Oil Shock Model
Interactive Compartmental Production Simulator
Peak Production
—
Gb/year
Peak Year
—
Model peak
Cumulative (to 2023)
—
Gigabarrels
Remaining (2024–2060)
—
Gigabarrels
US Crude Oil Production vs. OSM Model
Annual production rate (Gb/year). Bars = EIA observed data. Line = Oil Shock Model simulation.
EIA Observed
OSM Model
Cumulative Production
Total oil produced since 1900 (Gb). Dashed line marks 2023.
How the model works: Oil reserves move through four compartments — each governed by an exponential (Markov) decay with mean delay τ.
dF/dt = D(t) − F/τ_f | dC/dt = F/τ_f − C/τ_c | dP/dt = C/τ_c − P/τ_x | Q(t) = P/τ_x Adjust the τ sliders to see how delays shift and broaden the production curve.
OSM Compartment States
Reserves in each pipeline stage (Gb). Production rate Q(t) = P(t)/τ_x is the model output.
Fallow F(t)
Construction C(t)
Producing P(t)
Production Q(t)
Discovery Input D(t)
Sum of logistic pulses representing distinct eras of oil discovery (Gb/year found).
Total Discovery D(t)
Pulse 1
Pulse 2
Discovery → Production Delay
Comparing discovery rate and resulting production rate — showing the time lag imposed by τ_f + τ_c + τ_x.

The Oil Shock Model

The Oil Shock Model (OSM) is a compartmental Markov-chain model that simulates oil production as reserves move through sequential pipeline stages. Developed by Paul Pukite, Dennis Coyne, and Dan Challou in Mathematical GeoEnergy (Wiley, 2019).

Each compartment transition is modeled as an exponential delay — the memoryless property of a Markov process. This converts the convolution integral into a tractable system of linear ODEs.

Discovery D(t)
→
Fallow
τ_f
→
Construction
τ_c
→
Production
τ_x

Discovery Input

The discovery function D(t) is modeled as a sum of logistic growth pulses — first derivatives of the logistic function, producing bell-shaped curves:

D(t) = scale·k·e^{-k(t-t₀)} / (1 + e^{-k(t-t₀)})²

Two pulses represent the US: the conventional onshore era (~1930–1970) and the offshore + shale era (~2010–2020).

Parameter Guide

τ_f (Fallow delay): Years between discovery and start of development drilling. Typically 3–10 years for conventional oil.

τ_c (Construction): Time to drill wells and build surface infrastructure. Typically 2–6 years.

τ_x (Extraction): Mean time to deplete producing reserves — the inverse of the decline rate. Longer τ_x → more gentle long-term production plateau.

Data Source

Observed data from the US Energy Information Administration (EIA), annual crude oil production 1900–2023, in gigabarrels per year (Gb/yr = 10⁹ barrels/yr).

Source code available at github.com/pukpr/OilShockModel.