Method for separating helium from natural gas
Input(s)
\(\boldsymbol{D}_{\boldsymbol{A} \boldsymbol{B}}\): Diffusivity of Helium and Natural gas \(\left(\mathrm{cm}^{2} / \mathrm{s}\right)\)
\(\boldsymbol{c}_{\boldsymbol{H} \boldsymbol{1} \mathbf{1}}\): Concentration of Helium \((\mathrm{g} / \mathrm{s})\)
\(\boldsymbol{c}_{\boldsymbol{H e} 2}\): Concentration of Natural gas \((\mathrm{g} / \mathrm{s})\)
\(\boldsymbol{R}_{2}\): Outer Radius \((\mathrm{cm})\)
\(\boldsymbol{R}_{\mathbf{1}}\): Inner Radius (cm)
L: Length (cm)
Output(s)
\(\boldsymbol{W}_{\boldsymbol{H} \boldsymbol{e}}\): Mass Flux \((\mathrm{g} / \mathrm{cm})\)
Formula(s)
\[
\mathrm{W}_{\mathrm{He}}=2 * \pi * \mathrm{~L} * \frac{\mathrm{D}_{\mathrm{AB}} *\left(\mathrm{c}_{\mathrm{He} 1}-\mathrm{c}_{\mathrm{He} 2}\right)}{\ln \left(\frac{\mathrm{R}_{2}}{\mathrm{R}_{1}}\right)}
\]
Reference(s)
Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 18, Page: 573.