"The story suggests that Audi engineers made basic mistakes or its management made dubious claims. Both are unlikely, considering the name and history of Audi."
Not only are they likely, you can take it to the bank. They made dubious claims. They simply assumed dirty cheap electricity, and that they could run this process on dirt cheap intermittent power. But if you could consistently get dirt cheap electricity, why are Germans paying much higher electricity prices than the U.S., and indeed even most of Europe?
I can show you a long, long list of companies either making dubious claims or investing in dubious technologies that failed. Arguments from authority do not impress me. Chemistry and physics do.
"Whether their power-to-Diesel plants will be viable depends mainly on the price of electricity."
It would also be highly dependent on competing uses for that electricity. Why would I jump through all those hoops of pushing that rock up the hill when I could just run an electric car at a far greater efficiency? The car itself has a higher efficiency, but you don't lose all that energy producing the fuel.
"As the capital and fixed operating costs for these plants will be relative low, it will be also optimal for these plants to buy only electrictiy (and run only) if the price is low and run only part of the time."
Two problems in that sentence. First, capital costs will be incredibly high. Those various pieces are all very expensive pieces of kit. I know, because I have worked in plants that utilized them. Second, you don't run a plant like that "part time." This is a chemical process. It requires time to heat up, come to steady state, and and then cool off. Processes are at their highest risk of an accident during startup and shutdown. I am just trying to imagine running a chemical plant and starting it up and shutting it down every day. That would be madness.
So, the lesson here is that if you make a bunch of unrealistic assumptions, then indeed you could argue that this process makes economic sense. But in reality, there is the problem of those unrealistic assumptions. If they really could make fuel for that price, they would have no problem at all raising money and scaling up as quickly as possible. Instead, the press release said they are ready to commercialize as soon as they "get their first order."