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23-Chem-A5 Chemical Plant Design and Economics · May 2015

Question 2 of 6: Cost Estimation

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

Notes on this paper

National Exams — May 2015 — 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; the candidate answers any five and only the first five are marked. All six are worked below for completeness. Questions 2, 3 and 5 carry the numerical work (equivalent-annual-cost equipment selection, a discounted-cash-flow rate-of-return analysis, and a gravity-decanter sizing); questions 1, 4 and 6 are design / materials-selection / safety questions answered as organised prose, with Question 1 supported by a process flow sheet and a light overall material balance.

Reference texts: M.S. Peters, K.D. Timmerhaus & R.E. West, Plant Design and Economics for Chemical Engineers (5th ed., McGraw-Hill) — the exam's named primary text (cost–capacity estimation Ch. 6, interest and investment Ch. 7, profitability and rate of return Ch. 10); R.K. Sinnott & G. Towler, Chemical Engineering Design (Coulson & Richardson Vol. 6, 5th ed., Butterworth-Heinemann) — separator/decanter sizing (§10.6), materials of construction (Ch. 7) and the process-design safety checklist (Ch. 9); R. Turton et al., Analysis, Synthesis, and Design of Chemical Processes (4th ed., Prentice Hall) — flowsheet synthesis; supporting Canadian practice from CSA B51 / ASME BPVC (pressure vessels), API 650 (atmospheric storage tanks) and NACE corrosion guidance.

Question 2: Cost Estimation (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. Carbon-steel (CS) exchanger: purchase cost $C_{CS}=\$140{,}000$, service life 5 yr. Type-304 stainless-steel (SS) exchanger: material factor $f_m=1.3$ (so $C_{SS}=1.3\times\$140{,}000=\$182{,}000$), service life 10 yr. Cost of capital $i=12\%$. The Annual Capital Charge Ratio (ACCR) is tabulated for 10- and 20-year lives; at 12 % these are $0.177$ (10 yr) and $0.134$ (20 yr).

Find. Which exchanger is more economical, compared on an equal-life (annualised-cost) basis.

Approach. The two options have different lives, so compare them on an equivalent-annual-cost basis over a common 10-year study period: the stainless unit lasts the full 10 years (one purchase), whereas the carbon-steel unit must be bought again at year 5 (two purchases); annualise each option's present cost with the 10-year ACCR (which is exactly the capital-recovery factor $A/P$ at 12 %).

  1. Recognise the ACCR as the capital-recovery factor. The tabulated ACCR is $A/P = \dfrac{i(1+i)^n}{(1+i)^n-1}$; at $i=12\%$, $n=10$ it is $\dfrac{0.12(1.12)^{10}}{(1.12)^{10}-1}=0.177$, matching the table. Annualising a present cost $P$ therefore gives the equivalent uniform annual cost $\text{EAC}=P\times\text{ACCR}$.
  2. Stainless steel — one purchase over 10 years. The 304-SS exchanger costs $C_{SS}=f_m C_{CS}=1.3(\$140{,}000)=\$182{,}000$ and lasts the whole study period, so $$\text{EAC}_{SS}=C_{SS}\times\text{ACCR}_{10}= \$182{,}000\,(0.177)=\boxed{\$32{,}200/\text{yr}}$$
  3. Carbon steel — replaced once at year 5. Over the same 10-year horizon the CS exchanger is bought at $t=0$ and again at $t=5$; discount the replacement to present worth at 12 %: $$P_{CS}=C_{CS}+\frac{C_{CS}}{(1+i)^5}= \$140{,}000+\frac{\$140{,}000}{(1.12)^5}= \$140{,}000+\$79{,}440=\$219{,}440$$ Annualising this present cost over the 10-year period, $$\text{EAC}_{CS}=P_{CS}\times\text{ACCR}_{10}= \$219{,}440\,(0.177)=\boxed{\$38{,}800/\text{yr}}$$
  4. Compare. Substituting, $\text{EAC}_{SS}=\$32{,}200/\text{yr} < \text{EAC}_{CS}=\$38{,}800/\text{yr}$; the stainless unit is cheaper by about $\$6{,}600/\text{yr}$ (≈17 %). Paying the 30 % material premium once buys double the life and avoids the mid-life reinvestment, so type-304 stainless steel is the more economical choice.
QuantityValue
SS-304 purchase cost ($1.3\times\$140$k)$\$182{,}000$
CS present cost over 10 yr (buy at 0 & 5)$\$219{,}440$
Equivalent annual cost — stainless$\$32{,}200/\text{yr}$
Equivalent annual cost — carbon steel$\$38{,}800/\text{yr}$
Most economicalType-304 stainless steel
Check: the comparison must be made over a common life. Annualising each unit over its own life is invalid here because the table gives no 5-year ACCR; the 10-year common-horizon method (SS once, CS twice) is the correct like-for-like basis, and the 20-year ACCR column is a distractor for this pairing. The conclusion is robust: even the crude first-cost-only view ($\$182$k vs a single $\$140$k) hides that the carbon unit must be re-bought at year 5.