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

Question 2 of 6: Cost Estimation

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

Notes on this paper

National Exams — December 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 and the candidate answers any five; only the first five are marked. All six are answered below for completeness. Question 1 is a conceptual flowsheet-synthesis question (hydrodealkylation of toluene to benzene) answered with a process flow sheet and organised prose; questions 2, 3 and 6 are numerical (capacity-scaled and index-escalated plant cost, yield-improvement rate of return, and evaporator heat-transfer area); questions 4 and 5 are qualitative essays on materials selection against the common corrosion mechanisms and on process-hazard classification.

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 estimation Ch. 6, interest and profitability Ch. 7–10, materials of construction Ch. 12, plant safety and loss prevention Ch. 3); J.M. Douglas, Conceptual Design of Chemical Processes (McGraw-Hill) — the hydrodealkylation (HDA) flowsheet-synthesis case study used in Question 1; R. Turton et al., Analysis, Synthesis, and Design of Chemical Processes (4th ed., Prentice Hall) — flowsheet synthesis and equipment cost correlations; AIChE, Dow’s Fire & Explosion Index Hazard Classification Guide (7th ed.) — the process-hazard checklist behind Question 5; supporting Canadian practice from CCOHS/WHMIS 2015, the Canadian Environmental Protection Act (CEPA), and CSA/ASME materials and pressure-vessel codes.

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. Capacity $=750$ tonne/day of H2SO4; Garrett chart read at its two decade gridlines, $(100,\,\$3.7\text{ M})$ and $(1000,\,\$14\text{ M})$ on ton(US)/day vs. plant cost; CE Cost Index $I_{1987}=343$ (chart basis), $I_{2015}=558$.

Find. The order-of-magnitude installed cost of the plant in mid-2015 dollars.

Approach. Read the capacity–cost exponent implied by the two chart points (a six-tenths-type power law), read the 1987 cost at the required capacity from that law, then escalate to 2015 with the ratio of cost indices. The chart abscissa is US short tons/day, so convert the 750-tonne metric capacity first.

  1. Capacity–cost exponent from the chart. A straight line on log–log axes is a power law $C = C_0\,(Q/Q_0)^n$; reading the plotted line at the two decade gridlines gives $$n = \frac{\ln(14/3.7)}{\ln(1000/100)} = \frac{\ln 3.78}{\ln 10} = \boxed{0.578}$$ which is close to the familiar six-tenths rule.
  2. Convert capacity to chart units. The chart uses US short tons ($1$ tonne $=1.1023$ short ton): $$Q = 750\ \tfrac{\text{t}}{\text{day}}\times1.1023 = 826.7\ \tfrac{\text{ton(US)}}{\text{day}}$$
  3. Cost on the 1987 chart basis. Anchoring at $(100,\,\$3.7\text{ M})$, $$C_{1987} = \$3.7\text{ M}\left(\frac{826.7}{100}\right)^{0.578} = \boxed{\$12.5\text{ million}}$$ (the same figure is obtained by reading the chart line directly above $Q=827$.)
  4. Escalate to June 2015. Cost indices scale installed cost linearly: $$C_{2015} = C_{1987}\,\frac{I_{2015}}{I_{1987}} = \$12.5\text{ M}\times\frac{558}{343} = \boxed{\$20.4\text{ million}}$$
QuantityValue
Capacity–cost exponent (from chart)$n = 0.578$
Capacity in chart units$826.7$ ton(US)/day
Plant cost, 1987 basis$\approx\$12.5$ million
Plant cost, June 2015$\approx\$20.4$ million
Check: this is deliberately an order-of-magnitude (±30 %) estimate — the study-grade accuracy of a capacity-scaled chart cost, and the dominant uncertainty is how finely the log–log line can be read. If one skips the tonne→short-ton conversion and reads the chart at $Q=750$ directly, $C_{2015}\approx\$19.3$M — the same order, confirming the estimate is not sensitive to that refinement. The CE index used is the overall Plant Cost Index; using a more specific equipment index would shift the escalation by a few per cent only.