Considerations on the Disposal of Radioactive Wastes From Nuclear-Powered Ships Into the Marine Environment (1959)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

AT2s N< PPc 200 t, ,, t A (1) 1/2 /. PPc ,. PPc sdAdt This relationship is utilized in subsequent sections of this report to determine the limits of activity which may be introduced into the various segments of the marine environment without undue risk to man. EVALUATION OF HARBORS, ESTUARIES, AND OTHER INSHORE ENVIRONMENTS (ZONE 1) In this section the question of whether harbors, estuaries, and other inshore environments may serve as suitable receivers of any radioactive wastes from nuclear-powered ships is investigated. For the present purpose, inshore areas are those coastal regions within two miles of the shore. Harbors, estuaries, and other inshore environments are regions of high human waterborne activity. This fact, coupled with the normal relatively shallow depths in such environments, argues for a relatively high probability of accidental recovery of any solid wastes introduced there. It is therefore concluded that no solid wastes, packaged or other- wise, should be released in harbors or other nearshore environments. Our attention is then confined to liquid wastes which might be discharged in such waters. The potential sources of low level liquid wastes which would occur under normal operation of a nuclear-powered ship using a water cooled reactor have been described in an earlier section of this report. The fate of such wastes introduced into the marine environment will depend upon the following three processes: (1) Initial dilution, resulting from the mechanical mixture of the effluent with the receiving waters. This initial mixing depends upon the manner in which the effluent is introduced into the receiving waters. Thus a strong jet of effluent introduced below the surface of the receiving waters would result in a mechanical entrainment of the diluting waters until the energy of the jet was dissipated. A gentle flow of effluent at the surface of the receiving waters would result in rela- tively little initial dilution. (2) Advection of the effluent with the currents in the harbor or harbor approach and simultaneous turbulent diffusion leading to further reduction in concentration. (3) Concentration of activity from the water to the suspended silt, the bottom sediments, and the biota. 29

There is no way that man can directly influence the processes of advection. turbulent diffusion, and concentration in a given environ- ment. Man can, however, influence the degree of initial mechanical dilution through proper design of the discharge assembly. Since the rate of dispersion through turbulent processes is scale dependent, man can then influence indirectly the natural diffusion of the wastes by in- creasing the degree of initial mechanical dilution. Also, initial me- chanical dilution reduces the density difference between effluent and receiving waters, and hence aids diffusion. Considering the volumes of liquid effluent involved (a maximum of approximately 300 ft'), the incorporation of a discharge assembly capable of supplying an initial mechanical dilution of 100:1 should be no problem. Factors such as current velocity, depth, density stratification, wind velocity and fetch, and density difference between effluent and receiving waters all influence the process of turbulent diffusion. Since these factors differ so markedly from one harbor environment to an- other, it is virtually impossible to make any precise general statement regarding the subsequent fate of liquid wastes discharged into harbor environments. The degree to which harbors, harbor approaches and other inshore environments might be utilized as receivers of liquid radioactive effluent from nuclear-powered ships must ultimately be determined through an evaluation of each specific location involved. We can, however, consider the general characteristics of certain types of harbors, with the purpose of determining whether there is any possibility of utilization of any considerable fraction of the harbor en- vironments as receivers of liquid effluent from nuclear ships. Thus some important world harbors are approached through locks which limit exchange with the open coastal waters. In most cases such har- bors contain fresh water or water of very low salinity. The absence of tidal currents limits the turbulent diffusion within such harbors, and the lack of free exchange with the open coastal waters would result in accumulation within the harbor of any waste disposed therein. It therefore appears unlikely that harbors located in tideless basins, connected to the sea by a system of locks, can be utilized as receivers of any effluent from nuclear-powered ships. Another group of harbors are located well up estuaries of major river systems, and are characterized by fresh water, though tidal cur- rents of significant magnitude may occur. Possible restriction on the use of such harbors as potential receivers of liquid effluent from nu- clear ships is not so much due to the lack of a mechanism (such as tidal currents) to induce appreciable turbulent diffusion within the har- bor, but rather due to the much larger concentration factors to the biota which occur in fresh water as compared to sea water. The majority of harbors throughout the world are, however, lo- cated in the lower reaches of tidal estuaries or in coastal embayments. The waters of these harbors are normally characterized by salinities of from one-quarter to three-quarters that of full sea water; they are influenced to some degree by tidal currents and wind induced motion; 30

and these harbor waters exchange, to a greater or lesser degree, with the adjacent coastal waters. Consider such a harbor having a volume V and an exchange co- efficient of Y (per day). The exchange coefficient is the fraction of the volume of the water in the harbor which is renewed each day by ex- change with the adjacent coastal waters, and by inflow of land drainage. Y is thus comparable to the radioactive decay coefficient, and a "half- life" for the harbor water can be defined in the same way as radioactive half -life. The ti/2in equation 1 is then the half-life of the area, and is re- lated to Y by 0.693 Further, consider a particular discharge of effluent into the har- bor. Following the initial mechanical dilution, turbulent diffusion will lead to further dilution at approximately an exponential rate, at least during the early stages of diffusion when contaminated volume is small compared to the volume of the harbor. A major part of the analysis of the problem of disposal of nuclear wastes into the sea and coastal waters requires sufficient knowledge of the rates of mixing so that the dilution of any introduced liquid can be estimated correctly. The diffusion model employed in this analysis: It has always been difficult to make such an estimate because of the lack of a satis- factory general theory of diffusion in the sea; rates of diffusion (the so-called eddy diffusivity coefficients) required by existing theory were known adequately only for certain special cases where direct measure- ments had been made. Recently, however, Joseph and Sender (1958) have proposed a horizontal diffusion equation which seems to permit a useful statistical description of the time change of concentration of a diffusing substance. The following paragraphs discuss the application of this diffusion equation to the problem of waste disposal from nuclear- powered ships. Joseph and Sender consider the introduction at time t = 0 of an amount KI of a substance into a small area either of the sea surface or at some deeper level. This small area is regarded as the "point" source for isotropic horizontal diffusion along a thin homogeneous and isentropic layer. After time jt the distribution is described by concen- tric isopleths around the point of maximum concentration. This point is not fixed but moves downstream with the prevailing current. It is further postulated that the velocity of a diffusing particle is independent of distance from the origin, but that the mean dispersion increases in linear fashion with increasing distance. 31

The following diffusion equation was derived: a- 3t r 3r L" 3r where jS is the concentration, r the distance from the origin, and £ the constant mean velocity of diffusion. Solution of this equation gives: exp - — where ^ and M refer to the concentration and total amount of a given isotope introduced. Note that concentration in this equation has the di- mensions ML,' 2 ; in applying the equation, volume concentrations can be obtained by using an estimated layer thickness Q, as the third dimension. The diffusion velocity P. of this equation is related to the Fickian coefficient of eddy diffusivity A by the equation Pr A = — . 2 Joseph and Sender examined quantitative descriptions of diffusion in a variety of situations in the ocean and found £ to be relatively constant with a value of about 1 cm/sec. This equation applies to a region of unrestricted horizontal di- mensions. In restricted waterways, or near shore, the boundaries would limit diffusion. The principle of reflection of the solution ob- tained by Joseph and Sender, so that the angular range within which diffusion can occur is limited in accordance with the existence of a boundary, can be employed to obtain an approximate equation for use in harbors and other restricted waterways. Thus diffusion of a sub- stance released near an open shoreline would be limited to an arc of 180°. In such a case the reflection of the solution given by equation 2 would produce exactly the same equation, except that the right side would be multiplied by a factor of 2. In an elongated, restricted water- way in which the boundaries restrict diffusion to an arc of, say, 30° in the up-channel and 30°in the down-channel direction the approximate equation for the concentration of a diffusing substance released as a point source would be obtained simply by multiplying the right side of equation 2 by the factor 360°/2 x 30° = 6. Thus: s(r,t) 32

If 9n designates the arc within which diffusion is constrained by the boundaries, then, letting 360° (4) n = -T— we have in general <5* s(r.t) = „_._., exp 1 - — where s(r, t) is here concentration per unit volume, since the factor 1/D has been entered into the right side of the equation. The maximum concentration occurs at the center of the diffusing volume, and is given by nM (6) s(t) = 2nD(Pt)2 At the center the concentration decreases continually with time. At any distance _r from the center, the concentration first rises to a maximum value, and thereafter decreases with time. Thus, as- suming that the introduction is truly a point source (i. e. , neglecting initial mechanical dilution), there will be, for any finite amount of radioactive wastes introduced, an area within which the concentration exceeds, for a time, the ppc values for the environment. This area will at first increase in size to a maximum value, and thereafter will de- crease in size until a time is reached at which the concentration is everywhere less than ppc values. This time can be obtained from equation 6 by setting s0(t) equal to the ppc value for the particular iso- tope in question. Thus PPc r V?7II)H' V s ppc where tppc is the time after which the concentration everywhere is less than the ppc concentration, which is here designated by s pc . Equation 5 can be solved for the distance, at any time.t, at which the concentration has just reached ppc values, by setting s(r, t) equal to sppc. Thus nM (8) r = Ptln 2nD(Pt)2s ppc 33

The increment of area which, during the time interval t to t + dt, has a concentration varying from s - 1/2 ds to s + 1/2 ds, if given by: 2rcrdr and hence the integral which appears in equation 1 is given by PPc / PPc This integral can be evaluated using equations 5, 7, and 8. The solution is given by I I sdAdt = - - t 1 9 D PPc The criterion for establishing the number of discharges, N, each of strength M, which may be made into a marine locale of area A during the time interval T is then, from equation 1 (10) N < _ PPC . - 80° h/2 "tpp. The time period T, which must be short compared to a man's life span but long compared to the time required to reduce the maximum concentration resulting from a single release to below ppc values, is here taken as 30 days. Now consider a harbor having relatively poor mixing character- istics and a low rate of exchange with adjacent coastal waters. A re- view of available data indicates that most marine harbors of the United States have a half life of 30 days or less. Joseph and Sender (1958) found that for a number of phenomena of varying scale in the open sea the diffusion velocity.P was nearly constant at 1 cm/sec. A conserva- tive estimate of this parameter for inshore tidal waters is taken at 0.5 cm/sec. Further, assume that in this "typical" harbor the depth inter- val within which vertical mixing occurs is at least 6 meters. The boundaries of the harbor are considered to constrain diffusion to within an arc of 30°, both up-channel and down-channel; hence n = 6. We take for the volume and surface area of this "typical" small harbor the values 3 x 108 m' and 5.4 x 107 m2 respectively. Letting D = 6 meters, tj /2 = 30 days, and T = 30 days, then for this sample 34

computation in a "typical" harbor of poor flushing characteristics, equations 6, 7, and 10 become (11) s (t) = 6.4 x 103 0 t (12) t = 0.80 x 102 s ppc (13) M x t /M Pc I s I \ ppc/ s ppc \ ppc where sppc and s0(t) are expressed in nc/ml, M in curies, ^ and tppc in sees, and ^J in discharges per month. - An inspection of Tables 3 and 5 reveals that most of the signifi- cant isotopes in the primary coolant have ppc values for coastal water between the values 10'7 nc/ml and 10*9 ^c/ml. Table 7 presents, for this range of ppc values, some sample computations of the time (tppc) for the maximum concentration resulting from a single discharge of M curies to be reduced to the ppc value for the environment, and the per- missible number of such discharges, N, per month, for the "typical" harbor described above. The marine locale is considered unsuitable as a receiver of any discharge for which the value of N is less than 1 .0 per month. Thus, for this sample situation, it would be considered unsafe to introduce a single discharge in which the ratio M/sppc TABLE 7 Sample computations for a "typical" small harbor of poor flushing characteristics, giving the time (tppc) for the maximum concentra- tion resulting from a single discharge of M curies to be reduced to the ppc value for the environment Uppc), and the permissible num- ber of such discharges per month (N) for various values of s in nc/ml. (curies/nc/ml) IO4 10s 10* 107 108 M, in curies for W 'ppc (days) N (per month) SPPc sppc = 10'8 sppc (sscs) = 10'' = 10'7 8.0 x 103 2.6 x 104 9.3 x 10'2 3.0 x 10'1 1.2 x 10s IO'5 10'" io'3 io'2 3.7 x 103 10'" lO'3 8.0 x 104 9.3 x 10'1 1.2 x 102 io'3 io'2 10'' 2.6 x 10s 3.0 3.7 IO'2 10'1 1 8.0 x 10s 9.3 1.2x 10'1 10'' 1 10 35

(curies per iic/ml) was 108 or greater. Slightly less than four dis- charges per month could be made without undue risk for this ratio equal to 107 curies per These data are presented in graphical form in Figure 2, from which the values of the ratio M/sppc for ^J equal to one per month, one per day, and 10 per day have been obtained. Using these ratios, the maximum permissible activities which can be discharged in any single release in this "typical" harbor for the various important isotopes, listed in Tables 3 and 5 for the primary coolant of the SAVANNAH and the NAUTILUS, have been calculated for these three rates of discharge. The results are presented in Table 8. This computation applies to the hypothetical case in which the discharge is composed of only a single isotope. For the actual situation the additive effect of the combination of isotopes present must be con- sidered. Assuming that the relative composition of the isotopes in the primary coolant remains fairly constant (a condition which has been shown to exist for the NAUTILUS), then the weighted mean ppc value for the isotope mix may be utilized in computing a permissible gross activity, which can be compared to the gross activity in the actual dis- charge resulting from the listed isotopes. This has been done for the isotope mix in the primary coolant for both the SAVANNAH and the NAUTILUS. A comparison of the permissible activities given in Table 8 with the activities which have been predicted to exist in the warm-up volume discharge from the SAVANNAH, as given in Table 3, indicates that the predicted gross activity due to the listed isotopes exceeds the computed permissible activity even for only a single release per month. Also the predicted activity for Co 60 and Ta 182 both exceed the computed per- missible activities for these individual isotopes. It would thus appear undesirable to have a general operating doctrine which would allow liquid effluents of the volume and activity predicted for the warm-up volume of primary coolant from the SAVANNAH to be discharged into harbors and estuaries. It should again be pointed out that the basis of this conclusion involves the most conservative (safe) assumptions re- garding the eating habits of a selected segment of the population, and also regarding biological uptake of the radioisotopes. Such assumptions are not unduly conservative for a country such as Japan, where the bulk of the protein requirement is supplied from seafood. The assumptions may well be overly conservative for the coast of the United States. However, recommendations on general operating doctrine for nuclear- powered merchant ships must envision these ships operating in areas in which the most restrictive conditions as to waste discharge would apply. A comparison of the figures in Table 8 with the average measured activities in the primary coolant expansion volumes for the NAUTILUS as given in Table 5 suggests quite a different conclusion. The observed activities for each isotope, as well as the computed gross activity as- suming an isotope mix with the observed activities for the listed isotopes, 36

M/s (curies/iic/ml) FIGURE 2 The permissible number (N) of discharges of primary coolant which can be made, per month, into a "typical" harbor, as a function of the ratio of total activity per discharge, M, in curies, to the ppc values for coastal waters in c ml. 37

TABLE 8 Tabulation, for the discharge of primary coolant expansion volumes into a "typical1 harbor of low flushing rate (see text for assumed conditions), of the permissible total activity, for each isotope, per discharge, assuming the discharge contains only that single isotope, and the permissible gross activity for the isotope mix in the primary coolant of the SAVANNAH* and the NAUTILUS*. ppc for coastal waters Permissible activity for 1 discharge per month Permissible activity for 1 discharge per day Permissible activity for 10 discharges per day Isotope (ne/ml) (curies) (curies) (curies) Co 60 3 X IO'9 7 .5x io'2 7 ,5x 10'3 1.6 x io'3 Fe55 8 x IO'8 2 .0 2 .Ox 10'' 4.3 x io'2 Fe59 5 x 10'' 1 .2 x io'1 1 .2 x I0'2 2.7 x io'3 Cr51 2 x 10'6 5 .Ox 10 5 .0 1.1 To 182 4 x io'8 1 .0 1 .Ox 10'1 2.2 x I0'2 Cu64 4 x IO'8 1 .0 1 .Ox 10'1 2.2 x I0'2 Sr90 5 x 10'' 1 .2x io'1 1 .2x I0'2 2.7 x 10'3 Ce 144 1 x 10'' 2 .5x io'2 2 .5x io'3 5.4 x io'4 Cs 137 4 x io'7 1 .Ox 10 1 .0 2.2 x io'1 Ru 106 1 X IO'8 2 .5x io'1 2 .5x io'2 5.4 x io'3 1 131 3 X IO'8 7 .5x io'1 7 .5x I0'2 1.6 x io'2 Primary * 2 x 10'8 2.2 x 10'' 2.2 x 10'2 4.7 x 10'3 Coolant SAVANNAH Primary * 4 x 10'8 8.8 x 10'1 8.8 x 10'2 1.9 x 10'2 Coolant NAUTILUS 'Assuming that the isotope mix in the primary coolant is composed of only the isotopes listed in Table 3 for the SAVANNAH and Table 5 for the NAUTILUS. Operational experience on the NAUTILUS shows that due to the presence of very short lived isotopes, the measured gross activity of the primary coolant, 15 minutes after sampling, is about 3.5 times the gross activity resulting only from the isotopes listed in Table 5. 38