The economics of a chemical plant: costs, prices and profit: Operating cost: what each tonne costs to make

4.1 A four-term model separates performance from prices, and fixed from variable cost

Brennan's simplified model gives production cost per tonne of product as:

C = sum of (R x r) + sum of (E x g) + (M x m)/QU + (k x I)/QU

R is tonnes of each raw material per tonne of product and r its price. E is each utility used per tonne and g its price. M is the number of employees and m the annual cost of each, including payroll overheads. I is fixed capital and k a factor for capital-related costs such as maintenance, insurance and property taxes. Q is annual capacity and U capacity utilisation, so QU is the output actually made.

The model separates two kinds of number. R, E and M are performance parameters, set by the technology and by how well the plant is run. The prices r, g and m are mostly set outside the company and depend on location. When a cost changes, the first question is which kind of number moved.

Raw materials and energy rise in step with output, so they are variable costs. Personnel and capital-related costs stay much the same whatever the output, so they are fixed. Per tonne, fixed costs are divided by QU, so a plant running at half capacity carries twice the fixed cost per tonne.

The model is approximate: electricity per tonne, for example, rises at low output because pumps and lighting keep running. Marginal cost, the cost of one more tonne, is usually far below average cost, and in many continuous plants is little more than the variable cost.

• Brennan (2020), Ch 4 Operating cost estimation · pdf pp. 100-104
• Brennan (2020), Ch 6 Some examples in process economics · pdf pp. 161-162
• Wittcoff (2004), Appendix 1 A note on cost calculations · pdf pp. 646-648

4.2 Raw materials and utilities usually dominate, and their prices depend on place

Raw material use per tonne comes first from mass balances, then needs an allowance for real losses: off-specification product, evaporation, spills, purge streams and weather in open storage. Brennan's indicative consumptions include 0.57 t of methane per tonne of ammonia, 0.71 t per tonne of methanol and 3.2 t per tonne of hydrogen; 0.32 t of sulphur per tonne of sulphuric acid; and 1.68 t of salt per tonne of chlorine and caustic soda. Ethylene needs 1.24 t of ethane, 2.11 t of propane or 2.7 t of naphtha per tonne.

Utilities are estimated from energy balances too. Brennan adds about 20% to theoretical steam and cooling water figures for losses, and estimates electricity from the rated power of the running drives multiplied by operating hours. Electricity dominates electrochemical processes such as chlor-alkali and aluminium smelting, and is large in high-pressure processes like ammonia, where synthesis gas must be compressed.

Utility prices vary widely by place: in 2018 natural gas cost about US$3/GJ in the United States, thanks to shale gas, against about $9 in Japan, which imports liquefied gas.

The IEA shows why feedstock price so often decides where plants are built. Crude oil costs much the same everywhere, but natural gas prices vary by a factor of 4 between regions. Feedstock makes up 15-85% of the levelised production cost of HVCs, depending on route. Middle East ethane crackers were the cheapest source of HVCs in both 2010 and 2017, while Europe sits high on the cost curve for most primary chemicals.

• Brennan (2020), Ch 4 Operating cost estimation · pdf pp. 104-110
• Brennan (2020), Ch 2 Market evaluation and forecasting · pdf pp. 55-56
• IEA (2018), The Future of Petrochemicals, Ch 2 · pdf pp. 32-34

4.3 People, maintenance and overheads are estimated by counting and by factors

Personnel costs start with process operators. A continuous plant needs a shift roster, so the total number of shift operators is four to five times the number on duty at any time. Payroll overheads (leave, workers' insurance, payroll tax, pensions) add 30-50% to wages. Total personnel costs have typically been about three times process labour cost, so a poor count of operators distorts the whole estimate.

Staff numbers grow slowly with scale. Brennan's rule is that total personnel M is proportional to Q^a, with a of 0.3-0.4 for single-stream plants and 0.6-0.7 for parallel-stream plants such as aluminium smelters.

Capital-related costs are set as percentages of fixed capital. Maintenance runs at 2-11% a year, averaging 5-6%, higher for hot, high-pressure or corrosive service, and is roughly half materials and half labour. Insurance is 0.1-3%, averaging 0.5%. Depreciation spreads the capital over a life of typically 10-15 years for undifferentiated products. A capital recovery factor can replace it in a cost sheet: at 8% interest over 15 years it is 0.117 of capital a year.

Nonmanufacturing costs follow: selling expenses at 1-20% of manufacturing cost, research and development at 1-7% (about 3% on average) and corporate administration at 3-6%.

For quick estimates Brennan's factored method sets manufacturing cost = raw materials + utilities + (1 + kL) x process labour + kI x fixed capital, with typical kL of 2.8 and kI of 0.15. Total operating cost is then manufacturing cost x (1 + kC), with kC about 0.2.

• Brennan (2020), Ch 4 Operating cost estimation · pdf pp. 111-123
• Brennan (2020), Ch 6 Some examples in process economics · pdf pp. 168-171

4.4 A cost build-up shows which term controls the business

Brennan's Example 6.1 builds the full cost for a two-potline aluminium smelter of 600,000 t a year, integrated with an existing alumina refinery. Each tonne of metal uses 1.93 t of alumina and 0.42 t of carbon, both at $300/t, and 13.0 MWh of electricity at $60/MWh. Fixed capital is $2.5 billion, and 600 people work there at $80,000 each plus 40% payroll overheads. Capital-related costs take 13% of capital a year, including capital recovery at 5% over 20 years.

The result is about $2,139 a tonne, close to the 2018 aluminium price of roughly $2,100. Because capital recovery is included, Brennan likens the figure to a floor price. Electricity is the largest item at 36%, alumina 27%, capital charges 25%, carbon 6% and people only 5%. The levers follow: a cheap long-term power contract, and alumina from the refinery next door.

Cost structure decides how much scale and utilisation matter. Variable costs per tonne do not change with plant size, so a plant dominated by them gains little from scale. Brennan's scale curves show aluminium smelting flatter than ethylene or chlor-alkali, because power, a variable cost, is so large. His isomerisation unit, nearly all naphtha, gains little from doubling to 900,000 t a year: capital rises from $57 million to about $86 million, but cost per tonne falls only from $1,070.9 to about $1,067. The sulphuric acid plant in Part 5 is the opposite case.

Wittcoff adds that short-term run-or-shut decisions rest on cash cost, while in the long run a plant must earn its total cost.

• Brennan (2020), Ch 6 Some examples in process economics · pdf pp. 160-161, 173
• Brennan (2020), Ch 4 Operating cost estimation · pdf pp. 124-126
• Wittcoff (2004), Appendix 1 A note on cost calculations · pdf p. 649

See it in the table

Check your understanding

In Brennan's model C = sum(R x r) + sum(E x g) + Mm/QU + kI/QU, which quantities are performance parameters set by technology and management?

A continuous plant needs 3 operators on duty at all times. Roughly how many shift operators must it employ?

Why does Brennan's isomerisation unit gain so little from doubling its capacity?