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23-Chem-A3 Heat and Mass Transfer · May 2017

Question 4 of 6: Flash and Differential Distillation of Heptane / Ethyl Benzene

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exams — May 2017 — 16-Chem-A3 Heat and Mass Transfer. Three-hour, open-book exam; one textbook and any non-communicating calculator permitted. Format: two parts of three problems each (Part A — Heat Transfer, Part B — Mass Transfer), all problems worth 25 points; candidates attempt at least two per part and only the first two per part are marked. The six problems are renumbered 1–6 and all are solved below for completeness. Property data are taken from the problem statements and standard open-book tables (the paper supplies the air-property table A-9); values used are stated in each Given block.

Reference texts: Incropera, DeWitt, Bergman & Lavine, Fundamentals of Heat and Mass Transfer (Wiley) — conduction resistances, critical radius, fins, convection correlations; Coulson & Richardson, Chemical Engineering Vol. 1 (Butterworth-Heinemann) — the packed-bed, distillation and sublimation problems of this style; Treybal, Mass-Transfer Operations (3rd ed., McGraw-Hill) — differential distillation and gas adsorption; Geankoplis, Transport Processes and Separation Process Principles (4th ed., Prentice Hall) — packed-bed and convective mass-transfer coefficients; supporting data from Perry's Chemical Engineers' Handbook (9th ed.) and the paper's Table A-9 (properties of air).

Part A — Heat Transfer

Part B — Mass Transfer

Question 4: Flash and Differential Distillation of Heptane / Ethyl Benzene (25 points)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Feed $z = 0.40$ heptane (basis $F = 1$ mol); fraction vaporised $D/F = 0.60$, so residue $W/F = 0.40$. Vapour–liquid equilibrium as tabulated above.

Find. Residue $x_W$ and distillate $y_D$ for (a) a single equilibrium (flash) stage and (b) a differential (Rayleigh) batch distillation.

0.00.00.20.20.40.40.60.60.80.81.01.0x (heptane in liquid)y (heptane in vapour)equilibriumflash op. line(x_W, y_D)feed z=0.40
Figure 4 — Equilibrium $x$–$y$ diagram for heptane / ethyl benzene. The flash operating line $y = z/(D/F) - (W/D)x$ (slope $-\tfrac23$, through the feed point on the diagonal) intersects the equilibrium curve at the flash residue/distillate point $(x_W, y_D)$.

Approach. For the flash, intersect the material-balance operating line with the equilibrium curve. For the differential still, integrate the Rayleigh equation down from the feed composition until the residue fraction matches $W/F$.

  1. Flash operating line (part a). An overall and heptane balance on one equilibrium stage give $z = (D/F)y + (W/F)x$, i.e. $$y = \frac{z}{D/F} - \frac{W/F}{D/F}\,x = \frac{0.40}{0.60} - \frac{0.40}{0.60}x = 0.667 - 0.667x,$$ a line of slope $-2/3$ through the feed point $(0.40, 0.40)$ on the diagonal.
  2. Intersect with the equilibrium curve. Solving $y^\*(x) = 0.667 - 0.667x$ against the tabulated curve (interpolated) gives the flash result $$\boxed{x_W = 0.244\ \text{(residue)},\qquad y_D = 0.504\ \text{(distillate)}}.$$ Check: $0.6(0.504) + 0.4(0.244) = 0.400 = z$. ✓
  3. Rayleigh equation for the differential still (part b). A batch that vaporises differentially obeys $$\ln\frac{F}{W} = \int_{x_W}^{z}\frac{dx}{y^\*(x)-x}.$$ Here $F/W = 1/0.40 = 2.5$, so the integral must equal $\ln 2.5 = 0.916$.
  4. Find the residue composition. Numerically integrating $1/(y^\*-x)$ up from a trial $x_W$ to $z = 0.40$ and matching $0.916$ gives $$\boxed{x_W = 0.162\ \text{(residue)}}.$$
  5. Average distillate by overall balance. $$y_{D,\text{avg}} = \frac{z - (W/F)x_W}{D/F} = \frac{0.40 - 0.40(0.162)}{0.60} = \boxed{0.559}.$$ The batch differential still gives a leaner residue (0.162 vs 0.244) and a richer distillate (0.559 vs 0.504) than the single flash — differential contact always out-separates one equilibrium stage.
QuantityFlash (a)Differential (b)
Residue $x_W$ (heptane)0.2440.162
Distillate $y_D$ (heptane)0.5040.559 (avg)