Last week we touched on the subject of the effect of exponential growth on a finite resource. In this week’s blog we’ll discuss the concept of the static reserve along with production of resources against the rise in human population.
Clearly, the static reserve for a resource is NOT a reasonable way of judging how long that resource will last. What we need is a different measure that takes into account the exponential depletion of a resource. Exponential Reserve is the measure of a resource’s expected life at a given growth rate.
STATIC EXPONENTIAL
Widgeon RESERVE RESERVE
(Tons) (Years) (Years)
50,000 500 85
500,000 5,000 151
5,000,000 50,000 218
While the difference in 85 years and 218 years is significant when measured in lifetimes, it is not when considering the use of finite resources that have been on this planet for 4.5 billion years.
Ophuls completes his analysis with the following general principles:
1. Given steady exponential growth, the absolute size of the stock of any resource has very little effect on the time it takes to exhaust the resource.
2. Given already high absolute demand on a particular resource, the rate of growth in demand thereafter has almost no effect on the time it takes to exhaust the resource.
3. The time for concern about the potential exhaustion of a resource comes when no more than about 10% of the total has been used up.
Why talk about peak production with oil and gas?
In our discussion of human consumption of finite resources, we have made the tacit assumption that the number of resources available to us is the same as the identified reserve. This is not necessarily the case. In the 19th century, it took about one oil barrel’s worth of energy to produce 50 barrels of oil. Currently, one barrel’s worth of energy input yields one to five barrels output! When the cost approaches one barrel in for one barrel out, it is not economically viable to produce more oil. After all, what incentive is there to produce energy if you need to put as much energy into the endeavor as you get out?
The point when oil (or any resource) is no longer economically viable has less to do with how much of it is left in the ground and more to do with human factors, specifically economic costs and technical abilities. As technology improves and the price of oil increases, there are numerous examples of the reopening of oil wells which had previously been drained to the point where they became economically non-viable.
M. King Hubbert (1903-1989) was an American geologist who worked for a number of oil companies, the United States Geological Survey (USGS), and later became a bit of a philosopher and writer. Hubbert surmised that when fossil fuel reserves are first found, oil production increases geometrically until a peak is reached, at which time production begins to decline also in an exponential fashion.
Using his models, he observed the production characteristics of less-than-active oil fields and used this data to develop a method of estimating the size and production characteristics of individual, regional and world reserves.
Hubbert’s analysis of the life cycle of an oil resource revealed a bell curve as shown in Figure 3-15. The X-axis of this graph represents the time the reserve is in production from its start (-6) to peak production (0) to the end of production (+6). The Y-axis represents the output of the resource. The area under the bell curve represents the reserve.
Looking at the graph below we see that as a resource is opened it takes a while to ramp up. At the time when peak production is reached, about one half or the resource has been used up, and assuming continued use, the second half of the curve follows.
These characteristics have come to be called Hubbert’s Peak or just Peak Oil. In 1956, Hubbert predicted that US oil production would peak between 1969 and 1971, He was ridiculed, but his prophecy turned out to be correct.
Figure 3-15: M. King Hubbert, 1962, “Energy Resources,” National Academy of Sciences, Publication 1000-D, p.81-83
The left side of the graph represents easily available oil and therefore is the less costly side of the graph. Unlike the cost curve for technologies, which goes down with increased production, getting resources out of the ground is quite the opposite. You might imagine the left side of the curve represented in the opening scene of the Beverly Hillbillies TV show when Jed Clamped shoots his gun into the ground and oil comes gushing up like the well shown below.
Figure 3-16: The Lucas gusher at Spindletop, January 10, 1901.
This was the first major gusher of the Texas Oil Boom.
You might think of the right side of Hubbert’s graph as representing oil platforms in the raging North Sea, or building pipelines through the Alaskan permafrost where each successive barrel of oil costs a little more to extract than the previous one.
Here are graphs of Hubbert curves for Norwegian and US oil output:
Figure 3-17
Sources?
Figure 3-18
These curves predicting the actual output are remarkably accurate. Now, look at Hubbert’s analysis of United States natural gas production.
Figure 3-19: The curve is from the equation and figures in: M. King Hubbert, 1962, “Energy Resources,” National Academy of Sciences, Publication 1000-D, p.81-83.
In this graph, the blue line is the actual gas production and the red line is Hubbert’s prediction. Production followed the curve until somewhere around 1990. At that time, rather than dropping the way Hubbert’s curve predicted, natural gas production continued and in the last few years actually grew at an exponential rate.
What happened?
New technologies such as hydrofracturing (fracking) have expanded gas reserves.
While considering this, think back to our fictitious resource, Widgiton, where we started with 50,000 tons. We then ran other scenarios, using 500,000 tons and 5,000,000 tons. How were those great increases in resource availability explained? One reason was improved technology for finding and extracting resources. That is exactly what happened in the case of natural gas. Developments in technology have made resources available to us which were not physically accessible or economically viable.
While it is tempting to rejoice in this new-found supply of energy, perhaps this is the time to re-read Ophuls’ conclusions:
- Given steady exponential growth, the absolute size of the stock of any resource has very little effect on the time it takes to exhaust the resource.
- Given already high absolute demand on a particular resource, the rate of growth in demand thereafter has almost no effect on the time it takes to exhaust the resource.
- The time for concern about the potential exhaustion of a resource comes when no more than about 10% of the total has been used up.
The key resources upon which we depend are finite. Remember, we don’t need to run out of all, or even most, resources to reach the one or two critical ones which will eventually become limiting factors to humans, causing shortages of necessary goods if not replaced in some other way.
In M. King Hubbert’s “Economic Growth as a Transient Phenomenon in Human History”, published in 1976, he tells this story.
There is an old Persian Legend about a clever merchant who presented a beautiful chessboard to his king and, in return, requested that the king give him 1 grain of rice for the first square on the chessboard, 2 grains of rice for the second square, 4 grains for the third, and so forth. The king readily agreed and ordered rice brought from storage. One grain went on the first square, two on the second, and eight on the fourth square. The tenth square required 512 grains, the fifteenth square required 16,384 and the twenty first square gave the merchant more than a million grains of rice brought from the king’s stores.
By the fortieth square, a million (one billion) grains of rice had to be brought from the storerooms. The king’s entire rice supply was exhausted before he reached the sixty fourth square. The king solved the problem by having the greedy merchant put to death.
Hubbert goes on to say that for the 64th square, the amount of rice needed would be 264 grains of rice, or twice the total world supply of rice in 1976. If you totaled the rice from the whole chess board, it would be four times the world’s rice supply of 1976.
In the same paper, Hubbert points out that if human population started with two people, Adam and Eve, it would have taken thirty-one doubling periods (generations) to reach the population of 1976. Forty-six doubling periods would find humans with one square meter of land per person. This, of course, could never happen; nor could the supply of rice double sixty-four times.
As discussed previously, the laws of nature are fixed, and the ‘laws of man’ are not. The key point of Hubbert’s paper is:
“Our principal constraints are cultural. During the last two centuries, we have known nothing but exponential growth, and in parallel we have evolved what amounts to an exponential-growth culture, a culture so heavily dependent upon the continuance of exponential growth for its stability that it is incapable of reckoning with problems of non growth.”
“Economic Growth as a Transient Phenomenon in Human History,” M. King Hubbard 1976 page?
Are there any unintended consequences to producing raw materials?
Everything humans make comes from the earth, using material and energy sources which are finite. In nature, everything built up by natural processes (represented by the left side of figure 3-20) is broken down (represented by the right side of figure 3-20) by those same processes and reused again.
Figure 3-20 Wes Golomb
Not so with human use of matter since the Industrial Revolution. Some of the material we take from the earth, we synthesize into chemicals which never existed before and have no corresponding means to be broken down in our environment. We know that matter cannot be created or destroyed, so this matter, with no natural means to decompose it into its original components, persists. On an environmental scale, we call persisting matter that does not go away pollution. On a human scale, we call it a poison, carcinogen or toxin.
Figure 3-21 Wes Golomb
In Figure 3-20, the arrows representing materials cycle equally in both directions. However, the materials in Figure 2-31 only flow in one direction, and have no natural way of cycling back into the environment.
Matter also exists in a natural system. But as consumption of that natural material increases exponentially, the amount of matter being put into the environment is simply too much for the natural system to process and the system is overwhelmed by the excess material. Take the case of carbon. Carbon is a material which is cycled naturally. As we saw in Chapter 2, there is a long, geologic cycle where carbon is deposited in the earth and remains ‘locked up’ in the depths for millions of years. There is also a short cycle which moves carbon between oceans and land over much shorter periods of time. In nature, both parts of the carbon cycle achieve equilibrium. Today, the carbon ‘overwhelming’ the natural system is primarily carbon that has been moved by humans from the geologic portion to the short portion of the cycle as shown in Figure 3-22. Instead of the cycle time for carbon being in the millions of years, the time frame is days, months or years.
Figure 3-22 Source?
When seen in the light of resource availability, we are running ourselves off a cliff. The healthier our economy, the faster we use finite resources and the faster we approach exhaustion of those resources.
As we’ve seen with the examples of oil and natural gas, we are in short supply of many of the resources we need to sustain a technological society. This should give us pause to consider what can happen in nature when a population grows exponentially and encounters a limiting factor like running out of a key resource.
There is likely little direct evidence that a limiting factor has been reached.
I have a gas gauge in my car and a little red light comes on to tell me when I am running out of gas. We don’t have such a gauge for the earth and we will likely get little or no warning when an impending shortage will occur.
Consider a power grid approaching the maximum generating capacity of the utility. It’s a hot, humid summer day that otherwise seems perfectly normal. Lights, computer, air conditioner all hum like a dream until the limit is reached, passed, and, in an instant, all the power is gone.
Now consider if it was all gone; not temporarily, but because our growth in numbers and demand was great enough to actually run out. It could be electricity, fossil fuels, water or some obscure mineral you’ve never heard of which is an integral part of the material goods you have come to depend upon.
Our analysis of resource availability and economics shows us that any one of a number of events could lead to what ecologists call limiting factors and what historians describe as disastrous events.
Primary candidates for these potential shortages are our non-renewable energy resources, which brings us back to the question, “Why renewable resources?” With our understanding of matter, energy and exponential growth, part of the answer becomes clear.
One of the requirements for societies to survive and flourish is ample and available energy. Our analysis of exponential growth in the demand and consumption of finite natural resources should convince us that there is reason for concern about the continued availability and supply of non-renewable energy for the long term.
Next week we’ll start discussing Climate Change, the next topic in our Sustainability Matters series!
Wes Golomb
