ALGORITHMIC TOOLS FOR OPTIMIZING THE TEMPERATURE REGIME OF EVAPORATOR AT ABSORPTION-REFRIGERATION UNITS OF AMMONIA PRODUCTION

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 INDUSTRY CONTROL SYSTEMS


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

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: ( ) where φ 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 1CG Θ (t) of CG (13÷23 °C) and the concentration of ammonia  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 M R [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 Х(t), namely to a decrease in the level Н(t) of a liquid cooling agent and an increase in the temperature of CG cooling 2CG Θ (t).The result is a drop in cooling capacity Φ 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 ξ and increases boiling pressure .
IP P Such conditions will lead to an increase in temperature 2CG Θ and a decrease in cooling capacity Φ O .Therefore, the consumption of reflux M R (t), along with the consumption of cooling agent IN Х М (t), are among the main coordinates of control vector Y(t), which define the optimal vector of state OPT X (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 2 ,

Θ
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 M R (t) on the optimal vector of state OPT X (t) for ARU with a large cooling capacity, as well as constructing an algorithm for the optimization subsystem, is of special importance.

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.

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: CG V is the volumetric flow rate of CG, nm 3 /s; IN i a is the volumetric concentration of the constituent components of CG at the inlet, % by volume, F=520 m 2 is the total surface of heat exchange; ε=0.2 % is the preset error of calculation; 0,1Φ ∆Θ = °C is the step of change in the temperature; A CG Θ is the mean CG temperature, °С;

∆Θ
is the average logarithmic temperature difference, °С; , P q IP q are, respectively, the specific heat flow from the side of the pipe and intra-pipe space, W/m 2 ; , М 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; A r is the mean heat of ammonia condensation, kJ/kg; , , is the enthalpy, respectively, of the liquid cooling agent at the inlet, of reflux, and the ammonia vapor at the outlet, kJ/kg; X F is the effective heat exchange surface, m 2 ; 526 n = is the total quantity of heat-exchanging pipes; Φ P , Φ 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 X F at evaporator, under conditions of action of external perturbations, from the following formula: .
The algorithm consists of two main cycles of convergence.The first cycle determines temperature 2CG Θ and estimates a calculation error 1 δ under condition 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 2CG Θ and the effective heat exchange surface for the case 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.

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: 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 1CG Θ 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 M R at different pressure IP P on efficiency of the process of CG cooling at evaporator under the following constraints:

M = 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.% by volume

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 Φ O and CG cooling temperature 2CG Θ are of extreme character due to the control action related to the consumption of reflux M R .This is predetermined, in turn, by the extreme dependence of the cooling agent vapor consumption , OUT Y M which increases at the expense of reducing the temperature of a liquid cooling agent boiling temperature .

IP
Θ 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 M R from 0.  [11], reaching the critical limit of the bubbling boiling mode of the cooling agent.At the same time, lowering the temperature 2CG Θ by 1.14 ºC through the control action related to the consumption of reflux enables the reduction of natural gas consumption by 350 thousand nm 3 /year.
A further increase in control action M R , for example, to 0.5 t/h, leads to the increased concentration of , R ξ reduced temperature IP Θ and increased temperature difference ,

MLD
∆Θ respectively, to 0.9562 kg/kg, −10.1 °C, and 11.32 °C.That reduces the effective heat exchange surface from 520 m 2 to 481.27 m 2 , 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 Y OUT M to 9.52 t/h, a heat transfer coefficient K to 482.5 W/(m 2 K) and the cooling capacity Φ O to 2.63 MW.In this case, the temperature of CG cooling 2CG Θ will rise to −4.25 °C, that is, by 0.25 °C, and the consumption of natural gas will grow by almost 77 thousand nm 3 /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 IP P from 0.29 MPa to 0.3 MPa requires an increase in the magnitude of the consumption M R 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 MLD ∆Θ 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 2CG Θ 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 nm 3 /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 2CG Θ as a result of increasing the concentration IN X ξ from 0.994 kg/kg to 0.998 kg/kg reduces from −3.8 °C to −4.5 °C at a constant pressure 0,29Φ IP P = 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 2CG Θ 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 nm 3 .
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 ,

IN X
M 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 2CG Θ are achieved, namely at the level of −3.9 °C and -4.98 °C.At the same time, the maximum cooling capacity Φ 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 nm 3 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 3 , IN NH а which predetermines a change in the thermal load of the evaporator.According to the derived dependences (Fig. 5), a decrease in the concentration 3 ,

IN NH
а 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 2CG Θ respectively, at the level of −4.22 °C and -4.98 °C; 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 nm 3 .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 nm 3 on average.
The established extreme character of the CG cooling temperature dependence 2CG Θ on control action related to the consumption of reflux and the displacement of an extremum 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 2CG Θ 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.

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 nm 3 .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 nm 3 .
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.

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

EXPERIMENTAL STUDY INTO OPTIMAL INTER-DEPENDENCE OF ENERGY-TIME COSTS FOR EMPTYING A DRY DOCK P . K h r i s t o
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

3
coefficients, respectively, of the heat transfer from CG, of the cooling agent, and the overall coefficient of heat transfer, W/(m 2 K); E T R is the total thermal resistance, (m 2 K)/W; , CG P IP P is the pressure, respectively, of CG and a boiling cooling agent, MPa; R ξ is the weight concentration of reflux, kg/kg; IP Θ is the boiling temperature of refrigerant in the intra-pipe space, °С;

Fig. 1 .
Generalized flowchart of the algorithm to study the evaporator

Fig. 2 .
Fig. 2. Dependence of efficiency indicators of the ARU evaporator operation on a change in pressure P IP (-----P IP =0.29 MPa; -----P IP =0.3 MPa) and the control action related to the consumption of reflux M R : a -concentration of reflux ξ R , boiling temperature of refrigerant in the intra-pipe space Θ IP , consumption of the cooling agent vapor at the outlet from evaporator , OUT Y M temperature of CG cooling Θ 2CG ; b -cooling capacity Φ O , coefficient of heat transfer K, effective heat exchange surface F X , average logarithmic temperature difference ΔΘ MLD

Fig. 3 .Fig. 4 .
Fig. 3. Dependence of CG cooling temperature Θ 2CG and the ARU cooling capacity Φ O on the control action related to the consumption of reflux M R at different values of the refrigerant concentration IN X ξ at the inlet to the evaporator: -----0,998� IN X ξ = kg/kg; -----0,994� IN X ξ = kg/kg

Fig. 5 .
Fig. 5. Dependence of the CG cooling temperature Θ 2CG and the ARU cooling capacity Φ O on the control action related to the consumption of reflux M R at different values of the concentration of ammonia in CG 3 IN NH a at the inlet to the evaporator: -----3 9Φ IN NH a = % by volume; -----3 11Φ IN NH a = % by volume