Because heat pump actually doesn't solve the problem. The problem is that we need energy to heat our homes during the winter. And it doesn't matter where it comes from.
Except ... it does?! I mean, I don't really understand what you are trying to say here, but I would think the whole reason for switching to renewables is that it does matter where our enery comes from?!
My house heating comes from a waste energy of a power plant, how much is the efficiency of that?
There is no efficiency for that. But there is an efficiency for that power plant as a whole. And if you feed that power plant with methane from P2G, you get an efficiency that you can compare to directly using renewable electricity. And it's going to be atrocious.
You might compare 70% and 500% and say 500% is better. But 70% is during the summer, and 500% is during the winter. If the energy for that 70% conversion is provided by free (as in beers) solar energy, your efficiency doesn't matter one bit.
While you are right that I simplified quite a bit, your conclusion doesn't exactly follow.
If we all install solar panels, the upfront cost is 5-10K per house, depending on how big your roof and ambitions are. And it's getting cheaper. And we already see that it can cover 100% of our usage during certain days the summer. In these days electricity is cheap, sometimes even free.
You take this electricity, run it through P2G and make gas out it, that you burn during the winter.
OK ... and what is going to be the price of a kWh of methane from a P2G plant that sits idle 95% of the year in order to produce methane from free electricity the few hundred hours a year that that is available?
And mind you, if a kWh of electricity can make 4 kWh of heat in a heat pump, while your P2G plant needs 6 kWh of electricity to create 4 kWh of heat in a gas heating system, even if your P2G plant somehow magically was free, that gas is more expensive as soon as the electricity used by the P2G plant is more than a sixth of the average market price. So, "cheap" electricity really doesn't cut it, it has to be almost free for this to be economical, especially when considering that the plant probably isn't actually free in reality.
Either you have a plant that's idle most of the time, which is going to make the gas expensive, or you increase the load, which requires feeding increasingly expensive electricity into it, which is going to make the gas expensive, too.
Plus, there are limits to how much renewable electricity we can generate here. Like, people here in Germany use roughly 500 TWh of heat for heating homes per year. That's roughly 2.5 times the amount of renewable electricity generated last year. So, to feed those P2G plants for that purpose alone, we would have to install ~ 3.5 times what we already have in solar and wind. And then, the demands for transportation and industry comes on top.
Maybe, just maybe, it makes more sense to install 125 TWh of solar and wind and then use heat pumps to turn that into 500 TWh of heat?
Gas storage is a solved issue, unlike seasonal electricity storage.
Well, true, but also misleading.
For one, we don't need seasonal electricity storage. The wind doesn't stop blowing in the winter. Actually, you generally have more wind during winter than during summer. And also, funny enough, wind correlates with heating demand, because wind cools houses.
Then, there is a type of renewable energy source that doesn't depend on direct sun or wind that can be used to provide energy when both of those are in short supply. It's called a heat pump. It can be -10 °C, no wind, no sun outside, and my heat pump still manages to move multiple kW of renewable energy from the outside into my home, using relatively minor amounts of electricity for the purpose. I mean ... how about we use that rather than trying to generate tons of electricity that we then don't really know how to store, other than using rather inefficient methods?
And what is great about heat pumps is that they can run both with renewable electricity, but also with electricity from gas power plants, say. And that's where electrolysis and P2G come in: If you run a P2G plant 24/7, the capital costs per kWh aren't that high, so you can slowly fill gas storage all year. And the releatively little time per year when both sun and wind are lacking, you can then burn that gas in peaker plants (which also are relatively cheap to build) to fill the gaps. So, you have your heat pump running most of the time at ~ 400% efficiency, and only a few days a year, you feed it with electricity from P2G methane at a total efficiency of, let's say, 100% (those usually will be colder days, so probably not peak COP). This way, the inefficiency of the conversion process doesn't really matter all that much.
Oh, and those P2G plants then also can contribute to grid stability by shutting down production when needed. Because one alternative to storage is to have variable loads. With those, you can add generation capacity that doesn't just sit idle most of the time (which would be a waste of capital), which then still is available to keep vital things running in critical situations by shutting down some variable loads as needed.
Plus you use CO2 in the process, that you can capture for free at power plants, during the winter. In fact the price of CO2 could be negative, since the power plant doesn't have to pay the carbon tax if it captures the CO2. There just isn't an large industrial process that uses that much CO2 as we make now.
Except there won't be any power plants to provide CO2.
Mind you that we can't emit any more CO2, so burning fossil fuels, capturing the CO2, using that for P2G, and then burning that P2G gas and releasing the CO2 into the atmosphere afterwards is not a solution, as the CO2 would still end up in the atmosphere, and CO2 emissions would only be halved at best (because the carbon would essentially be used twice before being released).
So, the only way to implement this without CO2 emissions would be to implement a closed loop. But mind you that that then would mean that you would have to burn the gas as you are generating it in order to get the CO2 back to feed into the P2G plant. Which is obviously economical nonsense, are you are then trying to feed electricity back into the grid that you just bought it from, with additional costs and energy losses from your conversion processes. Well, or you could try storing the CO2 for half a year or something ... which would double the amount of gas storage you need. Or something.
Also, systems for capturing CO2 aren't free either.
This is just the most sensible way of handling the issue for the next decades.
If you ask me, that sounds more like a more uninformed way of handling things.
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