Problem Statement
Calculate the compressibility factor (Z factor) for air at the following temperature and pressure condition -
P = 15 barg
T = 600C
Solution
The compressibility factor or Z factor for air is calculated in following simple steps using linear interpolation technique and air compressibility factor table.
Step1
Temperature and Pressure unit conversion to 'Kelvin' and 'bara'.
T = 600C = 60+273.16 K = 333.16 K
P = 15 barg = 15 + atmospheric pressure = 15 + 1.013 bara
P = 16.013 bara ≈ 16 bara (roughly for purpose of this calculation)
Step2
Refer to EnggCyclopedia's air compressibility factor table to get air compressibility factors at neighboring temperature and pressure conditions. Air compressibility at following four points is noted.
| P(bara) | P(bara) | Air Compressibility (Z factor) |
| 10 | 300 | 0.9974 |
| 10 | 350 | 1.0004 |
| 20 | 300 | 0.9950 |
| 20 | 350 | 1.0014 |
Step3
First, mean air compressibility is calculated @ 10 and 20 bara by linear interpolation around the temperature values.
Z1 (@10bara & 333.16K) = 0.9974×(350.0-333.16)/(350-300)+1.0004×(333.16-300.0)/(350-300)
Z1 (@10bara & 333.16K) = 0.9974×0.3368+1.0004×0.6632= 0.9994
Similarly,
Z2 (@20bara & 333.16K) = 0.9950×0.33680+1.0014×.6632 = 0.9992
Then the air compressibility at given temperature and pressure conditions is estimated by linear interpolation around the pressure values.
Z (@16bara & 333.16K) = 0.9994×(20-16)/(20-10)+0.9992×(16-10)/(20-10)
Z (@16bara & 333.16K) = 0.9993