# Binary chromatographic retention times from perturbations in flowrate and composition

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- Received:
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- Accepted:

## Abstract

This work is a theoretical and experimental investigation of the binary retention time (*t*_{step}) when the disturbance is made to a chromatographic system by adding a small flow of one of the pure components. The established theory is for addition of a pulse: in this case, the retention time (*t*_{pulse}) depends on the two binary isotherm gradients, and should be independent of the choice of pulse gas. From the column material balance, the value of *t*_{step} also depends on the column pressure drop and perturbation gas—the value of *t*_{step} should always be greater for the more-adsorbed component. The theory has been validated from results on the nitrogen–argon–5A zeolite system at 25, 54 and 81 °C. For a 50% mixture at 25 °C with a column pressure drop of 0.1 bar, the values of *t*_{step} are 257 and 254 seconds for the nitrogen and argon perturbations. The values of *t*_{step} are different because addition of the perturbation flow causes a very small *increase* in average column pressure (about 0.5 mbar), which causes the binary isotherm gradients to be measured in (slightly) different directions along the isotherm surface. The intention is to determine the value of *t*_{step} for the case of a *zero change* in the average column pressure: experimentally, this would require a column with a zero pressure drop. The material balance shows that *t*_{step} for a column with a zero pressure drop is obtained from a simple weighted function of the values of *t*_{step} for the two pure-component perturbations. Accurate determination is essential because the “zero pressure drop” values are used to determine binary adsorption isotherms which are, of course, at a fixed pressure.

### Keywords

Binary adsorption Retention time 5A zeolite Column pressure drop### Abbreviations

*a*_{1}Henry’s constant for component A [m

^{3}kg^{−1}]*a*_{2}Langmuir constant for component A [m

^{3}mol^{−1}]*b*_{1}Henry’s constant for component B [m

^{3}kg^{−1}]*b*_{2}Langmuir constant for component B [m

^{3}mol^{−1}]*c*_{A}Gas-phase concentration of component A in column [mol m

^{−3}]*c*_{B}Gas-phase concentration of component B in column [mol m

^{−3}]*c*_{T}Total gas-phase concentration of components A and B in column [mol m

^{−3}]*F*_{A}Correction factor to allow for the change of

*c*_{A}in the column*F*_{B}Correction factor to allow for the change of

*c*_{B}in the column*G*Correction factor to allow for the change of

*c*_{A}in the column [m^{3}kg^{−1}]*K*_{A}Measured binary equilibrium constant for perturbation A [mL g

^{−1}]*K*_{B}Measured binary equilibrium constant for perturbation B [mL g

^{−1}]*K*_{CP}Binary equilibrium constant for constant column pressure [mL g

^{−1}]*K*_{step}Measured binary equilibrium constant for general perturbation [mL g

^{−1}]*K*_{mix}Measured binary equilibrium constant for mixture perturbation [mL g

^{−1}]*P*Dimensionless column pressure drop

*P*_{cmean}Mean column pressure [bar]

*P*_{cout}Outlet column pressure [bar]

*Q*Mean volumetric flowrate in column [mL s

^{−1}]*R*_{AB}Ratio of the Henry’s constants for components A and B

*t*_{A}Measured retention time for perturbation A [s]

*t*_{B}Measured retention time for perturbation B [s]

*t*_{CP}Retention time for column with negligible pressure drop [s]

*t*_{g}Measured retention time for unretained pulse [s]

*t*_{pulse}Measured retention time for pulse of one of components [s]

*t*_{step}Measured retention time for small and fixed perturbation flow [s]

*V*_{g}Volume of gas space in system between valve and detector [mL]

*W*Mass of adsorbent in column [g]

*w*_{A}Amount of component A adsorbed in mixture [mol kg

^{−1}]*w*_{A}^{0}Pure-component amount adsorbed of component A [mol kg

^{−1}]*w*_{B}Amount of component B adsorbed in mixture [mol kg

^{−1}]*w*_{B}^{0}Pure-component amount adsorbed of component B [mol kg

^{−1}]*y*_{A}^{0}Mole fraction of component A in main (or carrier) gas

*y*_{A}^{p}Mole fraction of component A in perturbation gas

*y*_{B}^{0}Mole fraction of component B in main (or carrier) gas

*y*_{B}^{p}Mole fraction of component B in perturbation flow

- Δ
*P*_{c} Pressure drop across column [bar]

- Δ
*P*_{r} Pressure drop across flow resistance [bar]

- \(\bigl[\frac{1}{\mu}\frac{\mathrm{d}\mu}{\mathrm{d}y_{\mathrm{A}}}(y_{\mathrm{A}}^{0})\bigr]\)
Normalised gradient of viscosity with composition at mole fraction

*y*_{A}^{0}

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