Cost Estimation

This Peters & Timmerhaus topic estimates capital cost. You scale a known cost to a new capacity with the six-tenths rule, escalate historical costs to the present with CEPCI or Marshall & Swift indices, and factor purchased-equipment cost up to total installed cost with the Lang factor, always stating the accuracy class of the estimate.

(six-tenths rule, capacity exponent n ≈ 0.6)

(cost index escalation)

(Lang factor, f_L ≈ 3–5)

Relation 1 —

(six-tenths rule, capacity exponent n ≈ 0.6)

Write this relation with symbols exactly as in Peters Timmerhaus Plant Design — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 2 —

(cost index escalation)

Write this relation with symbols exactly as in Peters Timmerhaus Plant Design — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 3 —

(Lang factor, f_L ≈ 3–5)

Write this relation with symbols exactly as in Peters Timmerhaus Plant Design — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Cost estimation exploits regularities. Equipment cost rises less than proportionally with size — the six-tenths rule (exponent about 0.6) captures the economy of scale — so doubling capacity costs far less than double. Because equipment prices drift with inflation and material markets, a cost index rescales an old quotation to today. Finally, the delivered equipment is only a fraction of the installed cost; piping, instrumentation, civil work and engineering multiply it by the Lang factor. The estimate’s accuracy depends on how much design detail exists, from a rough ±30% study estimate to a ±5% definitive estimate.

State assumptions explicitly before using any relation for cost estimation — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.

Wrong assumptions invalidate the entire solution even when the formula is correct. In Plant Design & Economics viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

1. Read the question and list given data with SI units (common in Plant Design & Economics papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to cost estimation.
4. Use equation 1: .
5. Use equation 2: .
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Cost Estimation appears in project feasibility studies. In Indian chemical curricula this topic is tested because it connects theory to PFD, costing, and profitability.

GATE and semester exams often combine cost estimation with earlier units — revise prerequisites before attempting mixed problems.

Industry interview panels sometimes ask: "Where did you use cost estimation?" — answer with a lab, mini-project, or plant visit example if possible.

Students use an exponent of 1 (linear scaling) instead of ~0.6, forget to escalate with a cost index, and confuse purchased with installed cost by omitting the Lang factor. Applying a scaling law far outside the valid capacity range is another error.

Before attempting cost estimation problems, confirm you can:

1. Accuracy classes: order-of-magnitude ±30%, preliminary ±15%, definitive ±5%
2. CEPCI or Marshall & Swift indices update historical costs
3. Installed cost far exceeds purchased-equipment cost

Revise the solved examples in Peters Timmerhaus Plant Design — Standard reference and one previous-year GATE or university paper for this unit.