Production rate versus time
Constrained plateau case against the deliverability potential at each depletion state. Potential sits above during plateau and merges with actual through decline.
Deliverability versus cumulative production
The depletion relationship q potential as a function of Gp. Fall off occurs where the plateau line meets this curve.
How the constrained case is calculated
Cumulative production Gp is integrated from the uploaded rate and time curve by the trapezoidal rule, with increment in Bcf = rate in MMscf/d times days divided by 1000. Because cumulative production rises monotonically, every value of Gp maps to a single deliverability, giving the backend relationship q deliverability = f(Gp).
The constrained case is then stepped through cumulative production, not calendar time. At each state the rate is actual = min(plateau, q deliverability at current Gp). While deliverability sits above the plateau the asset holds flat and depletes slowly. When cumulative production reaches the point where deliverability has fallen to the plateau, the asset falls off plateau and follows the deliverability curve down.
This is why a lower plateau pushes the fall off later. The fall off always happens at the same cumulative production, but a lower plateau takes longer in calendar time to reach it. Modelling fall off as a simple crossing of the plateau against the original calendar time curve would place it too early and is not used here.
The dashed deliverability potential is plotted along this same constrained timeline, as q deliverability at the current Gp. It is the maximum the asset could flow given how depleted it is in this case, so the actual rate, being min(plateau, potential), is never above it. During plateau the potential sits above the flat actual and declines slowly. At fall off the two meet, and through decline they are identical. Because the depletion pace depends on the plateau, both curves stretch in time together as the slider moves.