A crude biodiesel stream leaving a reaction process is flowing at 3900 kg/hour and contains 12% by mass methanol in methyl oleate (C18H330-O-CH3) (surrogate molecule to represent biodiesel). To meet fuel specifications the methanol concentration must be reduced to less than 0.2 wt% methanol. a. Convert the weight fractions of methanol in the feed and required methanol in the biodiesel product to mole fractions. Convert the mass flowrate of the feed to mole flowrate (in mol/s). b. Suppose the excess methanol is removed by flash distillation, where the flash operates as a single equilibrium stage at atmospheric pressure with relative volatility 4= 1000. Calculate the flowrates (in mol/s) and compositions (in mole fractions) of the vapor and liquid product streams when the purity specification is met. Use the following T-X-Y diagram to estimate the temperature of the flash drum. NOTE: if the relative volatility is assumed constant, then the mole fractions of methanol and water in the exiting vapor (y,) and liquid (x) phases are related by the following equation: this is Wankot equation (2-7b) BAB ZA 1+(AB-1)=A NOTE: this problem can be solved sequentially (does not require trial-and-error) c. Suppose the excess methanol is removed by washing with water, where the washing process acts as a single-stage equilibrium liquid-liquid extraction stage. A stream of pure water is fed to the stage. You can assume that water does not dissolve in methyl oleate and that methyl oleate does not dissolve in water. The equilibrium partitioning of methanol between the organic and aqueous phases can be approximated by y=Kx with K=0.38; y is the mole fraction of methanol in the organic phase and x is the mole fraction of methanol in the aqueous phase. Calculate the flowrate of water (in mol/s and in kg/h) required and the methanol compositions in the exiting organic and aqueous streams. NOTE: this problem can be solved sequentially (does not require trial-and-error) d. Discuss the advantages and disadvantages of the approaches in part (b) and part (c) for purification of biodiesel. YA = Temperature (C) 350 300 250 200 150 100 50 0 T-X-Y Diagram for Methanol and Methyl Oleate at 1 ATM -Bubble Point -Dew Point 0.2 0.4 0.6 mole fraction, x, y 0.8 I Temperature (C) 350 300 2250 200 150 100 0 T-X-Y Diagram for Methanol and Methyl Oleate at 1 ATM 0.02 -Bubble Point --Dew Point 0.04 0.06 mole fraction, x, y 0.08 01