Many natural object geometry are well described by a fractal (e.g. a coastline). In particular, fractal self-similarity is a powerful concept that has been investigated by Benoît Mandelbrot. However, in practice the self similarity law is not always perfectly respected. To remedy to this, Jean Laherrère has proposed the Parabolic Fractal Law (PFL) which adds a parabolic deviation to the pure self-similar law, I quote: A complete or near complete distribution of the larger objects, which in practice are usually readily identified and quantified, can be used to define the parabola following a rule of self-similarity, and hence describe the full distribution down to the smallest object. The distribution can in turn be used to determine the total population of the objects. I believe that the PFL could be a complementary tool to analyze production data under a different angle especially when the Hubbert Linearization technique does not produce a clear result. For instance, when applied to the United Kingdom production data, the resulting Ultimate Recoverable Ressource (URR) is very close to the value estimated by the Hubbert Linearization technique. I intend here to apply this technique to Saudi Arabia oil fields. Despite using coarse oilfield size estimates, the PFL seems to point toward an URR close to the ASPO estimate at 270 Gb.