The only carbon capture systems currently working are a continuation of fossil fuel extraction operations where it is pumped back into the well or stratum (though not all of it) to extract yet more fossil fuel. Every other carbon capture projects are abject failures and remain likely to stay that way.
Fossil Fuel extractive industries are not so stupid as to take carbon capture seriously given their raison d’etre is to make money, and not to invest in impossible and unprofitable schemes. Ah! Capitalism eh? Who’d have it?