Issue 060 - AI infrastructure - Natural-gas fuel and emissions
How much natural gas does a 250-MW AI data center require?
Meta is developing a large AI data center in Alberta. Reuters reports that Capital Power expects to supply the site with about 250 MW of electricity until a dedicated generating facility is completed, and Alberta has attracted more than 100 proposed data-center projects partly because of its natural gas supply.
The problem
If a data center continuously requires about 250 MW of electrical power, about how much natural gas would have to be burned each day to generate that electricity?
Then estimate the resulting mass of carbon dioxide emitted per day.
You will need to make your own assumptions about natural-gas plant efficiency, natural-gas energy content, gas density or mass, and how much CO2 is produced when the fuel burns.
As an extra check, estimate how many average U.S. households could theoretically be supplied with the same continuous electrical power.
Because Fermi problems target an order of magnitude, I normally use no more than two significant digits and write most calculations in scientific notation; the Fermi reference explains both conventions.
Grounding facts
Capital Power says its long-term agreement with Meta covers 250 MW of capacity and energy for a data center in Sturgeon County, Alberta. Reuters later reported that Capital Power will provide 250 MW to the site until Meta's dedicated natural-gas-fired power project comes online, while Alberta has more than 100 proposed data-center projects.
EIA says modern efficient natural-gas combined-cycle plants typically have heat rates below 7,000 Btu/kWh. EPA's 2026 power-sector analysis uses 6,226 Btu/kWh for a new combined-cycle plant and assumes natural gas emits 117 lb CO2/MMBtu.
EIA also gives methane, the primary component of natural gas, a heat content near 1,010 Btu/ft3. For a Fermi estimate, it is also useful to remember that methane contains about 50 MJ/kg, and burning 1 kg of methane produces about 2.75 kg of CO2.
After checking sources
Checked answer and calculation
The electrical load is straightforward:
daily electricity
~= 250 MW x 24 h/day
~= 6,000 MWh/day
~= 6 x 10^6 kWh/day
~= 2.2 x 10^13 J/dayUsing a round combined-cycle heat rate of about 7,000 Btu/kWh:
fuel energy input
~= 6 x 10^6 kWh/day x 7 x 10^3 Btu/kWh
~= 4.2 x 10^10 Btu/day
~= 42,000 MMBtu/dayThat is the same as dividing the electrical output by roughly 50% efficiency. Convert that fuel energy into gas volume and mass:
gas volume
~= 4.2 x 10^10 Btu/day / 1.0 x 10^3 Btu/ft3
~= 4.2 x 10^7 ft3/day
~= 42 million cubic feet/day
gas mass
~= 4.2 x 10^7 ft3/day x 0.020 kg/ft3
~= 8 x 10^5 kg/day
~= 800 tonnes/dayThe emissions check is even more compact if we use EPA's 117 lb CO2/MMBtu factor:
CO2 emissions
~= 42,000 MMBtu/day x 117 lb CO2/MMBtu
~= 4.9 x 10^6 lb CO2/day
~= 2.2 x 10^6 kg CO2/day
~= 2,200 tonnes CO2/daySo the best checked scale is roughly 800 tonnes of natural gas per day, producing roughly 2,000 tonnes of CO2 per day. The precise number depends on plant efficiency, but a reasonable range is about 700 to 1,000 tonnes of gas per day and about 2,000 to 2,500 tonnes of CO2 per day.
For household scale, a 250-MW continuous load produces about 2.2 billion kWh per year. At about 10,500 kWh per U.S. household-year, that is electricity for roughly 200,000 U.S. homes.
household equivalent
~= 250 MW x 8.8 x 10^3 h/year / 1.05 x 10^4 kWh/home-year
~= 2.1 x 10^5 homesIf ten more facilities of the same size eventually ran continuously on similar gas-fired power, they would add about 2.5 GW of demand, burn on the order of 8,000 tonnes of natural gas per day, and emit roughly 8 million tonnes of CO2 per year.
Before checking sources
Matt's original estimate
This is the unverified estimate Matt wrote before checking sources, not the checked answer.
I assumed:
- energy efficiency of a modern natural gas power plant is about 60%
- natural gas has an energy density of about 4.5 x 10^7 J/L
- a liter of natural gas is about 0.9 kg
- natural gas is about 3/4 carbon by mass
- CO2 is about 27% carbon by mass
First, 250 MW of power production is 2.5 x 10^8 J/s. That times about 8.6 x 10^4 seconds daily means the power plant is producing about 2.2 x 10^13 J of energy daily.
daily electrical output
~= 2.5 x 10^8 J/s x 8.6 x 10^4 s/day
~= 2.2 x 10^13 J/dayAt 60% efficiency, 2.2 x 10^13 J / 0.6 is about 3.7 x 10^13 J of natural gas required.
fuel energy required
~= 2.2 x 10^13 J / 0.6
~= 3.7 x 10^13 J/dayAt 4.5 x 10^7 J per liter of fuel, it would require about 8 x 10^5 L, or about 800,000 liters, of natural gas daily to produce that energy.
fuel volume
~= 3.7 x 10^13 J/day / 4.5 x 10^7 J/L
~= 8 x 10^5 L/day8 x 10^5 L is about 7 x 10^5 kg of natural gas, and if 3/4 of that is carbon, that is about 5.3 x 10^5 kg of carbon.
Since CO2 is 27% C, combusting the 8 x 10^5 L of natural gas should produce 5.3 x 10^5 kg C / 0.27, or about 2 x 10^6 kg of CO2 daily.
CO2
~= 5.3 x 10^5 kg C / 0.27
~= 2 x 10^6 kg CO2/dayCalibration Score
Matt's Calibration Score: 90 / 100
Higher is better: earn points for accurate pegs, sound models, correct math, and a result close to the sourced answer. The image shows percent full of it: 100 minus the Calibration Score.
Pegs: 20/30. The plant-efficiency and combustion-chemistry pegs were strong, and the fuel mass came out right. The main miss was treating natural gas volume like a liquid-fuel volume, even though the energy-per-mass effect mostly canceled that out.
Model: 30/30. The structure was reliable: convert continuous power to daily energy, adjust for plant efficiency, convert fuel to carbon, then carbon to CO2.
Math: 10/10. The arithmetic followed cleanly from the assumptions.
Result: 30/30. The final gas-mass and CO2 estimates landed inside the checked Fermi range.
Post-check reflection
Matt's reflection
Two big "errors" corrected themselves, mainly because I was thinking in terms of mass instead of volume.
Otherwise this was a pretty straightforward problem, and my answers were about right. And that is a lot of CO2 being put into the atmosphere daily.
Recommended memory peg
For natural-gas electricity, remember: 1 MW running all day needs roughly 3 tonnes of natural gas and emits roughly 9 tonnes of CO2 from a reasonably efficient gas plant. So a 250-MW always-on load is about 250 times that: roughly 800 tonnes of gas and 2,000 tonnes of CO2 per day.
Reader results
Bars show how submitted estimates sort into the answer choices from the gut-check prompt.