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23-Chem-A2 Unit Operations and Separation Processes · December 2013

Question 6 of 6: Tubular Heat-Exchanger Sizing

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

Notes on this paper

Paper format. National Exam 04-Chem-A2 Mechanical and Thermal Operations, December 2013 — open-book, 3 hours, any non-communicating calculator. Two sections: Section A (Mechanical Operations, A1–A3) and Section B (Thermal Operations, B1–B3); every problem is 25 marks. The rubric asks candidates to attempt two problems per section, but all six are solved in full below.

Reference texts: McCabe, Smith & Harriott, Unit Operations of Chemical Engineering (7th ed., McGraw-Hill) — pipe friction, loss coefficients, packed beds and centrifugal separation (Ch. 5–7); de Nevers, Fluid Mechanics for Chemical Engineers and Brodkey & Hershey, Transport Phenomena: A Unified Approach — the mechanical-energy balance and the appended friction-factor chart and fitting table; Geankoplis, Transport Processes and Separation Process Principles — tubular-centrifuge neutral-zone analysis; Incropera & DeWitt, Fundamentals of Heat and Mass Transfer (7th ed., Wiley) and Çengel, Heat and Mass Transfer — conduction with generation, annular-fin efficiency (Fig. B1) and LMTD/correction-factor exchanger design (Fig. B2). Loss-coefficient, friction-factor, fin-efficiency and correction-factor data are read from the appended Table A1, Fig. A1, Table B1 and Figs. B1–B2.

Section A — Mechanical Operations

Question B3: Tubular Heat-Exchanger Sizing (25 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. Benzene $\dot m_b=6800\ \mathrm{kg/h}$, $22\to70\ \mathrm{^\circ C}$, $c_p=1880\ \mathrm{J/(kg\cdot K)}$, $\rho=857\ \mathrm{kg/m^3}$; water $\dot m_w=4500\ \mathrm{kg/h}$ in at $100\ \mathrm{^\circ C}$, $c_p\approx4200$; $U_i=284\ \mathrm{W/(m^2\cdot K)}$, $D_i=13$ mm, $v_{max}=1.2$ m/s, $L_{max}=6$ m.

Find. (i) number of tube passes; (ii) tubes per pass; (iii) tube length.

water in 100°C water out 67.5°C benzene 22°C 70°C 1 outer vessel / 8 tube passes × 14 tubes = 112 tubes, L≈4.6 m
Figure B3 — Single outer-vessel, multi-tube-pass exchanger. The duty fixes the total area; the tube-side velocity limit sets tubes per pass (parallel); the 6-m length ceiling forces the remaining area into more passes in series.

Approach. Compute the duty and water outlet, then LMTD with its correction factor $F$ and the required area; size tubes per pass from the velocity limit and pick the pass count that keeps the tube length under 6 m.

  1. Duty and water outlet. $$q=\dot m_b c_{p,b}\Delta T=\tfrac{6800}{3600}(1880)(70-22)=\boxed{170.5\ \mathrm{kW}},$$ and with $c_{p,w}\approx4200$ (Table B1), $T_{w,\text{out}}=100-170\,500/[(1.25)(4200)]=67.5\ \mathrm{^\circ C}$.
  2. LMTD and correction factor. Counter-current $\Delta T_1=30$, $\Delta T_2=45.5\ \mathrm{^\circ C}$: $$\Delta T_{lm}=\frac{45.5-30}{\ln(45.5/30)}=37.2\ \mathrm{^\circ C};\qquad P=\frac{70-22}{100-22}=0.615,\ R=\frac{100-67.5}{70-22}=0.676\Rightarrow F=0.77.$$
  3. Required area. $$A=\frac{q}{U_i F\,\Delta T_{lm}}=\frac{170\,500}{284(0.77)(37.2)}=\boxed{21.0\ \mathrm{m^2}}.$$
  4. Tubes per pass from the velocity limit (ii). Benzene $Q_b=\dot m_b/\rho=1.889/857=2.20\times10^{-3}\ \mathrm{m^3/s}$; one 13-mm tube has $a=1.327\times10^{-4}\ \mathrm{m^2}$: $$N_t=\frac{Q_b}{a\,v_{max}}=\frac{2.20\times10^{-3}}{1.327\times10^{-4}(1.2)}=13.8\Rightarrow\boxed{N_t=14\ \text{tubes/pass}}\ (v=1.19\ \mathrm{m/s}).$$
  5. Passes and tube length (i, iii). With $A=n_p N_t(\pi D_i)L$: $n_p=6\Rightarrow L=6.1$ m (just over the ceiling), $n_p=8\Rightarrow L=4.6$ m. Therefore $$\boxed{\text{(i) }n_p=8\ \text{passes},\quad\text{(ii) }14\ \text{tubes/pass (112 total)},\quad\text{(iii) }L\approx4.6\ \mathrm{m}}.$$ The correction factor $F=0.77$ stays above the usual 0.75 acceptability threshold, so a single outer vessel is adequate.
QuantityResult
Duty $q$ / water outlet170.5 kW / 67.5 °C
$\Delta T_{lm}$ / $F$ / area37.2 °C / 0.77 / 21.0 m$^2$
(ii) Tubes per pass14 ($v=1.19$ m/s)
(i) Tube passes8 (112 tubes)
(iii) Tube length≈ 4.6 m
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