Omar Campos Ferreira
Energy Planning Course UFMG
English version: Frida Eidelman

The assessment of the amount of the world oil reserves is a question of strategic interest since oil is responsible for one third of all energy used in the world and for almost all fuel used in transportation.

Several attempts of assessment, using different methodologies, were made and were frustrated perhaps due to insufficient data. It should be noted that as data accumulates the projections tend to converge. Recent examples of concurrent projections are given in works presented by the World Energy Council -WEC
( "Energy for Tomorrow’s World" , St. Martin’s Press/1993) and by Petroconsultants ("An Oil Depletion Model" - C.J.Campbell/1994). The former does not give details about the methodology used for the projection and informs that in 1990 he remnant reserve of "conventional oil" (excluding, therefore, schist oil and bituminous sand ) was 57% of the total reserve. The latter uses an analysis method of Fractal Geometry and concludes that around 1995 the remnant was 50% of the total reserve.

In the present work we present our analysis of this question using the methodology of logistic function projection that was presented in the last issue of e & e, whose results are concurrent with both referred works.

The data base was extracted from the work of C. J. Campbell and contains the necessary information for applying the logistic function methodology: the known world reserve, year by year, from 1930 on and the decennial average rate of new fields discovered ( Table 1). The use of decennial average is justifiable, considering the random character of discoveries, as a way of smoothing the curves used in the projections, since de differential equation of the logistic curve assumes the continuity of the involved variable; the disadvantage is the loss of resolution in the determination of the period in which the rate reaches its maximum value.

Table 1 - Evolution of the world oil reserve








Accumulated Discoveries Gb* (N)







Average Discovery Rate Gb/year (dN/dt)







ln F/(1=F)**







* Gb = giga-barrel = 1 1012 barrel
** F = N/

The data treatment starts by studying the evolution of the accumulated reserve. For this first prospect, the value of the final reserve is any value, since it does not affect the nature of equation ln

Staring from the value of WEC’s study, we take = 1.500 Gb.. The adjustment of the data to the law ln F/(1-F) = at + b by linear regression gives for the correlation coefficient R2 = 0,9953, which demonstrates that the logistic function model is suitable for the interpretation (Fig.1). The perfect fit would correspond to R2 = 1,000.


Figure 1: Accumulated world oil discoveries - Logistic curve fit


The second step would be to estimate by fitting the average discovery rate to the parabola. .

The fitted curve resulted in

The observed values are marked together with the fitted curve (Fig.2).

Figure 2 : Average Decennial of Yearly Oil Discoveries

The methodology used indicates that the accumulated world reserves are 1,630 1012 barrels, equivalent to 220 1012 t. The projected evolution for the accumulated reserves is shown in Figure 3.

Figure 3: projected evolution for the accumulated oil reserves

WEC’s study gives a value of 220 1012 t while that of Petroconsultants, 243 1012 t, which demonstrates the convergence of the independent projections. Taking the average value of the three projections for the total reserve, 222 10 12 t and considering that until 1996 103 12 t have been extracted and consumed, one concludes that the oil extraction will reach its maximum rate until the year 2 000.

What will come in the next century is a matter of speculation. Maybe it will not occur a new price shock as in the seventies because the world economy prepared itself for the new situation. Nevertheless, a gradual raise of prices is inevitable. In physical terms, the world energy income will decrease. The distribution of the burden will certainly penalize mainly the poorer countries.

The energy problem will be more serious in the transportation sector, since the industrial and domestic uses will be satisfied by the electricity produced by nuclear power plants, in spite of the world unwillingness to accept them.

For Brazil, it will be the opportunity for developing biomass energy due to the exceptional conditions of territorial extension, small population, tending to stabilize itself around 250 million inhabitants, and the edaphic-climatic characteristics of its territory. It would be also the case of moderating the adhesion to the global economy model or, at least, to carefully negotiate it.

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