We have, actually, a lot of information. I recommend to you table 5.5 of the IPCC report, which summarizes the key lines of argument we have for understanding the long-term stability of storage. Let me just give you two of them: one engineered and one natural.
There are CO2 accumulations underground that have been there in excess of a hundred million years. We know for certain there are--in fact, they're ubiquitous--cap rock formations that are capable of holding gases underground for in the order of a hundred million years or longer, essentially infinity on any time scale that matters to the climate problem.
Now, you might say, “Oh, that's true, but the problem is going to be that they will have leaking wells or leaking engineered structures.” We have now almost a hundred years of cumulative experience with natural gas storage, and for the IPCC report we tried to estimate what the total leakage rate was. To be clear, there have been leaks, and there have been people killed by natural gas storage accidents. None of this is zero-risk. But the overall leakage rate from natural gas storage is something less than one part in one hundred thousand a year, and that number is about one hundred times better than what you would need to have in order to do a sufficient job of managing the climate problem.
In my view, the big issue is actually local risk, not the long-term leakage.