Mineral Resource Fixity and Boundary Effects

“We don’t observe the boundary effects in our modern economy and haven’t throughout oil’s history because reserve estimates have grown over time and will continue to grow for the foreseeable future.”

Mineral resource alarmists, reflecting a fixity/depletionist view of the world, begin by arguing that “you must admit that there is a fixed amount of oil on this earth.” This is true in the purely physical sense that roughly 2 million barrels annually are created by the earth versus the 35 billion barrels consumed in a year.

Oil is a non-renewable resource, but that doesn’t mean our economic models should treat it as a drawdown of static inventory. A great example for the issue of fixity in resource economics is reservoir modelling for a singular oil well. In reservoir engineering, there are flow regime equations that model how the fluid moves from the formation into the wellbore.

The four flow regimes are transient, steady state, pseudo-steady state, and boundary-dominated flow. Each differs in how they treat the pressure boundary throughout the life cycle of the well. From Fekete, a leading provider of reservoir engineering software, these are defined as follows:

• Transient Flow — Pressure transient migrates outward from the well without encountering any boundaries.
• Steady State Flow — Pressure transient has reached all of the boundaries but the static pressure at the boundary does not decline. This is often called “constant pressure boundary”.
• Pseudo-Steady State Flow — Pressure transient has reached all of the boundaries and the static pressure is declining at the boundary and uniformly throughout the reservoir.
• Boundary-Dominated Flow — Pressure transient has reached all of the boundaries and the static pressure is declining at the boundary, but not uniformly because the flow rate is not constant. This is also often called “tank-type flow”.

A pressure boundary exists in all wells ever drilled, and all wells do have a set reservoir size. However, the use of a transient flow model is much more accurate in the early-time production of a well by ignoring the limits to the reservoir.

The boundary effects have not been observed by the reservoir engineer, and the transient flow equation is superior to other assumptions that account for the reservoir’s fixity. When boundary effects are observed, the reservoir engineers will change the modeling equation to steady state or pseudo-steady state flow, and the theoretical flow regime of a completely discovered reservoir is modeled by the boundary-dominated flow. Ignoring the boundary when modeling early-time flow is not being stubborn to reality but simply being a good reservoir engineer.

Now let’s apply this to resource economics and the claim of fixed resources. Yes, I will wave a white flag and admit there is a fixed amount of oil on the planet…. But for purposes of economic modeling, it is important to ignore the boundary effects of the limited oil.

We don’t observe the boundary effects in our modern economy and haven’t throughout oil’s history because reserve estimates have grown over time and will continue to grow for the foreseeable future.

When we do start to see boundary effects (in some future century?) we will see oil prices rise over time and eventually approach the rate of interest to fulfill Hotelling’s rule. Harold Hotelling’s rule was that resource prices for a commodity of known size would rise with the rate of interest, but it has often been mistakenly assumed to apply for resources of unknown recoverable quantities, which generally see prices fall over time in inflation-adjusted measures.

Just because a statement is true doesn’t mean it adds clarity to economic models or policy decisions. In The Moral Case for Fossil Fuels, Alex Epstein makes the point (p. 180):

Telling us that there is only so much matter and energy to create resources from is like telling us that there is only so much galaxy to visit for the first time. True, but irrelevant.

Limited space in the galaxy is not factored into real estate prices or rent control policies, and, in the same way, the technical fixity of oil should not lead to alarmist sentiment against recovery of available resources. I will admit that we will see boundary effects of fixed oil supply (perhaps in some future century) before we are limited by the space of the galaxy, but Epstein’s point still stands that models are judged on their foresight and not on the wordplay involved in their assumption.

In closing, I yield to resource alarmists that there is indeed a fixed amount of oil. But in forecasting reserve growth, production growth, or commodity prices, they would be wise not to assume a fixed volume in their economic models.