Figure 2.8 Simple refrigeration — evaporation/condensation cycle

In the case of refrigeration at sea, a non-flammable and non-toxic fluid (such as R22) can be used as a refrigerant in the condenser. These refrigerants have similar vapour pressure/temperature characteristics to LPG.

The principles as shown in Figure 2.8 also apply to the reliquefaction cycle of liquefied gas cargo vapours. Here the cargo tank and its boil-off vapours replace the evaporator as shown in Figure 2.8. Practical cargo reliquefaction is discussed in more detail in 2.19 and 4.5.

2.12 CRITICAL TEMPERATURES AND PRESSURES

The critical temperature of a gas is the temperature above which it cannot be liquefied no matter how great the pressure. The critical pressure of a gas is the pressure required to compress it to a liquid state at its critical temperature. Critical temperatures and pressures for the principal gases are listed in Table 2.5. As will be seen, all the gases, with the exception of methane (at times also ethane and ethylene), can be liquefied by pressure alone at temperatures within the normal ambient range. Accordingly, for the carriage or storage of ethane or ethylene as a liquid, a reliquefaction process is required. In the case of LNG carriers, reliquefaction is seldom an option and boil-off from the pre-refrigerated cargo is restricted by the efficiency of tank insulation. In this case the remaining boil-off is used in the ship's boilers as fuel.

2.13 LIQUID/VAPOUR VOLUME RELATIONSHIPS

As a guide to the relative sizing of equipment to handle a vapour compared with that to handle its liquid condensate, it is useful to note the condensing ratio of the various liquefied gases. This ratio gives that quantity of liquid (in dm³) at its atmospheric boiling point which will condense from one cubic metre of its vapour at the standard conditions of one bar absolute and 0°C. If at 0°C the gas is at a higher temperature than its critical temperature (such as for methane), the ratio is given for the vapour at the atmospheric boiling point of the liquid. Condensing ratios are listed in Table 2.5.

2.14 IDEAL GAS LAWS

The ideal gas laws are appropriate just to vapours; indeed, they are most appro­priately applied to non-saturated vapours. Liquid/vapour mixtures and liquids possess characteristics different from those described below. Relating what follows to the principles of refrigeration (as described in 2.11) that portion of the cycle involving vapour compression is most relevant.

An ideal gas is one which obeys the gas laws by virtue of its molecules being so far apart that they exert no force on one another. In fact, no such gas exists, but at room temperature and at moderate pressures many non-saturated gases approach the concept for most practical purposes. The ideal gas laws govern the relationships between absolute pressure, volume and absolute temperature for a fixed mass of gas. The relationship between two of these variables is commonly investigated by keeping the third variable constant.

For a gas to perform according to these principles, it must be in its unsaturated form and removed from its own liquid.

Figure 2.9(a) Boyle's Law for gases(constant temperature)

 

Figure 2.9(b) Charles' Law for gases (constant pressure)

 

Figure 2.9(c) Pressure Law for gases (constant volume)

Boyle's Law states that, at constant temperature, the volume of a fixed mass of gas varies inversely with the absolute pressure. This relationship is illustrated in Figure 2.9(a) and can be written:—

Charles' Law states that, at constant pressure, the volume of a fixed mass of gas increases by 1/273 of its volume at 0°C for each degree Centigrade rise in tempera­ture. An alternative definition is that the volume of a fixed mass of gas at constant pressure varies directly with its absolute temperature. This law is illustrated in Figure 2.9(b) and can be written:—

The Pressure Law states that, at constant volume, the pressure of a fixed mass of gas increases by 1/273 of its pressure at 0°C for each degree Centigrade rise in temperature. Alternatively, it can be stated that the pressure of a fixed mass of gas at constant volume, varies directly with its absolute temperature. The pressure law is illustrated graphically in Figure 2.9(c) and can be written:—

These three laws may be combined into

or, more generally, for an ideal gas, using the Universal Ideal Gas Constant

where all the quantities are in consistent units, e.g.

 

where P is absolute pressure in pascals (N/m²)

V is in cubic metres

T is in degrees Kelvin

M is the mass of the gas in kilograms

m is the molecular weight (dimensionless), and

R is the Universal Gas Constant = 8.314 kJ/kg mol.K.

Figure 2.9 outlines the three basic gas laws. They cover changes at constant tem­perature (isothermal); changes at constant pressure (isobaric); and changes at con­stant volume (isovolumetric).

However, a fourth process involving the ideal gas is also of relevance to refrigeration. This is called the adiabatic compression and may be reversible or irreversible. A reversible process is one involving constant entropy (see definitions). Changes in pressure, involving constant entropy (isentropic), are shown on the Mollier diagram in Figure 2.16.

A reversible adiabatic (or isentropic) expansion is one where the heat flow to or from an external source is zero. In the compressor of a refrigeration plant, work is done on the gas as it passes through the compressor, although no heat is assumed to be transmitted to or from the outside. The work is converted into internal energy and, hence, the temperature of the gas is increased. By this means, temperatures at the compressor discharge are raised (a) by increased pressure and (b) by increases in internal energy.

In practice, to approximate to an adiabatic compression, work on the gas must be carried out very quickly. By this means, little time is allowed for heat to escape from the system. The adiabatic curve is shown by the curve A/B in Figure 2.10. On the other hand, and by way of comparison, an isothermal compression, as shown by the curve A/C, must be carried out very slowly otherwise temperature changes will become obvious.

It follows, therefore, that the actual changes taking place, say in a compressor (with respect to pressure, volume and temperature), follow a curve somewhere between the adiabatic and the isothermal. This could approximate to the curve A/D shown in Figure 2.10.

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