> devoted just 2x our current renewable and nuclear production to capture, paying "as much energy as we got", we'd be removing it 1/3 as fast as we emitted it, which is a pretty good pace.
Some quick and dirty back of the envelope math.
According to this source, https://ourworldindata.org/energy-production-consumption, oil, coal, and nat gas, the big culprits, currently account for 137,000 TWh of energy use per year, or 76.5%. Bump that up to 82.5% if you include traditional biomass burning.
So, only 31,000 TWh per year come from renewables and nuclear. One third of that is hydropower, which is largely tapped out and certainly doesn't have exponential growth potential. So, we currently have about 20,000 TWh of renewable and nuclear generation capacity as a civilization, compared to 179,000 total consumption.
So, just to maintain current civilization standards without fossil fuels, we need to grow our renewable nuclear fleet by a little less than a single order of magnitude. Does it make sense to devote any of our renewable fleet to renewing atmospheric carbon if we are still emitting any of it? Seems like the more prudent action would be to use 100% of renewables to decrease emissions in the first place, because emission/extraction is always going to be an inefficient process.
Now, this doesn't account for the fact that most humans in the world are still incredibly energy poor. Your refrigerator uses more energy than the total use of the average person in Nigeria, which is expected to become more populous than China by the end of the century. Let's say that we agree that US levels of energy consumption is too high to target, and we would like a world where everyone has a European standard of living. The average European consumes about 38 MWh per year, US is double at 79 MWh, https://ourworldindata.org/grapher/per-capita-energy-use.
This means by the year 2100, human civilization would need control of about 400,000 TWh of energy to accommodate an expected population of 10.4 billion humans. Therefore, we need a 20x increase in the renewable and nuclear fleet just to serve all humans with a good standard of living without any fossil fuel consumption.
Now that we have people taken care of and we're not adding more carbon, we can start talking about removing carbon.
Back to the first data source, human civilization has currently consumed an aggregate of 5,341,110 TWh of fossil fuels since 1800. Assuming carbon capture can be 100% efficient (preposterous) meaning it takes an equal amount of energy to remove the carbon as we got when we burned it, then we would have to devote an equal amount of renewable energy watt hours to the project. Dedicated our current fleet of renewables, that would take 178 years. Let's assume that by the year 2100, we have 100,000 TWh of excess energy and we somehow have the political will to devote 20% of collective energy to the reversal project. That would take 53 years to remove the carbon added as of 2023 assuming 100% efficiency, and not accounting for the growing rate of carbon emissions until 100% carbon free. Given the fact we've been way overly generous with efficiency assumptions, we're looking at a project that takes multiple centuries.
So to your initial point, I am wrong. Not really several orders of magnitude, but between 1 and 2 orders of magnitude even in the most generous case where we don't make social progress eliminating poverty and just maintain the status quo. And that's assuming the crisis isn't that urgent and we can lazily take on the order of centuries to remove all the carbon we've added.