The efficiency of CHP is mentioned, but not that it only applies if the heat is required at that particular moment.  All of this begs the question of where to get the carbon to make the methane, and how much energy overhead is involved.  Mobile uses will dump the carbon back to the atmosphere, adding to the amount requiring re-capture.  I notice that NONE of these news releases ever mentions cost.

The efficiency of the E-gas scheme is even lower than straight hydrogen, and engines far lower than fuel cells.  Unless and until all the RE involved gets compensated purely at market rates (no feed-in tariff), E-gas from RE is going to be horrendously expensive due to all the losses.  Batteries will have a huge cost advantage.  That is something that the E-gas advocates want everyone to forget.

They can afford to as long as they are otherwise dependent on Russia for energy.

The most interesting part is the bit about the world's first undersea gas compressors. There is talk of extracting gas intermixed with brine off the Gulf of Mexico. The temperature of the brine is hundreds of degrees. Given the impracticality of sending air undersea to combust,wouldn't geothermal make the scheme work, and even form the basis of an electric grid to complement gas energy?

Dr. Georg Pachta-Reyhofen seems to be disregarding the second law of thermodynamics

PS he does seem to be aware of the first law of Politics

Storing energy as gas also has much greater losses.  Hydrogen requires several times the volume to store the same energy as methane and requires major re-work of distribution and consumption systems, but converting power to methane is a lossy step itself.

All of this costs money.  Have you noticed that none of the gushing news pieces about E-gas ever mention price?

All of this grows out of one assumption:  that humanity must rely on the intermittent supplies of the wind and sun, and we have to bank them ourselves against later need.  The assumption is false.  Uranium is continually leached out of rocks by weathering and delivered to the world's oceans at about 32,000 tons per year.  Fission of 1 ton of uranium per year is enough to deliver about 1 GW of electric power, so uranium can deliver roughly 32 TW(e) to humanity into the indefinite future.  Uranium can be mined as required.

Going "forward" by trying to live off diffuse, intermittent energy flows extracted over vast areas isn't even all that environmentally friendly.  The one guaranteed result of the Energiewende is to give Germany a choice between carbon-belching Russian gas and filthier lignite.  We can only pray for sanity to finally come back to Berlin.

Chapter 4 of this thesis - is the only place I've seen capital costs of power to gas mentioned.

A PhD dissertation, not exactly proof of anything (especially the assumptions which went into it).  But there are some very interesting quotes in that Chapter 4, such as page 105:

The necessity to bridge two weeks of wind calms can only be met by long-term storage facilities. So far, the only option available for this purpose was hydrogen. However, hydrogen as storage option is limited due to high costs, security challenges, missing infrastructure and short lifetimes of fuel cells.

In other words, a massive build-out of something to bridge supply gaps is required, and for "renewables" most of those options do not produce a joule of energy themselves.

The gas network is the largest existing storage facility with proven and available technology (Cerbe, 2008). It has a capacity of hundreds of TWh

Yet Germany's natural gas storage cannot carry through even one winter without massive help from continued imports, coal and the remaining nuclear plants.  At 50% conversion efficiency, Germany's 70 GW(e) of grid load burns through about 3.4 TWh of fuel per day.  Add space heat and transport, and "hundreds of TWh" disappears awfully fast.

There's also the question of where you get the carbon for this "renewable power methane".  I look at the diagram on page 106, and it includes... "Fossil fuels".

The energy demand for CO2 extraction from flue gas (biomass or fossil fuels) are far smaller, as the concentration is much higher (about 10%-vol) and not included in the calculation of the energy storage efficiency.

Not exactly legitimate, given that such capture would be mandatory and actual figures for carbon capture from fossil-fired plants are high enough to be very troublesome.

Using atmospheric CO2 reduces the renewable-power-to-methane efficiency by approximately 15% down to 48%.

Less than half.  On to page 111:

After upscaling to a commercial scale of 20-200 MWel by 2020 and later, investment costs are likely to drop below 1000 EUR/kWel and power-to-gas efficiency are likely to rise to 65-68%.

Presumably that does not include atmospheric-capture overhead, so knock that down to 50-53% for a large fraction of the total storage.  The system must be sized for peak generation, not average, and the lower the capacity factor of the generators the bigger the system must be.  By the time you're done, the capital cost of the storage system alone will be several thousand euros per kilowatt, and it's a net absorber of power to the tune of at least 1/3 of each kWh input.  And here's one of the key assumptions in his analysis:

In future power grids, wind power is likely to be very economic and available at 0-2 EUR-cents/kWhel in times of high wind penetration and low residual load.

In other words, he assumes that generators will be paid unsubsidized market prices, not feed-in tariffs.  When is THAT ever going to happen... and who'll ever build a wind farm if it does?  They're currently needing replacement in roughly 20 years, so there's no way off that particular treadmill.

But keep on betting on your nuclear pony, meanwhile renewables will continue to be built.

Only because legislators demand it while hobbling nuclear power or banning it outright.  Nuclear power requires no storage system to capture fickle power flows until needed.  There's no such thing as "two weeks of atomic calm".  And the author has the gall to assume that nuclear's slow ramp rate is a problem.  Does he bother to analyze the economics of his preferred storage systems with excess base-load energy cranking 24/7?  Nope, that's outside the narrow scope of his thesis... and yours.