>This is seemingly in opposition to your statement. I think the diff comes from considering all the other energetics - precipitation of CaO from the hydroxide is thermodynamically quite favorable, reducing the overall theoretical cost by 65% relative to the chloralkali process. So to the extent that Heimdal can usefully harness that energy gradient, that's the difference.

I guess the crux of my argument is that it is impossible[0] to capture the energy from CaO precipitation. E.g.[1] one has to spend 2J of electrical to create the hydroxide in Ca(OH)2, but the 1.5J get released on precipitation of CaO comes as heat[2], rather than a reduction in energy input.

So, in summary, Electrochemical CaCO3 would have [approximately] equal theoretical electrical demand to chloralkali and, to borrow your term, a higher reality factor overhead[3], to make a product an order of magnitude cheaper than NaOH.

[0]For a loose definition of impossible, to be fair reality's never quite so black and white.

[1]Made up numbers.

[2]And heat in sub-boiling water is not useful for doing work.

[3]I broadly agree with your position on reality factor overhead, just made less of an emphasis on it trying for 'equivalent but worse and creates less value'

According to their web site, one of their premises is that renewable electricity is now cheap and plentiful. If that's so, I'm led to wonder if there is a more direct way to reduce CO2 emissions in cement manufacture, namely, use resistive or carbon-arc heating to fire the ovens, thus replacing fossil fuels in the manufacturing process.

Sorry I don't have the chops to work out if that's economically feasible.

The thing you are firing in the oven (limestone) releases CO2. Fossil fuels aren't the only source of CO2.

We need zero CO2.

> The thing you are firing in the oven (limestone) releases CO2.

I'm aware of that. There are two main sources of CO2 in cement manufacture: the calcium carbonate raw material, and the fossil fuel required to cook the raw materials into clinker. Heimdal only deals with one. The questions I'm interested in are which source contributes more CO2 and which can be most economically eliminated.

> We need zero CO2.

Agree, but Heimdal won't get us there. We'll either have to find a replacement for cement, or devise a practical method to convert CO2 waste to something benign, like an improved Bosch process.