Compressor Sizing and CalculationMany 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 of centrifugal 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 = 6,171 cfm inlet volumeWm = 437.5 Ibs/min Weight FlowMw = 28.46 molecular weightP1 = 14.7 psia inlet pressuret1 = 90.0 oF inlet TemperatureT1 = 550 oR Absolute TemperatureK = 1.395 isentropic exponent for airP2 = 40 psia discharge pressure

Assumptions:Assume Average Compressibility factor (Zavg) = 1.0Assume polytropic efficiency ηp = 0.75Assume FT head per stage = 10,000 ft-Ib/IbAssume mechanical loss = 1%Assume head coefficient (u) = 0.48

Step 1. Calculate the polytropic exponent using

n - 1 = k – 1 n k × ηp

n - 1 = 1.395 – 1 × 1 =0.378 n 1.395 0.75

n - 1 = 0.378 n

Calculate the pressure ratio

rp = P2 = 40/14.7 P1

rp = 2.721 pressure ratio

Step 2. Calculate the total required polytropic head using

Hp = Zavg RT1 kNp rp (k – 1/kNp) -1

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 = 36,338.4/4Hp = 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 rp

(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 1st 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, ηp = .79 δ = .051, ηp = .79 The average is rather is to calculateηp = .79 the average efficiency

Step 6. Recalculate the polytropic exponent using the new efficiency

n - 1 = k – 1

n k × ηp

n - 1 = 1.395 - 1 × 1 n 1.395 .79

n - 1 = .359 n n = 1.559

Using the new polytropic exponent, calculate the discharged temperature using equation;

n-1T2 = T1 rp n

T2 = 550 × 2,721.359

T2 = 787.8oR

t2 = 787.8 – 460t2 = 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 × ηp 33,000 × .79Ghp = 437.5 × 36,338.4 33,000 × .79Hp = 609.8 hpWhere,Mechanical loss = 1% × Ghp = .01 × 609.8 = 6.1Thus, 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

1) 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.