Study guide
3.1 Capacity Factoring & the Six-Tenths Rule
AACE Certified Cost Professional CCP
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1 Chapter 1: Introduction & Total Cost Management (TCM) Framework
1.1 AACE CCP Exam Structure, Eligibility & the In-Exam Memo 1.2 The Total Cost Management (TCM) Framework & PDCA Cycle 1.3 Strategic Asset Management vs. Project Control Processes
2 Chapter 2: Cost Estimating Fundamentals & Classification
2.1 AACE Recommended Practice 18R-97 Estimate Classification System 2.2 Direct vs. Indirect Costs and Cost Element Breakdown 2.3 Quantity Takeoff, Standard Cost Databases & Pricing Sources
3 Chapter 3: Conceptual & Parametric Estimating Techniques
3.1 Capacity Factoring & the Six-Tenths Rule 3.2 Parametric Estimating, Lang Factors & Hand Factors 3.3 Cost Indices, Location Adjustments & Escalation Modeling
4 Chapter 4: Cost Engineering Economics & Time Value of Money
4.1 Simple & Compound Interest, Equivalence & Cash Flow Diagrams 4.2 Discrete Compounding Formulas & Uniform Series Factors 4.3 Nominal vs. Effective Interest Rates & Continuous Compounding
5 Chapter 5: Project Profitability & Capital Investment Decision-Making
5.1 Net Present Value (NPV) & Present Worth Analysis 5.2 Internal Rate of Return (IRR) & Incremental IRR Analysis 5.3 Payback Period, Benefit-Cost Ratio (BCR) & Breakeven Analysis
6 Chapter 6: Depreciation Methods, Taxes & Asset Valuation
6.1 Classical Depreciation Methods (Straight-Line, DDB, Sum-of-Years-Digits) 6.2 Modified Accelerated Cost Recovery System (MACRS) & Tax Shield 6.3 After-Tax Cash Flow Analysis & Asset Replacement Economics
7 Chapter 7: Project Scope, Work Breakdown Structure (WBS) & Baselines
7.1 Work Breakdown Structure (WBS) Principles & the 100% Rule 7.2 Organizational Breakdown Structure (OBS) & Control Accounts 7.3 Establishing the Performance Measurement Baseline (PMB)
8 Chapter 8: Critical Path Method (CPM) Planning & Scheduling Logic
8.1 Precedence Diagramming Method (PDM) & Dependency Relationships 8.2 Forward Pass, Backward Pass & Float Calculations (Total vs. Free Float) 8.3 Schedule Baseline Development, Calendar Constraints & Milestones
9 Chapter 9: Schedule Optimization, Compression & Probabilistic PERT
9.1 Schedule Crashing & Least-Cost Slope Optimization 9.2 Fast-Tracking Risks, Overlap Analysis & Execution Strategies 9.3 PERT Three-Point Estimating & Probabilistic Duration Variance
10 Chapter 10: Resource Management, Productivity & Learning Curves
10.1 Resource Loading, Leveling vs. Resource Smoothing 10.2 Labor Productivity Factors, Work Sampling & Efficiency Loss 10.3 Learning Curve Theory (Wright Cumulative vs. Crawford Unit Models)
11 Chapter 11: Earned Value Management (EVM) Core Principles & Metrics
11.1 ANSI/EIA-748 EVM Framework & Core Metrics (PV, EV, AC) 11.2 EVM Variances & Performance Indices (CV, SV, CPI, SPI) 11.3 Work Progress Measurement Techniques (0/100, 50/50, Milestone Weighting)
12 Chapter 12: EVM Forecasting, Indices & Baseline Change Control
12.1 Estimate at Completion (EAC) & Estimate to Complete (ETC) Formulas 12.2 To-Complete Performance Index (TCPI) & Variance at Completion (VAC) 12.3 Integrated Change Control, Baseline Revisions & Trend Management
13 Chapter 13: Risk Management Planning & Qualitative Risk Analysis
13.1 Risk Management Framework & Risk Breakdown Structure (RBS) 13.2 Qualitative Risk Assessment & Probability-Impact (P-I) Matrix 13.3 Risk Response Strategies & Threat/Opportunity Management
14 Chapter 14: Quantitative Risk Analysis, Monte Carlo & Contingency Estimating
14.1 Expected Monetary Value (EMV) & Decision Tree Analysis 14.2 Monte Carlo Simulation & Probability Distributions in Cost/Schedule 14.3 Contingency Estimating & AACE Recommended Practice 40R-08
15 Chapter 15: Contract Types, Procurement Strategy & Commercial Terms
15.1 Contract Types & Risk Allocation (Firm Fixed Price, Cost-Plus, T&M) 15.2 Project Delivery Systems & Procurement Lifecycle (DBB, DB, EPC, CMAR) 15.3 Commercial Terms, Bonds, Retainage & Claims Management
16 Chapter 16: Quality Management, Value Engineering & Technical Communication
16.1 Quality Management & Cost of Quality (CoQ) 16.2 Value Engineering, Function Analysis System Technique (FAST) & Life Cycle Costing 16.3 The CCP Memo, Cost Report Writing, Data Presentation & AACE Ethics 16.4 AACE CCP Capstone Review & High-Yield Exam Strategies
17 Chapter 17: Cost Accounting, Budget Administration & Cost System Governance
17.1 Historical Cost Databases, Data Organization & Benchmarking 17.2 Committed Costs, Accruals, Work-in-Place & Invoice Validation 17.3 Budget Creation, Operating Budgets & Funding Requirement Forecasting 17.4 Cost System Governance, the Code of Accounts & Preserving Project Controls Data
18 Chapter 18: Estimate Preparation, Review & Cost Driver Analysis
18.1 ROM, Summary-Level and Detailed Estimates: Preparing and Reviewing 18.2 Verifying the Basis of Estimate & Analyzing Estimates 18.3 Cost Drivers, Change Order Impact & Resource Utilization Analysis
19 Chapter 19: Interfacing with Other Disciplines & Stakeholders
19.1 Coordinating with Internal Disciplines & Supporting Project Leadership 19.2 Communicating Cost Estimates and Cost/Schedule Key Performance Indicators 19.3 Supporting Tenders, Procurement, Audits, Field Verification & Recovery
20 Chapter 20: Cost Reporting, Dashboards & Profitability Analysis
20.1 Cost Reports, Performance Dashboards & the Reporting Cycle 20.2 Variance Reports & Explaining Project Financial Health 20.3 Profit Margin Analysis & Profitability Enhancement
21 Chapter 21: Cost Support to Scheduling & the CCP Exam Memo
21.1 Cost and Resource Loading Summaries from the Project Schedule 21.2 Translating Schedule Change into Cost Impact 21.3 Writing the CCP Exam Memo: A Worked Domain 7 Walkthrough
3.1 Capacity Factoring & the Six-Tenths Rule
Key Takeaways Explain This Topic AI
The capacity exponent equation C2 = C1 * (Q2 / Q1)^x models the non-linear relationship between facility/equipment capacity and capital cost.
The classic Six-Tenths Rule (x = 0.6) originates geometrically from the 2/3 (0.67) surface-area-to-volume scaling ratio of cylindrical and spherical process vessels.
An exponent x < 1.0 reflects economies of scale (decreasing unit cost with increasing size), x = 1.0 represents linear scaling (modular additions), and x > 1.0 denotes diseconomies of scale.
Exponents vary significantly by equipment category: atmospheric tanks (0.50–0.60), heat exchangers (0.55–0.65), compressors (0.60–0.75), and thick-walled reactors (0.70–0.85).
When required capacity exceeds the maximum fabrication or transport limit for a single vessel, piecewise multi-train scaling must be applied, preventing massive budget underestimation.
Last updated: August 2026
3.1 Capacity Factoring & the Six-Tenths Rule
In early-stage capital project development—specifically during Class 5 (Concept Screening) and Class 4 (Feasibility Study) estimating as defined by AACE Recommended Practice 18R-97 —detailed engineering deliverables such as piping and instrumentation diagrams (P&IDs), structural drawings, and isometric takeoffs do not yet exist. Under these conditions of limited project definition (0% to 15% scope maturity), cost engineers rely on capacity factoring (also known as the power-sizing model or exponential method ) to derive reliable order-of-magnitude capital cost estimates from historical reference facilities.
Capacity factoring leverages empirical non-linear relationships that correlate the capital cost of an entire process plant, system, or individual piece of equipment to its production capacity, throughput, or physical sizing parameter.
1. Mathematical Formulation of the Power-Sizing Model
The fundamental governing equation for capacity factoring relates the known cost and capacity of an existing base facility ( C 1 , Q 1 C_1, Q_1 C 1 , Q 1 ) to the estimated cost of a newly proposed facility ( C 2 , Q 2 C_2, Q_2 C 2 , Q 2 ): C 2 = C 1 × ( Q 2 Q 1 ) x C_2 = C_1 \times \left( \frac{Q_2}{Q_1} \right)^x C 2 = C 1 × ( Q 1 Q 2 ) x
Where:
- C 2 C_2 C 2 = Estimated capital cost of the proposed facility or equipment of capacity Q 2 Q_2 Q 2
- C 1 C_1 C 1 = Known capital cost of the reference facility or equipment of capacity Q 1 Q_1 Q 1
Q 2 Q_2 Q 2 = Sizing capacity or throughput rating of the proposed asset (e.g., barrels/day, metric tons/year, MW, gallons/min)
Q 1 Q_1 Q 1 = Sizing capacity or throughput rating of the reference asset (expressed in identical engineering units)
x x x = Capacity scaling exponent (power-sizing coefficient), typically ranging between 0.30 0.30 0.30 and 1.10 1.10 1.10
Equivalent Logarithmic Formulation
When analyzing historical cost records across multiple operational units to empirically determine the specific scaling exponent x x x , the power-sizing equation is linearized using natural logarithms: ln ( C 2 C 1 ) = x × ln ( Q 2 Q 1 ) ⟹ x = ln ( C 2 / C 1 ) ln ( Q 2 / Q 1 ) \ln\left(\frac{C_2}{C_1}\right) = x \times \ln\left(\frac{Q_2}{Q_1}\right) \implies x = \frac{\ln(C_2 / C_1)}{\ln(Q_2 / Q_1)} ln ( C 1 C 2 ) = x × ln ( Q 1 Q 2 ) ⟹ x = ln ( Q 2 / Q 1 ) ln ( C 2 / C 1 )
2. Geometric & Physical Origin of the Six-Tenths Rule
The classic Six-Tenths Rule ( x = 0.6 x = 0.6 x = 0.6 ) is one of the oldest and most widely recognized heuristics in chemical, petroleum, and industrial process engineering. It traces its theoretical foundation to the geometric relationship between the surface area and volume of three-dimensional containment geometries.
The Surface Area to Volume Derivation
For cylindrical vessels, spherical storage tanks, piping systems, and heat exchanger shells:
Capacity ( Q Q Q ) is directly proportional to internal Volume ( V V V ) : V ∝ r 3 V \propto r^3 V ∝ r 3 (where r r r is the characteristic linear dimension).
Material Quantity & Fabrication Cost ( C C C ) is proportional to vessel Surface Area ( A A A ) : A ∝ r 2 A \propto r^2 A ∝ r 2 .
Expressing surface area as a function of volume: r ∝ V 1 / 3 ⟹ A ∝ ( V 1 / 3 ) 2 = V 2 / 3 ≈ V 0.667 r \propto V^{1/3} \implies A \propto \left(V^{1/3}\right)^2 = V^{2/3} \approx V^{0.667} r ∝ V 1/3 ⟹ A ∝ ( V 1/3 ) 2 = V 2/3 ≈ V 0.667
Because the structural cost of shell plates, insulation, external paint, structural support frames, and foundation footprints scales with surface area rather than internal holding volume, vessel capital cost initially scales with an exponent near 0.67 0.67 0.67 .
When empirical adjustments for manufacturing efficiencies, standard nozzle attachments, tooling setup, instrumentation hookups, and bulk purchasing discounts are factored into overall plant packages, the empirical cross-industry average exponent stabilizes around x ≈ 0.60 x \approx 0.60 x ≈ 0.60 . +-----------------------------------------------------------------------------------------+
- | THE ECONOMIC MECHANISM OF THE SIX-TENTHS RULE |
- | |
- | Capacity Factor: Q2 / Q1 = 2.0 (Doubling Capacity) |
- | |
- | Cost Multiplier = (2.0)^0.60 = 1.5157 (+51.6% Cost Increase for +100% Capacity) |
- | |
- | Unit Capital Cost ($/unit) = 1.5157 / 2.0 = 0.7579 (-24.2% Reduction in Unit Cost) |
- +-----------------------------------------------------------------------------------------+
- 3. The Exponent Continuum: Economies vs. Diseconomies of Scale
The numerical value of the capacity scaling exponent x x x defines the economic behavior of the asset during scale-up: x < 1.0 x = 1.0 x > 1.0
[ ECONOMIES OF SCALE ] [ LINEAR SCALING ] [ DISECONOMIES OF SCALE ]
Unit cost decreases as size grows. Constant unit cost. Unit cost increases as size grows.
Dominates process equipment, tanks, Replicated parallel Extreme metallurgy, transport limits,
pumps, chemical process plants. trains, modular skids. structural foundation penalties.
- <---------------------------------------|-----------------------|--------------------------------------->
- 0.30 0.60 0.85 1.00 1.20
- 1. x < 1.0 x < 1.0 x < 1.0 (Economies of Scale / Increasing Returns to Scale)
Capital cost increases slower than capacity. Doubling capacity ( Q 2 / Q 1 = 2.0 Q_2/Q_1 = 2.0 Q 2 / Q 1 = 2.0 ) increases total capital cost by only 2 x 2^x 2 x .
Unit capital cost (e.g., $ / BPD \text{\textdollar}/\text{BPD} $ / BPD or $ / ton \text{\textdollar}/\text{ton} $ / ton ) decreases continuously as capacity expands.
Typical of single-train pressure vessels, storage tanks, rotating equipment, and large integrated chemical facilities.
2. x = 1.0 x = 1.0 x = 1.0 (Constant Returns to Scale / Linear Modular Scaling)
Cost increases in direct 1:1 proportion with capacity ( C 2 / C 1 = Q 2 / Q 1 C_2/C_1 = Q_2/Q_1 C 2 / C 1 = Q 2 / Q 1 ).
Occurs when expansion is achieved by simply duplicating identical modular units (e.g., adding a second identical gas turbine generator skid, modular reverse-osmosis skid, or containerized battery storage rack).
3. x > 1.0 x > 1.0 x > 1.0 (Diseconomies of Scale / Decreasing Returns to Scale)
Cost accelerates faster than capacity ( x > 1.0 x > 1.0 x > 1.0 ).
Occurs when physical dimensions exceed standard fabrication machinery capabilities, requiring on-site field machining, extreme structural wall thicknesses to withstand internal hydraulic head pressures, specialized high-alloy forgings, or oversized crane mobilization to lift super-heavy vessels.
4. Equipment & Facility Capacity Exponent Spectrum
Cost engineers must never apply the generic x = 0.60 x = 0.60 x = 0.60 blindly across all equipment classifications. The following reference table presents empirical scaling exponents recognized in AACE body of knowledge publications and engineering economics literature:
Asset Classification Typical Exponent ( x x x ) Key Sizing Parameter ( Q Q Q ) Physical / Economic Scaling Driver
Atmospheric Storage Tanks (Carbon Steel) 0.50 – 0.60 Working Volume (Gallons / m 3 m^3 m 3 ) Pure geometric surface-area-to-volume ratio ( A ∝ V 2 / 3 A \propto V^{2/3} A ∝ V 2/3 ).
Floating Roof Storage Tanks 0.55 – 0.62 Capacity (Barrels / m 3 m^3 m 3 ) Roof seal and rolling ladder mechanisms add fixed linear costs.
Centrifugal Pumps & Electric Motors 0.35 – 0.50 Shaft Horsepower / Flow Rate (GPM) High base casting/machining fixed costs; motor frame sizes scale efficiently.
Shell & Tube Heat Exchangers 0.55 – 0.65 Heat Transfer Surface Area ( f t 2 ft^2 f t 2 / m 2 m^2 m 2 ) Tube bundle count scales volumetrically within shell diameter.
Plate & Frame Heat Exchangers 0.65 – 0.75 Surface Area ( f t 2 ft^2 f t 2 ) Plate stamping tooling amortized; frame structural stiffness required.
Centrifugal Gas Compressors 0.60 – 0.72 Driver Power Rating (BHP / kW) Heavy-duty casing, seals, lubrication skid, and driver scaling.
Reciprocating Compressors 0.70 – 0.85 Brake Horsepower (BHP) High mechanical complexity, cylinder count, and reciprocating vibration foundations.
Distillation / Fractionation Towers 0.60 – 0.70 Shell Weight / Internal Volume Height-to-diameter aspect ratio, internal tray spacing, and wind load design.
High-Pressure Autoclaves / Reactors 0.75 – 0.90 Volumetric Capacity ( m 3 m^3 m 3 ) ASME Section VIII Div 1/2 wall thickness equations force exponential plate thickness increases.
Wastewater Treatment Facilities 0.65 – 0.75 Hydraulic Throughput (MGD) Basin excavation, concrete aeration tanks, clarifier surface geometry.
Petroleum Refinery Units (Crude Unit/FCC) 0.62 – 0.70 Throughput (BPD / BPSD) Integrated thermal network, piping rack diameters, furnace radiant areas.
Fossil Fuel / Combined Cycle Power Plants 0.70 – 0.82 Net Output (Megawatts Electric - MWe) Steam generator boilers, condenser vacuum shells, balance of plant cooling towers.
- 5. Step-by-Step Worked Mathematical Examples
- Example 1: Sizing an Industrial Storage Tank Farm
A chemical manufacturing company completed a 40,000-gallon carbon steel storage tank in 2025 at an installed cost of $220,000 . The engineering team is preparing a Class 4 feasibility estimate for an expanded production facility requiring a 100,000-gallon tank of identical metallurgical and pressure specification. Historical cost records indicate a sizing exponent of x = 0.56 x = 0.56 x = 0.56 for this tank category. Capacity Ratio = Q 2 Q 1 = 100 , 000 40 , 000 = 2.50 \text{Capacity Ratio} = \frac{Q_2}{Q_1} = \frac{100,000}{40,000} = 2.50 Capacity Ratio = Q 1 Q 2 = 40 , 000 100 , 000 = 2.50 Scaling Factor = ( 2.50 ) 0.56 = e 0.56 × ln ( 2.50 ) = e 0.56 × 0.91629 = e 0.51312 ≈ 1.6705 \text{Scaling Factor} = (2.50)^{0.56} = e^{0.56 \times \ln(2.50)} = e^{0.56 \times 0.91629} = e^{0.51312} \approx 1.6705 Scaling Factor = ( 2.50 ) 0.56 = e 0.56 × l n ( 2.50 ) = e 0.56 × 0.91629 = e 0.51312 ≈ 1.6705 C 2 = C 1 × ( 2.50 ) 0.56 = $ 220 , 000 × 1.6705 = $ 367 , 510 C_2 = C_1 \times (2.50)^{0.56} = \$220,000 \times 1.6705 = \mathbf{\$367,510} C 2 = C 1 × ( 2.50 ) 0.56 = $220 , 000 × 1.6705 = $367 , 510
Unit Cost Comparison:
Reference Unit Cost: $ 220 , 000 / 40 , 000 gal = $ 5.50 / gallon \text{\textdollar}220,000 / 40,000\text{ gal} = \mathbf{\text{\textdollar}5.50 / \text{gallon}} $ 220 , 000/40 , 000 gal = $ 5.50/ gallon
Proposed Unit Cost: $ 367 , 510 / 100 , 000 gal = $ 3.68 / gallon \text{\textdollar}367,510 / 100,000\text{ gal} = \mathbf{\text{\textdollar}3.68 / \text{gallon}} $ 367 , 510/100 , 000 gal = $ 3.68/ gallon
Unit Capital Savings: 5.50 − 3.68 5.50 = 33.1 % reduction in cost per gallon of storage \frac{5.50 - 3.68}{5.50} = \mathbf{33.1\%\text{ reduction in cost per gallon of storage}} 5.50 5.50 − 3.68 = 33.1% reduction in cost per gallon of storage .
Example 2: Plant-Level Expansion with Exponent Derivation
A cost engineer needs to evaluate the historical performance of two previously built sulfur recovery plants to establish an in-house exponent for future conceptual estimates:
Plant A (Built 2022): Capacity = 500 Long Tons/Day (LTD) ; Cost = $45,000,000
Plant B (Built 2024, normalized to 2022 dollars): Capacity = 1,200 Long Tons/Day (LTD) ; Cost = $82,000,000 x = ln ( C B / C A ) ln ( Q B / Q A ) = ln ( $ 82 , 000 , 000 / $ 45 , 000 , 000 ) ln ( 1 , 200 / 500 ) = ln ( 1.8222 ) ln ( 2.4000 ) = 0.60007 0.87547 = 0.6854 x = \frac{\ln(C_B / C_A)}{\ln(Q_B / Q_A)} = \frac{\ln(\$82,000,000 / \$45,000,000)}{\ln(1,200 / 500)} = \frac{\ln(1.8222)}{\ln(2.4000)} = \frac{0.60007}{0.87547} = \mathbf{0.6854} x = ln ( Q B / Q A ) ln ( C B / C A ) = ln ( 1 , 200/500 ) ln ( $82 , 000 , 000/$45 , 000 , 000 ) = ln ( 2.4000 ) ln ( 1.8222 ) = 0.87547 0.60007 = 0.6854
Using this derived empirical exponent ( x = 0.6854 x = 0.6854 x = 0.6854 ), the estimated cost for a proposed 1,800 LTD plant is: C proposed = $ 45 , 000 , 000 × ( 1 , 800 500 ) 0.6854 = $ 45 , 000 , 000 × ( 3.60 ) 0.6854 = $ 45 , 000 , 000 × 2.4093 = $ 108 , 418 , 500 C_{\text{proposed}} = \$45,000,000 \times \left( \frac{1,800}{500} \right)^{0.6854} = \$45,000,000 \times (3.60)^{0.6854} = \$45,000,000 \times 2.4093 = \mathbf{\$108,418,500} C proposed = $45 , 000 , 000 × ( 500 1 , 800 ) 0.6854 = $45 , 000 , 000 × ( 3.60 ) 0.6854 = $45 , 000 , 000 × 2.4093 = $108 , 418 , 500
6. The "Parallel Train" Trap: Single Train vs. Multi-Train Scaling
A critical pitfall on the AACE CCP examination involves scaling facilities beyond the maximum physical or fabrication capacity of a single process train.
In heavy industrial processes, major vessels, compressors, and furnaces face physical manufacturing and transit limits (e.g., maximum overland shipping diameter of 16 ft 16\text{ ft} 16 ft , maximum single forge crane capacity, maximum single-impeller gas flow). When project demand exceeds this threshold, the facility must be constructed using multiple parallel trains ( N N N ) rather than one giant single train. +-----------------------------------------------------------------------------------------+
- | SINGLE TRAIN VS. MULTI-TRAIN SCALING TRAP |
- | |
- | Scenario: Base plant = 30,000 BPD at $180M. Proposed plant = 90,000 BPD. |
- | Maximum Single-Train Limit = 45,000 BPD. Capacity Exponent x = 0.65. |
- | |
- | [WRONG] Single-Train Extrapolation (Ignoring physical limits): |
- | C = $180M * (90,000 / 30,000)^0.65 = $180M * 3.0^0.65 = $367.6M |
- | |
- | [CORRECT] Two Parallel Trains of 45,000 BPD each: |
- | Cost per 45,000 BPD Train = $180M * (45,000 / 30,000)^0.65 |
- | = $180M * (1.50)^0.65 = $234.3M |
- | Total Facility Cost (2 Trains) = 2 * $234.3M = $468.6M |
- | |
- | BUDGET SHORTFALL IF TRAP IS MISSED: $468.6M - $367.6M = $101.0M (21.6% Underestimate) |
- +-----------------------------------------------------------------------------------------+
Warning
Exam Trap Alert: Whenever an exam question specifies a maximum single-train capacity or indicates that an expansion requires multiple parallel production lines , you must scale the cost to the maximum allowable single-train size first, and then multiply by the required number of parallel trains ( N N N ). Failing to do so produces an erroneous, heavily underfunded estimate!
7. Boundaries of Applicability & Scale-Up Risk
AACE International guidelines establish clear boundaries regarding the valid application of capacity factoring:
Recommended Sizing Ratio Limits:
Sizing ratios ( Q 2 / Q 1 Q_2 / Q_1 Q 2 / Q 1 ) between 0.5 0.5 0.5 and 2.0 2.0 2.0 represent the highest confidence zone.
Ratios between 0.2 0.2 0.2 and 5.0 5.0 5.0 are acceptable for Class 5 screening estimates, but carry significant contingency requirements ( 30 % to 50 % 30\%\text{ to }50\% 30% to 50% ).
Ratios below 0.2 0.2 0.2 or above 5.0 5.0 5.0 are strictly invalid. Scale-downs below 0.2 0.2 0.2 hit fixed minimum cost floors (controls, valves, structural skirts cost the same regardless of tiny vessel size). Scale-ups above 5.0 5.0 5.0 cross metallurgical and aerodynamic regime thresholds.
Technological Identity Assumption:
The reference asset and proposed asset must utilize the identical chemical or thermodynamic process route . For example, one cannot scale a coal-fired power plant to estimate a combined-cycle natural gas plant using a capacity exponent.
Scope and Scope Boundary Parity:
Capacity factoring applies strictly to Inside Battery Limits (ISBL) process units. Outside Battery Limits (OSBL) infrastructure (e.g., raw water intake, electrical high-voltage substations, administrative buildings, rail spurs) must be estimated separately using site-specific parametric rules.