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Calibration and uncertainty analysis of a fixed-bed adsorption model for CO2 separation

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Abstract

Fixed-bed adsorption is widely used in industrial gas separation and is the primary method for atmosphere revitalization in space. This paper analyzes the uncertainty of a one-dimensional, fixed-bed adsorption model due to uncertainty in several model inputs, namely, the linear-driving-force (LDF) mass transfer coefficient, axial dispersion, heat transfer coefficients, and adsorbent properties. The input parameter uncertainties are determined from a comprehensive survey of experimental data in the literature. The model is first calibrated against experimental data from intra-bed centerline concentration measurements to find the LDF coefficient. We then use this LDF coefficient to extract axial dispersion coefficients from mixed, downstream concentration measurements for both a small-diameter bed (dominated by wall-channeling) and a large-diameter bed (dominated by pellet-driven dispersion). The predicted effluent concentration and temperature profiles are most strongly affected by uncertainty in LDF coefficient, adsorbent density, and void fraction. The uncertainty analysis further reveals that ignoring the effect of wall-channeling on apparent axial dispersion can cause significant error in the predicted breakthrough times of small-diameter beds.

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Notes

  1. See references Lo and Alok (1996), Farhadpour and Bono (1996), Abdel-Jabbar et al. (2001), Ko et al. (2001), Gomez-Salazar et al. (2003), Worch (2004), Chakraborty et al. (2005), Glover and LeVan (2008), Lv et al. (2008), Richard et al. (2010), Abu-Lail et al. (2012), Likozar et al. (2013), Nur et al. (2014), Gupta et al. (2015), Davila-Guzman et al. (2016), and Shao and Chen (2016).

  2. See references Hartzog and Sircar (1995), Ratto et al. (1996), Yu et al. (2009), Reijers et al. (2009a), Lu et al. (2016), Aguilera and Gutiérrez Ortiz (2016), and Zheng et al. (2016).

  3. See references Lo and Alok (1996), Farhadpour and Bono (1996), Ko et al. (2001), Hartzog and Sircar (1995), Reijers et al. (2009a, b), and Zheng et al. (2016).

  4. See references Abdel-Jabbar et al. (2001), Nur et al. (2014), Hartzog and Sircar (1995), Ratto et al. (1996), Yu et al. (2009), Naja and Volesky (2008), Maring and Webley (2013), and Kalyanaraman et al. (2014).

  5. See references Glover and LeVan (2008), Ratto et al. (1996), Reijers et al. (2009a), Maring and Webley (2013), Sircar et al. (1983), Delage et al. (2000), Sircar (2005), and Walton and LeVan (2005).

  6. See references Lo and Alok (1996), Farhadpour and Bono (1996), Abdel-Jabbar et al. (2001), Ko et al. (2001), Gomez-Salazar et al. (2003), Worch (2004), Chakraborty et al. (2005), Lv et al. (2008), Richard et al. (2010), Abu-Lail et al. (2012), Likozar et al. (2013), Nur et al. (2014), Gupta et al. (2015), Davila-Guzman et al. (2016), Shao and Chen (2016), Lu et al. (2016), Aguilera and Gutiérrez Ortiz (2016), Zheng et al. (2016), Naja and Volesky (2008), Kalyanaraman et al. (2014), and Borina and Pavko (2009).

  7. See references Lo and Alok (1996), Farhadpour and Bono (1996), Abdel-Jabbar et al. (2001), Ko et al. (2001), Likozar et al. (2013), Hartzog and Sircar (1995), Ratto et al. (1996), Yu et al. (2009), Reijers et al. (2009a), Zheng et al. (2016), Naja and Volesky (2008), Maring and Webley (2013), and Kalyanaraman et al. (2014).

Abbreviations

A :

Area, m2

A fr :

Free-flow area \((\pi {d_{{\text{can}},{\text{in}}}}^{2}/4),\) m2

\(c\) :

Molar concentration, mol/m3

\({c_p}\) :

Specific heat capacity, J/(kg K)

d :

Diameter, m

D eff, j :

Effective diffusivity of species j in the gas-phase mixture, \({(1/{D_{{\text{M}},j}}+1/{D_{{\text{K}},j}})^{ - 1}},\) cm2/s

\({D_{jk}}\) :

Binary diffusion coefficient of species j in species k, cm2/s

\({D_{{\text{K}},j}}\) :

Knudsen diffusivity of species j in the gas-phase mixture, cm2/s

\({D_{{\text{M}},j}}\) :

Molecular diffusivity of species j in the gas-phase mixture, cm2/s

\({D_{{\text{ax}}}}\) :

Axial dispersion coefficient, m2/s

h :

Heat transfer coefficient, W/(m2 K)

k :

Thermal conductivity, W/(m K)

k n :

Linear-driving-force (LDF) mass transfer coefficient, 1/s

\(k_{{{\text{eff}}}}^{0}\) :

Effective axial thermal conductivity of a quiescent bed, W/(m K)

\({k_{{\text{eff}}}}\) :

Effective axial thermal conductivity of bed with flow, W/(m K)

L :

Adsorbent bed length, m

M :

Molar mass, g/mol

p :

Pressure, kPa

q :

Adsorbate concentration in the adsorbed phase, mol/m3

q * :

Equilibrium adsorbed-phase concentration, mol/m3

t :

Time, s

t b :

Breakthrough time, s

\({\bar {t}_{{\text{stoich}}}}\) :

Stoichiometric breakthrough time, s

T :

Temperature, K

\(\Delta {T_{\text{g}}}\) :

Temperature change of gas across the bed, K

\({u_\infty }\) :

Superficial fluid velocity, m/s

\({u_{\text{i}}}\) :

Interstitial fluid velocity \(({u_\infty }/\varepsilon ),\) m/s

V :

Volume, m3

\({V_{{\text{bed}}}}\) :

Total bed volume \((\pi {d_{{\text{can}},{\text{in}}}}^{2}L/4)\), m3

\(\dot {V}\) :

Volumetric flow rate, SLPM (at 1 atm and 273.15 K)

\(z\) :

Axial position, m

\({y_j}\) :

Mole fraction of species j, (mol/mol)

\(\beta\) :

Radial dispersion factor

\(\varepsilon\) :

Void fraction of the adsorbent bed

\(\lambda\) :

Isosteric heat of adsorption, J/mol

\(\mu\) :

Dynamic viscosity, kg/(m s)

\(\rho\) :

Density, kg/m3

\({\rho _{{\text{env}}}}\) :

Pellet envelope density, kg/m3

\(\tau\) :

Tortuosity

\(\chi\) :

Total capacity measured as mass of CO2 adsorbed, g

0:

Inlet condition

amb:

Ambient

can:

Canister containing adsorbent

CO2 :

Carbon dioxide

g:

Gas-phase

init:

Initial

in:

Inner, inside

ins:

Insulation

max:

Maximum

mean:

Mean

out:

Outer, outside

p:

Pellet

s:

Adsorbent

\(Nu\) :

Nusselt number

\(Pe\) :

Peclet number \((Re \times Pr )\)

\(P{e_\infty }\) :

Peclet number at infinite velocity

\(Pr\) :

Prandlt number \((\mu {c_p}/k)\)

\({{Re} _{\text{p}}}\) :

Pellet Reynolds number \(({u_\infty }{d_{\text{p}}}{\rho _{\text{g}}}/{\mu _{\text{g}}})\)

\(S{c_j}\) :

Schmidt number of species j\(({\mu _{\text{g}}}/{\rho _{\text{g}}}{D_j})\)

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Acknowledgements

The first author acknowledges financial support from a National Aeronautics and Space Administration (NASA) Space Technology Research Fellowship (NSTRF Grant #NNX13AL55H). We thank Robert F. Coker for his assistance and invaluable advice in setting up the one-dimensional adsorption model.

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  1. School of Mechanical Engineering, Purdue University, West Lafayette, IN, 47907, USA

    Karen N. Son, Justin A. Weibel & Suresh V. Garimella

  2. George C. Marshall Space Flight Center, National Aeronautics and Space Administration, Huntsville, AL, 35812, USA

    James C. Knox

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  1. Karen N. Son
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Son, K.N., Weibel, J.A., Knox, J.C. et al. Calibration and uncertainty analysis of a fixed-bed adsorption model for CO2 separation. Adsorption 24, 781–802 (2018). https://doi.org/10.1007/s10450-018-9982-x

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