1. Introduction - Firenze University Press

2. Numerical model
The purpose of this section is to provide an analysis of an optimal production point through
optimization problem with multi-objective functions and constraints. The multi-objective functions
are the clinker production cost, NOx and SO2 emissions. The constraints refer to operational
parameters and clinker quality.
2.1. Objective functions
Clinker production cost function:
The clinker production cost taking into consideration raw materials cost as well the energy
consumption requested for grinding. This last can be written with respect to the specific surface of
the cement, silica modulus and electricity cost (Eq. (1)).
E ce A
( )
exp BS
(1)
Where:
A 5,76(
SM ) -5,82
B -0,2( SM)
0,98
SM = Silica Modulus; ce = electricity cost; S = specific surface of cement
Silica modulus (SM) is the ratio of the silicates oxide with the sum of the ferric oxide and alumina
oxide in the clinker. The Silica Modulus has influence on the burning of raw materials, clinker
granulometry and liquid phase. The raw materials and fuel costs are written as linear combination,
Eq. (2):
n
C p (
x )
Where:
i1
i i
pi = raw materials and fuels medium cost.
xi = raw materials and fuel quantity.
The raw materials of clinker production are limestone (x1), clay (x2), sand (x3), and iron ore (x4).
The fuels used are mineral coal (x5), petroleum coke (x6), and the alternative fuel used is the scrap
tires (x7). The mineralizers applied in this work are CaF2 (x8) and CaSO4 (x9), these mineralizers
proceed from industrial wastes and it is considered as revenue for the cement industry, with a
symbolic income of US$ 1/ton. The final cost equation (clinker production cost) is presented in Eq.
(3):
f ( x) 1.25x 1.45x 0.87 x 10x 63.11x 40x 1x 1x 1x
1 1 2 3 4 5 6 7 8 9
ce SM e
Where
( 0.2( SM) 0.98)*
S
*{(5.76( ) 5.82)* }
264
(2)
(3)