Hydrodynamic Simulations of Seepage Catalytic Packing Internal for

Article pubs.acs.org/IECR

Hydrodynamic Simulations of Seepage Catalytic Packing Internal for Catalytic Distillation Column Xingang Li,†,‡ Hui Zhang,† Xin Gao,*,‡ Rui Zhang,† and Hong Li*,† †

School of Chemical Engineering and Technology, Tianjin University, Tianjin, 300072, China National Engineering Research Center of Distillation Technology, Tianjin, 300072, China

‡

ABSTRACT: A seepage catalytic packing internal (SCPI) consisting of catalyst containers with avert-overflow baffles and corrugated metal sheets was developed for a catalytic distillation column. Models used for predicting the pressure drop of the SCPI and the height of liquid above the catalyst bed were built by using a commercial CFD package CFX13.0. Simulation strategies, flow geometry, and boundary conditions of SCPI were described in detail. Taking into account the structure of the corrugated metal sheets indirectly, the porous media model was used to acquire the dry pressure drop of the SCPI. Pseudo single phase formulation was utilized to process two-phase flow simulation for irrigated pressure drop determination. The Euler−Euler two-fluid model was employed to simulate the height of liquid above the catalyst bed and aid in designing the height of catalyst containers with avert-overflow baffles. The dry pressure drop (SCPI-I, SCPI-II), irrigated pressure drop (QLS = 14.06, 23.44 m3/ m2/h), and height of liquid above the catalyst bed (HC = 50, 75 mm) were calculated and compared to their experimental counterparts. The average relative error between CFD predictions and the experimental data is in the range 4.26−11.2%. In all cases, the CFD predictions show a good agreement with the experimental data, indicating that these simulation methods are feasible and CFD is a reliable, cost saving, and suitable technique for the design and optimization of SCPI.

1. INTRODUCTION Reactive distillation (RD) is one of the most important methods for process intensification in chemical engineering, as it has great potential to lower process costs and reduce environmental emissions.1 This process combines the reaction and separation in a single vessel, and has been widely used in etherification, hydrogenation, etc.2 Catalytic distillation (CD) is a RD process of which chemical reactions occur over a solid catalyst. Catalytic packing not only plays the catalytic role but also acts as the role of surface mass transfer in CD process. Therefore, catalytic packing with high catalytic efficiency and good separation ability should be required. At present, the catalysts for CD are mainly ion exchange resins and zeolites. The catalyst particle sizes used in such operations are usually in the 1−3 mm range.3 Larger particle sizes lead to intraparticle diffusion limitations. To avoid limitations of “flooding” and excessive pressure drop during counter-current gas−liquid flow in a packed column, special catalyst loading methods should be taken. The catalyst loading method is one of the key issues of industrial applications. Various catalyst loading methods have been developed to meet the practical requirements.3−9 In the design of the catalyst packing internal for CD columns, two main factors for liquid phase reversible reaction must be considered:10 (1) efficient contact between the liquid phase and the solid catalyst with enough residence time; (2) efficient separation by distillation with a high capacity or low pressure drop. Seepage catalytic packing internal (SCPI) is devised on the basis of the above-mentioned factors. SCPI is manufactured by the National Engineering Research Center of Distillation Technology of China and developed by combining the characteristics of the cross-flow plate and fixed bed reactor.11 © 2012 American Chemical Society

The structure of SCPI used in the experimental column has been described in detail by Gao12 and is shown in Figure 1. The

Figure 1. Laboratory scale element of SCPI: (1) catalyst zone (catalyst container); (2) corrugated metal sheets.

gas−liquid flow characteristics in the SCPI are shown in Figure 2. The liquid flows downward, driven by its own gravity, uniformly through the corrugated metal sheets and catalyst container. Gas flows upward driven by a pressure gradient only through corrugated metal sheets, which can avoid contact between gas and liquid in the catalyst particle bed and reduce the pressure drop of the column. The special structure of SCPI ensures that catalyst particles are reasonably, effectively, and equably distributed in the CD column. At a given liquid flow rate, proper height of avert-overflow baffles above the catalyst bed ensures that liquid seepage flows through the catalyst bed Received: Revised: Accepted: Published: 14236

April 17, 2012 September 27, 2012 October 10, 2012 October 10, 2012 dx.doi.org/10.1021/ie3010034 | Ind. Eng. Chem. Res. 2012, 51, 14236−14246

Industrial & Engineering Chemistry Research

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The current study presents CFD models to predict dry pressure drop, irrigated pressure drop of SCPI, and the height of liquid above the catalyst bed. First, a brief introduction about the experimental setup and methods for measuring the pressure drop and the height of avert-overflow baffles are presented. Then, the calculation strategies including theoretical approach and governing equations are discussed. Next, an overview of geometry and boundary conditions is given. Finally, comparisons between simulation results and the experimental data are drawn to verify the accuracy of the models.

2. EXPERIMENT 2.1. Pressure Drop. A schematic drawing of the cold model experimental apparatus is shown in Figure 3. The column is a Figure 2. Schematic diagram of an integrated element of SCPI: (1) avert-overflow baffles; (2) corrugated metal sheets; (3) liquid layer; (4) catalyst particles; (5) the middle height of SCPI; (6) metal wire mesh.

successfully without overflow. In the design of the CD process, the ratio of separation to reaction section can be adjusted according to requirements of different processes. Experimental studies on the pressure drop and the flooding point curves of SCPI have been carried out to evaluate the novel internal.12 The results showed that SCPI had a lower pressure drop and higher operational capability than conventional column internals for heterogeneous catalytic distillation. Lots of empirical flow models have already been published for air−water systems, but most of them have some limitations; they are feasible for conventional distillation columns or catalyst distillation columns. SCPI is a new internal for catalytic distillation columns and has its own characteristics. The empirical flow model should be revised to apply to the new internal. CFD simulation is not only performed for the fitting and verification of the revised model13 but also can make up for the defection of experiments. Although some experiments have been conducted to determine the flow pattern and macroscopic results in packed columns, due to the limited experimental data available, the use of the CFD tool is essential to study the complex fluid flow regimes and to obtain large amounts of data for analyzing and interpreting the macroscopic phenomenon and results. The main advantage of using CFD simulation is its potential to reduce the extent and amount of experiments required to describe such a type of flow.14 Different motivations have been developed to apply CFD modeling to structured packing and CD column. Yuan15 used the CFD tool to simulate pressure drop and liquid holdup for the G-L cross/countercurrent flow in a CD column with a novel internal. Raynal16 carried out CFD to determine the holdup and pressure drop calculations within structured packing and proposed that irrigated pressure drop can be predicted by combining dry pressure drop and liquid holdup. Higler17 used the CFD tool to obtain information on the liquid phase dispersion and mass transfer based on the ideal flow situation in the KATAPAK-S structures. Baten18 used CFD to study the radial and axial liquid-phase dispersion within the catalytic packed crisscrossing sandwich structures of KATAPAK-S and obtained that the radial dispersion coefficient is about 1 order of magnitude higher than that for conventional packed (trickle) beds, etc.

Figure 3. Cold model experimental apparatus: (1) air blower; (2) Pitot tube flowmeter; (3) U-tube manometer; (4) liquid distributor; (5) SCPI; (6) catalyst zone; (7) column; (8) liquid rotameter; (9) gas distributor; (10) liquid lever meter; (11) water tank; (12) pump.

PMMA tube of 600 mm i.d. Table 1 gives an overview of the two kinds of SCPI with different RCC/CMS values used in this work. Air and water at ambient temperature and pressure were used as the test fluids. For the solid phase, catalyst particles with an average diameter of about 0.7 mm were used. The bulk Table 1. Main Geometric Parameters of Two Types of SCPI

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parameter

SCPI-I

SCPIII

specific surface area, a (m2/m3) volume fraction of the catalysts in the column, FCC (m3/m3) width ratio of catalyst container to corrugated metal sheets, RCC/CMS volume fraction of the corrugated metal sheets in the column, FCMS (m3/m3) height of the catalyst bed, hC (m) height of the avert-overflow baffle, hA (m) height of corrugated metal sheets of Z1,Z3 section, Z1,Z3 (m)

260 0.111

180 0.151

1:1

2:1

0.611

0.481

0.1 0.25 0.1

0.1 0.25 0.1

dx.doi.org/10.1021/ie3010034 | Ind. Eng. Chem. Res. 2012, 51, 14236−14246


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the condition is no pressure difference between the top and bottom of the catalyst bed, the air cylinder was closed and the bottom of the column was opened. In contrast, when there is a pressure difference, the air cylinder was opened and the pressure difference at the bottom of the column was adjusted to a certain value.

porosity fraction of the catalyst bed was determined to be 0.38. The corrugated metal sheets, serving as the separation section, were the metallurgic orifice corrugated packing widely used in industrial distillation columns. The main geometric parameters are shown in Table 2. The flow rates of gas and liquid were Table 2. Main Geometric Parameters of Metallurgic Orifice Corrugated Packing parameter

value

packing surface, ap (m2/m3) channel side, S (mm) void fraction of packing, ε (dimensionless) corrugation height, b (mm) corrugation angle, θ (deg)

298.7 25 0.97 10 45

3. PROBLEM FORMULATION AND NUMERICAL SIMULATION The pressure drop is one of the most important design parameters of the catalytic distillation column, for its direct impact on energy consumption and operating capacity of the equipment. 3.1. Single-Phase Flow Simulation for Dry Pressure. The dry pressure drop model is based on the following assumptions: (1) Gas is continuous phase. (2) Gas flows only through the corrugated metal sheets. (3) Gas phase distribution is uniform in the column. On the basis of the above assumptions, single-phase flow of gas is first simulated and indirectly taken into account by the influence of corrugated metal sheets to acquire the dry pressure drop of SCPI. 3.1.1. Calculation Strategy. For Newtonian fluid, under isothermal conditions, the conservation equation of mass and momentum in an inertial reference frame can be respectively written as follows: Continuity equation

determined by a Pitot tube flowmeter and rotameter, respectively. The pressure drop across the bed was measured by a water-filled U-tube manometer.12 2.2. Height of Avert-Overflow Baffles. A 100 mm diameter column (shown in Figure 4) was used to determine

∂ρ + ∇·(ρU ) = 0 ∂t

(1)

Momentum equation ∂(ρU ) + ∇·(ρUU ) = −∇P + ∇·τ + Fd ∂t

(2)

Due to computational constraints, corrugated metal sheets are treated as porous media, which is modeled by the addition of a momentum source term Fd to the standard fluid flow equations. The source term is composed of two parts, a viscous loss term and an inertial loss term: Fd = −(C R1U + C R2|U |U ) R1

(3) R2

where C represents the linear resistance coefficient, C is the quadratic resistance coefficient, and U is the superficial velocity vector of fluid. A more descriptive quantity for simulating the flow in the porous media is the interstitial velocity UT, which represents the local average velocity in the pores occupied by the fluid phase. The relationship between them is as follows:

Figure 4. Flow sheet of experimental apparatus: (1) gas cylinders; (2) connecting flanges; (3) catalyst bed; (4) metal wire mesh; (5) column; (6) liquid distributor; (7) U-tube manometer; (8) liquid rotameter; (9) liquid seal device; (10) water tank; (11) pump.

U = εUT

the height of liquid above the catalyst bed at different pressure differences and liquid velocities. A centrifugal pump was used to transport water from a storage tank to the liquid distributor. After seepage through the catalyst container (metal wire meshes were installed at the top and bottom surfaces of the catalyst bed to fix the catalyst particles), water was collected at the bottom of the column and removed into the tank. The bottom of the column was provided with a liquid sealing device. The U-tube manometer was used to measure the pressure difference of the bed. The top of the column was open and maintained an atmospheric pressure. The air cylinder was used to regulate the pressure of the bottom of the catalyst bed. When

(4)

where ε represents the porosity of porous media. Fitting experimental data, the pressure and velocity correlation (5) about structured packing is obtained by Gualito.19 In this case, eq 5 is employed to predict the resistance coefficients CR1 and CR2 of the porous medium. Aρ Bμ dp = 2 G 2 UG 2 + 2 G UG dz Sε (sin θ) S ε sin θ

(5)

where S represents the channel side and θ is the angle of the channel. Under atmospheric conditions, the values of 0.1775 and 88.774, respectively,19 are proposed for A and B in eq 5. 14238



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3.1.2. Geometry Models and Boundary Conditions. Geometry models of SCPI-I and SCPI-II are shown in Figure 5. 419 200 and 312 000 unstructured cells are set, respectively, after thorough preliminary simulations until grid-independent solutions are yielded.

Due to complexity of the structured packing geometry of SCPI and the limited CPU resources, it is difficult to run CFD simulation at the scale of a column while taking gas−liquid− wall interactions into account at the scale of the liquid film.24 Two or more sheets of structured packings have been considered by authors21−23 to deal with these problems. In the subsequent section, the pseudo single phase method is taken to deal with two-phase flow simulation to acquire irrigated pressure drop. The irrigated pressure drop model is based on the following assumptions: (1) Both gas and liquid are continuous phases. (2) Gas flows only through the corrugated metal sheets. (3) Gas and liquid phase distribution are uniform. (4) The surface of the packing is completely irrigated. 3.2.1. Calculation Strategy. In the present study, as shown in Figure 6, three steps are used for irrigated pressure drop determination: (1) Two-dimensional (2D) simulation using the VOF models as described in the literature24−27 is used for gas− liquid flow in corrugated sheets. From such calculations, the mean thickness of liquid film and liquid holdup within the packing are essentially determined from CFD-post.28 (2) Considering gas−liquid interaction, pseudo single phase formulations20,24,29 are applied to deal with two-phase flow simulation. Only gas flow is explicitly simulated by CFD in the simulation, and the presence of liquid can be simulated by imposing a moving wall condition on the geometric model (see Figure 7). Then, the relationship between the pressure drop coefficient KZ and the gas−liquid flow characteristics can be obtained. (3) The corrugated metal sheets in SCPI are considered as anisotropic porous media with equal pressure loss coefficients in two directions and one pressure loss coefficient in the third direction. In practice, the third pressure loss coefficient would be 1000 times larger than the two others.24 From such calculations, the irrigated pressure drop of SCPI (Figure 5) can be obtained. Due to the above assumption (4), the liquid holdup is simply given by

Figure 5. Computational domain in single-phase flow simulation: (a) SCPI-I; (b) SCPI-II (H = 0.1 m).

All the domains in these geometry models are set as porous domains. At the bottom faces of the SCPI-I and SCPI-II, the “velocity inlet” (true velocity) boundaries are set as the gas inflow. The magnitude of the inlet velocity is specified, and the direction is taken to be normal to the boundary. At this boundary, the appropriate values for the velocity components and turbulent quantities must be specified. At the top faces, the “opening” boundaries are set as the gas outflow and relative static pressure is specified over the outlet boundary. The remaining faces are set as the “no-slip” boundary condition. The flow regime is under turbulent flow conditions. Calculations are run in steady mode, convergence in terms of mass flux often requires about 300 iterations, and residual values are less than 10−5. The CPU time for dry pressure calculation takes about 10 min. 3.2. Pseudo Single-Phase Flow Simulation for Irrigated Pressure Drop. The influence of the liquid phase on the velocity field of the gas phase contains two aspects.20 First, the existence of liquid narrows the width of the channels along which the gas is flowing; therefore, the average interstitial gas velocity is greater under irrigated conditions than under dry conditions. Second, the falling liquid film drags the gas downward at the liquid−gas interface, as being operated in counter-current mode.

hL = αpδ

(6)

where αp is the specific surface area of the packing and δ is the mean thickness of the liquid film and determined from CFDpost in the simulation of the 2D geometry model as shown in Figure 6a. The effective interstitial velocities of the gas and liquid phases used in step 2 are as follows:20,24

Figure 6. The corresponding geometry models of the three steps in pseudo single-phase flow: (a) step 1; (b) step 2; (c) step 3. 14239



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3.3. Two-Phase Flow Simulation for the Height of Liquid above the Catalyst Bed. The simulation for the height of liquid above the catalyst bed has provided a basis for the coupling chemical reaction in the catalytic distillation process and aids in designing the height of avert-overflow baffles of the catalyst container. The model is based on the following assumptions: (1) Both gas and liquid are continuous phases. (2) The porosity of the catalyst bed is assumed to be uniformly distributed. 3.3.1. Calculation Strategy. This case models a process of water column filling and then seepage flowing through a catalyst bed. Free fluid and porous media flow area coupled in this case and solved as a two fluid multiphase case (air and water). Two-phase flow simulation is carried out with the inhomogeneous model for multiphase calculations. For inhomogeneous multiphase flow, each fluid has its own flow field solved using individual transport equations. In this case, air is entrained in the water, and unequal velocity fields of the inhomogeneous model allow the air and water phases to separate and form a distinct interface30 above the catalyst bed. The conservation equations based on the Euler−Euler twofluid model are listed below: Continuity equation

Figure 7. Views of the computational domain used for setting the slipping velocity on walls.

ULe =

UL εhL sin θ

(7a)

UGe =

UG ε(1 − hL) sin θ

(7b)

∂ (ερ γ ) + ∇·(ε(ρβ γβUβ)) = 0 ∂t β β

The pressure drop coefficient can be obtained from Raynal:24 ∇P KZ = = KZ(Q G , Q L , UL) 0.5ρG UG 2L

β = L, G

(9)

Momentum equation ∂ (ερ γ Uβ) + ∇·{εγβ[ρβ UβUβ − μeβ (∇Uβ + (∇Uβ)T )]} ∂t β β

(8)

where QG and QL are, respectively, the gas and liquid flow rates. 3.2.2. Geometry Models and Boundary Conditions. Geometry model and boundary conditions in Figure 6a have been reported in quantities of previous literature.26,27 The detailed boundary conditions of the 3D geometry model with openings uniformly distributed on its corrugated sheets in Figure 6b are shown in Figure 7. The computational domain consists of two contacting corrugated packing sheets (the structure in the rectangle) immersed into a parallelepiped (100 × 20 × 104 mm3). Gaps of 2 mm are arranged between inlet/ outlet and interior sheets. The numerical domain is constructed in such a way that it can capture the thickness of the packing sheets.23 The geometry model consists of up to 1 320 000 cells, and these numbers of grid cells are set after thorough preliminary simulations until grid-independent solutions are yielded. Four kinds of walls are set on two corrugated metal sheets (only two walls in Figure 7 are shown here in order to facilitate the presentation); the local coordinate systems are established on walls, respectively, and the slipping velocity of liquid is set on each wall. At the bottom face of the model, the “velocity inlet” boundary is set for the gas inflow. The appropriate values for the velocity and turbulent quantities must be specified at this boundary condition. The “outlet” boundary is set for the gas outflow at the top face of the model. At this boundary, the outlet static pressure is stated. The front and back faces of the model are set as the periodical interface. Geometry models in Figure 6c have the same boundary conditions as the singlephase flow simulation. Calculations are run in steady mode, and about a total time of 3 h is needed for the irrigated pressure drop simulation.

= εγβ(Bβ − ∇p) + Fβ

β = L, G

(10)

Constraint equation γL + γG = 1

(11)

where ε represents the volume porosity of the catalyst bed, γ is the volume fraction occupied by each phase, ρ is the fluid density, μe is the effective viscosity including the contribution from turbulent stress, U is the fluid superficial velocity vector, B is the body force (including the gravity and the flow resistance), P is the pressure, F is the interphase drag force, and β is the phase index, where L represents the liquid phase and G the gas phase. To solve the above two-fluid model (9−11), closure models are required for the interphase drag forces such as gas−solid (BG) and liquid−solid (BL). They are formulated as below:31,32 BG = R GSUG + ρG g

(12)

BL = RLSUL + ρL g

(13)

where RGS and RLS are the resistance tensors of the gas and liquid flow in the packed bed, respectively. The interphase drag forces between gas and liquid (FG, FL) can be expressed as FG = CGL(UL − UG)

(14)

FL = −FG = −CGL(UL − UG)

(15)

A drag coefficient CGL of 0.44 is chosen as referenced by the CFX 13.0 tutorial.33 In this case, the parameters (RGS, RLS) are calculated by the model based on the Ergun equation:34 14240


Industrial & Engineering Chemistry Research R=

E1(1 − ε)2 μ 2 2

dp ε

UT +

E2(1 − ε)ρ 2 UT d pε

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about 0.03 m by fitting the experimental data at various velocities and different heights of the catalyst bed. In this case, transient simulations are carried out until reaching a pseudo steady state and the time step is set to 0.005 s. The pseudo steady state is typically achieved when negligible changes are observed in the outlet mass flow rate. Initially (at time t = 0), only the catalyst bed (porous domain) is assumed to be filled with liquid of zero velocity and gauge pressure and other domains are filled with stable gas. To obtain good convergence of the iterations, the steady-state flow is first calculated, and then as the initial condition for unsteady simulation. To speed up the simulation, they were carried out in parallel with distribution over eight processors. About 5 h of CPU time is needed from the start of the transient simulations.

(16)

The Ergun constants E1 and E2 are 180 and 1.75, respectively, as recommended by McDonald.35 μ and ρ in eq16 are treated as dynamic variables in the simulation. 3.3.2. Geometry Models and Boundary Conditions. The geometry model and boundary conditions are shown in Figure 8. Due to computational constraints, only one-half of the

4. RESULTS AND DISCUSSION To obtain a solution of the CFD model, the geometry structures with a numerical grid must be inserted in the program. The mesh preparation for the geometry is performed in ICEM CFD 13.0. A commercial CFD package, CFX 13.0 (ANSYS Inc.), is used to solve the previous equations. The model equations are solved numerically with the finite volume method. The SIMPLEC algorithm is employed to solve the pressure−velocity coupling in the momentum equations. For turbulent flow calculations, the RNG k−ε turbulence model is employed with standard wall functions, which has been successfully applied to model both single phase and multiphase flows in structurally packed columns in previous works.23,24,29 All calculations were carried out on an HP-Z800 workstation sporting a pair of 4-core Xeon X5687 CPUs running at 3.6 GHz. The results are shown in the following items. 4.1. Dry Pressure Drop Simulation. Figure 9 shows the comparison between the dry pressure drops calculated by the proposed model and measured by experiments with the SCPI internals. The pressure drops of the two structures predicted by CFD are close to experimental data, and the relative error is 10.23% for SCPI-I and 4.26% for SCPI-II. The small differences observed in Figure 9a are caused by the uneven gas distribution. In the CFD models, it is assumed that the gas phase distribution in the packed bed is uniform, and therefore, the predicted pressure drop is lower than the experimental pressure drop. This model can be used to simulate dry pressure drops of various structures (the ratio of separation to reaction section can be varied according to different catalytic distillation process requirements) of SCPI. Velocity streamline and velocity vector profiles of singlephase simulation are shown in Figure 10. Figure 10a shows a fair amount of bypass flow phenomenon around the catalyst bed. This will result in high pressure (velocity decreases shown in Figure 10b) and low efficiency of gas−liquid contact. To minimize bypass flow, the middle height H (see Figure 2) of SCPI can be enlarged. Dry pressure drop per meter of SCPI-I at different heights of the middle is simulated by the above proposed model. The influence of enlarging H on the pressure drop obtained by CFD simulation is shown in Figure 11. Dry pressure drop per meter decreases gradually with the height H increase in the range of H up to approximately 100 mm, whereas it is no significant change for higher values. Apparently, a higher height will give a lower pressure drop in the catalyst bed. However, the catalyst loading space of the column will reduce at the same time. Therefore, the structural optimization should be done to balance the two factors. The details

Figure 8. Geometry model and boundary conditions in two-phase flow simulation.

column is simulated. The total number of unstructured triangular cells up to 176 228 is set after thorough preliminary simulations until grid-independent solutions are yielded. From the top to bottom of the column, the three domains are the fluid domain, porous domain, and fluid domain, and the fluid− porous interface is set between the fluid domain and porous domain. In this paper, only no pressure difference condition at the top and bottom of the catalyst bed is simulated. In the simulation, the following boundary conditions are used: At the top face of the column, holes of equilateral triangle arrangement (inlet) evenly distributed are set for the liquid “mass flow inlet” boundary. Suitable values of the mass flow rate component, volume fraction, and turbulent quantities in each phase must be specified at this boundary condition. The remaining region outside the holes is set as the “opening” boundary condition for gas outflow, and the relative static pressure is set over this boundary. At the bottom face of the column, the “outlet” boundary condition is used for liquid outflow. The relative static pressure and volume fraction in each phase must be specified at this boundary condition. At the column wall, the no-slip boundary condition and nopenetration boundary condition are specified for liquid and gas velocities. Plane z = 0 (see Figure 8) is the plane of symmetry, and the “symmetry” boundary condition is set over this boundary. Laminar flow and the RNG k−ε turbulence model are used for the liquid and gas phases, respectively. The height of the catalyst bed in simulation is 50 and 75 mm, respectively. Metal wire meshes at the top and bottom surfaces of the catalyst bed are equivalent to a certain height of the catalyst bed, and the equivalent height of the metal wire mesh is 14241



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Figure 11. Dry pressure drop of SCPI-I at different heights of the middle H (see Figure 5).

Figure 9. Comparison of the dry pressure drop between experimental data and CFD simulation: (a) SCPI-I; (b) SCPI-II.

Figure 12. Irrigated pressure drop of SCPI-I predicted by CFD simulation and experiment (liquid sprayed density QLS = 14.06 m3/ m2/h; 23.44 m3/m2/h).

surrounding the optimizations of this structure will be presented in a subsequent article. 4.2. Irrigated Pressure Drop. Figure 12 shows a comparison of experimental data and CFD simulation results for the irrigated pressure drop with the internal SCPI-I. As described in McCabe36 and Treybal,37 the gas pressure drop increased with the increase of liquid sprayed density at a fixed F-factor, principally because of the reduced free cross section

available for the flow of gas resulting from the presence of the liquid. Figure 12 demonstrates a very good agreement between the predicted irrigated pressure drops and measured data of Ffactor up to approximately 1.7. However, for higher F-factor values, especially for gas with an F-factor of nearly 1.8 (QLS = 23.44 m3/m2/h), the predicted values are significant deviations from the experimental values and the error is high up to 21.5%.

Figure 10. CFD single-phase simulation of SCPI-I (without considering corrugated metal sheets): (a) velocity streamline (H = 0.065 m); (b) velocity vector at plane 1 (Z = 0) (H = 0.065 m). 14242



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This deviation happens when the gas−liquid interaction increases, inducing an increase in experimental pressure drop values. This difference is thus explained by the fact that the present methodology is not able to determine strong gas− liquid interactions exactly as it happens at high F-factor (above 1.7). In the model applicable range, the average relative errors between the CFD predictions and experimental data are 8.68 and 7.64% for a liquid sprayed density (QLS) of 14.06 and 23.44 m3/m2/h, respectively. The discrepancy observed could be explained by the following reasons: First, as described in Haghshenas Fard et al.,21 there are some important phenomena which have a major effect on pressure drop, such as uneven gas and liquid phase distribution, which are neglected in the CFD models. Second, the simplistic approach does not take into account nonuniform wetting of the packing, eventual formation of drops, flow of the liquid through preferential paths, etc. Third, at the same sprayed density, liquid film is stable at low gas F-factor and the film thickness and pressure coefficient predicted by simulation are relatively accurate. With increasing gas F-factor, the liquid film instability is exacerbated and the pressure coefficient predicted in the second step may be lower than the true value, thereby resulting in the decrease of pressure drop. 4.3. The Height of Liquid above the Catalyst Bed. As shown in Figure 13a, the average relative error of the height of

liquid above the catalyst bed (hc = 75 mm) between simulated values (without considering the influence of metal wire mesh) and experimental data is high up to 31.7%. However, the average relative error is about 6.5% when metal wire meshes (on the top and bottom surfaces of the catalyst bed) are considered. Then, a 50 mm catalyst bed is chosen to simulate the average relative error between CFD simulation result and experimental data is 11.2% (see Figure 13b). It is clear that the height of liquid above the catalyst bed predicted from the CFD simulation is lower than the experimental data. The discrepancy may be caused by the simplifications of CFD models, in which the porosity of the catalyst bed is assumed to be uniformly distributed. The pseudouniform porosity distribution maybe underestimates the true value of porosity in the packed bed, and therefore, the predicted height of liquid above the catalyst bed is lower than the experimental value. It can be seen from these curves, at the same velocity of liquid, the liquid level will increase as the height of the catalyst bed increases. At a certain height of catalyst bed, there is a linear relationship between the liquid level on the catalyst bed and liquid velocity. Sequences of contours of liquid-phase volume fraction at different time steps (the inlet mass flow rate of liquid is 0.08868 kg/s, and the height of catalyst bed is 0.05 m) are shown in Figure 14. As described in the preceding paragraph, initially (at time t = 0), only the catalyst bed is filled with liquid and other domains are filled with gas. In the first 0.1 min of the simulation, the liquid flows out of the catalyst bed at a greater rate than it is flowing in and the liquid level is gradually decreasing with time; therefore, two phases (air and water) exist in the catalyst bed. With liquid flowing from the top of the column, during the time interval from t = 0.25 to 0.8 min, the liquid flows into the catalyst bed at a greater rate than it is flowing out, gas is squeezed out of the catalyst bed, and the liquid level is gradually increasing with time. During the time interval from t = 0.8 to 1 min, due to liquid gravity and internal resistance of the catalyst bed, dynamic equilibrium is reached when the liquid rate of flowing into the catalyst bed equals the rate of flowing out, and finally, the liquid level stabilizes at a certain height. Liquid superficial velocity vector (t = 1 min) is shown in Figure 15, while the free fluid zone and the porous zone are also indicated. Driven by its own gravitational force, the liquid flows uniformly downward through the catalyst bed and conducts chemical reactions in the catalyst bed. In the free fluid zone, two phases (air and water) exist; obvious liquid backmixing appears in this region due to the effects of gas. In the porous zone, due to the reduced flow cross-sectional area, liquid superficial velocity is relatively greater than velocity in the free fluid zone. The residence time of liquid in the catalyst bed can be adjusted by the height of the catalyst bed and the average liquid velocity in the catalyst bed. At a constant spray density of the liquid, as the height of the catalyst bed increases, the residence time of liquid in the catalyst bed will increase, and correspondingly, chemical reactions will proceed more fully. However, the height of the catalyst bed is not as high as possible and the kinetics of the reaction equilibrium also need to be considered. Simulation results of Figure 14 are used to aid in designing the height of avert-overflow baffles. The design process is illustrated by the drawing shown in Figure 16. First, considering chemical reaction kinetics, the residence time (t) (the needs of industry) is determined at a certain liquid sprayed density of the catalytic distillation column. The height of the catalyst bed

Figure 13. Comparison of the height of liquid on the catalyst bed between experimental data and CFD simulations: (a) catalyst bed (hc = 0.075 m); (b) catalyst bed (hc = 0.05 m). 14243



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Figure 14. Sequences of contours of liquid-phase volume fraction at different time steps (where the inlet mass flow of liquid is 0.08868 kg/s, the height of the catalyst bed is 0.05 m).

otherwise, adjust the height of the catalyst bed (h0) gradually until the error requirement is met. Third, based on the height of the catalyst bed, the height of the liquid layer (h1) above the catalyst bed can be determined by CFD simulation. Finally, the height of overflow baffles can be determined according to the height of liquid above the catalyst bed.

5. CONCLUSIONS In the present study, an attempt has been made to determine the hydrodynamic parameters of a seepage catalytic packing internal (SCPI) for a structured packed distillation column by means of CFD. On the basis of the hydrodynamic experiments, CFD models were proposed to predict dry pressure drop, irrigated pressure drop of SCPI, and the height of liquid above the catalyst bed. In the single-phase flow simulation, two kinds of structures (SCPI-I and -II) were simulated to predict dry pressure drop; the average relative errors between simulation result and experimental data are 10.23 and 4.26%, respectively. Then, the model was used to predict the pressure drop of different height (the middle height) of SCPI. The results indicate that increasing the middle height appropriately is favorable to reduce the pressure drop of SCPI, but the catalyst loading space of the column should be carefully considered at the same time. Pseudo single phase formulation was used to determine the irrigated pressure drop of SCPI at different sprayed densities. On the basis of the results of the simulation, it was shown that this approach can provide a reasonably good prediction of

Figure 15. Liquid superficial velocity vector in steady state predicted by CFD simulation (t = 1 min).

(h0) can be estimated according to the residence time and the liquid flow velocity; then, h0 is set as the initial value. Second, CFD software is used to simulate the residence time of liquid (t′). If the relative error between the simulated residence time (t′) and the demand value (t) is less than e, output the value h1; 14244



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body force vector, N/m3 corrugation height, m interphase drag coefficient linear resistance coefficient, (kg/m3/s) quadratic resistance coefficient, (kg/m4) Ergun constant relative error volume fraction of the catalysts in the column, m3/ m3 FCMS volume fraction of the corrugated metal sheets in the column, m3/m3 F interphase drag force, N/m3 Fd momentum source, kg/m2/s2 g acceleration vector, 9.81 m/s2 H the middle height of SCPI, m liquid holdup, m3/m3 hL hA height of avert-overflow baffles, m hC height of catalyst bed, m h0 initial height of catalyst bed, m h1, h2, h3 height (variable), m Δh height variation, m KZ pressure drop coefficient QLS liquid sprayed density, m3/m2/h P pressure, Pa ΔP/ΔZ pressure drop per unit packed height, Pa/m QG gas flow rate, m3/s QL liquid flow rate, m3/s RGS resistance tensors of gas flow in the packed bed RLS resistance tensors of liquid flow in the packed bed RCC/CMS width ratio of catalyst container to corrugated metal sheets, dimensionless S side dimension of corrugation, m t residence time of requirement, s t′ residence time of simulation, s UT fluid interstitial velocity vector, m/s U fluid superficial velocity vector, m/s Ue fluid effective velocity vector, m/s UTe the interstitial velocity vector of the gas, m/s UGe effective interstitial velocity vector of the gas, m/s ULe effective interstitial velocity vector of liquid phase, m/s Z1 height of corrugated metal sheets of Z1 section, m Z3 height of corrugated metal sheets of Z3 section, m B b CGL CR1 CR2 E1, E2 e FCC

Figure 16. Sketch of the present design process.

irrigated pressure drop of SCPI, with error no more than 10%. The models for pressure drop determination could be used to calculate the pressure drop of various structures of SCPI and aid in optimizing the structure of the internal. In the two-phase flow simulation, catalyst beds of 50 and 75 mm were simulated to determine the height of liquid above the catalyst bed. The average relative errors between simulation results and experimental data are 11.2 and 6.5%, respectively. The model could be used to aid in designing the height of the catalyst container with avert-overflow baffles, and the detailed design processes have been illustrated in the paper.

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AUTHOR INFORMATION

Greek Symbols

Corresponding Author

β r δ τ ρ ε ε0 θ μ μe

*Tel.: +86-22-27404701-8503 (H.L.); +86-22-27404701-8509 (X.G.). Fax: +86-22-27404705 (H.L., X.G.). E-mail: lihongtju@ tju.edu.cn (H.L.); [email protected] (X.G.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful for the financial support from the National Basic Research Program of China (No. 2009CB219905), Program for Changjiang Scholars and Innovative Research Team in University (No. IRT0936), National Natural Science Foundation of China (No. 21176172), and Municipal Natural Science Foundation of Tianjin (No.11JCYBJC05400).

■ a ap

phase index the volume fraction occupied by each phase mean thickness of the liquid film, m stress tensor, kg/m/s2 density of fluid, kg/m3 porosity of porous media, dimensionless void fraction of packing bed, dimensionless angle of channel of structured packing, degree viscosity, kg/m/s effective viscosity of fluid, kg/m/s

Subscripts

L liquid G gas

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REFERENCES

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NOMENCLATURE specific surface area of SCPI, m2/m3 specific surface area of structured packing, m2/m3 14245



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Hydrodynamic Simulations of Seepage Catalytic Packing Internal for

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