Journal of Power and Energy Engineering, 2014, 2, 81-85
Published Online September 2014 in SciRes. http://www.scirp.org/journal/jpee
How to cite this paper: Leonidovich, R.A., Alexandrovna, K.M. and Dydarovish, B.B. (2014) Optimization of Thermal Proc-
esses in Industrial Conditions. Journal of Power and Energy Engineering, 2, 81-85.
Optimization of Thermal Processes in
Rutkowki Alexandr Leonidovich, Kovaleva Maria Alexandrovna,
Bilaonov Batraz Dydarovish
North Caucasian Institute of Mining and Metallurgy (State Technological University), Vladikavkaz, Russia
Received July 2014
On basis of the developed models of dependences of thermal processes, industrial conditions are
received, having extreme character.
Mathematical Model, Op tim i za ti on, Dynamic Characteristic, Static Characteristic, Process of
Burni ng, System Control of Extreme
Presently, constitutive and operational data of the thermal technological units are described by the broad disper-
sion used in metallurgy and other industries impeding the comparative analysis of their operation. As a result, in
the process of calculating the units the characteristics of the burning of a torch are set on the approximate em-
pirical equations. This decreases the accuracy of the calculation and leads to the losses of thermal energy in in-
dustrial units causing an essential decrease in technical and economic indicators at the time of continuously in-
creasing fuel prices.
The share of the burned-out fuel on torch length s ignificantly depends on coefficie nt of surplus of blasting (a
consumption of air on fuel unit). This is the share of the burned-out fuel reaches a maximum in some point on the
torch length wh ic h designates a kernel of a t orch [ 1 ]. The deviation of coefficient of surplus of blasting from op-
timum value at a size of ±0.1 leads to reduction of a thermal stream from a torch on a surface of heating to 10%
that leads to significant increa se in fuel consumption.
To optimize the processes for a torch kernel in the course of fuel burning, the researchers formulated the
equation of thermal balance:
ffvvvf f ft
GqdtG сT dtGсTdtGc Tdt⋅ ⋅+⋅⋅⋅+⋅⋅⋅=⋅⋅⋅
where Gf: fuel consumption, kg/sec; qf: calorific ability of fuel, kJ/kg; Ga: air consumption, kg/sec; сv: thermal
capacity of air, kJ/(kg·˚C); Тa: air temperature, ˚C; cf: a thermal capacity of fuel, kJ/(kg·˚C); Tf: fuel temperature,
GG G= +
: consumption of products of burning, kg/s; c: a thermal capacity of products of burning,
kJ/(kg·˚C); Tt: torch temperature, ˚C; Р: mass of burn ing fuel, kg .
R. A. Leonidovich et al.
In the established mode,
Having made a number of substitutions, the temperature of products of burning of a torch will become:
As a solution to the problem, the researchers developed the mathematical model of the burning of a torch of
the gaseous fuel as a valid process in the broad spectrum of the change of parameters, which will lead to the jus-
tified thermal calculations of the industrial units .
The research investigated the fuel of the following structure: CH4 = 60%, C2H6 = 4%, C3H8 = 10%, C4H10 = 0.5
of %, C5H12 = 0.05 of %, % H2O = 10.45, N2 = 15%. For this fuel, calculated values of parameters as as follows:
thermal capacity of products of combustion с = 1.4707 (kJ/kg·˚C), calorific ability of fuel qf = 34927.81 (kJ/kg),
amount of air necessary for full oxidation of 1 (kg) of fuel equals 12.49 (kg). Therefore, the consumption of air in
a kernel of a torch will be Gvt = 12.49 (kg/sec) with the fuel consumption of 1 (kg/sec).
The program for calculating the temperature of a torch depending on a consumption of air has the following
vfvfv v v
ffvfv v v
The researchers conducted a calculating experiment using Mathсad software and identified the dependence of
the torch temperature on the air consumption with varying gas consumption (Figure 1).
The sensitometric curve has an extreme character and the temperature maximum is reached with the complete
full fuel combustion at optimal air consumption in a torch kernel. The optimum is displaced with the change in
fuel consumption, change in fuel composition, or change in burning conditions.
The ultimate research task involved the search of the air consumption optimum, w hich will provide complete
burning of the fuel corresponding to the extreme value of the temperature.
Figure 2 shows schedules of dependence of temperature of a torch from composition of natural gas with
change of air consumption. The researchers obtained these schedules using Equation (3).
Fuel composition and conditions of its combustion in industrial conditions change continuously. Necessary air
consumption that provides fuel savings when burning in an optimum mode must be adjusted to these changing
Figure 1. Charts of the dependence of the torch tempera-
ture from the gas consumption in a torch kernel.
R. A. Leonidovich et al.
Figure 2. Shift of temperature maxima depending on air
conditions. For this purpose, it is necessary to use the system of optimum control of burning process that has to
conduct continuous search of the maximum of temperature in a torch kernel changing air consumption .
Researchers received similar results for the p rocess of the kiln roasting of the zinc concentrates in the “fluidized
bed” and production of zinc in general. The process of roasting is characterized by the complex dynamics and
belongs to the inertial objects of control. Theref ore, the purpose of control of the process consists in the provision
of an optimal static mode of operation. To solve the stated problem, the researchers developed the mathematical
model of process of kiln roasting of zinc concentrates, basing their mathematical on the ratios of material and
thermal balance .
The equation of thermal balance for the zone of bo iling layer in the establis hed mode is defined by the ratio:
cc vvv cccb
where Gс: concentrate consumption (kg/sec); qс: calorific ability of the concentrate, (kJ/kg); Gv: air consumption
(kg/sec); cv: a thermal capacity of air (kJ/kg·˚C); Tv: air temperature, ˚C; cc: thermal capacity of the concentrate
(kJ/kg·˚C); Tc: temperature of the concentrate, ˚C;
: consumption of products of roasting, (kg/sec); с:
thermal capacity of products of roasting (kJ/kg ·˚C), Tb: temperature in the boiling layer, C.
Ratio (4) shows that the amount of heat arriving with the concentrate and air as a result of roasting is coun-
terbalanced by waste heat and temperature increase in th e boiling layer. From here temperature in a boiling layer
can be determined as follows:
cc vvv ccc
Let us make some assumptions that essentially will not affect the type of the s tatic characteristic of burning. We
will neglect the member Gc cc Tc, as this amount of heat with constant concentrate consumption is disparagingly
small in comparison with the member Gc qc. Besides, we believe that the thermal capacity of products of burning
is independent of the temperature, that is c = const in the entire interval of temperatures.
Let us review an ex ample. According to the practical experience of one of the factories, ther e is a furnace charge
of the following structure: Zn: 50% , Pb: 1.5%, S: 32%, Cu: 1%.
Full oxidation of 1.852 kg of the concentrate requires Gvc = 5.54 kg of air. Therefore, the amount of air needed
for full oxidation of 1 kg of a concentrate will make kg. Composed Gc qc will depend on the air consumption until
this consumption equals 5.54 kg/sec. The proportion that defines this dependence is
To calculate the temperature of the boiling layer, the Equation (5) is formulated through the Mathcad-program:
R. A. Leonidovich et al.
Concentrate consumption (kg/h)
Figure 3. Dependence of the temperature of the boiling layer on
the concentrate consumption.
( )( )
TG Gq GсT
Researchers conducted the calculating experiment using the Mathсad software and identified the dependence of
the boiling layer temperature on the concentrate consumption (Figure 3).
The sensitometric curve displays the extreme character of the dependence. The inf lu ence of the per tu rba tion
action on the dependence leads to th e shif t of the ex t remum and the rise of drift of the static characteristic.
Output parameter of the roasting pr oces s, temperature in the “fluidized bed” furnace, is defined by the amount
of the burned cinder and by the amount and temperature of the incoming air. The cinder does not burn completely
with the small amount of air, and this, therefore, reduces productivity of the process. With excess of air in the
“fluidized bed ” furnace, fuel of the furnace charge burns completely, but much of the heat released during its
combustion is used to heat the excess air and is carried away from the furnace with products of burning and excess
At a certain ratio of the amount of cinder and incoming air, the temperature mode of the “fluidized bed” furnace
will be optimal corresponding to an extremum of the output parameter of the process.
At the optimum consumption of the concentrate, its full oxidation is provided, and the temperature reaches its
maximum. Consequently, the purpose of managing the roasting process is redu c ed to maintaining optimum per-
formance of the “fluidized bed” furnace operation, where in a continuous mode its maximum productivity is
reached with the change of conditions of conducting the process and limited aprioristic infor mation about it.
The process of roasting of zinc con centrates belon gs to in ertial control objects and is characterized by difficult
dynamics. Change of the key regime parameters of the proces s may lead to a drift of the position of th e optimum of
studied dependence. Consequently, provision and long-term maintenance of the optimum static mode of the
studied process may be realized based on the use of the extreme control systems. Stabilization of the process is
reduced to the repeated solution of the interconnected problems of defining the extreme position of the working
point and the organization of movement toward it.
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R. A. Leonidovich et al.
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