## Example

For a sample problem that will include some of the additional losses that are normally encountered in an actual situation, size a compressor to the following given conditions for a hydrocarbon gas:

mw = 53.0 ki = 1.23 Z, = 0.97 t! = 85°F P, = 40 psia P2 = 120 psia w = 2,050 lb/min

Step h Use Equation 2.5 to calculate the specific gas constant.

Step 2. Convert the inlet temperature to absolute.

Step 3. Calculate the polytropic exponent using Equation 2.71. Assume an efficiency of t|p = .75. Use as kavg = kj = 1.23.

rp = 3,0 pressure ratio

Step 5. Calculate the estimated discharge temperature using Equation

T2 = 716.7°R absolute discharge temperature estimate

Correct for the balance piston leakage using 1% for pressures of 150 psia and under. The weight flow into the impeller must be increased to account for the leakage.

w = 2,070.5 lb/min net flow to the impeller.

The temperature at the entrance to the impeller is increased because of the hot leakage. Calculate the corrected impeller inlet temperature using Equation 5.20.

tw 86.7°F corrected impeller inlet temperature

Convert to absolute:

Step 6. Substitute into Equation 2.10 and using 144 in2/ft2.

_ .97x29.15x546.7

40x144

Qi = 5,557 cfm inlet flow to the impeller

Step 7. Calculate the total required poly tropic head using Equation 2.73, assuming the average value of Zavg = .97.

Hp = ! 9,508 ft-lb/lb total polytropic head required

Step 8. Determine the number of stages required using the modified rule of thumb on head per stage, Hstg.

19,508

Calculate a new head per stage using three stages.

Step 9. Use the geometric portion of Equation 5.12 to calculate a required tip speed, which will produce the head per stage. Use the recommended head coefficient [i = .48 for the calculation.

u2 = 660.5 fps impeller tip speed

Step 10. From Figure 5-26 and the inlet volume, select an initial impeller diameter.

d j = 17.3 in. initial impeller diameter

Use Equation 5.17 to calculate the initial speed, N.

XT 60x12x660.5

71x17.3

N -8.750 rpm compressor shaft speed

Step 11. The volume into the last impeller is calculated with the use of

Equation 5.18.

5,557

Is ^1-1/3 y/1.332 Qk ~ 3,206 cfm volume into last stage

With the volumes just calculated, calculate the inlet flow coefficient for each of the two stages using Equation 5.19.

8 = .086 first stage flow coefficient

8 = .050 last stage flow coefficient

Look up the efficiencies for the two flow coefficients on Figure 5-27.

rip = .79 first stage efficiency x\p = .79 last stage efficiency x\p - ,79 average of the two efficiencies

Step 12. Recalculate the polytropic exponent using Equation 2.71 and the new average efficiency.

With the new polytropic exponent, calculate the discharge temperature by substituting into Equation 5.16.

T2 = 708.5°R absolute discharge temperature t2 = 708.5 - 460

h = 248.5°F discharge temperature

Step 13. Calculate the power required using Equation 2.78, allowing 1% for the mechanical losses. Use the conversion 33,000 ft-lb/min/hp.

... 2,070.5x19,508 w — ---+ ,01Wn p 33,000 x.793 p

1,558.5 hp shaft horsepower

There is no need to recalculate the polytropic head for the changed efficiency because the head difference from the original value is negligible. Another item to note is that the horsepower is 1.5% higher than if the balance piston had been neglected. The interesting part is not the value itself, but the fact that the slight temperature addition at the impeller inlet is responsible for .5% of the increase and the remainder is the 1% weight flow increase through the compressor. As the small, but significant "real life" items are included, the actual efficiency is being eroded. If the calculation had been made with only the original weight flow, the equivalent efficiency would prorate to .781.

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