A1 - Revision of some concepts used in this

Normally the "energy content" of primary sources is obtained by accounting for its capacity of dissipating heat into the environment. For fuels it is used the "superior calorific power". Primary sources are less suitable for direct use and they are submitted to a transformation operation that converts, for example petroleum into its products for different uses, coal into coke, firewood into charcoal, etc. These products are secondary sources. Several fuels, primary or secondary, are converted into electricity before their final use.

In the energy balances this is expressed by the equation:

Primary Energy = Final Energy + Transformation losses

Where Final Energy = Secondary Energy + Primary Energy of direct use.

In the useful energy balances it is considered, for each use j, the efficiency or yield of fuel i, so that

Useful Energy (i,j) = Final Energy (i) * Yield (i,j)

or

The uses considered in the Brazilian Energy Balance are motive force, direct heating, process heat, illumination, electrochemistry and others.

From the distribution D(i,j) of the final energy of each energy source by type of use we have:

The sum on the right is the conversion factor from useful energy to final energy for energy source j, with distribution D(i,j) and yield Y(i,j).

Equivalent Energy is defined as

Equivalent Energy (i,j) = EE(i,j) /Y(io,j),

where Y(io,j) is the yield in the considered sector of the reference fuel.

EE(i,j) = UE(i,j)/Y(io,j) = FE(i,j) * Y (i,j) / Y(io,j).

Once a reference energy source io chosen, we have by definition:

The coefficients between final and useful energy for each energy source were obtained by applying for this source and the different k sectors of the economy that constitute each aggregate:

CUa(i) = UEa(i)/FEa(i).

In a similar way, for equivalent energy we obtain the coefficients using:

CEa(i) = EEa(i)/FEa(i).

All energy values are expressed in this work in tons equivalent petroleum (1 toe = 10,800 Mcal). This unit is practically used in all energy balances and that is why we preferred to use it instead of creating a ton equivalent NG or equivalent cubic meter of NG.

A2- Electrical and Hydraulic Energy in BEN

The National Energy Balance (BEN) values hydraulic energy considering the thermal energy necessary to generate it. Electrical energy is valued in its final form by the same criterion. When the useful energy balance in its final form is elaborated one should consider energy as its caloric equivalent. Values presented in toe in BEN are multiplied by 0.272. In the main text of the present work we have maintained the primary energy value as it is represented in BEN for didactic reasons. Actually in most countries thermal generation is predominant and the ratio between primary and final energy would be similar to those shown in Figure 2. In what follows the Primary and Final energy using the concepts of BEN/MME Brazil and that of OECD are shown in Figure 1A.

In a certain way the equivalent energy concept is a generalization of the criterion adopted for electrical and hydraulic energies in BEN. In the methodology proposed here the efficiency differences or transformation need are taken into account for all energy sources while the uses of electricity where there are substitutes as electrical heating are not overvalued

Figure 1A: Data from Figure 2 using BEB'S and OECD's criteria

Final Energy

(*) Others: Transport Equipment, Machinery, Wood and Wood Products, Construction, Non-specified industry

Equivalent Energy