Steam is priced by pressure
Nobody hands you a utility table and explains it, so you take the number, put it in the economics sheet and move on. But the same kilogram of steam costs more at forty bar than it does at six, and the reason is not that the hot steam carries more heat, because it carries less. It costs more because of what it could have done on the way down. Here is the ladder, the reason each rung is priced the way it is, and the chain that turns a heat duty into cents per kilogram of product.
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Heat has grades, and the ladder is the price list
A furnace and a boiler sit at the top. They are high grade and expensive and they will heat anything you point them at. Cooling water sits at the bottom at a few cents per cubic metre, and it is the cheapest thing in the plant. Steam sits in between in levels, and each level is priced by its pressure.
Why the top of the ladder costs more
It is tempting to assume high pressure steam costs more because it carries more energy, and that is backwards. A kilogram of saturated steam at 40 bar gives up about 1 714 kJ when it condenses and a kilogram at 6 bar gives up about 2 086 kJ, so the cheap steam is the one that carries more latent heat per kilogram.
What high pressure steam actually has is potential. It could have expanded through a turbine on its way down and produced shaft work, and that work is worth about thirteen cents a kilowatt hour in Ontario. Let it down through a valve instead and you get the same heat at the bottom and none of the work, so the lower level is discounted by exactly the work you threw away. That is why the pressure you pick for a reboiler is a design decision and not a utility detail, and it is why steam pricing looks like a ladder rather than a single number.
Fuel is up to 90 per cent of the cost of steam, which is the other half of the story: the top rung is expensive because something is burning to make it.
What it costs a kilogram of product
Take a product that needs 2 100 kJ of heat per kilogram. A kilogram of steam at ten bar gives up about 2 015 kJ when it condenses, so you need just over a kilogram of steam per kilogram of product, and at the Ontario price the whole thing lands at about a cent and a half. Every kilogram. Forever.
Only the units carry a stroke. The numbers never cancel, and striking 2 100 kJ against 2 015 kJ would claim that they do.
2 100 ÷ 2 015 = 1.0422 kg steam per kg product
1.0422 ÷ 1 000 × $14 = $0.0146 per kg of product
| 2 100 kJ/kg | the basis | a reboiler or evaporator duty of this order. It is the given, not a claim. |
|---|---|---|
| 2 015 kJ/kg | latent heat | saturated steam at 1 000 kPa: hg − hf = 2 777.1 − 762.52 = 2 014.6 kJ/kg at 179.9 °C, from the NIST WebBook. This is the term the pressure enters through. |
| $14 /t | steam price | CHE 480 Week 7, typical current Ontario costs: steam $13.60 to $15.20 per tonne, cooling water 3.4 to 5.9 cents per cubic metre, electricity about 13 cents per kilowatt hour. |
| 1 000 kg/t | conversion | the bookkeeping that makes the units land on dollars per kilogram. |
Where the level actually gets chosen
In a flowsheet the steam level is usually implicit. You set a reboiler duty or a heater outlet temperature, the block solves, and the utility that would deliver it never appears as a decision. The moment you attach a real utility the level stops being free, because the approach temperature you need at the exchanger sets the minimum pressure, and the minimum pressure sets which rung you are buying from.
- Ask what the lowest level is that still gives you the approach you need. That is the cheapest steam you are allowed to use.
- Ask whether the let down between two levels is going through a valve. If it is, that is shaft work leaving the plant as nothing.
- Ask what the duty costs per kilogram of product rather than per hour. Per hour is a number nobody remembers, and per kilogram rides on every kilogram you ever make.
Ask the model which level it just spent
Reflux drives Aspen Plus directly, so the question "what steam level is this reboiler on, and what does the duty cost per kilogram of product" is one you can ask of the flowsheet you already have rather than a spreadsheet you have to build beside it.
Sources
- Latent heat of saturated steam at 1 000 kPa, 2 014.6 kJ/kg at 179.9 °C: NIST Chemistry WebBook, thermophysical properties of water.
- The steam ladder and the turbine credit, with a worked example of $6.48, $5.47 and $4.03 per 1 000 lb at 40, 20 and 6 bar: Towler and Sinnott, Chemical Engineering Design, 2nd edition, Chapter 3, Example 3.2.
- Fuel as up to 90 per cent of the cost of steam: US Department of Energy, How to Calculate the True Cost of Steam.
- Ontario utility prices: CHE 480 Week 7, Heat Exchanger Networks.