Adiabatic-Corrected Flash of an Ethanol–Water Mixture: 23-Chem-A1 Process Balances and Chemical Thermodynamics, May 2015, Q2

Question 2: Adiabatic-Corrected Flash of an Ethanol–Water Mixture (Part A — 15 marks)

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 $F=100$ mol/s of 20 mol% ethanol / 80 mol% water, liquid at 50 °C; the vessel flashes at 1.0 atm and 90 °C. From the ethanol–water T-xy diagram at 90 °C the tie line reads liquid $x_E\approx0.06$ and vapour $y_E\approx0.36$. Property estimates: $C_{p,\text{water,liq}}=0.0754$, $C_{p,\text{EtOH,liq}}=0.112$ kJ/mol·°C; latent heats at 90 °C $\lambda_{\text{water}}\approx41.1$, $\lambda_{\text{EtOH}}\approx37.5$ kJ/mol.

Find. (a) compositions and molar flow rates of the vapour ($V$) and liquid ($L$); (b) the heat duty $Q$.

Check

The tie-line reads ($x_E=0.06$, $y_E=0.36$ at 90 °C) are taken off the supplied ethanol–water T-xy chart; the graph is coarse, so treat these to ±0.02. The method is exact; a small read error only shifts the split slightly.

Figure 2 — Ethanol-water T-xy at 1 atm; the 90 C tie line reads x=0.06 (liquid) and y=0.36 (vapour).

Approach. Part (a) is a two-equation lever-rule problem: a total balance and an ethanol balance across the flash close $V$ and $L$. Part (b) is an energy balance referenced to the pure liquids at the 50 °C feed temperature.

Total and ethanol balances (lever rule). With $V+L=F$ and $F z=V y_E+L x_E$ ($z=0.20$): $$V=F\,\frac{z-x_E}{y_E-x_E}=100\cdot\frac{0.20-0.06}{0.36-0.06}=\boxed{46.7\ \text{mol/s}},\qquad L=100-46.7=53.3\ \text{mol/s}.$$ So the vapour is 36 mol% ethanol and the liquid 6 mol% ethanol. That is part (a).
Enthalpy of the outlet liquid (per mol, ref = pure liquids at 50 °C). Only sensible heating 50→90 °C: $$\hat H_L=\big(x_E C_{p,E}+(1-x_E)C_{p,W}\big)(90-50)=(0.06\cdot0.112+0.94\cdot0.0754)(40)=3.10\ \text{kJ/mol}.$$
Enthalpy of the outlet vapour (per mol). Heat each component 50→90 °C and vaporise it at 90 °C: $$\hat H_V=y_E\big(C_{p,E}\Delta T+\lambda_E\big)+(1-y_E)\big(C_{p,W}\Delta T+\lambda_W\big)=0.36(4.48+37.5)+0.64(3.02+41.1)=43.4\ \text{kJ/mol}.$$
Energy balance for the duty. With the feed at the reference state ($\hat H_F=0$), an open-system balance gives $$Q=V\hat H_V+L\hat H_L-F\hat H_F=46.7(43.4)+53.3(3.10)=\boxed{2190\ \text{kW}}.$$ That is part (b) — heat must be added because the flash both warms the feed and vaporises 47 mol/s.

Quantity	Result
(a) Vapour: composition / flow	36 mol% ethanol / 46.7 mol/s
(a) Liquid: composition / flow	6 mol% ethanol / 53.3 mol/s
(b) Heat duty $Q$	≈ +2190 kW (heat added)

Concept & Theory

Topic. Single-stage flash: VLE tie line (lever rule) coupled with an energy balance.

Key relations. Lever rule $V/F=(z-x)/(y-x)$; open-system energy balance $Q=\sum_{out}\dot n\hat H-\sum_{in}\dot n\hat H$; enthalpy via sensible ($\int C_p\,dT$) plus latent ($\lambda$) contributions.

Why this works. The T-xy diagram supplies the equilibrium end-points of the tie line, and mass conservation fixes how the feed splits between them. The duty then follows from tracking each species along a convenient path (sensible heating, then vaporisation for the part that leaves as vapour).

Common pitfall. Reading the wrong branch of the T-xy chart (swapping $x$ and $y$), or referencing enthalpies inconsistently — the heat of mixing is neglected only if the same reference (pure liquids at the feed temperature) is used for every stream.

Question 2 of 7: Adiabatic-Corrected Flash of an Ethanol–Water Mixture

Question 2: Adiabatic-Corrected Flash of an Ethanol–Water Mixture (Part A — 15 marks)