Computation of mass transfer coefficient and Sherwood number in circulating fluidized bed downer using computational fluid dynamics simulation

Chemical Engineering and Processing 59 (2012) 22–35

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Chemical Engineering and Processing: Process Intensification journal homepage: www.elsevier.com/locate/cep

Computation of mass transfer coefficient and Sherwood number in circulating fluidized bed downer using computational fluid dynamics simulation Yongyoot Prajongkan a , Pornpote Piumsomboon a,b , Benjapon Chalermsinsuwan a,b,∗ a b

Fuels Research Center, Department of Chemical Technology, Faculty of Science, Chulalongkorn University, 254 Phayathai Road, Patumwan, Bangkok 10330, Thailand Center of Excellence on Petrochemical and Materials Technology, Chulalongkorn University, 254 Phayathai Road, Patumwan, Bangkok 10330, Thailand

a r t i c l e

i n f o

Article history: Received 1 November 2011 Received in revised form 25 January 2012 Accepted 4 May 2012 Available online 15 May 2012 Keywords: Circulating fluidized bed Computational fluid dynamics Downer Hydrodynamics Mass transfer coefficient Ozone decomposition reaction

a b s t r a c t In this study, the Eulerian–Eulerian computational fluid dynamics simulation with the kinetic theory of granular flow model was successfully used to compute mass transfer coefficients and Sherwood numbers in a circulating fluidized bed downer using the concept of additive chemical reaction and mass transfer resistances. The simulation was also used to determine the ozone molar concentration, axial gas velocity and solid volume fraction. The effects of reaction rate constant and circulating fluidized bed downer height were investigated. The mass transfer coefficients and the Sherwood numbers had minimum values at moderate or central value of each effect. The low mass transfer coefficients and Sherwood numbers were observed due to the formation of solid particle sheet or loose solid particle cluster. In addition, the system flow and chemical reaction behaviors were discussed using the obtained mass transfer characteristics. For high reaction rate constant case, the ozone molar concentrations were decreased with the increasing of the system height. This is because mass transfer dominances the system. For low reaction rate constant case, the ozone molar concentrations were slightly changed with the system height. This is the chemical reaction control. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Circulating fluidized bed (CFB) reactor is widely applied in many industrial operations, such as petrochemical and power-generation industries, due to some distinct advantages over the other methods of gas–solid reactors, e.g. high solid mixing and high heat and mass transfer rates between gas and solid phases [1]. CFB has been designed with having two major reactor parts: a riser and a downer. For the CFB riser, the gas and solid particle reactants are fed at the bottom and flown upward to the exit at the top of the system. This flow behavior provides many advantages when comparing to the classical fluidized bed such as easily to operate and control. On the contrary, severe axial backmixing which can greatly influence in some applications affecting reduced selectivity and irregular distribution of the desired product, is the main disadvantage of CFB riser [2–4]. In recent years, another major part of CFB reactor, the downer, has been developed and attracted in

∗ Corresponding author at: Fuels Research Center, Department of Chemical Technology, Faculty of Science, Chulalongkorn University, 254 Phayathai Road, Patumwan, Bangkok 10330, Thailand. Tel.: +66 2218 7682; fax: +66 2255 5831. E-mail address: [email protected] (B. Chalermsinsuwan). 0255-2701/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cep.2012.05.002

industrial operations. For the CFB downer, the gas and solid particle reactants are fed from the top of the downer, resulting in the co-currently downward gas–solid flow along the direction of gravity [3,4]. This flow behavior is claimed to overcome the main drawback of the CFB riser which then lead to desirable hydrodynamic qualities [5]. The CFB downer can provide many advantages over the CFB riser, such as increasing uniformity of gas–solid particle contacting, decreasing solid particle aggregation, shortening residence time and lowering system pressure drops since gravity acts in the same direction as the system flow when comparing to the one in CFB riser [4,5]. These properties are very important, lead to its application especially to Fluid Catalytic Cracking (FCC) and Residual Fluid Catalytic Cracking (RFCC) processes where a short and uniform gas–solid particle contact is necessary [6]. Pilot plant studies have already shown encouraging results to the use of CFB downer for FCC process [7]. Therefore, clearly understanding of hydrodynamics and chemical reaction of CFB downer reactors is important to realize its full potential in various applications. Before the 1990s, both the theoretical and computational efforts were not observed. The research development of the CFB downer has taken place since then. Cheng et al. [8,9] studied the computational fluid dynamics (CFD) simulation of a downer. Their model was capable to handle transient or unsteady state system

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conditions. Good comparison of the model prediction with a set of flow structure experimental data was obtained. Subsequently, many research studies on the CFB downer system hydrodynamics and chemical reaction were investigated [7,10–12]. In spite of the hydrodynamic and chemical reaction studies, there have been very few attempts to explore and explain the mass transfer behavior in the CFB downer, which also plays an important role in the CFB reactors. Mass transfer involves in diffusive and convective transports of atoms and molecules within physical and chemical systems [13]. The driving force for mass transfer is a difference in concentration; atoms and molecules move from an area of high concentration to that of low concentration. The amount of mass transfer can be quantified through the calculation and application of mass transfer coefficient. The diffusion controlled dimensionless mass transfer coefficient is called the Sherwood number, which is generally equal to two, based on the diameter of solid particle [14]. However, the mass transfer coefficient is known to be much lower for fine solid particles than those given by correlations for the large ones [15–17]. Breault and Guenther [18] and Chalermsinsuwan et al. [19] reviewed the literature and showed that the Sherwood numbers in fluidized bed systems differ up to seven orders of magnitude ranging from a low value of 10−5 to a high value of 200. Luo et al. [20] explored the effect of operating conditions on gas–solid mass transfer with the adsorption of CO2 by activated charcoal particle. Their results concluded that the gas velocity and solid circulation rate has a significant effect on the mass transfer coefficient. Besides their studies, the other literatures were not mainly focused on the mass transfer behavior in the CFB downer [21–24]. Mass transfer in CFB downer is a crucial issue because the CFB downer is a short-contact time reactor and hence the time-scale of mass transfer has to be fast enough so as to be compatible with the processing time or residence time of the solid particles. The use of CFB downer mode of flow for a successful chemical reaction thus will depend largely on effective gas–solid mass transfer. To improve the performance of the CFB reactors, the understanding about value of the mass transfer coefficient in the CFB downer is needed to be known. In the past decades, CFD has been conducting to solve multiphase flows using advanced numerical techniques [25]. Two CFD approaches for studying the gas–solid flows are the Lagrangian–Eulerian model [26,27] and the Eulerian–Eulerian model [26,28]. Using the Lagrangian–Eulerian model, the solid particles are tracked individually by solving Newtonian equations of motion, while the gas phase is treated as a continuum that is coupled to the motion of solid particles via an interphase interaction term. The calculation then needs huge computing resources and cannot be used yet for the simulation of large scale CFB reactor. Using the Eulerian–Eulerian model, the base assumption is that gas and solid phases are treated as interpenetrating continua. The used equations are a generalization of the Navier–Stokes equations for interacting mediums. For most of recent continuum models, constitutive equations according to the kinetic theory of granular flow (KTGF) are incorporated [29–31]. This model has been successfully used to predict and validate lots of gas–solid particle multiphase flow phenomena in the CFB downers [8,9,32–34]. Therefore, the Eulerian–Eulerian model with KTGF is the suitable model to predict the gas–solid particle dynamic behavior in the CFB downers. In the present study, the system hydrodynamics, chemical reaction and mass transfer behaviors in the downer of a CFB reactor were investigated using the Eulerian–Eulerian CFD model with KTGF. The main objective of this study is to explain the system flow and chemical reaction in a CFB downer using the obtained mass transfer characteristics.

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2. Ozone decomposition reaction In order to obtain the mass transfer behavior or compute the mass transfer coefficient (or Sherwood number) using the methodology described in Chalermsinsuwan et al. [19] and Chalermsinsuwan and Piumsomboon [35] as being discussed later in Section 3, one representative chemical reaction is needed. The ozone decomposition reaction is one of the candidate chemical reactions to be selected for the study because it is a simple irreversible first-order catalytic chemical reaction [19,36–39]. In this chemical reaction, two moles of ozone gas reactant are changed to three moles of oxygen gas product as shown below: 2O3 (g) → 3O2 (g)

(1)

The ozone decomposition reaction requires low concentrations of ozone reactant and the heat produced by the chemical reaction is negligible. Therefore, this chemical reaction follows an isothermal operation. The rate of reaction can be written as: Ozonedecompositionreactionrate (−r O3 ) = −kreaction C O3 εs

(2)

where CO3 represents the ozone reactant molar concentration, εs represents the concentration or solid volume fraction of catalyst/solid particle used in the reaction and kreaction represents the reaction rate constant. Besides the above advantages, the ozone decomposition reaction is selected in this study because this chemical reaction occurs at ambient temperature and the experiment or computation is easy to conduct. 3. Computational fluid dynamics model descriptions 3.1. System configuration description The simulated system in this study was based on the experimental setup of Cao and Weinstein [40]. All the numeric values used within the simulations thus were obtained from their experimental condition values. In their experiments as shown in Fig. 1, the Plexiglas CFB system was consisted of four main components: a riser, a cyclone, a downer and a return system. The CFB downer had a diameter of 0.127 m and an overall height of 5.00 m. The solid particles were Grace Davison fluid cracking catalysts with an average solid particle diameter of 82 ␮m and a solid particle density of 1480 kg/m3 . However, in this study, only the CFB downer was investigated by using a two-dimensional system, instead of the actual three-dimensional system. Chalermsinsuwan et al. [35] found that the mass transfer coefficients from two- and three-dimensional simulations gave the comparable numerical results. Although the three-dimensional simulation represents more realistic than the two-dimensional simulation, it requires much more computational efforts. Thus, the two-dimensional simulation was selected in this study. The extended figure shown as Fig. 1 depicts the schematic drawing of the CFB downer used in the present numerical simulation. This configuration had a two inlet designs because a one inlet design for the two-dimensional downer could not capture the actual phenomena throughout the system height as observed in Chanchuey et al. [41]. The two-dimensional CFB downer was consisted of 6000 computational mesh cells. The cells were consisted of 30 grids of non-uniform mesh in the horizontal direction and 200 grids of uniform mesh in the axial direction. Fig. 2 illustrates the computational domain of the CFB downer used in this study. A study of the grid resolution or grid independence was already described in Chanchuey et al. [41]. The employed mesh cells were the appropriate ones in which the computational results were not changed when the mesh cells were increased. For the simulation, the time step of 1 × 10−3 s was used, and the simulation was conducted for 50 s of simulation

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Fig. 1. The schematic drawing of circulating fluidized bed downer used in Cao and Weinstein’s [40] experimental setup.

time, which was estimated at about 2 days of computational time on the Pentium 1.80 GHz with 2 GB RAM workstation. The timeaveraged (quasi steady state) results in this study were computed using the results with simulation time between 30 s and 50 s as already verified in Chanchuey et al. [41]. 3.2. Mathematical (computational fluid dynamics) model description The numerical simulations were performed using Eulerian–Eulerian gas–solid multiphase flow model in ANSYS FLUENT 6.3.26. With this model, the mass, momentum, energy and species governing equations for the two phases were separately solved. The constitutive equations for this system were based on the kinetic theory of granular flow, as reviewed by Gidaspow [28]. The behavior of the solid particles was described by taking into account the energy associated with solid particle fluctuating motions (granular temperature) and collisions. A summary of the used computational fluid dynamics model is given in Table 1. About the momentum interphase exchange or drag coefficient model, it was claimed that this model had a significant effect on the obtained results. In our previous study [41], the effect of momentum interphase exchange coefficient model was explored in this CFB downer system. The Gidaspow model was summarized as a suitable momentum interphase exchange coefficient. Therefore,

the Gidaspow model was selected to use in this study. This drag function is a combination of the works of Ergun [42] and Wen and Yu [43]; the model presented by Ergun [42] is used when the flow is dense, whereas the model of Wen and Yu [43] is used when the flow is dilute. About the adjusting model parameters, the restitution coefficient between solid particles, the restitution between solid particle and wall and the specularity coefficient were also selected from our previous study [41] with the values as shown in Table 2. The restitution coefficients are the elastic of collisions between the objects where the value of zero represents fully inelastic collisions and the value of unity represents fully elastic collisions. The specularity coefficient is the degree of slippage where the value of zero and unity indicate that the wall is smooth and rough, respectively. In this study, the restitution coefficient between solid particles being very high, it implied that these solid particles were nearly fully elastical collisions or only slightly loss taking place due to the collision. The above computational fluid dynamics model, governing and constitutive equations, were solved with finite volume method. The second-order upwind scheme was used as the discretization schemes for convection terms while the first-order upwind scheme was used for the other terms. In addition, the conventional SIMPLE algorithm [44] was used for relating the velocity and pressure corrections to recast the continuity equation in terms of a pressure correction calculation.

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Table 1 The summary of computational fluid dynamic model in this study. A. Governing equations: (a) Conservation of mass: - Gas phase: ∂ (εg g ) + ∇ · (εg g vg ) = 0 ∂t - Solid phase: ∂ (εs s ) + ∇ · (εs s vs ) = 0 ∂t (b) Conservation of momentum: - Gas phase: ∂ (εg g vg ) + ∇ · (εg g vg vg ) = −εg ∇ P + ∇ · g + εg g g − ˇgs (vg − vs ) ∂t - Solid phase: ∂ (εs s vs ) + ∇ · (εs s vs vs ) = −εs ∇ P + ∇ · s − ∇ Ps + εs s g + ˇgs (vg − vs ) ∂t (c) Conservation of energy: - Gas phase: ∂ ∂P (εg g hg ) + ∇ · (εg g vg hg ) = −εg + g : ∇ · vg + Qsg + Sg ∂t ∂t  with hg = cp,g dTg - Solid phase: ∂ ∂Ps (εs s hs ) + ∇ · (εs s vs hs ) = −εs + s : ∇ · vs − Qgs + Ss ∂t ∂t  with hs = cp,s dTs

(3)

(4)

(5)

(6)

(7)

(8)

(d) Conservation of species (i = O3 , O2 and N2 (Air)): ∂ (9) (εg g yi ) + ∇ · (εg g vg yi ) = ri ∂t Conservation of solid phasefluctuating energy or granular temperature: (e)  3 ∂ (εs s ) + ∇ · (εs s )vs = (−∇ Ps I¯ + s ) : ∇ vs + ∇ · (s ∇ ) − s + ϕgs (10) 2 ∂t B. Constitutive equations: (a) Gas phase stress: 2 T g = εg g [∇ vg + (∇ vg ) ] − εg g (∇ · vg )I (11) 3 (b) Solid phase stress:   2 T (12) s = εs s [∇ vs + (∇ vs ) ] − εs s − g ∇ · vg I 3 of solid fluctuating energy: (c) Collisional dissipation  Fig. 2. The computational domain of circulating fluidized bed downer used in this study.

4 dp

s = 3(1 − e2 )ε2s s g0 





(13)

(d) Radial distribution function:



3.3. Chemical reaction (ozone decomposition reaction) model description The needed parameter in a chemical reaction model for the CFD simulation is the reaction rate constant. In the literature reviews, the reaction rate constants for the ozone decomposition were varied depending on the types of catalyst/solid particle. There are the result of Ouyang et al. [45,46] which studied the FCC catalyst coated with ferric nitrate and that of Jiang et al. [47] which studied the FCC catalyst coated with ferric oxide. Thus, five different values of reaction rate constant were selected to study the effect of this parameter on the mass transfer coefficients and the Sherwood numbers. The range of the values was obtained from the previous experiments [45–47]. Those reaction rate constants are summarized in Table 2. 3.4. Initial and boundary conditions description

g0 =



1−

(14)

εs,max

(e) Solid phase pressure: Ps = εs s [1 + 2g0 εs (1 + e)] (f) Solid phase shear viscosity:

(15)



√

10s dp   4 2 ε s dp g0 (1 + e) + 5 s 96(1 + e)g0 εs (g) Solid phase bulk viscosity:

s =



2

1+

4 g0 εs (1 + e) 5

(16)



 4 2 ε s dp g0 (1 + e) 5 s (h) Conductivity of the fluctuating energy:  √  2 150s dp  6  s = 1 + εs g0 (1 + e) + 2s ε2s dp (1 + e)g0 5 384(1 + e)g0 (i) Exchange of the fluctuating energy between phases: ϕgs = −3ˇgs  (j) Gas–solid phase interphase exchange coefficient: - Gidaspow model: when εg > 0.80; s =

2

ˇgs = 150

About the initial conditions, the velocity and volume fraction of both the gas and solid particle phases were specified. Inside the CFB downer, there were no gas and solid particle. About the boundary conditions, the gas was fed at the top of the CFB downer. The solid particle was fed from the two side inlets at 0.303 m below the top of the CFB downer with a width of 0.127 m and an angle of 45◦ with respects to the system vertical axis. The gas and solid particles went out of the system with a pressure outlet of 15,000 Pa above the atmospheric pressure. For the system wall, no-slip boundary conditions were applied for gas normal, gas tangential and solid normal velocities. However, for the solid tangential velocity (vs,W ) and the granular temperature ( W ), the boundary conditions of Johnson and Jackson [48] were used. These

1/3 −1

εs

(1 − εg ) g εg dp2

+ 1.75

24 Rek

CD0 =

Rek ≥ 1000;

CD0 = 0.44

(18) (19)

(1 − εg )g vg − vs

(20)

dp

when εg ≤ 0.80; 3 (1 − εg )εg g |vg − vs |CD0 ε−2.65 ˇgs = g 4 dp with Rek < 1000;

(17)

(1 + 0.15Rek0.687 );

(21) Rek =

g εg |vg −vs |dp

g

conditions were successfully applied to many kinetic theories of granular flow modeling [19,30,49] which can be expressed below:

vs,W = −

6 s εs,max ∂vs,W √ s εs g0 3 ∂n

(22)

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Table 2 The summary of model parameters in this study. No.

Description

Value(s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Diameter of downer Height of downer Gas density Gas viscosity Solid particle density Solid particle diameter Gas inlet velocity Gas inlet temperature Ozone species inlet mass fraction Air species inlet mass fraction Solid inlet velocity Solid inlet temperature Solid inlet volume fraction Gas/solid particle outlet pressure Molecular diffusivity Restitution coefficient between solid particles Restitution coefficient between solid particles and wall Specularity coefficient Reaction rate constants

0.1270 m 5.00 m 1.2 kg/m3 2 × 10−5 kg/m s 1480 kg/m3 82 ␮m 3.70 m/s 298.15 K 0.00004 0.99996 1.11 m/s 298.15 K 0.15 116,325 Pa 2.88 × 10−5 m2 /s 0.999

17 18 19

√ W

s  ∂W =− + W ∂n

with W =

√

0.70 0.001 3.96, 39.60, 99.00, 198.00 and 396.00 1/s

3 s εs v2s,slip g0  3/2 6εs,max W

2 )ε  g  3/2 3 (1 − eW s s 0

4εs,max

(23)

.

All the parameters and constants stated in Eqs. (22) and (23) are at system wall where s is the shear viscosity of solid particle, εs,max is the volume fraction of solid particle at maximum packing condition (=0.60), is the specularity coefficient, s is the density of solid particle, εs is the volume fraction of the solid particle, g0 is the radial distribution function,  is the solid fluctuating kinetic energy or granular temperature, n is the unit vector, s is the conductivity of solid fluctuating kinetic energy, vs,slip is the slip velocity of the solid particle and eW is the restitution coefficient between solid particle and wall. 4. Results and discussion 4.1. Model validation with the Cao and Weinstein [40] experimental results In our previous study [41], the effects of each modeling parameter on the simulation results were studied. Here, the best suitable parameter values or models were selected to simulate the system. The experimental results which were used for comparison are the solid volume fraction and solid mass flux. The radial distributions of computed time-averaged (a) solid volume fraction and (b) solid mass flux at 1.65 m below the top of CFB downer comparing with the experimental data are displayed in Fig. 3. It can be seen that both the simulation results were consistent with the corresponding experimental data. This validates the accuracy of employed numerical model. From Fig. 3(a), the results predicted the core-annular flow structure in the CFB downer. The solid volume fraction was low at the center and high at the wall. This is a general observation for a flow structure in the CFB riser [29–31,37]. However, the solid volume fraction at the wall or annular region of CFB downer was lower than the one of CFB riser. This system position is the region that the particle cluster is mostly occurred. This implies that a loose cluster or solid sheet is occurred in CFB downer when comparing to the dense one in CFB riser [19,29–31]. From Fig. 3(b), the numerical simulations confirmed

Fig. 3. The radial distributions of computed time-averaged (a) solid volume fraction and (b) solid mass flux at 1.65 m below the top of circulating fluidized bed downer comparing with the experimental data.

the prediction of a very dilute flow in the center region and a relatively dense phase near the wall region. The solid velocity which can be obtained from the typical relationship with the solid mass flux was low at the center and high at the wall. This is in opposite direction to the results in CFB riser [29–31,37] which the solid velocity was high at the center and low at the wall. This situation can be explained by the effect of system wall on the main system flow direction. 4.2. Computation methodology of mass transfer coefficient and Sherwood number As mentioned above, this study used the same methodology as mentioned in Chalermsinsuwan et al. [19] and Chalermsinsuwan and Piumsomboon [35] to compute the mass transfer coefficients and the Sherwood numbers. The ozone decomposition reaction was the selected chemical reaction for the study due to many advantages. From the previous study in the CFB riser [19] and the bubbling bed [35], the integration of equation for conservation of ozone reactant species over computational time and CFB downer diameter or system horizontal/radial direction can be illustrated as shown below:

vy εg

dCO3 dY

= −rO3

(24)

vy where represents the axial/vertical direction velocity of gas phase, εg represents the volume fraction of gas phase, CO3 represents

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the ozone molar concentration and Y represents the axial/vertical distance. Since the decomposition of ozone is a first-order reaction, the reaction rate constant is independent of the gas concentration. The rate of reaction is already shown in Eq. (2). Substitution of the rate of reaction into the steady state one-dimensional ozone conservation equation or Eq. (24) gives:

vy εg

dCO3 dY

= −KCO3 εs

(25)

where K represents the overall resistance or effective rate constant. Then, solving Eq. (25) gives: ln CO3 = ln CO3 ,0 −

Kεs

vy εg

Y

(26)

where the subscript “0” represents the initial parameter condition. From Eq. (26) with the time-averaged and area-averaged computational results, it will provide the overall resistance. The linear relation from the plot of natural logarithm of the ozone molar concentration versus the CFB downer axial/vertical height gives the slope, which then can be computed to obtain the overall resistance. Then, the additive resistance concept allows us to compute the mass transfer coefficients and the Sherwood numbers. At quasi steady state condition, the external mass transfer in terms of global rate is comparable to the mass transfer from the bulk gas to solid particle surface [17,50]: kmass

transfer av (CO3

− CO3,surface ) = kreaction CO3,surface

(27)

where kmass transfer represents the mass transfer coefficient, av represents the external surface per volume of catalyst/solid particle (note that the catalyst/solid particle is assumed to be spherical in this study) and CO3 ,surface is the molar concentration of ozone at the catalyst/solid particle surface. Solving Eq. (27) and expressing the global reaction rate per unit mass of catalyst/solid particle (rp ) in terms of CO3 gives: rp s εs =

1 CO εs = KCO3 εs (1/kmasstransfer av ) + (1/kreaction ) 3

(28)

Therefore, the average mass transfer coefficients and the Sherwood numbers (Sh) can be computed with the following formulas: kmass Sh =

transfer

=

1 av ((1/K) − (1/kreaction ))

kmass transfer dp D

(29) (30)

where dp represents the diameter of catalyst/solid particle and D represents the molecular diffusivity. 4.3. Computation and comparison of mass transfer coefficient and Sherwood number From the previous section, the computed variables that are required for computing the mass transfer coefficients and the Sherwood numbers are the ozone molar concentration, axial gas velocity, solid volume fraction and gas volume fraction. In this section, all the above stated variables are displayed which were obtained from the Eulerian–Eulerian CFD multiphase flow model. Subsequently, the mass transfer coefficients and the Sherwood numbers were computed. Solbrig and Gidaspow [51] and Kulacki and Gidaspow [52] found that the mass transfer is a function of the reaction rate constant with a very well defined system, surface reaction of hydrogen on the surface of a tube or plate. Therefore, the effects of reaction rate constant and CFB downer height on the mass transfer coefficients and the Sherwood numbers were then discussed. In addition, the obtained mass transfer coefficients and the

Fig. 4. The axial distributions of computed time-averaged and area-averaged ozone molar concentration with various reaction rate constants.

Sherwood numbers were compared with the available literature experimental data in fluidized bed systems. The axial distributions of computed time-averaged and areaaveraged ozone molar concentration with various reaction rate constants are shown in Fig. 4. As already stated above, five different reaction rate constants were employed in this study. The displayed height represents the distance below the top of the CFB downer (at 0.00 m is the top inlet region and at 5.00 m is the bottom outlet region). For approximately 0.50 m height, the ozone molar concentrations were almost constant. This is because the ozone reactant was fed at the top inlet while the catalyst/solid particle was fed from the two side inlets at 0.40 m. At the inlet positions, the ozone molar concentrations dropped and, after that, they slightly increased which was due to the improper mixing between gas and catalyst/solid particles. Then, the ozone molar concentrations decreased along the CFB downer height due to the increasing of contacting time between gas and catalysts/solid particles inside the system. The ozone molar concentrations also decreased with the increasing of reaction rate constant. For the highest reaction rate constant (kreaction = 396.00 1/s), the ozone molar concentration was used up due to high reaction rate. As the reaction rate constant decreased (kreaction = 198.00, 99.00 and 39.60 1/s), the rate of ozone decomposition reactions were also decreased. For the lowest reaction rate constant (kreaction = 3.96 1/s), the ozone molar concentration was mostly unchanged due to slow reaction rate. Fig. 5 shows the axial distributions of computed time-averaged and area-averaged axial gas velocity with the same various reaction rate constants. All the reaction rate constants gave the similar results of axial gas velocity profiles. These observations can be used to conclude that this ozone decomposition reaction does not have any effect on the system hydrodynamics. The reason is that the ozone decomposition is the low or ambient temperature chemical reaction. About the effect of CFB downer height, the axial gas velocities decreased as the increasing of CFB downer height except at the near top inlet and bottom outlet regions. This can be explained by the expansion of system area from system flow structure when the CFB downer height increases. The axial gas velocity will make an effort to balance the momentum inside the system. At the near top inlet and bottom outlet regions, the axial gas velocities suddenly increased. This is because the inlet and outlet effects at those two system positions. For the gas volume fraction and solid volume fraction results, only the solid volume fraction will be selected to illustrate and

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Fig. 5. The axial distributions of computed time-averaged and area-averaged axial gas velocity with various reaction rate constants.

explain. The gas volume fraction then can be calculated as unity minus the solid volume fraction (εg = 1 − εs ). The trends or profiles of gas volume fraction thus will be known from the solid volume fraction. The axial distributions of computed time-averaged and area-averaged solid volume fraction with the same set of various reaction rate constants are displayed in Fig. 6. For all the reaction rate constants, the computed results also gave the similar solid volume fraction profiles. These observations then come up with the same conclusion earlier that the ozone decomposition does not affect the system hydrodynamics. As already stated, the catalyst/solid particle was fed at the two side inlets at 0.40 m. The solid volume fractions which were higher than these points then equated to zero. After that, all the computed solid volume fractions readily increased due to the entering of catalyst/solid particles and continuously decreased due to system flow structure inside the CFB downer. These axial distributions are similar to the core-annulus flow structure in CFB riser. This validates Chanchuey et al. [41] work

Fig. 6. The axial distributions of computed time-averaged and area-averaged solid volume fraction with various reaction rate constants.

Fig. 7. The axial distributions of natural logarithm of computed time-averaged and area-averaged ozone molar concentration with various reaction rate constants.

which observed the dilute core-annulus flow structure in the CFB downer. Fig. 7 illustrates the axial distributions of natural logarithm of computed time-averaged and area-averaged ozone molar concentration with the same various reaction rate constants. This figure was employed for testing of the computation methodology of mass transfer coefficients and Sherwood numbers. Generally, for a firstorder reaction with specific axial gas velocity, solid volume fraction and gas volume fraction, the natural logarithm of ozone molar concentration will vary linearly with system height, as derived in Eq. (26). The linear line slope then enables to determine the mass transfer coefficients and the Sherwood numbers. From the figure, all the graph lines could be estimated by using linear trendlines. Therefore, these were consistent and verified with the assumption used in the computation methodology. About the effects of reaction rate constant and CFB downer height, the obtained profiles had similar trends with the obtained computational ozone molar concentration results in Fig. 4. Table 3 summarizes the fitted equation parameters at each CFB downer height with various reaction rate constants. The obtained values of the slope varied with respect to the reaction rate constants. The negative slope values increased with the increasing of reaction rate constants. From the table, the highest negative slope was obtained from the highest reaction rate constant so as the lowest negative slope obtained from the lowest one. For the low reaction rate constants (kreaction = 3.96 and 39.60 1/s), the slopes were increased with the system height while, for the other reaction rate constants (kreaction = 99.00, 198.00 and 396.00 1/s), the slopes were initially increased and then decreased after some moderate system heights. These fitted slopes were consistent with the profiles of computed ozone molar concentration in Fig. 4. The reason for this situation can be explained by the rapid drop of ozone molar concentration near the CFB downer outlet for the high reaction rate constant cases. For all the obtained intercept values, the constant values were set to match with the initial ozone molar concentration. The computed information on mass transfer coefficients and Sherwood numbers at each CFB downer height with various reaction rate constants are summarized in Table 4. The computed results are shown at four different system heights and at the height-averaged values. From the table, the values of mass transfer coefficients and Sherwood numbers for the low reaction rate

Y. Prajongkan et al. / Chemical Engineering and Processing 59 (2012) 22–35 Table 3 The fitted equation parameters at each circulating fluidized bed downer height with various reaction rate constants. No.

kreaction (1/s)

Downer height (m)

Slope

Intercept

1

3.96

1.00 2.00 3.00 4.00

−0.2375 −0.0918 −0.0577 −0.0450

−13.8290 −13.8290 −13.8290 −13.8290

2

39.60

1.00 2.00 3.00 4.00

−0.4316 −0.2189 −0.1786 −0.1776

−13.8290 −13.8290 −13.8290 −13.8290

3

99.0

1.00 2.00 3.00 4.00

−0.6152 −0.3513 −0.3275 −0.3604

−13.8290 −13.8290 −13.8290 −13.8290

4

198.00

1.00 2.00 3.00 4.00

−0.7959 −0.5250 −0.5480 −0.6455

−13.8290 −13.8290 −13.8290 −13.8290

5

396.00

1.00 2.00 3.00 4.00

−1.0345 −0.8232 −0.9577 −1.1897

−13.8290 −13.8290 −13.8290 −13.8290

constant cases, which are kreaction = 3.96 and 39.60 1/s (at the top positions), could not be computed because the reaction rates were too low. The chemical reaction resistance then controls the system. On the other hand, for the high reaction rate constants, which are kreaction = 39.60 (at the bottom positions), 99.00, 198.00 and 396.00 1/s, the diffusional resistance becomes large and the mass transfer coefficients and the Sherwood numbers could be computed using the proposed concept of additive resistances. The computed mass transfer coefficients and the Sherwood numbers have similar trends since the Sherwood numbers is the function of the mass transfer coefficients, the diameter of solid particle and

29

molecular diffusivity and, in this study, the diameter of solid particles and molecular diffusivity were constant. Since most of the computed mass transfer coefficients were comparable with/higher than reaction rate constant, therefore, the mass transfer was not the limitation of the reaction inside the CFB downer. The reason for obtaining small values of Sherwood numbers is due to the very small diameter of solid particles as described by Chalermsinsuwan et al. [19]. They stated that the mass transfer coefficient for fine solid particles must be extremely high to give a Sherwood number of two as observed in a typical case. Thus, the mass transfer in this study is not as poor as being implied by the small Sherwood numbers. To better understand the effects of reaction rate constant and CFB downer height, the computed information will be plotted as the following figures. The effect of reaction rate constant on the mass transfer coefficients and the Sherwood numbers at four different CFB downer heights are displayed in Fig. 8. These four CFB downer heights were the same four heights as used in the previous results. For the results with low reaction rate constants (kreaction = 3.96 and 39.60 1/s (at the top of CFB downer)), the mass transfer coefficients and the Sherwood numbers could not be plotted. As already discussed, this is because the chemical reaction resistance controls the system at that position. The mass transfer coefficient and the Sherwood number values then will be extremely high. From the figure, the mass transfer coefficients and the Sherwood numbers had a minimum value at each CFB downer height. These could be apparently seen at the CFB downer height of 3.00 and 4.00 m. It can be explained by the following. For the low reaction rate constant, the ozone reactant is slowly converted. This results in the dominance of chemical reaction resistance inside this system and gives high values of mass transfer coefficient and Sherwood number. For the high reaction rate constant, the chemical reaction rate is also low due to the reactant depletion throughout the system. This also gives high values of mass transfer coefficient and Sherwood number. Therefore, minimum parameter values were existed when

Table 4 The computed information on mass transfer coefficients and Sherwood numbers at each circulating fluidized bed downer height with various reaction rate constants. No.

kreaction (1/s)

Downer height (m)

kmass transfer av (1/s)

kmass transfer (m/s)

Sherwood number

1

3.96

1 2 3 4 Averaged

– – – – Chemical reaction controlled

– – – –

– – – –

2

39.60

1 2 3 4 Averaged

– – 655.84 788.33 Chemical reaction controlled

– – 0.0090 0.0108

– – 0.0255 0.0307

3

99.00

1 2 3 4 Averaged

813.76 185.75 222.15 336.94 389.65

0.0111 0.0025 0.0030 0.0046 0.0053

0.0317 0.0072 0.0086 0.0131 0.0152

4

198.00

1 2 3 4 Averaged

269.76 188.30 272.02 445.21 293.82

0.0037 0.0026 0.0037 0.0061 0.0040

0.0105 0.0073 0.0106 0.0173 0.0114

5

396.00

1 2 3 4 Averaged

237.40 244.94 405.16 697.51 396.25

0.0032 0.0033 0.0055 0.0095 0.0054

0.0092 0.0095 0.0158 0.0271 0.0154

30

Y. Prajongkan et al. / Chemical Engineering and Processing 59 (2012) 22–35

Fig. 8. The effect of reaction rate constant on mass transfer coefficients and Sherwood numbers at each circulating fluidized bed downer height.

the reaction rate constant increases. This phenomenon are clearly observed in Fig. 9 which displays the effect of reaction rate constant on mass transfer coefficients and Sherwood numbers at averaged CFB downer height. The observed behaviors are partially consistent with the previous study resulting in the CFB riser, by Chalermsinsuwan et al. [19], where the ozone reactant was mostly reacted due to dense core-annulus flow structure. Their mass transfer coefficients and Sherwood numbers in the CFB riser were increased when the reaction rate constant increased. This implies that the reaction phenomena in the CFB downer is more homogeneous than those in the CFB riser due to its low solid volume fraction flow structure as can be seen in Fig. 6. Fig. 10 shows the effect of CFB downer height on mass transfer coefficients and Sherwood numbers at each reaction rate constant. Similar to the previous figures, there are some points that the graph cannot be plotted due to the chemical reaction resistance. From the figure, the computed mass transfer coefficients and Sherwood numbers also had a minimum value. They decreased at the near inlet region and then increased with the CFB downer height. This is not ordinary mass transfer behavior as observed in the convective mass transport in single phase flow

Fig. 9. The effect of reaction rate constant on mass transfer coefficients and Sherwood numbers at averaged circulating fluidized bed downer height.

Fig. 10. The effect of circulating fluidized bed downer height on mass transfer coefficients and Sherwood numbers at each reaction rate constant.

or CFB riser multiphase flow [14,19] in which the mass transfer coefficients and the Sherwood numbers decreased with the system length/height and reached constant values at the upper region. The explanation is that, at the top of the CFB downer or near inlet region, the chemical reaction resistance is high. Therefore, the high values of mass transfer coefficients and Sherwood numbers were obtained. At the bottom of the CFB downer or near outlet region, the chemical reaction resistance is still high due to the low solid volume fraction or system conversion. The chemical reaction then occurred throughout the system height and resulted in the high values of mass transfer coefficient and Sherwood number. At the central of the CFB downer or near center region, the mass transfer coefficients and Sherwood numbers were the minimum due to the improper gas–solid mixing inside the system. Fig. 11 displays the comparison of the computational Sherwood numbers with the experimental values in the literature. The plotted values were the time-averaged, area-averaged and heightaveraged values of each reaction rate constant cases where the information at four different heights was available. The computational results of low Sherwood numbers were in good agreement with the phenomena from the experimental data in the multiphase

Fig. 11. The comparison of the computational Sherwood numbers with the experimental values in the literature.

Y. Prajongkan et al. / Chemical Engineering and Processing 59 (2012) 22–35

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Fig. 12. The radial distributions of computed time-averaged solid volume fraction at (a) 1.00 m, (b) 2.00 m, (c) 3.00 m and (d) 4.00 m below the top of circulating fluidized bed downer with various reaction rate constants.

flow system [1,50,53–56]. In the literature, no direct experimental data in the CFB downer is presented. The lower value of Sherwood number from the single particle or fixed bed system can be explained by the effect of particle agglomeration. For the single particle or fixed bed system, the solid particle is considered as the individual solid particles. Therefore, it is ideally behaved corresponding to the well-known correlation of Ranz and Marshall [57] or Gunn [58] which the Sherwood number equals two, the diffusion limit, plus a contribution due to convection expressed in terms of Reynolds and Schmidt numbers. However, the particle cluster was occurred in this CFB downer system which then increased the system diffusional resistance and gave lower value of Sherwood number. This is consistent with the results by Shuyan et al. [21,22] and Breault and Guenther [24]. It can be explained by the decreasing of mass transfer driving force or concentration difference as the particle cluster size increases or void fraction decreases. Although the single particle or fixed bed system have higher value of Sherwood number, their system application will limit to some restriction processes such as the non-continuous or the chemical reaction which requires low gas–solid contacting surface area. For the continuous process and the chemical reaction which needs high gas-solid contacting surface area, the CFB downer or CFB riser system is still needed. From the results, it raises the challenging for engineers

and scientists to improve the mass transfer in CFB downer in order to effectively use these systems. The different reaction rate constant values had slightly affected on the computational results. The obtained Sherwood numbers still lied in the same order of magnitudes. However, the minimum value was obtained at the moderate reaction rate constant which is consistent with the result in the previous figures. 4.4. Confirmation and explanation of mass transfer coefficient and Sherwood number In this section, the obtained mass transfer coefficients and Sherwood numbers were confirmed. The reason why the low mass transfer coefficients and Sherwood numbers had occurred would be explained. In addition, the system flow and chemical reaction in the CFB downer were discussed using the obtained mass transfer characteristics. Fig. 12 illustrates the radial distributions of computed timeaveraged solid volume fraction at (a) 1.00 m, (b) 2.00 m, (c) 3.00 m and (d) 4.00 m below the top of the CFB downer with various reaction rate constants. From the figure, all the results with various rate constants showed similar trends of dilute core-annular flow characteristics throughout the downer heights, with the high

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Y. Prajongkan et al. / Chemical Engineering and Processing 59 (2012) 22–35

Fig. 13. The radial distributions of computed time-averaged ozone molar concentration at (a) 1.00 m, (b) 2.00 m, (c) 3.00 m and (d) 4.00 m below the top of circulating fluidized bed downer with various reaction rate constants.

catalyst/solid particle concentration at the near wall region and the low concentration at the center region. At the near wall region, there is a force which effects on the motion of catalysts/solid particles. These profiles confirm the flow structure as the ones in fast fluidization flow regime of the CFB riser [19]. When the CFB downer height increases, the profiles become more fully developed. This can be explained by the better mixing at the lower or bottom region of the system. The radial distributions of computed time-averaged ozone molar concentration at (a) 1.00 m, (b) 2.00 m, (c) 3.00 m and (d) 4.00 m below the top of CFB downer with various reaction rate constants are displayed in Fig. 13. The chemical reaction will be reacted at the area which has both the ozone reactant gas and catalyst/solid particles. Due to the high catalyst/solid particle concentration near the wall region as mentioned in the previous figure, this resulted in the low ozone molar concentration near the wall or annulus region. With the same token, the ozone molar concentration was high at the center or core region of the CFB downer. About the effect of the system height, the ozone molar concentrations were decreased with the increasing of the system height except at the lowest reaction rate constant. In that case, the chemical reaction controls throughout the system height. Thus, there was some ozone reactant which was not reacted inside the system. For the other cases, the mass transfer controls the system. The ozone reactant then mostly reacted consistently with the surface area of

the catalyst/solid particle. The higher rate constant gave the lower ozone concentration. For the confirmation and explanation of the low mass transfer coefficients and Sherwood numbers, Fig. 14 shows the instantaneous distribution of computed solid volume fraction contour in CFB downer at 40 s simulation time. At the near wall region which has high ozone decomposition, the high solid volume fraction was also observed. The solid particle sheets or loose solid particle clusters were clearly seen. This is the reason why the low mass transfer coefficients and Sherwood numbers were occurred. In the CFB riser [19], the solid particle clusters were also occurred at the near wall region however they were agglomerated as dense ones. This makes the mass transfer coefficients and Sherwood numbers in the CFB downer become larger than the ones in the CFB riser. Fig. 15 shows the variation of instantaneous computed solid volume fraction and computed ozone molar concentration profiles with kreaction = 39.60 1/s at the near wall region in each CFB downer height. The results were at 40 s. This figure verifies the result in the previous figure that the ozone concentration was decreased when the solid volume fraction increased or when it passed through the catalyst/solid particles. The ozone molar concentrations were not symmetric within the solid particle cluster due to the unequal surrounding flow structure. The solid particle cluster formation increases the mass transfer resistance in the system. This makes the mass transfer coefficients and the Sherwood numbers been

Y. Prajongkan et al. / Chemical Engineering and Processing 59 (2012) 22–35

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used to compute the mass transfer coefficients and the Sherwood numbers in a circulating fluidized bed downer using the additive resistances concept. In addition, the obtained model was efficiently used to calculate the ozone molar concentration, axial gas velocity and solid volume fraction. 2. The mass transfer coefficients and the Sherwood numbers had minimum values with the increasing of reaction rate constants. For low reaction rate constant, the ozone reactant is slowly reacted and resulted in high values of mass transfer coefficient and Sherwood number. For high reaction rate constant, the chemical reaction is also low due to the fast reactant depletion. This also gives high values of mass transfer coefficient and Sherwood number. 3. The mass transfer coefficients and the Sherwood numbers had minimum values with the increasing of system height. At near inlet region, the chemical reaction resistance is high and results in the high values of mass transfer coefficient and Sherwood number. At near center region, the mass transfer coefficients and Sherwood numbers are the minimum due to the system improper mixing. At near outlet region, the chemical reaction resistance is still high because of the low solid volume fraction and results in the high values of mass transfer coefficient and Sherwood number. 4. The solid particle sheet or loose solid particle cluster formation decreases the mass transfer coefficients and the Sherwood numbers to be much lower than the limiting values of Sherwood number for single solid particle. Also, the system flow and chemical reaction were discussed using the obtained mass transfer characteristics. For high reaction rate constant, the ozone molar concentrations were decreased with the increasing of the system height due to the mass transfer resistance. For low reaction rate constant, the ozone molar concentrations are slightly changed with system height since it is the reaction-controlled. Fig. 14. The instantaneous distribution of computed solid volume fraction contour in circulating fluidized bed downer at 40 s simulation time.

Acknowledgements This study was financially supported by the Research Strategic Plan (A1B1), Research Funds from the Faculty of Science, Chulalongkorn University, and also partially supported by the Grant from the Center of Excellence on Petrochemical and Materials Technology, Chulalongkorn University. Appendix A. Notation

Fig. 15. The variation of instantaneous computed solid volume fraction and computed ozone molar concentration profiles with kreaction = 39.60 1/s in the near wall region at each circulating fluidized bed downer heights.

much lower than the limiting Sherwood number for single solid particle. 5. Conclusions 1. The Eulerian–Eulerian computational fluid dynamics simulation with the kinetic theory of granular flow model was successfully

General letters av external surface per volume of catalyst/solid particle (m−1 ) heat capacity at constant pressure (J/kg K) cp C molar concentration (kgmol/m3 ) CD0 drag coefficient diameter of catalyst/solid particle (m) dp D molecular diffusivity (m2 /s) e restitution coefficient between solid particles eW restitution coefficient between solid particle and wall gravity force (m/s2 ) g g0 radial distribution function h specific enthalpy (J/kg) I unit tensor kmass transfer resistance due to mass transfer (m/s) kreaction resistance due to chemical reaction or reaction rate constant (s−1 ) overall resistance (m/s) K n unit vector gas pressure (Pa) P

34

Ps Qgs Qsg ri Re S Sh t T

v vs,slip

vs,W yi Y

Y. Prajongkan et al. / Chemical Engineering and Processing 59 (2012) 22–35

solid particle pressure (Pa) intensity of heat exchange from gas phase to solid particle phase (J/s m3 ) intensity of heat exchange from solid particle phase to gas phase (J/s m3 ) reaction rate of species “i” (kg mol/s m3 ) Reynolds number source term (e.g. due to chemical reaction) (J/s m3 ) Sherwood number time (s) temperature (K) velocity (m/s) slip velocity of solid particle at the wall (m/s) tangential velocity of solid particle at the wall (m/s) mass fraction of species “i” axial/vertical distance (m)

Greek letters ˇgs gas–solid particle interphase exchange or drag coefficient (kg/s m3 ) ε volume fraction solid volume fraction at maximum packing εs,max

specularity coefficient s collisional dissipation of solid fluctuating energy (kg/m s3 ) collisional dissipation of solid fluctuating energy at the W wall (kg/m s3 ) s conductivity of the solid fluctuating energy (kg/m s)

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