Some comments and expansion on your analysis, which I enjoyed reading and provided a nice excuse to dust some mental cobwebs. I'd also like to clarify up front

Some comments and expansion on your analysis, which I enjoyed reading and provided a nice excuse to dust some mental cobwebs. I'd also like to clarify up front that I'm limiting my analysis to the proposed electrochemical mechanism, and have no information on the specifics of Heimdal's proposed implementation - which may vary significantly and materially: The theoretically minimum electrical energy input (often) winds up being set by one of the reaction intermediates, rather than the overall reaction enthalpy. Typically these analyses are done via determining the corresponding half cell potentials, then counting electrons and computing power via P = IV.[0] So we only need to consider H2O (and its dissociation -0.83[1]) and Cl- to Cl2 at 1.36). That sums to approx 2.19V for the cell, and 2 electrons to do 2H2O + 2Cl- -> H2 + 2OH- + Cl2. That the formed OH-'s pair with Ca2+, and/or CO2 is immaterial to the theoretical electrical efficiency of the cell. Accordingly, the cell energy requirement is on a molar basis identical to the chloralkali process. The only difference is the presence of 2Na+ vs. Ca2+. Less concretely the lower reactant concentrations have two specific negative effects: Cell potential is adversely affected (per the Nernst equation) and Cell current can be adversely affected if/when depletion occurs. At 0.01M of Ca2+, vs. 6+M Na+[2], current densities could be 1-3 orders of magnitude lower. Cell count (CAPEX) is inversely proportional to current density. Ultimately making CaCO3 this way (and CaO) winds up substituting a 400$/tonne product in NaOH for an approx 40$/tonne product in CaCO3. It is a very technically feasible approach for turning $$$ into sequestered carbon via non emission from natural limestone. The analyzed approach reminds me a lot of Calera, who had an apparently similar electrochemical approach to CaCO3. [0]Not that it can't be done from Gibb's energies, indeed the standard potentials for a reaction can be computed from the delta Gibbs, but the specific species the electrons are being pulled from/pushed into matters. Phrased a different way: electrical energy and overall reaction enthalpy are not necessarily fungible. e.g. (at a simple level) the reaction of CO2 with Ca(OH)2 doesn't affect the electrical energy requirement, nor does CaCO3 --> CaO because neither reaction involves electrons. Any exotherm just winds up 'wasted' as heat, instead of lowering the electrical demand. [1]Per 2H2O + 2e- --> H2(g) + 2OH-(aq) #6.8.11 https://chem.libretexts.org/Courses/Mount_Royal_University/Chem_1202/Unit_6%3A_Electrochemistry/6.8%3A_Industrial_Electrolysis_Processes https://chem.libretexts.org/Courses/Mount_Royal_University/C... [2] Saturated near room temp, don't have a better source handy.