As a semi-educated layman in this area (too many years since stochastics and diff-E in college!), I appreciate your effort to keep the math relatively simple.

Simple transformations to yield linear results is obviously a perfectly valid approach and makes a intuitive level of understanding simpler, at the risk of obscuring the underlying data a bit for neophytes (the notion if reciprocal time is easy to calculate, but hard to grasp meaninfully!). If you can take previously published real-world data for various fields, plot them using your model, and universally have lines fall out, that certainly provides value.

Of course the whole point for us engineers to linearize situations (and of course many times that requires us to limit the part of a situation we look at so that a linear approximation is reasonable for that domain) is so that we can design or predict something.

What valuable predictions can be ascertained from the newly linearized model? The bounds of likely reserve growth for given existing fields over any reasonable time frame?

Can the model help predict the find rate for a given field size going forward, as a sort of global dispersive model, maybe normalized by some notion of search effort?

Having a model that helps profile the future potential of existing fields is valuable, but having one that quantifies future finds would be divine.