Assessment of CFD−VOF Method for Trickle-Bed Reactor Modeling in the Catalytic Wet Oxidation of Phenolic Wastewaters

Assessment of CFD-VOF Method for Trickle-Bed Reactor Modeling in theCatalytic Wet Oxidation of Phenolic Wastewaters

Rodrigo J. G. Lopes and Rosa M. Quinta-Ferreira*

Group on EnVironmental, Reaction and Separation Engineering (GERSE), Department of ChemicalEngineering, UniVersity of Coimbra, Rua SılVio Lima, Polo II - Pinhal de Marrocos, 3030-790 Coimbra, Portugal

A multiphase volume of fluid (VOF) model was developed to provide a more detailed understanding of thetransient behavior of a laboratory-scale trickle-bed reactor. The gas-liquid flow through a catalytic bed ofspherical particles was used to compute velocity field and liquid volume fraction distributions consideringinterfacial phenomena as well as surface tension effects. The computational model was used to simulate thecatalytic wet air oxidation of a phenolic model solution in the multiphase reactor. Several runs were carriedout under unsteady-state operation to evaluate the dynamic performance addressing the total organic carbonconcentration and temperature profiles. In all runs, some level of backmixing was predicted, being lower athigh operating temperatures. These axial concentration profiles were then correlated with the radial onesrevealing a poor radial mixing for the simulated flow regime, namely, at the hot spots. The influence of theoperating temperature on the thermal profiles illustrated the existence of such hot spots located in the firstquarter of the axial coordinate with an intensity about 6% higher than the inlet and wall temperatures. Thetransient radial temperature profiles corresponding to the hot spot showed the same intensity as was foundfor the axial thermal profiles, indicating the existence of considerable radial gradients that sustained the poorradial mixing in downflow operating mode. Despite the qualitative differences attained for the shapes of thethermal profiles, one should bear in mind that the maximum difference between the computed results andexperimental data was lower than 1.5%, which reinforces the validation of the computational fluid dynamics(CFD) approach at reacting flow conditions.

1. Introduction

The integrated treatment of polluted water streams typicallyincludes a combination of physical, chemical, and biologicalmethods.1 It is worthwhile to mention that wastewater streamshaving organic pollutant loads in the range of a few hundred toa few thousand parts per million are too dilute to incinerate buttoo toxic and concentrated for biological treatment.2 Within thisrange of concentrations and toxicities, the subcritical solid-catalyzed wet air oxidation (CWAO) technique is among themost suitable disposal routes. CWAO technology is based onthe catalytic oxidative breakdown of oxidizable contaminantsinto water and carbon dioxide at elevated oxygen pressures andhigh temperatures. Solid catalysts offers a practical and tech-nological alternative to the conventional noncatalytic or homo-geneously catalyzed routes because the treatment can be carriedout under much milder conditions at notably shorter residencetimes within more compact installations and, in addition, thecatalyst can, in principle, be easily recovered, regenerated, andreused.3,4 An excellent review on the use of carbon materialsas catalytic supports or direct catalysts in the catalytic wet airoxidation of organic pollutants is provided by Stuber et al.,5

with detailed information on relevant engineering aspectsincluding the characterization, activity, and stability of carbon.

Liquid-phase-catalyzed oxidation processes fall into thecategory of gas-liquid-solid reactions and are still not at amature stage of development and technological implementation.6

At the time of proper and reliable industrial design, the chemicalreactor engineer must overcome the complex nature of theinterphase and intraparticle heat and mass transport, chemicalkinetics, thermodynamics, flow patterns, and hydrodynamics.Several laboratory studies that are being reported in the academic

and patent literature are merely intended for the developmentof stable and economical catalysts for wastewater remediation.7,8

Only a few studies on computer-aided tools have been reportedin the open literature for the design of catalytic wet oxidationin trickle-bed reactors (TBRs)9,10 and bubble column reactors.11,12

To date, following the progress of computing technology andcomputational fluid dynamics (CFD), several numerical modelsbased on numerical simulation of the Navier-Stokes equationshave been developed for multiphase flows. Numerous studieshave been devoted to the transport of nonreacting bubble anddroplet sprays in order to fully understand their dynamic nature,but it clearly appears that specific approaches must be carriedout for the concomitant description of interfacial behavior ingas-liquid-solid systems. The computation of interface motionin multiphase flows is a wide field of research, and severalapproaches can be used. Front tracking methods,13 volume offluid methods,14 and level set methods15 are the most commonnumerical strategies used to predict interface motion. Fronttracking methods are based on the Lagrangian tracking of markerparticles that are attached to the interface motion, but appearnumerically limited for three-dimensional geometries, especiallyfor the distribution of the marker particles when irregularitiesoccur on the interface. Volume of fluid (VOF) methods arebased on the description of the volumetric fraction of each phasein grid cells. The main difficulty of such methods is that,although two-dimensional interface reconstruction is workable,three-dimensional reconstruction is numerically expensive. Aconsequence can be some uncertainties in the interface curvatureand, thus, in the surface tension forces. The basis of the levelset methods, described elsewhere,16 is that the interface isdescribed with the zero-level curve of a continuous functiondefined by the signed distance from the interface. To ensurethat the function remains the signed distance from the interface,a predestining algorithm is applied, but it is well-known that

* To whom correspondence should be addressed. Tel.: +351-239798723. Fax: +351-239798703. E-mail: [email protected].

Ind. Eng. Chem. Res. 2010, 49, 2638–26482638

10.1021/ie901412x 2010 American Chemical SocietyPublished on Web 02/04/2010

the numerical computations can generate mass losses in under-resolved regions, which is the main drawback of level setmethods. To describe the interface discontinuities, two ap-proaches can be used, namely, the continuous force formulation(“delta” formulation), which assumes that the interface is twoor three grid meshes thick, and the ghost fluid method, whichwas derived to capture jump conditions on the interface.17

As wetting characteristics play a dominant role in thehydrodynamic operation of trickle beds at reacting flow condi-tions, the VOF model was used to compute the axial/radialconcentration and temperature profiles accounting at the sametime for the liquid spreading on the catalyst solid surfaces in ahigh-pressure TBR. The hydrodynamic and reaction parametersare correlated in terms of how they can be affected by thewetting phenomenon through the simulation of the catalytic wetoxidation on the TBR. As the trustworthy design and scale-upof reactors, as well as process optimization, requires detailedknowledge and information from the perspective of multiphasereactor engineering for gas-liquid-solid catalytic wet oxidation,this work is focused on the VOF model for TBR modeling withapplications in environmental pollution abatement. Liquideffluents arising in agro-alimentary plants, specifically, oliveoil mill wastewaters, are characterized by a high total organiccarbon (TOC) fraction so that three-phase reactors are requiredfor continuous wastewater treatment operating in the trickle-flow regime in trickle-bed reactors. The VOF model is used togain insight and quantitative information about the concentrationand temperature profiles when a phenolic model solution isemployed to simulate CWAO in a multiphase reactor.

2. Mathematical Model

2.1. Governing Flow Equations. A trickle-bed reactor ofnonoverlapping spherical particles in cylindrical geometry wasmodeled with a specified void fraction and a set of fluid physicalproperties. The computational geometry shown in Figure 1 wasdesigned so that a distance gap of about 3% of the spherediameter facilitated grid generation, avoiding numerical dif-ficulties that arise in the calculation of convective terms asdescribed elsewhere.18,19 The purpose of this work was todevelop a computational model to analyze the fluid flow throughthe fixed bed including the evaluation of axial and radial profilesfor TOC concentration and temperature variables. In particular,liquid-gas flow was considered through a catalytic bed consist-ing of monosized, spherical, solid particles arranged in acylindrical container of a laboratory-scale TBR unit (50 mmi.d. × 1.0 m length). The VOF method was used to compute

the velocity field and liquid volume fraction distributions. Themultiphase flow was assumed to be vertical downward andincompressible, with the mathematical description of the flowof a viscous fluid through a three-dimensional catalytic bedbased on the Navier-Stokes equations for momentum and massconservation.

In the VOF model, the variable fields (pressure, velocity, etc.)are shared by both phases and correspond to volume-averagedvalues. It is thus necessary to know the volume fraction, Rq, ofeach phase, q, in the entire computational domain. This ispossible through the resolution of the volume fraction equationfor phase q

where G and L denote the gas and liquid phases, respectively,and t is the time, and through the resolution of the momentumequation shared by the two considered fluids

where p, g, and the physical properties (density, F; and viscosity,µ) are determined by volume-weighted averages. Iq is theinterphase momentum-exchange term similarly derived by Lopesand Quinta-Ferreira,18 and τcq and τct,q are the viscous stress tensorand the turbulent stress tensor, respectively, defined as

and

The tracking of the interface is done in the cells where thevolume fraction is different from 0 or 1 through the use of thegeometric reconstruction scheme. This calculation schemerepresents the actual interface as a piecewise-linear geometry.

2.2. Free Surface Model: Surface Tension and WallAdhesion. The surface tension is modeled by means of thecontinuum surface force model proposed by Brackbill et al.20

The pressure drop across the surface depends on the surfacetension coefficient, σ, and the surface curvature as measuredby two radii in orthogonal directions, R1 and R2, as expressedby the equation

where p1 and p2 are the pressures in the two fluids on eitherside of the interface. The surface curvature is computed fromlocal gradients in the surface normal at the interface. n is thesurface normal, defined as the gradient of Ri: n ) ∇Ri. Thecurvature, κ, is defined in terms of the divergence of the unitnormal, n: κ ) ∇ · n, where n ) n/|n|. The forces at the surfaceare expressed as a volume force using the divergence theoremassuming the form

Figure 1. Configuration of catalyst particles for the trickle bed used in VOFsimulations.

∂

∂t(RqFq) + ∇·(RqFqUq) ) 0 with q ) G or L (1)

∂

∂t(RqFqUq) + ∇·(RqFqUqUq) ) -Rq∇p + RqFqg +

∇·Rq(τq + τt,q) + Iq with q ) G or L (2)

τq ) µq(∇Uq + ∇Uqt ) + (λq - 2

3µq)∇UqI (3)

τt,q ) µt,q(∇Uq + ∇Uqt ) - 2

3(kq + µt,q∇Uq)I (4)

p2 - p1 ) σ( 1R1

+ 1R2

) (5)

Fj ) ∑pairs ij,i<j

σij

RiFiκj∇Rj + RjFjκi∇Ri

12

(Fi + Fj)(6)

Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010 2639

2.3. Species Continuity and Energy Equations. The pre-dicted flow field including velocities and volume fractions ofboth phases was further used to solve species-transport equationsin order to simulate the catalytic wet air oxidation of a modelphenolic solution in the trickle-bed reactor. These equations areexpressed in the mass balance equation for any species, i

where Ci,q is the concentration of species i in the qth phase (gasor liquid) and Fq and Rq are the density and volume fraction,respectively, of the qth phase. Si,q is the source for species i inphase q. Volume-averaged properties of fluids were used tocalculate the flux across the control cell. Two-film theory wasused to account for mass transfer. The resistance in thegas-liquid film was considered as the rate-limiting resistance.21

The mass-transfer coefficient was computed according to theSatterfield et al.22 correlation, and the heat-transfer coefficientwas calculated according to the correlation developed byBoelhouwer et al.23 as expressed by eqs 8 and 9, respectively

The energy equation, also shared between the phases, is

The VOF model treats energy, E, and temperature, T, as mass-averaged variables

where Eq for each phase is based on the specific heat of thatphase and the shared temperature.

The properties F and keff (effective thermal conductivity) areshared by the phases. The source term, Sh, contains contributionsfrom volumetric reaction heat sources.

2.4. Two-Phase k-ε Turbulence Model. Taking into ac-count that the Reynolds number range for the gas phase is wide(from a minimum of 10 to a maximum of 2500), the mixturek-ε approach was used for turbulence modeling.24 For incom-pressible flows, the turbulence parameters are calculated fromthe equations

and the production of the turbulence kinetic energy, Gk,m, iscomputed as

C1ε and C2ε are constants of the standard k-ε model, with values

of 1.44 and 1.92, respectively, whereas σk and σε are theturbulent Prandtl numbers for k and ε with values of 1.0 and1.3, respectively.

2.5. Numerical Simulation. A tetrahedral mesh representingthe interstitial space of the trickle-bed reactor was created usingthe integrated solid modeling and meshing program GAMBIT,25

mimicking the characteristic dimensions of commercial catalystN-140 supplied by the Sud-Chemie Group, Munich, Germany.Numerical details of the cell sizes and the boundary layertreatment have been described elsewhere.26 The VOF methodsimulates free-surface flow by means of a fluid fraction function,which has values between unity and zero. The discretization ofthe governing equations is done by the finite-volume method.The grid independency was established after the evaluation ofdifferent mesh natures and apertures in order to isolate mesh-related discretization errors. All transport equations werediscretized to be at least second-order accurate in space. Asegregated implicit solver available in the commercial CFDpackage FLUENT 6.127 was employed to evaluate the resultinglinear system of equations. The conditions required for grid-convergent results are based on a 1% relative error criterion,and the simulation accuracy was assessed by comparisons toexperimental data available in the literature. At the interface,the additional interaction conditions depend on the interfacialvelocity and gradient of the surface tension.

The CWAO kinetic parameters for the commercial catalystN-140 were derived similarly to the work developed by Lopeset al.28 The right-most term in eq 7, Si,q, includes the reactionrates in terms of the total organic carbon concentration of thelumped species A, B, and C as represented by the equation

where first-order reactions were assumed for each mechanismstep of the generalized kinetic model. Upon integration of theseequations, a mathematical expression for TOC evolution isobtained as

The activation energies and pre-exponential factors werecalculated by using the Arrhenius plot for the N-140 kineticstudies. These values were used in the corresponding expressionsfor the reaction rate constants k1′ , k2′ , and k3′ as functions oftemperature, according to the Arrhenius law

Our case study is based on kinetic studies performed withcommercial and laboratory-made catalysts carried out in batchmode. Several authors, including Manole et al.,29 illustrated thatdata in continuous trickle-bed reactor in downflow or upflowflooded-bed reactor indicate oxidation behavior similar to that

∂RqFqCq,i

∂t+ ∇·(RqFquqCq,i) ) ∇·(RqFqDi,m∇Cq,i) + RqFqSi,q

(7)

Sh ) 0.815Re0.822Sc1/3 (8)

Nu ) 0.111Re0.8Pr1/3 (9)

∂

∂t(FE) + ∇·[Vb(FE + p)] ) ∇·(keff∇T) + Sh (10)

E )∑q)1

n

RqFqEq

∑q)1

n

RqFq

(11)

∂

∂t(Fmk) + ∇·(Fmubmk) ) ∇·(µt,m

σk∇k) + Gk,m - Fmε

(12)

∂

∂t(Fmε) + ∇·(Fmubmε) ) ∇·(µt,m

σε∇ε) +

εm

km(C1εGk,m - C2εFmε)

(13)

Gk,m ) µt,m[∇ubm + (∇ubm)T]:∇ubm (14)

-rTOCA) -

dCTOCA

dt) (k1′ + k2′)CTOCA

-rTOCB) -

dCTOCB

dt) k3′CTOCB

- k2′CTOCA

(15)

CTOC

CTOC0

)k2′

k1′ + k2′ - k3′e-k3′t +

k1′ - k3′k1′ + k2′ - k3′

e-(k1′+k2′)t

(16)

k1′ ) 452 exp(-3.121 × 103

T ) min-1

k2′ ) 28.1 exp(-3.612 × 103

T ) min-1

k3′ ) 4.32 × 106 exp(-9.814 × 103

T ) min-1

(17)

2640 Ind. Eng. Chem. Res., Vol. 49, No. 6, 2010

observed in batch mode, despite very different liquid-solidratios for the catalytic wet air oxidation of 4-hydroxybenzoicacid.

The inlet turbulence quantities such as the turbulent kineticenergy and turbulent dissipation rate were specified based onFLUENT documentation.27 The turbulent kinetic energy (k) wasestimated from the turbulence intensity as

where I is the turbulence intensity being given by

The turbulent dissipation rate (ε) was estimated from theturbulent viscosity ratio as expressed by

where Cµ is an empirical constant specified in the turbulencemodel (0.09). At 30 bar and 200 °C, the inlet turbulent kineticenergies for the liquid phase (uL ) 0.0055 m/s) and the gasphase (uG ) 0.020 m/s) were 0.518 and 8.117 mm2/s2,respectively, whereas the corresponding turbulent dissipationrates were 0.0654 and 2.934 mm2/s3.

Initial and boundary conditions for the gas and liquid phasesare listed in Table 1, whereas the relevant gas and liquidthermophysical properties at P ) 30 bar used in the VOFsimulations are summarized in Table 2. In eq 10, Sh includesthe source of enthalpy due to the chemical reaction of phenoliccompounds: -3000 kJ/mol.30 Water properties, dissolvedoxygen, phenolic compound diffusion coefficients, water andgas heat capacities, water heat of evaporation, heats of reaction,water vapor pressure, and water density were obtained fromdata or methods included in Reid et al.30 Henry constants foroxygen solubility in water were taken from Himmelblau.31

Phenolic compound and oxygen molecular diffusion coefficientswer ealso estimated by the methods of Wilke and Chang32 andSiddiqi and Lucas.33 The effective diffusion coefficient ofpollutant in water and the gaseous oxygen-solid mass-transfercoefficient were estimated according to Piche et al.34 The

phenolic compound liquid-solid mass-transfer coefficient wascalculated from Goto and Smith,35 and the gaseous oxygen-liquidvolumetric mass-transfer coefficient was derived from Iliuta etal.36

The computations were time-dependent and were carried outuntil steady-state conditions were reached. Standard wallfunctions were employed for turbulent flow conditions. AlthoughFLUENT documentation27 recommends a range of 30-50 forthe cell thickness (y+) in packed-bed flow, it was almostimpossible the meet the y+ criterion everywhere on the spheresurface, so this value computed by the CFD solver was alwaysbelow 200. Until liquid reached the outlet, the time step wasvery low (about 10-7 s). The time step was increased graduallyfrom 10-7 s to a final value of 10-4 or 10-3 s, the latter valuedepending mostly on the density ratio between the two fluids.The time-stepping strategy depended on the number of iterationsby time step needed to ensure very low residual values (all lessthan 10-3). The time step value was increased by a factor of 4after 10 consecutive time calculations with less than fouriterations per time step. In the representative case of a multiphasereactor, the time step was increased to 5 × 10-4 s, and thecalculation was stopped after 1000 iterations with this time stepwithout any significant change in the outlet concentration,temperature, and mass flux values. The three-dimensionalsimulations was carried out on a Linux cluster based on AMD64dual-core 2.2 GHz processors.

3. Experimental Section

3.1. Materials. Syringic, vanillic, 3,4,5-trimethoxybenzoic,veratric, protocatechuic, and trans-cinnamic acids obtained fromSigma-Aldrich were used to replicate the phenolic content ofagro-industrial wastewaters.37 An aqueous solution of phenolicacids (1200 mg/L, 200 mg/L for each phenolic acid) was usedas the simulated effluent. Commercial catalyst was supplied bythe Sud-Chemie Group (Munich, Germany): CuO-MnOx (N-140: CuO, 22%; MnOx, 50%) with a bulk density of 0.9 kg/L.N-140 has been used in the oxidation of carbon monoxide inprotective masks, protective dresses, superclean gases, nitrogenmonoxide oxidation, catalytic combustion of volatile organiccompounds (VOCs), and adsorption of toxic aggressive gasesin the semiconductor industry. In our previous works, thecatalytic activity and stability of this manganese/copper catalystwas addressed in terms of metal leaching and catalyst poisoningin batch mode. N-140 exhibited low levels of carbon andhydrogen adsorption and revealed itself as an interestingformulation with further industrial implementation in the CWAOof olive oil mill wastewaters when compared to laboratory-mademanganese/cerium catalyst.38

3.2. Equipment. Experiments were conducted in a trickle-bed flow reactor as illustrated in Figure 2. The cylindrical reactorwas made of stainless steel (SS-316) with a 50-mm internaldiameter and a 1.0-m length. All tubing and fittings used werestainless steel with a distributor on the top and a gas-liquidseparator on the bottom. The liquid pollutant and gas phase wereintroduced downward into the reactor through the distributor.

The gas flow rate was adjusted and controlled by a mass flowcontroller. The gas stream discharge was controlled by a Brooks5866 series back-pressure controller (maximum pressure opera-tion of 100 bar) to maintain constant pressure inside the reactor.It was installed after the condensation liquid system andconnected to the gas-liquid separator in order to obtain a gasstream free of liquid toward the controller. This system wascontrolled by a back-pressure regulator from Brooks Instrument(Read Out & Control Electronics 0154). The liquid feed high-

Table 1. Initial and Boundary Conditions for the Gas and LiquidPhases

t ) 0 z ) 0

RG 0.25 0.25RL 0.15 0.15G [kg/(m2 s)] 0.1-0.7 0.1-0.7L [kg/(m2 s)] 1-15 1-15P (bar) 30 30k (m2/s2) eqs 18-20ε (m2/s3) eqs 18-20

Table 2. Relevant Thermophysical Properties of Gas and LiquidPhases at P ) 30 bar

value (P ) 30 bar)

property T ) 25 °C T ) 200 °C units

Liquid Phase

viscosity 8.925 × 10-4 1.340 × 10-4 Pa sdensity 998.4 866.9 kg/m3

surface tension 7.284 × 10-2 3.770 × 10-2 N m

Gas Phase

viscosity 1.845 × 10-5 2.584 × 10-5 Pa sdensity 35.67 21.97 kg/m3

k ) 32

(uI)2 (18)

I ) 0.16(RedH)-1/8 (19)

ε ) FCµk2

µ (µt

µ )-1

(20)


pressure pump was obtained from Dosapro Milton Roy (modelXB140K5A100, SS 316) and could operate up to 100 bar and114 L/h.

Heating was provided by using seven electrical heatingjackets: one in the bottom (φ 140 × 35 mm; 300 W), five inthe reactor cylinder (each φ 78 × 180 mm; 800 W), and one atthe top (φ 140 × 50 mm; 500 W). Additionally, the liquid feedwas also preheated by an external oven (from Carbolite PeakSeriesPN1201500W)equippedwithaproportional-integral-derivative(PID) controller for temperature stability of (0.5 K.

Total organic carbon was measured with a Shimadzu 5000TOC analyzer that operates based on the combustion/nondis-persive infrared gas analysis method. The parameter uncertaintyin TOC measurement, quoted as the deviation of three separatemeasurements, was never larger than 2% for the range of TOCconcentrations encountered.

3.3. Experimental Procedure. The liquid feed was prewet-ted with the phenolic feed stream to guarantee the saturation ofthe catalytic bed, and pure air (99.999%) was used as the oxygensource and flowed from the rack of gas cylinders through themass flow controller into the top of the reactor, where it wasmixed with the phenolic acid solution feed at the gas-liquiddistributor before entering the reactor. The trickle-bed reactorconfiguration was such that the feed passed over a short bed(length of 5 cm) of inert glass beads before entering the catalystzone. After exiting the reactor, the effluent was cooled anddepressurized.

The reactor was heated at the temperature set point (160 or200 °C) and loaded with around 990 g of N-140 catalyst andrun continuously until the completion of the flow reactor studies.To avoid disruptive cooling/heating and reactor shutdown, waterwas run through the reactor during extended periods when nodata were collected. The liquid flow rate was maintainedconstant in the range of 1-10 kg/(m2 s), and the air inlet flowrate was maintained in the range of 0.1-0.7 kg/(m2 s), whichallowed for operation under trickling flow conditions. The flowrates were kept constant throughout the trickle-bed studies inorder to maintain consistent hydrodynamics (liquid holdup andtwo-phase pressure drop) in the reactor to eliminate side effectssuch as natural pulsing flow that would exist at the upper valuesfor the gas and liquid flow rates. Space time was monitoreduntil the steady-state conversion was reached in terms of totalorganic carbon removal. Pressure was maintained at ap-proximately 30 bar, whereas the temperature range studied was

from 160 to 200 °C. The temperature along the different axialpoints of the reactor was monitored by means of six Omegathermocouples (K-type) inserted in one single rod in the radialcenter of the reactor.

4. Results and Discussion

4.1. Nonreacting Flow Validation. To gain insight into theeffects of various parameters such as liquid velocity, surfacetension, and wetting phenomena, the current VOF model wasstudied in nonreacting flow conditions to simulate the multiphaseflow in the high-pressure trickle-bed reactor. The accuracy ofthe simulations was evaluated in terms of the tetrahedral meshsize, and several model solution parameters were optimized,including time step and convergence criteria. On the discreti-zation of the volume fraction equation, high-order differencingschemes were found to give better computed results for bothliquid holdup and two-phase frictional pressure drop, asdescribed elsewhere.26 According to the numerical simulationscarried out so far, the VOF model was used to evaluate theeffect of the gas flow rate in the range G ) 0.1-0.7 kg/(m2 s)on the hydrodynamics, demonstrating its considerable influenceon the liquid holdup in comparison with the effect of the liquidflow rate. The optimum values for the numerical solutionparameters were further used in the VOF model to evaluate thehysteresis in both hydrodynamic parameters at high pressure.During the VOF simulations, Lopes and Quinta-Ferreira39 foundthat wetting efficiency can be captured through the evaluationof successive radial planes of liquid volume fraction at differentpacked-bed cross sections. Additionally, the effect of the gasflow rate on the numerical accuracy produced by either laminaror several turbulent flow models was investigated for bothhydrodynamic parameters. At lower gas flow rates, the VOFpredictions performed with the laminar flow model were foundto produce qualitatively and quantitatively the same computedresults as turbulent flow models for both liquid holdup andfrictional pressure drop, whereas for higher flow rates, theturbulent flow models performed better, indicating the consider-able degree of turbulence induced by the gas phase.26 Followingthe VOF hydrodynamic validation, those optimum numericalsolution parameters were integrated into the multiphase flowmodel aiming to evaluate the axial and radial mapping ofreaction parameters (temperature and total organic carbonconcentration) in the catalytic wet air oxidation of phenolicwastewaters.

4.2. Reaction Studies. After the VOF model validation,several test cases were performed with initial perturbation ofthe inflow total organic carbon concentration and/or temperatureconditions in order to illustrate the potentialities of the method.The dynamic behavior of the trickle-bed reactor was studiedby evaluating the concentration and temperature profiles for thestartup of the process until the steady state was reached. Thisunsteady-state operating strategy leads to a further increase inthe complexity of the physical and chemical processes determin-ing the overall TBR behavior and therefore necessitates a morerefined modeling approach, with special attention being givento the axial and radial profiles under the dynamic operatingconditions. The VOF multiphase model was employed to modelthe surface flow including surface tension effects mainly dueto the increased importance of reaction, convection, anddiffusion for mixing phenomena.

The reactor was initially heated at the wall temperature (Tw

) 160 and 200 °C), and at the time t* ) 0, the feed streamentered the reactor, representing a step change in the inlet totalorganic carbon concentration. This fact led to the use of high-

Figure 2. Schematic diagram of experimental setup of trickle-bed reactor.


order discretization schemes in order to suppress the so-called“numerical diffusion”, which is simply numerical errors beingaccumulated by the algorithm and introduced by step perturba-tions at the system boundary. The concentration and temperatureshock waves and contact discontinuities were smoothed overthe available grid points by performing upwind-biased dif-ferentiation of the fluxes, but flows involving turbulence requireda different strategy because the complicated flow structuredemands a more versatile numerical algorithm. To avoidinterference with the flow physics, transport schemes must becarefully studied in order to deal with the discontinuityintroduced at the system boundary.

4.2.1. Axial Total Organic Carbon Profiles. Figures 3 and4 show the transient axial profiles predicted by the VOF modelfor the mean radial values of the bulk-phase concentration forT0 ) Tw ) 160 and 200 °C, respectively. According to theseconcentration profiles, the total organic carbon conversion ishigher when the catalytic wet air oxidation is simulated at highertemperatures because the oxidation reaction is exothermic andfollows an Arrhenius dependence; therefore, the reaction rateincreases with increasing temperature. For example, for T0 )Tw ) 160 °C and t* ) 6, the TOC conversion is about 78%,but it is 92% for T0 ) Tw ) 200 °C, indicating the positiveeffect on pollutant degradation. The steady state was reachedafter t* ) 10 for both operating temperatures, resulting in TOC

conversion of 88% and 94% for T0 ) Tw ) 160 and 200 °C,respectively. As can be seen, the VOF model overpredicted theexperimental data on TOC removal for both operating temper-atures. Moreover, the computed relative error increased withincreasing axial coordinate at the steady state.

The axial dispersion observed in the total organic carbonconcentration for t* < 1 indicates some degree of backmixingin the trickle-bed reactor operating in downflow mode. In fact,the backmixing effect when the system operated at T0 ) Tw )200 °C was slightly lower than when it operated at T0 ) Tw )160 °C. At this temperature and for t* ) 0.25, the concentrationprofile spanned the axial coordinates between 0.18 and 0.4 m,whereas for T0 ) Tw ) 200 °C and at the same operation time,the concentration spanned between 0.18 and 0.26 m. Thisindicates that the backmixing decreased with an increase in thewall/inlet temperature for downflow operation mode. A similarphenomenon was observed experimentally by Saroha andKhera,40 who reported that backmixing decreases with anincrease in the liquid flow rate for both upflow and downflowmodes of operation. Therefore, the liquid flow rate plays thesame role as the temperature in the downflow mode of trickle-bed operation.

4.2.2. Axial Temperature Profiles. The influence of theoperating temperature on the thermal profiles is plotted inFigures 5 and 6. Upon comparison between these temperatureaxial profiles and the TOC profiles already plotted in Figures 3and 4 for the same operating conditions, it can be concludedthat the propagation velocities of the mass and thermal shockwaves are not very different. The operation times required forthe thermal wave and for the TOC wave to achieve steady statewere almost the same, t* ) 10. Once again, the VOFoverpredicted the temperature elevation in comparison with theexperimental data measured at the two different operatingconditions. As can be seen from Figure 5, the qualitativebehavior between the temperature predicted by the VOF modeland experimental data was reasonably similar at T0 ) Tw )160 °C. However, upon increasing the operating temperatureto T0 ) Tw ) 200 °C, a considerable divergence was foundbetween the VOF predictions and the experimental data for thebulk temperature obtained at steady state.

The main intrinsic difference between the two VOF axialprofiles is related to the intensity of the maximum mean radialbulk temperature when the catalytic wet air oxidation is modeledat T0 ) Tw ) 160 and 200 °C. In fact, one can observe that thehot spot was achieved earlier when the operating temperature

Figure 3. Mean radial bulk total organic carbon profiles for axial coordinatesat transient conditions for different dimensionless operating times, t* [T0

) Tw ) 160 °C, L ) 5 kg/(m2 s), G ) 0.5 kg/(m2 s), P ) 30 bar].

Figure 4. Mean radial bulk total organic carbon profiles for axial coordinatesat transient conditions for different dimensionless operating times, t* [T0

) Tw ) 200 °C, L ) 5 kg/(m2 s), G ) 0.5 kg/(m2 s), P ) 30 bar].

Figure 5. Mean radial bulk temperature profiles for axial coordinates attransient conditions for different dimensionless operating times, t* [T0 )Tw ) 160 °C, L ) 5 kg/(m2 s), G ) 0.5 kg/(m2 s), P ) 30 bar].


was higher (T0 ) Tw ) 200 °C: z ) 0.2 m) than when the reactorwas operated at lower temperature (T0 ) Tw ) 160 °C: z )0.25 m). This fact can be supported by the chemical reactionthermodynamics, so that higher temperatures favor the oxidationrates and then the heat delivery from this exothermic reactionwill be higher. For T0 ) Tw ) 160 °C, in the hot spot, amaximum temperature of about 164.5 °C was achieved, whichcorresponds to a difference of 4.5 °C with respect to the wall/inlet temperature, but when the same chemical reaction wasprocessed at T0 ) Tw ) 200 °C, the maximum temperature forthe hot spot was 212 °C, which corresponds to 6% more thanthe wall operating temperature. For both cases, the steady statewas accomplished at the same operating time, t* ) 10.Therefore, one can conclude that, for higher inlet and walltemperatures, the magnitudes of the hot spots and the finalreactant conversions are also higher, demonstrated by the meanradial bulk temperature and concentration profiles along thecatalytic bed. One should also bear in mind that an increase intemperature also increases the equilibrium water vapor pressureso that an increase in operating temperature requires an increasein total operating pressure in order to maintain the oxygen partialpressure. Because the catalytic wet air oxidation of phenolicacids is exothermic, it releases energy, which raises thetemperature of the liquid and gas streams, leading to furtherwater evaporation. This fact can be advantageous because waterwill act as a heat sink, preventing the reaction from runningaway.

4.2.3. Radial Total Organic Carbon Profiles. For T0 ) Tw

) 160 °C and z ) 0.25 m, which corresponds to the hot spotzone, Figure 7 presents the transient radial profiles of totalorganic carbon for different times, whereas Figure 8 plots thesame radial TOC profiles for the corresponding hot spotachieved for T0 ) Tw ) 200 °C. These concentration profilesindicate that the radial gradients attained for T0 ) Tw ) 160 °Care about 10% of the difference between the centerline and wallvalues, which demonstrates a considerable degree of poor radialmixing, specifically at the hot spot. As the multiphase flow isdriven by pressure, the hydrodynamic parameters are the resultof frictional forces building up where the gas and liquid phasesare in contact with solid surfaces. These frictional forces resultin decreases of the velocity in the fluid phases at these interfaces,and this creates a parabolic flow profile in the reactor whenoperating at low Reynolds numbers. For T0 ) Tw ) 200 °Cand t* < 2, the concentration profile observed in Figure 8 issomewhat similar to the parabolic velocity distribution in laminar

flow in which the velocity of the fluid phase is large in thecenter but drops to zero next to the walls. Additionally, the TOCprofile obtained for T0 ) Tw ) 200 °C plotted in Figure 8indicates a maximum difference of 6% for the total organiccarbon degradation. For t* > 2, the maximum concentrationdifference is achieved at the steady state (t* ) 10), which canbe explained by the higher temperature achieved in the centerthat leads to higher TOC oxidation rates and, therefore, largevariations for the TOC radial values.

4.2.4. Radial Temperature Profiles. Figures 9 and 10present the transient radial temperature profiles computed forthe hot spot at z ) 0.2 and 0.25 m for T0 ) Tw ) 160 and 200°C, respectively. In this case, the thermal distributions are notvery different whether the TBR is operated at 160 or 200 °C.For T0 ) Tw ) 160 °C, it can be observed in Figure 9 that themaximum temperature difference obtained radially is 4 °C,which is similar to the value already obtained for the axialtemperature profile at the same operating temperature. Thisconfirmation points out that the trickle-bed reactor underwentpoor radial mixing because, despite of the ratio between thereactor length and diameter (L/d ) 20), the same orders ofmagnitude for the axial and radial temperature profiles wereachieved. Figure 10 illustrates this fact preeminently for T0 )Tw ) 200 °C, in which the maximum radial temperaturedifference was 12.8 °C and, once more, a value slightly higher

Figure 6. Mean radial bulk temperature profiles for axial coordinates attransient conditions for different dimensionless operating times, t* [T0 )Tw ) 200 °C, L ) 5 kg/(m2 s), G ) 0.5 kg/(m2 s), P ) 30 bar].

Figure 7. Radial total organic carbon profiles at the hot spot for differentdimensionless operating times, t* [T0 ) Tw ) 160 °C, L ) 5 kg/(m2 s), G) 0.5 kg/(m2 s), P ) 30 bar].

Figure 8. Radial total organic carbon profiles at the hot spot for differentdimensionless operating times, t* [T0 ) Tw ) 200 °C, L ) 5 kg/(m2 s), G) 0.5 kg/(m2 s), P ) 30 bar].


than the difference attained for the axial coordinate. ComparingFigures 7-10, in which TOC concentration and temperatureradial profiles are plotted, one can observe opposite behaviorsalready advanced for the explanation of these radial distributions.In fact, whereas the concentration profiles decrease from thewall to the center, the thermal profiles increases from the wallto the center, reaching a maximum at r ) 0. As the chemicalreaction is favored by higher operating temperatures, it isexpected that the higher conversions will also be obtained inthose cases, so that the TOC degradation reaction rates are higheras well, leading to the sharp radial mass and thermal profilesobtained. In all cases, the steady state is reached at t* ) 10.These computational results show that the radial gradients arequite severe at the hot spot, as observed in the temperature colormaps presented in Figure 11a,b for different operating times,t* ) 2 and 10, where the difference between the centerline andwall temperatures corresponds to about 6% of the wall and inlettemperature. Therefore, the hotspot formation phenomenon canbe attributed to the predicted radial dispersion being itsrelationship with underlying fluid dynamics demonstrated byFigure 12a,b. However, according to Figure 12, the gas andliquid holdup radial distributions at the hot spot for t* ) 10did not show the same behavior as the thermal profiles (Figure11) already exhibited. Phase holdup seems to not have a directcorrelation with temperature nonuniformity and hotspot forma-

tion. Moreover, the VOF snapshots for the gas (Figure 13a)and liquid (Figure 13b) velocities at the hot spot [t* ) 10, T0

) Tw ) 200 °C, L ) 5 kg/(m2 s), G ) 0.5 kg/(m2 s), P ) 30bar] also demonstrate that the local variations of the gas-liquidvelocities are practically independent of the temperature profile.In fact, only the VOF snapshot for the total organic carbonconcentration at the hot spot (Figure 14) showed behavior similarto that observed for the radial distribution of the bulk-phasetemperature. According to Figure 14, the radial profile TOCshowed that the lower pollutant concentrations were achievedin the TBR center, with the maximum values being attained atthe wall. Consequently, it can be assumed that the hydrodynamicparameter that can have a major effect on hotspot formationseems to be the catalyst wetting efficiency given that neitherthe phase holdup nor the velocity exhibited a direct outcomeon the thermal profile.

It should be stressed that these hot spots could initiateundesired side reactions and damage the catalyst, leading, inextreme cases, to reactor runaway. Our computational runsconfirmed that nonisothermal effects in trickle-bed reactoroperation have to be taken into account in CFD modeling. TheVOF model allows for the computation of local mass and heat

Figure 9. Radial temperature profiles at the hot spot for differentdimensionless operating times, t* [T0 ) Tw ) 160 °C, L ) 5 kg/(m2 s), G) 0.5 kg/(m2 s), P ) 30 bar].

Figure 10. Radial temperature profiles at the hot spot for differentdimensionless operating times, t* [T0 ) Tw ) 200 °C, L ) 5 kg/(m2 s), G) 0.5 kg/(m2 s), P ) 30 bar].

Figure 11. Radial temperature color maps at the hot spot for t* ) (a) 2and (b) 10 (steady state).


transfer, and recent simulation activities have indicated that onecan evaluate external wetting of the catalyst pellets39,41 andminimize the poor liquid distribution, which is the main causefor hot spot formation. In fact, during our CFD simulations,the mean value of the wetting efficiency was computed as beingalmost 82% at L ) 5 kg/(m2 s), G ) 0.5 kg/(m2 s), and P ) 30bar.

The current VOF formulation can be an interesting option tocapture wetting phenomena and the effects of flow regimes inthree-phase packed-bed reactors. A VOF method can thereforebe used to probe the hydrodynamic behavior of a TBR in termsof pressure drop, liquid holdup, and catalyst wetting efficiencyin detail as never before. These computational results allow abetter understanding of the fundamental physics governing theefficiency of multiphase reactors for advanced wastewatertreatment facilities and the CWAO technology deployment incommercial-scale TBRs to be obtained.

5. Conclusions

A trickle-bed reactor (TBR) was modeled by means of thevolume of fluid (VOF) model to provide reaction behavior

analysis in transient conditions. Because conventional modelingtechniques are unable to address multiphase flow distributions

Figure 12. VOF snapshots of the (a) gas and (b) liquid holdups at the hotspot for t* ) 10 [T0 ) Tw ) 200 °C, L ) 5 kg/(m2 s), G ) 0.5 kg/(m2 s),P ) 30 bar].

Figure 13. VOF snapshots of the (a) gas and (b) liquid velocities (cm/s) atthe hot spot for t* ) 10 [T0 ) Tw ) 200 °C, L ) 5 kg/(m2 s), G ) 0.5kg/(m2 s), P ) 30 bar].

Figure 14. VOF snapshot of the total organic carbon concentration (ppm)at the hot spot for t* ) 10 [T0 ) Tw ) 200 °C, L ) 5 kg/(m2 s), G ) 0.5kg/(m2 s), P ) 30 bar].


and local temperature variations, the VOF model was used toinvestigate the dynamic performance under reaction conditionsproviding a more rigorous physical description of the underlyingflow process. Catalytic wet air oxidation was taken as anexample to evaluate axial and radial profiles for total organiccarbon depletion and temperature along the packed bed.

Computational runs were compared against experimental data,and the VOF model was then used to understand the influenceof operating temperature on the total organic carbon distributionand to describe its interaction with the chemical oxidationreaction. The computational runs exhibited backmixing effectsthat were more pronounced for lower operating temperatures.The mean radial temperature profiles revealed the existence ofhot spots in the simulated flow regime. Furthermore, poor radialmixing was noted mainly at the hot spot locations addressed inmass and thermal profiles.

Acknowledgment

The authors gratefully acknowledge the financial support ofREMOVALS, 6th Framework Program for Research andTechnological Development, FP06 Project 018525, and Fun-dacao para a Ciencia e Tecnologia, Lisboa, Portugal.

Nomenclature

C ) species concentration, ppmcp ) specific heat, J/(kg K)Cµ, C1ε, C2ε ) k-ε model parameters, with values of 0.09, 1.44,

and 1.92, respectivelyD ) mass diffusivity, m2 s-1

dp ) catalyst particle nominal diameter, mE ) thermal energy, Jgb ) gravitational acceleration, 9.81 m/s2

G ) gas mass flux, kg/(m2 s)GkL ) generation rate of turbulent kinetic energyh ) convective heat-transfer coefficient, W/(m2K)Iq ) interphase momentum-exchange termk ) k-ε model kinetic energyK ) mass-transfer coefficient, m s-1

kf ) thermal conductivity, W/(m K)keff ) effective thermal conductivity, W/(m K)l ) characteristic length, mL ) liquid mass flux, kg/(m2 s)nw ) unit vector normal to the wallNu ) Nusselt number ) hl/kf

p ) pressure, barPr ) Prandtl number ) Cpµ/kf

Req ) Reynolds number of the qth phase ) Fquqdp/µq

Si ) source mass for phase i, ppmSh ) Sherwood number ) Kl/DSh ) source term containing volumetric reaction heat, Jt ) time, st* ) dimensionless time ) t/τtw ) unit vector tangent to the wallT ) temperature, KTOC ) total organic carbon, ppmub ) superficial vector velocity, m/sz ) axial coordinate, mGreek LettersRi ) volume fraction of the ith phase∆p ) total pressure drop, Paε ) k-ε model dissipation energyθw ) contact angle at the wall (deg)κ ) gas-liquid interface curvature

µq ) viscosity of the qth phase, Pa sFq ) density of the qth phase, kg/m3

σ ) surface tension coefficientσk, σε ) k-ε model parameters, with values of 1.2 and 1.0,

respectivelyτ ) residence time, sτcq ) viscous stress tensor of the qth phase, Paτct,q ) turbulent stress tensor of the qth phase, PaSubscriptsG ) gas phaseL ) liquid phasem, n ) Cartesian coordinate directionsq ) qth phaseS ) solid phase

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Accepted January 08, 2010

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Assessment of CFD−VOF Method for Trickle-Bed Reactor Modeling in the Catalytic Wet Oxidation of Phenolic Wastewaters