Illustrative material · modelling a continuous production process
How I model the scale effect of an industrial plant
An economics model for a continuous plant in the chemical-technology space. It shows how capital expenditure (CAPEX) and operating costs (OPEX) scale more slowly than revenue — thanks to the “six-tenths” power rule — and at what throughput the plant crosses successive thresholds: operating profitability, investment viability (NPV), and the regulatory threshold for an integrated permit. Move the sliders to trace the effect of each assumption.
Operating point
Throughput of the analysed plant
Scale effect
Power-law exponents of the cost rule
Financial parameters
Discount rate and NPV horizon
CAPEX
PLN m
Annual EBITDA
PLN m/year
EBITDA margin
% of revenue
NPV
PLN m · horizon
RevenueOPEXCAPEXEBITDA (area)◆ operating point · ▮ regulatory threshold 3 Mg/h
Revenue grows linearly with throughput, but CAPEX and the fixed share of OPEX grow more slowly (the power rule). The gap between revenue and OPEX is the EBITDA margin — the larger the plant, the better the unit economics. The shaded area shows EBITDA.
The NPV curve crosses zero at the throughput marking investment viability. Comparing the three thresholds — operating profitability, investment viability and the regulatory requirement — sets the minimum sensible scale for the plant.
Reading the thresholds.
What the model does. In a continuous plant, cost does not grow in proportion to throughput — a larger vessel, pipeline or reactor is cheaper per unit of product. This is captured by the power rule: cost ~ throughputx, where x≈0.6–0.7 for capital expenditure. The model splits OPEX into a variable part (utilities, feedstock — scaling linearly) and a fixed part (staffing, administration — scaling more slowly), computes EBITDA and discounts it over the operating horizon to NPV. The effect: there is a minimum viable scale below which the process is unprofitable — and finding it is the essence of the investment decision in chemical technology.