### Wednesday, August 6, 2008

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There was a question raised in CR4 forum related to conversion from Nm3/h to m3/h and the equation can be known by many of you. Nevertheless, the derivation and relation in between ideal gas and real gas and the derived equation could be useful and handy for some of you.

First for most important thing is the definition of Normal and actual condition. Normal condition in this case is define as 1 ATM @ 0 degC whilst actual is at P @ T.

From Universal gas law for ideal gas,

PV = (m/MW) RT [Eq.1]

where

P = the absolute pressure of the gas, in Pa

m = mass, in kg

MW = molecular weight, in kg-mole

V = the volume of the gas, in m3

T = the absolute temperature of the gas, in K

R = the universal gas law constant of 8.3145 m3·Pa/(mol·K)

To relate it to real gas condition, compressibility factor (z) is added.

PV = z (m/MW) RT. [Eq.2]

At condition 1 ==> P_{1} x V_{1} = z_{1} (m_{1 }/ MW_{1}) R x T_{1} [Eq.3]

At condition 2 ==> P_{2} x V_{2} = z_{2} (m_{2 }/ MW_{2}) R x T_{12} [Eq.4]

Same gas composition and flow or quantity

==> MW_{1}=MW_{2}, m_{1}=m_{2},

[Eq.4] / [Eq.3]

==> (P_{2}/P_{1}) x (V_{2}/V_{1}) = (z_{2}/z_{1}) x (T_{2}/T_{1})

==> V_{2} = (z_{2}/z_{1}) x (T_{2}/T_{1}) x (P_{1}/P_{2}) x V_{1}

Using Volumetric rate (Q),

==> Q_{2} = (z_{2}/z_{1}) x (T_{2}/T_{1}) x (P_{1}/P_{2}) x Q_{1}

If condition 2 is actual (act) and condition 1 is normal(N) (i.e. 1.01325 bar abs @ 0 degC)

At Normal condition Z_{1}=Z_{n}~1, P_{1} = 1.01325 bar abs

_{act}= z

_{act}x Q

_{N}x (T

_{act}/ 273.15) x (1.01325 / P

_{act})

where

Q_{act} in m3/h

P_{act} in bar abs

Q_{N} in Nm3/h

T_{act} in K

Above equation with inclusion of compressibility factor to relate ideal to real gas condition,The z_{act} factor could be range from 0.5 to 1.2 subject to composition, pressure and temperature. At low pressure, z could be closed to 1.

Above equation could be useful and handy for general purpose.

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Labels: Fluid Flow

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