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Yana Kravchenko
PhD, National Technical University "Kharkiv Polytechnic Institute"
Anatoliy Babichenko PhD, Associate Professor, National Technical University "Kharkiv Polytechnic Institute" Juliya Babichenko
PhD, Associate Professor, Ukrainian State University of Railway Transport
DOI: 10.24412/2520-6990-2023-9168-20-24 ALGORITHM FOR OPTIMIZING THE OPERATION OF THE EVAPORATOR OF ABSORPTION-REFRIGERATION INSTALLATIONS UNDER THE CONDITIONS OF THE MULTI-PARAMETER
EFFECT OF EXTERNAL DISTURBANCE
Abstract.
An analysis of the operating conditions of the evaporators of absorption-refrigeration units of the secondary condensation unit of ammonia production as control objects is carried out. There is a well-founded need to minimize the cooling temperature of the circulating gas, the reduction of which increases the energy efficiency of ammonia production by reducing consumption of natural gas.
Algorithmic support for optimizing the operation of the evaporator of absorption-refrigeration units in the conditions of multiparametric action of disturbing factors with the determination of the optimal flow ofphlegm to minimize the cooling temperature of the circulation gas in the evaporators has been developed.
Key words: ammonia production, evaporator, phlegm consumption, absorption-refrigeration plant, optimization algorithm, energy efficiency.
Introduction. Formulation of the problem. The
final removal of production ammonia is provided by the technological complex of secondary condensation, which is one of the main ones in the synthesis department of ammonia production. As a part of many complexes of this production, as well as in the complex of secondary condensation, air and water cooling devices are actively used, which sometimes has a very negative effect on the quality of work of individual departments, and therefore on the production of ammonia in general. The disadvantage of such devices is the significant impact on their work of seasonal and daily fluctuations in temperature and humidity of the surrounding air [1].
In particular, the use of air cooling devices in the refrigerant condensation unit of absorption refrigera-
tion units (ARU) included in the secondary condensation complex causes constant disturbances in their operation. This, in turn, leads to significant fluctuations in the cooling temperature of the circulating gas (CG) in the evaporators of the ARU (-8°C - +4°C) [2]. Such fluctuations lead to significant changes in the flow of natural gas into the additional steam boiler, and an increase in this temperature, as is known [3], due to an increase in the flow of natural gas causes a decrease in the energy efficiency of the synthesis unit in general.
Therefore, the minimization of the temperature regime of cooling of CG in the evaporators of ARU is an urgent task in the general process of increasing economic efficiency of ammonia synthesis units.
The peculiarity of the operation of the evaporator is connected with the inflow of refrigerant (ammonia)
with water impurities, which necessitates the removal (drainage) of the remaining water in the form of phlegm. However, in the literature [4] there is practically no information on determining the necessary intensity of phlegm drainage depending on constantly acting external disturbances. At the same time, insufficient as well as excessive drainage ultimately reduces the cooling capacity of the unit, which negatively affects the energy efficiency of production.
The purpose of research. The purpose of the research is to develop algorithmic support for establishing a quantitative assessment of the optimal value of phlegm consumption from the evaporator of the ARU of the secondary condensation complex in the production of ammonia under the conditions of multiparamet-ric action of external disturbing factors and making decisions for its implementation. This will determine the solution to the problem of minimizing the cooling temperature of the central heating system in the context of increasing the energy efficiency of ammonia production.
Main research results. Previous studies [5-7] have proved the significance of the influence of phlegm consumption for such powerful ARU on the efficiency of cooling CG, and therefore on the energy efficiency of production. At the same time, the use of controlling action on the consumption of phlegm in the range from 0.2 t/h to 0.8 t/h ensures a decrease in the annual consumption of natural gas by an average of 500 thousand cubic meters.
The analysis of the conducted studies [5, 6, 8], as well as the literature [9-13], shows that the most appropriate method for solving the optimization problem in the conditions of multi-parameter action of external disturbances will be a gradient-free step-type method using one-dimensional extremum search algorithms, namely the method scanning in the space of only one variable. Due to the application of a small search step, this method guarantees that the extremum will not be missed [14].
The results of the studies on the effect of external disturbances on the efficiency of cooling of CG in the evaporators of ARU allow to determine the parametric sensitivity of disturbing factors and the amount and direction of the shift of the optimal flow rate of phlegm, which determines the minimum temperature regime for cooling CG. Parametric sensitivity [15] is determined by a dimensionless coefficient that can be calculated using the formula
K =
_ (MR1 - MR2 )
Mn
( ^ - Z 2 )
(1)
where MB1 and MR2 - optimal consumption of
phlegm, respectively, under the disturbing factors Zn and Z,,.
The results of calculations according to Formula (1) are presented in the Table 1.
Table 1
Parametric sensitivity of the optimal amount
Limits of changes in the optimal flow of phlegm mr (t/h) under the relevant disturbing factors z Coefficient of parametric sensitivity K
Zi - pressure of the boiling refrigerant in the evaporator, MPa MR = (0,35-0,45) Pr = (0,29-0,3) 8,28
Z2 - refrigerant concentration at the evaporator inlet, kg/kg MR = (0,8-0,35) ^ = (0,994-0,998) -320,78
Z3 - consumption of liquid refrigerant to the condenser receiver, t/h MR = (0,3-0,4) Miv = (9,5-10,5) 3,16
Z4 - concentration of ammonia in CG at the evaporator inlet, % vol. MR = (0,3-0,4) a N = (9-11) aNH3 v ' 1,5
Analysis of the data of Table 1 shows that the concentration of the refrigerant at the evaporator inlet has the greatest influence on the value of the optimal flow of phlegm, and therefore on the extreme value of the CG cooling temperature ^, and the least - the concentration of ammonia aN in the CG at the evaporator
In Figure 1 an algorithm is showsn that provides an extremum search for the CG temperature at the evaporator outlet © using the scanning method for only
one variable M .
inlet.
Figure 1 Algorithm for finding the extremum for the temperature of the circulating gas at the outlet of the evaporator © by the method
of scanning one variable M
The designations shown in Figure 1, correspond to the following physical values: v - volume flow rate
of CG, nm3/s;
- volume concentration of constitu-
ent components of CG at the entrance, % vol.; F=520 m2 - total heat exchange surface; e=0.2% - is the specified value of the calculation error; A© = 0,1 °C - temperature change step; ^ - refrigerant concentration, kg/kg; M% - consumption of liquid refrigerant to the condenser receiver, kg/s; p p - pressure of CG
and boiling refrigerant, respectively, MPa; n = 526 -total number of heat exchange pipes; © , © , ©N
1CG 2CG X
- temperature, respectively, of CG at the evaporator inlet, CG at the evaporator outlet and refrigerant at the evaporator inlet, °C; mb - phlegm consumption, kg/s.
The obtained indicators for the coefficient allow determining the initial value for in the algorithm for finding the extremum for the cooling temperature of the central heating system. At the same time, according to research, the following conclusion can be drawn.
Under the condition of ^ > 0.998 kg/kg, which
is observed in the spring-summer season of operation of the ARU, the initial value for the flow of phlegm should be at the level of 0.2 t/h, and the search direction should be carried out in the direction of increase M
MR
with a step of A=0.02 t/h. In the case of < 0.998 kg/kg observed in the autumn-winter period, the initial value for phlegm consumption should be at the level of 0.8 t/h, and the search direction should be carried out in a decreasing direction M and with a
slightly increased search step A=0.05 t/h. The latter is explained by a much lower steepness of the dependence of the characteristics on the change mr .
This algorithm, unlike the previously developed one [16], additionally contains two transition conditions, namely the determination of the initial value of the phlegm flow and the search step and the determination of convergence and comparison of the objective function © with the previously calculated one. If the
previously calculated one © turns out to be less than
the next one, the cycle ends, otherwise, the transition to the next search step is carried out.
Conclusion. The developed algorithmic support for establishing a quantitative assessment of the optimal value of phlegm consumption from the evaporator of the ARU under the conditions of multiparametric action of external disturbing factors provides the solution of the optimization problem by a gradient-free steptype method using the methods of one-dimensional search for extremum. The parametric sensitivity of the optimal flow of phlegm to the change of disturbing factors acting on the evaporator is established. The application of the developed algorithm ensures the creation of a decision-making subsystem in the mode of supervisory optimal software control of low-temperature evaporators of absorption-refrigeration units of the technological complex of secondary condensation of ammonia production.
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