**ARTICLES (2)**

**Drilling for Oil in the Arctic National Wildlife Refuge **

*Richard J. Wiener*

**Introduction**

To drill or not to drill? That is a question I will not attempt to answer. The answer requires weighing the benefits of 10 billion barrels of oil against the costs of damaging an ecologically significant pristine wilderness. This quandary is part of the much greater problem of supplying energy for an increasing world population while simultaneously limiting environmental degradation to an acceptable level. Ultimately, physical scientists are no better (or worse) prepared to make the value judgments needed to solve this problem than philosophers, artists, economists, theologians, or politicians. But scientists often do have a critical contribution to make by analyzing the factual claims that are made in debates over energy versus the environment.

Thus, I will address one misleading argument that is frequently made by proponents of drilling in ANWR. Proponents often claim that drilling in this great northern wildlife refuge will reduce U.S. dependence on foreign oil. This claim is true in the narrow sense that any additional U.S. oil used to meet a given U.S. demand means that less foreign oil is used to meet that demand. However, even if all the oil from ANWR is consumed domestically, it would only slow the rate of increase of U.S. dependence on foreign oil. Extraction of oil from ANWR cannot reverse the overall downward trend in U.S. oil production, and U.S. dependence on foreign oil will continue to grow unless U.S. demand for oil is substantially reduced. I arrived at this conclusion by making a “back of the envelope” estimate of the effect that drilling in ANWR would have on future U.S. oil production. The remainder of this essay explains how the estimate was made and what it implies.

**Hubbert**** ****Peak**** modeling**

Hubbert pioneered the idea of using logistic growth to model oil production.^{1} The logistic growth curve satisfies the logistic differential equation _{}, where *Q* is the quantity which is growing, *P* is the derivative of *Q*, *r* is the initial rate of growth, and *Q*_{tot} is the value to which *Q* is asymptotically growing. Logistic growth is a first approximation to any growth process in which the per capita growth rate, _{}, decreases as *Q* increases. The logistic differential equation specifies that the per capita growth rate decreases linearly as *Q* increases. In the case of oil production, *P* represents the production (e.g. in barrels per year), *Q* represents the cumulative oil produced, and *Q*_{tot}* *represents the total recoverable oil that ultimately will be produced from a reservoir or, more broadly, from an oil producing region. _{} is the logistic growth curve, where *t*_{m} is the midpoint time at which *Q* has grown to half its asymptotic value (which is determined by the conditions of the problem). _{} is the logistic production curve. The logistic growth curve has an *S*-shape with the midpoint time *t*_{m} corresponding to the inflection point of the *S*, and the logistic production curve is bell-shaped with the midpoint time *t*_{m} corresponding to the peak. In 1956 Hubbert fit data for U.S. oil production using a logistic production curve and correctly predicted that U.S. production would peak in 1970. The phenomenon of a peak in oil production in an oil producing region has since come to be known as *Hubbert’s** Peak*.

There are several ways to justify the use of logistic growth to model oil production. On heuristic grounds, one expects that oil production in an oil producing region will initially grow exponentially, since more wells will be drilled as more oil is produced and the most easily recoverable oil is often produced first. However, since there is a finite quantity of recoverable oil in any region, the production per cumulative production, _{}, will ultimately decline as the cumulative production, *Q*, grows and the fraction of remaining recoverable oil, _{}, declines. If the relationship between _{} and *Q* is approximately linear, then the production is well modeled by the logistic production curve. Alternatively, one might consider a physical model for the pressure-driven extraction of oil from a finite reservoir and show that logistic growth arises for plausible conditions under which oil is produced.^{2} Laherrère has argued that for many countries, and the world as a whole, oil production is better modeled using multiple logistic production curves.^{3} One must separate production into several cycles with each cycle modeled with its own production curve. Then the overall production is modeled with a sum of the individual curves. The approach can be justified if one considers that many countries have oil regions that are developed at different times.

*Estimating future **U.S.* *oil production*

The U.S. Energy Information Administration publishes data for U.S. oil production from 1859 through 2005. The data is available at http://tonto.eia.doe.gov/dnav/pet/pet_crd_crpdn_adc_mbbl_a.htm. Figure 1 is a plot of this data. The solid line is a fit to this data extended to 2050 as an estimate of future U.S. oil production. In order to construct the fit to the data, I divided U.S. oil production into two cycles—production from the North Slope of Alaska and production from the rest of the U.S. The data for North Slope Alaska oil production which is available on the EIA web site only goes from 1981 to 2004, although there was some production prior to 1981. However, since almost all production of North Slope Alaska oil is after 1981, the lack of data for production before 1981 does not have much effect on the estimate of future U.S. oil production. I fit individual logistic production curves to each of the cycles. The three parameters in a logistic production curve are the initial growth rate *r*, the total recoverable oil* Q*_{tot}, and the midpoint year of peak production *t*_{m}. Figure 2 is a plot of the production per cumulative production, _{}, versus cumulative production, *Q*, for U.S. oil production without North Slope Alaska oil production. I only show data from 1951 to 2005, the range over which the plot is approximately linear. The deviation from linearity prior to 1951 indicates that the growth is only approximately logistic. Figure 3 is an analogous plot for North Slope Alaska oil production. The three parameters for the logistic production curve can be estimated from a straight line fit to the data for _{} versus *Q* for each cycle. The y-intercept for each linear fit is approximately the initial growth rate *r*, and the x-intercept is approximately the total recoverable oil* Q*_{tot}. The year that production peaked is determined by finding the year in which *Q* surpassed *Q*_{tot}/2. For the U.S. (without the Alaska North Slope) the estimates are: total recoverable oil, 201 billion barrels; initial growth rate, 0.063; and year peaked, 1972. For the Alaska North Slope the estimates are: total recoverable oil, 14 billion barrels; initial growth rate, 0.18; and year peaked, 1991. The actual peak years are 1970 and 1988 for U.S. and North Slope Alaska oil production, respectively. Laherrère has noted that North Slope Alaska oil production is less well fit by a logistic production curve than production in many other regions, perhaps because a large amount of production came online at once with the opening of the Trans-Alaska Pipeline System.^{3} I found that a logistic production curve with the above parameters underestimates the data for North Slope Alaska oil production prior to peak production but fits post peak production reasonably well.

The solid line fit to total U.S. production in Fig. 1 is a sum of the two individual production curves and it fits well for purposes of estimation. The secondary peak in the early 1980s appears to be due to North Slope Alaska oil production and this effect is captured by summing the two logistic production curves, whereas a secondary peak cannot be modeled by a single logistic production curve. The fit underestimates the data after 2000, which might indicate a fluctuation or this might be due to new oil regions being developed such as offshore drilling. Regardless, the overall trend is apparent— U.S. oil production has been declining for 35 years since 1970, with only a small temporary reversal when the Alaska pipeline was opened.

**The effect of drilling for oil in ANWR**

To estimate the effect of drilling in ANWR on future U.S. oil production I added a hypothetical logistic production curve to represent what will be a new production cycle. I used the United States Geological Survey’s mean estimate of 10 billion barrels for ultimately recoverable oil *Q*_{tot} in ANWR.^{4} My order of magnitude estimates for the midpoint year *t*_{m} and initial growth rate *r* are 2030 (with recovery beginning in 2010) and 0.12, which is halfway between the rate for the U.S. and the rate for the Alaska North Slope. The estimate of the year recovery begins assumes a few years will be needed for the infrastructure of oil production to be built even if the U.S. Congress gives the go ahead in 2006. The result is a hypothetical production curve for ANWR in which over 8.3 billion barrels of oil will be extracted by 2050. The peak production is 300 million barrels per year which is roughly equal to the USGS mean peak production estimate of 325 million barrels per year. The dashed line after 2010 in Figure 1 is the sum of all three logistic production curves, i.e. one for U.S. production without the Alaska North Slope, one for Alaska North Slope production, and one for the hypothetical ANWR production. There is a noticeable effect from adding the hypothetical oil production from ANWR, as would be expected from 8.3 billion barrels of oil. But the key point is that recovering this oil from ANWR cannot stop the overall downward trend in U.S. oil production. Therefore, recovering this oil is highly unlikely to stop U.S. dependence on foreign oil from growing. At best it will slow the rate of increase of this growing dependence.

Indeed, we cannot reasonably expect to end our dependence on foreign oil by increased access to a new supply of U.S. oil. There just isn’t enough oil left in the U.S. The discovery of new oil in the U.S., despite large fluctuations in the data, clearly peaked decades before oil production peaked in 1970. As the 21^{st} century unfolds we will become more and more dependent on foreign oil unless we almost completely eliminate U.S. demand for oil.

**Acknowledgment**

I would like to thank Danny Abrams for helpful suggestions on the manuscript and useful discussions on the topic of oil production and logistic growth.

**Endnotes**

1. Marion K. Hubbert, “Nuclear Energy and the Fossil Fuels”, American Petroleum Institute Drilling and Production Practice, Proceedings of Spring Meeting, San Antonio (1956), pp. 7-25.

2. Richard J. Wiener and Daniel M. Abrams, “A Physical Basis for Hubbert’s Decline from the Mid-Point Empirical Model of Oil Production”, in preparation.

3. Jean H. Laherrère, “The Hubbert Curve: Its Strengths And Weaknesses”, Oil & Gas Journal (April 17, 2000), p. 63.

4. “Analysis of Oil and Gas Production in the Arctic National Wildlife Refuge”, Service Report prepared by the Energy Information Administration (March 2004).

**Figure 1.*** U.S. production of oil in billions of barrels per year from 1859 to 2005. The solid line is a fit to the data projected to 2050. The dashed line after 2010 is an estimate of total U.S. oil production if oil is extracted from ANWR*.

**Figure 2.*** Production per cumulative production, *_{}, plotted against cumulative production, Q, for U.S. oil production other than North Slope Alaska oil production. The straight line is a fit to the data. The y-intercept estimates the initial growth rate r and the x-intercept estimates the total recoverable oil Q_{tot}.

*Figure 3.** Production per cumulative production, *_{}, plotted against cumulative production, Q, for North Slope Alaska oil production. The straight line is a fit to the data. The y-intercept estimates the initial growth rate r and the x-intercept estimates the total recoverable oil Q_{tot}.

*Richard J. Wiener*

Department of Physics

Pacific University

Forest Grove, OR 97116

wienerr@pacificu.edu