Accurate blank corrections for zero length column experiments
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Accurate blank corrections for zero length column experiments Maarten Verbraeken1 · Alessio Centineo1 · Luigi Canobbio1 · Stefano Brandani1 Received: 14 October 2020 / Revised: 26 October 2020 / Accepted: 29 October 2020 © The Author(s) 2020
Abstract In this study we present a new methodology for correcting experimental Zero Length Column data, to account for contributions to the measured signal arising from extra-column volumes and the detector. The methodology considers the experimental setup as a series of mixing volumes with diffusive pockets whose contributions to the overall measured signal can be accurately described by simple model functions. The composite effect of the individual contributions is subsequently described through the method of convolution. It is shown that the model parameters are closely related to the physical characteristics of the setup components and as such they remain valid over a range of process conditions. The methodology is firstly validated through fitting to experimental experiments without adsorbent present. The inverse procedure of deconvolution can in turn be applied to experimental data with adsorbent, to yield corrected data which can readily be modelled using standard tools for equilibrium and kinetic analysis. A number of case studies is finally presented exemplifying the effect of applying accurate blank corrections, demonstrating also the application to a nonlinear adsorption system. Keywords Blank correction · Zero length column experiment · Deconvolution · Adsorption equilibrium · Adsorption kinetics Abbreviations Apipe Cross sectional area of diffusive pipe (m2) C Dimensionless concentration Cin Dimensionless inlet concentration c Concentration at time t (mol m–3) c0 Concentration at time zero (mol m–3) c∞ Concentration at infinite time (mol m–3) cT Total gas concentration (mol m–3) D Diffusivity (m2s–1) F Flowrate (m3 s–1) Fin Flowrate entering ZLC (m3 s–1) F(t) Function defined by Eq. (15) G(t) Laplace transfer function LMS Dimensionless parameter described by Eq. (21) LT1 Dimensionless parameter described by Eq. (12) Ldiff Diffusion length in slab side pocket (m) P Pressure (Pa)
Q Dimensionless concentration in diffusive side pocket Q Average dimensionless concentration in diffusive side pocket q∗ Equilibrium amount adsorbed (mol m–3) R Ideal gas constant (J mol–1 K–1) T Temperature (K) t Time (s) u Convolution integrand (s) VCSTR Volume of well mixed cells (m3) Vdiff Volume of diffusive side pocket (m3) Vf Fluid volume ZLC (m3) Vmix Volume in mixing cell connected to diffusive side pocket (m3) Vs Volume of adsorbent (m3) x Spatial coordinate (m) yin Mole fraction of adsorbate entering ZLC yout Mole fraction of adsorbate leaving ZLC
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10450-020-00281-w) contains supplementary material, which is available to authorized users.
Greek symbols 𝛼 Correction factor for diffusive length (m) 𝛽slab,n Roots of Eq. (15) 𝛽spher
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