Modeling Catalytic Trickle-Bed and Upflow Packed-Bed Reactors for

6634

Ind. Eng. Chem. Res. 2005, 44, 6634-6642

Modeling Catalytic Trickle-Bed and Upflow Packed-Bed Reactors for Wet Air Oxidation of Phenol with Phase Change Jing Guo* and Muthanna Al-Dahhan Chemical Reaction Engineering Laboratory (CREL), Department of Chemical Engineering, Campus Box 1198, Washington University, St. Louis, Missouri 63130

In this study, to simulate the steady-state behavior of packed-bed reactors for catalytic wet oxidation of phenol, one-dimensional (1D) axial dispersion model for the liquid phase is coupled with a cell stack model for the gas phase, providing considerable phase change under the selected operating conditions. The reactor scale governing equations, reaction kinetics involved, and solution strategy are discussed. The computational approach accounts for the observed catalyst activities, combined with local transport and catalyst wetting effects. The approach selected is shown to be suitable and efficient in dealing with the problem in question. Comparisons of simulated model predictions and lab scale experimental data are presented. Reasonably simulating the concentration profiles in the reactor at steady-state operation, the model allows designers to determine the effects of catalyst activity and operating and feed conditions on reactor performance. The model also clearly demonstrates the importance of including the phase change effect in the reactor scale flow distribution. 1. Introduction Considerable capital and operational costs have been invested in providing experimental data and investigating reaction course and mass-transfer processes in packed-bed reactors. Many attempts have also been made to provide rational, physically based models for successful commercial exploitation. Although literature on packed-bed reactors is abundant, the majority of studies consider nonvolatile liquid reactants and constant phase velocities. However vaporization during steady-state reaction in the multiphase is often encountered.1 In many situations, liquid evaporation influences the behavior of the packed-bed reactor, especially in downflow packed-bed (i.e., trickle-bed) operation. Liquid evaporation makes possible a formation of dry zones in catalyst pellets. Reaction then occurs on dry catalyst surfaces, which may result not only in poor product selectivity but also in catalyst destruction. In fact, several possible states of the catalytic pellet can result from the evaporation of liquid flowing over the external catalyst surface. A considerable part of the overall mass transfer resistance within the external trickling liquid film disappears.2 Because of the much higher reactant diffusion coefficients in the gas phase than in the liquid phase, the internal surface of catalyst gets more effective use.3 The more rapid mass transport and less efficient heat removal associated with the gaseous system can lead to significant increases in undesirable side reaction rates. Therefore, the interactions among phase transition, multiphase transport, and catalytic chemical reactions greatly complicate the reactor design and operation. Among the investigations in the field of reactions in trickle beds with volatile components, Collins et al.4 studied hydrodesulfurization of benzothiophene at a constant pressure of 68 atm and a temperature range * To whom correspondence should be addressed. Tel.: (314) 935-4729. Fax: (314) 935-7211. E-mail: [email protected].

of 546-606 K by simulating the global reaction rate in the presence of phase equilibrium effects at each point. The rate was simulated based on four solvents with different volatility to study the influence of relative solvent volatility on the reaction rate. Gianetto and Silveston5 modeled their reaction by assuming a series of plug flow reactors, where each was preceded by a vapor-liquid separator, and local thermodynamic equilibrium was reestablished after the reaction stage. The model was tested for the hydrodesulfurization of dibenzothiophene at 325 °C and 3.15 MPa. The assumptions included that liquid flow was not affected by the evaporation of solvent and that catalyst particles were completely covered by liquid. These assumptions were valid for the reaction system at dilute liquid reactant concentrations. LaVopa and Satterfield6 studied the effect of volatility using two test reactions, namely, the hydrideoxygenation of dibenzofuran and hydrogenation of n-butylbenzene. Their reactor model assumed a series of stirred tanks with both liquid and vapor flows going in and out of each stage, analogous to a distillation tray. The effect of changing the gas/liquid feed ratio on the conversion in the trickle flow regime was examined. The complete vapor regime was also studied in the presence of solvents with different volatilities (hexadecane and squalene). An increase in conversion was observed with a decrease in the gas/liquid ratio, due to an increase in liquid reactant partial pressure. Bhatia7 theoretically demonstrated the effect of capillary condensation for a vapor mixture containing a volatile and an inert component and examined the possibility of internal recondensation of the volatile reactants and products when the vapor phase is near or at saturation. In our previous work,8 the reactor scale model has been applied to account for the multiphase mass transfer occurring in the packed-bed process. The selected test reactions in that work were held at ambient temperatures and moderate pressures (1.5 MPa), where the liquid vaporization effect was negligible. The comparison between the model simulation and the experimental observations showed that the original model was

10.1021/ie050335v CCC: $30.25 © 2005 American Chemical Society Published on Web 07/21/2005

Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005 6635

sufficient for evaluation of the reaction system without considerable vaporization effects. However, when this model was employed to predict a lab scale packed-bed reactor under mild temperature (110-170 °C) and moderate pressure (1.5-3.2 MPa), significant deviation was present.9 Such deviation was attributed to the lack of accounting for phase change (evaporation or condensation) and its effect on phase compositions and velocities. Therefore, this work is to assess the effects of reaction parameters on the local flow distribution and on the performance of the catalytic wet oxidation (CWO) process, by accounting for the phase change. Comparisons are presented between simulation results and experimental findings for different sets of conditions with the steady-state behavior. The supporting experimental work10 has been carried out in an isothermal packed-bed reactor operated in both downflow and upflow, where the operating parameters investigated included temperature, reactor pressure, gas flowrate, liquid hourly space velocity (LHSV), and feed concentration. The model presented in this study could be used to facilitate the scale-up of these experimental results, to aid the design and optimization of a pilot plant or commercial unit, and to effectively design future experiments. 2. Model Description The reported experimental conditions10 resulted in significant axial dispersion effects in the liquid phase (PeL)21-39 for downflow mode and PeL)3-5 for upflow mode). In fact, axial dispersion has strong impacts on the reactant concentration at the reactor outlet. The differences between the predicted concentrations calculated by the plug flow type and the axial dispersion model depend on the conversion level. For a first-order hydrotreating reaction, Thanos et al.11 found that the differences are not significant for conversions up to 85%, and the differences can be close to the random experimental error or the error of the concentration measurements. But as the space velocity decreases the conversion increases, and the differences become important. For the extrudates of equivalent diameter (deq)1.9 mm), the relative deviation of the exit concentration compared to the plug flow case is 5.4% at LHSV ) 2 h-1, and the relative deviation increases to 170% at LHSV )0.5 h-1. For the extrudates of equivalent diameter (deq)3.1 mm), the corresponding relative deviations are 11% and 440%, respectively. These relative deviations are very high and may lead to considerable errors in the reactor design and scale-up. It is noted that the dimension of Al-Fe pillared clay catalyst extrudates (deq)3.6 mm) employed in this work is similar to the cylindrical extrudates used by Thanos et al.11 Considering the low LHSV investigated in this CWO process (0.2-2 h-1), the effect of axial dispersion was considered significant, and hence, the axial dispersion model (ADM) was employed to describe the liquid phase. 2.1. Model Description for Liquid Phase. Governing equations for liquid-phase ADM are listed as follows to describe the liquid phase in the whole packed-bed reactor, with appropriate inlet and outlet boundary conditions.

DEL,k

d2Ck,L 2

dz

dCk,L + (KLaGL)k[Ck,e - Ck,L] - uSL dz (kLS)kaLS[Ck,L - Ck,LS] ) 0 (1)

Mass transfer

kLS,kaLS[Ck,L - Ck,LS] )

∑r [νr,k(-Rr)(Ck,LS,T)]

(1 - B)ηCE ‚

(2)

Boundary conditions

-DEL,k

dCk,L ) uSL[Ck,0-Ck,L] at z ) 0 dz

(3)

dCk,L ) 0 at z ) L dz

(4)

1 1 1 ) + (KLaGL)k kLaGL HkkG aGL

(5)

where

At steady-state conditions, axial dispersion and convection of liquid reactants are in equilibrium with liquid-solid mass transfer and the volumetric mass exchange between the gas and liquid. The dissolution of gaseous O2 into liquid is one type of gas-liquid mass exchange. So are the water evaporation and the escape of the low boiling point products (e.g. CO2, acetic acid) to gas. Even though these processes undergo different pathways, they are driven by the same force, the difference of species concentrations between gas and liquid phase. Hence, a generalized mass transfer rate expression can be obtained based on the two film theory for straight gas-liquid mass transfer.12 The amount of mass exchange can be predicted by the product of the overall mass transfer coefficient (KLaGL)k and the driving force [Ck,e-Ck,L]. The exchange flow direction between gas and liquid depends on the relative values between the hypothetical equilibrium concentration of gaseous species in liquid (Ck,e) and the species concentration in liquid bulk (Ck,L). The overall gas-liquid mass transfer coefficient 1/(KLaGL)k is calculated by eq 5, with the liquid film and gas film resistances given as 1/kLaGL and 1/HkkGaGL, respectively. Catalyst pellets are described in the form of a onedimensional slab with both sides exposed to either gas or liquid. For the down flow operation, catalyst pellets are divided into three liquid-solid contacting categories: (a) both catalyst surfaces are completely dry, i.e., gas-covered, (b) one of the catalyst surfaces is actively wetted and the other one is dry, and (c) both catalyst surfaces are completely wetted, i.e., liquid covered. The corresponding weights for each category are taken as (1-ηCE)2, 2ηCE(1-ηCE), and ηCE2, respectively.13 This way, the sum of the weights turns out to be unity, and the fraction of the external catalyst surface that is actively covered with liquid is ηCE. The half wetted and completely wetted catalyst pellets are assumed to be internally completely wetted because of the capillary forces, and the diffusion of all species occurs in the liquid inside the particles. Since the primary reactant, phenol, is relatively nonvolatile, it hardly accesses a completely externally dry pellet, category (a), where no reactions are present. The reactions are assumed to take place only in the partially wetted and fully wetted particles, i.e., categories (b) and (c). For these two wetting types, the species concentrations over the wetted catalyst surface are assumed to be the same and can be calculated from the liquid phase governing eqs 1-5. The

6636

Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005

species over the actively dry catalyst surface are involved in the gas-solid mass transfer and thus can be derived from the governing equations for gas phase. On the contrast, for the upflow operation, all catalyst particles are surrounded and fully wetted by the liquid phase, which means only the third wetting category (c) exists, and the catalyst wetting efficiency is assumed to be 1.0. The mass transfer resistance between the liquid and solid phases is reflected in a separate algebraic equation (eq 2). Solid particles are usually large to minimize pressure drop in packed bed reactors, and this implies the liquid diffusion within the particle pores. The actual reaction rate (-Rr) used in eq 2 is calculated from apparent kinetics rate expression, which is evaluated for the catalyst extrudate cylinders and based on the concentration of species k in the liquid phase at the solid external surface. According to the definition of effectiveness factor (η), the actual reaction rate (-Rr) is equal to the product of the effectiveness factor (η) and the intrinsic reaction rate (-Rr,in). Suppose the intrinsic kinetics rate (-Rr,in) is known and that η has been determined as a function of local operating conditions in the reactor, then the term η(-Rr,in) can be applied in eq 2 as the rate expression. However, our focus is on the effect of the catalyst extrudate on the packed bed performance, rather than the catalyst internal mass diffusion. Therefore, instead of calculating η and intrinsic kinetics separately, it is adequate to use the apparent reaction rate expression rate in eq 2 to directly derive the actual reaction rate. 2.2. Model Description for Gas Phase. The liquidphase ADM is combined with the discrete cell stack model for the gas phase, so that the flow distribution and the phase change in the packed bed are accounted for in a realistic way. The packed bed is visualized separately for liquid and gas. The liquid phase resumes axial dispersion in the whole reactor, while gas flows through N cells of stirred tanks in series, as shown in Figure 1. For N ) 1, gas phase performs with complete back mixing. For Nf∞, plug flow will prevail for the gas phase, although the grid independence may be obtained after N gets to a certain limit. Flow patterns for the gas phase between these two extremes can be represented by an intermediate value of N. As the fundamental for the cell stack, an element cell with one inlet and one outlet for gas phase was built as a module to contain the chemical reaction and mass transfer based on the local species concentration, external wetting efficiency, and flow characteristics. The volatilities of solvent water and product are incorporated, including the change in gas velocity and other parameters. By considering the interaction between cells along the axial direction, the cell stacks create a one-dimensional (1D) model that is suitable for interpretation of bench scale and pilot scale data. Since the gas-phase velocity is 2 orders of magnitude higher than the liquid phase, and its axial dispersion is usually several orders lower than the liquid phase, the gas phase is assumed to be in plug flow (Nf∞), which is usually expressed as a first-order ODE. However, instead of simultaneously solving the first-order ODE for the gas phase together with the second-order ODE for the liquid phase, a sequential solution scheme is adopted to facilitate the simulation convergence. The first-order ODE for the gas phase is modified as the following eq 6, where liquid-phase concentrations have

Figure 1. Schematic representation of liquid-phase ADM and gasphase cell stacks model.

been explicitly known by solving the liquid-phase governing equation.

1 (u C - uG,inφk,G) ) -(KLaGL)k[Ck,e - Ck,L] Lc G,out k,G (kGS)k(aGS)[Ck,e - Ck,GS] (6) Mass transfer

kGS,kaGS[Ck,e - Ck,GS] ) (1 - B)(1 - ηCE)ηCE ‚

∑r [νr,k(-Rr)(Ck,GS,T)]

(7)

Boundary conditions

Ck,G )φk,G at z ) 0

(8)

where Ck,G, the unknown variable, is the concentration of species k at the cell outlet. φk,G represents the cell inlet concentration for species k, i.e., the feed composition from the previous cell. For the downflow operation, the gas reactants enter the pellet either through the wetted part after first dissolving in the liquid film or through the dry part of the catalyst surface, as seen in eq 6. The latter is in equilibrium with the reactions over the partially wetted catalysts. While for the upflow operation, due to the full catalyst wetting contact with the liquid bulk (ηCE ) 1.0), the direct mass transfer between gas and the solid external surface is no longer present. In such case, the mass transfer between liquid and gas becomes the only source for the change of gas molar flux. 2.3. Apparent Reaction Kinetics. In the experiments for phenol oxidation over packed-bed reactor, only small amounts of intermediate (catechol, hydroquinone, benzoquinone, etc.) were detected at the outlet.10 Hence, the numerical simulation for the overall lumping rate for phenol mineralization is focused instead of the detailed reaction rates for all intermediates in a com-

Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005 6637

prehensive reaction network. Mineralization of phenol is described as

log10(Pk,vap/mmHg) ) A + B/T + C ‚log10(T) + D ‚T + E ‚T2 (13) Accounting for the high-pressure effect, the vaporization pressure is corrected based on eq 14

The apparent kinetics for phenol oxidation over the pillared clay catalyst extrudates has been studied by using a stirred tank reactor from 110 °C to 210 °C, at 1.5-3.2 MPa and with catalyst loading from 3 to 10 kg/ m3. Adequate agitation speed was kept in order to minimize the external mass-transfer resistance between liquid and catalyst external surface. The following Langmuir-Hinshelwood rate expression (eq 10) has been reported, and the corresponding values for the rate and adsorption equilibrium constants were given.14 The denominator of this apparent kinetic expression consists of the adsorption/desorption terms for both reactants. Both the reaction rate constant kr and the adsorption equilibrium constant Kk contain the terms of the prefactor and activation energy. To apply this apparent kinetics in the simulation for packed-bed reactor, the activation energy E for the reaction rate constant kr, together with prefactor and activation energy ∆E for the adsorption equilibrium constant Kk, are maintained as the reported value. However, the Arrhenius prefactors for reaction rate constant kr, derived from apparent kinetics experiments in the stirred tank reactor with high liquid/solid ratio, may not be applicable for the packed-bed reactor with low liquid/solid ratio. Accordingly, the Arrhenius prefactors for reaction rate constant kr are adjusted as a fitted parameter using packed-bed experimental data. After the rate constant was fitted to match the conversion at one space-time, it was maintained and used to compare with the experimental data at all other space times, and the rate form was retained as eq 10.

Rr )

k1KAKO20.5[A][O2]0.5 (1 + KA[A])(1 + KO20.5[O2]0.5)

Ccat0.82 (10)

2.4. Parameter Calculation and Update. The physical properties of the fluids, including Henry’s constant, are accounted for as functions of temperature and pressure. Henry’s constant for O2 is a well-targeted area in the literature. The effect of diluted aqueous phenol on the solubility of O2 is assumed to be negligible. The Henry’s constant of solubility HeO2 can be expressed by the following function of solution temperature15

ln(HeO2/MPa) ) -35.4408 + 5.5897 × 104/T 2.6721 × 107/T2 + 5.8095 × 109/T3 4.9167 × 1011/T4 (11) where T is the temperature expressed in K. Henry’s law constants of solubility (Hek) for the other species, H2O, and CO2, are connected to their vaporization pressure and calculated as

Hek )

Ck,G Pk,vap ) Ck,e RTCtotal,L

(12)

The vaporization pressure for species k at given temperature is given by the Chemical Properties Handbook.16

ln

( )

P ˜ L - PL P ˜ k,vap ) Pk,vap RTCL,total

(14)

where Pk,vap is the vaporization pressure without correction, and PL is the pressure of the gas surrounding the liquid. Usually vaporization pressure Pk,vap of species k at temperature T and standard pressure PL is calculated based on eq 13. If the liquid is surrounded by high gas pressure P ˜ L, then vaporization pressure ˜ k,vap according to eq 14, and the Pk,vap is corrected to P corrected vaporization pressure P ˜ k,vap is substituted back into eq 12 to get the Henry’s constant.16 When the bed is operated in the trickle flow regime under partial wetting conditions for the pellets, the catalyst wetting efficiency, ηCE, is obtained by using ElHisnawi correlation.17 On the contrast, the packedbubble column operates in the bubbly flow regime with fully wetted pellets. The mass transfer coefficient in the liquid film, kL, is evaluated by the correlation of Fukushima and Kusaka18 for downflow operation mode and by the correlation of Reiss19 for upflow operation mode. The mass transfer coefficient in the gas film, kG, is calculated using the correlation reported by Dwivedi and Upadhyah20 for both downflow and upflow mode. The liquid-solid mass transfer coefficient, kLS, is evaluated from the Tan and Smith correlation21 for trickle beds and the Specchia correlation22 for packed-bubble columns. Different liquid-phase axial dispersion coefficients (DEL) for trickle beds and for packed-bubble columns are taken from Cassanello et al.23 The external liquid holdup, L, is calculated adopting the correlation of Fukushima and Kusaka24 for trickle beds and using the correlation of Bensetiti et al.25 for the packed-bubble column. Required for the calculation of some coefficients, the molecular diffusivity (Dm) is evaluated from the correlation of Wilke and Chang.26 A number of studies have investigated the heterogeneous model parameters: mass-transfer coefficients,27 dispersion coefficients,23 and wetting efficiency.17 An implicit assumption in all the heterogeneous models is that each model parameter is of a constant value throughout the reactor. However, in an actual reactor, these parameters are affected by the local two-phase flow distribution. Hence, it is necessary to adjust all the corresponding variables from one cell to the other based on the local cell conditions. In the targeted operating conditions, reactor pressure ranges from 1.5 to 3.2 MPa, and temperature ranges from 110 to 210 °C. As shown in Figure 2, at each operating temperature, the corresponding vapor pressures of water and phenol have been shown together with the operating pressures. These vapor pressures and the operating pressures are represented by different type of columns with the top of columns standing for the pressure values. Water vaporization becomes more significant as the temperature increases. At high temperatures, simulation results are subject to distortion if the phase change of water is not accounted for properly.9 In contrast, as a nonvolatile species, phenol’s phase change is negligible. Species concentrations in both liquid and gas are affected by gas-liquid mass exchange. In addition, pressure drop

6638

Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005

Figure 2. Comparison between operating pressure and vapor pressure at different temperatures.

Figure 3. The properties and parameters studied in the model.

takes place when the gas and liquid flow through the packing materials. Figure 3 shows that the physical properties, gas velocities, mass transfer rates, and reaction rates involved in this model are calculated as functions of the local pressure, temperature, and species concentrations. Therefore, from one cell to the other, after species concentrations and pressure are updated, they are used together with temperature as input to compute the coefficients employed in the liquid and gasphase governing equations. The change in total gas flux (FG) from the inlet to the outlet of an element cell can be derived by summing up the mass transfer between gas and other phases for all the species. Therefore,

1 Lc

(FG,out - FG,in) )

∑k {-(KLaGL)k[Ck,e - Ck,L] (kGS)k(aGS)[Ck,e - Ck,GS]} (15)

Because of the mass transfer to the gas from the flowing liquid film and the static liquid inside the catalyst pore, the total molar gas flux undergoes changes and the gas velocity has to be updated. The variation in gas velocity is accounted for as follows

uG,out ) uG,in

( )

Pin RT + (FG,out - FG,in) ‚ Pout Pout

(16)

where the two-phase pressure drop in one cell is calculated explicitly from the correlation reported by Ramachandran and Chaudhari.28 2.5. Numerical Solution. The ADM was solved for the liquid phase along the whole reactor with the given boundary conditions. Then the cell stack model was solved for the gas phase by dividing the reactor into a series of cells (NG)100). The reactor scale ADM for the liquid phase involves coupled nonlinear second-order

ordinary differential equations, which demand numerical solutions. The use of multicomponent transport equations adds a large set of simultaneous nonlinear algebraic equations for the interphase concentrations. The source terms involve evaluation of interphase mass fluxes, reaction rates, and temperatures by solution of nonlinear equations at the interface. Hence, on the basis of the orthogonal collocation method, which is known as a robust method for solving boundary value problems,29 a FORTRAN program using the solver subroutine COLDAE was developed to solve the coupled nonlinear ODE with algebraic constraints (eqs 1-4). The solver required a user supplied analytical Jacobian for computational efficiency. However, for cases with involved nonlinear kinetics expressions, it was difficult to exactly evaluate the analytical Jacobian due to the implicit nature of the algebraic equations. The numerical Jacobian evaluated by a finite difference approximation generalized the application of the program to any type of kinetics expression and yielded the correct values of the derivatives with respect to the concentrations series. This improved the convergence accuracy at the cost of the large computational effort required due to repetitive function calls for evaluation of each element in the Jacobian matrix. The number of collocation points was specified along the reactor length from inlet to outlet for the liquid phase. For the purpose of spatial discretization, all the concentrations and other scalar variables were defined at the structured grids. Grid independence was reached with a large number of collocation points (N>80). The section between two adjacent collocation points forms one cell for gas phase. The local information at each collocation point, including component concentrations in the liquid phase, provided the boundary conditions for the gas phase in each cell. The computation of the cell stack model for gas phase was in a sequential mode. A set of boundary conditions for flow velocities and feed concentrations was given at the first layer of cells (input cells). A whole set of solutions for species concentrations in the gas phase at each cell interface was accomplished layer-by-layer, starting from the entrance of the bed and accounting for the necessary parameter updates. The change of gas superficial velocities and pressure led to a newly obtained group of mass transfer coefficients and wetting efficiency in each local cell. Hence, these values were then employed again to compute the ADM for the liquid phase at every axial collocation point, to update the axial species concentration profile in the liquid phase. The boundary conditions for gas phase in each cell, therefore, were updated. Based on the newly obtained local values, the cell stack model for gas phase was solved again layer-by-layer from the reactor entrance to exit. These iterative steps were repeated until convergence was achieved, when the latest values of the species concentrations along all the reactor axial collocation points adequately matched the ones obtained in the previous iteration. The convergence and stability of the numerical calculation in each cell were tracked and analyzed. 3. Results and Discussion Details of the experimental setup and findings have been reported elsewhere.9 The summary of operating conditions used in the simulation is listed in Table 1. In this simulation work temperature ranges between 110 and 210 °C. When temperature increases from 170

Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005 6639 Table 1. Operating Conditions Used in the Simulation property

range

reactor diameter, cm bed height, cm bed porosity catalyst particle size, mm temperature, °C equilibrium vapor pressure, MPa total pressure, MPa phenol feed concentration, mg/L LHSV, h-1 superficial gas velocity, cm/s superficial gas mass flux, kg/m2/s

2.5 60 ∼0.4, ∼0.6 φ2 × 8 110-210 0.14-1.8 1.5-3.2 500-2000 0.2-2 0.13-2.45 0.03-0.13

to 210 °C, the equilibrium water vapor pressure jumps more than 2 times from 0.8 to 1.8 MPa, which becomes 25% to 56% of the operating pressure of 3.2 MPa. Hence, at elevated temperature, the evaporation phenomenon becomes pronounced. The simulation for trickle bed and upflow packed bed reactors for phenol oxidation was conducted over a range of operating conditions. As shown in Figure 4(a),(b), phenol conversion was calculated as a function of liquid hourly space velocity (LHSV), using the liquid-phase ADM and considering or neglecting phase change. The simulated values for phenol conversion are also compared with the experimental observations. In the tricklebed reactor, at the given operating conditions the catalyst surface was only partially wetted, and the resulting wetting efficiency was estimated to be in the range of 0.5-0.8. For high LHSV (>0.6 h-1) and lower temperatures (110 °C), reasonable agreement between simulation results neglecting phase changes and the experimental data is observed, as shown in Figure 4(a). The reasonable model predictions at lower temperatures (110 °C) imply that the selected hydrodynamics correlations and kinetics rate parameters are applicable. However, compared with experimental data, simulation neglecting phase changes actually failed at 150 °C, underpredicting by 30% at low LHSV (0.3 h-1) and overpredicting by 70% at high LHSV (1.2 h-1). The assumption of insignificant phase change is one factor for the unsatisfactory prediction. The solvent water and the low molecular weight products (acetic acid and oxalic acid) are more volatile, compared with phenol and intermediate products (benzonquinone and pyrocatechol). At high temperatures and at low LHSV, the resulting high driving force and long residence time enhance the phase change. The low boiling components pass into the vapor phase and are swept out more rapidly than the high boiling material. Hence, based on the model’s changing capability at different temperatures, the phase change is necessary to be incorporated into the model, which makes the model more generalized. At both low temperature with marginal evaporation and high temperature with significant evaporation, the model can vary the mass transfer driving force between gas and liquid by adjusting the corresponding species equilibrium vapor pressure. Compared with the model predictions neglecting the phase change, incorporating a cell stack for the gas phase, and accounting for the update of its velocity and compositions considerably alters the phenol removal profiles for the downflow reactor and causes the simulation result to better meet experimental observations. A good agreement between the model predictions and the experimental data obtained at three different temperatures is observed. With the LHSV decreasing at 150 °C, phenol conversion increases from 20% to 100% for

Figure 4. Phenol conversion as a function of LHSV at different temperatures in (a) trickle-bed and (b) upflow packed-bed reactors (pressure)3.2 MPa, [phenol])500 ppm, uG)0.53 cm/s). Solid line: simulation considering phase changes. Dashed line: simulation neglecting phase changes.

the case accounting for phase change, while it increases from 30% to 77% without considering phase change. In the downflow mode, the catalyst pellet, assumed to be internally filled up with liquid, is exposed partially to the gas phase. For longer liquid residence time, water evaporation and phenol mineralization to CO2 become more favorable. The fraction of liquid within the pores of the pellet has more chance to transfer to the gas phase from the dry pellet surface, which creates the capillary driving force for the liquid diffusing from the wet pellet surface into the pellet pores. Thus, more reactant from the liquid phase gets inside the catalyst pellet and reaches the catalyst’s active site. When the reaction is limited by the liquid-phase reactant, such limitation is alleviated by better availability of liquid reactants at longer residence time. On the other hand, the dry pellet surface facilitates the gas reactant diffusing into catalyst pores. The contact between O2 and liquid-phase phenol over the catalyst’s active sites is therefore enhanced, which results in higher phenol conversion. It is evident that the phase changes, including water evaporation, have a substantial influence on trickle bed performance at the conditions studied. However, employing the same operating condition in the upflow packed bed, the incorporation of phase change insignificantly affects the simulation results for phenol conversion. As shown in Figure 4(b), model simulations accounting for or neglecting phase changes have similar results. Comparison between the model predictions and the experimental data at three different temperatures are satisfactory. This finding is not surprising, since in reality the catalyst is always fully surrounded by liquid, and gas bubbles through the packed bed. Hence, in the

6640

Ind. Eng. Chem. Res., Vol. 44, No. 17, 2005

upflow packed bed, water evaporation between liquid and gas phase has little impact on the mass transfer of phenol between the catalyst pellet and the surrounding liquid phase, and on the resulting reaction rates over the catalyst surface. For downflow operation, the gas velocity is increased by 20-40% at temperature range of 130-170 °C due to the water evaporation and CO2 release from liquid to gas, while for upflow the gas velocity is increased below 10% under the same conditions. The phase change is the reason to set up the gas-phase governing equations. The adjustment in the gas molar flux along the reactor is connected with the variations of both gas velocity and gas-phase species concentrations (Ck,G). The former directly affects the interphase mass transfer resistance, while the latter marks the impact on species concentration of liquid in hypothetical equilibrium with bulk gas (Ck,e). Consequently, the driving force between the gas and liquid and the resulting reaction rates over the catalysts are considerably affected. These changes in turn alter the solutions of liquid-phase governing equation, which are the species concentrations in liquid phase. In contrast, had the phase change not been accounted for, gas-phase governing equations would have been absent, and liquid-phase governing equations would have been solved with the assumption of constant gas velocity and gas-phase species concentrations along the reactor axis. According to the taxonomy proposed by Khadilkar et al.,30 the ratio of the diffusion fluxes of the two reactants (γ)(DeACA/νA(DeBCB,e) is indicative of the relative availability of the species at the reaction site. The reaction can be considered gas reactant limited for γ . 1 or liquid reactant limited for γ < 1. Based on the employed operating conditions, the resulting values of γ are less than unity (γ