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.