Engineering Problem 4: Nuclear Fuels ACE533 Applied Chemical Engineering II: Energy Uranium enrichment using the gas diffusion method relies on the use of a specialized membrane to separate 2350 and 238U UF6 molecules based on their very slight difference in molecular weight. The slightly lighter and therefore faster moving) 235U-containing molecules impact the membrane slightly more frequently and thereby pass through in greater amounts than the heavier 238U. The unit used to achieve this separation is called a diffuser. A diffuser splits its feed stream into an enriched (235U-rich) stream, and a depleted (238U-rich) stream. Of the UF6 that passes into the enriched stream, UF6 containing 235U transfers 1.0043* faster than 2380 across the membrane (i.e. concentration of 235U increases by 1.0043xin each diffuser). a) How many diffusers in series are required to increase the concentration of 2350 from its raw feed concentration of 0.72 w/w% to enriched fuel concentration of 3.50 w/w%? b) Recalling mass transfer, gaseous diffusive mass transport processes like this one are governed by Fick's Law of Diffusion: NAB = CDABA(Ay/Az) where N = diffusive mass flow (e.g. mol/s) of species "A" through species "B" = total concentration of gases (e.g. mol/mof all gases) DAB = diffusivity (physical property) of species "A" through species "B" A = area over which mass transfer is occurring AYA = difference in gas phase mole fraction of species "A" over the distance across which mass transfer is occurring Az = distance across which mass transfer is occurring Determine what membrane area should be used in each diffuser, in cm? Du235 in UF6, membrane = 6.24 x 10-8cm/s Membrane thickness = 20 nm 175 kg/h of UF6 feed at 60C, 1.5 atm, 0.72 w/w% 235U 85% of feed is recovered as product Assume diffusive mass flow (N) is the same in all diffusers =