquid water, water vapour and hydrogen gas); 2) occurrence of exchange reactions and much more complex column configuration; 3) the material balances for the six molecular species (H 2 O, HDO, HTO, D 2 O, DTO, T 2 O) do not hold and that's why the calculation using the procedure BeCompE is carried out not for each of six components, but only for three atomic fractions (ah, ad, at); 4) the temperature on each of the tray is not calculated but given as initial condition ; 5) presence of the Exchange procedure which allows to define the equilibrium water composition (6 species) in each tray and equilibrium gas composition (6 species) after each catalyst bed and calculates new separation factors both for the water/vapour scrubbing step and for the catalytic exchange step which are used by the BeCompE procedure ; 6) the consideration of the heat balances is not needed. A model column composed of N trays and (N-1) catalyst beds is illustrated in Fig. 4. The computer code "KIO" has been created on the base of the considered procedure. The case 3 in Reference 4 required more than 1000 iterations for the Successive iteration method ( Nonconvergence -- see Table 2 in Ref. 4) and only 4 iterations for the Newton- Raphson method. The case that is very close to this case (see Fig. 4) requires 4 iterations and 8 second for its calculation by code "KIO" on the IBM PC 486DX 33. The results are given in Table 4. Hence we can see that presented method is as good as the Newton-Raphson one in this instance. The case 4 given in Table 5 is interesting from the point of view of the heavy water waste contained tritium reprocessing. Thus in this case (Table 6) we obtain heavy water as the bottom product that can be used for fission nuclear reactors and the raw material as the top product for further reprocessing with the aim to derive the heavy water containing a small tritium amount. The case 5 demonstrates good possibilities of CECE process for the heavy water waste reprocessing. G, W, Bot, Top [kmol/h] G - flow rate of hydrogen gas W - feed flow rate Bot - flow rate of bottom product Top - flow rate of top product Temperature [degrees Centigrade] Tb - operating temperature at the bottom Tt - operating temperature at the top Tc - condenser temperature N - the number of tray Nw - feed tray number N = 60 Nw = 20 Atomic fractions of elements in feed water: ah = 0.899999 ad = 0.1 at = 0.000001 The pressure at the top P = 105.3 kpa The pressure drop across the column P = 4 kpa Fig. 4 The model of CECE process with initial data for the case that is close to the case 3 from Reference 4. Table 4 Results of calculations in the case 3 4. Case 3 4 Feed Composition Bottom Top H 2 O 0.8102534 0.0245763 0.9658506 HDO 0.1794894 0.2609214 0.0338435 HTO 1.793e-6 3.054e-6 7.29e-10 D 2 O 0.0102552 0.7144823 0.00030586 DTO 2.07e-7 1.694e-5 1.34e-11 T 2 O 1.06e-12 1.01e-10 1.47e-19 ah 0.8999990 0.1550385 0.9827724 ad 0.1000000 0.8449515 0.0172276 at 1.00e-6 1.000e-5 3.71e-10 Fedorchenko 5

The numerical analyses on the base of the programme "KIO" generally agree with experimental data, which have been obtained during experiments on the model installation described in Ref. 8. The authors hope that in the near future the paper wholly dedicated to the considered model will be published where the detailed analysis on wider experimental base will be done. Table 5 Calculation conditions for two cases. Case 4 5 N 70 90 Nw 22 45 P, kpa 110 110 P, kpa 10.0 10.0 Bot, mol/h 30 50 Top, mol/h 15 50 G, mol/h 220 220 Tb, C 78 85 Tt, C 78 84 Tc, C 20 20 ad, at 0.8, 1.00e-7 0.5, 1.00e-5 The number of iteration 3 7 The time of calc. 6 s 20 s Table 6 Result of calculations in the cases 4 and 5. KIO Case 4 Case 5 Feed Bottom Top Feed Bottom Top H 2 O 0.0407 5.40e-6 0.3561 0.2517 2.33e-6 0.9990 HDO0.3186 4.57e-3 0.4786 0.4967 9.53e-4 9.93e-4 HTO3.95e-8 6.79e-101.41e-10 9.88e-6 1.89e-8 3.68e-11 D 2 O 0.6407 0.9954 0.1653 0.2517 0.9990 2.53e-7 DTO1.61e-7 2.99e-7 9.88e-11 1.01e-5 4.00e-5 1.90e-14 T 2 O1.01e-142.26e-141.48e-201.02e-104.02e-103.58e-22 ah 0.2000 2.29e-3 0.5954 0.5000 4.77e-4 0.9995 ad 0.8000 0.9977 0.4046 0.5000 0.9995 4.97e-4 at 1.00e-7 1.50e-7 1.20e-10 1.00e-5 2.00e-5 1.84e-11 V. CONCLUSIONS The suggested in the code "NestRect" approach allows to calculate a dynamic behaviour of a water distillation column operating at total reflux sufficiently rapidly and to see the interesting alteration in time of the concentration profile within the column. In our view this approach may be used and for other non steady-state processes' studies. The mathematical simulation procedure and computer code "Cry_En" for a single cryogenic column used for hydrogen isotope separation have been developed. The code allows to carry out the calculation in a wide range of conditions and has good convergence characteristics though needs further enhance (to make shorter a computation time). The simulation procedure and computer code "KIO" for a multistage water/hydrogen exchange column has been developed. The static behaviour of a similar column can be studied in detail. The procedure is applicable in cases with any deuterium concentration and has good convergence characteristics. Both steady-state procedures do not use Newton- Raphson method. This is due to the fact that the convergence characteristics of the plate separation factors are much less sensitive to the type of the iterative method than plate temperatures (or concentrations). That's why large computation efforts are not needed and computer storage requirement is small. REFERENCES 1. M. Kinoshita and Y. Naruse, "Separation Characteristics of Cryogenic Distillation Column with a Feed-back Stream for Separation of Protium and Tritium," Nucl. Technol./Fussion, 2, 410 (1982). 2. M. Kinoshita, "An Efficient Simulation Procedure Especi-ally Developed for Hydrogen Isotope Distillation Columns," Fusion Technology, 6, 574 (1984). 3. M. Kinoshita and Y. Naruse, "A Mathematical Simulation Procedure for a Multistage-type Water/Hydrogen Exchange Column in Tritium System," Nucl. Technol./Fussion, 3, 112 (1983). 4. T. Takamatsu, I.Hashimoto and M. Kinoshita, "A New Simulation Procedure for Multistage Water/Hydrogen Exchange Column for Heavy Water Enrichment," J. Chem. Eng. Japan, 17, 255 (1984). 5. Y.D.Zelvensky, V.V.Shitikov Batch Water Distillation at Total Reflux Visokochistie Veshchestva (Russian) N6, 83 (1987). 6. L.V.Streltsov, N.M.Zavoronkov, Y.D.Zelvensky Closed Flow Sheed Water Distillation Calculation for Any Concentration Theoretical Foundations of Chemical Engineering, 3, N2, 302 (1969). 7. V.D. Trenin et al., "Full-scale Experimental Assembly for Hydrogen Isotopes Separation Studies by Cryogenic Distillation. Assembly and Results of The Studies.," to be published in Fusion Technology. 8. B.M. Andreev at al., "Installation for Separation of Hydrogen Isotopes by the Method of Chemical Isotopic Exchange in the "Water - Hydrogen" System." to be published in Fusion Technology. Fedorchenko 6