Problems 2.1. Is the statement "The U.S. has 1,300,000 tons of uranium resources" complete? 2.2. Figure 2.16 shows the discovery rate of U308, per foot drilled, in a certain price range. Based on these data, estimate the total amount of uranium that can be recovered in this price range. R (lb/ft) 10 40 80 160 (108) 120 FEET DRILLED FIGURE 2.16 Feet drilled versus the number of pounds per foot of uranium discovered. 2.3. Assuming Eq. (2.1) is correct, what fraction of the earth's uranium can be found within the first 1000 m of the earth's crust? 2.4. In 1976, the U.S. nuclear industry needed about 10,000 tons of U3O8. Assuming that enrichment and tails requirements do not change and the industry increases at a rate of x% per year, how long would it take for the $130/kgU reserves to be exhausted? Assume that the reserves are 600,000 tons of U3Og. After you develop the equation for the time, obtain numerical results for x = 2%, 4%, and 6%. 2.5. Assume that a decision is made to start ordering reactors at a constant rate per year from 1990 until 2030, at which time orders will stop, so that all known uranium reserves of 2.3 million tons (with price up to $260/kgU) will be used up. Assume the following: (a) All plants are identical and need 150 tons of natural uranium per year. (b) It takes 10 years to build a plant. (c) Every plant has a 30-year lifetime. (d) There are 120 plants operating in 1990. (e) Reactors operating in 1990 start retiring in 2000, at the rate of 10/year. For these reactors, consider their needs only after 1990. Calculate how many reactors per year could be ordered and the maxi- mum number of reactors operating at any single time. 2.6. How many 1000-MWe LWRs can the world reserves of uranium serve? Consider the price category up to $80/kgU. Assume that each reactor needs 150 tons of natural uranium per year and has a lifetime of 30 years. Also assume annual refuelings of one-third of the core.