Chris,

I applaud your effort. I appreciate that you're coming from a math background and not petroleum engineering. I think that allows a useful different perspective. And I suspect you probably understand part of your characterization of a "typical field decline curve" has limitations but I understand modeling needs to start at a simple base and then allow more complexity to enter. Ignoring gas fields for the moment, oil fields tend to fall into two general reservoir drives: water drive and pressure depletion. The build up to peak production results from the time span to bring all field wells online so I skip that section. Your basic model most closely fits that of a pressure depletion drive. As oil is produced the natural gas saturating the oil comes out of solution and aids in the production. But as pressure is drawn down there is less energy to drive the process. But this model is often complicated by the reinjection of produced NG back into the reservoir to maintain reservoir pressure as high as possible. This would alter you basic curve significantly if the pressure maintenance effort is very effective.

In strong water drive reservoirs the oil production rates drops very slowly initially as the buoyancy force of the water pushing the oil up the well bore remains fairly constant. But when the water level approaches the perforations in a producing well the oil rate can drop very quickly. But after the oil/water ration reaches a very low level (let’s say less than 20% oil) the oil decline rate may become very low. I’ve worked with fields that have recovered 100’s of millions of bbl of oil but produced 70% of their cumulative production at oil rates of less than 20% of the total fluid produced. Many of these fields took over 50 years to recover the bulk of their production. Many of these fields are still producing today even though the “oil cut” is down to 1% or 2%.

In applying a model to current global production and looking forward one must look at the drive mechanism of the remaining super fields. Ghawar in Saudi Arabia is a good place to start. Being a strong water drive reservoir its production rate remained fairly level during the early part of its life. But its total production profile is complicated by various secondary recovery efforts including late life horizontal drilling. I can imagine such analysis could be beyond you capabilities. In time perhaps you can have someone with reservoir engineer expertise to assist in this regard. Good luck with your future effort and don’t let the geobabble get you down. Reservoir dynamics are governed by physical laws which lend themselves well to strict math rules.

Ghawar has a reasonably strong water drive, but the early (vertical) wells were so prolific that just a few of them were able to overwhelm the natural water drive.

So, perhaps up to the onset of powered water injection, the depletion profile might be described as suggested by Dudley. After that, however, any simple model might be completely washed out by other factors, including the ones you suggested.

Elsewhere in KSA, maybe the offshore fields, the early fields such as Dammam (shut it after a many years), and Shaybah would be amenable -- although they are injecting gas in the latter.