350h is a lifespan, and you're quoting a speculative paper. I haven't read the story extract, but I assume the plan would be to bleed matter into the micro black hole to maintain it. (Arthur C Clarke posited the same concept 40 odd years ago in his Imperial Earth novels.)
I assume your point is that a GeV is a minuscule amount of energy, which isn't going to push 130kT around at any speed.