Hydromet Equipment Cost Estimation: Six-Tenths Rule Worked

Last updated: 2026-11-07

Early-stage equipment cost estimation in hydrometallurgy starts with capacity-factored methods: the six-tenths rule, C2 = C1 × (Q2/Q1)^0.6, converts one known delivered equipment price into an order-of-magnitude figure for a different capacity at roughly ±30% accuracy — long before any vendor quotation exists. A delivered $185,000 filter press at 120 m² scales to roughly $251,400 at 200 m² (synthetic worked example below). This page builds the full method ladder behind that number, from solvent extraction mixer-settlers to leach tankage, so a project manager can defend a screening budget before engineering has started.

Key Takeaways

• The six-tenths rule, C2 = C1 × (Q2/Q1)^0.6, gives ±30% screening numbers from a single known equipment price.
• Exponents are equipment-specific, roughly 0.4–0.9; 0.6 is a generic default, not a law.
• Capacity extrapolation beyond about 10× the base case invalidates the correlation.
• A Lang factor of roughly 3.1–4.7 converts delivered equipment cost into total installed cost.
• Every early estimate carries a stated basis: year, currency, freight, materials of construction, and accuracy band.

What Is Equipment Cost Estimation Before Vendor Quotations Exist?

Long before a flowsheet reaches the request-for-quotation stage, a project manager must answer the board’s first question: what will this plant cost? Formal equipment cost estimation at that stage does not come from vendors — it comes from scaling, and four definitions frame the vocabulary used throughout this page.

A capacity-factored estimate is a scaling method that converts the known purchase price of one piece of equipment into the expected price of a similar unit at a different size, using a power-law relationship between cost and capacity. It is the fastest tool in early equipment cost estimation, and the least precise.

The equipment (Lang) factor is a multiplier that converts the total delivered cost of the major equipment items into an approximate total installed cost of the plant, absorbing piping, electrical, civil, structural, instrumentation, and indirect costs. For hydrometallurgical solids-and-solutions plants of the kind found in copper SX-EW flowsheets, the factor typically sits between about 3.1 and 4.7 (indicative, to be confirmed against project specifics).

Battery limits is a scope boundary that defines exactly what a delivered price includes and excludes — tie-in points, foundations, utilities, spares, and freight. Two quotations that differ by 40% are frequently quoting the same machine across different battery limits, which is why the basis must be written down before numbers are compared.

Installed cost is a total figure that adds to the delivered equipment price all the field work needed to make it run: foundations, erection, piping, electrical and instrumentation, plus indirects such as construction management, commissioning support, and spares. Delivered cost, by contrast, is the price of the equipment arriving on site, freight paid, nothing erected. Confusing the two is the single most common error in early plant costing, and it biases budgets downward by roughly a factor of three to four.

The Method Ladder of Equipment Cost Estimation: ±30% Down to ±10%

No single estimating method serves a whole project. Mature organizations climb a ladder: each rung costs more engineering effort and buys tighter accuracy. Table 1 summarizes the ladder as typically applied to hydrometallurgical projects (accuracy bands and engineering hours are indicative, synthetic-typical values for planning discussion only).

Two conclusions follow from the ladder, and both are worth stating explicitly. First, a capacity-factored number is a screening instrument, not a price: presenting ±30% to a board without the accuracy band invites someone to treat it as a bid. Second, the ladder is cheap to climb early and expensive to climb late — moving from ±30% to ±10% costs roughly fifty times the engineering hours, so the ranking decisions that kill weak flowsheet options should always be made on the cheap rungs. Our own page on copper SX-EW plant cost walks the same ladder for a full copper circuit; the logic there generalizes to any hydromet equipment cost estimation exercise.

How Does the Six-Tenths Rule Work in Practice?

The six-tenths rule states that the cost of a piece of equipment scales with capacity to the power of roughly 0.6:

C2 = C1 × (Q2/Q1)^0.6

where C1 is a known delivered cost at capacity Q1, and C2 is the estimated delivered cost at capacity Q2. The exponent is a correlation fitted across many equipment classes, and it is genuinely equipment-specific. Published correlations report exponents from about 0.4 to 0.9: crushing and screening machinery tends toward the low end (large machines are mostly steel, whose cost grows nearly with surface area), while high-pressure pumps and some thermal equipment trend toward the high end. A value of 0.6 is the defensible generic default when class-specific data are unavailable — always flagged as an assumption in the estimate record.

Three cautions govern every application of the rule:

1. Extrapolation limit. The correlation is fitted near the base case. Scaling beyond roughly 10× the base capacity — or below about one-tenth of it — exits the fitted region, and errors grow faster than the exponent suggests. If the ratio exceeds 10×, break the problem into parallel trains or find a nearer benchmark.
2. Materials of construction. The rule assumes the same materials at both scales. Scaling a 316L stainless vessel correlation to a titanium or rubber-lined service silently changes the cost basis; materials multipliers are handled separately (see the adjustments section below).
3. Scope differences. The base price must be stripped to a common scope: delivered, excluding spares, drives, platforms, and instrumentation unless the target scope carries them too. A vendor quote including a spare set of cloths and hydraulic power pack is not the same number as a bare-machine quote at another capacity.

Used within those limits, the rule delivers what it promises: an order-of-magnitude figure in minutes, at roughly ±30% accuracy, before any vendor is contacted.

How Do You Scale Equipment Cost With the Six-Tenths Rule? A Worked Example

The arithmetic below is a synthetic worked example — the base prices are illustrative quotes, not references to any real vendor — but every digit closes.

Worked example 1: plate-and-frame filter press. A plant holds a 2025 quotation for a delivered 120 m² plate-and-frame filter press at $185,000, 316L-wetted construction. The upgrade flowsheet needs 200 m² of filtration area at the same duty and materials.

• Capacity ratio: Q2/Q1 = 200/120 = 1.667
• Exponent: 0.6 (filter presses fall near the generic default; a class-specific exponent should be confirmed when available)
• Scaling factor: (1.667)^0.6 = exp(0.6 × ln 1.667) = exp(0.6 × 0.5108) = exp(0.3065) = 1.359
• Estimated delivered cost: $185,000 × 1.359 ≈ $251,400 — carry $251,000 into the estimate sheet.

Worked example 2: agitated leach tank, different exponent. Equipment classes do not share exponents, and the tank case shows why. The plant has a delivered price of $95,000 for a 50 m³ agitated, rubber-lined leach tank; the revised flowsheet needs 120 m³. For agitated tanks of this size class, published exponents cluster roughly between 0.5 and 0.7 (confirm class-specific value); use 0.65.

• Capacity ratio: Q2/Q1 = 120/50 = 2.4
• Scaling factor: (2.4)^0.65 = exp(0.65 × ln 2.4) = exp(0.65 × 0.8755) = exp(0.5691) = 1.767
• Estimated delivered cost: $95,000 × 1.767 ≈ $167,800.

Two lessons sit inside those numbers. The tank ratio (2.4×) is much larger than the press ratio (1.667×), yet its scaling factor is only moderately larger — the exponent, not the ratio alone, controls the outcome. And because exponents differ by class, every scaled line in an estimate must record its exponent and its source, or the roll-up becomes unauditable.

The Six-Step Estimating Workflow

Applied consistently, capacity-factored equipment cost estimation follows six steps:

1. Fix the basis. Write down capacity, materials of construction, delivered-versus-installed scope, currency, and the price year of the benchmark quote. An unstated basis is the root cause of most estimate disputes.
2. Harvest one credible benchmark. Use a recent delivered quotation or a documented purchase for equipment of the same class and duty; a benchmark at a wildly different capacity is a liability, not an asset.
3. Apply the class exponent. Use a class-specific exponent where known; use 0.6 with a recorded caveat otherwise, and flag any ratio beyond 10×.
4. Adjust the price year and currency. Move the benchmark to the estimate date using a published plant cost index and stated exchange rates — never mix cost years inside one table.
5. Apply materials multipliers. Scale for titanium, lined, or exotic-alloy construction relative to the benchmark basis, using indicative multipliers confirmed for the duty.
6. State the accuracy band. Publish ±30% alongside the number. A screening estimate without its error bar is a promise nobody can keep.

How Do You Go From Equipment Cost to Total Installed Cost?

Delivered equipment prices are only the entry ticket. The installed plant adds piping, structures, electrical, instrumentation, and a hundred indirect costs, and the Lang factor bundles all of that into one multiplier applied to the delivered equipment subtotal. For hydrometallurgical plants with substantial solids handling and corrosive liquors, indicative factors of roughly 3.1–4.7 are typical, with wet-intensive circuits ( SX-EW, leach-SX-EW trains) toward the upper-middle of that band (indicative; confirm against comparable project data). Table 2 rolls up a small synthetic leach–SX-EW train to show the arithmetic end to end. All equipment prices are synthetic delivered figures for illustration.

The arithmetic closes: 180,000 + 520,000 + 210,000 + 185,000 + 430,000 + 390,000 + 165,000 + 120,000 = 2,200,000, and 2,200,000 × 3.8 = 8,360,000. Three practice points surround that result. The factor must match the basis: a Lang factor drawn from a fluid-processing plant will undershoot a solids-heavy hydromet train. The subtotal must be complete — omitting an equipment class (here, say, the reagent delivery skid) biases the installed total down by the factor times the omission. And because the factor is itself an uncertainty, report the roll-up as a range, for example 3.4–4.2 × the subtotal in sensitive cases.

Which Adjustments Turn a Base Estimate Into a Site-Specific Estimate?

A capacity-scaled number reflects neither time, place, nor materials. Five adjustments convert it into a site-specific figure.

Escalation. The benchmark quote carries the year it was issued. Move it to the estimate date with a published chemical-plant cost index — applied generically as a ratio of index values, without re-deriving the underlying basket — and record both index dates in the estimate file. Escalation compounds across multi-year projects, so a two-year procurement schedule needs a mid-point convention, stated explicitly. The same discipline applies to operating-cost screening: energy-consuming items such as evaporators and reboilers carry running costs that dwarf their purchase price, as our page on evaporator energy consumption quantifies.

Currency. Delivered prices embed the vendor’s currency. If the benchmark was quoted in one currency and the project buys in another, convert at a stated rate and flag the exchange-rate risk separately; currency movement of 10% can erase an entire accuracy band.

Freight to site. “Delivered” means delivered to the reference destination of the quote. Remote mine sites add measurable freight, port handling, and customs costs, particularly for heavy vessels and tankage — carry them as explicit lines rather than hiding them inside contingencies.

Materials-of-construction multipliers. The scaling rule assumed identical materials. Where the duty demands titanium or rubber-lined equipment against a 316L benchmark, apply indicative multipliers of roughly 2–5× on the affected items (typical range, to be confirmed per duty and vendor), not on the whole subtotal. This is where tank and pump costs escape their exponents: a titanium-class agitator for chloride liquor is a different product family, not a bigger 316L one. Wall thickness is the quiet driver behind much of that spread — pressure containment requirements scale metal mass nonlinearly with design pressure, as shown in our pressure vessel wall thickness calculation page.

Spares and commissioning allowances. Commissioning spares, two-year wear parts, and vendor commissioning presence are routinely excluded from bare equipment prices. Add them as explicit percentages of affected equipment value, and do the same for vendor field service during ramp-up. For thermal equipment classes, the delivered price itself varies widely with the selected technology — the trade-offs are laid out in our MVR evaporator selection guide, and the same selection-before-pricing logic applies to any energy-intensive class.

Six Pitfalls That Break Equipment Cost Estimation

The same six errors recur across review meetings; each is listed as symptom, cause, and remedy.

1. Base-versus-installed confusion. Symptom: a board compares one team’s total against another team’s equipment subtotal. Cause: nobody labeled the cost basis on the tables. Remedy: stamp every figure DELIVERED or INSTALLED, and restate comparisons on a common basis before discussion.
2. Vendor scope differences. Symptom: two quotes for nominally identical machines differ by 40%. Cause: one includes drives, platforms, spares, and commissioning; the other is a bare machine at different battery limits. Remedy: normalize both to a written scope checklist before scaling either number.
3. Nonlinear spare capacity. Symptom: a design margin of +25% capacity is assumed to add +25% cost. Cause: cost rises with capacity to the exponent, so 1.25^0.6 = 1.143 — the margin costs about 14%, but the reverse (trying to buy cost savings by shrinking capacity) does not scale down linearly either. Remedy: apply the exponent to every capacity decision, both directions.
4. Mixing cost bases and years. Symptom: an estimate built from a 2023 pump price, a 2025 tank quote, and an escalated 2024 crusher number quietly averages three economies. Cause: the roll-up skipped the escalation step. Remedy: escalate every line to a single estimate date, or reject the roll-up in review.
5. Forgotten materials multipliers. Symptom: a titanium-circuit estimate comes in suspiciously close to its 316L benchmark. Cause: the scaling was done on prices, not on materials class. Remedy: audit every scaled line against the benchmark’s materials basis and apply the 2–5× multipliers where duties diverge.
6. Treating ±30% as a price. Symptom: procurement issues an inquiry at the screening number and treats vendor quotes 25% higher as overpricing. Cause: the accuracy band was dropped from the document. Remedy: carry the band into every downstream document until budget quotations replace it.

How Does a Screening Estimate Decide Between Two Flowsheets? A Synthetic Case

A project team screening recovery options for a 12,000 t/y copper cathode project illustrates the method end to end (synthetic case; all figures illustrative, not attributable to any project).

Option A, a standard leach–SX-EW train, was estimated by capacity factoring from a comparable circuit: delivered equipment subtotal of $2.2 million, Lang factor 3.8, total installed cost $8.4 million, accuracy ±30%. Option B, a finer-grind, higher-recovery variant with an additional washing stage, factored to a $2.9 million subtotal and $11.0 million installed. The differential — about $2.6 million of installed capital — was the decisive number. At ±30% each, the bands overlap ($5.9–10.9 million versus $7.7–14.3 million), so the screening estimate could not prove Option B uneconomic, but it did something more useful: it showed the recovery premium had to be worth more than roughly $2.6 million of capital plus its operating cost to justify itself.

That conclusion shrank the pilot program. Instead of piloting both flowsheets fully, the team ran a pilot-scale continuous solvent extraction mini-plant on Option B’s SX configuration only, to test whether the claimed recovery uplift survived continuous operation. It did, at a level that justified the next rung: budget quotations for both flowsheets’ major equipment returned Option A at $8.9 million installed-equivalent and Option B at $10.6 million — within the screening bands, confirming the method ladder had done its job. The decision, recorded with exponents, factors, and index dates attached, survived audit because every number had a documented lineage.

FAQ

What accuracy should I claim for a six-tenths rule estimate?

State roughly ±30% on delivered equipment cost, and say so on the document itself. The band reflects the method’s nature: a single-price correlation applied without vendor input. If a reviewer needs better than ±30%, the answer is the next rung of the ladder — an equipment-factored roll-up with a Lang factor — not a tighter claim on the same data.

Where does the 0.6 exponent come from, and when is it wrong?

The 0.6 value is a fitted average across many equipment classes, with published class-specific exponents ranging from about 0.4 to 0.9. It is wrong when applied far outside the benchmark’s capacity (beyond roughly 10×), when materials of construction differ between benchmark and target, or when the two prices carry different vendor scopes. Record the exponent and its source on every scaled line.

What is the difference between delivered cost and installed cost?

Delivered cost is the price of equipment arriving at site, freight paid, with nothing erected — foundations, piping, electrical, instrumentation, and construction management all excluded. Installed cost adds all of those field costs. In hydrometallurgical plants the ratio between them is commonly in the 3–5× range, which is why mixing the two bases corrupts a comparison immediately.

How do I choose a Lang factor for a hydrometallurgical plant?

Start from the closest comparable project, not from a generic table. Indicative factors for hydromet-type solids-and-solutions plants run roughly 3.1–4.7, biased upward by corrosive duties, solids handling, and remote sites. Confirm the factor’s basis (delivered equipment, price year, scope) matches yours, and where the stakes are high, present the roll-up as a factor range rather than a single point.

Can I apply the six-tenths rule to a whole plant instead of one machine?

It is sometimes done, but the error compounds: a plant combines dozens of equipment classes with different exponents, so a single plant-level exponent blurs them into one number with widening uncertainty. The defensible practice is to scale item by item or class by class, roll the delivered equipment subtotal up with a Lang factor, and reserve plant-level power laws for very early napkin comparisons only.

How do I handle a benchmark whose capacity is far from my target?

Treat ratios beyond roughly 10× in either direction as outside the correlation’s validity. Options, in order of preference: find a benchmark nearer the target capacity; split the requirement into parallel trains of benchmark-like size; or flag the line as low-confidence and let budget quotations replace it early. Never stretch the exponent to force a distant benchmark to fit.

When should capacity-factored numbers be replaced by vendor quotations?

When a decision depends on the number, replace it. Screening comparisons can live on ±30% facts; budget approvals, vendor shortlisting, and feasibility economics cannot. The usual trigger is flowsheet selection: once two options are within one accuracy band of each other, budget quotations for the major items on both options are cheaper than arguing about exponents.

Conclusion

Equipment cost estimation in early-stage hydrometallurgy is a disciplined ladder, not a guess: the six-tenths rule turns one credible delivered price into a ±30% screening number, class-specific exponents and materials multipliers keep each scaled line honest, and a Lang factor of roughly 3.1–4.7 converts delivered equipment into total installed cost with the basis stated on every page. Worked digit by digit and documented with its exponents, index dates, and accuracy bands, a screening estimate will survive the audit that kills undocumented ones. When your flowsheet shortlist is ready for the next rung, request a budget quotation with your capacity, duty, and materials basis — our process team will return priced equipment scopes you can factor with confidence, and the resources hub holds the companion calculation pages behind this one.

References

1. Peters, M.S., Timmerhaus, K.D., and West, R.E., Plant Design and Economics for Chemical Engineers, McGraw-Hill — chapters on capital cost estimation and cost-capacity correlations.
2. Towler, G., and Sinnott, R., Chemical Engineering Design, Butterworth-Heinemann — sections on cost scaling, capital cost estimating, and Lang factors.
3. Richardson, J.F., Harker, J.H., and Backhurst, R., Coulson & Richardson’s Chemical Engineering, Volume 6: Chemical Engineering Design (related editions), Elsevier/Butterworth-Heinemann — cost estimation methodology.
4. AACE International, Cost Estimate Classification System overview publications, https://www.aacei.org/ — estimate classes, accuracy ranges, and maturity of engineering deliverables.
5. Guthrie, K.M., capital cost factor correlations published in Chemical Engineering magazine (1969) — equipment cost-capacity exponents and installed-factor data.
6. Perry, R.H., and Green, D.W., (eds.), Perry’s Chemical Engineers’ Handbook, McGraw-Hill — section on capital investment and project cost estimation.
7. Sinnott, R., and Towler, G., Chemical Engineering Design supplementary worked examples on equipment factored estimating — cited as general methodology literature.

Changelog

• 2026-11-07: Initial publication.