The Oil Shock Model and Compartmental Models

The coronavirus pandemic and the global oil economy

Chapter 5 of our book Mathematical Geoenergy describes a model of the production of oil based on discoveries followed by a sequence of lags relating to decisions made and physical constraints governing the flow of that oil. As it turns out, this so-named Oil Shock Model is mathematically similar to the compartmental models used to model contagion growth in epidemiology, pharmaceutical/drug deliver systems, and other applications as demonstrated in Appendix E of the book.

One aspect of the 2020 pandemic is that everyone with any math acumen is becoming aware of contagion models such as the SIR compartmental model, where S I R stands for Susceptible, Infectious, and Recovered individuals. The Infectious part of the time progression within a population resembles a bell curve that peaks at a particular point indicating maximum contagiousness. The hope is that this either peaks quickly or that it doesn’t peak at too high a level.

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US GoM 2019 Summary: Part I – Exploration, Drilling and Discoveries

A Guest Post by George Kaplan

Introduction

In many ways the US side of the Gulf of Mexico shows signs of a production basin at the end of life. Most of the sort historic of charts that would normally plotted – discoveries, drilling, active wells, active leases, leasing activity, natural gas production – show classic bell shapes, with current conditions on the tail; and yet oil production is still just about increasing, and the fall in remaining reserves has been reversed in recent years.  Examples for some parameters are shown in the chart, and others in subsequent sections. (Note the units used for production, it was the only way to get everything on the same axis.)

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