It is logical to detect from the general gas equation (formula 2.3.1.1) that heat must, in principle, be generated when air is being compressed. In order to arrive at a theoretical calculation of the quantity of heat, one looks at the simplified case at which compression takes place theoretically without any heat being added or withdrawn.
Formula 2.4.1
As part of the heat of compression is conducted away from every compression chamber, compression in practice proceeds in between adiabatic2 and isothermal3, i.e. in a polytropic4 mode. The following interrelations can be deduced from the gas laws: Temperature change as a function of pressure at constant volume as isochores5
Formula 2.4.2
The volume change as a function of temperature at constant pressure as isobars6.
Formula 2.4.3
Pressure change as a function of volume at constant temperature as isotherms
| 2 Exponent x | 4 Exponent n > x | 6 Exponent n = 0 |
| 3 Exponent n = 1 | 5 Exponent n = |
Formula 2.4.4
Supplementing the formulae indicated above, which are more of theoretical interest, there are the following equations which have greater practical importance. The adiabatic pressure change as a function of temperature at constant volume,
Formula 2.4.5
respectively the adiabatic volume change as a function of pressure at constant temperature
Formula 2.4.6
Polytropic change of pressure as a function of temperature at constant volume,
Formula 2.4.7
Respectively the polytropic change of volume as a function of pressure at constant temperature,
Formula 2.4.8
The change of state of a gas is established by taking into account the relationship of specific heat capacities exponent x. In doing so, one differentiates between: cp = specific heat at constant pressure respectively referred to 1 kg (kcal/kg°C)
cv = specific heat at constant volume respectively referred to 1 kg (kcal/kg°C) Based on experiments, the relationship of specific heats x = cp/cv is: with uniatomic gases x = 1.666 = 5/3
with biatomic gases x = 1.400 = 7/5
with triatomic gases x = 1.333 = 8/6
The following illustration shows the interpretations of the various specific cases of the general polytropic law.
Figure 2.4.1
The difference of the specific heat referred to 1 m3 at constant pressure and volume is a constant. For ideal gases, the following applies when applying the above x values: With uniatomic gases
| | 5 | | | |
| cp = |
| = 0.22 kcal/m3°C | | cV = 0.13 kcal/m3°C |
| | 22.4 | | | |
A certain oil content with the most varied structure of oil molecules is always contained in compressed air, whatever the design of compressor used. Oil injected rotary screw compressors have conquered the compressor market and, given their many advantages over other systems of compression, now form an element without which compressed air generation can no longer be imagined. With this type of compression system, oil is intentionally added to the drawn in ambient air when compression takes place. The residual oil content at the pressure outlet of screw compressors amounts, as a rule, to about 3 - 15 mg/m3. Not only with oil injected screw compressors but also with established types of piston or vane compressors, oil is used for cooling and lubrication. Whereas oil injected screw compressors reach a maximum oil temperature of about 85 - 90°C, the oil of piston compressors or rotary vane types reaches far higher temperatures. Even compressed air from non lubricated compressor systems is not always free from oil. For one thing, moving components (eg. sliding bearings) within the compressor are lubricated, for another, it is not impossible that hydrocarbons are drawn in from the surrounding air and thus conveyed into the pipe network in concentrated form. The vapour content of hydrocarbons diminishes with falling temperature.
Table 2.5.5.1| Temperature °C | Vapour Pressure | Oil Vapour |
|---|
| 10 | 0,000010 | 0,245 |
| 30 | 0,000037 | 0,801 |
| 60 | 0,000100 | 1,941 |
| 100 | 0,000298 | 5,170 |
The values given in table 2.5.5.1 and otherwise referred to in this section are based on a particular compressor lubricating oil and can not be generally applied. The values indicated are derived from a compressor oil with the following technical data:
Table 2.5.5.2| Ignition Point | 250 | 250 | °C |
| Equilibrium Temperature | 60 | 150 | °C |
| Vapour Pressure | 0,0001 | 0,035 | Torr |
| Density at 15°C | 0,88 | 0,88 | g/ml |
| Average Molecular Weight | 520 | 520 | - |
| Oil Vapour Content | 0,002 | 0,6 | mg/l |
| | 2 | 600 | mg/m3 |
With lubricants based on mineral oil, it is often sufficient to estimate the vapour pressure on the basis of the ignition point. For every lubricating oil, the applicable vapour pressure diagram should be studied. The oil vapour content of air can be estimated from knowledge of the average molecular weight of the oil. On the basis of the definition: 1 mol of a gas fills a volume of 22.4 litres at 273°K and 760 TorrThe volume applying to 1 mg/L for oil vapour in air with 1.29 g/dm3, 760 Torr and 273°K can be deduced from the following formula:
Formula 2.5.5.1
And, after simplification through multiplying the constants, this leads to:
Formula 2.5.5.2
So that, after conversion, Formula 2.5.5.3 is available as a basis in order to determine the degree of saturation by oil vapour content in the volume of air, where the reciprocal value of 10-3 and the dimension m3/dm3 are taken into account through 103:
Formula 2.5.5.3
The result is displayed in the following diagram 2.5.5.1 and shows the oil vapour content for mineral oil7 as a function of pressure and temperature. For practical application one does, however, have to consider how far the gaseous phase is really saturated with the oil vapour and at what temperatures this takes place. Furthermore, the question arises whether finest oil droplets are not floating as a mist in the air current, thereby causing a much higher content of oil than would correspond to the theoretical saturated vapour pressure. It is also important to bear in mind that the compressor, depending on temperature, pressure and system of compression, can either promote or inhibit the occurrence of volatile decomposition products. Being subjected to the effect of oxygen in the air and considerable heat, these decomposition products can falsify the oil vapour concentration in the air current strongly and sometimes lead to a far reaching scatter of values when it is attempted to measure the residual oil.
Diagram 2.5.5.1 - Mineral Oil Vapour Content in Compressed Air
7 molecular weight = 520; vapour pressure = 0.0001 Torr
