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Economy and Energy
Year II - No 6
Jan/Feb/1998








Graphical Edition:
MAK
Editora?o Eletr?ic
MAK
Editora?o Eletr?ica

marcos@rio-point.com
Revisado:
Monday, 21 July 2003.

http://ecen.com

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Otto Cycle Demand
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WB00969_.GIF (261 bytes) Para Vers? em Portugu?

Projection of Fuel Demand for the Otto Cycle in Brazil

Omar Campos Ferreira
omar@ecen.com

English Version:
Frida Eidelman
frida@password.com.br

The intended projection has the obvious interest for planning of production or of supply of the concerned fuel. The projected function is proportional to the driving force used in the transportation of passengers and light loads. It is calculated as the product of the fuel volume, the density, the enthalpy (calorific power) and efficiency of the fuel in the Otto Cycle. Since the efficiency of gasoline engine has not varied significantly in the analyzed period (1980 - 1995), a normalization factor of 1.17 was introduced in the calculation relative to hydrated alcohol to take into account the better efficiency of the respective engine. This figure was extracted from "Escolha Certa", published annually by the former Industrial Technology Department and in which the autonomies of vehicles using C gasoline and hydrated alcohol was compared. As the Department was extinguished during the turbulent administrative reform of the Collor Administration, that important information has not been disseminated anymore. Data about demand were extracted from the Brazilian Energy Balance, 1997 and 1986 issues (data pertaining to the seventies). Data previous to 1980 show abrupt oscillations in fuel consumption, explainable by the price crisis and by the fast variation of engines’ efficiency, due to the rise of anhydrous alcohol content in gasoline, which is difficult to be quantified.

The graphic of demand (Figure 1) along the period suggests that the most appropriate function for the projection is the logistic function, which also describes the evolution of electric power demand in the residential sector, as has been verified. This function applies in general to transitory phenomena in isolated systems such as the two above mentioned cases. In fact, there was not available then in the country other fuels for the Otto Cycle and the electric power has not adequate substitute for residential light and power supply; the considered systems are therefore functionally isolated for these applications.

The projection elaboration follows the orthodox path: once the demand data are obtained, the average demand is calculated in intervals small enough for an adequate quantity of data and large enough for smoothing the function in a convenient way.

The average rates are fitted to the parabola

where the derivative is substituted by the average rates.prjott1.jpg (708 bytes) and prjott2.jpg (698 bytes)  represent respectively the demand at time t and the final demand. The fitting supplies the best estimates for the constant a and for prjott2.jpg (698 bytes), allowing for the projection using the equation

by way of which the observed consumption and the time values are fitted through linear regression.

or

ln f/(1-f) = at + b

for f = prjott1.jpg (708 bytes)/ prjott2.jpg (698 bytes)

 The data elaborated from the Brazilian Energy Balance, according to the exposed above are given in the following table:

YEAR

DEMAND
P cal

AVERAGE DEMAND IN TRIENNIUM  

AVERAGE RATE BETWWEN TRIENNIUMS

ln F/(1-F)

FITTED  DEMAND

1981

106,3

82

108,9

106,3

-1,769

106

83

103,6

5,0

84

105,8

85

119,5

121,3

-1,613

121

86

138,6

5,4

87

130,9

88

133,5

137,4

-1,462

138

89

147,7

5,7

90

149,5

91

158,7

154,6

-1,314

157

92

155,7

8,3

93

163,7

94

176,4

179,4

-1,121

177

95

198,1

96

220,7

-1,031

192

 

Fitting Results

 Fitting the average rates of demand variation between trienniums to the parabola gives for the Otto Cycle the maximum demand value of 730 P cal, about 4,1 times the average demand in the 93/95 triennium. Fitting ln F/(1 - F) as a function of the average demand in the triennium allows for the demand projection beyond the observed interval and therefore for determining the triennium where the demand curve is inflected. The inflection point indicates the midway of the maximum demand. According to Figure 1, the inflection will occur in the 2013 - 2015 triennium, when demand will be twice of that observed between 1993 and 1995.

Figure 1

wpe16.jpg (19852 bytes)

Obviously, the projection exercise supposes that the demand’s determinant conditions such as fuel prices policies, petroleum products offer, currency stability, etc. will remains the same as in the period studied. Expectations are those of fall of petroleum offer, recovery of hydrated alcohol demand, due to the need of lowering the foreign commerce trade balance deficit, and also by increase of  unemployment, which would be aggravated by production decrease of this fuel. It is still hoped the increase of engine efficiency in about 10 %.

To satisfy the projected demand in the 2013 - 2015 triennium only with C gasoline ( A gasoline with 22% of anhydrous alcohol) it would be necessary about 35.1 million m 3 of A gasoline and 9.9 million m 3 of anhydrous alcohol. If the present participation of hydrated alcohol is maintained ( 34% in driving energy) it would be necessary 24.4 million m 3 of A gasoline, 6.9 million m 3 of anhydrous alcohol and 19.6 million m 3 of hydrated alcohol. It should be noted that the average content of anhydrous alcohol in C gasoline in the 1993 - 1995 triennium was 20%.