Determination of Pore and Surface Diffusivities from Single Decay Curve in CSBR Based on Parallel Diffusion Model
Abstract
:1. Introduction
2. Parallel Diffusion Model in Dimensionless Form
3. Results and Discussion
3.1. RD Dependence of Adsorption Profiles and Decay Curves
3.2. Determination of the Time Ratio T0.2/T0.8 from Concentration Decay Curves
3.3. Relationship between T0.2/T0.8 and RD
3.4. Determination Procedure with Experimental Data
3.5. Summary of the Determination Procedure
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
ap: | Surface area based on solid particle | [cm2/cm3] |
Bi: | Biot number = kfrp/(Dsβρs) | [-] |
ce: | Equilibrium concentration at time = infinity | [mg/L] |
cs: | Fluid concentration at r = rp | [mg/L] |
ct: | Concentration within the vessel at time t | [mg/L] |
c0: | Concentration within the vessel at time = 0 | [mg/L] |
Cm: | Dimensionless concentration | [-] |
Dp: | Pore diffusivity | [cm2/s] |
Ds: | Surface diffusivity | [cm2/s] |
kf: | Fluid film mass transfer coefficient | [cm/s] |
m: | Weight of adsorbent | [g] |
1/n: | Freundlich exponent | [-] |
qe: | Amount adsorbed in equilibrium with ce | [mg/g] |
qt: | Average amount adsorbed within the adsorbent at time t | [mg/g] |
q0: | Amount adsorbed at equilibrium with fluid concentration c0 | [mg/g] |
Qm: | Dimensionless amount of adsorption | [-] |
r: | Internal radial length (length from the solid center) | [cm] |
rp: | Particle radius | [cm] |
RD: | Ratio of diffusion resistance = Dp/(Dsβρs) | [-] |
t: | Time | [min] |
V: | Volume of the vessel | [L] |
β: | q0/c0 | [L/g] |
ε: | Porosity | [-] |
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Seida, Y.; Sonetaka, N.; Noll, K.E.; Furuya, E. Determination of Pore and Surface Diffusivities from Single Decay Curve in CSBR Based on Parallel Diffusion Model. Water 2022, 14, 3629. https://doi.org/10.3390/w14223629
Seida Y, Sonetaka N, Noll KE, Furuya E. Determination of Pore and Surface Diffusivities from Single Decay Curve in CSBR Based on Parallel Diffusion Model. Water. 2022; 14(22):3629. https://doi.org/10.3390/w14223629
Chicago/Turabian StyleSeida, Yoshimi, Noriyoshi Sonetaka, Kenneth E. Noll, and Eiji Furuya. 2022. "Determination of Pore and Surface Diffusivities from Single Decay Curve in CSBR Based on Parallel Diffusion Model" Water 14, no. 22: 3629. https://doi.org/10.3390/w14223629
APA StyleSeida, Y., Sonetaka, N., Noll, K. E., & Furuya, E. (2022). Determination of Pore and Surface Diffusivities from Single Decay Curve in CSBR Based on Parallel Diffusion Model. Water, 14(22), 3629. https://doi.org/10.3390/w14223629