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Recycling plutonium in heavy-water power reactors
Journal of Nuclear Energy, 1967, Vol. 21. pp. 81 to 85.
RECYCLING
Pergamon Press Ltd.
Printed in Northern Ireland
PLUTONIUM IN HEAVY-WATER POWER REACTORS* P. I. KHRISTENK~
(First received 25 August 1964 and injinalform
27 April 1965)
Abstract-We consider the operation of a heavy-water reactor using as fuel 238U with equilibrium concentrations of *39U, zaQPuand 241Punuclei and small additions of z3sU when the reactor is fed with natural and depleted uranium. Part of the irradiated fuel taken from the reactor is purified of fission fragments and returned to the reactor. The other, smaller, part, after extraction of the plutonium, is removed from the cycle and replaced by natural uranium.
power reactors operating without fuel regeneration, only a small fraction of the natural uranium is usefully consumed. If it were possible to increase the consumption of natural uranium in these reactors by a factor of 5-10, and consequently to decrease to an equal extent the expenditure of fuel in the generation of electricity, it would be possible to broaden the fuel base of thermal neutron nuclear energetics very considerably, and so to increase the power of atomic power stations. Approximate calculations show that when high-power heavy-water reactors are run on 238U with an equilibrium concentration of plutonium and supplementary introductions of 235U, natural and depleted uranium can be used in them, bringing the fuel burn-up to more than 30 kg to 1 tonne of natural uranium used in the fuel cycle. This conclusion also has some application to other types of thermal reactor operating on natural and enriched uranium. The concentrations of plutonium isotopes in the fuel of thermal power reactors using natural or enriched uranium without recycling are far from equivalent, and in this case electricity is generated mainly at the expense of burn-up of 235U. Let us consider the operation of a thermal reactor with continuous transposition of fuel, in steady-state conditions, with steady (or nearly so) equilibrium concentrations of 239Pu, %OPuand 241Pu, and with the concentrations of 235Uand fission fragments in the 238U kept constant. In order to realize these conditions, when an inadmissible concentration of fragments has been reached in part of the fuel, this part must be withdrawn from the reactor and replaced by fresh fuel. The greater part of the discharged fuel has to be purified of fission fragments and returned to the reactor, together with plutonium, for recycling, while the smaller part, after extraction of the plutonium (2W with a minimal 235Ucontent) is withdrawn from the cycle as spent fuel and replaced by natural or depleted uranium in such quantity as to maintain the given mean calculated concentration of 235Uin the reactor. The plutonium extracted from the smaller fraction of the fuel is either returned to the reactor or withdrawn from the cycle, depending on whether the reactor is operated purely as a generator or whether it also produces plutonium for fast power reactors. Thus in practice chemical processing reduces to purifying the spent fuel of fragments. It might appear that the reprocessing of fuel in connexion with maintaining a
IN THERMAL
* Translated by J. 6
STUART
from Atomnuyu Energiya 20,26 (1966). 81
82
P. I. ~TENKO
constant quantity of fission fragments and constant concentrations of mu and plutonium in the =*U would entail considerable increase in plant facilities for processing irradiated fuel and producing fuel elements. This is not so, however, since when the time spent by the uranium in the reactor and in its burn-up is the same, the amount of fuel discharged from the reactor and sent for chemical processing will be the same both in the case of operation with natural uranium and in that of operation with an equilibrium concentration of plutonium. Equilibrium concentrations of 23nPu, %OPu,%lPu, 242Pu and 23aU in the =I_J, the 235Uconcentration being held constant, can be found from the equations describing the numbers of uranium and plutonium atoms in non-stationary operating conditions(1,2) if we assume the numbers of 238U and neptunium atoms to be constant (pNI, = const.), ignore the isotope 23QU,which has a brief lifetime, and assume that p5a”= const., but dp,/dz # 0 and dpQ
dpo
0.
-=
dz
3
-=
0. 3
dz
dp1
df32
0.
-=
dz=‘dz
0.
3
dP6 _
dz
o
’
(1)
where the are the concentrations of 235U,23QPu,=OPu, 241Pu, 242Pu and =‘XJ. We take as unity psO-the concentration of mu in natural uranium; z, is the effective time (dz = nvZEdt) in the case of operation on natural uranium, and is connected with the time z (in the case of operation on %*U with equilibrium concentrations of plutonium and constant 23sU content) by the equation pi
05~ ~5~~95
z = 2,
(2)
a5fpiiE5 + a9fp&Q + a,fplEl’
where the Ei are the energies generated by fission of %U, 23QPuand %lPu. The number of fission neutrons per absorption in the fuel can be determined from the expression y5f'5 + rl=
C2 +
i&,pQ +
p5 +
yQvQ~Q + ZQpQ +
vl'lpl'l
SIP1 +
'2P2 +
(3)
%d
where the vi are the number of secondary neutrons per absorption in 232U,239Puand =Pu (v~ = 2.06; yQ= 2.00; Yl = 2*26)*. The figure shows the dependence of @9 = ~~~,I.J(z)~~Q on psav-the average 235U content in the fuel during operation of a heavy-water reactor with continuous transposition in steady-state conditions with equilibrium concentrations of the plutonium isotopes, at a constant given average content in the reactor of mu and slags; graphs of the values of the equilibrium concentrations and are also given. The curve for k/i3 was constructed for the value val = 1; in evaluations of burn-up resonance absorption in the slag is taken into account by a corresponding increase of their thermal absorption, i.e. by decreasing 0. The following constants were accepted in the evaluation of the as = 2.75; cs = 0.573; ah = 667; ahf = 555; oQ = 1235; aQf = 846; asc = 389; a, = 330; a, = 1480; aIf = 1100; a2 = 30; a, = 5.5; 4 = 1; a, = l-85; aQf = 1.27; go = 0.495; $ = 2.22; L?2= 0.045; Z6 = 0.008. pQ,
p.
p1
pi:
* The values of Ye,vgand v1 correspond to neutron temperatures of 425°K (Bulletin of the N&ear Data Information Centre No. 1, p. 285, Atomizdat, Moscow (1964).
Recycling plutonium
83
in heavy-water power reactors
The following values for the resonance integrals (in barns) were also used: Z9= 2600; ZJ = 1620; Zor = 980; Z5= 556; Z5f= 400; Z6w 400 (ES = 0.22 eV). The moderating power of heavy water was assumed to be L,/E = 5.54. In the calculations the 242Puand 236Ucontent in the fuel was only partly taken into account, since, owing to the small 235U and 241Pu content of the fuel, equilibrium concentrations of 242Pu and 236U cannot be arrived at in less than forty years continuous operation, not taking into account the time taken up in delays and fuel processing. %lArn and 242Pu and all their high-mass isotopes have been ignored,
/
I.
l-4
P,
3-
Pg.'
3-3 CD
2
‘.2-
C c! Q? 0.2
0.1 0
0.1
0.2
0.3
0.4
0.5
av, P5 FIG. I.--I@
as a function of psav.
since it is not clear at present whether =lArn should be extracted from the fuel in processing. The curves in Fig. 1 were obtained for a gas-cooled heavy-water reactor operating on natural uranium; the diameter of the fuel elements was 10.5 cm, the coefficient of filling of the cross section with uranium E = 0.25, the probability of avoiding resonance capture in mu pl = 0.9, the fast neutron multiplication factor ,u = 1.027. These values are not optimum from the point of view of operation with the proposed fuel cycle. Obviously in this case it would be advantageous to increase fast neutron multiplication by increasing the uranium content in the channels and decreasing the specific power arriving at the uranium. Absorption and fission during moderation [,u (z)] are taken into account by the formulae of IOFFE and OKUN’(~), resonance absorption in %OPu by the equation v. = l/e40, a n d in the slag by the coefficient vsi. The relative expenditure per operational run x of the natural or depleted uranium used to increase the concentration of 235U in recycled fuel can be determined from the condition xpga + (1 - x)&‘t = p; (4) where pp”’is the 235Uconcentration
in the parent fuel (natural or depleted uranium),
84
P.
I. KHIU~TENK~
ppit is the initial concentration of mu in fuel elements charging in the reactors, and pp is the final concentration. Then
par = 1 (natural uranium). if P6 In a fast reactor generating electricity and breeding plutonium, x/(1 + X) of the channels are charged with natural uranium, and the plutonium extracted from them is not recycled; the other l/(1 + X) channels operate in power conditions, on YJ with an equilibrium concentration of plutonium. Additions of 235Uto these channels are effected by using the waste fuel from the channels with natural uranium. Thus such a reactor will supply (1 + x)/x times less plutonium than one of equal power operating on natural uranium. The delivery of plutoniumper tonne of uranium used in the cycle, however, is the same in both. The effective time z and initial concentration of 235U in the fuel rods before insertion into the reactor can be approximately determined; the first from (l), and the second from 1
&nit = &8Y
.
(6)
I-f
The average and final concentrations in Fig. 1 and from the equation
of 235U, pays and pp, are found from the graph
respectively. In choosing the values of z, pLtit and p? for calculation of the specific fuel consumption we must take into account the non-uniformity of the neutron flux along the vertical of the reactor and the potentialities of withdrawing from the fuel cycle the most extensively burnt up parts of the fuel from the central region of the reactor, and also the different enrichments of the fuel both vertically in the reactor and along the diameter of the fuel elements. The equilibrium concentrations of 23sPu, %OPuand %lPu, depending on the 235U content in the fuel of the reactor in question, lie within the limits ps = 0.36-O-39; po = 039-0.41; p1 = 0~11-0~14. Conditions close to equilibrium can be attained fairly rapidly. After returning to the reactor the plutonium from two charges of natural uranium (with z. = O-5), a fs of 023 x 2 = 0.46 may be obtained, which is more than is necessary for equilibrium concentration of 23sPu. The values p. = O-045 x 2 = 0.09 and pr = 0.007 x 2 = O-014 after two operating periods are still far from equilibrium; equilibrium values may be attained in the course of subsequent operation. However, operation of the reactor with an equilibrium concentration of 23sPu only and increasing concentrations of =OPu and 241Pu does ensure a burn-up close to the steady-state regime. Approximate calculations carried out for a large heavy-water reactor with neutron leakage of 2-3 % and with the neutron flux well equalized in the vertical direction, or with burn-up of fuel having source-push rods for rapid triggering during enforced
8.5
Recycling plutonium in heavy-water power reactors
shut-downs, show that when the fragments accumulating in the fuel in an operating period amount to 5-8 kg/te and when the reactor operates in the fuel cycle under consideration it is possible to achieve burn-ups corresponding to a fragment accumulation of more than 30 kg/te of the natural uranium used in the cycle. It is also possible to burn depleted uranium with a 235U content of 2-3 kg/te, and to bring the 235U content in the spent fuel to 05-l kg/te. Estimates of the burn-up can also be obtained from more general considerations. If m is the 235Ucontent in natural uranium, X, is the reproduction factor, and pp is the concentration of 235Uin the spent fuel, then the amount of fissile isotopes vanishing in the reactor with repeated cycling of the fuel can be obtained as the sum of the series
I
b’ = m
(8)
The amount of burnt-up uranium is given by b = m(1 The plutonium
pt)
ratio can be found
f =
V5P5 +
Y9P939 +
% z5sf+ 1 - x,
P9%lf+ PI4 P909 +
PI+
(9)
from (1):
WJl.
The evaluations of burn-up thus obtained agree with those already obtained above. It should also be noted that the values for uranium burn-up obtained above are not the maximum possible values. In fact, it appears from the preliminary evaluation, even in the case of a reactor which is not optimum, that when pgav = 0.05, that is, in concrete terms, when a considerable part (more than 100 kg/te) of all the natural uranium has been burnt, it is possible to obtain k/0 = 1.07 (see Fig. 1). If in this case we take the neutron leakage to be 2 per cent, the necessary thermal utilization factor 19= l-02/1.07 = 0.95. Bearing in mind the fact that in future it will be possible to reduce neutron losses in the moderator and structural materials, to increase the dimensions of the reactor and the proportion of fast neutron fissions, to attain the optimum value of @3 and, with repeated prolonged irradiation of the plutonium, to count upon plutonium isotopes with mass numbers higher than 241 taking part in the process, it may be assumed that there are good prospects of utilizing a considerable part of the uranium in thermal reactors. Our results contain nothing unexpected, since in operating with equilibrium concentrations of plutonium, in practice almost all the fuel is produced in the reactor. REFERENCES 1. GALANIN A. D. Theory of Thermal Nuclear Reactors, Atomizdat, Moscow (1957). 2. IOFFEB. L. and OKUN’L. B. Atomn. Energ. 4,80 (1956).
RECYCLING
Pergamon Press Ltd.
Printed in Northern Ireland
PLUTONIUM IN HEAVY-WATER POWER REACTORS* P. I. KHRISTENK~
(First received 25 August 1964 and injinalform
27 April 1965)
Abstract-We consider the operation of a heavy-water reactor using as fuel 238U with equilibrium concentrations of *39U, zaQPuand 241Punuclei and small additions of z3sU when the reactor is fed with natural and depleted uranium. Part of the irradiated fuel taken from the reactor is purified of fission fragments and returned to the reactor. The other, smaller, part, after extraction of the plutonium, is removed from the cycle and replaced by natural uranium.
power reactors operating without fuel regeneration, only a small fraction of the natural uranium is usefully consumed. If it were possible to increase the consumption of natural uranium in these reactors by a factor of 5-10, and consequently to decrease to an equal extent the expenditure of fuel in the generation of electricity, it would be possible to broaden the fuel base of thermal neutron nuclear energetics very considerably, and so to increase the power of atomic power stations. Approximate calculations show that when high-power heavy-water reactors are run on 238U with an equilibrium concentration of plutonium and supplementary introductions of 235U, natural and depleted uranium can be used in them, bringing the fuel burn-up to more than 30 kg to 1 tonne of natural uranium used in the fuel cycle. This conclusion also has some application to other types of thermal reactor operating on natural and enriched uranium. The concentrations of plutonium isotopes in the fuel of thermal power reactors using natural or enriched uranium without recycling are far from equivalent, and in this case electricity is generated mainly at the expense of burn-up of 235U. Let us consider the operation of a thermal reactor with continuous transposition of fuel, in steady-state conditions, with steady (or nearly so) equilibrium concentrations of 239Pu, %OPuand 241Pu, and with the concentrations of 235Uand fission fragments in the 238U kept constant. In order to realize these conditions, when an inadmissible concentration of fragments has been reached in part of the fuel, this part must be withdrawn from the reactor and replaced by fresh fuel. The greater part of the discharged fuel has to be purified of fission fragments and returned to the reactor, together with plutonium, for recycling, while the smaller part, after extraction of the plutonium (2W with a minimal 235Ucontent) is withdrawn from the cycle as spent fuel and replaced by natural or depleted uranium in such quantity as to maintain the given mean calculated concentration of 235Uin the reactor. The plutonium extracted from the smaller fraction of the fuel is either returned to the reactor or withdrawn from the cycle, depending on whether the reactor is operated purely as a generator or whether it also produces plutonium for fast power reactors. Thus in practice chemical processing reduces to purifying the spent fuel of fragments. It might appear that the reprocessing of fuel in connexion with maintaining a
IN THERMAL
* Translated by J. 6
STUART
from Atomnuyu Energiya 20,26 (1966). 81
82
P. I. ~TENKO
constant quantity of fission fragments and constant concentrations of mu and plutonium in the =*U would entail considerable increase in plant facilities for processing irradiated fuel and producing fuel elements. This is not so, however, since when the time spent by the uranium in the reactor and in its burn-up is the same, the amount of fuel discharged from the reactor and sent for chemical processing will be the same both in the case of operation with natural uranium and in that of operation with an equilibrium concentration of plutonium. Equilibrium concentrations of 23nPu, %OPu,%lPu, 242Pu and 23aU in the =I_J, the 235Uconcentration being held constant, can be found from the equations describing the numbers of uranium and plutonium atoms in non-stationary operating conditions(1,2) if we assume the numbers of 238U and neptunium atoms to be constant (pNI, = const.), ignore the isotope 23QU,which has a brief lifetime, and assume that p5a”= const., but dp,/dz # 0 and dpQ
dpo
0.
-=
dz
3
-=
0. 3
dz
dp1
df32
0.
-=
dz=‘dz
0.
3
dP6 _
dz
o
’
(1)
where the are the concentrations of 235U,23QPu,=OPu, 241Pu, 242Pu and =‘XJ. We take as unity psO-the concentration of mu in natural uranium; z, is the effective time (dz = nvZEdt) in the case of operation on natural uranium, and is connected with the time z (in the case of operation on %*U with equilibrium concentrations of plutonium and constant 23sU content) by the equation pi
05~ ~5~~95
z = 2,
(2)
a5fpiiE5 + a9fp&Q + a,fplEl’
where the Ei are the energies generated by fission of %U, 23QPuand %lPu. The number of fission neutrons per absorption in the fuel can be determined from the expression y5f'5 + rl=
C2 +
i&,pQ +
p5 +
yQvQ~Q + ZQpQ +
vl'lpl'l
SIP1 +
'2P2 +
(3)
%d
where the vi are the number of secondary neutrons per absorption in 232U,239Puand =Pu (v~ = 2.06; yQ= 2.00; Yl = 2*26)*. The figure shows the dependence of @9 = ~~~,I.J(z)~~Q on psav-the average 235U content in the fuel during operation of a heavy-water reactor with continuous transposition in steady-state conditions with equilibrium concentrations of the plutonium isotopes, at a constant given average content in the reactor of mu and slags; graphs of the values of the equilibrium concentrations and are also given. The curve for k/i3 was constructed for the value val = 1; in evaluations of burn-up resonance absorption in the slag is taken into account by a corresponding increase of their thermal absorption, i.e. by decreasing 0. The following constants were accepted in the evaluation of the as = 2.75; cs = 0.573; ah = 667; ahf = 555; oQ = 1235; aQf = 846; asc = 389; a, = 330; a, = 1480; aIf = 1100; a2 = 30; a, = 5.5; 4 = 1; a, = l-85; aQf = 1.27; go = 0.495; $ = 2.22; L?2= 0.045; Z6 = 0.008. pQ,
p.
p1
pi:
* The values of Ye,vgand v1 correspond to neutron temperatures of 425°K (Bulletin of the N&ear Data Information Centre No. 1, p. 285, Atomizdat, Moscow (1964).
Recycling plutonium
83
in heavy-water power reactors
The following values for the resonance integrals (in barns) were also used: Z9= 2600; ZJ = 1620; Zor = 980; Z5= 556; Z5f= 400; Z6w 400 (ES = 0.22 eV). The moderating power of heavy water was assumed to be L,/E = 5.54. In the calculations the 242Puand 236Ucontent in the fuel was only partly taken into account, since, owing to the small 235U and 241Pu content of the fuel, equilibrium concentrations of 242Pu and 236U cannot be arrived at in less than forty years continuous operation, not taking into account the time taken up in delays and fuel processing. %lArn and 242Pu and all their high-mass isotopes have been ignored,
/
I.
l-4
P,
3-
Pg.'
3-3 CD
2
‘.2-
C c! Q? 0.2
0.1 0
0.1
0.2
0.3
0.4
0.5
av, P5 FIG. I.--I@
as a function of psav.
since it is not clear at present whether =lArn should be extracted from the fuel in processing. The curves in Fig. 1 were obtained for a gas-cooled heavy-water reactor operating on natural uranium; the diameter of the fuel elements was 10.5 cm, the coefficient of filling of the cross section with uranium E = 0.25, the probability of avoiding resonance capture in mu pl = 0.9, the fast neutron multiplication factor ,u = 1.027. These values are not optimum from the point of view of operation with the proposed fuel cycle. Obviously in this case it would be advantageous to increase fast neutron multiplication by increasing the uranium content in the channels and decreasing the specific power arriving at the uranium. Absorption and fission during moderation [,u (z)] are taken into account by the formulae of IOFFE and OKUN’(~), resonance absorption in %OPu by the equation v. = l/e40, a n d in the slag by the coefficient vsi. The relative expenditure per operational run x of the natural or depleted uranium used to increase the concentration of 235U in recycled fuel can be determined from the condition xpga + (1 - x)&‘t = p; (4) where pp”’is the 235Uconcentration
in the parent fuel (natural or depleted uranium),
84
P.
I. KHIU~TENK~
ppit is the initial concentration of mu in fuel elements charging in the reactors, and pp is the final concentration. Then
par = 1 (natural uranium). if P6 In a fast reactor generating electricity and breeding plutonium, x/(1 + X) of the channels are charged with natural uranium, and the plutonium extracted from them is not recycled; the other l/(1 + X) channels operate in power conditions, on YJ with an equilibrium concentration of plutonium. Additions of 235Uto these channels are effected by using the waste fuel from the channels with natural uranium. Thus such a reactor will supply (1 + x)/x times less plutonium than one of equal power operating on natural uranium. The delivery of plutoniumper tonne of uranium used in the cycle, however, is the same in both. The effective time z and initial concentration of 235U in the fuel rods before insertion into the reactor can be approximately determined; the first from (l), and the second from 1
&nit = &8Y
.
(6)
I-f
The average and final concentrations in Fig. 1 and from the equation
of 235U, pays and pp, are found from the graph
respectively. In choosing the values of z, pLtit and p? for calculation of the specific fuel consumption we must take into account the non-uniformity of the neutron flux along the vertical of the reactor and the potentialities of withdrawing from the fuel cycle the most extensively burnt up parts of the fuel from the central region of the reactor, and also the different enrichments of the fuel both vertically in the reactor and along the diameter of the fuel elements. The equilibrium concentrations of 23sPu, %OPuand %lPu, depending on the 235U content in the fuel of the reactor in question, lie within the limits ps = 0.36-O-39; po = 039-0.41; p1 = 0~11-0~14. Conditions close to equilibrium can be attained fairly rapidly. After returning to the reactor the plutonium from two charges of natural uranium (with z. = O-5), a fs of 023 x 2 = 0.46 may be obtained, which is more than is necessary for equilibrium concentration of 23sPu. The values p. = O-045 x 2 = 0.09 and pr = 0.007 x 2 = O-014 after two operating periods are still far from equilibrium; equilibrium values may be attained in the course of subsequent operation. However, operation of the reactor with an equilibrium concentration of 23sPu only and increasing concentrations of =OPu and 241Pu does ensure a burn-up close to the steady-state regime. Approximate calculations carried out for a large heavy-water reactor with neutron leakage of 2-3 % and with the neutron flux well equalized in the vertical direction, or with burn-up of fuel having source-push rods for rapid triggering during enforced
8.5
Recycling plutonium in heavy-water power reactors
shut-downs, show that when the fragments accumulating in the fuel in an operating period amount to 5-8 kg/te and when the reactor operates in the fuel cycle under consideration it is possible to achieve burn-ups corresponding to a fragment accumulation of more than 30 kg/te of the natural uranium used in the cycle. It is also possible to burn depleted uranium with a 235U content of 2-3 kg/te, and to bring the 235U content in the spent fuel to 05-l kg/te. Estimates of the burn-up can also be obtained from more general considerations. If m is the 235Ucontent in natural uranium, X, is the reproduction factor, and pp is the concentration of 235Uin the spent fuel, then the amount of fissile isotopes vanishing in the reactor with repeated cycling of the fuel can be obtained as the sum of the series
I
b’ = m
(8)
The amount of burnt-up uranium is given by b = m(1 The plutonium
pt)
ratio can be found
f
V5P5 +
Y9P939 +
% z5sf+ 1 - x,
P9%lf+ PI4 P909 +
PI+
(9)
from (1):
WJl.
The evaluations of burn-up thus obtained agree with those already obtained above. It should also be noted that the values for uranium burn-up obtained above are not the maximum possible values. In fact, it appears from the preliminary evaluation, even in the case of a reactor which is not optimum, that when pgav = 0.05, that is, in concrete terms, when a considerable part (more than 100 kg/te) of all the natural uranium has been burnt, it is possible to obtain k/0 = 1.07 (see Fig. 1). If in this case we take the neutron leakage to be 2 per cent, the necessary thermal utilization factor 19= l-02/1.07 = 0.95. Bearing in mind the fact that in future it will be possible to reduce neutron losses in the moderator and structural materials, to increase the dimensions of the reactor and the proportion of fast neutron fissions, to attain the optimum value of @3 and, with repeated prolonged irradiation of the plutonium, to count upon plutonium isotopes with mass numbers higher than 241 taking part in the process, it may be assumed that there are good prospects of utilizing a considerable part of the uranium in thermal reactors. Our results contain nothing unexpected, since in operating with equilibrium concentrations of plutonium, in practice almost all the fuel is produced in the reactor. REFERENCES 1. GALANIN A. D. Theory of Thermal Nuclear Reactors, Atomizdat, Moscow (1957). 2. IOFFEB. L. and OKUN’L. B. Atomn. Energ. 4,80 (1956).