For reference LWR: thermal efficiency is 32%, power

 

• For reference LWR: thermal efficiency is 32%, power 1150 MWe, uranium is $20.85/lb. U3O8, SWU is $39/kgSWU, conversion is $6.30/kgU, fabrication and transportation cost $300/kgU, losses in fabrication 0.11%, losses in conversion 0.12%, product enrichment of 4.3wt%, tails assay of 0.25wt%, core contains 89 tonne fuel. Data for recycling: Price of reprocessing ($/kg used fuel)=900, Price of MOX fabrication ($/kg)=500, Price of DU ($/kg)=5, used fuel is 0.93 kg used fuel/kg fresh fuel, used fuel has 7.0 g fissile Pu/kg used fuel, fissile Pu has a reactivity equivalency of 0.81 g U235equivalent/g fPu), loss in reprocessing=0.01 Financial/economic data: nominal interest rate is 4.5%; cost of new build is $5000/kW installed capacity; 6-year construction time (for first new plants).

 

1. The referenced reactor is operated on a 3-batch equilibrium core with18-month cycles. a) The reactor is started up from zero power to full power over a period of one week and at the end of cycle is shut down over a period of one week. It is shutdown for refueling for 4 weeks. Calculate the capacity factor over one 18-month cycle. b) What is the average discharge burnup of the fuel?

 

2. Evaluate a UO2 fuel for LWR:

a. What would be the cost per kg of the fabricated UO2 fuel?

b. Now, considering the time value of money, calculate the cost of the fuel ($/kg) and the cost of the initial load of fuel to the point it is loaded in the reactor for operation assuming you purchase in advance: uranium 36 months, conversion 30 months, enrichment 24 months, and fabrication services 18 months.

c. Using the capacity factor calculated in 1a., what is the cost per kWh associated with the fuel (use cost computed in part 2a ignoring the time value of money)?

d. Accepting the US resource data (Identified Resources: RAR and IR) given in your handouts from the OECD Red Book, how long could you fuel the 99 current reactors in the US? Assume each has the same power as the reference LWR and computed capacity factor. Recalculate including the US Prognosticated and Speculative Resources? Be sure to clearly state the resource values you are referencing in this calculation.

3. Evaluate a MOX fuel for LWR:

a. Calculate the total plutonium and fissile Pu loading of a MOX fuel that is equivalent to the UO2 fuel referenced in the given data above (report as kg Pu per kg fuel and kg fissile Pu per kg fuel respectively).

b. What would be the cost per kg of this MOX fuel?

c. Considering the time value of money, calculate the cost of the MOX fuel ($/kg) and the cost of the initial load of the reactor at the point it is loaded into the reactor (one-third MOX, two-thirds UO2). Assume reprocessing costs are paid 30 months in advance and fabrication costs paid 20 months in advance.

d. Assuming approximately 80,000t used fuel in the US with the specifications given above, how long could you fuel the 99 current reactors in the US? Assume each has the same power as the reference LWR and computed capacity factor from 1a and operates on a 3cycle/3batch core. Ignore the restrictions on the amount of MOX fuel that can be utilized in a reactor at any given time. The problem is asking for an evaluation of fuel energy value in comparison to demand.

 

 

4. Assume the average home requires an electrical power of 1.2kW, an average life expectancy of 75 years, and only power from nuclear energy. For such a homeowner, what would be the lifetime generation of vitrified high level waste (HLW) in kg and liters (assuming reprocessing and recycling of U and Pu). Recall from our notes and handouts for chapter 7, the vitrified waste containers in France hold the HLW equivalent of 1.5 fuel recycled assemblies with an energy production of 1 TWh (1E+12 Wh). Compare this to some common size object such as a soda can for ease of conversation. Of course, this ignores other energy needs/requirements for such a person. Explain. How might nuclear power be used to meet these needs also?

 

 

5. Using the comparison of the life cycle carbon emissions for different technologies in terms of grams Carbon equivalent per kWh (from introductory slides for Chapter 1) and assuming a carbon tax of $16/t CO2, what would be the savings (in carbon taxes) afforded by the referenced nuclear plant per year over an equal production of electricity by coal? By natural gas? Show all work. Read average values from below as: Nuclear: 4 gCO2_eq/kWh (read as grams CO2 equivalent per kWh), Coal: 300 gCO2eq/kWh, Natural gas: 180 gCO2eq/kWh

 

 

 

INSTRUCTION:

• Points are assigned for various elements such as correct equations used or derived, correct values used, correct units applied to all quantities, correct procedures for analysis, etc. If you don’t show these in your solution then you will not receive credit. See rubric below.
• Clearly identify the governing equations as well as known and unknown quantities including those requested by the problem.
• Provide units for each variable or quantity and include units for each value or answer reported.
• Work the problem methodically showing all work. Show your steps in analysis clearly and provide interim results as needed to make your analysis clear just as you would to a reviewer (e.g. report values of intermediate quantities such as feed factors, SWU factors, separation potentials, etc.).
• Report your final answer(s) requested by the problem including units and place a box around this answer.
• Rubric for grading each problem with points assigned for:

 Is all work shown and the solution legibly and logically developed? If the answer is “no” then the grade is zero automatically since the problem can’t be graded as given in the assignment instructions. If the answer is “yes”, then continue grading.

 Are the correct governing equations clearly identified?

 Are all referenced or assumed values given correctly with proper units?

 Was the problem worked properly (e.g. correctly complete steps for a solution)?

 If graphs or tables are required, properly label and title all parts.

 Did the student get the correct final answer with proper units given?

 Is the problem free of conceptual errors?

 

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