“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

## Saturday, July 21, 2007

### Exponential growth versus exponential decline

I would like to direct my readers' attention to a web site created by an organization called "Negative Population Growth." As its name implies, the organization is devoted to bringing attention to and finding solutions for the problems of humankind caused by overpopulation (pretty much all the problems, as nearly as I can tell). The link above is to a presentation of exponential growth by Dr. Albert Bartlett, who has become famous in peak oil circles and rightly so.

I would direct the reader's attention to section II, subsections IV and V. These address the mathematics of exponential growth of consumption of a finite resource. Obviously, here I'm thinking of growth in energy (specifically, fossil fuel) use versus the finite total of recoverable fossil fuel resources. Dr. Bartlett presents the concept of the "exponential expiration time," a mathematical expression relating the size of a resource, the consumption rate of the resource, and the rate of growth of consumption of the resource.

While none of the numerical quantities involved (population growth, economic growth, total recoverable resources) are known precisely and the growth rates are not constant, the conclusions will hold qualitatively as long as the rates are positive and the resource is finite. Let's calculate a model scenario that doesn't even require an estimate of what is referred to in the peak oil community as "ultimately recoverable resources" or "URR."

The idea is to determine the rate at which so-called "renewable energy" production must increase to make up for a shortfall in availability of energy derived from fossil fuels. I'll make some assumptions, based on the best information at my disposal, regarding rate of growth of demand for fossil fuels, rate of decline of fossil fuel production, and the current rate of fossil fuel consumption. I'll cite the sources of data and the pertinent dates. The reader should keep in mind that experts have done these calculations with better models and more accurate information (not to mention higher IQ's) than I have at my disposal, so my results are meant only to help grasp the magnitude of the dilemma we face.

I found an absolute goldmine of data on energy consumption and production - BP (the old British Petroleum) has a downloadable excel spreadsheet that has a spectacular amount of information. I utilized it to find a trend line for worldwide primary energy consumption and determined that, based on data from 1965 through 2006, we have a doubling time on the order of 36 years at an annual growth rate of 1.9%/year. It's certainly possible that many developed countries could moderate their growth in energy consumption, but India and China combined are exhibiting a growth rate on the order of 5% on a curve form 1965 through 2006, and represent about a third of the world's population. It doesn't look good on the consumption side.

On the "production" side (in quotation marks because energy is never produced, it is only converted) the sum of oil plus natural gas production has every appearance of increasing linearly. The peak oil community contends that this curve will plateau (or has plateaued), but the data I see doesn't show it. Unfortunately, the situation is plenty grim even without the plateau. Assuming present trends continue, we must make up the shortfall between exponentially increasing consumption and linearly increasing production with alternative sources of primary energy (hydroelectric, wind, solar, geothermal, tidal, nuclear, etc).

This gap increases exponentially as well, and though energy production through means other than fossil fuels also is increasing exponentially, it is not doing so at a rate that will enable the shortfall to be overcome. I estimate that, in 2010, the shortfall will be on the order of 500 MTOE (million tonnes oil equivalent). In fact, my crude estimates and calculations indicate that alternative sources will be required to be equal to fossil fuel sources in about 2026. If, that is, the plateau and decline don't happen. A mighty big if.

Further, it must be noted that this quick estimate takes no account of the myriad other fossil fuel "sinks" such as plastic products, fertilizer, pharmaceutical products, etc. I believe that the time has come, and possibly gone, for a radical restructuring of how we live our lives. Every assumption and simplification I've made has underestimated the magnitude of the crisis (no other uses of fossil fuel, continuing increase in primary energy production, etc.) I'm neither a socialist nor a utopian, however, every trend I've analyzed indicates that we're whistling past the graveyard and that only the most extreme measures will suffice to avoid catastrophe.

And driving more slowly in an LR3 is not going to get it done.