Thermochemical modelling of electrotransport of uranium and plutonium in an electrorefiner

Nuclear Engineering and Design 179 (1998) 75–99 Thermochemical modelling of electrotransport of uranium and plutonium in an electrorefiner H.P. Nawada, N.P. Bhat * Metallurgy Di6ision, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India Received 30 December 1996; accepted 4 September 1997 Abstract Electrotransport behaviour of U and Pu in a molten salt electrorefining cell has been numerically simulated with an improved thermochemical model. Depending upon saturated or unsaturated states of the liquid Cd electrodes with respect to U or Pu or with both U and Pu, 16 conditions of electrorefiner cell operation have been categorised and electrotransport simulated for all the realistic conditions. Algebraic equations for determining the compositions of the salt phase and the two electrodes under each condition of electrotransport are derived. Fractional mass transport coefficients and relative fractional mass transport coefficients are derived for each condition to illustrate the electrotransport behaviour. Comparison is made between modeling with concentration dependent and concentration independent activity coefficients for U and Pu in liquid Cd. The electrotransport to a solid cathode and anodic dissolution have also been simulated. Application of the model to reprocessing of spent metallic fuel is discussed with respect to U recovery, Pu enrichment and reconstitution of the spent fuel with desired fuel composition. © 1998 Elsevier Science S.A. 1. Introduction The molten-salt electrorefining process for re- processing spent metallic fuel of advanced liquid metal cooled fast breeder reactors (ALMFBRs), apart from being a relatively compact facility has the added advantage of recovering the minor ac- tinides (Np, Am and Cm) along with the fuel actinides (U and Pu) for further transmutation by recycling in the reactor, thereby considerably re- ducing the long term hazards of the nuclear waste (Wade and Chang, 1987). The proposed elec- trorefining process for recycling spent metallic fuel from the integral fast reactor (IFR) is now in an advanced state of development at ANL (Bat- tles et al., 1991). Johnson (1988) had developed a thermochemical model which predicts electro- transport of U and Pu in the electrorefiner cell (ER). Liaw and Ackerman (1990) and Ackerman (1991) extended the model to a multicomponent system to include fission products and developed a comprehensive code for modelling the pyro- chemical process for reprocessing spent fuel of the IFR. In our efforts to develop our own code for reprocessing spent fuel of our proposed prototype fast breeder reactor (PFBR), the above model has been reviewed and some modifications are incor- * Corresponding author. Fax: �91 411440360; e-mail: [email protected] 0029-5493:98:$19.00 © 1998 Elsevier Science S.A. All rights reserved. PII S0029 -5493 (97 )00245 -8 H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–9976 Table 1 The possible modes of electrotransport in the electrorefiner considering U and Pu solubilities in the LCA and the LCC Nature of anode (LCA) Nature of RemarksSL. no. Transport be- cathode (LCC) haviour Unsaturated anode with U Ideal co-transport, composition can be con-1(a) Unsatu- co-transport1 and Pu trolled, large LCCrated cathode 1(b) U saturated U dominated transportCo-transport cathode Diminishing cathode due to PuCd6 ppt and ex-Pu transport1(c) Pu satu- solution of U from cathoderated cathode (1d) U and Pu Small LCC used, ideal co-transport, diminish-Co-transport ing cathode, composition can be controlledsaturated cathode U dominated transport but initially someUranium saturated anode Co-transport2 2(a) Unsatu- amount of Pu gets transported{Pu unsaturated} rated cathode Pu concentration fixed at anode (LCA) andU transport2(b) U saturated cathode (LCC)cathode — Unrealistic2(c) Pu satu- rated cathode — Unrealistic2(d) U and Pu saturated cathode Co-transport Expanding anode due to PuCd6 dissolution andPlutonium saturated anode 3(a) Unsatu-3 {U unsaturated} transports higher Pu fractionrated cathode Unrealistic—3(b) U saturated cathode Expanding anode and diminishing cathode andPu transport3(c) Pu satu- rated cathode U ex-solution from cathode Unrealistic3(d) U and Pu — saturated cathode Small LCA and large LCC, fixed transport, PuCo-transportSaturated anode with both4 4(a) Unsatu- content 67%, composition can not be controlledU and Pu rated cathode — Unrealistic4(b) U saturated cathode Unrealistic—4(c) Pu satu- rated cathode Calculations are not possible will be similar to4(d) U and Pu Co-transporta 4(a) by general trend, small LCA and smallsaturated LCCacathode — Model can not be applied. a Model can not yield solution. porated with respect to concentration dependent activity coefficients (g) for U and Pu in liquid Cd and corrections for ‘expanding anode’ and ‘dimin- ishing cathode’ due to dissolution or precipitation of PuCd6 in the respective electrodes. Sixteen possible initial conditions are categorised and electrotransport behaviour of U and Pu is simu- lated for ten realistic conditions, the other six conditions being unrealistic (Table 1). This paper gives a detailed picture of electro- transport behaviour of U and Pu in the ER with the improved thermochemical model. Numerical simulation of electrotransport is initially demon- strated for all the ten realistic conditions with concentration independent activity coefficients for U and Pu in liquid Cd. Numerical simulation with H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–99 77 concentration dependent activity coefficients is demonstrated subsequently for a few conditions and comparison is made between modeling with concentration independent and concentration de- pendent activity coefficients for U and Pu in liquid cadmium. Electrotransport behaviour is discussed with respect to fractional mass transport coefficients (FMTCs), relative fractional mass transport coefficients (RFMTCs) and fuel compo- sitions fPu (mole fraction of Pu with respect to U and Pu) of the salt phase and the two liquid cadmium electrodes. Electrotransport behaviour during anodic dissolution of the fuel and during deposition of U on a solid cathode have also been simulated. Application of the model to reprocess- ing of spent metallic fuel is discussed with respect to U recovery, Pu enrichment and reconstitution of the spent fuel with desired fuel composition. 2. Thermodynamic data Thermodynamic data utilised for the present computations are presented in Table 2. Utilising Fig. 1. Activity coefficients of U and Pu in liquid Cd as a function of concentration. Calculated from excess free energy data of Johnson and Feder (1962), Johnson et al. (1965) and Martin et al. (1961). the excess Gibbs energy data of Johnson and Feder (1962), Johnson et al. (1965) and Martin et al. (1961) for solutions of U and Pu in liquid Cd, the g of U and Pu computed as a function of their concentrations respectively yielded the following relations. gU,Cd�a�b nU,Cd nCd�nU,Cd (1) gPu,Cd�c�d nPu,Cd nCd�nPu,Cd (2) where gU,Cd and gPu,Cd are activity coefficients and nU,Cd and nPu,Cd are number of moles of U and Pu in solution in liquid Cd, respectively, and nCd is number of moles of liquid Cd. Values of the intercepts and slopes for the Eq. (1) and Eq. (2), respectively, are a�81.208, b�840.376, c� 13.12�10�5 and d�5.8�10�3. As shown in Fig. 1, gU and gPu vary linearly with concentration and obey Henry’s Law up to the saturation concentra- tion. Whereas gU varies from 81.5 to 88.7 as the concentration of U in liquid Cd varies from zero to the saturation value (1.128 at.%), gPu varies from 1.39�10�4 to 2.37�10�4 as the Pu concen- tration varies from zero to the saturation value (1.805 at.%). Johnson (1988) had earlier estimated the gPuCl3:gUCl3 ratio equal to 3.74 for MgCl2 solutions and utilised this value for LiCl–KCl solutions while modeling electrotransport be- Table 2 Thermodynamic data from literature utilised in the calcula- tions corresponding to 773 K temperature Ref.Thermodynamic Data DG°f UCl3 �162.3a Koyama et al., 1993 Koyama et al.,DG°f PuCl3 �183.8a 1993 Johnson et al.,gPu (in Cd) 1.88�10 �4 b 1965 75bgU (in Cd) Johnson and Feder, 1962 5.79�10�3 cgUCl3 (in LiCl–KCl) Koyama et al., 1993 6.62�10�3 cgPuCl3 (in LiCl–KCl) Koyama et al., 1993 0.01141dSolubility of U in liquid Johnson and Cd Feder, 1962 Johnson et al.,0.01838dSolubility of Pu in liquid Cd 1965 a DG f° are in kcal mol�1. b Average value. c At infinite dilution. d Solubility expressed in terms of mole fraction. H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–9978 haviour of U and Pu in the ER. However, this value is much different from 1.08 estimated by Koyama et al. (1993) for LiCl–KCl solution. Koyama’s data derived from distribution coeffi- cient measurements in LiCl–KCl melts appears to be more reasonable compared to that of Johnson and hence Koyama’s data has been utilised in the present calculations. The Gibbs energy of forma- tion data for UCl3 and PuCl3 are also from Koyama et al. (1993). 3. The electrorefining process Chopped fuel pins are dissolved in the elec- trorefiner (ER) either by chemical oxidation or by anodic dissolution. In the electrorefining step, the spent fuel gets purified by electrolytic transport of fuel elements from a liquid Cd anode (LCA) to either a liquid Cd cathode (LCC) or a solid cathode through a molten electrolyte salt eutectic of LiCl–KCl. Essentially pure U is electrotrans- ported to a solid cathode and U and Pu are co-transported to the LCC. Minor actinides ac- company U and Pu to the LCC. Most of the fission products, i.e. alkali metals, alkaline earths and rare earths remain in the electrolyte. The noble metal fission products remain in the LCA. 4. The thermochemical model The electrorefining operation is essentially com- bination of electrotransport of the solute metals from the anode to the cathode under a voltage gradient followed subsequently by relatively fast redox exchange reaction between one element in the Cd phase and another element in the salt phase. For example, UCl3(salt)�Pu(Cd)UU(Cd)�PuCl3(salt) (3) The distribution of the solute metals between the liquid metal phase and the salt phase is gov- erned by the activity based equilibrium constant Keq for the reaction, Keq�exp� (DG f°:RT)� nU,CdnPuCl3 nPu,CdnUCl3 � gU,CdgPuCl3 gPu,CdgUCl3 (4) where DG°f is the difference between Gibbs ener- gies of formation of PuCl3 and UCl3. The terms n and g are number of moles and activity coeffi- cients, respectively, for the specified components indicated by the subscripts. Eventhough Eq. (4) involves mole fractions, they get reduced to num- ber of moles ‘n ’ due to cancellation of the same denominator terms (nU,Cd�nPu,Cd�nCd) and (nUCl3�nPuCl3�nKCl�nLiCl). The above equation may be rearranged to define Kx the concentration based equilibrium constant. Kx� nU,CdnPuCl3 nPu,CdnUCl3 �Keq gPu,CdgUCl3 gU,CdgPuCl3 (5) Since both the Cd electrodes are in equilibrium with the same salt phase, compositions of both the electrodes will be related to the salt phase composition. nU,a nPu,a � nU,c nPu,c �Kx nUCL3 nPuCl3 (6) where nU,a and nPu,a, are moles of U and moles of Pu, respectively, in the anode and nU,c and nPu,c are moles of U and moles of Pu, respectively, in the cathode (for the present they are assumed to be in solution in the liquid Cd electrodes). The above equation is also equivalent to, nU,a�nU,c nPu,a�nPu.c � nPuCl3 nUCl3 �Kx (7) The concentration based equilibrium constant Kx is calculated from the thermodynamic data. Following mass balance equations are considered for deriving the values of nPuCl3 and nUCl3. NU�nU,a�nU,c�nUCl3 (8) NPu�nPu,a�nPu,c�nPuCl3 (9) ns�nUCl3�nPuCl3 (10) nc�nU,c�nU,c (11) where NU and NPu are total moles of U and total moles of Pu, respectively, in the ER, ns is total moles of U�Pu in the salt phase and nc in total moles of U�Pu in the cathode. Substituting rele- vant quantities in Eq. (7), H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–99 79 x ns�x � NU�ns�x NPu�x �Kx (12) where x�nPuCl3 and (ns�x)�nUCl3. Eq. (12) is solved for deriving the value of x, and composi- tions of the anode and cathode are calculated (for a given amount of transfer of U�Pu from the anode to the cathode) from Eq. (6) which can be re-written as, nU,a nPu,a � nU,c nPu,c �Kx ns�x x (13) Johnson (1988) who developed a thermochemi- cal model based on the above principles, demon- strated the electrotransport behaviour of U and Pu for a few initial conditions. Depending on initial feed to the ER, the LCA at the start of electrorefining may be (1) unsaturated with U and Pu; (2) saturated with U but unsaturated with Pu; (3) saturated with Pu but unsaturated with U; and (4) saturated with both U and Pu. With gradual electro-transport of the fuel material from the LCA to the LCC, the latter may get saturated with either U or Pu or with both U and Pu. Taking the saturated or unsaturated states of both the electrodes under consideration, there can be 16 conditions in the ER as summarised in Table 1, each requiring different set of equations for mod- eling the electrotransport behaviour. Abbrevia- tions given in Table 1 for each electrotransport condition are used in the subsequent text. For example, electrotransport from the LCA which is unsaturated with U and Pu to the LCC which is also unsaturated with U and Pu is denoted as ‘1a’ condition. Summary of the results of the numeri- cal simulation which is discussed elaborately in Section 6 is also presented in Table 1. As will be seen later, some of the conditions in Table 1 are unrealistic, unless specifically created. The unreal- istic electrotransport conditions are discussed later in Section 6.6. The above Eqs. (3)–(13) are valid only for 1a condition when moles of both U and Pu in the Cd electrodes are within the solubility limits. When one of the solutes or both exceed the solubility limits in either or both the Cd electrodes, the mass balance equations as well as Eq. (13) require modifications to account for precipitation of the solute:solutes in the liquid Cd electrodes. For example, when U gets precipitated in the cathode under 1b condition, the mass balance Eqs. (8) and (11) and Eq. (13) get modified as, NU�nU,a�nU,c,s�nU,c,p�nUCl3 (14) nc�nU,c,s�nU,c,p�nPu,c (15) nU,a nPu,a � nU,c,s nPu,c �Kx ns�x x (16) where nU,c,s is moles of U in solution (at satura- tion) in the LCC and nU,c,p is moles of U as solid precipitate. The former is equal to nCd,c�b, where nCd,c is total moles of liquid Cd in the LCC and b is the saturation solubility of U in liquid Cd at 773 K. Since U in liquid Cd precipitates as metal on supersaturation, moles of liquid Cd in the liquid state in the LCC, nCd,c,l remains unaltered and is equal to nCd,c. On the other hand, precipita- tion of Pu as PuCd6 under 1c condition leads to reduction in moles of liquid Cd in the LCC. Moles of liquid Cd in the LCC, when nPu,c,p moles of Pu precipitates as PuCd6 is nCd,c,l�nCd,c�6nPu,c,p (17) The mass balance Eqs. (9) and (11) and Eq. (13) get modified as NPu�nPu,a�nPu,c,s�nPu,c,p�nPuCl3 (18) nc�nU,c�nPu,c,s�nPu,c,p (19) nU,a nPu,a � nU,c nPu,c,s �Kx ns�x x (20) where nPu,c,s is moles of Pu in solution at satura- tion in the LCC, and is equal to nCd,c,l�v, where v is the saturation solubility of Pu in liquid Cd at 773 K. When the LCC gets saturated with both U and Pu as in 1d condition the mass balance Eqs. (8), (9) and (11) and Eq. (13) are modified as, NU�nU,a�nU,c,s�nU,c,p�nUCl3 (21) NPu�nPu,a�nPu,c,s�nPu,c,p�nPuCl3 (22) nc�nU,c,s�nU,c,p�nPu,c,s�nPu,c,p (23) nU,a nU,c,s � nU,c,s nPu,c,s �Kx ns�x x (24) where nU,c,s� (nCd,c,l)b (25) H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–9980 Similar corrections are incorporated in the mass balance Eqs. (8), (9) and (11) and Eq. (13) when the LCA is saturated with either U or Pu or with both U�Pu (2a, 3a and 4a conditions, respec- tively) and also when both the LCA and LCC are similarly saturated (2b, 3c and 4d conditions, respectively). Algebraic equations for deriving the value of x, obtained by incorporating the above corrections for the nine realistic conditions are presented in Appendix B. Numerical simulation of electrotransport of U and Pu (with concentra- tion independent activity coefficients for U and Pu in liquid Cd) that is presented in Section 6 has been carried out based on the above equations. So far, the thermochemical model has been developed with concentration independent activity coefficients (average values) for U and Pu in liquid Cd. This model is sufficient to get a fairly good picture of the transport behaviour of U and Pu in the ER. However, in order to get accurate data on the transport behaviour, variation of activity coefficients with concentration has to be taken into account. Eq. (4) for the equilibrium at the cathode–salt interface may be re-written as, Keq� gUCl3 gPuCl3 � nU.cnPuCl3 nPu,cnUCl3 � gU,c gPu,c (26) Denoting the LHS as K1 and incorporating intercepts and slopes from Eq. (1) and Eq. (2), Eq. (26) gets modified as, K1� nU,cnPuCl3 nPu,cnUCl3 � a�b nU,c nCd,c�nU,c a�b nPu,c nPu,c�nPu,c (27) Equations similar to Eq. (26) and Eq. (27) may be written for the equilibrium at the anode–salt interface. Making use of the relevant mass bal- ance equations, the system could be completely solved for 1a condition when the LCA and the LCC are unsaturated with respect to U and Pu. When the LCC gets saturated with U in 1b condi- tion, the activity of U in the LCC is fixed and suitable corrections have to be made to Eq. (27) by replacing nU,c with nU,c,s. When the LCC gets saturated with Pu in 1c condition, corrections are required to account for the fixed Pu activity in the LCC and also for the phenomenon of diminishing cathode. Eq. (27) gets modified for 1c condition, K1� nU,cnPuCl3 nCd,c,lvnUCl3 � a�b nU,c nCd,c,l�nU,c c�d v 1�v (28) When the LCC gets saturated with U and Pu in 1d condition, activities of both U and Pu are fixed and it is diminishing cathode. Eq. (27) gets modified to a simple form for this condition. K1� nPuCl3 nUCl3 � b v � a�b b 1�b c�d v 1�v (29) Electrotransport behaviour of U and Pu has been first simulated with concentration indepen- dent g for U and Pu in Cd for all the realistic conditions in the ER operation. Results are dis- cussed in Section 6. Secondly electrotransport be- haviour has been simulated for a few conditions with concentration dependent g for U and Pu. These results are discussed in Section 7 and com- pared with the results of Section 6. 5. Fractional mass transport coefficients Following fractional mass transport coefficients are defined in order to explain the electrotrans- port behaviour of U and Pu at any point of electrorefining. aU� d(nU,c) d(nc) (30) aPu� d(nPu,c) d(nc) (31) eU� aU (NU�nUCl3):(NU�NPu�ns) (32) ePu� aPu (NPu�nPuCl3):(NU�NPu�ns) (33) At any point of electrotransport, nc� (NU�NPu�ns)pt�0.01 (34) H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–99 81 aU, the fractional mass transport coefficient (FMTC) for U, expresses the mole fraction of U pumped per mole of transfer from the LCA to the LCC at any point of electrotransport. It is similar to the transport number in conventional electro- chemistry. eU, the relative fractional mass transport coeffi- cient (RFMTC) for U, expresses the mole fraction of U pumped, relative to the mole fraction of U initially present in the LCA, per mole of transfer from the LCA to the LCC at any point of electro- transport. The FMTC and RFMTC for Pu, aPu and ePu, respectively, have similar significance. The value of aU�aPu will be equal to unity. The FMTC for Pu, aPu will show the rate of change of fuel composition of the LCC as a function of percentage transport under a given electrotransport condition. However, depending upon the input fuel composition to the ER at the start of electrotransport, the initial condition of electrotransport will be changing sequentially to other conditions as more and more fuel material is electrotransported from the LCA to the LCC. When aPu remains unaltered under an electro- transport condition, the ER will be pumping fuel material to the LCC in a Pu:U mole ratio corre- sponding to the fuel composition of the LCA. When aPu or aU approaches unity the ER will be pumping essentially pure Pu or pure U, respec- tively, to the LCC. While the FMTC for Pu shows the rate of change of fuel composition of the LCC, The RFMTC for Pu will show the rate of change of fuel composition of the LCC relative to the fuel composition of the total fuel material in the ER (or in other words, fuel composition of the feed to the LCA) as a function of percentage transfer from the LCA to the LCC. As will be seen later, the ER operation may be engineered to obtain desired fuel composition of the cathode product. This may be achieved by operating the ER under a chosen condition or reaching the chosen condi- tion starting from a different condition. The latter strategy will become necessary when enrichment of the fuel is required. It will be essential to know the value of ePu for such conditions for adjust- ment of fuel composition of the feed to the ER or for termination of ER operation at the required point. While both FMTC and RFMTC for Pu show the rate of change of fuel composition of the LCC, they don’t give the fuel composition of the cathode, fPu,c at any stage of electrotransport un- der most of the conditions. The fPu,c has to be derived separately. Algebraic equations of derived mass transport coefficients a and e are presented in Appendix C and Appendix D, respectively. Appendix C also contains algebraic equations of derived fPu,c. It should be noted that the FMTCs and RFMTCs are based on differential equations and describe the composition of the cathodic current while fPu,c describes the composition of the total charge in a cumulative fashion. Whereas the mass transport coefficients illustrate only a particular point in a given electrotransport condition, the fPu terms describe the compositions of the phases as a result of redox exchange reactions reaching equi- librium at every stage of electrotransport. The overall fuel composition is decided by the equi- librium condition and hence the composition terms are independent of the path taken by the ER. In fact the path of electrotransport is decided by the equilibrium condition irrespective of the initial condition of electrotransport. Similar mass transport coefficients may be defined for any solute while dealing with a multi- component system. 6. Electrotransport of U and Pu with two liquid cadmium electrodes (numerical simulation with concentration independent activity coefficients) (constant Kx) 6.1. Electrotransport starting with U and Pu unsaturated LCA Electrotransport starting with U and Pu unsat- urated LCA and a fresh LCC represents 1a condi- tion. Depending on the fuel composition fPu,a of the LCA, successive electrotransport under this condition gradually leads to either U saturated LCC (1b condition) or Pu saturated LCC (1c condition). Further electrotransport under the H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–9982 above two conditions eventually leads to 1d con- dition. If the fPu,a is \0.617 (this fuel composition corresponds to the saturation solubilities of Pu and U in liquid Cd at 773 K) further electrotrans- port under 1a condition leads to Pu saturated LCC (1c condition) and if it is B0.617 the LCC gets saturated with U leading to 1b condition (Fig. 2). If the fPu,a is equal to 0.617, electrotrans- port leads to simultaneous saturation of the LCC with U and Pu. Electrotransport behaviour of U and Pu as a function of percentage transport from the LCA to the LCC starting with 1a condition is shown in Fig. 3a. The initial 1a condition changes to 1b condition at 5.1% transfer and to 1d condition at 71.1% transfer. Variation of FMTCs and RFMTCs as a function of percentage transport under 1a“1b“1d conditions is illustrated in Fig. 3b. Another fuel composition is chosen for 1a condition in order to reach 1c condition. Typical results of electrotransport behaviour and varia- tion of FMTCs and RFMTCs under 1c condition are illustrated in Fig. 4a, b, respectively. Electro- transport behaviour under the above four condi- tions are discussed below. Fig. 3. Electrotransport behaviour of U and Pu as a function of percentage transfer, starting with U and Pu unsaturated LCA. Modelling is with concentration independent activity coefficients for U and Pu in liquid Cd. The initial 1a condition changes to 1b condition at 5.1% transfer and to 1d condition at 71.1% transfer. NU�1.999, NPu�0.465, ns�0.134, nCd,a�100, nCd,c�5. (a) Variation of U and Pu contents in the LCA and the LCC and Pu content in the salt phase. (b) Variation of the mass transport coefficients. Fig. 2. Transition from 1a condition to 1b or 1c condition depending on fuel composition of the LCA. Modelling is with concentration independent activity coefficients for U and Pu in liquid Cd. NU�NPu�1.0, ns�0.2, nCd,a�100, nCd,c�10. 6.1.1. When the LCC is unsaturated with U and Pu (1a condition) Both U and Pu are co-transported to the LCC under this condition (Fig. 3a; 0–5.1% transfer). As shown in Fig. 3b and Appendix B and Ap- pendix C, both the RFMTCs, eU and ePu are equal to unity and the FMTCs, aU and aPu corre- spond to the initial mole fractions of U and Pu respectively in the LCA. Since aPu is also equal to fPu,c, the ER pumps U and Pu to the LCC in a Pu:U mole ratio corresponding to the initial fuel composition fPu,a of the LCA. This composition is the equilibrium composition as a result of redox H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–99 83 exchange reaction at the LCA-salt interface before starting electrolysis and is different from the fuel composition of the initial anodic feed to the ER. The fuel composition of the salt phase is also different from the input fuel composition due to redox exchange reaction. The FMTCs and RFMTCs for U and Pu remain constant through- out this condition of electrotransport. Hence, the fuel compositions of the LCA and the LCC are equal and remain unaltered throughout 1a condi- tion till the LCC gets saturated with either U leading to 1b condition or with Pu leading to 1c condition. fuel composition of the LCC can be easily controlled under this condition by suitably adjusting the fuel composition of the LCA. How- ever, no enrichment is achieved and electrotrans- port under this condition would require a large size LCC or frequent replacement of the LCC in case a smaller size is used. 6.1.2. When the LCC is saturated with U (1b condition) Both U and Pu are co-transported to the LCC under this condition (Fig. 3a; 5.1–71.1% transfer). However, the co-transport differs from that under 1a condition. When the LCC is saturated with U, the activity of U in the electrode gets fixed and the ER pumps higher mole fraction of U (com- pared to its mole fraction in the LCA) to the LCC in order to maintain the redox equilibrium which does not take into account the precipitated U in the LCC. This results in an increase of aU and a decrease of aPu at the start of electrotransport under this condition (Fig. 3b). The RFMTCs eU and ePu also change in a similar fashion. The FMTC aU being much larger than aPu, the elec- trotransport is predominantly U dominated with negligible amounts of Pu being pumped to the LCC. The RFMTC, ePu being smaller than eU the ER pumps U and Pu to the LCC in a Pu:U mole ratio much lower than that corresponding to the input fuel composition of the LCA. With the electrotransport of higher fraction of U to the LCC, the salt phase becomes richer in PuCl3 resulting in gradual increase of x. (Due to gradual variation of x and in turn fPu,s with electrotrans- port, derivation of the mass transport coefficients are more complicated than for 1a condition and they were calculated by taking numerical deriva- tives of typical NU, NPu and ns as input parame- ters). This in turn results in gradual decrease of aU and eU with simultaneous increase of aPu and ePu. This change is more perceptible when the LCC approaches 1d condition. The fuel composition fPu,c gradually decreases and due to preferential pumping of U, the LCA gets enriched with Pu, the fPu,a approaching the value of 0.617 (the com- position corresponding to the saturation solubili- ties of U and Pu in liquid Cd at 773 K). Compositional control of the cathode product becomes difficult under this condition due to gradual change of the FMTCs. 6.1.3. When the LCC is saturated with Pu (1c condition) Since the activity of Pu is fixed at the LCC, the ER pumps higher mole fraction of Pu (compared to its mole fraction in the LCA) to the LCC in order to maintain the redox equilibrium which does not take into account the precipitated Pu in the LCC. Hence, aPu increases and aU decreases at the start of 1c condition. The RFMTCs also change in a similar manner. With the electrotrans- port of higher fraction of Pu to the LCC, more and more PuCd6 gets precipitated in the LCC. Since Pu precipitates as an intermetallic compound, PuCd6 transforming stoichiometric amount of liquid Cd to the solid phase, the size of the LCC with respect to liquid Cd gets gradually reduced resulting in what is called ‘diminishing cathode’ effect (Fig. 4b). This results in increase in gU in the LCC and marginal decrease of PuCl3 in the salt phase. (Since the salt phase composition changes with electro- transport, the derivation of FMTCs and RFMTCs are much more complicated. The mass transport coefficients e and a and the fuel composition fPu,c are not independent of ‘pt, the percentage transfer unlike in 1a and 1b conditions). Marginal decrease of x with electrotransport results in marginal de- crease of aPu and ePu. With relatively high values for aPu and ePu, the electrotransport is highly Pu dominated with negligible amounts of U electro- transported to the LCC leading to negative values for eU and aU. These negative values for aU and eU signify transport of U in the opposite direction and is termed ‘ex-solution’ of U from the LCC. H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–9984 Fig. 4. Electrotransport behaviour of U and Pu as a function of percentage transfer, under 1c condition. This condition is reached (at 7% transfer) starting with U and Pu unsaturated LCA. Modelling is with concentration independent activity coefficients for U and Pu in liquid Cd. NU�0.4, NPu�1.838, ns�0.134, nCd,a�100, nCd,c�10. (a) Variation of U and Pu contents in the LCC, size of the LCC and activity of U in the LCC. (b) Variation of the mass transport coefficients. (c) Three modes of U transport for the above input conditions except nCd,c�10.35. With aU and eU being negative quantities, es- sentially pure Pu is electrotransported to the LCC. However, the LCC may be contaminated with small amounts of U since this condition is reached from 1a condition. This condition will be suitable when substantial Pu enrichment of the cathode product is required. The ex-solution behaviour has been found to depend on input parameters such as NU, NPu, ns, nCd,a nCd,c and the equilibrium constant Kx. The transport behaviour of U and Pu under this con- dition changes depending on the value of aU which is a function x. aU�1� (1�6v)� d(x) d(nc) �f(x) (35) where f(x) �1� (NU�ns�x) Kx(ns�x) � x Kx(ns�x) � (NU�ns�x)x Kx(ns�x)2 (36) Since the value of ‘x ’ changes gradually with electrotransport (Appendix B), the above function also changes affecting the transport behaviour. When numerical simulation was carried out with the same input parameters (Fig. 4a) but with size of the LCC being 10.35 mol of Cd, the electro- transport (Fig. 4c) varied from Pu dominated co-transport to pure Pu transport (with no U transport) and finally to pure Pu transport (with H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–99 85 ex-solution of U) as the value of aU varied from \0 to �0 and to B0, respectively. aU\0: Pu dominated co-transport of U and Pu to the LCC. aU�0: Essentially pure Pu transport with no U transport to the LCC. aUB0: Essentially pure Pu transport with ex- solution of U in the LCC. All the three conditions prevail in Fig. 4c pro- gressively as a function of percentage transport. The first condition prevails from 12 to 24% trans- port when the condition changes to the second and beyond 24% transfer the third condition pre- vails. All the three conditions are demonstrated in one sequence of electrotransport by judicious se- lection of the size of the LCC rather than varying the initial input parameters to demonstrate the three conditions individually. 6.1.4. When the LCC is saturated with both U and Pu (1d condition) Electrotransport under 1d condition results in precipitation of more and more U and Pu in the LCC (Fig. 3a, after 71.5% transfer). Precipitation of PuCd6 leads to ‘diminishing cathode’ as in 1c condition. While the RFMTCs, eU and ePu and the fuel composition fPu,c are dependent on input parameters NU, NPu and ns, the FMTCs. aU and aPu are independent of the above input parame- ters. The RFMTC, ePu being much higher than eU (Fig. 3b), the ER pumps U and Pu to the LCC in a Pu:U mole ratio much higher than the input Pu:U mole ratio to the LCC. The FMTCs and RFMTCs, remain constant throughout electro- transport under this condition. The fuel composi- tion of the LCA, ( fPu,a) and the salt phase ( fPu,s) also remain unaltered under this condition. With aPu�0.617, the electrotransport is Pu dominated, the ER pumping U and Pu to the LCC in a fixed Pu mole fraction equal to 0.617 (mole fraction corresponding to the saturation solubilities of U and Pu in liquid Cd). Even though the co-trans- port of U and Pu to the LCC is in a fixed ratio, the fPu,c of the cathode product changes depend- ing on fPu,c at the start of 1d condition (1d condi- tion being reached starting with 1a and through 1b). The 1d condition requires a small size LCC (in order to maintain it in U and Pu saturated condi- tion) and compositional control of the cathode product is relatively easy. Hence, this condition appears to be most ideal for reconstitution of the spent fuel when the electrotransport is engineered to obtain the cathode product with specified fuel composition. 6.2. Electrotransport starting with U saturated LCA Typical results of numerical calculation for electrotransport starting with the LCA saturated with U and to a fresh LCC are shown in Fig. Fig. 5. Electrotransport behaviour of U and Pu as a function of percentage transfer, starting with U saturated LCA. Mod- elling is with concentration independent activity coefficients for U and Pu in liquid Cd. The initial 2a condition changes to 2b condition at 4.85% transfer. NU�3.0, NPu�0.8, ns� 0.134, nCd,a�100, nCd,c�10. (a) Variation of U and Pu contents in the LCA and the LCC and Pu content in the salt phase. (b) Variation of the mass transport coefficients. H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–9986 5a, b. The initial 2a condition changes to 2b con- dition at 4.85% transfer. Electrotransport under 2b condition will lead to U unsaturated LCA (1b condition) and eventually to U and Pu saturated LCC (1d condition). Hence, possibilities of ob- taining 2c and 2d conditions does not exist. These two conditions are unrealistic by electrotransport unless they are specifically created. Such hypo- thetical conditions are discussed in Section 6.6. The electrotransport behaviour under 2a and 2b conditions alone are discussed below. 6.2.1. When the LCC is unsaturated with U and Pu (2a condition) Since the activity of U is fixed in the LCA, the ER pumps higher fraction of Pu to the LCC (compared to its mole fraction in the LCA) in order to maintain the redox equilibrium which does not take into account the insoluble U in the LCA. This is reflected in the relatively high value for ePu compared to that of eU. However, due to relatively high mole fraction of U in the LCA, aU is slightly higher than aPu. The fuel composition of the salt phase decreases with electrotransport resulting in gradual increase of aU and eU and simultaneous decrease of aPu and ePu (due to gradual decrease of fPu,s, the algebraic solutions for the transport coefficients and fPu,c become quite cumbersome. The values for a and e were obtained from some numerical examples). The overall electrotransport is U dominated and the fPu,c gets reduced with electrotransport. 6.2.2. When the LCC also is saturated with U (2b condition) The activity of U gets fixed at both the LCA and the LCC and in order to maintain the redox equilibrium, the Pu activity also gets fixed at both the electrodes. The ER pumps only U to the LCC without altering the redox equilibrium which takes into account only dissolved U in both the U saturated liquid Cd electrodes. The value for aU being unity compared to almost zero value for aPu, the ER pumps essentially pure U to the LCC. In effect the insoluble U gets dissolved in the LCA and gets electrotransported to the LCC where it gets precipitated. The fuel composition of the salt phase remains unaltered so also the FMTCs and RFMTCs. This condition appears to be ideal (barring small amounts of Pu in the LCC electrotransported under 2a condition) for recov- ering essentially pure U. However, as will be seen later this condition is not utilised for U recovery. 6.3. Electrotransport starting with PU saturated LCA Notable feature of this condition is that when the Pu is electrotransported from the Pu saturated LCA, equivalent amount of PuCd6 gets dissolved in the LCA releasing solvent Cd into liquid phase of the LCC leading to what is called the ‘expand- ing anode’ effect. Typical results of numerical simulation of electro-transport starting with Pu saturated LCA and a fresh LCC are presented in Fig. 6a, b. The initial 3a condition changes to 3c condition at 4.2% transfer. Depending on input nU,a and nPu,a either the LCA will get unsaturated with Pu leading to 1c condition or the LCC eventually may get saturated with U also (pro- vided the LCC is not solidified) leading to 1d condition. The 3b and 3d conditions are unrealis- tic by electrotransport. Hence, only 3a and 3c conditions are discussed below. 6.3.1. When the LCC is unsaturated with Pu (3a condition) Transport behaviour of U and Pu under this condition is exactly opposite to that under 2a condition. Since the activity of Pu is fixed at the LCA, the ER pumps higher mole fraction of U to the LCC compared to its mole fraction in the LCA. This is reflected in higher value for eU compared to that of ePu. However, due to rela- tively high mole fraction of Pu in the LCA, the electrotransport is Pu dominated the aPu being higher than aU. With Pu dominated transport the fuel composition of the salt phase gradually in- creases with increase in aPu and ePu and decrease in aU and eU. (Since ‘x ’ varies continuously with electrotransport as in earlier discussed 1b and 2a conditions the values for the transport coefficients were obtained from some numerical examples). The electrotransport being Pu dominated the fuel composition of the LCC increases with electro- transport. Compositional control of the cathode H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–99 87 Fig. 6. Electrotransport behaviour of U and Pu as a function of percentage transfer, starting with Pu saturated LCA. Mod- elling with concentration independent activity coefficients for U and Pu in liquid Cd. The initial 3a condition changes to 3c condition at 4.2% transfer. NU�0.4, NPu�5.0, ns�0.134, nCd,a�100, nCd,c�10. (a) Variation of U and Pu contents in the LCA and the LCC and Pu content in the salt phase. (b) Variation of the mass transport coefficients. value of aPu being unity with almost zero value for aU, the ER pumps essentially pure Pu to the LCC. The ePu is very high compared to eU which is a negative value signifying ex-solution of U from the LCC. The net effect is dissolution of insoluble Pu in the LCA and its transport to the LCC (where it gets precipitated as PuCd6) with minor transport of U from the LCC to the LCA. The fPu,c increases rapidly with electrotransport under this conditions. The electrotransport under this condition differs from 1c condition where ex-solution can be prevented by careful selection of the input conditions. The difference is also evident in substantial reduction in the size of the LCC under this condition. This condition is ideal for recovery of essentially pure Pu (barring small amounts of U in the LCC transported under 3a condition). However, maintaining the LCA under Pu saturated condition would involve large inven- tory of Pu in the ER. 6.4. Electrotransport starting with U�Pu saturated LCA Electrotransport leads to the LCC getting simultaneously saturated with U and Pu (4d con- dition) and subsequently to 1d condition. The 4b and 4c conditions are unrealistic by electrotrans- port and hence electrotransport behaviour under 4a and 4d conditions only are discussed below. 6.4.1. When the LCC is unsaturated with U and Pu (4a condition) Co-transport of U and Pu under this condition is identical to that for 1d condition. However, this is a case of ‘expanding anode’ compared to ‘di- minishing cathode’ in 1d condition. The transport coefficients are identical to that for 1d condition and remain constant. The ER pumps U and Pu to the LCC in a fixed Pu mole fraction (0.617) and the fPu,c of the LCC remains constant (0.617) throughout the electrotransport. To illustrate the independence of the mass transport coefficients and the fuel composition fPu,c on input parame- ters, computations were carried with two sets of input inventories and the values of the mass trans- port coefficients and fPu,c were found to be identi- cal for both cases (Table 3). The LCC gets product is difficult under this condition due to variation of the FMTCs with electrotransport. 6.3.2. When the LCC gets saturated with Pu (3c condition) When both the LCA and the LCC are saturated with Pu it is a combination of ‘expanding anode’ and ‘diminishing cathode’. Since the activity of Pu gets fixed at both the electrodes, U activity also gets fixed at both the electrodes. The ER pumps only Pu to the LCC without altering the redox equilibrium. The fuel composition of the salt phase fPu,s remains constant throughout this con- dition so also the FMTCs and RFMTCs. The H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–9988 simultaneously saturated with U and Pu leading to 4d condition. 6.4.2. When the LCC gets saturated with both U�Pu (4d condition) This is also a case of ‘expanding anode’ and ‘diminishing cathode’. The electrotransport equa- tions could not be solved for this condition. How- ever the electrotransport can be considered to be identical to that for 1d and 4a conditions (due to similarity of FMTCs and RFMTCs of Pu satu- rated electrodes). The LCA gets unsaturated with U and Pu simultaneously leading to 1d condition. 6.5. Possible sequences and unrealistic conditions Even though 16 possible conditions are listed in Table 1, only certain conditions discussed above are realistic whereas conditions such as 2c, 2d, 3b, 3d, 4b and 4c are not encountered in electrotrans- port starting with 4 initial conditions at the LCA and with a fresh LCC. Possible sequences for the four initial conditions may be summarised as 1. 1a“1b“1d � 1c“1d 2a“2b“1b“1d2. � 1a“1b“1d 3a“3c“1c“1d3. � 1a“1c“1d 4. 4a“4d“1d 6.6. Equilibrium and non-equilibrium gal6anic cells For all the realistic conditions the ER repre- sents an equilibrium galvanic cell, the galvanic potential E for the cell being E� RT 3F ln aU,a aU,c � RT 3F ln aPu,a aPu,c (37) The unrealistic conditions represent non-equi- librium cells which do not satisfy Eq. (37). These cells will reach equilibrium (before the electro- transport could be effected) by way of salt trans- Table 3 Effect of input parameters on mass transport coefficients for 4a condition of electro-transport (modelling with concentra- tion independent activity coefficient) Fractional transport Computation result for the in- ventoryterm nU�5 mol nU�10 mol aU 0.38280.3828 0.6172 0.6172aPu 0.6172fPu,c 0.6172 0.7604eU 0.5710 1.2407 1.8728ePu Numerical calculation with two sets of values for total inven- tory of U: other details of the ER; nPu�5, nCd,a�100; nCd,c�10; ns�0.134. port (redox reactions) or by way of flow of galvanic current (by short circuiting the elec- trodes). On reaching equilibrium they would rep- resent one of the equilibrium cells discussed above. Unstable cells may be created by selecting an initial condition where the LCC also contains U and Pu. Since redox reactions are considered to be quite rapid compared to electrotransport the cells will reach equilibrium by salt transport in a shorter time. Ackerman (1992) made use of such an unstable cell to deposit Pu in the LCC thereby considerably reducing the time for electrodeposi- tion. 7. Electrotransport of U and Pu with two liquid cadmium electrodes Numerical simulation with concentration dependent activity coefficients of U and Pu in liquid Cd (variable Kx) Electrotransport of U and Pu was simulated for 1a“1b“1d conditions with concentration de- pendent T for U and Pu in liquid Cd. The trans- port behaviour is illustrated in Fig. 7a, b. The fuel composition of the salt phase remains unaltered under 1a condition of electrotransport. Change of nPu in the salt phase is less than 0.0003%. As a result, Eq. (26) for 1a condition can be modified as, H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–99 89 Fig. 7. Electrotransport behaviour of U and Pu as a function of percentage transfer, starting with U and Pu unsaturated LCA. Modelling is with concentration dependent activity coefficients for U and Pu in liquid Cd. The initial 1a condition changes to 1b condition at 5.1% transfer and to 1d condition at 75.1% transfer. NU�1.999, NPu�0.465, ns�0.134, nCd,a�100, nCd,c�5. (a) Variation of U and Pu contents in the LCA and the LCC and Pu content in the salt phase. (b) Variation of the mass transport coefficients. (c) Variation of fuel compositions of the salt phase. Comparison of results with that of numerical simulation with concentration independent g for U and Pu. (d) Variation of fuel composition of the LCC. Comparison of results with that of numerical simulation with concentration independent g for U and Pu. aU,a aPu,a � aU,c aPu,c �K1 ns�x x (38) Eq. (38) is similar to Eq. (13), the mole frac- tions on the LHS being replaced by respective activities. The computational results are com- pared in Fig. 7c, d with the results of earlier computations (with fixed g) with respect to fuel compositions of the salt phase and the LCC. Under 1a condition, eventhough the fuel composi- tion of the salt phase differs for the two computa- tions, the difference in the fuel composition of the LCC is marginal. Hence, electrotransport be- haviour under 1a condition with concentration independent g is almost identical to that with concentration dependent g. However, under 1d condition the electrotrans- port behaviour with concentration dependent g differs significantly from that with concentration independent g. The fuel compositions of the salt phase and the LCC differ significantly for the two H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–9990 computations. Additionally, while the FMTCs and RFMTCs vary with electrotransport for the former, they remain constant for the latter. Com- parison between the two computations has been made only with respect to 1a and 1d conditions in view of the fact that these two conditions appear to be ideal (as will be evident in Section 9.3) for co-transport of U and Pu to the LCC when accurate control of fuel composition of the cathode product is required. It is evident from the above that if 1d condition is used for co-transport of U and Pu to the LCC the improved model with the concentration dependent activity coefficients will have to be used to arrive at accurate composi- tion of the cathode product. 8. Electrotransport with one solid electrode and one liquid cadmium electrode 8.1. Electro-transport from a solid anode to the LCC (anodic dissolution) Anodic dissolution of the fuel in the ER is essentially electrotransport from a solid anode to the LCC (LCA of the ER acting as the LCC during anodic dissolution). The equilibrium con- stant Keq for the redox reaction (Eq. (3)) at the fuel-salt interface is of the order of 106. Since the Pu:U activity coefficients ratio in the metallic fuel will be in the range 0.1–1, this will effect the value of Keq only marginally. With this assumption electrotransport of U�Pu from a solid fuel to the LCC was simulated and the results are illustrated in Fig. 8. In the initial stages of electrotransport, the salt phase consists of pure Pu (the value of fPu,s of the order of 104) and hence essentially pure Pu is electrotransported to the Cd pool. This trend continues with electrotransport as long as signifi- cant qualities of Pu is present in the anode. When the Pu content of the fuel reaches very low con- centration ( fPu,a of the order of 10�4) and at around 20% transfer U starts getting deposited in the Cd pool. The concentration of Pu in the salt phase gradually decreases thereafter and U and Pu are electrotransported to the Cd pool. The anode being a solid phase (chopped spent fuel pins), attaining equilibrium for the redox reaction (Eq. (1)) may not be as fast as in the case of a liquid Cd electrode. Although, after chemical oxidation with CdCl2 and some amount of disso- lution, the anode material may become suffi- ciently porous for the redox reaction (Eq. (3)) to reach equilibrium in a reasonable time. 8.2. Electrotransport from the LCA to a solid cathode After dissolution of the fuel in the ER, essen- tially pure U is electrotransported from the LCA to a solid cathode. Since the activities of the metals deposited on the solid cathode are equal to unity. The redox reaction Eq. (3) at the solid cathode–salt interface proceeds to the right. As a result only pure U gets deposited on the solid cathode. The fPu,s of the salt phase gradually increases with electrotransport. When there is sig- nificant increase in the fPu,s (approximately be- yond 90% transfer from the LCA), Pu starts depositing on the solid cathode. This behaviour has been demonstrated experimentally by Tom- czuk et al. (1992), the results being in close agree- ment with the thermochemical modeling. Fig. 8. Electrotransport behaviour of U and Pu in the anodic dissolution. H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–99 91 9. Application to spent fuel reprocessing 9.1. Reco6ery of uranium In the reprocessing of spent fuel by elec- trorefining, U is deposited on a solid cathode prior to electrotransport of U and Pu to the LCC. This step helps in Pu enrichment of the ER inven- tory for subsequent recovery of Pu enriched cathode product. Essentially pure U gets trans- ported to the solid cathode till the salt phase gets highly enriched with PuCl3. Among various realis- tic conditions with the LCC, pure U gets trans- ported to the LCC only under 2b condition. However, the cathode product under this condi- tion is likely to be contaminated with small amounts of Pu due to the initial redox exchange reaction. This condition will be suitable only when the cathode product is used for refabrica- tion of the core fuel by blending with Pu rich product and may not be suitable when the recov- ered U is used for blanket refabrication. More over, 2b condition would require both the LCA and the LCC to be maintained in a U saturated state throughout the electrotransport. Since a small LCC is used in the ER for easy maneuver- ability, frequent replacement of the loaded LCC will also effect the process efficiency. On the other hand, relatively large amounts of U can be de- posited on a solid cathode. Electrodeposition on a solid cathode will have much higher current effi- ciency due to the large surface area of the dentrite structure of the U deposit. Product consolidation of the cathode product is also relatively simpler compared to the LCC deposit. In view of the above, solid cathode is preferred for recovery of U. 9.2. Reco6ery of plutonium Removal of major amounts of U on a solid cathode prepares the ER, for subsequent co-trans- port of U and Pu to the LCC to recover Pu enriched cathode product. Among various realis- tic conditions for co-transport of U and Pu, 1b and 2b conditions are not suitable since the cathode product becomes poorer in fuel composi- tion under these conditions. Electrotransport un- der 1a condition yields the cathode product with fuel composition equal to the initial fuel composi- tion of the LCA. Even though some amount of enrichment of the LCA can be achieved by prior removal of U on a solid cathode, the LCC has to be maintained in a U unsaturated state and would require frequent replacements. Electrodeposition under 1d, 3a, and 4a conditions give moderate enrichment of the cathode product and electro- transport under 1c and 3c conditions give sub- stantial enrichment. However, 3a, 3c and 4a conditions would require the LCA to be main- tained in a Pu saturated state amounting to large inventory of Pu in the ER. Accordingly, 1c and 1d conditions appear to be ideal for Pu recovery when substantial and moderate enrichment re- spectively of the cathode product is required. 9.3. Reco6ery of U and Pu with specified fuel composition Normal practice in spent fuel reprocessing is to recover a Pu enriched cathode product which on product consolidation is blended with U (or Pu depleted fuel) for refabrication of the fuel ele- ments. However, it may be economical and pru- dent if the fuel composition of the cathode product is adjusted to the required value at the reprocessing stage itself so that the cathode product after product consolidation is suitable for direct refabrication of the fuel elements. This would help reduce the number of processing steps and Pu loss. Since maximum burn-up in FBR’s is of the order of 2 at.%, the enrichment required for the refabricated fuel is only slightly higher than that of the spent fuel. Hence, the electrorefining step involves only moderate enrichment. This can be achieved by prior enrichment of the LCA by U removal on a solid cathode followed by electro- transport under 1a condition. Alternately 1c or 1d conditions can be used without prior Pu enrich- ment. Large amounts of U may have to me removed on a solid cathode while reprocessing spent clad elements for Pu enrichment. This is not the case with core fuel elements where only mod- erate enrichment is required. Electrorefining core fuel under 1c condition may not require prior removal of U since this condition gives substantial H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–9992 Fig. 9. Fuel composition of the cathode product as a function of fuel composition of the total inventory, at various catholyte concentrations (NSP). Electrotransport is under 1d condition and the relation obtained is at 90% transfer. operation of the ER with optimum current effi- ciency. Incidentally, the above relation has also been found to be independent of various other parameters such as relative sizes of the electrodes, the ER inventory and value of the equilibrium constant Keq. 9.4. Reprocessing a typical spent metallic fuel Numerical simulation of the electrorefining pro- cess for reprocessing spent metallic fuel of a typi- cal 500 MWe FBR has shown the possibility of getting the cathode products with desired fuel compositions suitable for direct fabrication of the fuel pins for the inner core, the outer core and the blankets. The required fuel composition is ob- tained by proper adjustment of the feed to the ER and by following certain electrorefining sequences. The capacity of the electrorefiner considered for calculation is presented in Table 4. The mass flow data for a 500 MWe FBR is shown in Table 5. The data given in the above table is for oxide fuel. This data is taken for calculation in the absence the data on metallic fuel. The fuel compositions of the inner core and outer core being 0.209 and 0.283, respectively, the electrorefining is engi- neered to get the cathode products with these fuel compositions and also to get Pu free U for the blankets. This is achieved by proper blending of the spent core and blanket fuel elements as feed to enrichment. However, compositional control of the cathode product is difficult under this condi- tion. Accordingly this condition cannot be utilised when the cathode product with specified fuel com- position is required. On the other hand, composi- tional control of the cathode product is relatively simple under 1d condition provided this condition is reached starting with 1a condition. In order to make the ER operation relatively simple, the com- positional control should be possible by simple adjustment of the fuel composition of the anodic feed or by proper blending of the core and blan- ket fuels or by adjustment of the fuel composition of the LCA by deposition of U on a solid cathode. As shown in Figs. 9 and 10, fuel compo- sition of the cathode product fPu,c under 1d condi- tion is a linear function of (a) fuel composition of the ER inventory and (b) fuel composition of the LCA. However, while the former relation exhibits dependence on the catholyte concentration ns, the latter relation is independent of the catholyte concentration. The latter relation has considerable significance in spent fuel reprocessing in view of the fact that electrorefining may be engineered to get the specified cathode product just by adjust- ment of the initial fuel composition of the LCA. Moreover, non-dependence of the relation on the catholyte concentration (which remains unaltered throughout 1d condition) gives ample freedom for Fig. 10. Fuel composition of the cathode product as a function of fuel composition of initial fuel composition of the LCA. Electrotransport is under 1d condition and the relation ob- tained is at 90% transfer. H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–99 93 Table 4 Capacity of the electrorefiner for reprocessing fuel from typical 500 MWe FBR in molsin kgComponent 89901010.5(1) Liquid Cd Anode (LCA) (bottom Cd pool) 64.1 570 (285�285)(2) Liquid Cd cathode (2 LCCs) 102.524.4(3) U needed to saturate LCA 39.5 165.2(4) Pu needed to saturate LCa (5) U needed to saturate LCC 1.55 6.5 (6) Pu needed to saturate LCC 2.5 10.5 6950386.35(7) Electrolyte salt LiCl-KCl eutectic 65.0 272.7(8) Batch size shown in Fig. 11. However, this aspect is outside the purview of this paper and has been presented elsewhere in detail (Nawada et al., 1995). 10. Conclusions Thermochemical modeling of the elec- trorefining process for spent fuel reprocessing has shown the electrotransport behaviour of U and Pu under various possible conditions in the ER. Out of 16 possible conditions, only ten con- ditions were found to be realistic for which the electrotransport behaviour has been modelled. Out of the other six unrealistic conditions suit- able one may be manually created for facilitat- ing salt transport operation (prior to electrotransport) in order to reduce the time of electrotransport. Out of the ten realistic condi- tions, 1c and 1d conditions are suitable for sub- stantial and moderate Pu enrichment respectively of the cathode product. However, 1d condition is most ideal for co-transport of U and Pu to the LCC in spent fuel reprocessing, when the cathode product should conform to specific fuel composition for direct refabrication of the fuel elements. Modelling with concentra- tion independent and concentration dependent activity coefficients is likely to show minor dif- ferences for most of the cases and significant differences for one or two conditions. The im- proved thermochemical model with concentra- tion dependent activity coefficients for U and Pu in Liquid Cd will have to be used when accu- rate assessment of the cathode product is re- quired. Thermochemical modeling can be utilised for engineering the electrorefining pro- cess for effective management of the core and blanket fuels of an FBR. Application of the model to a multicomponent system for repro- cessing a typical spent metallic fuel will be able to illustrate the recovery of minor actinides and DFs for the fission products. This study along with the work reported earlier (Nawada et al., 1995, 1996) are expected to give more or less comprehensive scenario of electrorefining of spent metallic fuel of an FBR based on thermo- chemical modeling. the ER. After removal of required quantity of U on a solid cathode the LCA reaches the required fuel composition when U and Pu are co-trans- ported to the LCC under 1d condition. The elec- trorefining is divided in to three campaigns: (1) the inner core campaign; (2) the outer core cam- paign; and (3) the blanket and leftover campaign. A blend of the inner core and axial blankets undergo electrorefining in the first campaign, a mix of the outer core and radial blankets in the second campaign and the leftovers in the third campaign. Results of computations for the inner core campaign are presented in Table 6. Further details regarding other campaign, material bal- ance and number of cells required to meet the refuelling schedule, etc. are presented in detail elsewhere (Nawada et al., 1996). The thermochemical model has also been ex- tended to a multicomponent system with respect to reprocessing of a typical spent fuel containing minor actinides and fission products. Transport behaviour of the fuel actinides, minor actinides and rare earths as a function electrotransport under 1a“1b“1d conditions has been shown by numerical simulation. Typical results under 1a condition are presented in Table 7. Variation of decontamination factors (DFs) for minor ac- tinides and rare earths and minor actinide recov- ery as a function of some important parameters has been elucidated. The variation of DFs with electrotransport under 1a“1b“1d condition is H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–9994 Table 5 Mass flow data for 500 MWe FBR No. of sub assemblies In one sub assembly Total of respective subassemblies Heavy metals RatioU Pu U Pu U�Pu Pu:(Pu�U) Equilibrium loading (3 months kg�1) 113.10 0.209538.36Inner core 425.2613 32.71 8.70 538.46 0.283Outer core 13 29.65 11.77 385.45 153.01 679.40nilAxial blankets 679.3813�13 26.13 nil 1031.22 nil 1031.20Radial blankets 9 114.58 nil 2521.31 2787.42Total 266.11 Average equilibrium discharge (3 months kg�1) 0.206500.76103.74Inner core 397.0213 30.54 7.98 134.94 505.83Outer core 13 28.53 10.38 370.89 0.266 15.08 679.38Axial blankets 13�13 25.55 0.58 664.30 0.0221 999.13 1025.53Radial blankets 0.02569 26.41111.014 2.934 2711.51Total 2431.34 280.17 All units are in kg except ratio. Total U loss is 89.96 kg and total Pu gain is 14.08 kg. Residence time for fuel�axial blankets is 1.5 calender years. Residence time for radial blankets is 5 calender years. Table 6 Details of the inner core campaign U�Pu (kg) Pu:(U�Pu)Description Uranium (kg) Plutonium (kg) ratio 1. Permanent inventory of the Electrorefiner 2.1701 0.75452.87620.7061(a) Salt 2.0842 1.3680(b) Anode 0.61881.2838 0.68136.24424.25431.9899Total inventory 0.100764.45002. Anodic feed for one batch 57.9612 6.4888 34.27533. U recovered with solid cathodes in one batch 34.2753 — 4. ER state after step 3 33.5467 0.28379.518424.0283(a) Anode; with fresh LCC 2.8722 0.4264(b) Salt; with fresh LCC 1.6475 1.2247 0.295036.418910.743125.6758Total 0.215030.17475. U and Pu removed with LCC in one batch 23.6859 6.4888 6. ER state after step 5 2.1701 2.8762(a) Salt; after LCC removal 0.75450.7061 0.61881.2838 3.36802.0842(b) Anode; after LCC removal 616.95547. Total U recovered with solid cathodes in 18 batches 616.9554 — 116.7984 543.14468. Total U and Pu recovered with LCC in 18 batches 426.3462 0.2150 0.1007118.8200 1180.141061.32009. Total anodic feed (spent axial and inner core sub- assemblies) 0.10071043.3016 1160.0946116.798410. Total material recovered 18.0184 2.0216 20.0400 0.100911. Inner core campaign leftover H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–99 95 Table 7 Calculation results of electro-transport under 1a condition (with 10% material electro-transported) SF Distribution of elements in the ER (no. moles)Element Composition (normalised at.%) LCA LCC Salt 5.149E-024.634E-01 1.647E-021.0U 73.7084 3.167E-01 3.519E-02Pu 20.8161 1.9 2.138E-02 1.261E-02 1.401E-03Nd 1.8557 43 1.927E-02 8.670E-047.806E-03 1.331E-0248Ce 1.2260 4.900E-05 5.000E-06Sm 0.4926 5000 8.779E-03 4.070E-04 7.816E-03La 0.6630 60 3.667E-03 7.000E-06 7.226E-07Eu 0.0648 5000 1.155E-03 6.400E-05 7.000E-07 1.129E-025000Y 0.2215 3.610E-04 3.580E-04Am 0.1463 3.1 3.252E-03 1.580E-042.470E-04Np 0.1137 2.0 2.219E-03 3.8 1.640E-04Cm 1.800E-050.0114 2.200E-05 Total feed of actinides and REs to the ER is 1.0 mol. Total actinides and REs in the salt is 0.1 mol. Fig. 11. Variation of decontamination factors for minor ac- tinides and rare earths as a function of electrotransport in reprocessing a typical spent metallic fuel. The initial 1a condi- tion changes to 1b condition at 10% transfer and subsequently to 1d condition at 50% transfer. Appendix A. Nomenclature ER electrorefiner liquid cadmium anodeLCA liquid cadmium cathodeLCC NM moles of component M in the ER (M�U, Pu, Cd, UCl3, PuCl3) moles of component MnM nM,i moles of component M in i (i�a, c, Cd, s,—anode, cathode, cadmium phase and salt, respectively) moles of component M in i in j statenM,i,j ( j� l, sat, p, in solution, in solution at saturation and as precipitate, re- spectively) total moles of U�Pu in the saltns phase (�nUCl3�nPuCl3) percentage (of NU�NPu�ns) transferpt from the LCA to the LCC nc total moles of U�Pu in the cathode (�nU,c�nPu,c �0.01pt(NU�NPu�ns)) activity of component MaM aM,i activity of component M in i (i�a, c) gM activity coefficient of component M Acknowledgements The authors are grateful to Dr O.M. Sreedha- ran, Head, Thermodynamics Section, Shri. J.B. Gnanamoorthy, Head, Metallurgy Division, Dr Baldev Raj, Director, MMG and Dr Placid Ro- drigues, Director, IGCAR for their encourage- ment. H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–9996 gM,i activity coefficient of component M in i (i�a, c,) b saturation solubility of U in liquid cadmium at 773 K saturation solubility of Pu in liquidv cadmium at 773 K r �b:v ch � (1�6v) intercept and slope, respectively, ina and b Eq. (1) intercept and slope, respectively, inc and d Eq. (2) Keq activity based equilibrium constant Kx mole fraction based equilibrium con- stant K1 �Keq (gUCl3:gPuCl3) aM fractional mass transfer coefficient for component M relative mass transfer coefficient foroM component M mole fraction of Pu designated asfPu ‘fuel composition’ (�nPu:(nPu� nU)) fPu.j fuel composition of j ( j�a, c, s) NSP catholyte concentration�100(ns: (NU�NPu) DF decontamination factor� mole frac- tion of element in the spent fuel- mole fraction of element in the cathode product SF separation factor with respect to ura- nium, SF� nU,CdnMCl3 nU,CdnUCl3 Appendix B. Algebraic solutions for deriving value of x Condition 1a Kx(ns�x)[NPu�x ]�[NU�ns�x ]x �Ø 1b � NU�ns�x�nc�nCd,cb � xnCd,cb Kx(ns�x) n x�Kx ns�x x �Ø 1c ˆ ˆ ˆ ˘ ¨ nCd,cv � Kx ns�x x �1 n �nc Kx ns�x x 6v�(1�6v) ˆ ˆ ˆ ˙ É �nPu�x� [NU�ns�x ]x Kx(ns�x) �Ø 1d x� [Kxvns][b�Kxv ]�1 2a ns�x x [nPu�x ]Kx� Kxnc(ns�x) Kx(ns�x)�x �nCd,ab�Ø 2b � xnCd,cb Kx(ns�x) n� 1� nCd,c nCd,a n �x�NPu �Ø 3a nCd,av�ch � NPu�x � [NU�ns�x ]x Kx(ns�x) n � ncx x�Kx(ns�x) �x�NPu�Ø 3c NPu�x� [NU�ns�x ]x Kx(ns�x) � NPu�[nCd,c�nCd,a]v�x 1�6v �Ø 4a x� Kxvns b�Kxv 4d x� Kxvns b�Kxv H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–99 97 Appendix C. Derived fractional mass transport coefficients and fuel composition of the LCC fPu,caPuCondition [NPu�x ][NPu�NU�ns]�1 [NPu�x ][NPu�NU�ns]�11a 1d v b�v [[NPu�x ]r ]�[NU�x�ns�nc] (1�r)nc 2b Ø xnCd,cb nc(ns�x) 3c 1�6v 1�6v � 1�Kx ns�x x n nCd,cv nc � ch [K1�[nc�nCd,cv ]] (K16v�ch)nc v(b�v)�1v(b�v)�14a 1b nCd,cb Kx · d dnc � x ns�x n nCd,cbx Kx(ns�x)nc 1c d dpt · [nPu,c ] nCd,cv�ch K1nCd,cv�nc�nCd,cv (K1�1)6v�1 nc2a [x�Kx(ns�x)]�1x 1 1�K1 �nc d dnc � 1 1�K1 n 3a 1 1�K1 �nc d dnc � 1 1�K1 n 1 1�K1 Appendix D. Derived relative fractional mass transport coefficients Condition eU ePu 111a 1d �NU�NPu�ns NU�ns�x � b b�v nn �NU�NPu�ns NPu�x � v b�v nn [NU�NPu�ns][NU�ns�x ]�1 Ø2b H.P. Nawada, N.P. Bhat : Nuclear Engineering and Design 179 (1998) 75–9998 3c NU�NPu�ns NU�ns�x < 1� 1�6v 1�6v � 1�Kx ns�x x n= NU�NPu�ns NPu�x < 1� 1�6v 1�6v � 1�Kx ns�x x n= 4a �NU�NPu�ns NU�ns�x � b b�v nn �NU�NPu�ns NPu�x � v b�v nn 1b [[(K1�1)dx�Kx [NPu�x ]dx1]] NU�NPu�ns NU�ns�x nCd,cb Kx dx1 NU�NPu�ns NPu�x 1c �NU�NPu�ns NU�ns�x �� d dpt [nU,c]nnn �NU�NPu�ns NPu�x �� d dpt [NPu,c]nnn 2a NU�NPu�ns NU�ns�x �� K1 1�K1 n �nc � d dnc � K1 1�K1 nnn NU�NPu�ns NPu�x �� 1 1�K1 n �nc � d dnc � 1 1�K1 nnn 3a NU�NPu�ns NU�ns�x �� K1 1�K1 n �nc � d dnc � K1 1�K1 nnn NU�NPu�ns NPu�x �� 1 1�K1 n �nc � d dnc � 1 1�K1 nnn where � d dpt [nU,c]n�� d dpt �� nc�nCd,cv�ch K1nCd,cv�nc�nCd,cv (K1�1)6v�1 nnn dx1� d dnc � x ns�x n � d dpt [nPu,c]n�� d dpt �� nCd,cv�ch K1nCd,cv�nc�nCd,cv (K1�1)6v�1 nnn dx� d(x) dnc References Ackerman, J.P., 1991. Chemical basis for pyro-chemical repro- cessing of nuclear fuel. Ind. Eng. Chem. Res. 30, 141. Ackerman, J.P., 1992. US Patent No. US 5096545. 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