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Abstract

In a broad-scale risk analysis of hazardous waste isolation by incorporating it into rock, the principal failure scenario is for the waste material to be dissolved out of the rock by groundwater, to be carried with the groundwater close to the surface, and then to be ingested by humans. Based on average conditions and average rock behavior, the probability per year for an atom of this waste rock to be dissolved in groundwater and, after it reaches the surface, the probability of it being ingested by a human via various pathways are negligible. These pathways include potable water derived from rivers and from wells, freshwater fish as a food, agricultural use of irrigation, deposition by rivers of silt that is later used for agriculture, and—after the material has reached the ocean—human consumption of seafood. The time delay between waste burial and human ingestion, courtesy of common geologic features and processes, is the key to effective long-term isolation.

Introduction

One of the key issues in the use of nuclear power is “What are we going to do with the highly radioactive waste products?” the simple answer is “We are going to convert them into rocks and emplace them in the natural habitat of rocks, deep underground.” Numerous analyses have demonstrated that this provides safe disposal, which raises the question of whether that process may be applicable to other toxic waste products. The purpose here is to contribute to answering that question.

Let us assume that the “artificial rock” created from the toxic waste behaves like average natural rock underlying the United States (48 contiguous states). Hopefully, the architects of the system would be able to provide a waste package and locate a burial site so as to assure behavior no less favorable than average rock. The results of an analysis should then be a conservative, i.e., more likely to overestimate than to underestimate the hazard, representation of the average result for burial at randomly selected locations in the United States. A safety analysis for this waste rock can be reduced to the problem of evaluating the probability, P, for an atom of an average rock to escape its burial site and eventually be ingested by a human being. The mechanism is assumed to be as follows: the atom is dissolved from the rock material by groundwater with the probability P(GW), it moves without permanent loss with the groundwater to the surface, and thence it gets ingested with human food or drinking water with probability P(I). Thus,  

formula
(1)

In evaluating P(GW), the burial depth is assumed to be 600 m below the surface, although a brief discussion is included for other depths.

The next section discusses time delays between the atom's escape from the rock and its human ingestion, and the subsequent sections describe different methods for estimating P(GW) in Equation 1 and various contributions to P(I) that should be summed to give P(I) in Equation 1.

Time Delays Between Escape from Rock and Human Ingestion

For most toxic wastes, the time delay between burial and eventual human ingestion may be an important consideration. For example, radioactive wastes lose their toxicity with their half-lives for natural decay; as another example, for materials that can cause cancer when ingested, a delay of thousands of years before ingestion may be considered adequate because cancer will very probably be curable by that time.

Since groundwater in aquifers reaching deep underground typically takes many hundreds or thousands of years to reach the surface (Heath, 1998), the slowness of groundwater movement alone should provide an important time delay. Moreover, nearly all materials dissolved in groundwater are held up by ion exchange and other adsorption processes in the rock through which the water travels and, hence, move hundreds or thousands of times more slowly than the groundwater itself (Schneider and Platt, 1974). In many, if not most, situations, this would extend the time delay before the toxic material gets to the surface to a million years or more. These time delays vary with the chemical composition of the toxic material and the nature of the rock.

A substantial fraction of human ingestion occurs promptly after the material reaches surface waters, but for some materials, there would be additional significant time delays for some pathways to ingestion. These will be noted in the discussion of those pathways.

Approach 1 For Estimating P(Gw)

From the rate at which rivers carry dissolved and suspended material into the oceans, it is estimated (Garrels and MacKenzie, 1971) that the surfaces of the U.S. land mass (contiguous 48 states) are eroding away at an average rate of 5 × 10−5 m of depth per year. About 28% of this material is in solution, which corresponds to 1.4 × 10−5 m/yr being removed by chemical dissolution. It is estimated (Todd, 1980; Ad Hoc Panel on Hydrology, 1962) that ∼15% of the water flow in rivers is derived from groundwater (aquifers); if the concentrations of dissolved material were the same in rivers as in aquifers, this would mean that the latter dissolve 2.1× 10−6 m/yr (= 0.15 × 1.4 × 10−5) of rock thickness. The average concentrations of some dissolved materials in aquifers (White et al., 1963) and in river water (Bowen, 1979) are shown in Table 1. Because silica and calcium are quite significant constituents of rock, these data are taken to indicate that the concentration of dissolved matter is twice as high in aquifers as in rivers. This leads to the conclusion that 26% (= 0.30/[0.30 + 0.85]) of the dissolved material in rivers, 3.6 × 10−6 m/yr (= 0.26 × 1.4× 10−5) of rock depth, is contributed by groundwater dissolution of rock.

Table 1.

Average Concentrations of Materials Dissolved in Aquifers and in River Water

ElementAquifers (mg/kg)Rivers (mg/kg)
Silica207
Calcium3015
Magnesium34
Potassium22.2
Iron0.30.5
Uranium3 × 10-44 × 10-4
ElementAquifers (mg/kg)Rivers (mg/kg)
Silica207
Calcium3015
Magnesium34
Potassium22.2
Iron0.30.5
Uranium3 × 10-44 × 10-4

The next problem is to estimate what fraction of this material, f, is removed per meter of depth at 600 m depth, i.e., from between 599 and 600 m deep. The largest value of f that one might consider is f = 1/600, which would be valid if all depths down to 600 m contributed equally, with no contribution from lower depths. However, no justification for such an assumption is possible; if it were correct, one could achieve perfection by going to slightly lower depths. As a rough first estimate, let us take half of this maximum value, f = 1/1200. The quantity of rock eroded away per meter of depth at 600 m then becomes 3 × 10−9 m/yr (= 3.6× 10−6/1200).

A better estimate than assuming f = 1/1200 can be obtained as follows: the annual circulation of groundwater, defined as the quantity per year entering or leaving aquifers at the stated depth, is given as (Todd, 1980; Ad Hoc Panel on Hydrology, 1962):  

formula

Let us define q(y)dy as the annual circulation between depths y and y + dy and, as suggested by these data, assume a simple but not unreasonable functional dependence  

formula

Setting the integral of q(y)dy between 0 < y < 800 m = 310, and between 800 m and infinity = 6.2, determines the values of a and b, leading to the result  

formula
(2)

The groundwater circulation per meter of depth at 600 m is then determined by setting y = 600 m in Equation 2, giving  

formula

It is reasonable to assume that the amount of material eroded is proportional to the groundwater circulation; f is then the fraction of all groundwater that circulates per meter of depth at 600 m. Dividing q(600 m) by the total groundwater circulation, 316 × 109 (310 + 6.2) m3/yr, then gives f = 2.6 × 10−4, or about one-third of our previous crude estimate of 1/1200. Multiplying this by the value of total rock depth eroded by groundwater (3.6 × 10−6 m/yr) gives the quantity eroded per meter of depth at 600 m: 0.9 × 10−9 m/yr (= 3.6 × 10−6 × 2.6 × 10−4).

If 0.9 × 10−9 m/yr of rock thickness is eroded from one meter of rock thickness between 599 and 600 m depth, the probability per year for a given atom of this rock to be eroded is  

formula
(3)

This result applies for burial at a depth of 600 m. For burial at other depths, in units of ×10−9 per year, the results of analogous calculations give P(GW) = 1.5 at 500 m, P(GW) = 2.5 at 400 m, P(GW) = 4.1 at 300 m, P(GW) = 6.7 at 200 m, and P(GW) = 11 at 100 m. Thus, burial at 600 m rather than at 100 m depth improves safety by a factor of 12 (=11/0.9). It also provides additional time delays since aquifers at shallow depths reach the surface in a much shorter time than deeper aquifers.

To extend the estimate in Equation 3 to times more than a million years into the future, it is necessary to consider the change of depth of the buried waste with time due to erosion of the overlying rock. An average erosion rate of 5 × 10−5 m/yr of depth reduces the burial depth by 100 m for each 2 million years (= 100/5 × 10−5), leading to the increased values of P(GW) at each succeeding depth given in the previous paragraph.

Approach 2 For Estimating P(Gw)

A typical aquifer reaching to the waste burial depth of 600 m is ∼100 km long and has a flow velocity of ∼10 m/yr (Heath, 1998). For a typical porosity of 10%, the annual water discharge per square meter of aquifer cross-sectional area is then 10% of a volume 1 m2 in cross section and 10 m long, or 1 m3. Chemical analyses of groundwater (White et al., 1963) indicate that it typically contains 30 mg/L of calcium (Ca), so that 1 × 103 L of water in this 1 m3 would carry 0.03 kg yr−1 (per square meter of cross-section area) of water into the river it feeds. This is the first entry in column 2 of Table 2, and other entries in column 2 were obtained analogously. Since the aquifer is 1.0 × 105 m long, the volume of rock traversed by the aquifer is 1.0 × 105 m3 per square meter of cross-sectional area, which weighs ∼3 × 108 kg/m2. Typical rock contains (Garrels and MacKenzie, 1971) ∼5% calcium, so the calcium content in the rock traversed by the aquifer is ∼15 × 106 kg/m2 (= 0.05 × 3× 108). This is the first entry in column 3 of Table 2, and the other entries in that column were obtained analogously. If the rock contains 15 × 106 kg/m2 of Ca, and 0.03 kg/m2 of Ca are removed each year, the fractional removal of Ca is 2× 10−9 per year (= 0.03/15× 106). This is the first entry in column 4 of Table 2. This example shows that column 4 is obtained as column 2/column 3, which then allows determination of the other entries in column 4

Table 2.

Calculation of Fractional Removal Per Year of Rock Materials from a Typical Deep Aquifer

Element or ionAmount discharged (kg m-2yr-1)Amount in rock (×106 kg/m2)Fraction removed per year (×10-9)
Ca0.03152
Mg0.00331
K0.00230.7
Fe0.000390.03
U3 × 10-78 × 10-40.3
Silica0.021500.13
Carbonate0.15188
Element or ionAmount discharged (kg m-2yr-1)Amount in rock (×106 kg/m2)Fraction removed per year (×10-9)
Ca0.03152
Mg0.00331
K0.00230.7
Fe0.000390.03
U3 × 10-78 × 10-40.3
Silica0.021500.13
Carbonate0.15188

The probability per year for a given atom to be dissolved out of the rock is just the fraction of all atoms in the rock that are dissolved out per year. Thus, P(GW) is simply the value in column 4 for the element of interest. As a rough average, this is  

formula
which is in agreement with Equation 3. For a specific case, one might use the value in column 4 (Table 2) for the material under consideration.

Estimate of P(I) Due to Ingestion of Potable Water

Important contributions to P(I) derive from the use of rivers and wells drilled into shallow aquifers to provide potable water. The average person ingests ∼2.0 L/d of potable water (ICRP, 1975), which corresponds to ingestion by the U.S. population of 2.0 × 1011 L/yr (= 2.0 × 365 × 2.8 × 108). About 45% of this is derived from wells, and 55% comes from rivers (Byrne, 1974), corresponding to 9 × 1010 and 1.1 × 1011 L/yr, respectively, entering human stomachs. The water flow in U.S. rivers has been estimated to be 1.7 × 1015 L/yr (Garrels and MacKenzie, 1971) and 1.9 × 1015 L/yr (Todd, 1980); we use 1.8 × 1015 L/yr. The water flow in aquifers is estimated to be 16% of the flow in rivers (Ad Hoc Panel on Hydrology, 1962), or 2.9× 1014 L/yr. The contributions to P(I) from use of rivers and wells for potable water are then the ratio of the quantity ingested to the total quantity of flow,  

formula
and  
formula
Note that this ignores the removal of material by filtration processes commonly used for potable water supplies, making these conservative estimates (that is, they are more likely to be high than low).

Estimation of P(I) Via the Freshwater Fish Pathway

About 7 × 107 lb of fish per year are taken from the Mississippi River and its tributaries (U.S. Census Bureau, 1975); the total water flow in this system is 600,000 ft3/s (Britannica, 1978), or 1.2 × 1015 lb/yr. If materials were distributed with equal density between fish and water, and if half of the material in fish enters human bodies (heads, tails, bones, and internal organs are not normally eaten), this would give a P(I) value from freshwater fish of 3 × 10−8 (= 1/2 × 7 × 107/1.2 × 1015). However, most elements concentrate more per unit weight in fish than in the water in which they live by a factor called “the bio-accumulation factor” for freshwater fish, B(fwf). Thus,  

formula
Values of B(fwf) (NRC, 1977) and P(I)fwf values calculated from them using this expression are listed in Table 3. The variations are very large, but with few exceptions, which should be considered individually, they are not larger than 300–400. For such a value, P(I)fwf = 1 × 10−5, which is negligible in comparison with the contributions to P(I) from ingestion of potable water.

One might expect large differences where lakes are involved, but that apparently is not the case. The annual fish catch from the Great Lakes is 7 × 107 lb, about the same as from the Mississippi River and its tributaries (U.S. Census Bureau, 1975); the total water flow through that system is 60% as high (Britannica, 1978). This increases the value of P(I)fwf by a factor of 1.7 (=1/0.6) where lakes rather than rivers are involved.

Both the potable water and freshwater fish pathways lead to prompt human ingestion after the material of interest reaches surface waters. However, there are other pathways by which the material is ingested gradually over a very long time period. These are the subject of the next few sections.

Table 3.

Bio-Accumulation Factors (Nrc, 1977) for Freshwater Fish, B(Fwf), and Probability for Human Ingestion Via Pathway, P(I)fwf, Calculated from Them

ElementB(fwf)P(I) (×10–5)ElementB(fwf)P(I) (×10–5)ElementB(fwf)P(I) (×10–5)
C460014Br4201.3Te4001.2
Na1000.3Rb20006I150.05
P100,000300Sr300.1Cs20006
Cr2000.6Y250.08Ba40.01
Mn4001.2Zr3.30.01La250.08
Fe1000.3Nb30,000100Ce10.003
Co500.15Mo100.03Pr250.08
Ni1000.3Tc150.05Nd250.08
Cu500.15Ru100.03W12003.6
Zn20006Rh100.03Np100.03
ElementB(fwf)P(I) (×10–5)ElementB(fwf)P(I) (×10–5)ElementB(fwf)P(I) (×10–5)
C460014Br4201.3Te4001.2
Na1000.3Rb20006I150.05
P100,000300Sr300.1Cs20006
Cr2000.6Y250.08Ba40.01
Mn4001.2Zr3.30.01La250.08
Fe1000.3Nb30,000100Ce10.003
Co500.15Mo100.03Pr250.08
Ni1000.3Tc150.05Nd250.08
Cu500.15Ru100.03W12003.6
Zn20006Rh100.03Np100.03

P(I) from the Irrigation Pathway

About 1.2 × 1011 gallons of water per day are used for irrigation (Byrne, 1974) in the United States (63% from surface waters and 37% from groundwater); if we multiply this by the conversion factors 3.6 L/gallon and 365 d/y, we find irrigation water use to be 1.6 × 1014 L/yr, or 9% of the total water flow in rivers. Half of this 9% eventually reaches the water table and returns to rivers by groundwater flow (Heath, 1998), presumably bringing with it the dissolved material. This leaves the material dissolved in 4.5% of the total original water permanently in the ground where it can eventually be picked up by plant roots and get into food supplies. The rate of this transfer into human stomachs can be estimated from information on daily per capita dietary intake, D, for various chemical elements (ICRP, 1975; Gunderson, 1983, personal commun. [Food and Drug Administration]; Pennington, 1983, personal commun. [Food and Drug Administration]). Multiplying D by the U.S. population and 365 d/yr gives the annual transfer rate, R(I), from the ground under the United States into human ingestion to be  

formula
where D is in mg d−1 person−1. This transfer would go on year after year indefinitely, except for the fact that soil is being removed by erosion and transferred into the oceans. The rate of this process for the contiguous 48 states is 1.0 × 1012 kg/yr (Garrels and MacKenzie, 1971). If C is the concentration of an element in soil in mg/kg, the rate of removal by erosion, R(E), is then  
formula
The probability for an atom to be ingested by a human before it is eroded away, P(I/E), is then  
formula
where D is in mg/d and C is in mg/kg. The total probability for an atom originally dissolved in groundwater to enter a human stomach, P(I), is the probability that the water in which it is dissolved will be used for irrigation and will leave the dissolved material in the ground; this is given above as 0.045 times P(I/E), or  
formula
(4)
Values of D/C for various elements and P(I)irrig values calculated from them with Equation 4 are listed in Table 4; for elements that do not occur in nature, an alternative method for determining the equivalent of D/C (Cohen, 1984) is used there. Table 4 shows that P(I)irrig values vary by several orders of magnitude for different elements. For half of the elements listed, including the heaviest ones, P(I)irrig < 1.0 × 10−4, irrigation is a relatively negligible contributor to P(I) in comparison with the contributions from use of potable water. For a few elements with large values of D/C, the very long-term effects of irrigation could be much more important and should be considered separately.

Table 4.

Data For Determining Probability For Ingestion Via The Irrigation Pathway

ElementD (mg/d)C(mg/kg)P(I)irrig (×10–4)ElementD(mg/d)CP(I)irrig (×10–4)
Li2.0254Zr4.24000.6
Be0.0120.32Nb0.62103.1
B1.3203.2Mo0.31.212
Mg34050003.4Tc33
Al4571,0000.33Ag0.070.0570
Ca116015,0003.8Cd0.0280.354
Ti0.8550000.009Sn4450
V2901.1Sb0.0512.5
Cr0.15700.1l0.252
Mn3.510000.17Cs0.0140.12
Fe1840,0000.022Ba0.755000.08
Co0.381.9Hg0.0040.063.4
Ni0.4500.4Tl0.00150.20.38
Cu1.5302.5Pb0.070120.29
Zn15908.5Ra2.3 × 10-98 × 10-70.15
Ge1.5175Th0.00390.016
As0.05560.4U0.00192.70.035
Se0.120.416Np0.23
Br7.51038Pu0.001
Rb2.21500.8Am0.007
Sr1.92500.4Cm0.0003
ElementD (mg/d)C(mg/kg)P(I)irrig (×10–4)ElementD(mg/d)CP(I)irrig (×10–4)
Li2.0254Zr4.24000.6
Be0.0120.32Nb0.62103.1
B1.3203.2Mo0.31.212
Mg34050003.4Tc33
Al4571,0000.33Ag0.070.0570
Ca116015,0003.8Cd0.0280.354
Ti0.8550000.009Sn4450
V2901.1Sb0.0512.5
Cr0.15700.1l0.252
Mn3.510000.17Cs0.0140.12
Fe1840,0000.022Ba0.755000.08
Co0.381.9Hg0.0040.063.4
Ni0.4500.4Tl0.00150.20.38
Cu1.5302.5Pb0.070120.29
Zn15908.5Ra2.3 × 10-98 × 10-70.15
Ge1.5175Th0.00390.016
As0.05560.4U0.00192.70.035
Se0.120.416Np0.23
Br7.51038Pu0.001
Rb2.21500.8Am0.007
Sr1.92500.4Cm0.0003

Note: D—human dietary intake; C—concentration in soil.

P(I) Through Seafood Derived from the Oceans

Eventually, nearly all of the material dissolved in ground-water and rivers goes into the oceans, from which the most important pathway to human ingestion is through seafood. The annual world seafood catch is 2.5 × 107 tonne of fish plus 0.5 × 107 tonne of shell fish (Byrne, 1974), giving a total of 3.0 × 107 tonne, whereas the total mass of water in the world's oceans is 1.4 × 1018 tonne (Garrels and MacKenzie, 1971). Assuming that half of this seafood catch enters human stomachs, the transfer probability per year for an atom in the ocean into human stomachs, P′, is  

formula
(5)
where C(SF) and C(O) are the concentrations of the element of interest in seafood and in oceans, respectively.

Values of C(SF) (Hall et al., 1978), C(O) (Quimby-Hunt and Turekian, 1983), and P values calculated from them using Equation 5 are listed in Table 5. In calculating C(SF), it is assumed that seafood consists of 84.3% fish, 10.2% crustacea, and 5.6% mollusca. Table 5 shows that the median value of P′ is ∼5 × 10−8 yr−1.

To assess the total probability for this transfer, it is necessary to estimate how long an atom remains in the ocean before settling permanently into the bottom sediments. Assuming that the quantity of each chemical element in the oceans is in equilibrium—that is, the rate of settling into bottom sediments is equal to the rate at which new material is brought into the oceans by rivers—the average residency time in the ocean, T(O), is the ratio of the total quantity of the element in the oceans, given previously as 1.4 × 1018C(O), to the quantity inserted by rivers. The total river flow into the world's oceans is 3.2 × 1013 tonne/yr (Garrels and McKenzie, 1971). Thus,  

formula
(6)
where C(R) is the concentration in rivers (Bowen, 1979). Values of C(R) and T(O) calculated from Equation 6 are listed in Table 5. The total eventual probability for transfer from the ocean via seafood to human dietary intake is then  
formula
(7)

Values of P(I)sf calculated from Equation 7 are listed in Table 5. It shows that the probability for ingestion via the seafood pathway can be an important contributor to P(I). This ingestion of seafood is distributed over the world population; the probability of ingestion by the U.S. population would represent only a few percent of the values in Table 5.

Table 5.

Data for Determining Probability for Eventual Ingestion Via the Seafood Pathway

ElementC(SF)(×10–6)C(O) (×10–9)C(R) (×10-9)P'(×10-8 yr-1)T(O)(×10-4 yr-1)P(I)sf(×10-4)
V0.341.00.50.348.62.9
Cr0.180.331.00.541.40.77
Mn0.390.0108390.00540.21
Ni0.270.480.50.564.12.3
Cu1.620.123130.172.3
Zn12.80.3915330.113.7
As3.82.00.51.91733
Se0.790.170.24.63.717
Mo0.27110.50.025952.3
Ag0.060.0030.3200.0430.86
Cd0.080.0700.11.133.4
Sn0.60.00050.00912000.24300
Sb0.860.20.24.34.318
Hg0.0940.0060.1160.264.0
Pb0.510.0010.55100.0094.4
ElementC(SF)(×10–6)C(O) (×10–9)C(R) (×10-9)P'(×10-8 yr-1)T(O)(×10-4 yr-1)P(I)sf(×10-4)
V0.341.00.50.348.62.9
Cr0.180.331.00.541.40.77
Mn0.390.0108390.00540.21
Ni0.270.480.50.564.12.3
Cu1.620.123130.172.3
Zn12.80.3915330.113.7
As3.82.00.51.91733
Se0.790.170.24.63.717
Mo0.27110.50.025952.3
Ag0.060.0030.3200.0430.86
Cd0.080.0700.11.133.4
Sn0.60.00050.00912000.24300
Sb0.860.20.24.34.318
Hg0.0940.0060.1160.264.0
Pb0.510.0010.55100.0094.4

Note: C(SF)—concentration in seafood; C(O)—concentration in the oceans; C(R)—concentration in rivers; P—probability per year for the material to be ingested by a human; T(O)—time the material spends in the oceans; P(I)sf—total probability for eventual human ingestion.

Probability For Human Ingestion Via Silt Deposited by Rivers

The preceding discussion assumes that all of the material carried by rivers eventually enters the oceans. However, some of this material is deposited as silt before it reaches the ocean. The contribution of this material to P(I), P(I)silt, can be estimated by the same procedure as was used for the irrigation pathway, where it was assumed that 4.5% of the material in rivers behaves effectively as deposited silt. As a hypothetical example, if 9% of the material in rivers is deposited as silt, the contribution to P(I) would be twice the values given in Table 4. However, the amount of material delivered to the oceans would then be 9% less than we have assumed previously, reducing the value of P(I)sf from Table 5 by 9%.

The fraction of material in rivers that is deposited as silt is highly variable for different rivers and also according to where in a given river the material is introduced. No data were found for the average fraction of material in rivers so deposited. For nearly all elements, the contribution to P(I) in Table 5, via the seafood pathway, is larger than the contribution in Table 4 that is interpreted as applying to the silt pathway. Thus, the assumption that none of the material is deposited as silt, and all of it gets into the oceans, does not underestimate the harmful effects.

Inhalation Pathway

Some of the material at the surface may get into the air as suspended particulate and subsequently be inhaled by people. Typical suspended particulate levels are generally below 50 ×10−6 g/m3, and humans inhale ∼20 m3 of air per day. This means they inhale less than 0.001 g per day of particulate (=20 × 50 ×10−6) (and 95% of this is filtered out by hairs in the nose, pharynx, trachea, and bronchi and is removed by mucous flow), whereas they consume ∼1000 g per day of food and 2000 g per day of water. Exposures to various body organs from a given intake of material depend on whether the intake is by inhalation or by oral ingestion, but they rarely differ by more than a factor of 1000 (ICRP, 1979). Thus, the fact that we take in by oral ingestion millions of times more material than by inhalation of suspended particulate indicates that the latter is negligible. Moreover, the direct pathway from groundwater to human oral ingestion through the use of potable water is much stronger than any pathway involving suspension as airborne particulate. It is therefore safe to ignore the inhalation pathway as a contributor to P(I).

Summary

The probability, P, for an atom of dangerous waste, converted into a rock and buried deep underground, to eventually be ingested by a human is given by Equation 1, where P(GW) may be determined by one of the two methods given, and where P(I) is taken to be the sum of contributions via pathways of potable water, freshwater fish, irrigation, silt deposition, and seafood, all of which are presented here. For many elements, including the important contributors to the toxicity of high-level radioactive waste from nuclear power plants, P(GW) is ∼1.0 × 10−9, and P(I) is dominated by the potable water pathway, giving P(I) = 4 × 10−4, whence  

formula

For a few elements, P(I) may be as much as 100 times higher, leading to P values as high as 4 × 10−11. For practical considerations, the most important advantage of converting the hazardous material to a rock and burying it deep underground is the long time delay before the material can reach human ingestion. In essentially all situations, this delay is tens of thousands of years or longer. It is highly probable that the consequences of these hazards will be greatly reduced by progress in medical science well within such time periods.

However, the economics of spending large sums of money today to save lives in the far future is even more worthy of consideration (Cohen, 1983). There are now many ways to save lives by spending money (Cohen, 1980). Cancer screening programs and highway safety measures could save lives for a few hundred thousand dollars each. Money could be spent on improved medical care, improved nutrition, public health, etc., to save lives. There will undoubtedly be many ways to spend money to save lives in the far future in ways that cannot now be foreseen. Thus, rather than spending lots of money now to save those lives, it would be much more effective to set up a trust fund for future generations to spend for that purpose. This has the tremendous added advantage that the trust fund would accrue interest in the meantime. One dollar invested now at 3% real interest (discounting inflation) would be worth $3,000,000 after 500 yr, and $9,000,000,000,000 after 1000 yr. With the better understanding that future generations would have about threats to their lives, and with the advanced technology available to them, this would surely be a much more effective life-saving strategy.

If it seems impractical to set up a trust fund, the current generation could simply not spend the money, reducing the national debt that future generations will otherwise have to pay. That effectively transfers money to future generations. Another alternative is to spend the money on biomedical research, which will save lives in future generations. Every $600,000 spent on biomedical research in the period 1930–1975 now saves one U.S. life per year plus many more in the rest of the world. With these perspectives, the time delay achieved by converting toxic materials to rock and burying them deep underground is a very effective life-saving strategy.

References Cited

Ad Hoc Panel On Hydrology
,
1962
,
Scientific Hydrology
:
Washington, D.C.
,
Scientific Council for Science and Technology.
 
37
p.
Bowen
,
H.J.M.
,
1979
,
Environmental Chemistry of the Elements
:
New York
,
Academic Press.
333
p.
Britannica Encyclopaedi
,
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New York
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W.W. Norton.
397
p.
Hall
,
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Zook
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E.G.
Meaburn
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G.M.
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National Marine Fishery Service Survey of Trace Elements in the Fishery Resource
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National Oceanic and Atmospheric Administration Technical Report NMFS SSRF-721.
 
314
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Heath
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U.S. Geological Survey Water-Supply Paper 2220.
 
84
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ICRP (International Commission on Radiological Protection)
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 :
International Commission on Radiological Protection Publication No. 23: Oxford, Pergamon Press.
480
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ICRP
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International Commission on Radiological Protection Publication 30
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3
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1–4
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555
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,
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,
Calculation of annual doses to man from routine releases of reactor effluents for the purpose of evaluating compliance with 10 CFR Part 50, Appendix I, Regulatory Guide 1.109
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Washington, D.C.
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U.S. Nuclear Regulatory Commission.
 
69
p.
Quimby-Hunt
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M.S
Turekian
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K.K.
,
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Distribution of Elements in Sea Water
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Eos (Transactions, American Geophysical Union)
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64
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130
131
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Schneider
,
K.J.
Platt
,
A.M.
,
1974
,
High Level Radioactive Waste Management Alternatives
:
Battelle Northwest Laboratory Report BNWL-1900
 .
Todd
,
D.K.
,
1980
,
Ground Water Hydrology
 :
New York
,
John Wiley & Sons.
535
p.
U.S. Census Bureau
,
1975
,
Statistical Abstract of the United States
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Washington, D.C.
,
U.S. Government Printing Office.
White
,
D.E.
Hein
,
J.D.
Waring
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G.A.
,
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: in
Data of Geochemistry
 :
Reston, Virginia
,
U.S. Geological Survey
.

Figures & Tables

Table 1.

Average Concentrations of Materials Dissolved in Aquifers and in River Water

ElementAquifers (mg/kg)Rivers (mg/kg)
Silica207
Calcium3015
Magnesium34
Potassium22.2
Iron0.30.5
Uranium3 × 10-44 × 10-4
ElementAquifers (mg/kg)Rivers (mg/kg)
Silica207
Calcium3015
Magnesium34
Potassium22.2
Iron0.30.5
Uranium3 × 10-44 × 10-4
Table 2.

Calculation of Fractional Removal Per Year of Rock Materials from a Typical Deep Aquifer

Element or ionAmount discharged (kg m-2yr-1)Amount in rock (×106 kg/m2)Fraction removed per year (×10-9)
Ca0.03152
Mg0.00331
K0.00230.7
Fe0.000390.03
U3 × 10-78 × 10-40.3
Silica0.021500.13
Carbonate0.15188
Element or ionAmount discharged (kg m-2yr-1)Amount in rock (×106 kg/m2)Fraction removed per year (×10-9)
Ca0.03152
Mg0.00331
K0.00230.7
Fe0.000390.03
U3 × 10-78 × 10-40.3
Silica0.021500.13
Carbonate0.15188
Table 3.

Bio-Accumulation Factors (Nrc, 1977) for Freshwater Fish, B(Fwf), and Probability for Human Ingestion Via Pathway, P(I)fwf, Calculated from Them

ElementB(fwf)P(I) (×10–5)ElementB(fwf)P(I) (×10–5)ElementB(fwf)P(I) (×10–5)
C460014Br4201.3Te4001.2
Na1000.3Rb20006I150.05
P100,000300Sr300.1Cs20006
Cr2000.6Y250.08Ba40.01
Mn4001.2Zr3.30.01La250.08
Fe1000.3Nb30,000100Ce10.003
Co500.15Mo100.03Pr250.08
Ni1000.3Tc150.05Nd250.08
Cu500.15Ru100.03W12003.6
Zn20006Rh100.03Np100.03
ElementB(fwf)P(I) (×10–5)ElementB(fwf)P(I) (×10–5)ElementB(fwf)P(I) (×10–5)
C460014Br4201.3Te4001.2
Na1000.3Rb20006I150.05
P100,000300Sr300.1Cs20006
Cr2000.6Y250.08Ba40.01
Mn4001.2Zr3.30.01La250.08
Fe1000.3Nb30,000100Ce10.003
Co500.15Mo100.03Pr250.08
Ni1000.3Tc150.05Nd250.08
Cu500.15Ru100.03W12003.6
Zn20006Rh100.03Np100.03
Table 4.

Data For Determining Probability For Ingestion Via The Irrigation Pathway

ElementD (mg/d)C(mg/kg)P(I)irrig (×10–4)ElementD(mg/d)CP(I)irrig (×10–4)
Li2.0254Zr4.24000.6
Be0.0120.32Nb0.62103.1
B1.3203.2Mo0.31.212
Mg34050003.4Tc33
Al4571,0000.33Ag0.070.0570
Ca116015,0003.8Cd0.0280.354
Ti0.8550000.009Sn4450
V2901.1Sb0.0512.5
Cr0.15700.1l0.252
Mn3.510000.17Cs0.0140.12
Fe1840,0000.022Ba0.755000.08
Co0.381.9Hg0.0040.063.4
Ni0.4500.4Tl0.00150.20.38
Cu1.5302.5Pb0.070120.29
Zn15908.5Ra2.3 × 10-98 × 10-70.15
Ge1.5175Th0.00390.016
As0.05560.4U0.00192.70.035
Se0.120.416Np0.23
Br7.51038Pu0.001
Rb2.21500.8Am0.007
Sr1.92500.4Cm0.0003
ElementD (mg/d)C(mg/kg)P(I)irrig (×10–4)ElementD(mg/d)CP(I)irrig (×10–4)
Li2.0254Zr4.24000.6
Be0.0120.32Nb0.62103.1
B1.3203.2Mo0.31.212
Mg34050003.4Tc33
Al4571,0000.33Ag0.070.0570
Ca116015,0003.8Cd0.0280.354
Ti0.8550000.009Sn4450
V2901.1Sb0.0512.5
Cr0.15700.1l0.252
Mn3.510000.17Cs0.0140.12
Fe1840,0000.022Ba0.755000.08
Co0.381.9Hg0.0040.063.4
Ni0.4500.4Tl0.00150.20.38
Cu1.5302.5Pb0.070120.29
Zn15908.5Ra2.3 × 10-98 × 10-70.15
Ge1.5175Th0.00390.016
As0.05560.4U0.00192.70.035
Se0.120.416Np0.23
Br7.51038Pu0.001
Rb2.21500.8Am0.007
Sr1.92500.4Cm0.0003

Note: D—human dietary intake; C—concentration in soil.

Table 5.

Data for Determining Probability for Eventual Ingestion Via the Seafood Pathway

ElementC(SF)(×10–6)C(O) (×10–9)C(R) (×10-9)P'(×10-8 yr-1)T(O)(×10-4 yr-1)P(I)sf(×10-4)
V0.341.00.50.348.62.9
Cr0.180.331.00.541.40.77
Mn0.390.0108390.00540.21
Ni0.270.480.50.564.12.3
Cu1.620.123130.172.3
Zn12.80.3915330.113.7
As3.82.00.51.91733
Se0.790.170.24.63.717
Mo0.27110.50.025952.3
Ag0.060.0030.3200.0430.86
Cd0.080.0700.11.133.4
Sn0.60.00050.00912000.24300
Sb0.860.20.24.34.318
Hg0.0940.0060.1160.264.0
Pb0.510.0010.55100.0094.4
ElementC(SF)(×10–6)C(O) (×10–9)C(R) (×10-9)P'(×10-8 yr-1)T(O)(×10-4 yr-1)P(I)sf(×10-4)
V0.341.00.50.348.62.9
Cr0.180.331.00.541.40.77
Mn0.390.0108390.00540.21
Ni0.270.480.50.564.12.3
Cu1.620.123130.172.3
Zn12.80.3915330.113.7
As3.82.00.51.91733
Se0.790.170.24.63.717
Mo0.27110.50.025952.3
Ag0.060.0030.3200.0430.86
Cd0.080.0700.11.133.4
Sn0.60.00050.00912000.24300
Sb0.860.20.24.34.318
Hg0.0940.0060.1160.264.0
Pb0.510.0010.55100.0094.4

Note: C(SF)—concentration in seafood; C(O)—concentration in the oceans; C(R)—concentration in rivers; P—probability per year for the material to be ingested by a human; T(O)—time the material spends in the oceans; P(I)sf—total probability for eventual human ingestion.

Contents

References

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High Level Radioactive Waste Management Alternatives
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Ground Water Hydrology
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John Wiley & Sons.
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U.S. Census Bureau
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Washington, D.C.
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U.S. Government Printing Office.
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Waring
,
G.A.
,
1963
,
Chemical composition of sub-surface waters
: in
Data of Geochemistry
 :
Reston, Virginia
,
U.S. Geological Survey
.

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