13 billion tons of propellant is nowhere close to the mass of the Earth, which is around 6.6 billion trillion tons. (6,600,000,000,000,000,000,000 US tons).To move a one ton spacecraft to 1% of light speed, you would need more chemical fuel than the entire mass of the Earth. 13 billion tons of propellant. An Ion drive craft might reach Proxima B in 40,000 years.
If you use a ship setting off nuclear bombs one after another for thrust you might reach Proxima B in 40-50 years.
I've probably already said this, earlier in the thread, but I see the fallacy starting to pop up again-
DO NOT assume any and/or all alien life is "carbon based" or that it must conform to the limitations of what we understand as the limitations of our form of life.
The nuclear bomb propellant idea is a great one, it's too bad that the ORION PROJECT wasn't developed further.