I guess if you ignore the facts in Simmon's book then there isn't much evidence there.
But wait! Maybe the facts are important here? Maybe facts have something to do with evidence? Can you comprehend that idea?
If so, then lets examine the question of whether or not KSA is "about to experience a peak" as you put it.
Simmons pointed out in his book that the amount of oil that has already been produced from Ghawar is enormous. The fact that a huge amount of oil has already been produced at Ghawar is indisputable. Are you with me so far on that FACT or do I have to explain it all again for you?
Actually that is not what Simmons mostly wrote about in his book....perhaps you actually didn't read it.
What he did spend a lot of time doing was suggesting a bunch of papers he had supposedly read from SPE indicated that Ghawar was in trouble.
As it turns out (and I pointed to this a number of years back on the Twighlight in the Desert thread) he either didn't actually read anything other than the abstracts (you need a membership to SPE to get anything more than the abstract) or he didn't understand what the papers were actually saying. I actually read all of the papers he referenced (at the time I had a membership with SPE) and as it turns out where he reported the authors had indicated a serious problem and left it at that the authors had actually identified a problem and then spent the majority of the paper indicating how that problem was solved or was being solved.
And as to the reserves in Ghawar we now have two independent audits from Gaffney Cline & Associates and DeGolyer and MacNaughton two of the largest firms involved in reserve audits that indicate agreement with the official numbers Saudi Arabia has been saying for reserves. We don't know if that is P1 or P2 but there weren't a bunch of alarm bells going off and the Saudis wouldn't be listing on exchanges that required the maximum amount of reporting transparency unless they had little to hide.