Look, I'm not trying to prove anyone right or wrong here, I'm just pointing out certain details that have to be considered in the design of such a system.
We are intentionally tossing this heat in order to optimize the energy going into the PV of the gas.
That is a problem. Because for an ideal gas, increasing the pressure isothermally does not increase the energy stored in the gas. For an ideal gas, both internal energy and enthalpy are a function only of temperature. Reference here, but you can find others:
https://www.ecourses.ou.edu/cgi-bin/ebook.cgi?doc=&topic=th&chap_sec=03.4&page=theoryFurthermore, this has an interesting consequence for isothermal compression.
All of the work done compressing the gas will be lost as heat to the surroundings. If you pump 100 kWh into your storage system isothermally, 100 kWh of heat will flow through the walls of the tank and into the ground. This comes from the thermodynamic relation that dU = Q + W, and if dU = 0, then Q = -W. Reference here:
https://en.wikipedia.org/wiki/Isothermal_process#:~:text=It%20is%20also,of%20ideal%20gases.You can say you are "getting that heat back", but the reality is you aren't. You are getting heat from the isothermal expansion and the surroundings. It's not the heat you lost in the isothermal compression, it's just heat from the environment.
See below.
What is important as well is that the expansion be isothermal which happens with the heat sink providing energy which ends up compensating perfectly with the heat lost in the isothermal compression curve.
This is true, but it is also a matter of accounting. If I lend you $100 today, and you pay me back $100 tomorrow, is it the same $100? Is it important?
If I store 100 kWh into my system and 100 kWh disappears as heat lost to the surroundings, then if I have any hope of getting some of my 100 kWh back again, I need to get at least some of that heat back. Is it the same 100 kWh? Yes, from an accounting point of view it is, or the books won't balance.
Humpty Dumpty said, a word "means just what I choose it to mean—neither more nor less." "Effective" depends on the context and in this context we don't need large surface areas or radiators or high thermally conductive materials because the rate of heat generation is limited. The tanks aren't filling in 10 minutes. They are filling in a work day or maybe a full day or maybe a week. So how hard is it to allow the heat produced or absorbed to be exchanged in 8 hours or more?
See, I don't know. Maybe yes, maybe no. Without doing some engineering calculations and running some numbers, I couldn't say. However, I can say it is something to be considered in the system design.
I find it amusing that there is still much doubt. The system is amazingly simple once it is understood. I can't find any practicalities that would make it a problem. I'm assuming they have the material issues well in hand. Considering man has been burying tanks in the ground for a very large number of years I expect there won't be any surprises in that. The rest of the system is not new technology unless they decide to use some new turbine or pump to get another two percent efficiency improvement.
It's not a matter of doubt. Clearly the system can work with some level of efficiency. I don't think any of us know the actual numbers, though.
I believe that is a fallacy, the comparison between the two systems. A heat pump has to exchange the full heat flow into the ground or air. This system has to exchange the heat from compression/expansion which is only a part of the total energy flow. Also, you seem to only see A tank. The system is composed of many tanks with each one handling a small part of the total power flow. So each very large tank only needs to handle a small heat flow. An earlier estimate per tank was 100 kWh. Over an 8 hour day that would be 12.5 kW. I think the air in a 30m3 tank can exchange the level of heat produced without a significant temperature rise.
I really don't know without doing some calculations. Aren't you doing what you complained about with others, taking some numbers and supposing results without supporting analysis? Do keep in mind that for heat transfer to occur, there has to be a temperature difference. If the temperature does not rise in the tank there can be no heat exchange with the surroundings. So the temperature must rise at least somewhat.