A techno-economic case study on economies of scale, capital annualization, and multi-period capacity expansion under carbon pricing.
Lowest Baseline Cost
Site A
157.78 €/t (0 €/tCO₂ tax)
A → B Break-Even CO₂
122.66 €/t
Scale advantage eroded
B → C Break-Even CO₂
169.15 €/t
Cleanest tech switch (0.20 t/t)
2020 → 2030 Average Cost
177.75 €/t
Drops from 184.57 €/t (−3.7%)
Executive Summary & Core Insights
This tutorial models capacity planning and economic dispatch across three prospective biorefinery sites (A, B, and C) facing non-linear capital scaling (b = 0.70) and escalating carbon tax policies.
Scale Advantage (0–122.66 €/tCO₂): Site A dominates baseline economics (157.78 €/t) through economies of scale at its 120 kt/yr maximum size class and the lowest variable cost (90 €/t).
Carbon Tipping Points: Competitiveness transfers to Site B at 122.66 €/tCO₂, and to the lowest-emission facility (Site C) above 169.15 €/tCO₂.
Optimal 2020–2030 Path: Phased expansion at Site A (Medium → Large) coupled with an initial Small build at Site B minimizes the summed 2020 and 2030 annual system costs.
📄Problem Specification
Full technological data, constraints & formulation.
Unit Fixed Cost (Capital Annuity + FOM) and Variable Production Cost for Sites A, B, and C.⬇️ Raw Text File
Site
Largest Permitted Class
Nameplate Capacity (kt/yr)
Overnight Capital (MEUR)
Annual Fixed Charge (MEUR/yr)
Annual Output (Mt/yr)
Fixed Cost (EUR/t)
Variable Cost (EUR/t)
Total Unit Cost (EUR/t)
Site A
Large
120.0
48.74
6.913
0.1020
67.78
90.00
157.78
Site B
Medium
60.0
30.00
4.256
0.0510
83.44
105.00
188.44
Site C
Small
30.0
18.47
2.620
0.0255
102.73
128.00
230.73
Capital Annualization Principle & Economic Scaling:
Annualization reconciles lumpy upfront capital expenditure with recurring operational expenditure by converting overnight investment into an equivalent annual fixed charge via the capital recovery factor (CRF = 10.19% at 8% WACC over 20 years) plus 4% fixed O&M, yielding f = 14.19%/yr. Site A achieves the lowest levelized production cost (157.78 EUR/t) because it combines the lowest variable cost (90 EUR/t) with the lowest unit fixed cost: deploying its maximum permitted capacity (120 kt/yr) exploits economies of scale (b = 0.70) to dilute unit fixed costs to 67.78 EUR/t. Conversely, Site C is restricted to 30 kt/yr, yielding an adverse unit fixed cost of 102.73 EUR/t and the highest total cost (230.73 EUR/t).
Module 2 · Policy & Sensitivity Analysis
Cost Competitiveness Under Carbon Pricing (0 to 300 EUR/t CO₂)
Figure 2: Total unit production cost (EUR/t) vs. carbon tax with shaded least-cost competitiveness zones.⬇️ Download Break-Even CSV
Site Comparison
Break-Even Carbon Price (EUR/tCO₂)
Dominance Regime & Market Behavior
Site A vs Site B
122.66
0 to 122.66 EUR/tCO₂: Site A is least-cost
Site B vs Site C
169.15
122.66 to 169.15 EUR/tCO₂: Site B is least-cost
Site A vs Site C
145.91
Not on the lower envelope: Site B is cheaper than both A and C at this price
Carbon Price Crossover Insights:
Below 122.66 EUR/t CO2, Site A dominates on pure capital-scale efficiency despite being carbon-intensive (0.70 t CO2/t). In the intermediate bracket of 122.66 to 169.15 EUR/t CO2, Site B is least-cost, balancing moderate scale with lower carbon intensity. Above 169.15 EUR/t CO2, the scale advantage of large facilities is fully eroded by carbon liabilities, making Site C (the cleanest facility at 0.20 t CO2/t) the most cost-competitive option. Note that the A vs C crossover (145.91 EUR/t CO2) is not a regime boundary: at that price Site B is already cheaper than both A and C.
Module 3 · Dynamic Capacity Planning
Capacity Build-Up & Multi-Period Expansion Optimization (2020 to 2030)
Evaluating discrete plant additions, incremental capital scaling, and merit-order economic dispatch.
Figure 4: Total annual system expenditure (Capital vs. Variable OPEX) and unit average production cost.⬇️ Download System Costs CSV
#
Site
Year
Initial Class
Upgraded Class
Nominal Added (kt/yr)
Effective Added (kt/yr)
Incremental OCC (MEUR)
Annual Charge (MEUR/yr)
Active 2020
Active 2030
1
A
2020
- (new build)
Medium
60.0
51.0
30.00
4.256
Yes
Yes
2
A
2030
Medium
Large
60.0
51.0
18.74
2.658
No
Yes
3
B
2030
- (new build)
Small
30.0
25.5
18.47
2.620
No
Yes
Year
Demand (kt/yr)
Site A (kt/yr)
Site B (kt/yr)
Total Output (kt/yr)
Capital Charges (MEUR/yr)
Variable Costs (MEUR/yr)
Total System Cost (MEUR/yr)
Average Cost (EUR/t)
2020
45.0
45.0
0.0
45.0
4.256
4.050
8.306
184.57
2030
110.0
102.0
8.0
110.0
9.533
10.020
19.553
177.75
2030 Infrastructure Deficit & Average Cost Dynamics:
A single site cannot meet 2030 demand because the system-wide maximum permitted plant size is 120 kt/yr (Site A), yielding an effective output of only 102 kt/yr at 85% availability—short of the 110 kt/yr requirement. The system average production cost drops from 184.57 EUR/t in 2020 to 177.75 EUR/t in 2030 because capital-related cost per tonne falls from 94.57 to 86.66 EUR/t. In 2020 the Medium plant at Site A is only partly utilized (45 of 51 kt/yr effective, 88%). In 2030 Site A, upgraded to Large (102 kt/yr effective), runs at 100% and benefits from the stronger economies of scale of the larger class. Variable cost per tonne actually rises slightly (90.00 to 91.09 EUR/t) because 8 kt/yr must come from the more expensive Site B, whose Small plant is only about 31% utilized (8 of 25.5 kt/yr), which partly offsets the gain.