## Nuclear Radioactive Waste NUC

NUC.l CLASSIFICATION OF RADIOACTIVE WASTES

Provide answers to the following questions:

1. What is a radioactive waste?

2. What are the different categories of radioactive wastes?

3. Identify at least three sources of radioactive wastes.

4. Describe methods by which the volume of radioactive waste may be minimized.

### Solution

1. Radioactive wastes are waste materials that consist of unstable isotopes. Over time, the materials decay to a more stable form (or element) emitting potentially harmful energy in the process.

2. Radioactive wastes are present in several forms. These forms are identified as follows:

• Transuranic waste (TRU)

• Uranium mine and mill tailings

• Naturally occurring radioactive wastes

3. Sources of radioactive wastes include:

• Nuclear power

• Government waste (nuclear defense)

• Medical radiotherapy/hospitals

• Mining waste (particularly phosphate mining)

• Normally occurring radioactive materials

• Industrial waste

NUC.3 MECHANISMS OF RADIOACTIVE TRANSFORMATIONS

4. One method of radioactive waste minimization is to compact the waste into a smaller, more densely packed volume. A second method is by incineration, specifically of exposed organic materials. A third method of waste volume reduction is by either dewatering (filtration) and/or evaporation for water removal and recovery.

### NUC.2 NUCLEAR ACCIDENTS

Three historical events have been recognized as significant radiological accidents. These events include the meltdown at Chernobyl, the partial meltdown at Three Mile Island, and an incident of radioactive waste mishandling in Brazil. Elaborate on the events that occurred in Brazil. What were the impacts on the public health of the local community?

### Solution

A stainless steel container holding a small amount of radioactive cesium had been abandoned by a medical clinic in Brazil and ended up in a junkyard. Local inhabitants, in an attempt to salvage junk, discovered the container and forced it open to inspect the contents. Discovering the luminescent cesium, the locals used the materials as costume glitter, exposing their skin, face, and clothing to direct contact with the radioactive material. People exposed directly to the cesium suffered from severe illness and death. The release of approximately 1 g of the radioactive cesium generated over 40 tons of additional radioactive waste from exposed homes and clothing.

NUC.3 MECHANISMS OF RADIOACTIVE TRANSFORMATIONS

Identify the three mechanisms of radioactive transformation of unstable elements.

### Solution

Radioactive transformations are accomplished by several different mechanisms, most importantly alpha particle, beta particle, and gamma ray emissions. Each of these mechanisms are spontaneous nuclear transformations. The result of these transformations is the formation of different stable elements. The kind of transformation that will take place for any given radioactive element is a function of the type of nuclear instability as well as the mass/energy relationship. The nuclear instability is dependent on the ratio of neutrons to protons; a different type of decay will occur to allow for a more stable daughter product. The mass/energy relationship states that for any radioactive transformations the laws of conservation of mass and the conservation of energy must be followed.

An alpha particle is an energetic helium nucleus. The alpha particle is released from a radioactive element with a neutron-to-proton ratio that is too low. The helium nucleus consists of two protons and two neutrons. The alpha particle differs from a helium atom in that it is emitted without any electrons. The resulting daughter product from this type of transformation has an atomic number that is two less than its parent and an atomic mass number that is four less. Below is an example of alpha decay using polonium (Po); polonium has an atomic mass number (protons and neutrons) and atomic number of 210 and 84, respectively.

84Po210 - 2He4 + 82Pb206

The terms He and Pb represent helium and lead, respectively. This is a useful example because the lead daughter product is stable and will not decay further. The neutron-to-proton ratio changed from 1.50 to 1.51, just enough to result in a stable element. Alpha particles are known as having a high LET or linear energy transfer. The alphas will only travel a short distance while releasing energy. A piece of paper or the top layer of skin will stop an alpha particle. So, alpha particles are not external hazards but can be extremely hazardous if inhaled or ingested.

Beta particle emission occurs when an ordinary electron is ejected from the nucleus of an atom. The electron (e), appears when a neutron («) is transformed into a proton within the nucleus:

Note that the proton is shown as a hydrogen (H) nucleus. This transformation must conserve the overall charge of each of the resulting particles. Contrary to alpha emission, beta emission occurs in elements that contain a surplus of neutrons. The daughter product of a beta emitter remains at the same atomic mass number but is one atomic number higher than its parent. Many elements that decay by beta emission also release a gamma ray at the same instant. These elements are known as beta-gamma emitters. Strong beta radiation is an external hazard because of its ability to penetrate body tissue.

Similar to beta decay is positron emission, where the parent emits a positively charged electron. Positron emission is commonly called beta-positive decay. This decay scheme occurs when the neutron-to-proton ratio is too low and alpha emission is not energetically possible. The positively charged electron, or positron, will travel at high speeds until it interacts with an electron. Upon contact, each of the particles will disappear and two gamma rays will result. When two gamma rays are formed in this manner, it is called annihilation radiation.

Unlike alpha and beta radiation, gamma radiation is an electromagnetic wave with a specified range of wavelengths. Gamma rays cannot be completely shielded against but can only be reduced in intensity with increased shielding. Gamma rays typically interact with matter through the photoelectric effect, Compton scattering, pair production, or direct interactions with the nucleus.

NUC.4 FIELD SAMPLING AND MEASUREMENT OF RADIOACTIVE WASTES 467

NUC.4 FIELD SAMPLING AND MEASUREMENT OF RADIOACTIVE WASTES

Describe the varying individual investigations that can be included in a field sampling and measurements program involving nuclear and radioactive wastes.

### Solution

1. Characterization of radiologically contaminated wastes stored or disposed of onsite above or below ground. These may be found in tanks, drums, lagoons, impoundments, piles, pits, or a variety of wood or cardboard containers. The wastes may also be dispersed on the surface or mixed with other media (i.e., soil, water).

2. Hydrogeologic investigations to assess the horizontal and vertical distribution of radiological constituents in the underlying groundwater. This information will, in turn, permit the evaluation of the short- and long-term potential for contaminant dispersion in the groundwater both on- and offsite, and also provide a basis for evaluating the suitability of a site for long-term waste containment and isolation from the environment.

3. Surface and subsurface soils investigations to assess the location and extent of contamination from each significant constituent. In many cases, the prior mixing of the wastes with the soil makes the soil characterization a critical aspect of defining the source strength and extent.

4. Surface water investigation to evaluate the extent of contribution from the source to contamination of local surface water bodies. The sampling program should attempt to distinguish between contributions from runoff, deposition, or cross contamination from groundwater sources. In addition, both in the case of the surface and groundwater investigations, samples should be taken from up-gradient and down-gradient of the contaminant source to isolate the source contribution. Surface water investigations will also include collection and analysis of sediment samples since the sediment frequently acts as a preferential concentrator of contaminants.

5. Air investigations to determine the tendency of airborne particulates and gases to be released into the atmosphere, the on- and offsite migration and deposition patterns, and particularly the concentrations at significant locations such as site boundaries and local residences. In conjunction with the contaminant measurements program, it is also essential that local wind patterns (directions and stability classes) be determined to provide input to the airborne dispersion modeling program. Where wastes contain constituents of the uranium or thorium decay chains, it is necessary that the airborne releases of radon or thoron gas, respectively, be measured in terms of fluxes from the contaminated surface and concentrations at significant receptor points. The values establish the starting point for cleanup activities that will reduce the fluxes to essentially background levels.

6. Local flora and fauna analysis to permit determination as to whether the contaminants have entered the food chain and to assess the tendency of various species to concentrate or eliminate individual contaminants. In some cases, it is necessary to supplement the field investigations with controlled bench- or pilot-scale studies. These studies may be performed to simulate a mobilization or dispersion mechanism, or the complex chemical interactions between the waste form, surrounding matrix, or soil pathways, and/or the effectiveness of certain technologies in preventing migration or providing the required level of isolation. These pilot studies are often defined as feedback and obtained from the assessment of remedial alternatives.

NUC.5 REQUIRED NHV FOR THE INCINERATION OF A RADIOACTIVE WASTE

A radioactive mixture is to be burned in an incinerator at an operating temperature of 1900°F. Calculate the minimum net heating value (NHV) of the mixture in Btu/lb if 0, 20, 40, 60, 80, and 100% excess air is employed. Use the following equation to perform the calculations:

Solution

For this problem,

For 0% excess air:

Similarly,

NHV (20% excess air) = 1097 Btu/lb NHV (40% excess air) = 1313 Btu/lb NHV (60% excess air) = 1635 Btu/lb NHV (80% excess air) =2166 Btu/lb NHV (100% excess air) = 3209 Btu/lb

NUC.7 POWER REQUIREMENT CALCULATION

NUC.6 POTENTIAL LIABILITY

Ruocco Chemical Company transports slurry containing a solid nuclear waste slurry to a disposal site. On average, Ruocco's hauling trucks carry 4 tons of waste per trip for a total of 32,000 tons per year. In the event of a truck overturn, it can be assumed that 2 tons of the waste is spilled. US Department of Transportation (DOT) statistics indicate that 1 out of 4000 waste hauling trucks overturn during an average trip. Studies also indicate that cleanups resulting from transportation spills cost at a minimum as much as $10,000 per ton. Calculate the minimum total potential liability of producing and "disposing" of the waste in this manner. Express the answer on both an annual and per ton basis.

Solution

The potential liability (PL) is solved by the following equation:

$10,000

p^ . _________ x tons spilled\ /« tons of waste\ /I trip \ / spill \

\ton spilled/ \ overturn J\ yr / \z tons/ \4000 trips/

where x = 2 tons spilled/overturn « = 32,000 tons of waste/yr z = 4 tons

PL _ ( $10'000 \ (2 tons spilled\ /32,000 tons of waste\ /1 trip\ / spill \ ~ \ton spilled/ \ overturn / I yr ) \4 tons/ \4000 trips)

= $40,000 per year On a ton basis, the following can be obtained:

NUC.7 POWER REQUIREMENT CALCULATION

Estimate the power required for a conveyor belt system transporting 2.5 tons per hour of radioactive contaminated solids from a location in a utility to a storage bin. The process unit end of the conveyor is at ground level while the top of the storage bin is 25 ft high. The total length of the belt system is 75 ft. Typical power requirements for flat conveyors of this capacity may be assumed to be 2.13 hp per 100 ft. Assume a safety factor of 10%.

470 NUCLEAR/RADIOACTIVE WASTE (NUC) Solution

Calculate the power required to lift the solids:

= (2.5 tons/h)(2000 lb/ton)(25 ft)(l lbf/lb) = 125,000 ft - lbf/h

_ /125,000ft lbf\/ lh \/ hp \ ~ V h / \ 3600 s/ \ 500 ft ■ lbf/ s/

Calculate the power required to operate the conveyor if it were level:

The total power is

The total power, employing a 10% safety factors therefore

Most nuclear wastes are in liquid or solid form. If the waste is solid, it may be transported by various methods: in drums using forklifts, on conveyor belts, suspended in gases in pneumatic conveyors, suspended in liquids as slurries, in screw conveyors, in bucket elevators, etc.

### NUC.8 RADIOACTIVE DECAY

Exponential decay can be described using either a reaction rate coefficient (k) or a half-life (t). The equation that relates these two parameters is as follows:

0.693

Exponential decay can be expressed by the following equation:

NUC.8 RADIOACTIVE DECAY 471

where k = reaction rate coefficient (time- ') N0 = initial amount N = amount at time t

Determine how much of a 100-g sample of Po-210 is left after 5.52 days using:

1. The reaction rate coefficient

2. The half-life

3. Calculate the percent error between the two methods. The half-life for Po-210 is 1.38 days.

Solution

1. Determine the reaction rate coefficient:

The amount of substance left after 5.52 days is as follows:

2. The first step is to determine how many half-lives the 100-g sample has undergone in the given time period:

Therefore, in a 5.52-year period, the 100-g sample has undergone four half-lives.

The amount of the substance left after one half-life is calculated as follows: (0.5)' (100g) = 50g Therefore, the amount of substance left after four half-lives is

3. Since the two equations are, in principle, identical to each other, there is no difference between the two values. The small difference between the two results arises because of roundoff errors.

NIJC.9 PROBABILITY OF EXCESSIVE Pb CONCENTRATION IN TRANSPORT DRUMS

Tests indicate that radioactive sludge waste arriving in 5 5-gal drums to a storage facility has a mean lead content of 15 ppm with a standard deviation of 12 ppm. The drums are unloaded into a 300-gal receiving tank. The storage facility is required to keep the lead concentration at or below 20 ppm in order to meet the required standard. Assume that the lead content from one drum to the next are not correlated, and that the tank is nearly full. What is the probability that the lead content in any drum exceeds 45 ppm?

Solution

Refer to Chapter 52 for normal distribution information and equations.

For a standard deviation of 12 ppm and a mean of 15 ppm, a lead concentration of 45ppm represents (45—15)/12 or 2.5 standard deviations above (displaced from) the mean.

In Figure 85, the area in the "right-hand tail" (above z0) of the normal distribution curve represents the probability that the variable (an event) is z0 standard deviations above the mean. Applied to this problem, the area in the right-hand tail (above a z0 of 2.5) is the probability that the lead content in any drum exceeds 45 ppm. From the table, the area in the right-hand tail corresponding to a z0 of 2.5, is 0.006 or 6% of the total area under the curve. The probability that lead content in a drum exceeds 45 ppm is therefore 0.6%.

z0 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |

0.0 |
0.500 |
0.496 |
0.492 |
0.488 |
0.484 |
0.480 |
0.476 |
0.472 |
0.468 |
0.464 |

0.1 |
0.460 |
0.456 |
0.452 |
0.448 |
0.444 |
0.440 |
0.436 |
0.433 |
0.429 |
0.425 |

0.2 |
0.421 |
0.417 |
0.413 |
0.409 |
0.405 |
0.401 |
0.397 |
0.394 |
0.390 |
0.386 |

0.3 |
0.382 |
0.378 |
0.374 |
0.371 |
0.367 |
0.363 |
0.359 |
0.356 |
0.352 |
0.348 |

0.4 |
0.345 |
0.341 |
0.337 |
0.334 |
0.330 |
0.326 |
0.323 |
0.319 |
0.316 |
0.312 |

0.5 |
0.309 |
0.305 |
0.302 |
0.298 |
0.295 |
0.291 |
0.288 |
0.284 |
0.281 |
0.278 |

0.6 |
0.274 |
0.271 |
0.268 |
0.264 |
0.261 |
0.258 |
0.255 |
0.251 |
0.248 |
0.245 |

0.7 |
0.242 |
0.239 |
0.236 |
0.233 |
0.230 |
0.227 |
0.224 |
0.221 |
0.218 |
0.215 |

0.8 |
0.212 |
0.209 |
0.206 |
0.203 |
0.200 |
0.198 |
0.195 |
0.192 |
0.189 |
0.187 |

0.9 |
0.184 |
0.181 |
0.179 |
0.176 |
0.174 |
0.171 |
0.189 |
0.166 |
0.164 |
0.161 |

1.0 |
0.159 |
0.156 |
0.154 |
0.152 |
0.149 |
0.147 |
0.145 |
0.142 |
0.140 |
0.138 |

1.1 |
0.136 |
0.133 |
0.131 |
0.129 |
0.127 |
0.125 |
0.123 |
0.121 |
0.119 |
0.117 |

1.2 |
0.115 |
0.113 |
0.111 |
0.109 |
0.107 |
0.106 |
0.104 |
0.102 |
0.100 |
0.099 |

1.3 |
0.097 |
0.095 |
0.093 |
0.092 |
0.090 |
0.089 |
0.087 |
0.085 |
0.084 |
0.082 |

1.4 |
0.081 |
0.079 |
0.078 |
0.076 |
0.075 |
0.074 |
0.072 |
0.071 |
0.069 |
0.068 |

1.5 |
0.067 |
0.066 |
0.064 |
0.063 |
0.062 |
0.061 |
0.059 |
0.058 |
0.057 |
0.056 |

1.6 |
0.055 |
0.054 |
0.053 |
0.052 |
0.051 |
0.049 |
0.048 |
0.047 |
0.046 |
0.046 |

1.7 |
0.045 |
0.044 |
0.043 |
0.042 |
0.041 |
0.040 |
0.039 |
0.038 |
0.038 |
0.037 |

1.8 |
0.036 |
0.035 |
0.034 |
0.034 |
0.033 |
0.032 |
0.031 |
0.031 |
0.030 |
0.029 |

1.9 |
0.029 |
0.028 |
0.027 |
0.027 |
0.026 |
0.026 |
0.025 |
0.024 |
0.024 |
0.023 |

2.0 |
0.023 |
0.022 |
0.022 |
0.021 |
0.021 |
0.020 |
0.020 |
0.019 |
0.019 |
0.018 |

2.1 |
0.018 |
0.017 |
0.017 |
0.017 |
0.016 |
0.016 |
0.015 |
0.015 |
0.015 |
0.014 |

2.2 |
0.014 |
0.014 |
0.013 |
0.013 |
0.013 |
0.012 |
0.012 |
0.012 |
0.011 |
0.011 |

2.3 |
0.011 |
0.010 |
0.010 |
0.010 |
0.010 |
0.009 |
0.009 |
0.009 |
0.009 |
0.008 |

2.4 |
0.008 |
0.008 |
0.008 |
0.008 |
0.007 |
0.007 |
0.007 |
0.007 |
0.007 |
0.006 |

2.5 |
0.006 |
0.006 |
0.006 |
0.006 |
0.006 |
0.005 |
0.005 |
0.005 |
0.005 |
0.005 |

2.6 |
0.005 |
0.005 |
0.004 |
0.004 |
0.004 |
0.004 |
0.004 |
0.004 |
0.004 |
0.004 |

2.7 |
0.003 |
0.003 |
0.003 |
0.003 |
0.003 |
0.003 |
0.003 |
0.003 |
0.003 |
0.003 |

2.8 |
0.003 |
0.002 |
0.002 |
0.002 |
0.002 |
0.002 |
0.002 |
0.002 |
0.002 |
0.002 |

2.9 |
0.002 |
0.002 |
0.002 |
0.002 |
0.002 |
0.002 |
0.002 |
0.001 |
0.001 |
0.001 |

2o |
Detail of Tail (.2135, for example, means 0.00135) | |||||||||

2. |
0.,228 |
0.) 179 |
O.i 139 |
0.| 107 |
0.2820 |
0.2621 |
0.2466 |
0.2347 |
0.2256 |
0.2187 |

3. |
0.2135 |
0.3968 |
O.3687 |
0.3483 |
0.j337 |
0.3233 |
O.3I59 |
O.3IO8 |
0.4723 |
0.4481 |

4. |
0.4317 |
0.4207 |
O.4I33 |
O.5854 |
0.5541 |
O.534O |
O.52II |
O.5I3O |
0-6793 |
0.6479 |

5. |
0.6287 |
0.6170 |
0.7996 |
0.7579 |
0.7333 |
0.7190 |
0.7107 |
0-8599 |
0.8332 |
0.8182 |

0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |

a From R. J. Woonacott and T. H. Woonacott, Introductory Statistics, 4th ed., Wiley, New York, 1985.

a From R. J. Woonacott and T. H. Woonacott, Introductory Statistics, 4th ed., Wiley, New York, 1985.

NUC.10 PROBABILITY OF EXCESSIVE Pb CONCENTRATION IN RECEIVING TANK

With reference to Problem NUC.9, (1) what is the probability that the lead content in the receiving tank exceeds 20 ppm? (2) State the limitations of the analysis, and how these limitations could be accommodated.

### Solution

1. To determine the standard deviation of the mean lead concentration in the receiving tank, a basic theorem in probability called the central limit theorem must be employed. If <t represents the standard deviation of the lead concentrations in the drums, then the standard deviation of the mean lead concentration in the receiving tank is given by a/ *Jn where n is the number of drums:

n = 300 gal/(55 gal/drum) = 5.45 drums The standard deviation of the mean is then a 12ppm sfn 75^45

For a standard deviation of 5.1 ppm and a mean of 15 ppm, a lead concentration of 20 ppm is (20— 15)/5.1 or 0.98 standard deviations above the mean.

Again from the normal distribution table, for z0 = 0.98, the probability that the mean lead content in the receiving tank exceeds 20 ppm is 0.164 or 16.4%.

2. The limitations in the analysis and possible accommodations are:

a. The critical assumption made is that the lead content of the drums and waste shipments are not correlated in time. In other words, it has been assumed that it is unlikely that the facility will receive consecutive shipments of waste with a lead content higher than the mean. With multiple drums from a given source, it is highly likely, however, that the drum contents will be correlated.

b. The distribution of the lead content in the problem was assumed to be normal. Concentrations often have skewed distributions, e.g., log-normal.

c. With additional information, e.g., autocorrelation and skewness of the concentration distribution, much more complex and realistic problems can be solved using queuing or inventory techniques. Oversizing the tank would provide a margin of safety.

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