Unless the water velocity is pretty high, bubbles do float up. That is why if the wrong end of that horizontal reactor is higher than the other end, bubbles will collect at that end, out of the high velocity flow. If you introduce the CO2 as micro-bubbles, then they will never manage to float up, but will just follow the flow. But I didn't see anything in this one that would produce micro-bubbles.
ok if the co2 bubbles collect at the input end, they would continue to build up and grow to the point that they would interfere with the water flow, and at that point begin to travel along with the water flow? So one could have a build up of bubbles, but only to a point. just trying to think this out in a logical way?