5 and 7

5. Derive Equation (4.12) from Equation (4.11). What assumptions must be made in this derivation? 6. It is desired to produce 30 tonnes of uranium enriched to 3wt%235U using gaseous diffusion. (a) Compute the separation factor for 238UF6 and 235UF6 in a gaseous diffusion stage. (b) If the tails assay is 0.2 wt %, how much natural uranium is required as feed? (c) What is the SWU requirement for the process? (d) How many ideal stages would be required? 4.14. GAS CENTRIFUGATION 4-19 7. Repeat the previous problem for gas centrifuge enrichment. Assume that the Urenco TC21 centrifuge is used: 7 Material: Carbon-fiber composite Diameter: 20cm Length: 5m Speed: 770m/s Temperature: 333K nk=aMkTP1y1kP2y2k where nkaP1P2y1ky2kMkT=molarfluxofspeciesk=geometricfactor=highpressure=lowpressure=high-pressuremolefractionofspeciesk=low-pressuremolefractionofspeciesk=molecularmassofspeciesk=absolutetemperature 4.14. GAS CENTRIFUGATION 4-13 Hence, it can be shown that the stage separation factor for a binary mixture of 235UF6 and 238UF6 is given by =M(235UF6)M(238UF6) nk=aMkTP1y1kP2y2k where nkaP1P2y1ky2kMkT=molarfluxofspeciesk=geometricfactor=highpressure=lowpressure=high-pressuremolefractionofspeciesk=low-pressuremolefractionofspeciesk=molecularmassofspeciesk=absolutetemperature 4.14. GAS CENTRIFUGATION 4-13 Hence, it can be shown that the stage separation factor for a binary mixture of 235UF6 and 238UF6 is given by =M(235UF6)M(238UF6)