Optimization of Ethylene Refrigeration System Using Genetic Algorithms Method

Ethylene refrigeration for gases separation at low temperature and high pressure for olefin production is an important technique in the chemical industry. Since small changes in the operating conditions of such a process can have a significant influence on its economics, optimization is desirable. The present work was aimed to propose and establish a mathematical model for the ethylene refrigeration system of the ethylene plant in Basrah petrochemical complex NO.1 (PC1) and reformulated as a geometric programming problem using Visual Basic for predicting:(overall efficiency of the ethylene refrigeration system {% }and percent of energy saving %E). Through the formulated model shaft work consumption by the centrifugal compressor, refrigeration effect and coefficient of performance of the system were obtained and other parameters concerning the system. The results of simulation showed a good agreement with the manufacturer manual.In this study the effect of four factors as independent variables on the overall refrigeration system efficiency and percent of energy saving were studied ;evaporator low pressure (PL) in the range of (1-3)bar ,compressor discharge high pressure (Ph) in the range of ( 28-32)bar ,condenser degree of subcool temperature (Tsub-D) in the range of (6-22)C and evaporator degree of superheat temperature (Tsup-D) in the range of (1-5)C. And the optimum conditions that aimed to minimize the thermodynamic irreversibility i.e (maximize overall refrigeration system efficiency) and also lower operating cost i.e (maximize percent of energy saving) evaporator low pressure (PL) (2.8 bar), compressor discharge high pressure (Ph) (28.7 bar), condenser degree of sub-cool temperature (Tsub-D) (19C), and evaporator degree of superheat temperature (Tsup-D) (3.4C). At these conditions the overall refrigeration system efficiency is (81.8%) and percent of energy saving is 51.18% with respect to conditions in the factory. Keyword: Refrigeration System, Genetic Algorithms, Ethylene Plant, Optimization Method.


Introduction
In the chemical process industry (CPI), most relatively simple organic chemicals are produced such as ethylene, propylene and benzene. These chemicals (some through intermediates, e.g. mono vinyl chloride or styrene) form the building blocks for many products such as plastics, resins, fibres, detergents, etc [1] .In olefins plants, considerable refrigeration is required to separate the low-boiling products. Many industrial processes (petroleum refineries, petrochemical industries) generate waste heat sources, which are potentially usable in thermal processes i.e (45 to 50) % of heat removed by ethylene refrigeration system. The relation between energy requirement at refrigeration usage at different temperatures have been found to be very useful in evaluating alternative process arrangements in the ethylene recovery unit [2].An ethylene recovery plant comprises of several parts: the hot-end utilities, the raw gas compression train, the gas separation system and the cold-end utilities. In the cold-end E3 utilities, a refrigeration system interacts with the process through the HEN and cold box.   [3] .
Generally pure compounds like ammonia, Freon, propylene, propane, ethylene, ethane,etc.,are used as refrigerant in closed refrigeration circuits, therefore, the refrigeration process can be divided into low temperature heat transfer fluids that are crucial components in many application current heat transfer fluid technology include direct refrigerant and the refrigeration technique [4,5] . All cooling processing may be classified as either sensible or latent according to the effect of the absorbed heat upon the refrigerant. The operating costs for refrigeration systems are often dominated by the cost of shaft work to drive the compressors.
In sub ambient processes, such as ethylene plants and natural gas liquefaction plants, design of refrigeration systems is the major concern for energy consumption [6].
Applying the study ensures many advantages, among them are: 1. Ethylene refrigeration system is an important part of ethylene production in petrochemical industry, because of the complex cycle and plants is that high operating cost and very expensive compressors are involved. E4 2. Low temperature / cryogenic processes are cost-effective for the recovery of valuable products such as ethylene, propylene, charge gas, natural gas from process gas streams. Each process requires energy extraction "cold" at various temperature levels for the process to work efficiently.

Aim of the Present Study
Now the ethylene plant will be revamped for a different feedstock to produce more ethylene and also propylene which involves changes of loads at low temperature condensers and coolers that are involved with ethylene refrigeration system. This work is the first local contribution in studying optimization technique " Genetic Algorithm Method " to energy saving and improvements of the performance for ethylene refrigeration system existing in the ethylene unit in Basrah petrochemical complex No.1 (PC1). It is a necessary to start with the utmost attention being paid to thermodynamic fundamentals, which can be easily extended to analysis of the industrial ethylene refrigeration cycle. The main goal of this work is to computationally simulate the actual processes and optimize the percentage energy saving and overall performance efficiency for ERS. In order to achieve this task, the following sequence has been followed: a) The development of a computer program that simulates the material and energy balances for the present ERS and predict of the compressor in the cycle.
b) The study of the effect of the main operating variables (evaporator low pressure, compressor discharge high pressure, evaporator degree of superheat temperature and condenser degree of sub-cool temperature) on the overall performance efficiency and the percent of energy saving.

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c) The optimization of the studied operating variables for maximum performance efficiency and energy saving.

1) Ethylene Refrigeration System Under Study
Ethylene plant in Basra Petrochemical Complex (PC1) utilizes an ethylene refrigeration cycle.
This cycle involves a centrifugal compressor having three stages, five condensers of shell and tube type, nine kettle type evaporators, eleven expansion valves and two (vapor liquid )separators. The cycle provides three levels of refrigeration [7], as shown in figure (3).
Because the main process involves high pressure refrigeration of low boiling point components, such as methane, ethane, etc., several very low temperature levels of refrigeration are required for process stream cooling [8] . A refrigeration process involving ethylene as refrigerant is designed for this study.
In vapor compression refrigeration cycles, heat is removed from the process by boiling a liquid refrigerant at low pressure, and thus, low temperature. The vapor is compressed to a higher pressure at which the heat of vaporization can be removed at a convenient higher temperature. The critical temperature of ethylene (about 9.5 o C) is below ambient temperature.
Thus, ethylene cannot be condensed by air or cooling water. Rather, ethylene is condensed as it boils a liquid propylene refrigerant [9]. The physical properties of ethylene showed in the table (1).

1) Operating Cycle
The operating cycle is demonstrated on a P-h diagram as fallows [10]:

STATE POINTS 1-2
A liquid-gas mixture of refrigerant enters the evaporator at state point 1. The process cooling load, Qe , is absorbed from the chilled ethylene system by the liquid refrigerant, vaporizing the liquid to state point 2.

STATE POINTS 2-3
The refrigerant vapor flows from the evaporator into the first stage of the centrifugal compressor. This distance represents the heating of the vapor into a super heated condition.
Note that little heat has been added and that the pressure and temperature are raised to that corresponding to state point 3.

STATE POINTS 3-4
The refrigerant gas compressed to state point 3 and mixed in the first to second stage crossover with some cooler refrigerant gas from the economizer (Eco2).

STATE POINTS 4-5
Refrigerant gas in the first to second stage crossover pipe is now drawn into the second stage of the compressor. Here the refrigerant gas pressure and temperature are raised to that corresponding to state point 5.

STATE POINTS 5-6
The refrigerant gas is compressed to state point 5 and mixed in the second to third stage crossover with some cooler refrigerant gas from the economizer (Eco1).

STATE POINTS 6-7
Refrigerant gas in the second to third stage crossover pipe is now drawn into the third stage of the compressor. Here the refrigerant gas pressure and temperature are raised to that corresponding to state point 7.

STATE POINTS 7-8
The refrigerant gas enters the condenser at state point 7. Here the process cooling load Qe , plus the power input to the compressor ,is rejected to the condenser ethylene. The rejection of the total condenser load, Qc, occurs at a constant pressure Pc. The rejection of heat cools and condenses the hot refrigerant gas to a liquid at state point 8.

STATE POINTS 8-9
Liquid refrigerant exiting the condenser at state point 8 flows through the first level of expansion valve and enters the economizer. And the vapor outlet from economizer enters to the compressor third stage at a pressure PII.

STATE POINTS 9-10
Liquid refrigerant exiting economizer 1 is reduced by expansion valve second level , and enters economizer 2 at a pressure (PIII), intermediate to the evaporator. And the vapor outlet from economizer enters to the compressor second stage at a pressure PIII.

STATE POINTS 10-1
The liquid exiting economizer 2 now flows to the third level where the refrigerants pressure and temperature are reduced to the evaporator conditions. It is important to note the pressure difference between the evaporator and condenser as shown on the pressure-enthalpy diagram.
The pressure difference, Pc-Pe, is the pressure differential or head pressure that must be produced by the centrifugal compressor for the cycle to operate. Figure (2) shows the sketch (P-h) diagram for the ideal ethylene refrigeration cycle.

a-Model Assumptions
In constructing the system model, the following major assumptions were made: 1. Pressure drops for the refrigerant side in the heat exchanger and piping are negligible 2. Expansions across the valves are isenthalpic (Smith;1987).
3. Polytropic efficiency in the three stages of the compressor is equal to( 0.8) (Ludwig;1986).

Compression is non-adiabatic and the vapour in the superheat region is incompressible
(Ludwig;1986).

B-Model Equations
To aid in the organization of the modelling of refrigeration process, a simplification of the ethylene refrigeration system was used. Figure

2)Optimization By Genetic Algorithms Method (GAs)
Refrigeration system optimization can be defined as a process that produces the desired refrigeration effect at minimum cost. As energy become more expensive, the need for optimizing existing system will continue to grow [11].
The interest in GAs and their applications grew over the past few years due to a number of reasons. Some of these are [12]: 1. GAs considers many points in the search space simultaneously and therefore have a reduced chance of converting to local minimum.
2. GAs work directly with the strings of characters representing the parameter set, not the parameters themselves. Thus GAs is more flexible than most search methods.
3. GAs use probabilistic rules to guide search, not deterministic rules.
The problem formulation of any optimization problem can be thought of as a sequence of steps. In the present study, coefficient of performance for ethylene refrigeration cycle and energy saving of the refrigeration system are to be optimized and the following steps are followed: Choosing operating variables (Ph, PL, Tsup-D, Tsub-D).
Formulating objective function (overall efficiency, percentage energy saving).
Setting up variable bounds (discrete value for each variable).
Obtaining the solution (arriving at maximum overall efficiency and percentage energy saving).

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The entire strength of GA lies in the three genetic operators: selection, crossover and mutation, which make it a robust optimization technique. Selection is the first of the three operations in which individual strings are copied according to their objective function or fitness and it is known as selection operator, as it selects good strings from a population and form a mating pool. The commonly used selection operator is the proportionate selection operator, where a string is selected for the mating pool with a probability proportional to its fitness.
Tournament method approach is followed in selecting the mating pool.
From the mating pool and are altered in a manner such that some portions of the strings are exchanged between them as shown in figure (4) .

Effect of Evaporator Low Pressure (P L )
The shaft work of the compressor decreased with increasing the evaporator low pressure as shown in figure (5), because the enthalpy of vapour inlet to compressor increased with increasing evaporator low pressure and it leads to decrease the enthalpy difference about the compressor. These results are in agreement with works of [14,15].
It is necessary to minimize shaft work in order to avoid excessive energy consumption and accurse the increase in percentage energy saving; this was applied by increasing evaporator low pressure as shown in figure (6).
The effect of evaporator low pressure on the vapour fraction (refrigerant quality) is shown in figure (7) (12) shows that percentage energy saving decreased as compressor discharge high pressure increased at optimum evaporator low pressure , evaporator degrees of super heat temperature and condenser degree of sub-cool temperature.

Figure (13) shows the refrigerant vapor fraction increases for three levels of refrigeration
cycle when compressor discharge pressure increase because increasing in flashing into expansion valve that leads to decrease latent heat [17,18] .
The decrease in refrigeration effect with increasing compressor discharge high pressure Is shown in figure (14). The variation in the coefficient of performance verses compressor discharge high pressure shown in figure (15).
The key to overall efficiency of ethylene refrigeration cycle improvements by decreasing compressor discharge high pressure as shown in figure (16). Compressor discharge high pressure E20

Effect of Condenser Degree of SubCool Temperature (T sub -D)
The increasing in the cooling water and propylene flow rate promotes subcooling in the condensers, this represents the temperature of the liquid (ethylene refrigerant) leaving the condenser is lower than saturated temperature. Any such increase in condenser degree of sub-cooling temperature is at the expense only of additional secondary refrigerants such as cooling water [17]. Figure (19) indicates that an increase in condenser degree of sub-cooling temperature has no effect on the shaft work of compressor then the percentage energy saving remained constant as condenser degree of sub-cooling temperature is increased, as shown in figure (20), because the compressor power requirements remain unchanged [17]. show an inversely relation between degree of superheat temperature and the shaft work of compressor, stating from (1 to 5) o C, this behaviour is shown in figure (24) and are in agreement with the results of (Domanski) [20]. Figure (25) shows that shaft work of centrifugal compressor is decreased when the degree of superheat temperature increase to       Large amount of energy is used every year in ethylene refrigeration system . So, finding the optimum operating conditions for saving this energy is important, since saving energy means saving cost. This refrigeration system is incorporated with another refrigeration system serving other parts of the plant; therefore, any reduction in the refrigeration load will affect not only the economics of the ethylene refrigeration closed loop cycle but also the entire ethylene plant.
By applying various stated variables the following is concluded from the obtained results: 1. It is undesirable to operate with high vapor fraction at input to evaporator, as it will lead to inefficient absorption of heat from the process gases. High vapor fraction leads to low refrigeration load. The low refrigeration effect (Qe) is an indicator of performance of refrigeration in efficiency.
2. The adoption of evaporator degree of superheat temperature (Tsup-D)in the design of the evaporators is more efficient because of the reduction of shaftwork of the centrifugal compressor. In addition can be considered as safety factor in the design to avoid the detrimental of the compressor. It was found that the optimum value is (3.4 o C) in the range of (1-5) o C.
3. The effect of condenser degree of sub-cooling temperature (Tsub-D) on the refrigeration capacity shows that the evaporators is more efficient when the condensers are cooled down. This is right especially for high condenser degree of sub-cool temperature for a specific range (6-22) o C, where the refrigerant stream temperature outlet from condenser decreases is larger, and condensing process a more significant effect on the evaporators in heat absorbed from process gases. 4. Evaporator low pressure (PL) and compressor discharge high pressure (Ph) effect on the ethylene refrigeration system show that the refrigeration process is more efficient when it works at lower (Ph) and higher (PL) for a specific range. 5. The overall efficiency of the ethylene refrigeration system increases when:

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Increasing evaporator low pressure, decreasing compressor discharge high pressure, increasing evaporator degree of superheat temperature to about 3.4 o C, then it had no significant effect with further increasing of evaporator degree of superheat temperature and increasing with condenser degree of sub-cool temperature up to 19 o C. 6. The percentage energy saving for ethylene refrigeration system increases when: Increasing evaporator low pressure, decreasing compressor discharge high pressure, increasing evaporator degree of superheat temperature to about 3.4 o C . But the increasing with condenser degree of sub-7. The optimum operating conditions for the ethylene refrigeration system are 2.8bar evaporator low pressure, 28.7bar compressor discharge high pressure,3.4 o C evaporator degree of superheat temperature and 19 o C condenser degree of sub-cool temperature, which gave a maximum overall efficiency of 81.8% and percentage energy saving of 51.18% .