### Problem Statement

Calculate the compressibility factor (Z factor) for air at the following temperature and pressure condition -

P = 15 barg

T = 60^{0}C

### 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 = 60^{0}C = 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