Combined cycle is like at most 70% efficient, subtract 10% of distribution, you end up with 60%.
At 50f my 5T heat pump takes 6.6 kWh to generate 50,000 BTU.
6 kWh of energy takes 71cf of gas to make - accounting for transmission and generation losses.
71cf of gas will make 71,000 BTU of heat, assuming an 80% efficiency furnace, that comes out to 56,000 BTU usable.
Yes a heat pump will vastly outperform resistive strip heat - but not even an 80% gas furnace.
1 kWh = 3.6 megajoules and 1 BTU = 1055 joules
The 6.6 kWh of the heat pump is 23.76 MJ which is 22,521 BTU of energy. Assuming that the power plant and distribution are 60%, it would take 37,535 BTU of gas to produce (22,521/60%).
Instead, using that 37,535 BTU of gas in an 80% efficient furnace would only produce 30,028 BTU of heat, which is worse than the 50,000 BTU from the heat pump.
I'm pretty sure even a poor heat pump will be more efficient than heating directly with gas. (Of course, they have drawbacks, like they can leak their refrigerant that causes more of a greenhouse effect than CO2.)
https://www.eia.gov/tools/faqs/faq.php?id=667&t=8
I dont know where EIA gets those numbers, but that was the basis of my calculation. Maybe I shouldn't have multiplied that by the efficiency of the plant, but rather just taken of distribution losses.
However, it’s a misleading number in multiple ways because the fleet is made up of a mix of low and high efficiency turbines. Grid operators use a mix of turbine types as a cost optimization, a far cheaper and far less efficient turbine that’s only used 1% of the time it worth it. The average number of kWh per cf of gas is therefore heavily in favor of high efficiency turbines.
My heat pump contains 2.1 kg of R32 refrigerant. R32 has a GWP of 675, so that 2.1 kg is the equivalent of 1417 kgs of CO2. (older refrigerants were much worse!)
Heat pumps should never leak their refrigerant during their lifetime, and installers will remove and recycle the refrigerant when servicing or decommissioning systems. But of course, accidents happen, so let's pessimistically assume that 50% of systems installed will eventually leak. In the real world it's hopefully far less than that, but that would mean on average 708 kg CO2e in refrigerant is emitted per system over its lifetime.
On the other hand, heating a typical US home with natural gas emits 2900 kgs of CO2 per year.
I think it's safe to say that the climate impact of refrigerant leaks in modern heat pump systems is minuscule compared to that of the CO2 emitted from natural gas heating.
In sane units:
- 2 m^3 of gas generates 6.6 kWh of electricity
- which generates 14.7 kWh of heat (at some temperature differential).
- The same 2 m^3 of gas generates 20.8 kWh of heat
- of which about 16.4 kWh is usable assuming some losses.
Of course your implied electricity generation is only around 31% efficient, so I'm not sure what that 60% you mention in the beginning is about. The COP you're using is around 2.2, which together with a 60% efficiency for generating electricity would be greater than 1, outstripping anything that's physically possible to achieve with a furnace.
50,000 BTU = 5.27528 * 10 ^ 7 J = 14.6 kWh / 6.6 kWh = COP of 2.2 at 50f which is absolutely terrible. Modern heat pumps should have a COP around 4 at those temperatures and 3 near freezing.
Also, “Subtracting 10%” would mean your grid losses are 17%. “annual electricity transmission and distribution (T&D) losses averaged about 5% of the electricity transmitted and distributed in the United States in 2018 through 2022.” So, (70% * (1 - 5%)) = 66.5%, but resistive losses are reduced in the cold. https://www.eia.gov/tools/faqs/faq.php?id=105&t=3
4 * 0.665 = 2.66x though obviously what matters here is the annual average COP. (3 * 0.665) = 1.995 aka 2.
Also, should have been 60,000 BTU - its a 15 SEER unit.
PS: 2.7 COP * 0.665 = 180% efficiency which still crushes the 80% heat pump in your example but these numbers should be much higher.
The technology isn’t advancing fast enough to make upgrading every 10 years necessary. You could buy units in 2000 with a significantly higher COP than he was implying.