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Parametric sensitivity analysis and ozone mass transfer modeling in a gas–liquid reactor for advanced water treatment
Accepted Manuscript Title: Parametric sensitivity analysis and ozone mass transfer modeling in a Gas-Liquid reactor for advanced water treatment Author: Valent´ın Flores-Pay´an Enrique J. Herrera-L´opez Javier Navarro-Laboulais Alberto L´opez-L´opez PII: DOI: Reference:
S1226-086X(14)00293-7 http://dx.doi.org/doi:10.1016/j.jiec.2014.05.044 JIEC 2071
To appear in: Received date: Revised date: Accepted date:
17-12-2013 7-5-2014 8-5-2014
Please cite this article as: V. Flores-Pay´an, E.J. Herrera-L´opez, J. Navarro-Laboulais, A. L´opez-L´opez, Parametric sensitivity analysis and ozone mass transfer modeling in a Gas-Liquid reactor for advanced water treatment, Journal of Industrial and Engineering Chemistry (2014), http://dx.doi.org/10.1016/j.jiec.2014.05.044 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Parametric sensitivity analysis and ozone mass transfer modeling in a Gas-
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Liquid reactor for advanced water treatment
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4 Valentín Flores-Payána, Enrique J. Herrera-Lópeza, Javier Navarro-Laboulaisb,
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Alberto López-Lópeza,*
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Avenida Normalistas 800, Col. Colinas de la Normal, C.P. 44270, Guadalajara Jalisco,
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Centro de Investigación y Asistencia en Tecnología y Diseño del Estado de Jalisco A.C.,
México
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Camino de Vera s/n, 46022, Valencia España.
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Universidad Politécnica de Valencia, Departamento de Ingeniería Química y Nuclear,
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*Corresponding author. Tel: +52 33 33455200, Fax: +52 33 33455245
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E-mail address: [email protected]; [email protected] (Alberto López-López)
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Abstract
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A computational model for a reactor used in advanced water treatment was proposed to
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represent, simulate and predict the mass transfer process of ozone in water (gas-liquid). A
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graphic interface was designed to simulate the ozone gas transfer into the liquid. In addition,
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the values of the mass transfer coefficient, and the self-decomposition of ozone, could be
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determined for different initial conditions. The model for ozone mass transfer was represented
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by two differential equations derived from the mass balances of the system. Finally a
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sensitivity analysis was made to determine the effect of the parameters over the operating
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variables.
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11 Keywords: Modeling, Mass transfer, Parametric sensitivity, Ozone, Water treatment 12
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1 Introduction
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Advanced Oxidation Processes (AOPs) refers to highly competitive water treatment
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technology for the removal of organic pollutants not treatable by conventional techniques due
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to their high chemical stability and low biodegradability. AOPs using ozone (O3) can be
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applied in wastewater pre-treatment or post-treatment stages [1]. The main AOPs are O3/pH,
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O3/H2O2, O3/UV, O3/Cat++ O3/H2O2/UV and O3/Cat++/UV. In alkaline ozonation the averages
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speed of self-decomposition of O3 in water increases and with it, the speed of generation of
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radicals. The addition of hydrogen peroxide combined with ozone starts a cycle of radical
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ozone decomposition forming hydroxyl. Direct photo-oxidation with UV radiation has
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emerged as an alternative technology for the degradation of pollutants agents. On the other
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hand, the efficiency of ozone and the use of combined hydrogen peroxide with ultraviolet
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radiation increase the speed of refractory compound degradation [2-4]. The advanced
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oxidation processes using ozone consists of the combination of O3 with one or more oxidants
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to generate hydroxyl radicals (HO•) in sufficient amounts to interact with the organic
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compounds present in an aqueous medium. AOPs differ in the method used to generate
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hydroxyl radicals. AOPs using O3 in treating contaminated water with recalcitrant organic
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matter are carried out regularly in gas-liquid reactors (ozone-water). The successful
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implementation of the ozonation process in water treatment depends basically on two aspects
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[5]:
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i) The reaction kinetics: basically represented by the reactivity of ozone and organic matter,
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and the stoichiometric ratio or ozone consumption associated to the degradation rate constant.
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ii) The mass transfer process of ozone in water: represented by the overall mass transfer
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coefficient (kLa), the self-decomposition of O3 (kc), and the fraction of gas in the reactor (),
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among other hydrodynamic transfer parameters.
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Therefore, reaction kinetics and the mass transfer of ozone in the liquid are important
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parameters for designing and applying AOPs using ozone. It would be valuable to model and
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simulate these variables under different process conditions, i.e., greater process efficiency will
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be expected, with a combination of high mass ozone transfer to the liquid (kLa) and a lower
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ozone self-decomposition coefficient (kc). Adequate or even optimal conditions of (kLa) and
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(kc) can be obtained for the proper operation of the ozonation process from modeling the
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effect of temperature, pH, reactor agitation and ozone concentration in the liquid and gas
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phases [6-8]. Ozone is a scarcely soluble gas, and the transfer efficiency is mainly controlled
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by its thermodynamic properties [9-12].
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Benbelkacem et al., [6] reported a model of mass transfer in a semi continuous gas-liquid
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reactor, where the chemical reactions were irreversible. The model was solved using
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numerical computation and the results were included in the mass balance within the reactor.
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Navarro et al., [13] developed a model for monitoring a gas-liquid reactor in semi-continuous
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flow analysis. The model predicted an observed signal in a detector when a continuous flow
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analysis was used to monitor the ozone gas-liquid phase; the model combined the mass
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transfer and the kinetic process in the reactor.
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Wu and Masten [14] developed a mass transfer model to simultaneously predict
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concentrations of the dissolved and outlet gaseous ozone in a semibatch reactor from a well
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mixed liquid phase and a gas phase described as a plug-flow system. The self-decomposition
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of ozone was also incorporated into the model. The mass transfer coefficient augmented when
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the gas-flow rate, temperature, and ionic strength in the solution increased. In addition, these
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authors using parametric sensitive analysis found that the dissolved ozone was the factor that
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had the greatest effect over the concentrations profiles.
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The objective of this research was to propose: i) a graphic interface representing the process
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of transference of O3 in water; ii) simulate the response of O3 in gas and liquid phase,
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considering only the mass transfer process, regardless of the reaction kinetics; iii) to evaluate
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the performance of kLa and kc in function of the temperature, pH and dosage of O3; and iv)
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perform a parametric sensitivity analysis on the equations of O3 in the gas and liquid phase to
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determine the parameters having the greatest effect over the process variables. From the
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model and the parametric sensitivity results, optimization and control strategies could be
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designed in the near future for the AOP using O3 for water treatment. The first part of the
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results section describes the model and the graphical interface, as well as the model validation
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with a set of experimental data. The second part describes the developed sensitivity analysis
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used to evaluate the effect of operating variables in the transfer of gas-liquid mass (G-L)
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11 2 Material and methods
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2.1 System description for monitoring O3 on-line
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The experimental system to monitor the O3 on-line in the liquid and gas phase is shown in
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(Fig. 1). The system includes: 1) oxygen cylinder; 2) an ozone generator G11 Pacific Ozone
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with a production of 16.9 g/h, which was fed by 99% pure oxygen; 3) a flow control valve of
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the brand Bronkhorst model F-201CV-10K-AGD-22-V; 4) a three-way flow control valve
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of the brand SMC model VDW350-5G-3-02N-H-F; 5) flow meter of the brand
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Bronkhorst model F-11B-10k-AGD-22-V; 6) a reactor Applikon, with 4 litres of volume
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and a ratio height: diameter (H:D) equal to 1.5; 7) pH sensor; 8) temperature sensor; 9)
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stirring motor; 10) peristaltic pump; 11) liquid phase ozone sensor; 12) phase liquid ozone
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meter of the brand ATI model Q45H/64, ozone measurements were performed by a sensor
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which was introduced into an acrylic cell which is filled with the effluent extracted from the
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reactor by a peristaltic pump and Teflon hoses which are resistant to ozone corroding; 13) pH
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meter and controller of the brand B&C Electronics Model 7685; 14) a meter and
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temperature controller of the brand B&C Electronics Model TR7615, which has a platinum
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thermoresistance 100, this meter has a scale of 0-199 ºC; 15) a mechanical agitation controller
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Applikon Model ADI 1032 with a speed range of 0-1250 rpm; 16) a gas phase ozone meter
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of the brand Teledyne Model 465H, operating in a range of 0-400 g/Nm3 with an accuracy
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of 0.5%; 17) a thermal ozone decomposition unit of the brand Pacific Ozone, which
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transforms the residual ozone in oxygen; 18) data acquisition system based in the control card
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USB-1024SL of Computing; 19) computer and the user interface designed with the
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software Labview® 8.2. This interface was used to monitor and manipulate the experimental
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variables of the water treatment process.
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2.2 The mathematical model for the ozone mass transfer
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A mathematical model for the transference of ozone gas to the liquid phase (water) in a
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reactor used for advanced wastewater treatment can be established from the gas and liquid
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phase mass balances, and assuming the following hypothesis:
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The liquid phase was considered perfectly mixed.
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ii.
The concentration of ozone was considered constant in the entirely reactor volume.
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The concentration value corresponds to the result of integrating the balance equation
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of a piston flow reactor under steady conditions.
iii.
The gas hold-up is around ≈2.0%, therefore it was assumed that VL≈V in the reactor.
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The mass balance in the gas phase was expressed as:
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k L aVL (CL* C L )dt Qg C gin dt Qg C gout dt Vg dC g
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and in the liquid phase:
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k L aVL (C L* CL )dt VL dC L kcCLVL dt
(1)
(2)
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Isolating dC g / dt and dCL/dt from equations (1) and (2) the following expressions were
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obtained:
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Qg Vg
C
gin
C gout
VL k L a * CL CL Vg
(3)
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dCL k L a CL* CL kcCL dt
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Here, VL is the liquid volume in the reactor (m3), C L* is the concentration of ozone in water in
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equilibrium with the gas (mol·m-3), dC g is the average concentration in gas phase (mol·m-3),
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CL is the dissolved ozone concentration in the solution (mol·m-3), Qg is the gas flow (mol·s-1),
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Cgin and Cgout are the concentration of O3 at inlet and outlet of the reactor (mol·m-3), Vg is the
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volume of gas in the reactor (m3), kLa is the mass transfer coefficient and kc is the constant
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self-decomposition of ozone and could be determined by equation (5) suggested by Roth and
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Sullivan [15];
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kc 1.6352 106 OH
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The ozone solubility in water can be obtained from Henry’s law and expressed by the
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equation (6) [16]:
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CL*
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Here, T is the temperature (ºC). Equation (5) is dependent of the pH and equation (5) and (6)
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are dependent of temperature.
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C gin
1.59e( 0.0437T )
(5)
(6)
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2.3 Graphic interface to simulate the ozone mass transfer
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A graphic interface to simulate equations 3 and 4 was designed with the software Matlab®
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7.0 (Fig. 2). The user can set the initial values of Qg, Cgin, Vg, VL, T, pH, and dosage of O3.
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The values of kLa and kc and the behavior of the O3 in the liquid and gas phases are displayed
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in the interface.
3 2.4 Analytic techniques
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The ozone concentration in the liquid phase was determined by the colorimeter method [17]
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and was used to validate the on-line measurements.
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3 Results
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3.1 Simulation results for the ozone mass transfer
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Fig. 2 shows the evolution of the ozone gas transference to the liquid as a function of time for
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the following initial conditions: VL=0.004 m3, T=10 ºC, pH=7.0, Qg=2.7×10-5 m3·s-1, Vg=
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0.001 m3 and Cgin=33.2 mg·L-1. Once initial values of the variables were introduced and after
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executing the simulation, the interface showed the concentration profiles of ozone in the water
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and in the gas phase. The program determined the values of kLa using values of the ozone
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concentration in the water during the transitional phase transfer model (Fig. 3). Diverse
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simulations were performed varying the pH, temperature and ozone concentration to
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determine different values of kLa and kc given by the mathematical model. The results are
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shown in Tables 1, 2 and 3.
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3.1.1 Influence of the pH over kLa and kc
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The effect of pH over kLa and kc was investigated. The pH was varied according to the
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following values 1.5, 4, 7, 9 and 11, Qg and Cgin were kept constant to 2.7 x 10-5 m3·s-1 and
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33.2 mg·L-1 respectively. The Table 1 shows that for our model the value of kc increased as
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the pH of the medium rose. This is evident since in an alkaline medium the formation of free
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radicals HO• generate chain reactions by increasing the speed of destruction of ozone, as has
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been reported in the literature, [4] and [18]. However, the value of the transfer constant kLa
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practically had the same order of magnitude. This result was consistent with the literature [4,
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18], taking into account that with a pH greater than 7.0 the self-decomposition of the ozone
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increased, hindering the ozone transferred measurement into the transitional stage of the mass
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transfer process, consequently reflecting a decrease in the kLa. That is, the rate of self-
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decomposition of ozone was greater than the rate of the analyzer detection.
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3.1.2 Influence of the inlet ozone concentration over kLa and kc
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The influence of the inlet ozone concentration in the reactor over the parameters kLa and kc
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was evaluated. The concentration of O3 was varied according to the following values 8, 13.2,
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23.2, 33.2 and 40 mg·L-1, and maintaining constant Qg = 2.7 x 10-5 m3·s-1 and the pH=7.0. It
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can be seen in Table 2, that the value of kLa remained constant for all the conditions tested.
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This result was consistent with the fundamentals of hydrodynamics since by keeping the gas
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velocity, the rate transfer gas-liquid remained constant. The parameter kc also remained
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constant for all the conditions tested of the gas used, confirming that kc is a variable
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depending on chemical factors and nor on physical one [4].
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TABLE 2
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3.1.3 Influence of the temperature over kLa and kc
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Table 3 shows the influence of different temperatures (5, 10, 20, 25, and 30 ºC) on the
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parameters kLa and kc during the ozone transfer into liquid phase. The pH and Cgin were kept
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constant. It was observed that the value of kc increased as the temperature did. This result is
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logical since kc is a variable depending directly proportional to the temperature. On the other 9
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hand, the value of kLa decreased as the temperature increased because the molecular ozone in
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the bulk liquid is transformed into radicals HO• which are responsible for the oxidation in the
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ozone treatment process.
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Finally the model was validated with experimental data under the following conditions:
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Qg=2.7×10-5 m3·s-1, VL=4L and T=20ºC. Fig. 4 shows the concentration profiles of ozone in
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the gas phase and in the liquid phase obtained experimentally. Additionally Fig. 4 shows the
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concentration profiles generated by the graphic interface under the same experimental
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conditions. During the continuous process of saturation with O3 in demineralized water, two
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regions were observed, the transitory and the stationary. An error of 4.1 % and 2.68 % were
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obtained for the liquid and the gas phases, respectively. Once the correct performance of the
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mathematical model was validated (3-4), it would be helpful to determine which parameters
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in this model had more influence over the process variables.
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3.2 Parametric sensitivity analysis
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A sensitivity analysis is used to determine the effect of the operational parameters of the
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system such as temperature, pH and ozone dose over the state variables of the mathematical
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model; in this case the model of ozone mass transfer. The mathematical model (3-4) was
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expressed as:
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x f ( x, t , )
(7)
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where x is the state variable, x is the time derivative of x, t is the time, and ρ are the
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parameters of the model. It was possible to determine the effect of the parameters over the
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state equations from the following relationship:
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f f S S x
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where
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S1,1 S 2,1 S Si ,1
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and
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Si , j
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In order to perform a parametric sensitivity analysis to the mass balance of ozone in the gas
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(9)
(10)
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phase and liquid phase (3-4), it was defined Qg VL k L a * CL CL V C gin C gout V f ( x) g g k a C * C k C L L c L L
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S1, j S 2, j Si , j
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S1, 2 S1,3
(8)
(11)
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and
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ρ = (Qg, Cgin, Vg, VL, C L* , kLa, kc)
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The analysis begins with the partial derivatives of equations (11) with respect to x:
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Q VL k L a g f Vg Vg x 0 (k L a kc )
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Subsequently, equation (11) is partially derived with respect to the seven parameters
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contained in the vector ρ:
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f 0
CL * 0 CL CL 0 k L a 0 CL
(12)
(13)
(14)
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where:
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3
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C
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C
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C gin
Vg
C gout Vg
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CL VL Vg
CL k L a Vg
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Qg C gin C gout VL k L a CL* C L
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Then from equations (7) and (12) the following system of differential equations was obtained:
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C C gout Q Vk a S11 L L S11 g S 21 gin Vg Vg Vg
(15)
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Q Q Vk a S12 L L S12 g S 22 g Vg Vg Vg
(16)
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V C * CL Q Vk a S13 L L S13 g S 23 L L Vg Vg Vg
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Q Vk a S14 L L S14 g S 24 Vg Vg
(18)
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Q Vk a Vk a S15 L L S15 g S 25 L L Vg Vg Vg
(19)
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Qg C ge C g Q Vk a S16 L L S16 g S 26 2 Vg V Vg g
(20)
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(17)
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Q Vk a S17 L L S17 g S 27 Vg Vg
(21)
2
S21 k L a kc S11
(22)
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S22 k L a kc S12
(23)
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S23 k L a kc S13 CL* CL
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S24 k L a kc S14
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S25 k L a kc S15 k L a
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S26 k L a kc S16
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S27 k L a kc S17 CL
(24)
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(27) (28)
Equations (1-2) and (15-28) were simultaneously solved with the function ode45 in Matlab®
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7.0. The initial condition for equations (15-28) was set to zero. Fig. 5 shows the effect of the
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ozone flow (Qg) within the mass transfer model. It can be seen that Qg does not had an
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influence on the liquid phase (continuous line) since this variable remained equal to zero
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during the simulation. On the other hand, Qg had a significant positive effect (on the gas
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phase, dashed line) of 5.57×105 and 1.4×105 in the transition and stationary phases,
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respectively.
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In Fig. 6 the effect of ozone concentration of gas (Cgin) in the inlet of the reactor was
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analysed. This figure shows that the concentration of ozone in the liquid phase was not
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affected by this parameter. Indeed, the concentration of O3 in the liquid should not be affected
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by changing Cgin since this value is dependent on the thermodynamic conditions of the
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environment and the availability of the gas. Cgin had a positive effect on the concentration of
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ozone in the gas phase during the transitional stage of the process stabilizing during the
2
stationary stage.
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The effect of the volumetric mass transfer coefficient kLa in the gas and liquid phase is shown
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in Fig. 7. Clearly this parameter had influence in both variables of the model (3-4), having a
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significant negative effect on the concentration of ozone in the gas phase and a positive effect
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on the liquid phase during the transitional stage and less during the stationary stage of the
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mass transfer process. This is consistent, since the determination of the constant kLa according
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to our mass transfer model, was obtained in the transition stage.
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Fig. 8 shows that the reactor volume (VL) had an adverse effect on the ozone concentration in
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the gas phase during the transient stage of the process, stabilizing in the stationary phase. The
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concentration of ozone in the liquid was not affected during the mass transfer process. This
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can be explained from the fact that increasing the volume of the liquid at a constant flow rate
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and a constant inlet gas concentration will reduce the outlet gas concentration.
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The gas volume (Vg) had a negative significant effect in the ozone concentration in the gas
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phase during the transient stage and is stable in the stationary phase, (Fig. 9). On the other
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hand the concentration of ozone in the liquid phase was not influenced by this parameter.
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Finally, Fig. 10 shows that kc had a negative effect on the ozone concentration in the gas
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phase during the mass transfer process.
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If we suppose that kc was a variable depending only on chemical factors, but not on physical
23
factors, then, the increase in the pH or temperature in an aqueous medium favored the value
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of kc. In this sense the change of kc will be reflected negatively in the ozone gas profile in the
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reactor outlet. The constant kc is a variable that increased exponentially with temperature and
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pH, resulting in that the molecular ozone in the bulk liquid will be transformed into radicals
2
HO•.
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According to this sensitivity analysis it can be observed that the variable that had the greatest
4
influence in the mass transfer process was kLa, since it was the only variable showing an
5
influence on both the liquid and gas phases. Therefore, from the parametric sensitivity
6
analysis, the importance of using kLa to optimize and control the system was evident.
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Unlike the work of Wu and Masten [14] that analyzes parameters such as partition coefficient
9
and gas holdup, in this work it was performed a sensitivity analysis focused on parameters
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like VL, Qg, Cgin, pH, and T additionally to kLa and kc, which could be used to optimize the
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gas-liquid (ozone-water) transfer process for the treatment of water.
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12 Conclusions
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From the analysis of the sensitivity of the gas-liquid transfer model, we conclude that the
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transfer variable kLa is the parameter that had the most effect on the liquid phase and lesser in
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the gas phase mass transfer process. The variables such as: Qg, Cgin, and VL, had minimal
17
influence. In this study, particularly the sensitivity analysis, allowed us to estimate the
18
influence of the different variables involved in the mass transfer process. On the other hand,
19
the graphic interface helped us simulate and calculate the mass transfer and determine
20
variables like kLa and kc as function of the input conditions. The graphic interface and the
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sensitivity analysis will allow design control schemes for the water treatment system, in order
22
to make it more efficient from a technical standpoint.
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Acknowledgments
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The authors would like to thank the CONACYT for their support granted to the project
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CB/2007-84425, and the MSc fellowship 302539.
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4 References
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[4] A. Lopez-Lopez, J.S. Pic, H. Debellefontaine, Chemosphere 66 (2007) 2120-2126.
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[6] H. Benbelkacem, H. Debellefontaine, Chem. Eng. Process. 42 (2003) 723-732.
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[8] M. Novak, P. Horvat, Appl. Math. Model. 36 (2012) 3813-3825.
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[9] C.H. Kuo, K.Y. Li, C.P. Wen, J.L. Weeks, Absorption and decomposition of ozone in
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aqueous solutions, Am. Inst. Chem. Sym. Ser. 73 (1977) 230-241.
20
[10] H. Bader, Ozone-Sci. Eng., 4 (1982) 169-176.
21
[11] F.H. Yocum, Ozone mass transfer in stirred vessel, AIChE Symp., 76 (1979) 135-141.
22
[12] B. Langlais, D.A. Reckhow, D.R. Brink, Ozone in water treatment: Applicatin and
23
Engineering, Lewis publishers, United States of America, 1991.
24
[13] J. Navarro-Laboulais, L. Capablanca, A. Abad, S. Cardona, F. López, J. Torregrosa,
25
Ozone-Sci. Eng. 28 (2006) 17-27.
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[14] J.J. Wu, S.J. Masten, J. Environ. Eng. 127 (2001) 1089-1099.
2
[15]J.A. Roth, D.E. Sullivan, Ozone-Sci. Eng. 5 (1983) 37-49.
3
[16] A.K. Bin, Ozone-Sci. Eng. 28 (2006) 67-75.
4
[17] The American Water Works Association, fifth ed., McGraw-Hill, United States of
5
America, Water treatment plant design 1997.
6
[18] A. López-López, J.S. Pic, H. Bnbelkacem, H. Debellefontaine, Chem. Eng. Process. 46
7
(2007) 649-655.
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1 2 3
Table 1: kLa and kc values obtained at different pH conditions, with Cgin = 33.2 mg·L-1 and
4
Qg=2.7 x 10-5 m3·s-1.
5
Table 2: kLa and kc values obtained at different Cgin conditions and with pH=7.
6
Table 3: kLa and kc values obtained at different temperature conditions, Cgin=33.2 mg·L-1 and
7
with pH=7.
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TABLE LEGENDS
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Page 18 of 32
1
TABLE 1
2 kLa and kc values obtained at different pH conditions, with Cgin=33.2 mg·L-1 and Qg=2.7 x 10-5 m3·s-1 pH kc (s-1)* kLa (s-1)* kc (s-1)** kLa (s-1)** kc (s-1)*** kLa (s-1)*** 1.7·10-3
6.9·10-3
----
-----
----
----8.75·10-3
4
2.3·10-3
6.3·10-3
-----
-----
6.05·10-4
7
3.4·10-3
5.3·10-3
6.10·10-4
6.15·10-3
1.04·10-3
9
4.3·10-3
4.3·10-3
11
5.59·10-3
3.17·10-3
-------
---------
5.87·10-3
*This study, **[4]; ***[18]
6.54·10-3 -----
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3 4
7.61·10-3
cr
----
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1.5
19
Page 19 of 32
TABLE 2 kLa and kc values obtained at different Cgin conditions and with pH=7. Cgin (mg·L-1) kc (s-1)* kLa (s-1)* kc (s-1)** kLa (s-1)** 8
3.4·10-3
5.3·10-3
-3
-3
----
----4
-3
kc (s-1)***
kLa (s-1)***
-----
-----3
13.2
3.4·10
5.3·10
6.10·10
6.15·10
1.04·10
7.61·10-3
23.2
3.4·10-3
5.3·10-3
6.10·10-4
6.15·10-3
----
----
33.2
-3
3.4·10
-3
5.3·10
-4
6.10·10
-3
6.15·10
1.04·10
40
3.4·10-3
5.3·10-3
----
----
-----
-3
*This study, **[4]; ***[18]
-----
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2 3
7.61·10-3
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1
20
Page 20 of 32
TABLE 3
2
kLa and kc values obtained at different temperature conditions, Cgin=33.2 mg·L-1 and with pH=7 T (°C) kc (s-1) kLa (s-1) 5
1.2·10-3
7.5·10-3
10
1.7·10-3
6.9·10-3
20
3.4·10-3
5.3·10-3
25
4.7·10-3
4.0·10-3
30
6.4·10-3
2.3·10-3
cr
3
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1
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4 5
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Page 21 of 32
1 2 3 4
FIGURE CAPTIONS
5
Figure 2: Graphical user interface.
6
Figure 3: Graphical determination of kLa.
7
Figure 4: Evolution of the concentration of ozone in gas phase and liquid phase, experimental values.
8
Figure 5: Influence of the gas flow.
9
Figure 6: Analysis of the concentration of gas at the inlet.
11
Figure 8: Analysis of the volume of liquid.
12
Figure 9: Analysis of the gas volume.
13 14 15
Figure 10: Analysis of variable kc.
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Figure 7: Analysis of variable kLa.
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Figure 1: Schematic experimental system.
22
Page 22 of 32
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Figure 1
Page 23 of 32
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Figure 2
Page 24 of 32
Slope = kc + kLa
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2.5
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Figure 3
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1.5
1
Ac ce p
Ln(CL* − CL)
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2
0.5
0 0
50
100
150 200 Time (s)
250
300
350 Page 25 of 32
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Figure 4
Page 26 of 32
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Figure 5
5
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x 10
an
7
M
6
d te
4
3
2
Ac ce p
Sensitivity coefficient
5
1
0
−1 0
100
200
300
400 500 Time (s)
600
700
800
900 Page 27 of 32
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cr
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Figure 6
M
1
d te
0.6
0.4
0.2
Ac ce p
Sensitivity coefficient
0.8
0
−0.2 0
100
200
300
400 500 Time (s)
600
700
800
900 Page 28 of 32
cr
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Figure 7
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1000
d te
0
−500
Ac ce p
Sensitivity coefficient
M
500
−1000
−1500 0
100
200
300
400 500 Time (s)
600
700
800
900 Page 29 of 32
cr
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Figure 8
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0
an
−500
−2500
−3000
M te
−2000
d
−1500
Ac ce p
Sensitivity coefficient
−1000
−3500
−4000
−4500 0
100
200
300
400 500 Time (s)
600
700
800
900 Page 30 of 32
cr
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Figure 9
6
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x 10
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0
M
−1 −2
d te
−4 −5 −6 −7
Ac ce p
Sensitivity coefficient
−3
−8 −9 −10 0
100
200
300
400 500 Time (s)
600
700
800
900 Page 31 of 32
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Figure 10
6
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x 10
an
0
M
−1 −2
d te
−4 −5 −6 −7
Ac ce p
Sensitivity coefficient
−3
−8 −9 −10 0
100
200
300
400 500 Time (s)
600
700
800
900 Page 32 of 32
S1226-086X(14)00293-7 http://dx.doi.org/doi:10.1016/j.jiec.2014.05.044 JIEC 2071
To appear in: Received date: Revised date: Accepted date:
17-12-2013 7-5-2014 8-5-2014
Please cite this article as: V. Flores-Pay´an, E.J. Herrera-L´opez, J. Navarro-Laboulais, A. L´opez-L´opez, Parametric sensitivity analysis and ozone mass transfer modeling in a Gas-Liquid reactor for advanced water treatment, Journal of Industrial and Engineering Chemistry (2014), http://dx.doi.org/10.1016/j.jiec.2014.05.044 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1 2
Parametric sensitivity analysis and ozone mass transfer modeling in a Gas-
3
Liquid reactor for advanced water treatment
ip t
4 Valentín Flores-Payána, Enrique J. Herrera-Lópeza, Javier Navarro-Laboulaisb,
6
Alberto López-Lópeza,*
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5
7 8
a
9
Avenida Normalistas 800, Col. Colinas de la Normal, C.P. 44270, Guadalajara Jalisco,
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Centro de Investigación y Asistencia en Tecnología y Diseño del Estado de Jalisco A.C.,
México
11
b
12
Camino de Vera s/n, 46022, Valencia España.
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Universidad Politécnica de Valencia, Departamento de Ingeniería Química y Nuclear,
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*Corresponding author. Tel: +52 33 33455200, Fax: +52 33 33455245
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E-mail address: [email protected]; [email protected] (Alberto López-López)
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Page 1 of 32
Abstract
2
A computational model for a reactor used in advanced water treatment was proposed to
3
represent, simulate and predict the mass transfer process of ozone in water (gas-liquid). A
4
graphic interface was designed to simulate the ozone gas transfer into the liquid. In addition,
5
the values of the mass transfer coefficient, and the self-decomposition of ozone, could be
6
determined for different initial conditions. The model for ozone mass transfer was represented
7
by two differential equations derived from the mass balances of the system. Finally a
8
sensitivity analysis was made to determine the effect of the parameters over the operating
9
variables.
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11 Keywords: Modeling, Mass transfer, Parametric sensitivity, Ozone, Water treatment 12
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1 Introduction
2
Advanced Oxidation Processes (AOPs) refers to highly competitive water treatment
3
technology for the removal of organic pollutants not treatable by conventional techniques due
4
to their high chemical stability and low biodegradability. AOPs using ozone (O3) can be
5
applied in wastewater pre-treatment or post-treatment stages [1]. The main AOPs are O3/pH,
6
O3/H2O2, O3/UV, O3/Cat++ O3/H2O2/UV and O3/Cat++/UV. In alkaline ozonation the averages
7
speed of self-decomposition of O3 in water increases and with it, the speed of generation of
8
radicals. The addition of hydrogen peroxide combined with ozone starts a cycle of radical
9
ozone decomposition forming hydroxyl. Direct photo-oxidation with UV radiation has
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1
emerged as an alternative technology for the degradation of pollutants agents. On the other
11
hand, the efficiency of ozone and the use of combined hydrogen peroxide with ultraviolet
12
radiation increase the speed of refractory compound degradation [2-4]. The advanced
13
oxidation processes using ozone consists of the combination of O3 with one or more oxidants
14
to generate hydroxyl radicals (HO•) in sufficient amounts to interact with the organic
15
compounds present in an aqueous medium. AOPs differ in the method used to generate
16
hydroxyl radicals. AOPs using O3 in treating contaminated water with recalcitrant organic
17
matter are carried out regularly in gas-liquid reactors (ozone-water). The successful
18
implementation of the ozonation process in water treatment depends basically on two aspects
19
[5]:
20
i) The reaction kinetics: basically represented by the reactivity of ozone and organic matter,
21
and the stoichiometric ratio or ozone consumption associated to the degradation rate constant.
22
ii) The mass transfer process of ozone in water: represented by the overall mass transfer
23
coefficient (kLa), the self-decomposition of O3 (kc), and the fraction of gas in the reactor (),
24
among other hydrodynamic transfer parameters.
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Page 3 of 32
Therefore, reaction kinetics and the mass transfer of ozone in the liquid are important
2
parameters for designing and applying AOPs using ozone. It would be valuable to model and
3
simulate these variables under different process conditions, i.e., greater process efficiency will
4
be expected, with a combination of high mass ozone transfer to the liquid (kLa) and a lower
5
ozone self-decomposition coefficient (kc). Adequate or even optimal conditions of (kLa) and
6
(kc) can be obtained for the proper operation of the ozonation process from modeling the
7
effect of temperature, pH, reactor agitation and ozone concentration in the liquid and gas
8
phases [6-8]. Ozone is a scarcely soluble gas, and the transfer efficiency is mainly controlled
9
by its thermodynamic properties [9-12].
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Benbelkacem et al., [6] reported a model of mass transfer in a semi continuous gas-liquid
11
reactor, where the chemical reactions were irreversible. The model was solved using
12
numerical computation and the results were included in the mass balance within the reactor.
13
Navarro et al., [13] developed a model for monitoring a gas-liquid reactor in semi-continuous
14
flow analysis. The model predicted an observed signal in a detector when a continuous flow
15
analysis was used to monitor the ozone gas-liquid phase; the model combined the mass
16
transfer and the kinetic process in the reactor.
17
Wu and Masten [14] developed a mass transfer model to simultaneously predict
18
concentrations of the dissolved and outlet gaseous ozone in a semibatch reactor from a well
19
mixed liquid phase and a gas phase described as a plug-flow system. The self-decomposition
20
of ozone was also incorporated into the model. The mass transfer coefficient augmented when
21
the gas-flow rate, temperature, and ionic strength in the solution increased. In addition, these
22
authors using parametric sensitive analysis found that the dissolved ozone was the factor that
23
had the greatest effect over the concentrations profiles.
24
The objective of this research was to propose: i) a graphic interface representing the process
25
of transference of O3 in water; ii) simulate the response of O3 in gas and liquid phase,
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Page 4 of 32
considering only the mass transfer process, regardless of the reaction kinetics; iii) to evaluate
2
the performance of kLa and kc in function of the temperature, pH and dosage of O3; and iv)
3
perform a parametric sensitivity analysis on the equations of O3 in the gas and liquid phase to
4
determine the parameters having the greatest effect over the process variables. From the
5
model and the parametric sensitivity results, optimization and control strategies could be
6
designed in the near future for the AOP using O3 for water treatment. The first part of the
7
results section describes the model and the graphical interface, as well as the model validation
8
with a set of experimental data. The second part describes the developed sensitivity analysis
9
used to evaluate the effect of operating variables in the transfer of gas-liquid mass (G-L)
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11 2 Material and methods
13
2.1 System description for monitoring O3 on-line
14
The experimental system to monitor the O3 on-line in the liquid and gas phase is shown in
15
(Fig. 1). The system includes: 1) oxygen cylinder; 2) an ozone generator G11 Pacific Ozone
16
with a production of 16.9 g/h, which was fed by 99% pure oxygen; 3) a flow control valve of
17
the brand Bronkhorst model F-201CV-10K-AGD-22-V; 4) a three-way flow control valve
18
of the brand SMC model VDW350-5G-3-02N-H-F; 5) flow meter of the brand
19
Bronkhorst model F-11B-10k-AGD-22-V; 6) a reactor Applikon, with 4 litres of volume
20
and a ratio height: diameter (H:D) equal to 1.5; 7) pH sensor; 8) temperature sensor; 9)
21
stirring motor; 10) peristaltic pump; 11) liquid phase ozone sensor; 12) phase liquid ozone
22
meter of the brand ATI model Q45H/64, ozone measurements were performed by a sensor
23
which was introduced into an acrylic cell which is filled with the effluent extracted from the
24
reactor by a peristaltic pump and Teflon hoses which are resistant to ozone corroding; 13) pH
25
meter and controller of the brand B&C Electronics Model 7685; 14) a meter and
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Page 5 of 32
temperature controller of the brand B&C Electronics Model TR7615, which has a platinum
2
thermoresistance 100, this meter has a scale of 0-199 ºC; 15) a mechanical agitation controller
3
Applikon Model ADI 1032 with a speed range of 0-1250 rpm; 16) a gas phase ozone meter
4
of the brand Teledyne Model 465H, operating in a range of 0-400 g/Nm3 with an accuracy
5
of 0.5%; 17) a thermal ozone decomposition unit of the brand Pacific Ozone, which
6
transforms the residual ozone in oxygen; 18) data acquisition system based in the control card
7
USB-1024SL of Computing; 19) computer and the user interface designed with the
8
software Labview® 8.2. This interface was used to monitor and manipulate the experimental
9
variables of the water treatment process.
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2.2 The mathematical model for the ozone mass transfer
12
A mathematical model for the transference of ozone gas to the liquid phase (water) in a
13
reactor used for advanced wastewater treatment can be established from the gas and liquid
14
phase mass balances, and assuming the following hypothesis:
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i.
The liquid phase was considered perfectly mixed.
16
ii.
The concentration of ozone was considered constant in the entirely reactor volume.
17
The concentration value corresponds to the result of integrating the balance equation
18 19 20
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of a piston flow reactor under steady conditions.
iii.
The gas hold-up is around ≈2.0%, therefore it was assumed that VL≈V in the reactor.
21
The mass balance in the gas phase was expressed as:
22
k L aVL (CL* C L )dt Qg C gin dt Qg C gout dt Vg dC g
23
and in the liquid phase:
24
k L aVL (C L* CL )dt VL dC L kcCLVL dt
(1)
(2)
6
Page 6 of 32
1
Isolating dC g / dt and dCL/dt from equations (1) and (2) the following expressions were
2
obtained:
3 dC g dt
Qg Vg
C
gin
C gout
VL k L a * CL CL Vg
(3)
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4
5
dCL k L a CL* CL kcCL dt
6
Here, VL is the liquid volume in the reactor (m3), C L* is the concentration of ozone in water in
7
equilibrium with the gas (mol·m-3), dC g is the average concentration in gas phase (mol·m-3),
8
CL is the dissolved ozone concentration in the solution (mol·m-3), Qg is the gas flow (mol·s-1),
9
Cgin and Cgout are the concentration of O3 at inlet and outlet of the reactor (mol·m-3), Vg is the
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(4)
volume of gas in the reactor (m3), kLa is the mass transfer coefficient and kc is the constant
11
self-decomposition of ozone and could be determined by equation (5) suggested by Roth and
12
Sullivan [15];
13
kc 1.6352 106 OH
14
The ozone solubility in water can be obtained from Henry’s law and expressed by the
15
equation (6) [16]:
16
CL*
17
Here, T is the temperature (ºC). Equation (5) is dependent of the pH and equation (5) and (6)
18
are dependent of temperature.
5606 0.123 T
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C gin
1.59e( 0.0437T )
(5)
(6)
19 20
2.3 Graphic interface to simulate the ozone mass transfer
21
A graphic interface to simulate equations 3 and 4 was designed with the software Matlab®
22
7.0 (Fig. 2). The user can set the initial values of Qg, Cgin, Vg, VL, T, pH, and dosage of O3.
7
Page 7 of 32
1
The values of kLa and kc and the behavior of the O3 in the liquid and gas phases are displayed
2
in the interface.
3 2.4 Analytic techniques
5
The ozone concentration in the liquid phase was determined by the colorimeter method [17]
6
and was used to validate the on-line measurements.
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3 Results
9
3.1 Simulation results for the ozone mass transfer
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Fig. 2 shows the evolution of the ozone gas transference to the liquid as a function of time for
11
the following initial conditions: VL=0.004 m3, T=10 ºC, pH=7.0, Qg=2.7×10-5 m3·s-1, Vg=
12
0.001 m3 and Cgin=33.2 mg·L-1. Once initial values of the variables were introduced and after
13
executing the simulation, the interface showed the concentration profiles of ozone in the water
14
and in the gas phase. The program determined the values of kLa using values of the ozone
15
concentration in the water during the transitional phase transfer model (Fig. 3). Diverse
16
simulations were performed varying the pH, temperature and ozone concentration to
17
determine different values of kLa and kc given by the mathematical model. The results are
18
shown in Tables 1, 2 and 3.
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3.1.1 Influence of the pH over kLa and kc
21
The effect of pH over kLa and kc was investigated. The pH was varied according to the
22
following values 1.5, 4, 7, 9 and 11, Qg and Cgin were kept constant to 2.7 x 10-5 m3·s-1 and
23
33.2 mg·L-1 respectively. The Table 1 shows that for our model the value of kc increased as
24
the pH of the medium rose. This is evident since in an alkaline medium the formation of free
25
radicals HO• generate chain reactions by increasing the speed of destruction of ozone, as has
8
Page 8 of 32
been reported in the literature, [4] and [18]. However, the value of the transfer constant kLa
2
practically had the same order of magnitude. This result was consistent with the literature [4,
3
18], taking into account that with a pH greater than 7.0 the self-decomposition of the ozone
4
increased, hindering the ozone transferred measurement into the transitional stage of the mass
5
transfer process, consequently reflecting a decrease in the kLa. That is, the rate of self-
6
decomposition of ozone was greater than the rate of the analyzer detection.
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7 TABLE 1.
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3.1.2 Influence of the inlet ozone concentration over kLa and kc
11
The influence of the inlet ozone concentration in the reactor over the parameters kLa and kc
12
was evaluated. The concentration of O3 was varied according to the following values 8, 13.2,
13
23.2, 33.2 and 40 mg·L-1, and maintaining constant Qg = 2.7 x 10-5 m3·s-1 and the pH=7.0. It
14
can be seen in Table 2, that the value of kLa remained constant for all the conditions tested.
15
This result was consistent with the fundamentals of hydrodynamics since by keeping the gas
16
velocity, the rate transfer gas-liquid remained constant. The parameter kc also remained
17
constant for all the conditions tested of the gas used, confirming that kc is a variable
18
depending on chemical factors and nor on physical one [4].
20 21
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TABLE 2
22
3.1.3 Influence of the temperature over kLa and kc
23
Table 3 shows the influence of different temperatures (5, 10, 20, 25, and 30 ºC) on the
24
parameters kLa and kc during the ozone transfer into liquid phase. The pH and Cgin were kept
25
constant. It was observed that the value of kc increased as the temperature did. This result is
26
logical since kc is a variable depending directly proportional to the temperature. On the other 9
Page 9 of 32
1
hand, the value of kLa decreased as the temperature increased because the molecular ozone in
2
the bulk liquid is transformed into radicals HO• which are responsible for the oxidation in the
3
ozone treatment process.
5
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6 3.4 Experimental validation
8
Finally the model was validated with experimental data under the following conditions:
9
Qg=2.7×10-5 m3·s-1, VL=4L and T=20ºC. Fig. 4 shows the concentration profiles of ozone in
10
the gas phase and in the liquid phase obtained experimentally. Additionally Fig. 4 shows the
11
concentration profiles generated by the graphic interface under the same experimental
12
conditions. During the continuous process of saturation with O3 in demineralized water, two
13
regions were observed, the transitory and the stationary. An error of 4.1 % and 2.68 % were
14
obtained for the liquid and the gas phases, respectively. Once the correct performance of the
15
mathematical model was validated (3-4), it would be helpful to determine which parameters
16
in this model had more influence over the process variables.
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3.2 Parametric sensitivity analysis
19
A sensitivity analysis is used to determine the effect of the operational parameters of the
20
system such as temperature, pH and ozone dose over the state variables of the mathematical
21
model; in this case the model of ozone mass transfer. The mathematical model (3-4) was
22
expressed as:
23
x f ( x, t , )
(7)
24
10
Page 10 of 32
1
where x is the state variable, x is the time derivative of x, t is the time, and ρ are the
2
parameters of the model. It was possible to determine the effect of the parameters over the
3
state equations from the following relationship:
4
f f S S x
5
where
6
S1,1 S 2,1 S Si ,1
7
and
8
Si , j
9
In order to perform a parametric sensitivity analysis to the mass balance of ozone in the gas
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(9)
(10)
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xi j
d
phase and liquid phase (3-4), it was defined Qg VL k L a * CL CL V C gin C gout V f ( x) g g k a C * C k C L L c L L
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11
S1, j S 2, j Si , j
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10
S1, 2 S1,3
(8)
(11)
12
and
13
ρ = (Qg, Cgin, Vg, VL, C L* , kLa, kc)
14
The analysis begins with the partial derivatives of equations (11) with respect to x:
15
Q VL k L a g f Vg Vg x 0 (k L a kc )
16
Subsequently, equation (11) is partially derived with respect to the seven parameters
17
contained in the vector ρ:
18
f 0
CL * 0 CL CL 0 k L a 0 CL
(12)
(13)
(14)
11
Page 11 of 32
1
where:
2
3
4
C
5
C
6
C gin
Vg
C gout Vg
cr
* L
CL VL Vg
CL k L a Vg
us
* L
ip t
Qg Vg
Qg C gin C gout VL k L a CL* C L
an
VL k L a Vg
7
8
Then from equations (7) and (12) the following system of differential equations was obtained:
2 g
d
M
V
te
9
C C gout Q Vk a S11 L L S11 g S 21 gin Vg Vg Vg
(15)
11
Q Q Vk a S12 L L S12 g S 22 g Vg Vg Vg
(16)
12
V C * CL Q Vk a S13 L L S13 g S 23 L L Vg Vg Vg
13
Q Vk a S14 L L S14 g S 24 Vg Vg
(18)
14
Q Vk a Vk a S15 L L S15 g S 25 L L Vg Vg Vg
(19)
15
Qg C ge C g Q Vk a S16 L L S16 g S 26 2 Vg V Vg g
(20)
Ac ce p
10
(17)
12
Page 12 of 32
Q Vk a S17 L L S17 g S 27 Vg Vg
(21)
2
S21 k L a kc S11
(22)
3
S22 k L a kc S12
(23)
4
S23 k L a kc S13 CL* CL
5
S24 k L a kc S14
6
S25 k L a kc S15 k L a
7
S26 k L a kc S16
8
S27 k L a kc S17 CL
(24)
cr
(25)
us
(26)
an
ip t
1
9
(27) (28)
Equations (1-2) and (15-28) were simultaneously solved with the function ode45 in Matlab®
11
7.0. The initial condition for equations (15-28) was set to zero. Fig. 5 shows the effect of the
12
ozone flow (Qg) within the mass transfer model. It can be seen that Qg does not had an
13
influence on the liquid phase (continuous line) since this variable remained equal to zero
14
during the simulation. On the other hand, Qg had a significant positive effect (on the gas
15
phase, dashed line) of 5.57×105 and 1.4×105 in the transition and stationary phases,
16
respectively.
d
te
Ac ce p
17
M
10
18
In Fig. 6 the effect of ozone concentration of gas (Cgin) in the inlet of the reactor was
19
analysed. This figure shows that the concentration of ozone in the liquid phase was not
20
affected by this parameter. Indeed, the concentration of O3 in the liquid should not be affected
21
by changing Cgin since this value is dependent on the thermodynamic conditions of the
22
environment and the availability of the gas. Cgin had a positive effect on the concentration of
13
Page 13 of 32
ozone in the gas phase during the transitional stage of the process stabilizing during the
2
stationary stage.
3
The effect of the volumetric mass transfer coefficient kLa in the gas and liquid phase is shown
4
in Fig. 7. Clearly this parameter had influence in both variables of the model (3-4), having a
5
significant negative effect on the concentration of ozone in the gas phase and a positive effect
6
on the liquid phase during the transitional stage and less during the stationary stage of the
7
mass transfer process. This is consistent, since the determination of the constant kLa according
8
to our mass transfer model, was obtained in the transition stage.
us
cr
ip t
1
9
Fig. 8 shows that the reactor volume (VL) had an adverse effect on the ozone concentration in
11
the gas phase during the transient stage of the process, stabilizing in the stationary phase. The
12
concentration of ozone in the liquid was not affected during the mass transfer process. This
13
can be explained from the fact that increasing the volume of the liquid at a constant flow rate
14
and a constant inlet gas concentration will reduce the outlet gas concentration.
M
d
te
15
an
10
The gas volume (Vg) had a negative significant effect in the ozone concentration in the gas
17
phase during the transient stage and is stable in the stationary phase, (Fig. 9). On the other
18
hand the concentration of ozone in the liquid phase was not influenced by this parameter.
19
Ac ce p
16
20
Finally, Fig. 10 shows that kc had a negative effect on the ozone concentration in the gas
21
phase during the mass transfer process.
22
If we suppose that kc was a variable depending only on chemical factors, but not on physical
23
factors, then, the increase in the pH or temperature in an aqueous medium favored the value
24
of kc. In this sense the change of kc will be reflected negatively in the ozone gas profile in the
25
reactor outlet. The constant kc is a variable that increased exponentially with temperature and
14
Page 14 of 32
pH, resulting in that the molecular ozone in the bulk liquid will be transformed into radicals
2
HO•.
3
According to this sensitivity analysis it can be observed that the variable that had the greatest
4
influence in the mass transfer process was kLa, since it was the only variable showing an
5
influence on both the liquid and gas phases. Therefore, from the parametric sensitivity
6
analysis, the importance of using kLa to optimize and control the system was evident.
cr
ip t
1
7
Unlike the work of Wu and Masten [14] that analyzes parameters such as partition coefficient
9
and gas holdup, in this work it was performed a sensitivity analysis focused on parameters
10
like VL, Qg, Cgin, pH, and T additionally to kLa and kc, which could be used to optimize the
11
gas-liquid (ozone-water) transfer process for the treatment of water.
M
an
us
8
12 Conclusions
14
From the analysis of the sensitivity of the gas-liquid transfer model, we conclude that the
15
transfer variable kLa is the parameter that had the most effect on the liquid phase and lesser in
16
the gas phase mass transfer process. The variables such as: Qg, Cgin, and VL, had minimal
17
influence. In this study, particularly the sensitivity analysis, allowed us to estimate the
18
influence of the different variables involved in the mass transfer process. On the other hand,
19
the graphic interface helped us simulate and calculate the mass transfer and determine
20
variables like kLa and kc as function of the input conditions. The graphic interface and the
21
sensitivity analysis will allow design control schemes for the water treatment system, in order
22
to make it more efficient from a technical standpoint.
Ac ce p
te
d
13
23 24 25
15
Page 15 of 32
1
Acknowledgments
2
The authors would like to thank the CONACYT for their support granted to the project
3
CB/2007-84425, and the MSc fellowship 302539.
ip t
4 References
6
[1] I. Oller, S. Malato, J.A. Sánchez-Pérez, Sci. Total Environ. 409 (2011), 4141-4166.
7
[2] I. Arslan-Alaton, J. Environ. Manage. 82 (2007) 145-154.
8
[3] A. Rodríguez, P. Letón, R. Rosal, M. Dorado, S. Villar, J.M. Sanz, Tratamientos
9
avanzados de aguas residuales industriales, España, 2006.
us
cr
5
[4] A. Lopez-Lopez, J.S. Pic, H. Debellefontaine, Chemosphere 66 (2007) 2120-2126.
11
[5] A.K. Bin, M. Roustan, Mass transfer in ozone reactors. International specialised
12
Symposium of IOA/EA3G, Fundamental and Engineering Concepts for Ozone Reactor
13
Design, France, (2000), 99-131.
14
[6] H. Benbelkacem, H. Debellefontaine, Chem. Eng. Process. 42 (2003) 723-732.
15
[7] S.C. Cardona, F. López, A. Abad, J. Navarro-Laboulais, Can. J. of Chem. Eng. 88 (2010)
16
491-502.
17
[8] M. Novak, P. Horvat, Appl. Math. Model. 36 (2012) 3813-3825.
18
[9] C.H. Kuo, K.Y. Li, C.P. Wen, J.L. Weeks, Absorption and decomposition of ozone in
19
aqueous solutions, Am. Inst. Chem. Sym. Ser. 73 (1977) 230-241.
20
[10] H. Bader, Ozone-Sci. Eng., 4 (1982) 169-176.
21
[11] F.H. Yocum, Ozone mass transfer in stirred vessel, AIChE Symp., 76 (1979) 135-141.
22
[12] B. Langlais, D.A. Reckhow, D.R. Brink, Ozone in water treatment: Applicatin and
23
Engineering, Lewis publishers, United States of America, 1991.
24
[13] J. Navarro-Laboulais, L. Capablanca, A. Abad, S. Cardona, F. López, J. Torregrosa,
25
Ozone-Sci. Eng. 28 (2006) 17-27.
Ac ce p
te
d
M
an
10
16
Page 16 of 32
[14] J.J. Wu, S.J. Masten, J. Environ. Eng. 127 (2001) 1089-1099.
2
[15]J.A. Roth, D.E. Sullivan, Ozone-Sci. Eng. 5 (1983) 37-49.
3
[16] A.K. Bin, Ozone-Sci. Eng. 28 (2006) 67-75.
4
[17] The American Water Works Association, fifth ed., McGraw-Hill, United States of
5
America, Water treatment plant design 1997.
6
[18] A. López-López, J.S. Pic, H. Bnbelkacem, H. Debellefontaine, Chem. Eng. Process. 46
7
(2007) 649-655.
cr
ip t
1
Ac ce p
te
d
M
an
us
8
17
Page 17 of 32
1 2 3
Table 1: kLa and kc values obtained at different pH conditions, with Cgin = 33.2 mg·L-1 and
4
Qg=2.7 x 10-5 m3·s-1.
5
Table 2: kLa and kc values obtained at different Cgin conditions and with pH=7.
6
Table 3: kLa and kc values obtained at different temperature conditions, Cgin=33.2 mg·L-1 and
7
with pH=7.
cr
ip t
TABLE LEGENDS
Ac ce p
te
d
M
an
us
8 9
18
Page 18 of 32
1
TABLE 1
2 kLa and kc values obtained at different pH conditions, with Cgin=33.2 mg·L-1 and Qg=2.7 x 10-5 m3·s-1 pH kc (s-1)* kLa (s-1)* kc (s-1)** kLa (s-1)** kc (s-1)*** kLa (s-1)*** 1.7·10-3
6.9·10-3
----
-----
----
----8.75·10-3
4
2.3·10-3
6.3·10-3
-----
-----
6.05·10-4
7
3.4·10-3
5.3·10-3
6.10·10-4
6.15·10-3
1.04·10-3
9
4.3·10-3
4.3·10-3
11
5.59·10-3
3.17·10-3
-------
---------
5.87·10-3
*This study, **[4]; ***[18]
6.54·10-3 -----
Ac ce p
te
d
M
an
us
3 4
7.61·10-3
cr
----
ip t
1.5
19
Page 19 of 32
TABLE 2 kLa and kc values obtained at different Cgin conditions and with pH=7. Cgin (mg·L-1) kc (s-1)* kLa (s-1)* kc (s-1)** kLa (s-1)** 8
3.4·10-3
5.3·10-3
-3
-3
----
----4
-3
kc (s-1)***
kLa (s-1)***
-----
-----3
13.2
3.4·10
5.3·10
6.10·10
6.15·10
1.04·10
7.61·10-3
23.2
3.4·10-3
5.3·10-3
6.10·10-4
6.15·10-3
----
----
33.2
-3
3.4·10
-3
5.3·10
-4
6.10·10
-3
6.15·10
1.04·10
40
3.4·10-3
5.3·10-3
----
----
-----
-3
*This study, **[4]; ***[18]
-----
Ac ce p
te
d
M
an
us
cr
2 3
7.61·10-3
ip t
1
20
Page 20 of 32
TABLE 3
2
kLa and kc values obtained at different temperature conditions, Cgin=33.2 mg·L-1 and with pH=7 T (°C) kc (s-1) kLa (s-1) 5
1.2·10-3
7.5·10-3
10
1.7·10-3
6.9·10-3
20
3.4·10-3
5.3·10-3
25
4.7·10-3
4.0·10-3
30
6.4·10-3
2.3·10-3
cr
3
ip t
1
Ac ce p
te
d
M
an
us
4 5
21
Page 21 of 32
1 2 3 4
FIGURE CAPTIONS
5
Figure 2: Graphical user interface.
6
Figure 3: Graphical determination of kLa.
7
Figure 4: Evolution of the concentration of ozone in gas phase and liquid phase, experimental values.
8
Figure 5: Influence of the gas flow.
9
Figure 6: Analysis of the concentration of gas at the inlet.
11
Figure 8: Analysis of the volume of liquid.
12
Figure 9: Analysis of the gas volume.
13 14 15
Figure 10: Analysis of variable kc.
us
Figure 7: Analysis of variable kLa.
Ac ce p
te
d
M
an
10
cr
ip t
Figure 1: Schematic experimental system.
22
Page 22 of 32
Ac ce p
te
d
M
an
us
cr
ip t
Figure 1
Page 23 of 32
Ac ce p
te
d
M
an
us
cr
ip t
Figure 2
Page 24 of 32
Slope = kc + kLa
an
us
2.5
cr
ip t
Figure 3
te
1.5
1
Ac ce p
Ln(CL* − CL)
d
M
2
0.5
0 0
50
100
150 200 Time (s)
250
300
350 Page 25 of 32
Ac ce p
te
d
M
an
us
cr
ip t
Figure 4
Page 26 of 32
cr
ip t
Figure 5
5
us
x 10
an
7
M
6
d te
4
3
2
Ac ce p
Sensitivity coefficient
5
1
0
−1 0
100
200
300
400 500 Time (s)
600
700
800
900 Page 27 of 32
an
us
cr
ip t
Figure 6
M
1
d te
0.6
0.4
0.2
Ac ce p
Sensitivity coefficient
0.8
0
−0.2 0
100
200
300
400 500 Time (s)
600
700
800
900 Page 28 of 32
cr
ip t
Figure 7
an
us
1000
d te
0
−500
Ac ce p
Sensitivity coefficient
M
500
−1000
−1500 0
100
200
300
400 500 Time (s)
600
700
800
900 Page 29 of 32
cr
ip t
Figure 8
us
0
an
−500
−2500
−3000
M te
−2000
d
−1500
Ac ce p
Sensitivity coefficient
−1000
−3500
−4000
−4500 0
100
200
300
400 500 Time (s)
600
700
800
900 Page 30 of 32
cr
ip t
Figure 9
6
us
x 10
an
0
M
−1 −2
d te
−4 −5 −6 −7
Ac ce p
Sensitivity coefficient
−3
−8 −9 −10 0
100
200
300
400 500 Time (s)
600
700
800
900 Page 31 of 32
cr
ip t
Figure 10
6
us
x 10
an
0
M
−1 −2
d te
−4 −5 −6 −7
Ac ce p
Sensitivity coefficient
−3
−8 −9 −10 0
100
200
300
400 500 Time (s)
600
700
800
900 Page 32 of 32