Well, you can use a pencil and paper. Or a fairly simple spreadsheet. Or you can buy Olga (last I checked this was 6 figures per seat). You will have just about the same chance of success with any of these choices. You have a good start in seeming to realize that steady-state multiphase flow is not possible.
Multiphase flow is amazingly complex and chaotic. There are zero closed-form equations describing it. That leads us to simulations and empirical equations that try to solve the unsolvable. I read a PhD thesis once that was proposing a really complex algorithm, at about page 270 of 400 he said "with this approach I was able to match measured flow withing ±20% almost 30% of the time". He got the PhD. You could do better with a pencil and paper.
