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Industry control systems
INDUSTRY CONTROL SYSTEMS
Проведено аналiз випарникгв абсорбцгйно-хо-лодильних установок блоку вторинног конден-сацгг виробництва амгаку як об'ектгв керування. Визначенг координати векторгв стану, керування та зовнгшнгх збурень. Обгрунтована необхгднгсть розв'язання задачг мгнгмгзацгг температури охо-лодження циркуляцшного газу у випарниках для пгдвищення енергоефективностг виробництва. За результатами анализу промислового апаратур-но-технологiчного оформлення блокгв первин-ног i вторинног конденсацгг з'ясованг особливостг умов роботи випарникгв, що зумовлюють пара-метричну невизначенгсть у функцгонуваннг об'ектгв керування. Основна з таких невизначеностей пов'язана з керуючою дieю витрати флегми.
Методом математичного моделювання за розробленим алгоритмом визначенг закономгр-ностг керуючог дгг витрати флегми на ефектив-нгсть процесгв теплообмгну у випарниках абсор-бцтно-холодильних установок. Встановлено екстремальний характер залежностг теплового потоку (холодопродуктивностг) та температури охолодження циркуляцшного газу вiд витрати флегми. Максимальна холодопродуктивнгсть, а отже i мгнгмальна температура охолодження циркуляцшного газу за певного температурного напору, обумовленг досягненням критичного режиму бульбашкового кипгння холодоагенту. Подальше збгльшення температурного напору з пгдвищенням витрати флегми сприяе встанов-ленню переходного режиму i зниженню ефектив-ностг поверхнг теплообмгну. Визначенг показники енергоефективностг виробництва амгаку, а саме витрати природного газу в умовах змгни керуючог дп витрати флегми та значень координат вектора збурень. Розроблене алгоритмгчне забезпечен-ня дозволяе здшснити розв'язання задачi мгнгмг-зацгг температури охолодження циркуляцшного газу безградгентним способом крокового типу з використанням методгв одномгрного пошуку екс-тремуму. Показано, що за рахунок мтшгзацИ температури охолодження циркуляцгйного газу ргчна витрата природного газу може бути зни-жена в середньому на 500 тис. нм3
Ключовг слова: виробництво амгаку, абсорб-цгйно-холодильна установка, випарник, витрата флегми, алгоритм оптимгзаци температури
UDC 681.51:621.574.3:661.53
I DOI: 10.15587/1729-4061.2018.1396331
ALGORITHMIC TOOLS FOR OPTIMIZING THE TEMPERATURE REGIME OF EVAPORATOR AT ABSORPTION-REFRIGERATION UNITS OF AMMONIA PRODUCTION
А. Babichenko
PhD, Associate Professor* E-mail: babichenko_a_k@ukr.net Y. Kravchenko Postgraduate student* J. Babichenko PhD, Associate Professor Department of Thermal Engineering and heat engines Ukrainian State University of Railway Transport Feierbakha sq., 7, Kharkiv, Ukraine, 61050 I. Kras n i kov PhD, Associate Professor* I. Ly sac h e n ko PhD, Associate Professor* V. Velma PhD, Associate Professor Department processes and devices of chemical-pharmaceutical industries National University of Pharmacy Pushkinska str., 53, Kharkiv, Ukraine, 61002 *Department of Automation engineering systems and
environmental monitoring National Technical University "Kharkiv Polytechnic Institute" Kyrpychova str., 2, Kharkiv, Ukraine, 61002
1. Introduction
One of the main tendencies in improving the efficiency of production is to reduce energy consumption by introducing energy-technological systems that utilize the low-potential heat. Such an approach has led to renewed interest in the application of thermal absorption refrigeration units (ARU) in various industrial sectors where a refrigerant must be maintained at a temperature below 0 °C [1]. This led to the
widespread use in the composition of large tonnage units of series AM-1360 of two ARU, which ensure cooling of a circulating gas (CG) in the low-temperature evaporators at a unit for secondary condensation of discharge of the ammonia synthesis [2].
The unit for secondary condensation, ARU in particular, is characterized by the wide use of apparatuses with air and water cooling. Given the large-tonnage production of ammonia and the existing hardware design of the unit for
g
secondary condensation, changing the indicators of the environment predetermines not only the parametric uncertainty in the functioning of the object, but also leads to significant economic losses. According to the available studies, a rise in the atmospheric air temperature from -6 °C to 30 °C, despite the growth in the ARU cooling capacity from 2.44 MW to 3.25 MW, causes an increase in the temperature of cooling of CG from -8 °C to 4 °C [3]. However, raising this temperature even by 1 °C leads to a decrease in the energy efficiency of the unit for synthesis in general at the expense of the increased annual consumption of natural gas to an additional steam boiler by 307.3 thousand nm3 in order to obtain water vapor of high pressure, which ensures the drive of a centrifugal three-body compressor for CG compression and a fresh nitrogen-hydrogen mixture at the synthesis unit [4]. Thus, minimizing the temperature mode of CG cooling at ARU evaporators through the creation of an automated system of optimal software control acquires special relevance for the overall process of improving the energy efficiency of large tonnage units for ammonia synthesis.
2. Literature review and problem statement
Solving the task on minimizing (optimizing) a temperature mode of CG cooling aimed to improve economic efficiency of production requires, as is known from [5], the development of a specialized algorithm for the subsystem of optimization of control object. Regarding a low-temperature evaporator at the unit for secondary condensation, a problem on the synthesis of an optimization algorithm in a general form can be represented in the following way:
^(X, Y, Z)^ min (extr XOPT (t), (1)
X = F (Y, Z), (2)
where 9 is the objective function; X, Z is the coordinate vector in accordance with the state of the object and perturbations of a certain dimensionality. Y is the vector of controlling influences; F is an operator of the mathematical model.
Vaporizers are the pipe-casing heat exchangers of the immersed type with U-shaped tubes. CG is cooled in a pipe space by ammonia, which boils in the intra-pipe space. According to the available experimental data [6], a special feature in the operation of low-temperature evaporators as the objects of control is associated with a constant influence of the seasonal and daily disturbances driven by two circumstances. The first is related to the use, at the stage of primary condensation of synthesis separation, of the air-cooled apparatuses. The second is due to the use, in an ARU cycle, of water and air cooling, respectively, in the absorber and in condenser. All this leads to a change in the coordinates of perturbation vector Z (t) of evaporators, namely, temperature 01CG (t) of CG (13-23 °C) and the concentration of ammonia aNH (t) in CG (9-12 % by volume), temperature ©N (t) of the cooling agent (18-38 °C) and concentration (t) of the cooling agent at the inlet (0.993-0.998 kg/kg), as well as pressure Ppp (t) of boiling (0.296-0.16 MPa) of the cooling agent.
Another feature in the operation of evaporators relates to the fact that a liquid refrigerant enters it with an addition of water. In order to prevent the accumulation of water, the
evaporator is designed with the property of draining it in the form of a reflux with a certain consumption of MR [7]. An analysis of the draining process reveals that on the one hand the excessive discharge of a reflux leads to the loss of a cooling agent, which can be evaporated. This can lead to a change in the state vector of evaporator X(t), namely to a decrease in the level H(t) of a liquid cooling agent and an increase in the temperature of CG cooling 02CG (t). The result is a drop in cooling capacity ®O. On the other hand, the insufficient drainage of the reflux contributes to the accumulation of water, reduces the concentration of boiling cooling agent £,R and increases boiling pressure PIP. Such conditions will lead to an increase in temperature 02CG and a decrease in cooling capacity ®o. Therefore, the consumption of reflux MR(t), along with the consumption of cooling agent MXN (t), are among the main coordinates of control vector Y(t), which define the optimal vector of state XOPT (t). However, the scientific periodicals mostly consider variants on the expediency of reflux draining techniques from the evaporator, or to the absorber of the receiver, or to the generator-rectifier [1]. At the same time, there is almost no information on determining the quantitative dependences of influence of the flow rate on efficiency of the process of heat exchange in evaporator, particularly under conditions of action of a large number of external perturbations. Such an absence is predetermined by the wide use in ARU of only a periodic draining of reflux for the set temperature of CG cooling [8]. The downside to it is the low operational reliability under conditions of a possible simultaneous change in the above-specified external disturbances. Under these circumstances, it is impossible to uniquely identify the preset CG temperature 02CG, and, therefore, the moment of the onset of the periodic reflux drainage. In this case, the process of periodic reflux draining disrupts the regime of ARU and, if using it improperly, can stop its operation [9]. In addition, commonly used are such ARU, particularly at households and processing sectors, which have a small cooling capacity, in which the effect of the process of reflux drainage on economic efficiency is not so significant [10]. For ARU with a large cooling capacity, over 3 MW, exploited in the production of ammonia, such an effect can be quite considerable. Therefore, the problem on determining the quantitative dependence of control action MR(t) on the optimal vector of state XOPT (t) for ARU with a large cooling capacity, as well as constructing an algorithm for the optimization subsystem, is of special importance.
3. The aim and objectives of the study
The purpose of this study is to build a subsystem for the optimal software control over low-temperature evaporators in absorption-refrigeration units at a secondary condensation unit in the production of ammonia. That would enable solving the task on minimizing the temperature of CG cooling and on improving the energy efficiency of production by reducing the consumption of natural gas.
To accomplish the aim, the following tasks have been set:
- to establish patterns in the control action related to the consumption of reflux on efficiency of the processes of heat exchange at ARU evaporator;
- to determine the impact of control action related to the consumption of reflux on energy efficiency of the production of ammonia under conditions of a change in the coordinates of a perturbation vector;
- to develop software tools in order to provide for the minimization of the objective function and numerical estimation of the optimal vector of the evaporator state.
4. Materials and methods to study influence of the consumption of reflux on efficiency of the processes of heat exchange at evaporator
In our research, we applied method of mathematical modeling. To this end, we employed a mathematical model of the ARU evaporator; its adequacy was tested and substantiated based on the results of previous studies [6].
We determined quantitative dependences regarding the establishment of patterns in the influence of reflux drainage intensity on efficiency of the processes of heat exchange at evaporator using a specially constructed algorithm. A principal flowchart of this algorithm is shown in Fig. 1; its software implementation was executed in the Matlab package.
Denotations that are given in Fig. 1 correspond to the following physical quantities: VCG is the volumetric flow rate of CG, nm3/s; a™ is the volumetric concentration of the constituent components of CG at the inlet, % by volume, F=520 m2 is the total surface of heat exchange; e=0.2 % is the preset error of calculation; A0 = 0,1 °C is the step of change in the temperature; 0AG is the mean CG temperature, °C; A0MLD is the average logarithmic temperature difference, °C; qP, qIP are, respectively, the specific heat flow from the side of the pipe and intra-pipe space, W/m2; Мcs, M^UT, M^ is the mean flow rate, respectively, of the condensed ammonia from CG, of the cooling agent vapor at the outlet from the evaporator, and of the liquid cooling agent to the receiver of the condenser, kg/s; rA is the mean heat of ammonia condensation, kJ/kg; aP, aIP, K are coefficients, respectively, of the heat transfer from CG, of the cooling agent, and the overall coefficient of heat transfer, W/(m2K); RTf is the total thermal resistance, (m2K)/W; PCG, PIP is the pressure, respectively, of CG and a boiling cooling agent, MPa; t,R is the weight concentration of reflux, kg/kg; 0IP is the boiling temperature of refrigerant in the intra-pipe space, °C; iX, iR, i°UT is the enthalpy, respectively, of the liquid cooling agent at the inlet, of reflux, and the ammonia vapor at the outlet, kJ/kg; FX is the effective heat exchange surface, m2; n = 526 is the total quantity of heat-exchanging pipes; ®P, &IP are, respectively, the heat flow from the side of the pipe and intra-pipe space, MW.
The developed algorithm, in contrast to those generally known, makes it possible to calculate the effective surface of heat exchange FX at evaporator, under conditions of action of external perturbations, from the following formula:
Fx =*/ q.
(3)
Fig. 1. Generalized flowchart of the algorithm to study the evaporator
The algorithm consists of two main cycles of convergence. The first cycle determines temperature 02CG and estimates a calculation error 8j under condition AM™ > 0, when the consumption of a cooling agent vapor and the reflux do not exceed the possible feed of a liquid cooling agent to the evaporator from ARU condenser. The second cycle relates to determining the temperature 02CG and the effective heat exchange surface for the case AM™ < 0, that is, under conditions of the existing constraint on the flow rate of a liquid cooling agent from ARU condenser. In this case, both cycles, provided the level is constant, ensure maintaining the overall balance of the evaporator in terms of consumption and energy.
5. Results of studying the influence of the consumption of reflux on efficiency of the process of heat exchange at evaporator
Mathematical modeling makes it possible to establish regularities in the influence of variable, both a vector of external perturbations Z(t) and a control vector Y(t), on the vector of state X(t) of the evaporator. Passing over to the space of the state variables, these vectors will take the following form:
X (t) =
®2CG (t)
H(t)
Z (t ) =
0
1CG (t)
l'N
NH3
(t )
Y (t) =
0N (t ) 4 N (t )
p,p (t )
Vcg (t)
Mf (t )
Mr (t ) _
(4)
It should be noted that constraints in the research are predetermined by the range of change in the coordinates in the process of constructing a mathematical model of the evaporator. In this case, based on the results of building a new energy-efficient hardware-technological implementation of the unit for secondary condensation, the magnitude of temperature 01CG is a constant at the level of 9.2 °C at the maximum thermal load for CG at the inlet [4].
Fig. 2 shows selected results of studying the control action related to the consumption of reflux MR at different pressure PIP on efficiency of the process of CG cooling at evaporator under the following constraints:
VCG = 310798 nm3/s; a® = 0,103 % by volume;
a® = 0,544 % by volume; a® = 0,195 % by volume;
a'CNHt = 0,082 % by volume; a™ = 0,076 % by volume;
01CG = 9,2 °C; PCG = 23 MPa; Mf = 10 t/h;
= 0,998 kg/kg; 0'N = 26 °C.
¡U. kg/kg
IP'
°C
M
t/h
"C
//
/
s —
0,98
0,94
0,9 -7 -11
9,4
MW K,
W/(m2K)
Fx-
2
m
A0"
°C
0,2 0.
,4 0,( a
0,2
0,4 b
0,6
3
2,7
2,4 488 482 476 510 450 12 11 10
Fig. 2. Dependence of efficiency indicators of the ARU evaporator operation on a change in pressure
PP (--P/P=0.29 MPa;----- P/P=0.3 MPa) and the
control action related to the consumption of reflux
a — concentration of reflux boiling temperature of refrigerant in the intra-pipe space ©/P, consumption of the cooling agent vapor at the outlet from evaporator MOUT, temperature of CG cooling ©2CG; b— cooling capacity ®o, coefficient of heat transfer K, effective heat exchange surface FX, average logarithmic temperature difference A®MLD
Fig. 3-5 show results of studying the impact of control action related to the consumption of reflux MR on the target indicators of operational efficiency of the evaporator, specifically the temperature of CG cooling 02CG and the ARU cooling capacity ARU ®O under condition of change in the coordinates of perturbation vector and at the above-specified constraints. These include first of all such constraints as the concentration of cooling agent , the cooling agent consumption M'X®, which arrives from the condenser, and the concentration of at the inlet from the evaporator.
ammonia in CG a'NNH
®2CG,
°c
MW
V
\
N
— ,___ _ -
■V.
y
y s
/
2,9 2,5 2,3 1,9
0,3
0,5
0,7
0,9
Fig. 3. Dependence of CG cooling temperature ©2CG and the ARU cooling capacity ®o on the control action related to the consumption of reflux MR at different values of the refrigerant concentration at the inlet to the evaporator: --ZX = 0,998 kg/kg;----- ZX = 0,994 kg/kg
®2CG,
°c
MW
^^ «
_ -
\
N
V N
,___
-5
3,0 2,6 2,2 1,8 1,4
0,2
0,4
0,6
0,8
1,0
Fig. 4. Dependence of the CG cooling temperature ©2CG and the ARU cooling capacity ®O on the control action related to the consumption of reflux MR at different values of the cooling agent consumption MX at the inlet to the evaporator: --M'N = 10,5 t/h;----- MX = 9,5 t/h
In this case, the values for these coordinates were chosen at the levels that are most typical for summer and winter operation seasons of the unit for secondary condensation, specifically ARU.
4
®2CG,
°c
®o, MW
\
\\ \ >
\ ___- -
- —
-1 -3 -5
3,0 2,2 1,4
0,2 0,4
0,6
0,8
1,0
Fig. 5. Dependence of the CG cooling temperature ©2CG and the ARU cooling capacity ®O on the control action related to the consumption of reflux MR at different values of the concentration of ammonia in CG a'JL at the inlet to
the evaporator: ■
= 9 % by volume;
= 11 % by volume
6. Discussion of results of studying the control action related to the consumption of reflux on efficiency of the ARU evaporator performance
The dependences shown in Fig. 2 that were constructed based on the results of research in terms of cooling capacity O and CG cooling temperature 02CG are of extreme character due to the control action related to the consumption of reflux MR. This is predetermined, in turn, by the extreme dependence of the cooling agent vapor consumption M°UT, which increases at the expense of reducing the temperature of a liquid cooling agent boiling temperature 0IP. The latter contributes to a decrease in the CG cooling temperature and an increase in cooling capacity.
Thus, for example, an increase in the consumption of MR from 0.2 t/h to 0.35 t/h at a constant boiling pressure PIP = 0,29 MPa leads to that the mean concentration of a boiling cooling agent £,R increases from 0.9071 kg/kg to 0.9408 kg/kg. That in turn leads to a decrease in the boiling temperature ofthe cooling agent 0IP from -8.24 °C to -9.71 °C. Given this, there is an increase in the average temperature difference AQMLD from 10.68 °C to 11.24 °C and in the consumption ofa cooling agent M°UT, which vaporizes, from 9.08 t/h to maximum 9.65 m/h. Under these circumstances, temperature 02CG decreases from -3.36 °C to minimum -4.5 °C, while cooling capacity ®o increases from 2.66 MW to maximum 2.84 MW. Heat transfer coefficient K increases and reaches a maximum value of 485.5 W/(m2K). That indicates, as known from [11], reaching the critical limit of the bubbling boiling mode of the cooling agent. At the same time, lowering the temperature 02CG by 1.14 °C through the control action related to the consumption of reflux enables the reduction of natural gas consumption by 350 thousand nm3/year.
A further increase in control action Mr, for example, to 0.5 t/h, leads to the increased concentration of £,R, reduced temperature 0IP and increased temperature difference AQmld , respectively, to 0.9562 kg/kg, -10.1 °C, and 11.32 °C. That reduces the effective heat exchange surface from 520 m2 to 481.27 m2, indicating the establishment of
the transitional boiling regime of the cooling agent. Such a regime is characterized by that the large steam cavities form at the surface. As a result, "dry" plots appear at the surface that seem to rule out part of the surface from heat exchange. Under such circumstances, the supply of heat directly to vapor occurs less intensively. This causes a decrease in the consumption of vapor M'°UT to 9.52 t/h, a heat transfer coefficient K to 482.5 W/(m2K) and the cooling capacity ®o to 2.63 MW. In this case, the temperature of CG cooling 02CG will rise to -4.25 °C, that is, by 0.25 °C, and the consumption of natural gas will grow by almost 77 thousand nm3/year.
An increase in pressure is most often caused by an increase in the temperature of water that cools the absorber. According to Fig. 2, an increase in pressure PIP from 0.29 MPa to 0.3 MPa requires an increase in the magnitude of the consumption MR from 0.35 t/h to 0.45 t/h for establishing the critical limit of the bubble boiling mode of the cooling agent. In this case, due to an increase in the temperature difference A0MLD from 10.83 °C to critical 11.01 °C, the cooling capacity will increase from 2.73 MW to maximum 2.79 MW, and the temperature of CG cooling 02CG will drop from -3.7 °C to minimum -3.98 °C. The result of such a control action related to the consumption, the yearly consumption of natural gas could be reduced by 88 thousand nm3/year.
The concentration of a liquid cooling agent at the inlet to the evaporator , given the seasonal fluctuations in the temperature of air that cools the ARU condenser, also varies quite widely. It follows from Fig. 3 that the extreme (minimum) temperature value 02CG as a result of increasing the concentration tXN from 0.994 kg/kg to 0.998 kg/kg reduces from -3.8 °C to -4.5 °C at a constant pressure Pp = 0,29 MPa. At the same time, there is a shift in the direction of reducing the magnitude of the control action related to the consumption of reflux from 0.8 t/h to 0.35 t/h, at which the minimum values for 02CG are provided. Under such a condition, the cooling capacity increases from 2.69 MW to 2.84 MW and the annual consumption of natural gas could be reduced by 215 thousand nm3.
At a constant heat supply to the generator-rectifier and the seasonal fluctuations of condensation pressure, there is a change in the consumption of a cooling agent vapor that arrives to the condenser, and a liquid cooling agent to the evaporator. The result of such changes in the consumption MX, for example, from 9.5 t/h to 10.5 t/h (Fig. 4) is also a shift in the required control action related to the consumption of reflux from 0.3 t/h to 0.4 t/h, at which the minimum temperature values 02CG are achieved, namely at the level of -3.9 °C and - 4.98 °C. At the same time, the maximum cooling capacity ®o is reached, respectively, 2.71 MW and 2.96 MW. Given such a control action related to the consumption of reflux, a reduction by 332 thousand nm3 in the yearly consumption of natural gas is achieved.
The result of the application of CG air cooling at the stage of primary condensation is the significant decrease in the concentration of ammonia in CG a'NH , which predetermines a change in the thermal load of the evaporator. According to the derived dependences (Fig. 5), a decrease in the concentration a^H , from 11 % by volume to 9 % by volume leads to a shift in an extremum towards decreasing the control action related to the consumption of reflux, that is, from 0.4 t/h to 0.3 t/h.
Under such a condition, we observe extremes of temperature 02CG respectively, at the level of -4.22 °C and -4.98 °C;
— a
NH
a
NH
the cooling capacity reaches maximum values of 2.8 MW and 2.85 MW. In this case, the annual consumption of natural gas could be reduced by 234 thousand nm3.
The research we conducted proved the essential impact of the consumption of reflux for such powerful ARU on the CG cooling efficiency, and, therefore, on the energy efficiency of production. In this case, the application of control action related to the consumption of reflux in the range from 0.2 t/h to 0.8 t/h ensures a reduction in the annual natural gas consumption by 500 thousand nm3 on average.
The established extreme character of the CG cooling temperature dependence &2CG on control action related to the consumption of reflux and the displacement of an extre-mum under conditions of changing the values for the coordinates of perturbation vector Z(t) confirms the need to build a system of optimal software control over temperature mode of CG cooling. The main element of such a system must be a subsystem of optimization for calculating the magnitude of the coordinate of control action related to the consumption of reflux, which determines the optimal state vector X(t) of the evaporator.
An analysis of the above process of computation testifies to the possibility of solving a multidimensional optimization problem using a gradient-free method of the step type applying the algorithms for a one-dimensional search for an extremum. Gradient-free methods, as known from [12], in terms of a character, are most suitable for the optimization of existing industrial systems.
Given the sensitivity of the object to a change in the consumption of reflux, the most appropriate is to use a scanning method in the space of only one variable. Such a method ensures, by applying a small search step, that an extremum would not be omitted [13]. Given this, with respect to the derived dependences, we accepted a search step for the consumption of reflux at the level of 0.02 t/h. At the same time, the algorithm's flowchart shown in Fig. 1 was complemented with the third cycle of search for a global extremum.
The resulting algorithmic tools for minimizing the temperature 02CG of CG cooling makes it possible to employ it in the optimization subsystem. This subsystem is the main component in the general technical structure for the automated system of optimal program control over the ARU evaporator. In the future, we plan to build an information-control subsystem, based on the real-time database and hardware-software tools for collecting and processing current information about the state of a technological object.
7. Conclusions
1. Based on the results of mathematical modelling, we established the dependence of efficiency indicators of the processes of heat exchange at evaporator on a change in
the control action related to the consumption of reflux and the coordinates of the external perturbation vector. Among these indicators, we should highlight such of them as thermal fluxes, cooling capacity, the temperature of CG cooling coefficients, temperature head, and heat transfer coefficients. We established a pattern of the extreme character of dependence of cooling capacity, temperature of CG cooling on the consumption of reflux, an increase in which leads to an increase int the temperature head of evaporator. Reaching the maximum cooling capacity, and thus the minimum cooling temperature of CG at a certain temperature head, is predetermined by the critical mode of bubble boiling of a cooling agent. A further increase in the temperature head with a growing consumption of reflux contributes to the establishment of the transitional regime of boiling. Such a mode is characterized by the appearance at the heated surface of "dry" plots, which leads to a decrease in the efficiency of the heat exchange surface and cooling capacity and to an increase in the temperature of CG cooling. We built dependences of the CG cooling temperature on the control action related to the consumption of reflux, which characterize the displacement of an extremum under conditions of changing the values for the coordinates of the perturbation vector.
2. We have defined the efficiency indicators of ammonia production, namely the consumption of natural gas under conditions of change in the control action related to the consumption of reflux and coordinates of the perturbation vector. It is established that the underestimation of the control action related to the consumption of reflux for such a large-ton production significantly affects the temperature of CG, and therefore the energy efficiency of production. It is shown that given the existing constraints and stabilization of reflux consumption, for example, at the level of 0.35 t/h, decreasing the concentration of a refrigerant at the inlet to the evaporator from 0.998 kg/kg to 0.994 kg/kg, would provide for an increase in the temperature of CG from the evaporator by 2.5 °C, and therefore an increase in the annual consumption of natural gas by 768 thousand nm3. At the same time, increasing the control action related to the consumption of reflux to 0.8 t/h could decrease the temperature of CG from the evaporator only by 0.7 °C, which provides for a reduction in the annual consumption of natural gas by 553 thousand nm3.
3. We have developed the algorithmic tools for minimizing the temperature of CG cooling and for numerical estimation of the optimal state vector. The use of a given algorithm contributes to solving the optimization problem by a gradient-free technique of the step type applying the methods of one-dimensional search for an extremum. Employing a given algorithm ensures the construction of subsystem for an optimal software control over low-temperature evaporators at absorption-refrigeration plants in a unit for secondary condensation in ammonia production.
References
1. White S. D., O'Neill B. K. Analysis of an improved aqua-ammonia absorption refrigeration cycle employing evaporator blowdown to provide rectifier reflux // Applied Energy. 1995. Vol. 50, Issue 4. P. 323-337. doi: https://doi.org/10.1016/0306-2619(95)98802-9
2. Galimova L. V., Kayl' V. Ya., Vedeneeva A. I. Ocenka stepeni termodinamicheskogo sovershenstva na osnove analiza raboty dey-stvuyushchey absorbcionnoy holodil'noy ustanovki sistemy sinteza ammiaka // Vestnik mezhdunarodnoy akademii holoda. 2015. Issue 4. P. 55-60.
3. Babichenko A. K., Toshinskiy V., Babichenko Yu. A. Issledovanie energeticheskoy effektivnosti absorbcionno-holodil'nyh ustanovok krupnotonnazhnyh agregatov sinteza ammiaka // Vestnik «KhPI». 2007. Issue 32. P. 67-74.
4. System analysis of the secondary condensation unit in the context of improving energy efficiency of ammonia production / Bab-ichenko A., Velma V., Babichenko J., Kravchenko Y., Krasnikov I. // Eastern-European Journal of Enterprise Technologies. 2017. Vol. 2, Issue 6 (86). P. 18-26. doi: https://doi.org/10.15587/1729-4061.2017.96464
5. Lutska N. M., Ladaniuk A. P. Optymalni ta robastni systemy keruvannia tekhnolohichnymy obiektamy. Kyiv: Lira-K, 2016. 288 p.
6. Identification of heat exchange process in the evaporators of absorption refrigerating units under conditions of uncertainty / Babichenko A., Babichenko J., Kravchenko Y., Velma S., Krasnikov I., Lysachenko I. // Eastern-European Journal of Enterprise Technologies. 2018. Vol. 1, Issue 2 (91). P. 21-29. doi: https://doi.org/10.15587/1729-4061.2018.121711
7. Garimella S., Mostafa S., Sheldon M. Ammonia-water desorption in flooded columns. Georgia Institute of Technology, Sheldon, 2012. 148 p.
8. Sposob upravleniya rezhimom raboty absorbcionnoy holodil'noy ustanovki: A. S. No. 802745 SSSR. MKI F25 B49/00, F25 B15/02 / Babichenko A. K., Eroshchenkov S. A., Efimov V. G., Bukarov A. R., Mazur A. A., Meriuc V. I. No. 2721832/23-06; declareted: 07.02.1979; published: 07.02.1981, Bul. No. 5.
9. Bogart M. J. P. Ammonia absorption refrigeration // Plant/Operations Progress. 1982. Vol. 1, Issue 3. P. 147-151. doi: https:// doi.org/10.1002/prsb.720010306
10. C.O.P Derivation and thermodynamic calculation of ammonia-water vapor absorption refrigeration system / Shukla A., Mishra A., Shukla D., Chauhan K. // International journal of mechanical engineering and technology. 2015. Vol. 6, Issue 5. P. 72-81.
11. Yunus A. Q. Introduction to thermodynamics and heat transfer. New York: McGraw-Hill, 2009. 960 p.
12. Hare W., Nutini J., Tesfamariam S. A survey of non-gradient optimization methods in structural engineering // Advances in Engineering Software. 2013. Vol. 59. P. 19-28. doi: https://doi.org/10.1016/j.advengsoft.2013.03.001
13. Ravindran A., Ragsdell K. M., Reklaitis G. V. Engineering optimization: methods and applications. New York: John Wiley & Sons, 2007. 667 p. doi: https://doi.org/10.1002/9780470117811
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Оцтений вплив дискретних властивостей мжропроцесорнаИ сис-теми управлтня на основi Arduino Due на точтсть фiзичноi моделi доковог насосное станцп шляхом моделювання в MATLAB. При цьому враховувалися так чинники, як перюд комутацп Ш1П, крок кванту-вання по рiвню i за часом АЦП i ЦАП мгкропроцесора, час виконання програмного циклу, шум молодших рoзрядiв АЦП, шум i терщйтсть датчика струму, а також вгдхилення naрaметрiв емтсних фть-трiв, включених в канали зворотного зв'язку по нaпрузi, вiд номталь-них значень, навантаження перетворювача i перепад напруги на кле-мах aкумулятoрнoi бaтaреi.
За результатами розрахунтв стало ясно, що цим впливом можна знехтувати i дат, зiбрaнi за допомогою фiзичнoi мoделi дoкoвoi насосное станцп, е достовхрними. Шляхом фЬичного моделювання отримана експериментальна залежтсть мiж витратами енергп-ча-су на спорожнення камери сухого дока, яка тдтверджуе можливкть знaчнoi економп енергп, коли процес oптимiзуеться за вгдповгдним критер{ем. Це стало можливо завдяки багатократному чисельно-му рхшенню крайовт зaдaчi безпосередньо на фЬзичшй мoделi. Знята характеристика свiдчить про те, що при малих значеннях тривало-стг процесу спорожнення камери екoнoмiя енергп, яка досягаеться за рахунок оптимального управлтня електроприводом насоса, вiднoс-но невелика в пoрiвняннi з вaрiaнтoм нерегульованого електроприво-ду. Проте при затягуванш процесу вона може досягати значень на рiвнi 13 %. Також звертае на себе увагу той факт, що починаючи з деякого значення часу спорожнення камери сухого дока, енерггя вже практично не мтяеться, що робить рацональним введення нерoбoчoi паузи в закон оптимального управлтня об'ектом.
Таким чином, тдтверджена можливкть i дощльшсть оптимЪа-цп процесу спорожнення камер сухих (наповнення - наливних) доюв за критерiем енергоспоживання дoслiдним шляхом
Ключoвi слова: Arduino Due, U4814, наливний, сухий док, насос,
електропривод, оптимальне управлтня -□ □-
UDC 621.313.04
I DOI: 10.15587/1729-4061.2018.1396741
EXPERIMENTAL STUDY INTO OPTIMAL INTERDEPENDENCE OF ENERGY-TIME COSTS FOR EMPTYING A DRY DOCK
P. Khristo
Specialist, Senior Lecturer Department of Electromechanic systems with a computer control Odessa National Polytechnic University Shevchenka ave., 1, Odessa, Ukraine, 65044 Е-mail: Pavel.John.Khristo@gmail.com
1. Introduction
At shipbuilding and ship dock enterprises, which have dry or liquid dock-chambers, ensuring the optimal perfor-
mance of main pumps of the dock pumping station is quite an urgent issue today. A key feature of working modes of pumping stations serving dry docks is a continuous and significant change in the level of fluid in the process of
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