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ENGR5002 / Week 10
ENGR263 2019 Q A1(b)-(d)Past paperOld spec ENGR2632:115 marks18 min

ENGR263 Process of Mass Transfer 2019 Q A1[PARTIAL] Left out: (a) (5 marks), the Raoult's-law vapour composition, is ENGR5003 week 6 material and is in that bank as engr263-2019-a1a; its result is quoted in the stem below. (e) (5 marks), reading the ethanol-water azeotrope from the VLE diagram and alternative separation methods, is distillation and off-syllabus.

A binary mixture of ethanol and water in the reboiler of a batch distillation column (a liquid in contact with its vapour across a thin vapour-liquid film; Figure A1-1 of the paper shows yw=0.7y_w = 0.7 in the bulk vapour and xw=0.6x_w = 0.6 in the liquid) presents the following data:

  • Total pressure P=101 300 PaP = 101\,300\ \mathrm{Pa}
  • Temperature T=85∘CT = 85^\circ\mathrm{C}
  • Mole fraction of water in the liquid phase xw=0.6x_w = 0.6
  • Mole fraction of water in the vapour phase yw=0.70y_w = 0.70
  • Saturated vapour pressure of ethanol Pesat=135 087 PaP_e^{sat} = 135\,087\ \mathrm{Pa}
  • Thickness of vapour-liquid interphase film δ=0.002 m\delta = 0.002\ \mathrm{m}
  • Binary diffusivity De−w=1.6×10−5 m2/sD_{e-w} = 1.6 \times 10^{-5}\ \mathrm{m^2/s}
  • Gas constant R=8.314 J mol−1 K−1R = 8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}

[Part (a) asked for the ethanol vapour mole fraction in equilibrium with the liquid, assuming ideal phases (Raoult's law): ye∗=xePesat/P=0.4×135 087/101 300=0.533y_e^* = x_eP_e^{sat}/P = 0.4 \times 135\,087/101\,300 = 0.533. Use it below. Part (e), on the azeotrope, is omitted.]

Formulas you may need
  • Flux with bulk flow NA,z=−cDABdyAdz+yA(NA,z+NB,z)N_{A,z} = -cD_{AB}\dfrac{dy_A}{dz} + y_A(N_{A,z} + N_{B,z}) (on the formula sheet)
  • Equimolar counter-diffusion through a film (plane surface): NA=cDABδ(yA1−yA2)=DABcA1−cA2δN_A = \dfrac{cD_{AB}}{\delta}(y_{A1} - y_{A2}) = D_{AB}\dfrac{c_{A1} - c_{A2}}{\delta} (on the formula sheet)
  • Stagnant B: NA=cDABδln⁡1−yA21−yA1N_A = \dfrac{cD_{AB}}{\delta}\ln\dfrac{1 - y_{A2}}{1 - y_{A1}} (on the formula sheet)
  • NA=kcΔcA=kyΔyAN_A = k_c\Delta c_A = k_y\Delta y_A; film theory kc=DAB/δk_c = D_{AB}/\delta, ky=ckck_y = ck_c; c=P/(RT)c = P/(RT) (learn this)
  1. (b)
    Calculate the flux of mass transfer (mol m−2 s−1\mathrm{mol\,m^{-2}\,s^{-1}}) of ethanol from the liquid phase to the vapour phase in the reboiler.
    [5]2:2
  2. (c)
    Calculate the mass transfer coefficient of ethanol from the liquid phase to the vapour phase of the reboiler.
    [5]2:2
  3. (d)
    The batch distillation process is replaced by a simple evaporation process in a stagnant vapour phase, where the condensation of the less volatile component (water) is not taking place. Calculate the flux of mass transfer (mol m−2 s−1\mathrm{mol\,m^{-2}\,s^{-1}}) of ethanol in the reboiler.
    [5]