A 2019 study created alternative integrated assessment models to the IPCC's, that relied on direct air capture instead of BECCS or afforestation. They found that the energy cost for this could be as high as 300 exajoules.
The green bars show the energy requirements in 2100 for these models, using the average DACCS scale up rate across their scenarios, which is 1.5GtCO2/yr. The pink bars show how much energy the entire world used in 2021.