My understanding from the article and a couple related ones is that the energy required comes from naturally underground heat and pressure. I think the challenge here is going to be more-so about scalability: how do you create the necessary conditions for capturing a meaningful amount of carbon on an industrial scale.
It's a very interesting approach though, because this is the main way planet recaptures C02 anyway: through C02 reacting in the ocean with sea-floor basalt and eventually getting subducted.
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