Calculation of Power Required in Fan, Blower, and Compressor

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The function of Fans, Blowers, and Compressors is to increase the mechanical energy of gases.

Fans, Blowers, and Compressors are used for different services based on the required discharge pressure of the gases.

If the Required Discharge Pressure is less than 3.45 kPa g, then a Fan is used.

A Blower is used when the Required Discharge Pressure is higher than 3.45 kPa g. The maximum discharge pressure of the blower is 1 atm g.

Furthermore, if the Required Discharge Pressure exceeds 2 atm (absolute), then a Compressor is used. The discharge pressure of the compressor ranges from 2 atm a to thousands of atmospheres.

Calculation of Power Required by Fan

Fans are mainly classified into two categories

Centrifugal fans and
Axial flow fans.

The efficiency of a fan ranges from 40 to 70%, depending on its specific speed.

Power input to a fan is determined by the following equation

$P_0=\frac{2.72 \times 10^{-5} \; q_v \; p_d}{\eta}$

Where,
$P_0$ = Power required by fan, kW
$q_v$ = Capacity of fan, m³/h
p_d = Discharge pressure of fan, cm WC (gauge pressure)
= Sum of pressure and velocity head, developed by the fan, cm WC
η = Efficiency of fan

Calculation of Power Required in Blower and in Adiabatic Compressor

Blowers are always operated in an adiabatic manner.

Many compressors, such as air compressors up to 10 bar g, are also operated in an adiabatic manner. In an adiabatic compressor, jacketed cooling is not provided. While in other types; polytropic and isothermal compressors, jacketed cooling is provided around the compressor section.

In an isothermal compressor, the inlet temperature of a gas is equal to the outlet temperature of a gas. If both temperatures are not the same even after providing jacket cooling, the compressor is called a polytropic compressor.

PVT Relationship for adiabatic compression

$\frac{p_2}{p_1}=\left(\frac{V_1}{V_2}\right)^2$

$\frac{T_1}{T_2}=\left(\frac{V_1}{V_2}\right)^{k-1}$

$\frac{p_2}{p_1}=\left(\frac{T_2}{T_1}\right)^{\frac{k}{k-1}}$

Where,
k = C_p/C_v= ratio of specific heat at constant pressure to specific heat at constant volume
p₂, p₁ = outlet/inlet pressure of gas, kPa
V₂, V₁ = outlet/inlet volume of gas, m_³/kmol
T₂, T₁ = outlet/inlet temperatures of gas, K

Read Also: Process Design of Pump

Blower Power Calculation (kw)

Power required in single-stage blowers or single-stage adiabatic compressors (Blower Power Calculation Formula)

$P_0=\frac{2.78 \times 10^{-4}}{\eta}\left(\frac{k}{k-1}\right) q_{v1}\; p_1 \left[\left(\frac{p_2}{p_1}\right)^{\frac{k-1}{k}}-1\right]$

Where,
P₀ = Power required, kW
p₁, p₂ = Absolute inlet pressure, kPa
q_v1 = Volumetric flow rate of gas based on inlet condition, m³/h
η = Efficiency of blower

Discharge temperature of gas from the blower or single-stage adiabatic compressor,

$T_2=T_1\left(\frac{p_2}{p_1}\right)^{\frac{k-1}{k}}$

The value of k ranges from 1.39 to 1.41 for air and perfect diatomic gases.

X factor calculation for the value of k=1.395

$X=\left[\left(\frac{p_2}{p_1}\right)^{\frac{k-1}{k}}-1\right]=r^{\frac{k-1}{k}-1}$

Where,
k = 1.395 for air or a diatomic gas
r = Compression ratio

Power required for the blower and adiabatic compressor

$P_0=9.81\times10^{-4}\;q_{v1}\;p_1\;X/\eta$

Other gases have a value of k in the range of 1 to 1.4.

Power required by the blower or adiabatic compressor, for the gases having a value of k other than k =1.395, is given by the following equation:

$P_0=6.37\times10^{-4}\;q_{v1}\;p_1\;\frac{X_G}{d\eta}$

Where, d = 2.292 [(k – 1)/k]

Values of $\frac{X_G}{X}$ and d can be obtained from the graph (XG/X) vs k and d vs k available in the book (Perry, R. H., and Green D, Perry’s Chemical Engineer’s Handbook, 6th Ed., McGraw-Hill Education, USA, 1984.) for the different values of k and different values of r.

Read Also: Process Design of Piping

Multistage Compressor

For a multistage compressor with N stages of compression in which
1. Adiabatic compression takes place in each stage,
2. Near equal work done in each stage (i.e., equal compression ratio in each stage; r) and
3. Intercooling is provided between every two stages of compression to the same inlet
gas temperature (T1),

We can calculate the power requirement using the following equation:

For the multistage compressor, we can calculate the discharge temperature from the last stage using the following equation:

$P_0=\frac{6.37\times10^{-4}\;N\;q_{v1}\;p_1}{d}((X_G-1)^{\frac{1}{N}}-1)$

Where, N = Number of Stages

For the multistage compressor, the discharge temperature from the last stage can be predicted by the following equation:

$T_2=T_1(X_G-1)^{\frac{1}{N}}$

References

Sinnott, R. K., Coulson & Richardson’s Chemical Engineering, Vol. 6, Asian Book Private Ltd., Revised 2nd Ed., New Delhi, 1998.

Perry, R. H., and Green D, Perry’s Chemical Engineer’s Handbook, 6th Ed.,
McGraw-Hill Education, USA, 1984.

Thakore, S. B. and B. B. I. (2015). Introduction to process engineering and design. McGraw-Hill Education.

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Laws for Three Modes of Heat Transfer

Helmholtz Free Energy and Gibbs Free Energy