Economy and Energy
Year II - No 6
Jan/Feb/1998
Graphical Edition:
MAK
Editora?o Eletr?icMAK
Editora?o Eletr?ica
marcos@rio-point.com
Revisado:
Monday, 21 July 2003.
http://ecen.com
Main Page
Energy Project of ES
The Invisible Debt
Otto Cycle Demand
e&e team
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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. and represent respectively the demand at time t and the
final demand. The fitting supplies the best estimates for the constant a and for , 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 = /
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
Obviously, the projection exercise supposes that the demands
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%.
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