I use a combination of maturation rate and extraction rates to model this situation. The end result is a convolution of two exponentials, leading to something akin to a gamma distribution of order 2. An infinite extraction rate would correspond to a situation where all the taps were turned on at exactly the same time and at full extraction rate. In practice, after construction completes each will get turned on at a slightly different deferred time and with different ramp-up times. This puts the production plateau away from Time=0, or which as Luis describes leads to a production plateau.

This has a basis in stochastic modeling, and of course works best when one considers a range of fields that can be described by a statistical average for maturation and extraction (as well as fallow and construction times). I call it the oil shock model.

BTW, the best example of something that doesn't follow this general trend is the North Slope/Prudhoe Bay where it looks like the late completion of the Alaska Pipeline allowed the taps to immediately start flowing which leads to an almost immediate peak in production, i.e. the maturation was obscured by the concurrent initiation of a high-throughput delivery mechanism, which essentially deferred the production from gradual to steep.