A Stochastic Model for Adsorption Kinetics
A novel stochastic model is proposed to characterize the adsorption kinetics of pollutants including dyes (direct red 80 and direct blue 1), fluoride ions, and cadmium ions removed by calcium pectinate (Pec-Ca), aluminum xanthanate (Xant-Al), and reed leaves, respectively. The model is based on a tr...
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| Format: | Article |
| Language: | English |
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SAGE Publishing
2021-01-01
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| Series: | Adsorption Science & Technology |
| Online Access: | http://dx.doi.org/10.1155/2021/5522581 |
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| author | Silvia Rodríguez-Narciso Juan Antonio Lozano-Álvarez Rogelio Salinas-Gutiérrez Netzahualcóyotl Castañeda-Leyva |
| author_facet | Silvia Rodríguez-Narciso Juan Antonio Lozano-Álvarez Rogelio Salinas-Gutiérrez Netzahualcóyotl Castañeda-Leyva |
| author_sort | Silvia Rodríguez-Narciso |
| collection | DOAJ |
| description | A novel stochastic model is proposed to characterize the adsorption kinetics of pollutants including dyes (direct red 80 and direct blue 1), fluoride ions, and cadmium ions removed by calcium pectinate (Pec-Ca), aluminum xanthanate (Xant-Al), and reed leaves, respectively. The model is based on a transformation over time following the Ornstein–Uhlenbeck stochastic process, which explicitly includes the uncertainty involved in the adsorption process. The model includes stochastic versions of the pseudo-first-order (PFO), pseudo-second-order (PSO), and pseudo-n-order (PNO) models. It also allows the estimation of the adsorption parameters, including the maximum removal capacity (qe), the adsorption rate constant (kn), the reaction pseudoorder (n), and the variability σ2. The model fitted produced R2 values similar to those of the nonstochastic versions of the PFO, PSO, and PNO models; however, the obtained values for each parameter indicate that the stochastic model better reproduces the experimental data. The qe values of the Pec-Ca-dye, Xant-Al-fluoride, and reed leaf-Cd+2 systems ranged from 2.0 to 9.7, 0.41 to 1.9, and 0.04 and 0.29 mg/g, respectively, whereas the values of kn ranged from 0.051 to 0.286, 0.743 to 75.73, and 0.756 to 8.861 (mg/g)1-n/min, respectively. These results suggest a variability in the parameters qe and kn inherent to the natures of the adsorbate and adsorbent. The obtained n values ranged from 1.13 to 2.02 for the Pec-Ca-dye system, 1.0–3.5 for the Xant-Al-fluoride system, and 1.8–3.8 for the reed leaf-Cd+2 system. These ranges indicate the flexibility of the stochastic model to obtain fractional n values, resulting in high R2 values. The variability in each system was evaluated based on σ2. The developed model is the first to describe pollutant removal kinetics based on a stochastic differential equation. |
| format | Article |
| id | doaj-art-fcffca6951634095b8077f34653f9065 |
| institution | Kabale University |
| issn | 0263-6174 2048-4038 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Adsorption Science & Technology |
| spelling | doaj-art-fcffca6951634095b8077f34653f90652025-01-03T01:22:56ZengSAGE PublishingAdsorption Science & Technology0263-61742048-40382021-01-01202110.1155/2021/55225815522581A Stochastic Model for Adsorption KineticsSilvia Rodríguez-Narciso0Juan Antonio Lozano-Álvarez1Rogelio Salinas-Gutiérrez2Netzahualcóyotl Castañeda-Leyva3Departamento de Estadística, Universidad Autónoma de Aguascalientes, Av. Universidad 940, Ciudad Universitaria, Ags., 20131 Aguascalientes, MexicoDepartamento de Ingeniería Bioquímica, Universidad Autónoma de Aguascalientes, Av. Universidad 940, Ciudad Universitaria, Ags., 20131 Aguascalientes, MexicoDepartamento de Estadística, Universidad Autónoma de Aguascalientes, Av. Universidad 940, Ciudad Universitaria, Ags., 20131 Aguascalientes, MexicoDepartamento de Estadística, Universidad Autónoma de Aguascalientes, Av. Universidad 940, Ciudad Universitaria, Ags., 20131 Aguascalientes, MexicoA novel stochastic model is proposed to characterize the adsorption kinetics of pollutants including dyes (direct red 80 and direct blue 1), fluoride ions, and cadmium ions removed by calcium pectinate (Pec-Ca), aluminum xanthanate (Xant-Al), and reed leaves, respectively. The model is based on a transformation over time following the Ornstein–Uhlenbeck stochastic process, which explicitly includes the uncertainty involved in the adsorption process. The model includes stochastic versions of the pseudo-first-order (PFO), pseudo-second-order (PSO), and pseudo-n-order (PNO) models. It also allows the estimation of the adsorption parameters, including the maximum removal capacity (qe), the adsorption rate constant (kn), the reaction pseudoorder (n), and the variability σ2. The model fitted produced R2 values similar to those of the nonstochastic versions of the PFO, PSO, and PNO models; however, the obtained values for each parameter indicate that the stochastic model better reproduces the experimental data. The qe values of the Pec-Ca-dye, Xant-Al-fluoride, and reed leaf-Cd+2 systems ranged from 2.0 to 9.7, 0.41 to 1.9, and 0.04 and 0.29 mg/g, respectively, whereas the values of kn ranged from 0.051 to 0.286, 0.743 to 75.73, and 0.756 to 8.861 (mg/g)1-n/min, respectively. These results suggest a variability in the parameters qe and kn inherent to the natures of the adsorbate and adsorbent. The obtained n values ranged from 1.13 to 2.02 for the Pec-Ca-dye system, 1.0–3.5 for the Xant-Al-fluoride system, and 1.8–3.8 for the reed leaf-Cd+2 system. These ranges indicate the flexibility of the stochastic model to obtain fractional n values, resulting in high R2 values. The variability in each system was evaluated based on σ2. The developed model is the first to describe pollutant removal kinetics based on a stochastic differential equation.http://dx.doi.org/10.1155/2021/5522581 |
| spellingShingle | Silvia Rodríguez-Narciso Juan Antonio Lozano-Álvarez Rogelio Salinas-Gutiérrez Netzahualcóyotl Castañeda-Leyva A Stochastic Model for Adsorption Kinetics Adsorption Science & Technology |
| title | A Stochastic Model for Adsorption Kinetics |
| title_full | A Stochastic Model for Adsorption Kinetics |
| title_fullStr | A Stochastic Model for Adsorption Kinetics |
| title_full_unstemmed | A Stochastic Model for Adsorption Kinetics |
| title_short | A Stochastic Model for Adsorption Kinetics |
| title_sort | stochastic model for adsorption kinetics |
| url | http://dx.doi.org/10.1155/2021/5522581 |
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