iMixer
Calculations
iMixer
can generate blending plans using both
ideal and real gas calculations. Many
gasses follow the ideal gas law very
closely at low pressures. As gas
pressures increase blending calculations
using the ideal gas law begin to loose a
little accuracy. This is because no gas
is truly ideal. In most cases the
difference in blending plans created
using ideal gas verses real gas
calculations fall within an acceptable
margin of error. iMixer provides
both sets of calculations.
The Ideal
Gas Law describes the relationships
among the four variables temperature
(T), pressure (P), volume (V), and moles
of gas (n):
p V = n R T
p = absolute pressure
(not gauge pressure)
V = volume
n = amount of gas
(moles)
R = ideal gas constant
T = absolute temperature
(Kelvin)
Real gas laws try to predict the true
behavior of a gas by putting in terms to
describe attractions and repulsions
between molecules. One real gas law is
the van der Waals equation:
[P + (n^{2}a/V^{2})](V
 nb) = nRT
P  pressure
V  volume
n  number of moles
T – temperature (Kelvin)
R  ideal gas constant
The first parameter, a, is approximates
the attractive forces between molecules
while the second parameter, b, is
approximates the repulsive forces.
Tables for a and b values for a specific
gas can be found in many Chemical
Engineering textbooks.
If the units of P, V, n and T are atm,
L, mol and K, respectively, the metric
value of R is 0.0821 while the imperial
value is 10.73159. The constants a and b
for N_{2} is 1.408 and 0.03913.
For O_{2 }the a and b constants
are 1.378 and 0.03183. For He they are
0.03457 and 0.0237.
_{
}
To calculate the volume of a real gas, V
in term n^{2}a/V^{2} can
be approximated as: nR/T (from the ideal
gas calculation). Volume and pressure
can be calculated with these formulas:
V = nR^{3}T^{3}/(PR^{2}T^{2}+aP^{2})
+ nb
P = nRT/(V  nb)  n^{2}a/V^{2}
Calculations using the ideal gas law can
be performed in units of pressure (PSI,
BAR) or volume (FT^{3}, L^{3}).
Computations are simple and easy to
validate. Calculations using the van der
Walls equation are performed using
quantity of gas (mols).
Due to the correction factors a and b
approximating the attraction and
repulsion of molecules the process of
producing a blending plan is a little
more complex. We start by figuring out
the quantity of the O_{2}, N_{2},
and He components of the starting gas.
We then calculate the quantity of gas
(in mols) to be added at each step in
the process using either O2, He, bank
gas, or top off gas. After adding gas at
each step we recalculate the pressure
and continue adding gas until we reach
our target.
A good source for information on real
and ideal gasses can be found at
SoftChemistry online (www.molecularsoft.com).
