Compressor Sizing and Calculation Many of the steps used in sizing estimates are also useful for checking bids or evaluating existing equipment. After compression duty has been sufficiently defined, the following steps provides relations used for the computation computation of centrifugal compressor compressor with example to show how preliminary selections may be made by the project engineer Listed below are the fundamental parameters or conditions that have to be defined and before considering compressor sizing: •
• • •
Gas composition Flow rate Suction condition Discharged condition
Gas composition: This has to do with details about the types of gas and its composition. It also includes gas molecular weight. Suction condition: This gives details parametric suction condition like the temperature and pressure at the inlet. Discharge condition: Details about discharged temperature and pressure and flow conditions are expected in the process information given.
The following terms are to be calculated when sizing a centrifugal compressor: • • • • • • •
Polytropic Heads Tip speed Shaft speed Gas Volume Discharge Temperature (if not provided) Isentropic exponent Shaft horse power
Sizing of a Centrifugal compressor is better illustrated by sizing a typical centrifugal compressor given typical process information. Below are some process information supplies for use in sizing a centrifugal compressor: Q1 = Wm = Mw = P1 = t1 = T1 = K = P2 =
6,171 cfm 437.5 Ibs/min 28.46 14.7 psia 90.0 oF 550 oR 1.395 40 psia
inlet volume Weight Flow molecular weight inlet pressure inlet Temperature Absolute Temperature isentropic exponent for air discharge pressure
Assumptions: Assume Average Compressibility factor (Zavg) η p Assume polytropic efficiency Assume FT head per stage Assume mechanical loss Assume head coefficient (u) Step 1. Calculate the polytropic exponent using
n-1 =k–1 n k × η p n - 1 = 1.395 – 1 × 1 n 1.395 0.75
=0.378
n - 1 = 0.378 n Calculate the pressure ratio
r p =
P2 = 40/14.7 P1
r p = 2.721 pressure ratio
= 1.0 = 0.75 = 10,000 ft-Ib/Ib = 1% = 0.48
Step 2. Calculate the total required polytropic head using (k – 1/kNp)
-1 Hp = Zavg RT1 kNp r p K–1 = 1 × 54.29 × 550 × ( 2.721 .378 – 1 ) Hp = 36,338.4 ft-Ib/Ib Step 3. Determined the number of stages, z, required using the recommended 10,000 ft-Ib/Ib head per stage
z = Hp/10,000 = 36,338.4/10,000 z = 3.63 stages, round off to 4 Calculate a new head per stage using four stages: Hp = 36,338.4/4 Hp = 9,085 ft-Ib/Ib Step 4. Calculate a tip speed to produce the head per stage just calculated using recommended head coefficient µ
u = (Hp × g/ µ) .5 u = (9,085× 32.2/.48) .5 u = 780.7fps impeller tip speed Figure 5-26 showing the relationship between the volume and impeller diameter d = 17.3 inches impeller diameter corresponding to inlet volume 6,171cfm Hence calculate the shaft speed (N) using N = tip speed × 60 × 12 Impeller diameter × π N = 780.7 × 60 × 12 π × 17.3
N = 10,342 rpm Step 5. Calculate volume into the last impeller (stage 4) using
Qls =
Qin r p(1 – 1/z)^1/n
=
6.171 (2.7211-1/4)1/1.608
Qls = 3.869 cfm volume at last impeller Step 6.To calculates the efficiency at the last stage, there is need to calculate the coefficient of flow for the 1 st and last stage using equation;
δ = 700 Qls N d3 δ = (700×6,171)/ (10,342×17.33) δ = .081 first stage flow coefficient δ = (700×3,869)/ (10.342×17.33) δ = .051 last stage flow coefficient Looking up the corresponding efficiency in the figure 5-26 using the flow coefficients: δ = .081, η p = .79 δ = .051, η p = .79 The average is rather is to calculate η p = .79 the average efficiency Step 6. Recalculate the polytropic exponent using the new efficiency
n-1 = k–1 n k × η p n - 1 = 1.395 - 1 n 1.395
×
1 .79
n - 1 = .359 n
n = 1.559 Using the new polytropic exponent, calculate the discharged temperature using equation; n-1 T2 = T1 r p n T2 = 550 × 2,721.359 T2 = 787.8oR t2 = 787.8 – 460 t2 = 327.8oF Calculate the Power (Shaft power) required using Wp = Gas Horse power + Mechanical loss Where, Ghp = Inlet rate × Polytropic Head for 4 stages = Wm × Hp 33,000 × η p 33,000 × .79 Ghp = 437.5 × 36,338.4 33,000 × .79 Hp = 609.8 hp Where, Mechanical loss = 1% × Ghp = .01 × 609.8 = 6.1 Thus,
Power required (Wp) = 609.8 + 6.1 = 615.9 hp
Advantages of Centrifugal compressor 1)
Centrifugal compressor is known for its higher capacity/horsepower
2) It is quite simple and has appreciable size ratio hence does not require shaking force and massive foundation. 3)
It has higher volumetric flow rate in the range of 1,000 cfm to 150,000 cfm hence quite preferred where higher volumetric output is being sort for.
4)
Centrifugal compressor is relatively cheap in terms of energy, cost of maintenance, cost of fabrication, construction.
5) Because of its wide range of application in the process industry, it has been proven to have greater continuity of services dependable and reliable. 6) It has less operating attention. 7) Adaptability to high-speed low-maintenance-cost drivers.
Disadvantages of Centrifugal compressor Where much higher pressure ratio is required it is grossly not best suitable. 2) It is not best suitable for lower capacity services. 3) It’s efficiency is not higher compare to a well maintained other compressor example of such is reciprocating compressor. 1)
