Firstly, I'd say no, patterned isn't really a good replacement here. Patterned indicates that you're copying something, but it does not indicate what you're doing with the copy. Modelled or simulated would both be better, but you could use either of those words along with patterened.
Second, the sentence structure is rather off. It took me a few read-throughs to understand it. I'd suggest switching it around a bit:
Aiming to test the reproducibility of the present modelling setup, we ran simulations patterned on three spills that had occurred in the region
This indicates that you ran simulations, and that the simulations were copied from - or patterned on - spills that had really occurred.
Other uses of patterned in a similar context could be:
Germany launched a blitzkrieg attack, patterned on their successful strike against Poland.
A new product was designed, patterned on the most successful products of the last ten years.
In each case, patterned indicates that the action taken was being copied from something else, but patterned by itself does not indicate what action is being taken.