Albert A. Bartlett

An Analysis of U.S. and World Oil Production Patterns Using Hubbert-Style Curves

A quantitative analytical method, using a spreadsheet, has been developed that allows the determination of values of the three parameters that characterize the Hubbert-style Gaussian error curve that best fits the conventional oil production data both for the U.S. and the world. The three parameters are the total area under the Gaussian, which represents the estimated ultimate (oil) recovery (EUR), the date of the maximum of the curve, and the half-width of the curve. The “best fit” is determined by adjusting the values of the three parameters to minimize the root mean square deviation (RMSD) between the data and the Gaussian. The sensitivity of the fit to changes in values of the parameters is indicated by an exploration of the rate at which the RMSD increases as values of the three parameters are varied from the values that give the best fit. The results of the analysis are as follows: (1) the size of the U.S. EUR of oil is suggested to be 0.222 × 1012 barrels (0.222 trillion bbl) of which approximately three-fourths appears to have been produced through 1995; (2) if the world EUR is 2.0 × 1012 bbl (2.0 trillion bbl), a little less than half of this oil has been produced through 1995, and the maximum of world oil production is indicated to be in 2004; (3) each increase of one billion barrels in the size of the world EUR beyond the value of 2.0 × 1012 bbl can be expected to result in a delay of approximately 5.5 days in the date of maximum production; (4) alternate production scenarios are presented for world EURs of 3.0 and 4.0 × 1012 bbl.

Reflections on sustainability, population growth, and the environment

The related terms, “sustainable” and “sustainability,” have become popular and are used to describe a wide variety of activities which are generally ecologically laudable. At the same time, the term “compromise” is heard more frequently because the needs of the environment often are in conflict with the needs of humans. A brief examination of the question of compromise shows that a series of ten compromises, each of which saves 70% of the remaining environment, results in the saving of only 3% of the environment. Judging from the ways in which the terms “sustainable” and “sustainability” are used, their definitions are not very precise, especially when compromises are involved. An attempt is made here to give firm definition to these terms and to translate the definition into a series of laws and hypotheses which, it is hoped, will clarify the implications of their use. These are followed by a series of observations and predictions that relate to “sustainability.”

Forgotten fundamentals of the energy crisis

’’Facts do not cease to exist because they are ignored;’’ Aldous Huxley.’’Facts do not cease to exist because they are ignored;’’ Aldous Huxley.

The Arithmetic of Growth: Methods of Calculation

This is a tutorial on the relations between population data and the rates of growth that are calculated from the data. For the calculation of rates of growth, discrete and continuous compounding will be compared so that the reader can see the reasons for using the mathematics of continuous compounding, which is the mathematics of exponential growth. Some properties of exponential growth are developed. Semi-logarithmic graphs will be discussed as a device for representing the size of growing populations and for analyzing the nature of the growth. Illustrative examples will be worked out in order to emphasize applications and utility.

Zero growth of the population of the United States

It is sometimes said that there is no population problem in the United States because the U.S. fertility rate is approximately at the replacement level of 2.1 children per woman. However the population of the United States increased in 1992 by approximately three million people. There are two major causes of continued population growth even when fertility is approximately at the replacement level. One is population momentum; the other is immigration. This paper examines what must be done if we want to achieve zero growth of the population of the United States immediately, without the long delays caused by population momentum.

Sustained availability: A management program for nonrenewable resources

The continued extraction from the earth of nonrenewable mineral and fuel resources is a cause for concern, particularly where the rates of extraction are growing. If the rate of extraction declines a fixed fraction per unit time, the rate of extraction will approach zero, but the integrated total of the extracted resource between t=0 and t=∞ will remain finite. If we choose a rate of decline of the rate of extraction of the resource such that the integrated total of all future extraction equals the present size of the remaining resource then we have a program which will allow the resource to be available in declining amounts for use forever. This program is called Sustained Availability (SA) and it is somewhat analogous to the program of ‘‘sustained yield’’ in the management of renewable resources such as agriculture. The mathematics of this program, the opportunities it presents, and its consequences are examined in detail.

Note on a common virtual image

An observer above the plane surface of a liquid of index of refraction n, looking at a point object which is a distance Y below the surface, will see a virtual image of the object. For light rays which emerge in air at an angle of refraction θ2=0, the virtual image will be at a distance (Y/n) below the surface. The case where θ2≠0 is rarely discussed in texts. As a result, students may be left with the impression that the location of the virtual image is independent of θ2. The virtual image is astigmatic and the locations of the different components of the astigmatic image depend on the angle of refraction θ2. The location of the various components of the astigmatic image are derived; a laboratory experiment to measure the locations of the components is described. The results of the measurements are in good agreement with the theory.

Thoughts on Long-Term Energy Supplies: Scientists and the Silent Lie

The worlds population continues to grow. Shouldnt physicists care?The worlds population continues to grow. Shouldnt physicists care?

Arithmetic of growth: methods of calculation II.

This calculational tutorial continues the presentation of an earlier article (Bartlett,1993 ). It starts with a news item that features one elderly person who has 67 grandchildren and 201 great grandchildren. This tutorial develops simple mathematical models to show how to calculate approximate average rates of growth of descendants using very simple assumptions plus the data from the news story. The model is then enlarged to describe the growth of populations and to see how the growth of populations is related to the growth of descendants and to fertility. The analysis is then generalized so it can be applied to other reproductive phenomena, such as the production of Ph.D.s. The goal is to illustrate the essential features of the simplest elements of the population growth process by introducing modeling that is within the reach of those who can use algebra.

Critical point drying: Application of the physics of the PVT surface to electron microscopy

In electron microscopy of biological materials, the samples must be specially prepared before they can be placed in the high vacuum of an electron microscope. If the samples are prepared in water and if the last stages of the preparation involve evaporation of water from a liquid–vapor interface, surface tension at the interface can generate very high pressures in micrometer‐size structures that will distort the structures to the point where much information about their original shapes and configurations is lost. In order to avoid this damaging distortion, the samples are immersed in a fluid such as liquid CO2 in a pressure vessel and the fluid is heated to a temperature higher than its critical temperature where it becomes a gas and can then be removed without the damaging effects of surface tension. The physical details and the advantages and disadvantages of alternative ways of carrying out the process are reviewed. Optimum conditions for carrying out the process are identified, and it is noted that so...