Polytropic head

Compressor performance is quoted in terms of polytropic head. This is the work done on the gas and its definition is developed from basic gas laws. Firstly Boyle s Law states that the volume (V) occupied by a gas is inversely proportional to its absolute pressure (JP). 

Charles Law states that that volume is directly proportional to absolute temperature (T). 

R is the Universal Gas Constant. It has a value of 8.314kJ/kg-mole/K (1.9859 BTU/lb-mole/R). The law, in its normal form, is written on molar basis. On a weight basis we include the molecular weight (MW). 

Process Control A Practical Approach Myke King 

To accommodate the non-ideal behaviour of the gas, compressibility fzj is introduced into the equation. 

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HP = Gas horsepower W = Flow, Ib/min Hpoiy = Polytropic head Had = Adiabatic head Ep = Polytropic efficiency Ea = Adiabatic efficiency... 

One significant practical difference in use of polytropic head is that the temperature rise in the equation is the actual temperature rise when there is no jacket cooling. The other practical uses of the equation will be covered as they apply to each compressor in the later chapters. 

Similarly, for polytropic head, the head coefficient is defined as Pp and Equation 2.73 is recalled, the geometric and thermodynamic head relationships, on a per-stage basis, may be equated as above. 

To start, convert the flow to values estimated to be the compressor inlet conditions. Initially, the polytropic head equation (Equation 2.73) will be used with n as the polytropic compression exponent. If prior knowledge of the gas indicates a substantial nonlinear tendency, the real gas compression exponent (Equation 2.76) should be substituted. As discussed m Chapter 2, an approximation may be made by using the linear average ut the inlet and outlet k values as the exponent or for the determination of the polytropic exponent. If only the inlet value of k is known, don t be too concerned. The calculations will be repeated several times as knowledge of the process for the compression cycle is developed. After selecting the k value, u,se Equation 2.71 and an estimated stage efficiency of 15 / to de clop the polytropic compression exponent n. 

Step 2. Calculate the total required polytropic head using Equation 2.73, assuming a value for Zavg = 1 ... 

Step 7, Calculate the polytropic head for each section, using the overall average compressibility of Z2avg = -97. 

Pitch line velocity, 330 Polytropic compression exponent, 160 Polytropic efficiency, 34 Polytropic exponent, 34 Polytropic head... 

Adiabatic head, column (E), is a direct measure of the number of stages of centrifugal compression. In actual rating, the polytropic head must be used. As a guide, 8,000-10,000 ft of head are developed per stage of centrifugal compression, depending upon speed. 

The approximate number of stages for a centrifugal compressor, column (I), is a function of the adiabatic (and actually the polytropic) head and varies with the efficiency and physical properties of the gas. 

For approximation, polytropic head used in actual design. 

An important point to remember when calculating is that when you are using adiabatic head, use adiabatic efficiency and when using polytropic head, use polytropic efficiency. ... 

Polytropic Head. The polytropic head more closely approaches the conditions of an actual compressor and is the actual height of a gas column that can be maintained at... 

Vj = specific volume of gas at suction conditions, fP/lb n = polytropic exponent Hp = polytropic head, ft-lb/lb = ft Pj = discharge pressure, psia Tj = inlet temperature, °R... 

If the polytropic head and efficiency are known, these values can be substituted in ... 

From Table 12-9B, the nominal speed for a 29M is 11,500 rpm. Convert adiabatic head to polytropic head by the ratio of efficiencies. 

Example 12-9. Comparison of Polytropic Head and Efficiency with Adiabatic Head and Efficiency... 

Determine Polytropic head, adiabatic head, and adiabatic efficiency. 

Hg = Total polytropic head of wheel, ft-lb/lb (adiabatic or polytropic)... 

From Figure 12-67, solving polytropic head equation ... 

Required polytropic head from second case ... 

From Figure 12-65, by trial-and-error interpolation, when e = 0.7, ep = 0.735. Using ep in the horsepower equation, convert adiabatic head to polytropic head using Figure 12-67. 

This compares with 1,339 bhp calculated by the gas horsepower relation. The values should agree exacdy, and the difference may lie in the reading of charts to determine the polytropic head. Using the bhp calculated with the adiabatic efficiency, e. ... 

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