A3.5.1 Simple Gas Rrfiquefacliou Cycle
Figure A3.4 shows a simple reliquefaction cycle. The cycle comprises:
• The cargo tanks (1). In the direct reliquefaction systems these act as evaporators in which the liquid cargo is vaporised. Evaporation removes a certain quantity of heat Ql from the tank, the liqxiid in the tank, and its surroundings.
• A mechanical compressor (2). The vapour formed in the cargo tanks is at a pressure PI; the compressor draws and compresses it, and delivers it to the condenser at a pressure P2. In the process of compression an amount of heat energy Q2 is added to the gas; the compressor uses an equal amount of work energy Wl.
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K S I"A\ Kl- k
Figure A3.3 Propane - Ethane equilibrium diagram Pressure = 1.1 bar (A); Mole % propane = 100-Mole % ethane
Figure A3.4 Simple gas reliquefaction cycle
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ENTHALPY kj/kg Figure A3.5 Simple reliquification cycle shown on Mollier Chart
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• A condenser (3). The vapour supplied by the compressor is liquefied in the condenser, giving up a certain amount of heat Q3 to the cooling water.
• An expansion valve (4). This reduces the pressure of the condensate from P2 to PI while passing from the condenser to the cargo tank.
According to the First Law of Thermodynamics
Ql + Q2 = Q3 A3.5.2 The Mollier Diagram applied to the Simple Cycle
Figure A3.5 shows the Mollier Diagram for ammonia which is the cargo to be reliquefied. For example, suppose the cargo is refrigerated with a consequent temperature of -33 °C and assume the compressor draws the vapour at -33 "C (disregarding pressure losses in the suction piping and presuming that the gas is neither heated nor cooled). The starting point (1) of the cycle (saturated vapour) is therefore characterised by:
Temperature (Tl) -33 °C Pressure (PI) 1.031 bar Enthalpy (HI) 1636 kj/kg Vapour Density 0.905 kg/m3
Suppose that the gas is compressed adiabatically and condensed at 30 °C: i.e. following a line of constant entropy this gives a condensation pressure of about 11.7 bars.
At the end of compression the gas has the following characteristics at point (2): Temperature (T2) 140 °C
Pressure (PI) 11.7 bars Enthalpy (H2) 1999 kj/kg
The condensate in the condenser has the following characteristics at point (3) Temperature (T3) 30 "C
Pressure (P3) 11.7 bars Enthalpy (H3) 560 kj/kg
The difference in enthalpies between that of the condensate (H3) and that of the gas delivered by the compressor (H2) equals Q3 (the heat removed by the cooling water in the condenser):
i.e.H3 - H2 = Q3 560 - 1999 = -1439kJ/kg
(Note that Q3 is a negative figure as it represents heat given up to the surroundings).
The condensate liquid is then expanded through the expansion valve without giving up or receiving heat: i.e. the transformation is carried out at constant enthalpy and therefore follows a vertical straight line. After expansion the liquid has the following characteristics at point (4):
Temperature (T4) -33 "C Pressure (P4) 1.031 bar Enthalpy (H4) 560 kj/kg Dryness fraction (X) 22%
It can be seen, therefore, that to bring the temperature of the liquid down from 30C to -33 6C, a fraction of the liquid, 22% by volume, has evaporated to absorb the heat necessary to achipvp this cooling effect.
Finally, on entering the cargo tank the remaining condensate is evaporated by heat absorbed from the tank, the liquid in it and its surroundings, so the cycle is completed and initial point (1) is reached.
1CS TANKFK S-\ H- I Y (■ U I [)!• I I. IQU I-1-[ )■ H CAS) 183
The cold produced, or the refrigerating effect Ql, is therefore the difference in enthalpy between starting point (1) (saturated vapour) and that of the liquid entering the tank at point (4):
i.e. Refrigerating effect Ql = HI - H4 = 1636 - 560 = 1076 kj/kg
Since the vapour has a density of 0.905 kg/m3 the quantity of heat per unit volume of the gas drawn by the compressor will be:
1076 X 0.905 = 974 kl/m3 The energy absorbed in the compressor is equivalent to: Q2 = H2 - HI = 1999 - 1636 = 363 kj/kg
To summarise this cycle:
• At point (1) the saturated ammonia vapour in the cargo tanks at a pressure of 1.031 bar (PI) with a corresponding temperature of -33 "C (Tl) is drawn by the compressor. During compression the pressure is increased to 11.7 Bars (P2) at a temperature of +140 °C (T2). The energy absorbed in the compressor is equivalent to 363 kj/kg (Q2) and at point (2) the ammonia vapour is in the superheated region.
• In the condenser condensation takes place at a constant pressure of 11.7 Bars, and during the condensation process the vapour is first desuperheated, and the latent heat is then extracted which brings it to point (3). The heat extracted by the sea cooling water in the condenser is 1439 kj/kg (Q3). The condensate in the condenser is at +30 °C.
• Expansion from point (3) to point (4) takes place across the expansion valve between the condenser and the cargo tank. During this process the pressure drops from 11.7 Bars (P3) to 1.031 Bar (P4). It is assumed that the liquid does not give up or receive heat during this process and the enthalpy remains constant. The temperature also drops from 30 °C (T3) to -33 °C (T4) which is the cargo temperature. To produce this cooling effect 22% by volume of the condensate is vapourised.
• To complete the cycle the balance of the condensate returned to the tank is vaporised from point (4) to point (1), producing 1076 kj/kg of cooling which removes heat from the cargo tank, its contents and its surroundings. Finally according to the First Law of Thermodynamics
Ql + Q2 = Q3 1076 + 363 - 1439 kj/kg
refrigeration effect in the cargo tanks (in this case 1076 kj/kg), the difference being the heat absorbed in the compressor (in this case 363 kj/kg).
A3.5.3 Difference Between Real Cycles and the Simple Cycle
In practice, real reliquefaction cycles differ from the simple cycle described above because of heat losses that arise in the processes involved. The calculation of these losses is described below; the results are sufficiently accurate for practical purposes.
(a) Loss by Heating in the Compressor Suction Piping
These losses arise from the heating of the vapour in the suction line between cargo tank and compressor. Heat is absorbed if the line is uninsulated; if the line is insulated the heat absorption is greatly reduced, but is never totally eliminated. Some plants are arranged with a heat exchanger in the suction line; the compressor discharge gas is slightly desuperheated and this heats up the suction vapour.
184 1CS TANJKHK KATE I Y GUIDi: (l.lQU hl;l !■']> CiAS)
The extent of these losses can easily be evaluated from the Mollier diagram (Fig. A3.5).
Assume, for example, that the ammonia is at 3.98 bars in the tank, the temperature of the vapour on leaving the tank is -2°C and its specific volume is 0.315 rnVkg
(i.e. a specific weight of . = 3.17 kg/m3).
If this vapour enters a compressor at a temperature of 20'C, its specific volume at the same pressure will be about 0.350m3/kg (i.e. specific weight of 7p^ = 2.90 kg/m3).
Therefore there is a loss of weight per m3 drawn in by the compressor of: 3.17-2.90 = 0.27 kg/m3
0 27 or expressed as a percentage, ^-r^ x 100 - 8.5% that is, as a percentage per °C of heating -j = 0.4%
Whatever the cargo, it is found that the loss in weight per cubic metre is always in the order of 0.4% per °C of heating.
Therefore, if a curve of refrigerating power is established for a compressor, assuming that the vapour enters the compressor at the pressure of evaporation in the tank, the actual refrigerating power will be reduced by about 0.4% per degree of difference between the temperature of the tank and that at suction intake.
(b) Loss by Pipe Friction
Loss of pressure in the suction piping also causes a reduction in the weight of the gas per m3; this loss can also be established from Figure A3.5 and is approximately equal to:
Loss of pressure Suction pressure
If the tank is at 4 bars and the loss of pressure is 0.4 bar (that is, 3.6 bars at suction intake), the 0 4
loss expressed as a percentage will be—j— x 100 = 10% (c) Volumetric Efficiency of Reciprocating Compressors
Cargo compressors may be single or multi-stage, depending upon the refrigerant and its condensing pressure, and they may also be of variable capacity.
The efficiency of the compressor has to be maintained at maximum to achieve the design efficiency. Several factors reduce the compressor's efficiency:
• If the refrigerant condensing pressure is higher than necessary for a given condition, then the amount of gas pumped per stroke will decrease.
# If the suction pressure decreases because of low pressure, shortage of refrigerant or excessively low temperature, the amount of gas pumped per stroke will decrease.
• Any increase in the clearance pocket will reduce the amount of gas pumped. The clearance pocket is usually defined as the volume of gas left in the compressor cylinder at the top of the piston stroke.
• An escape of gas past the piston, and leaking compressor suction or discharge valves, will decrease the volume of gas pumped.
♦ Leakage of discharge gas across by-pass lines to the suction side of the compressor will reduce efficiency. # Overheating of the compressor due to friction will reduce the efficiency of the system by imparting superfluous superheat to the discharge gas.
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Compressors have a theoretical output per hour, which is the volume swept by the pistons. Taking into account piston head clearance and the resistance to vapour flow in the suction and discharge valves, the actual output is calculated from the theoretical volume by multiplying it by a volumetric efficiency coefficient of less than 1. This coefficient is given by:
actual volume of gas pumped theoretical output
The coefficient varies mainly according to compression ratio, which is the ratio between absolute suction and discharge pressures; it also varies according to suction and discharge pressures, but these are usually disregarded. (d) Condensers, Heat Exchangers, Evaporators
These items of plant are all designed to effect a heat exchange from one substance to another across a barrier. They may be described as evaporators when used to convert liquid to vapour; as condensers when used to convert vapour to liquid; and as heat exchangers when the main purpose is to effect a heat exchange without evaporation or condensation necessarily occurring. In cargo systems the same heat exchangers may act as condensers for one operation, and as evaporators in another. Shell and tube condensers are used extensively and are either water cooled, or refrigerant cooled as in cascade systems.
Condenser efficiency is directly proportional to the total surface area of the tubes, their conductivity, and the rate of flow and temperature differential between the substances passing through.
Refrigerant efficiency will be lost in the condenser when: • the temperature of the cooling medium is comparatively high; • the rate of flow of the cooling medium is low;
• the conductivity of the tubes is insulated by scale or deposit formation;
• when there is a decrease in the tube surface area due to leaking tubes which have been plugged; • when a 'back-up' of condensate covers the cooling tubes or shell and restricts the heat exchange area.
A3.&^^^lEUftUEFACTION
CVCLES
A3.6.1 General
The four common rcliqucfaction cycles used aboard gas carriers are described below. Each works on the principle of removing the excess heat from the boil-off vapour, condensing it and returning the liquid to the cargo tank. The heat removed is the latent heat of vaporisation of the cargo plus any extra heat (or superheat) the boil-off has absorbed. This heat leaks into the cargo through the insulation from the air, sea and sun; the reliquefaction plant removes the heat and returns it to the sea.
A3.6.2 Direct System: Single-Stage
The single-stage direct compression reliquefaction system is described and illustrated in Figure A3.6; the stages in the cycle are also shown on a schematic Mollier Diagram (see Figure A3.7).
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fCS TANKKK SAhTTY GUIDE (LIQUEFiKD CAS)
Figure A3.6 Single stage direct compression cycle
Enthalpy--->~
Figure A3.7 Schematic mollier chart Single stage direct compression cycle
Boil-off vapour (1) is taken from the cargo tank to the compressor (2) via a liquid separator; any liquid in the vapour would damage the compressor. The compressor is used to increase the temperature of the vapour so that a sea-water condenser can be used. The superheated vapour from the compressor (3) is condensed to an ambient temperature liquid in a sea-water cooled condenser (4), and is collected in a collecting vessel, known as a
condensate receiver, before being passed through an expansion valve (5) to cool it. The flow through the expansion valve is controlled by a level switch in the collecting vessel to prevent back-pressure from the cargo tank reaching the condenser and compressor. The throttling (expansion) valve is designed to ensure that there is sufficient pressure to press the liquid into the cargo tank.
This simple system can be used aboard semi-pressurised ships for high boiling point cargoes. A3.6.3 Direct
System: Two-Stage
If the compressor discharge-to-suction pressure ratio in a single stage system exceeds about 6:1 the efficiency of the machine is reduced and two stage compression is necessary. This can take place in two separate machines or in one two-stage compressor.
The first part of the two-stage cycle is the same as the single-stage cycle. Boil-off (1) is taken from the tank via a liquid separator to the first-stage compressor (2) where it is superheated (3). The
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vapour can then be cooled in an interstage cooler (or "intercooler") (4) before passing to the second stage compressor. The purpose of the intercooler is to reduce the suction pressure of the second stage and increase
efficiency; it is essential for a cargo such as fully refrigerated ammonia.
The second compression further superheats the vapour (5) which is then cooled and condensed in a sea-water cooled condenser (6). The ambient temperature liquid is then collected and passed through the expansion valve (8) as in the single stage cycle. Before the expansion valve, the condensed liquid can be used as the intercooler coolant (7).
This system can be used for semi-pressurised and fully refrigerated LPG ships.
Figure A3.8 Two stage direct compression cycle
Enthalpy
Figure A3.9 Schematic mollier chart Two stage direct compression cycle A3.6.4 Direct System: Cascade
This system is virtually identical to the single-stage direct system, except that the cargo condenser is cooled by liquid refrigerant gas such as R22. The heat from the cargo evaporates the R22 which is compressed, condensed in a sea-water cooled condenser, and cooled by passage through an expansion valvp Thp Ti?? ryrlp is also a direct cycle, working in a cascade with the cargo reliquefaction cycle. See Figures A3.10 and A3.11.
The system can be used for fully refrigerated cargoes. Its major advantage is that the capacity of the system is not affected by sea-water temperatures as much as other systems. The cycle is also more efficient, as the R22 temperature in the LPG condenser can be below 0°C.
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A3.6.5 Indirect System
Figure A3.11 Schematic mollier chart Cascade cycle
Indirect cooling is used for cargoes which cannot be compressed for chemical reasons. In Figure A3.12(a) the boil- off passes from the tank (1) under its own pressure to a condenser which cools and liquefies it (2). The condensate then returns to the tank under its own pressure or by pump. It is also possible (Figure A3.12(b)) to arrange condensation by cooling coils in the vapour dome, below the liquid surface or welded to the tank exterior.
The cycle has to use a very cold refrigerant in the condenser for efficiency; the common refrigerants are hydrogen, helium and propane. The refrigerant works in a cycle, in cascade with the cargo cycle.
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Figure A3.12 Indirect cycle