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23-Chem-A5 Chemical Plant Design and Economics · December 2016

Question 2 of 6: Cost of a Distillation-Column Retrofit

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

Notes on this paper

National Exams — December 2016 — 04-Chem-A5 Chemical Plant Design and Economics. Three-hour, closed-book exam; one two-sided aid sheet and an approved calculator permitted. Six equally weighted (20-mark) questions are posed and the candidate answers any five; only the first five are marked. All six are answered below for completeness. Question 1 combines conceptual process-synthesis (reactor and recycle structure for a series-reaction chlorination) with a short economic-potential calculation; Question 2 is a numerical retrofit-costing problem (replacing distillation trays with structured packing); Questions 3–6 are qualitative essays on equipment design procedures, materials of construction, inherently safer design, and equipment-selection factors.

Reference texts: R. Smith, Chemical Process Design and Integration (2nd ed., Wiley) — reaction path, reactor conversion and the recycle structure of the flowsheet, and the economic-potential screen behind Question 1 (the monochlorodecane example is worked there); R.K. Sinnott & G. Towler, Chemical Engineering Design (Coulson & Richardson vol. 6, 6th ed., Butterworth-Heinemann) — the equipment cost correlations and retrofit factors of Question 2, the heat-exchanger and cyclone design procedures (Ch. 12, Ch. 10), materials of construction (Ch. 7), and equipment selection (Ch. 10, 18); T.A. Kletz & P. Amyotte, Process Plants: A Handbook for Inherently Safer Design (2nd ed., CRC) — the inherently-safer-design changes of Question 5; M.S. Peters, K.D. Timmerhaus & R.E. West, Plant Design and Economics for Chemical Engineers (5th ed., McGraw-Hill). Canadian practice per CCOHS and CSA Z767 (Process Safety Management) where jurisdiction matters.

Question 2: Cost of a Distillation-Column Retrofit (20 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.

Retrofit data
QuantitySymbolValue
Column diameter$D$1.5 m
Total new packing height$H$30 m
Packing base cost (per 5 m unit at 0.5 m dia)$C_B$$\$18{,}000$
Base diameter / cost exponent$Q_B,\ n$0.5 m, 1.70
Tray-removal factor$f_{\text{rem}}$0.10
Packing-installation factor$f_{\text{inst}}$0.5–0.8

Find. The estimated total cost of the revamp project (purchase of new stainless-steel structured packing plus removal of the old trays and installation of the packing).

Approach

Cost the new packing from the capacity–cost correlation (diameter is the size variable; a 30 m column needs six 5 m units), then add the retrofit modification costs, which Table 2.8 expresses as multiples of that new-hardware cost.

Before: trayed column 70 sieve trays @ 0.61 m spacing feed After: packed column 6 beds x 5 m = 30 m SS packing feed revamp Vessel body unchanged: 46 m tall, 1.5 m dia
Figure 2.1 — The revamp: the 46 m × 1.5 m column body is retained; its 70 sieve trays (0.61 m spacing) are removed and replaced by 30 m of stainless-steel structured packing (six 5 m beds). Only the trays→packing swap is costed.
  1. Number of standard packing units. The correlation is quoted per 5 m of packing height, so a 30 m column requires $$N=\frac{H}{5}=\frac{30}{5}=6 \text{ units}.$$
  2. Cost of one 5 m unit at the actual diameter. Using $C_e=C_B\,(D/Q_B)^{n}$ with $D=1.5$ m (inside the 0.5–4.0 m validity range): $$C_{5\,\text{m}}=1.80\times10^{4}\left(\frac{1.5}{0.5}\right)^{1.70}=1.80\times10^{4}\,(3)^{1.70}=1.80\times10^{4}(6.473)=\$116{,}500.$$
  3. Delivered cost of the new hardware (all six units). $$C_{\text{pack}}=N\,C_{5\,\text{m}}=6\times116{,}500\approx\$699{,}100.$$ Delivered cost of the new SS structured packing: $\boxed{C_{\text{pack}}\approx\$699{,}100}$
  4. Retrofit modification costs (Table 2.8, as multiples of $C_{\text{pack}}$). Removing the old trays to install packing costs $$C_{\text{rem}}=0.10\,C_{\text{pack}}=0.10(699{,}100)\approx\$69{,}900,$$ and installing the new structured packing costs $$C_{\text{inst}}=(0.5\!-\!0.8)\,C_{\text{pack}}=\$349{,}600\ \text{to}\ \$559{,}300.$$
  5. Total project cost. Sum the hardware purchase, tray removal and packing installation: $$C_{\text{tot}}=C_{\text{pack}}\,(1+0.10+f_{\text{inst}})=699{,}100\times(1.60\ \text{to}\ 1.90).$$ $$C_{\text{tot}}\approx\$1.12\ \text{million (low)}\ \text{to}\ \$1.33\ \text{million (high)}.$$ Taking the mid-range installation factor (0.65): Estimated total project cost: $\boxed{C_{\text{tot}}\approx\$1.22\ \text{million}\ \ (\$1.12\text{–}\$1.33\ \text{million})}$
Cost itemBasisAmount
New SS structured packing (6 × 5 m)$6\,C_B(1.5/0.5)^{1.70}$$\$699{,}100$
Remove old trays, install packing$0.10\,C_{\text{pack}}$$\$69{,}900$
Install new structured packing$(0.5\text{–}0.8)\,C_{\text{pack}}$$\$349{,}600$ – $\$559{,}300$
Total project cost$C_{\text{pack}}(1+0.10+f_{\text{inst}})$$\$1.12$ M – $\$1.33$ M (≈ $\$1.22$ M)
Check: the estimate assumes the column body, reboiler, condenser and feed/liquid-distribution internals are adequate for the new duty, so only the trays→packing exchange is costed; the correlation and retrofit factors are order-of-magnitude (study-grade, roughly ±30 %) figures, hence the answer is reported as a range with a best estimate near $\$1.2$ million. The high diameter exponent (1.70) reflects that structured-packing cost scales roughly with cross-sectional area (and the packing value it contains), not just diameter.