Determination of Kinetic Parameter in a Unified Kinetic Model for the Photodegradation of Phenol by Using Nonlinear Regression and the Genetic Algorithm
-
Jesus Moreira
,
Benito Serrano-Rosales
Abstract
This study reports the kinetic parameter estimation in the photocatalytic degradation of phenol over different TiO2 catalysts by using the Genetic Algorithm (GA) and nonlinear regression. Reaction networks are based on a previously reported unified kinetic model (UKM) of the Langmuir–Hinshelwood type. Nonlinear least-squares fitting and GA are used to find the values for the kinetic constants. The computed parameters were found to predict experimental data for phenol photodegradation at different levels of concentrations. It is shown that both methods render close values for the kinetic constants. This suggests that UKM approach gives the global minimum and as a result, this method provides good and objective parameter estimates with low to moderate cross-correlation among kinetic constants and acceptable 95% Confidence Intervals (CIs). Global optimization by using GA requires extensive computer times of up to 5 minutes. Least square fitting provides the same results with computer times of seconds only. It is then concluded that the UKM approach effectively avoids overparameterization by finding the global optimum when optimizing the kinetic constants.
Acknowledgments
Jesus Moreira acknowledges CONACyT-Mexico for the graduate scholarship. We would also like to express our appreciation to the Natural Sciences and Engineering Research Council of Canada for the financial support provided to support this research. Dr. B. Serrano would like to thank Project CONACYT-Mexico-Ciencia Basica 2007–83144 and Federal program P/PIFI 2010–32MSU0017H-09 for their financial support.
Nomenclature
- C
concentration, mol l–1
- Ce
concentration in the liquid phase at equilibrium (mg-C l–1)
- i
denotes component i
- j
denotes component j
- LVRPA
Local volumetric rate of photon absorption, einsteins m–3
- K
apparent constants, min–1
- KA
adsorption constant of component (mg-C–1 l)
- ki
intrinsic kinetic constant, min–1
- kk
reaction kinetic constant, mol gcat–1 min–1
- Mcat
weight of the TiO2 catalyst, g
- mg-C
milligrams of carbon
- N
number of moles
- ppm-C
parts per million of carbon in the organic species
- Qe
amount of compound per unit weight (mg-C gcat–1)
- Qmax
maximum amount of absorbed compound per unit weight at equilibrium (mg-C gcat–1)
- r
reaction rate, mol gcat–1 min–1
- t
time, min
- V
volume of reactor, l
- Wirr
weight or irradiated catalyst, g
Acronyms
- 1,4-BQ
Benzoquinone
- Ac
acetic acid
- CI
confidence intervals
- CREC
Chemical Reaction Engineering Centre
- FoAc
formic acid
- KM
kinetic models
- L-H
Langmuir–Hinshelwood
- LuAc
lumped terms of carboxylic acids
- ODEs
Ordinary Differential Equations
- o-DHB
ortho-dihydroxybenzene or catechol
- OxAc
oxalic acid
- p-DHB
para-dihydroxybenzene or hydroquinone
- RN
reaction network
- TOC
total organic carbon
- UKM
Unified Kinetic Model
- UV
ultra violet
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©2013 by Walter de Gruyter Berlin / Boston
Articles in the same Issue
- Masthead
- Masthead
- Editorial
- In Honor of Alberto E. Cassano: Researcher, Engineer, and Academic
- Articles
- From Ideal Reactor Concepts to Reality: The Novel Drum Reactor for Photocatalytic Wastewater Treatment
- Synthesis, Characterization, and Comparison of Sol–Gel TiO2 Immobilized Photocatalysts
- Determination of Kinetic Parameter in a Unified Kinetic Model for the Photodegradation of Phenol by Using Nonlinear Regression and the Genetic Algorithm
- Mass Transfer and Conservation from a Finite Source to an Infinite Media
- Modelling and Simulation of Gas–liquid Hydrodynamics in a Rectangular Air-lift Reactor
- Two-Dimensional Modeling of an Externally Irradiated Slurry Photoreactor
- Role of Aspect Ratio and Joule Heating within the Fluid Region Near a Cylindrical Electrode in Electrokinetic Remediation: A Numerical Solution based on the Boundary Layer Model
- Solar Water Disinfection Using NF-codoped TiO2 Photocatalysis: Estimation of Scaling-up Parameters
- A Simple and Semi-Empirical Model to Predict THMs Generation in Water Facilities Including pH Effects
- On the Standardization of the Photocatalytic Gas/Solid Tests
- Microalgae Technology: A Patent Survey
- Influence of Physical and Optical Parameters on 2,4-Dichlorophenol Degradation
- Factors Capable of Modifying the Response of Pseudomonas aeruginosa to the Inactivation Induced by Heterogeneous Photocatalysis
- Enhanced Antibacterial Activity of CeO2 Nanoparticles by Surfactants
- Determination of Photochemical, Electrochemical and Photoelectrochemical Efficiencies in a Photoelectrocatalytic Reactor
- Correlations between Molecular Descriptors from Various Volatile Organic Compounds and Photocatalytic Oxidation Kinetic Constants
- Role of Joule Heating in Electro-Assisted Processes: A Boundary Layer Approach for Rectangular Electrodes
Articles in the same Issue
- Masthead
- Masthead
- Editorial
- In Honor of Alberto E. Cassano: Researcher, Engineer, and Academic
- Articles
- From Ideal Reactor Concepts to Reality: The Novel Drum Reactor for Photocatalytic Wastewater Treatment
- Synthesis, Characterization, and Comparison of Sol–Gel TiO2 Immobilized Photocatalysts
- Determination of Kinetic Parameter in a Unified Kinetic Model for the Photodegradation of Phenol by Using Nonlinear Regression and the Genetic Algorithm
- Mass Transfer and Conservation from a Finite Source to an Infinite Media
- Modelling and Simulation of Gas–liquid Hydrodynamics in a Rectangular Air-lift Reactor
- Two-Dimensional Modeling of an Externally Irradiated Slurry Photoreactor
- Role of Aspect Ratio and Joule Heating within the Fluid Region Near a Cylindrical Electrode in Electrokinetic Remediation: A Numerical Solution based on the Boundary Layer Model
- Solar Water Disinfection Using NF-codoped TiO2 Photocatalysis: Estimation of Scaling-up Parameters
- A Simple and Semi-Empirical Model to Predict THMs Generation in Water Facilities Including pH Effects
- On the Standardization of the Photocatalytic Gas/Solid Tests
- Microalgae Technology: A Patent Survey
- Influence of Physical and Optical Parameters on 2,4-Dichlorophenol Degradation
- Factors Capable of Modifying the Response of Pseudomonas aeruginosa to the Inactivation Induced by Heterogeneous Photocatalysis
- Enhanced Antibacterial Activity of CeO2 Nanoparticles by Surfactants
- Determination of Photochemical, Electrochemical and Photoelectrochemical Efficiencies in a Photoelectrocatalytic Reactor
- Correlations between Molecular Descriptors from Various Volatile Organic Compounds and Photocatalytic Oxidation Kinetic Constants
- Role of Joule Heating in Electro-Assisted Processes: A Boundary Layer Approach for Rectangular Electrodes
