Simulation of Flow Distribution in Radial Flow Reactors - Industrial

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Ind. Eng. Chem. Res. 2006, 45, 2862-2874

Simulation of Flow Distribution in Radial Flow Reactors A. A. Kareeri, H. D. Zughbi,* and H. H. Al-Ali Department of Chemical Engineering, King Fahd UniVersity of Petroleum & Minerals, Dhahran 31261, Saudi Arabia

Flow distribution in four possible configurations, CP-z, CP-π, CF-z, and CF-π, of a radial flow reactor is investigated using computational fluid dynamics (CFD). The CFD models are validated using published experimental data. It is found that one of the π-flow configurations always has the most uniform flow distribution. Results show that the ratio of the center pipe cross-sectional area to that of the annular channel has a significant effect on the flow distribution. For a ratio less than one, the CF-π configuration gives the most uniform flow, while the CP-π is preferred for a ratio larger than one. It was also shown that the uniformity of the flow distribution is enhanced by lowering the porosity of the center pipe and that of the bed. To ensure good distribution, partial blockage of the center pipe must be avoided. Introduction Many vapor phase catalytic processes are designed with radial flow reactors. The main advantage of a radial flow reactor is that it has a lower bed pressure drop in comparison with an axial flow reactor. There are two types of radial flow reactors depending on whether the catalyst bed is fixed or moving inside the reactor. They are the radial flow fixed bed reactor (RFBR) and the radial flow moving bed reactor (RFMBR). Both types can be found in catalytic reformer processes. An RFMBR is a reactor in which the solids move at a low velocity (about 1 mm/s) under the influence of gravity. Due to this low velocity, the moving bed void fraction is considered to be constant and, therefore, the hydrodynamics of an RFBR and an RFMBR are similar. Due to this similarity, this work is applicable to both types. The main internals that provide the radial flow pattern inside the reactor are the annular channel distributing header which consists of a perforated wall positioned between the reactor wall and the catalyst bed and the axial outlet collecting header in the form of a perforated cylinder which is called the center pipe. The catalyst is charged to the annular space between the annular channel and the center pipe. The top of the catalyst bed is covered with a cover plate. There are two types of annular channel distributors. One consists of a wire screen, while the other consists of a series of scallops,1 where each scallop is a small diameter perforated half cylinder. Radial flow reactors can be classified into a z-flow type or a π-flow type depending on the axial directions of the flow in the annular channel and the center pipe. If the axial flow directions in the annular channel and in the center pipe are the same, it is classified as the z-flow type, and if they are opposite, it is classified as the π-flow type. Moreover, radial flow reactors can be also classified into centripetal (CP) or centrifugal (CF) flow types depending on the reactor radial flow direction. In the CP-flow type, the gas is fed to the annular channel and travels radially inward from the annular channel to the center pipe. In the CF-flow configuration, the gas is fed to the center pipe and travels radially outward from the center pipe to the annular channel. Therefore, four flow configurations are possible for a radial flow reactor. They are classified as CP-z, CP-π, CF-z, and CF-π configurations as shown in Figure 1. All four configurations can be applied to an RFBR and an RFMBR. The RFBR was originally used in the catalytic synthesis of ammonia. Subsequently, it was used for catalytic reforming, * To whom correspondence should be addressed. E-mail: [email protected]. Tel.: 966 3 860 4729. Fax: 966 3 860 4234.

Figure 1. Four possible flow configurations for a radial flow reactor.

desulfurization, and nitric oxide conversion. Earlier analytical work on RFBRs concentrated on the effects of the radial flow direction on reaction conversion with the assumption of a perfect radial flow profile inside the reactor. Earlier work on RFBRs carried out by Hlavacek and Kubicek,2 Calo,3 and Balakotaiah and Luss4 showed that the direction of radial flow (CP or CF) has an effect on the reaction conversion. Genkin et al.5 performed theoretical and experimental investigations to determine the flow distribution inside CF-z and CF-π RFBRs. A significant maldistribution was found. The gas distribution inside the reactor was found to be a function of the center pipe porosity and the ratio of the cross-sectional area of the center pipe to that of the annular channel. Ponzi and Kaye6 performed analytical investigations to determine the effects of radial flow maldistribution and flow direction on RFBR performance. They were the first to show that a maldistribution in the radial flow profile inside the reactor has more influence on the reactor performance than the flow direction. Chang and Calo7 also performed analytical investigations to determine the effects of radial flow maldistribution and flow direction. They studied all four reactor configurations shown in Figure 1. Chang and Calo7 concluded that the optimum flow profile in an RFBR can be achieved by adjusting the reactor dimensions so that the radial pressure drop remains independent of the axial coordinate.

10.1021/ie050027x CCC: $33.50 © 2006 American Chemical Society Published on Web 03/21/2006

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An operating test on an RFBR in three commercial reforming units to investigate the axial flow distribution was performed by Lobanov and Skipin.8 All the reactors were of the CP-zflow type. It was concluded from this work that a relatively uniform flow distribution existed only at the lower part of the catalyst bed. However, a significant amount of the upper part of the catalyst bed was not fully utilized. Such a scenario can be well explained by the findings of the present study. Song et al.9 performed theoretical and experimental investigations of the axial flow distribution in an RFMBR without reaction. Their study was applied for all four reactor configurations shown in Figure 1. The ratio of the cross-sectional area of the center pipe to that of the annular channel was less than one. It was found that the CF-π-flow configuration had the most uniform axial flow over the other configurations under the same conditions. Heggs et al.10 performed a numerical investigation for all four RFBR configurations. The ratio of the cross-sectional area of the center pipe to that of the annular channel was greater than one. It was concluded that the CP-π-flow configuration gives the best flow distribution. Heggs et al.11 extended their previous model to predict the flow profiles for a multilayered radial flow air filter. A good agreement was found between the model predictions and the experimental results. Bolton et al.12 performed computational fluid dynamics (CFD) and experimental evaluation to determine the flow distribution in a novel design of an RFBR. The objectives of that study were to illustrate the use of an electrical tomography technique for flow visualization and to confirm CFD predictions. The velocity profiles obtained using CFD and a tomography method showed reasonable qualitative agreement. Mu et al.13 developed a two-dimensional hydrodynamic mathematical model for a CP-π RFMBR configuration. In the model, the bed was considered as a stationary bed. The model predictions were validated against RFMBR experimental results. Good agreement was found which indicates a similarity of the gas-flow profiles of an RFBR and an RFMBR. This is because the catalyst velocity in an RFMBR is very small, usually less than 1 mm/s. At such a low velocity, the bed porosity of an RFBR is almost the same as that of an RFMBR. This similarity of the gas flow profiles of RFBRs and RFMBRs was proved by the earlier experimental work of Song et al.14 However, this similarity will cease to exist if pinning phenomena is initiated in the RFMBR.14 Earlier work investigating pinning phenomena in an RFMBR was performed by Ginestra and Jackson,15 Doyle et al.16 and Pilcher and Bridgwater.17 The pinning phenomenon is further discussed in the next paragraph. In an RFMBR, the catalyst moves down by gravity. The gas stream flows perpendicular to the catalyst movement. It exerts a drag force on the catalyst particles. This drag force is a function of the gas radial velocity. The gas radial velocity can be increased by increasing the gas flow rate or by a flow maldistribution in the reactor. Under normal conditions, catalyst particles move down with normal friction at the upstream and downstream perforated walls. The gas enters and leaves the bed through the upstream and downstream perforated walls, respectively. If the drag force on the catalyst particles increases, the normal stress between the particles and the upstream wall will be decreased. When the normal stress is reduced to zero, the bed particles start to lose contact with the upstream wall. Under this condition, a thin cavity will open between the catalyst bed and the upstream wall. Under very high drag conditions, the size of cavity adjacent to the upstream face might be increased until it ultimately spans the full width of the catalyst bed. At

Figure 2. Typical flow distributions over the bed length in a radial flow reactor at the same feed flow rate for CP configurations (a-c) and for CF configurations (d-f). The arrow length represents the mass flow magnitude.

this point, the bed may not move down at all and the bed is said to be completely pinned. Another form of pinning phenomena is when the drag force on the catalyst particles adjacent to the downstream perforated wall is enough to cause a high friction force between the particles and the wall. This frictional force can pin at least part of the catalyst bed against the downstream perforated wall. In this case, the bed is said to be partially pinned. Therefore, the flow distribution and pinning phenomena in an RFMBR influence each other. The above survey of literature shows that previous analytical and numerical models for studying the flow distribution in a radial flow reactor are limited and rather simplified. None of these models were fully three-dimensional, and none of them took into consideration the change in the flow area of the bed as the flow moves toward the center pipe or away from it. The literature survey also showed that no detailed three-dimensional (3-D) CFD model of flow in a radial flow reactor has yet been reported. In this study, such a 3-D CFD model is reported. From the previous work, it is shown that flow distribution has a major effect on the operations of an RFBR and an RFMBR. The objective of this work is to use computational fluid dynamic (CFD) to study the flow distribution in a radial flow reactor and to show the effect of the flow distribution on pinning phenomena in the RFMBR. The CFD model is represented by a cylindrical RFBR. Since the flow profiles in an RFBR and an RFMBR are similar, the CFD model results are also applicable to an RFMBR prior to the initiation of the pinning phenomena. Such a CFD model can be used to check the existing designs and to recommend ways to reduce pinning. Flow Distribution in a Radial Flow Reactor The operating efficiency of a radial flow reactor largely depends on the gas stream distribution over the catalyst bed height. Figure 2 shows typical flow distributions in a radial flow reactor. To have a uniform flow distribution, the gas mass flow should be equally divided over the catalyst bed height. If the mass flow is not equally divided, some parts of the bed will be

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under utilized as found by Lobanov and Skipin.8 A nonuniform flow distribution over the bed height affects the reaction conversion and selectivity and the temperature profile.6,8,18 Consequently, in a catalytic process, a uniform flow distribution produces an even carbon concentration over the catalyst bed height. On the other hand, a nonuniform flow produces a nonuniform carbon concentration over the catalyst bed height. This influences the duration of the regeneration cycle for an RFBR process and disturbs the operation of the regeneration system in an RFMBR process. Moreover, in an RFMBR process, the nonuniformity of the flow can contribute to pinning phenomena since a higher radial velocity in some parts of the bed is produced. When a nonuniform flow distribution occurs in a CP-z or a CP-π configuration, there is an increased probability of having pinned catalyst against the center pipe or initiating a cavity between the annular channel and the catalyst bed at the bottom and the top of the bed, as shown in Figure 2b and c, respectively. In the CF-z or CF-π configuration shown in Figure 2e and f, the same problem exists; however, the pinning will be against the annular channel perforated wall, and the cavity is between the center pipe and the catalyst bed. Since the fixed and moving beds have almost the same gas flow profile prior to the initiation of pinning phenomena, analyzing the flow distribution in an RFBR can help in evaluating pinning phenomena in the moving bed reactor. The optimum utilization of the catalyst depends mainly on the pressure distribution inside the reactors. An important design criterion for the radial flow reactor is to have the radial pressure independent of the axial coordinate.19 This criterion makes the gas stream equally divided over the catalyst volume, as shown in Figure 2a for CP configurations and in Figure 2d for CF configurations. In other words, the uniformity criterion means achieving a uniform flow distribution in a radial flow reactor by having the same pressure drop between the center pipe and the annular channel at any axial level. Predictions of the Annular Channel and Center Pipe Pressure Profiles. The annular channel and the center pipe can be considered to be perforated pipe distributors. In a perforated pipe distributor, the total pressure drop is a combination of the frictional pressure drop and the pressure recovery due to the kinetic energy or momentum changes caused by the varying mass flow. The equations below show the effects of friction and momentum recovery on the total pressure drop along a perforated pipe distributor.20

∆Ρ )

FVi 4fL - 2K 3D 2

(

(discharge perforated pipe) (1)

∆Ρ )

FVe 4fL + 2K 3D 2

(collecting perforated pipe) (2)

2

)

2

(

)

where ∆P is the net pressure drop over the length of the distributor, f is the fanning friction factor, D is the pipe diameter, Vi is the inlet velocity for the discharge pipe, Ve is the exit velocity for the collecting pipe, and K is the momentum recovery factor. The first term in eqs 1 and 2 is the frictional pressure drop, and the second term is the inertial (momentum) pressure recovery. Both frictional and inertial effects cause a pressure drop in a collecting pipe, since the mass flow increases downstream. Therefore, the pressure always decreases along the length of the pipe. In a discharge pipe, the frictional and inertial effects oppose each other. Friction causes a pressure drop, and

since the mass flow decreases downstream, the momentum recovery causes a pressure rise. Therefore, the pressure may decrease or increase along the pipe length depending on the dominating term. When the friction is the dominating term, the pressure will decrease along the pipe length. Friction can be the dominating term in a long pipe and a small diameter pipe as can be seen from eq 1. When the momentum recovery is the dominating term, the pressure will increase along the pipe length. The momentum recovery can be the dominating term in a short pipe and a large diameter pipe as can be seen from eq 1. At high flow rates, the inertial effects may dominate the frictional effects in determining the pressure profile along the perforated pipe, unless the distance between the pipe holes is large.20 Therefore, at a high flow rate and a small distance between the pipe holes, which are true for most of the applications of the radial flow reactor, eqs 1 and 2 are reduced to

FVi2 (discharge perforated pipe) 2

(3)

FVe2 (collecting perforated pipe) 2

(4)

∆Ρ ) -2K ∆Ρ ) 2K

It can be seen, from eqs 3 and 4, that at a constant density the pressure profile in a perforated pipe mainly depends on the momentum recovery factor and the pipe velocity. Although eqs 1-4 are not used in the present CFD model, their concept is used to better understand and analyze the pressure profiles in the annular channel and the center pipe and to get a prediction for some parametric studies for any radial flow reactor numerical model. The flow can be discharged from the annular channel and collected in the center pipe as in CP-z and CP-π configurations or discharged from the center pipe and collected in the annular channel as in CF-z and CF-π configurations. Achieving uniform flow mainly depends on the pressure profiles in the annular channel and the center pipe. If the frictional pressure drop is negligible in the annular channel and the center pipe, a pressure rise is expected in the discharge channel and a pressure fall is expected in the collecting channel, as shown by eqs 3 and 4. Therefore, at a uniform flow distribution over the bed height, the pressure profiles in the discharge and collecting channels are as those shown in Figure 3. These profiles can be achieved only by the CP-π and CF-π configurations. Therefore, depending on the reactor geometry, one of the π-flow configurations will always have the most uniform flow distribution.5,7,9,10 The flow distribution in a radial flow reactor can be determined by knowing the flow profiles in the discharge and collecting channels. In the previous theoretical and numerical studies, three flow equations were used to describe the flow profile in each channel. They are the Bernoulli’s equation, the total energy equation,5 and a modified momentum equation.9,14 Previous investigations showed that Bernoulli’s equation gives a poor description of the motion of a gas stream with varying mass, such as that in a radial flow reactor.5 The total energy equation used by Genkin et al.5 is too complex to be applied to a commercial reactor design. The application of the modified momentum equation9,13 depends on empirical coefficients. One of these coefficients is the momentum recovery factor which is shown in eqs 1-4. This factor depends on the equipment geometry and the energy change along the axial direction and is determined experimentally.9 Empirical coefficients needed


Figure 3. Illustration of the discharge and the collecting channel pressure profile that leads to a uniform flow distribution inside a radial flow reactor.

in the modified momentum equation may not be available for all geometries and operating conditions. Moreover, they cannot be determined for certain cases, such as an operating commercial reactor. Hence, using the modified momentum equation is limited by the availability of the empirical coefficients. In the present study, the conservation equations of mass and momentum in conjunction with porous media and porous jump models are used to describe the flow in an RFBR. In addition, a three-dimensional geometry is used to take into account the effects of the cross-sectional flow area reduction toward the center pipe. The equations were solved using a general purpose three-dimensional CFD package, Fluent 6.1. Governing Equations. The flow in an RFBR reactor is classified as a single phase flow. The simulation of an RFBR is carried out under isothermal, incompressible, and steady-state conditions. The incompressible condition is justified since the pressure drop inside the bed is limited. The governing equations for the gas flow in an RFBR are the mass and momentum conservation equations. The mass conservation equation is

∇‚ν b)0

(5)

The general form of the momentum conservation equation is

ν + Fg b+B S F(ν b‚∇ν b) ) -∇p + µ∇2b

(6)

where S contains other model-dependent source terms. In the present study, two other models are used; these are a porous media and a porous jump model. The porous media model is used for the catalyst bed, and the porous jump model is used for the center pipe and annular channel perforated plates. At the catalyst bed,

||)

µ 1 ν B S)- b ν + C2 F ν b R 2

(

(7)

where R is the permeability and C2 is the inertial resistance factor. From the Ergun equation,21 which is a semi-empirical correlation applicable over a wide range of Reynolds numbers and for many types of packing, R and C2 can be represented as

R)

Dp2 3 150 (1 - )2

(8)

3.5 (1 - ) Dp 3

(9)

C2 )

where is the bed porosity and Dp is the catalyst diameter. In

this model, the bed porosity and catalyst diameter are assumed to be 0.3 and 1.8 mm, respectively. The porous jump model is a simplification of the porous media model where the flow is assumed to be one-dimensional and normal to the porous section of the plate. Since the velocity is high through the perforated plate, the inertial term is the dominating one. Neglecting the permeability term, the source term at the center pipe and annular perforated plates becomes

( ||)

1 B S ) Si ) - C2 F νi b νi 2

(10)

where i is the normal coordinate to the perforated plate, in this model it is the x-coordinate. For the perforated plate, C2 is determined from the equation of flow through square-edged holes on an equilateral triangular spacing.

C2 )

2 1 (Ap/Af) - 1 ∆x C2

(11)

where C is the orifice discharge coefficient. In this work, C is 0.62. This value is generally used for most of the perforated plates.20 Ap is the total area of the plate, Af is free area or total area of the holes, and ∆x is the plate thickness. Simulation of an RFBR. A schematic diagram of the radial flow reactor simulated in the present study is shown in Figure 4. The reactor consists of two perforated cylinders and a reactor wall. The gas stream enters the annular channel where it is distributed through the perforated plate. It then flows radially across the particle bed toward the center pipe. The driving force of the flow across the bed is the radial pressure drop between the annular channel and the center pipe. The reactor dimensions and operating conditions used in this study are shown in Tables 1 and 2. Figure 4 represents the conventional configuration, which is the CP-z configuration. The flows in the other three configurations were also simulated. The RFBR model consists of three different sections: an annular channel, a bed section, and a center pipe channel. All of them have the same length but different widths. The lengths and diameters of these three sections are given in Table 1. A three-dimensional numerical model is constructed using the information in Figure 4 and Table 1. The geometry is meshed using an unstructured tetrahedral mesh. A mesh size of 18 mm was used, and the total number of cells obtained is 535 573 cells. Simulation Results In discussing the results, many cuts are made along the height of the center pipe and the annular channel or across the width

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Figure 5. Schematic diagram of various values of x and z where cuts are taken in subsequent figures. Since the model is symmetric at y-plane ) 0, all cuts are at y-plane ) 0. The x ) 0 and x ) 0.2275 lines represent the axial flow profiles in the center pipe and the annular channel, respectively. The z ) 0.5 and z ) 1 lines represent the radial flow profiles in the reactor.

Figure 4. Schematic diagram of a radial flow reactor, where Ls, Lp, and Lb are the lengths of the seal layer, the perforation section, and the bed, respectively, Dcp and Dr are the diameters of the center pipe and the reactor, respectively, and Db is the outer bed diameter. Table 1. Reactor Dimensions dimensiona

Ls

Lp

Lb

Dcp

Db

Dr

value (mm)

160

1680

2000

130

410

500

a

See Figure 4.

Table 2. Boundary Conditions Used in the Present Simulations boundary condition

inlet flow rate (m3/h)

bed porosity

center pipe porosity

annular channel porosity

value

200

0.3

0.012

0.3

of the fixed bed. The coordinates where these cuts are taken are shown in Figure 5. Figure 5 shows the values of x and z at which cuts are taken and are frequently referred to while discussing the results in this and the next few sections. The model is kept isothermal at a temperature of 300 K. The feed material is air, and the diameter of the particles is 1.8 mm. Figure 6 shows the velocity profile in the annular channel and the center pipe. The feed gas with a velocity of 0.86 m/s enters the annular channel from the top. The velocity remains the same until the top of the perforated wall. As the gas flows down the annular channel, it loses mass through the perforated wall and, therefore, the velocity decreases along the annular channel. This annular velocity reaches zero at the bottom seal section. Due to the radial pressure driving force, the gas travels from the annular channel radially through the catalyst bed. The bed circumferential area open to the flow is much larger than the cross-sectional area of the annular channel. Consequently, the velocity in the bed is much lower than that in the annular channel and the center pipe, as shown in Figure 7. Due to the reduction in the circumferential flow area, the velocity increases toward the center pipe. The highest velocity in the catalyst bed is at the center pipe perforated wall. This high velocity is a concern when operating a moving bed reactor, since it may pin some of the catalyst against the center pipe perforated wall. The gas stream is collected in the center pipe along the bed length. The center pipe velocity increases axially as shown in Figure 6. Figures 6 and 7 show typical flow profiles for an

Figure 6. Velocity variation along the axial direction in the annular channel and the center pipe.

RFBR. However, before a detailed analysis is carried out, the numerical model will be tested to establish that the results are independent of the grid interval size. Effects of the Mesh Size. Using a small mesh size is likely to lead to a more accurate solution. However, using a small mesh size is limited by the computational power, memory and, consequently, the time required to reach a converged solution. On the other hand, using a large mesh size may lead to an incorrect solution. To optimize the availability of computational resources and ensure that the solution is independent of the mesh size, grid independency tests were performed. This was done by starting with a large mesh size and then decreasing the mesh size until there is no significant variation in the results. Different mesh sizes may be used, but in this study, all three zones (the annular channel, the bed, and the center pipe) were meshed using the same grid size. The annular channel has the smallest width, and therefore, it controls the mesh size. The widths of the annular channel, bed section, and center pipe channel are 45, 140, and 130 mm, respectively. To establish that the solution is independent of the grid size, five mesh sizes of 25, 22, 20, 18, and 15 mm were used. The corresponding


Figure 7. Velocity profile along the reactor diameter, at the center of the bed where z ) 1.

Figure 8. Velocity profile along the reactor diameter, at the center of the bed where z ) 1, for five different mesh sizes.

Figure 9. Annular channel velocity profile along the bed length for five different mesh sizes.

total numbers of mesh cells were 167 480, 295 723, 359 206, 535 573, and 825 846 cells, respectively. Since each section of the RFBR has a different flow profile, a thorough grid independency analysis was done. Figure 8 shows that all mesh sizes give the same velocity profile across the reactor’s radial direction. There is no significant difference in the results especially inside the catalyst bed since it has the largest gap and lowest velocity. However, Figure 9 shows that using mesh sizes of 25, 22, or 20 mm leads to an unstable velocity profile in the annular channel since it has the lowest gap. The velocity profiles in the center pipe along the bed length for different mesh sizes were very close to each other. The

Figure 10. Axial static pressure profile in the annular channel and the center pipe of CP-z and CP-π configurations.

closeness of the profiles was similar to that in Figure 8. From the grid independence test, it was concluded that there is no significant difference in the results of mesh sizes 15 and 18 mm. It was decided to use a mesh size of 18 mm in order to optimize the available computational resources. Flow Distribution in All Four RFBR Configurations. The reactor dimensions and operating conditions used to study the flow distribution are the same as those shown in Tables 1 and 2, except that the center pipe porosity used in the flow distribution analysis is 0.05. At a low center pipe porosity, there will be no significant flow maldistribution in all four configurations. Since a center pipe porosity of 0.012 is the lowest value used in this work and the most difficult one to get a converged solution for, it was used to select the proper mesh size. On the basis of the reactor geometry and the operating conditions, the Re values for the annular channel, the center pipe, and the catalyst bed are 17 000, 37 000, and 15, respectively. Turbulent flow exists in the annular channel and the center pipe, and laminar flow exists in the bed. Therefore, the simulation is done with a turbulent model (k-) limited to where it is needed especially in the annular channel and center pipe. Flow Distribution in CP-z and CP-π Configurations. Figure 10 shows the axial static pressure profile in the annular channel and the center pipe of the CP-z and CP-π configurations. The pressure in the annular channel is almost constant due to the opposite effects of friction and momentum recovery. This indicates that both friction and momentum recovery effects have almost the same magnitude but in opposite directions. In the center pipe (collecting channel), the pressure drop is higher, since both friction and momentum recovery act in the same direction. This high pressure drop affects the flow distribution inside the reactor. In the CP-z configuration, the pressure difference between the annular channel and the center pipe is very high at the bottom of the bed and, consequently, the mass flow will be higher at the bottom, which leads to a poor utilization of the upper part of the bed. In the CP-π configuration, there is a poor utilization of the bottom part of the bed. Figure 11 shows that the highest radial velocity exists at the bottom of the CP-z and at the top of the CP-π configurations. The flow distributions for the CP-z and CP-π configurations are the same as those shown in Figure 2b and c, respectively. To improve the flow distribution, the pressure drop in the center pipe should be lowered, and this can be done by increasing its diameter. This will reduce the velocity inside the pipe and lower the effect of both friction and momentum recovery as can be seen from eq 2.

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Figure 11. Variation of the radial velocity along the bed height for CP-z and CP-π configurations.

Figure 14. Radial velocity variation along the bed height for CF-z and CF-π configurations.

Figure 12. Axial velocity profile along the reactor radial direction for CP-z and CP-π configurations.

Figure 15. Axial velocity profile along the reactor radial direction for the CF-z and CF-π configurations.

Figure 13. Axial static pressure profile in the annular channels and the center pipes of CF-z and CF-π configurations.

Figure 12 shows the distribution of the axial velocity along the reactor radial direction. A symmetrical profile is found. This is due to a uniform inlet distribution. This profile may be impacted by the orientation of the reactor inlet section above the bed. A parabolic profile in the center pipe is caused by the pushing act of the radial forces. There is a negligible axial velocity in the bed section which is a desired condition to eliminate the maldistribution in the radial flow reactor. Flow Distribution in CF-z and CF-π Configurations. Figure 13 shows the axial static pressure in the annular channel and the center pipe for the CF-z and CF-π configurations. In

the CF configurations, the center pipe is the discharge channel and the annular channel is the collecting channel. A significant pressure rise occurs in the center pipe, which indicates that the inertial effect is dominating the frictional effect. The pressure drop in the annular channel is not significant at this flow rate. The difference between the pressure profiles for CF and CP configurations can be explained using eqs 3 and 4. Since the cross-sectional area of the annular channel is larger than that of the center pipe, the velocity in the annulus is much lower than that in the center pipe. Hence, the pressure rise in the annular channel for CP configurations is much lower than the pressure rise in the center pipe for CF configurations. Moreover, the pressure drop in the annular channel for CF configurations is much lower than the pressure drop in the center pipe for CP configurations. This indicates that the momentum recovery is the dominating term in determining the pressure profiles of the annular channel and the center pipe. Figure 13 also shows that the pressure difference between the annular channel and the center pipe is higher at the reactor bottom. Despite that, the annular channel and the center pipe pressure profiles are closer to a parallel profile than that of CP configurations. As a result, the CF-z and CF-π configurations show a small difference in the values of the radial velocity along the bed length, as shown in Figure 14. Figure 15 shows the axial velocity along the reactor radial direction. This profile is opposite to that of a CP configuration. A flat velocity profile in the center pipe is caused by the pulling act of the radial forces. The sharp peak in the annular channel profile is caused by the pushing effect of the radial forces.


Figure 16. Radial pressure drop variation along the perforated section length.

Figure 17. Deviation from uniform flow for the four radial flow configurations.

Uniformity Analysis for the Four Configurations. From the previous results, it was seen that each configuration of a radial flow reactor gives a different flow profile. One observation is that the radial velocities in CF configurations are much closer to each other than those for CP configurations. This difference in the radial velocity profiles is due to the unique radial pressure drop in each configuration. In this analysis, the uniformity criterion suggested by Chang et al.19 is used. In a uniform flow distribution, the pressure drop between the annular channel and the center pipe is the same along the bed height. Figure 16 shows the radial pressure drop along the bed height for the four configurations. Figure 16 also shows that the CP-z and CP-π configurations have a higher reactor pressure drop than the CF-z and CF-π configurations. This indicates that a flow maldistribution contributes to the reactor pressure drop. A flow maldistribution produces a high radial velocity in some parts of the bed and, hence, a high radial pressure drop. In all four configurations, the radial pressure drop profile shows dependency on the axial position, which is a deviation from uniformity. To have one basis for comparing the four configurations, the radial pressure drop profile of each configuration was normalized by dividing it by the maximum radial pressure drop. Figure 17 shows the deviation of each configuration from uniform flow. The normalized radial pressure drop for uniform flow is equal to 1.0 at any axial position. From this figure, it seems that the CF-π configuration is the best configuration which is closest to the uniform line. The second best is the CF-z configuration. The CP-z and CP-π configurations show almost the same deviation from uniformity. They have the least flow uniformity.

Validation of the Numerical Model. The CFD model is validated against two sets of published data. A quantitative validation is carried out against Heggs et al.,11 and a further quantitative validation is carried out against the data of Song et al.9 Following the validation of the model, the effects of a number of factors including the ratio of the cross-sectional areas of the annular channel and the center pipe are investigated. Validation against the Data of Heggs et al.11 A CFD model is constructed to simulate the radial flow multilayered air filter used by Heggs et al.11 A schematic diagram of the model of Heggs et al.11 is shown in Figure 18. It is a CF-z configuration. The present CFD model is used to simulate an RFBR identical to that used by Heggs et al.11 with the same flow and boundary conditions. Three flow rates of 85, 152, and 255 m3/h are used. Table 3 shows a comparison of the experimental and numerical results of Heggs et al.11 and the present CFD simulation results. Heggs et al.11 also compared their measurements with predictions of the pressure profiles in the center pipe and the annular channel. The pressure profile of the center pipe was normalized by dividing it by the maximum pressure rise, and the pressure profile of the annular channel was normalized by dividing it by the maximum pressure fall. Figures 19 and 20 show a comparison of the present study normalized pressure profiles of the center pipe and the annular channel, respectively, with those of Heggs et al.11 It can be seen from Table 3 and Figures 19 and 20 that the CFD model shows good agreement with experimental measurements. Furthermore, the CFD results are closer to the experimental results than the numerical predictions of Heggs et al.11 This is because Heggs et al.11 did not include the small inlet pipe above the center pipe which is shown in Figure 18. The inlet pipe above the center pipe has a smaller cross-sectional area which causes the flow to enter the center pipe as a high velocity jet. This causes a sharp pressure rise at the top section of the center pipe since a high velocity is maintained there and there is almost no flow reduction in the radial direction. Heggs et al.11 also mentioned that there are other flow obstructions at the inlet of the center pipe. There are no details about these obstructions. Implementing those details is likely to bring the CFD results even closer to the experimental measurements. Despite that, the model gives good prediction for such a complex flow in a multilayered radial flow filter. Another advantage of the current CFD model is that it can include any external piping that may affect the flow profile in the radial flow reactor. Validation against the Data of Song et al.9 The RFBR CFD model was also validated against experimental results of an RFMBR. Song et al.9 experimentally investigated the flow distribution in an RFMBR. All four configurations of the radial flow reactor were investigated. The experimental equipment of Song et al.9 was modeled without the sections above and below the particle bed. Figure 4 shows the model used to validate the present simulation model against the results of Song et al.9 The model dimensions are the same as those shown in Table 4. The flow and boundary conditions for this model are same as those shown in Table 2. To determine the flow distribution in the reactor, Song et al.9 calculated the maximum axial nonuniformity which is represented by

non-uniformity ) 1 -

x

Radial∆Pentrance Radial∆Pclosedend

(12)

where ∆Pentrance is the pressure difference between the annular channel and the center pipe at the entrance of the reactor and

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Figure 18. Schematic diagram of the multilayered radial flow air filter used by Heggs et al.11 Table 3. Comparison of the Pressure Measurements and Predictions at Different Flow Rates of Heggs et al.11 with the Current CFD Results flow rate (m3/h) 85 152 255

measurement and prediction

pressure rise in center pipe (Pa)

pressure fall in annular channel (Pa)

total pressure drop (Pa)

Heggs experimental results Heggs numerical results CFD simulation results Heggs experimental results Heggs numerical results CFD simulation results Heggs experim. results Heggs numerical results CFD simulation results

5.1 2.0 5.3 16.0 6.4 16.6 41.3 17.9 45.8

48.1 16.5 31.9 142.9 53.7 97.6 349.2 146.0 266.8

362.5 380.7 345 748 748.6 710 1400 1315 1428

∆Pclosed end is the pressure difference at the closed end of the bed. From Table 5, the CFD model shows that the CF-π configuration has the most uniform flow distribution, which qualitatively agrees with the experimental findings of Song et al.9 However, the values of the nonuniformities are much less than those determined by Song et al.9 One reason for that difference may be the value of C2 for the perforated plate. Since eq 11 was determined from the equation of the flow through square-edged holes on an equilateral triangular spacing, using it with different holes shapes and spacings may lead to the wrong prediction of the perforated plate flow resistance. It seems from the CFD model results that the center pipe and the annular channel perforated plates have a higher resistance which leads to lower nonuniformities. By decreasing the resistance of the

center pipe and the annular channel perforated plates, the CFD model results were significantly closer to the experimental results of Song et al.,9 as shown in Table 6. The predictions can be further improved by knowing more fine details about the reactor internals, such as the perforated plate resistance. For square-edged holes on an equilateral triangular spacing, eq 11 gives good prediction of the perforated plate resistance, as shown in the validation against Heggs et al.11 For other types of holes, the perforated plate resistance is usually given by the manufacturer or can be correlated from experimental results. Following the validation of the CFD model, the effects of the porosity of the center pipe, annular channel, and bed are investigated. The effects of partially blocking the center pipe


Figure 19. Profile of normalized pressure in the center pipe. Figure 21. Effects of the center pipe porosity on the flow distribution in a radial flow reactor.

Figure 20. Profile of normalized pressure in the annular channel. Table 4. Dimensions of the Reactor Used by Song et al.9 dimension

Ls

Lp

Lb

Dcp

Db

Dr

value (mm)

320

1680

2000

130

410

500

Table 5. Comparison of the Nonuniformities Obtained in the Present CFD Study with Those of Song et al.9 |nonuniformity| radial flow configuration

Song et al.9

CFD model

CP-z CP-π CF-π CF-z

0.2 0.2 0.04 0.08

0.032 0.028 0.011 0.015

Table 6. Comparison of the Nonuniformities Obtained by Song et al.14 with Those Found Using the CFD Model after Decreasing the Resistance of the Center Pipe and the Annular Channel Perforated Plates |nonuniformity| radial flow configuration

Song et al.9

CFD model


0.2 0.2 0.04 0.08

0.12 0.11 0.044 0.06

top section are also investigated. The dimensions and the boundary conditions shown in Tables 1 and 2 are used in the following sections. Effects of the Center Pipe Porosity. Figure 21 shows the effect of the center pipe porosity on the flow distribution in a radial flow reactor. As the center pipe porosity decreases, the uniformity of the flow distribution increases. It is also observed that the results of a CF-π configuration with a porosity of 0.05 are closer to the uniform line than those of a CP-π configuration with a porosity of 0.012. Therefore, it is not appropriate to select a CP-π configuration for this model. A reduction of the center pipe porosity in order to obtain a uniform flow distribution

produces a high pressure drop in the reactor. Hence, it increases the operating cost of the reactor. Effects of a Low Center Pipe and a High Annular Channel Porosity. In a radial flow reactor, the center pipe porosity is usually low since it controls the uniform distribution of the gas. Figure 22 shows that setting the center pipe porosity higher than the porosity of the annular channel perforated plate increases the deviation of the flow distribution from a uniform flow distribution. When the center pipe porosity is 0.012 and the annular perforated plate porosity is 0.3, the flow is close to a uniform distribution. Using a higher porosity of the center pipe causes more flow maldistribution. However, the advantage of this change is that it reduces the reactor pressure drop, as shown in Figure 23. Since the radial velocity at the bed outer diameter is lower than that at the bed inner diameter, using a high resistance at the bed outer diameter will produce a lower radial pressure drop. If the radial flow reactor is used in a process that is not highly impacted by a minor nonuniform flow distribution, such as a solid particle drying process, using the high flow resistance at the bed outer diameter may be an economical choice. Effects of the Bed Porosity. Figure 24 shows the effect of the bed porosity on the flow distribution. Low bed porosity improves the flow distribution. Therefore, a proper catalyst loading that maintains tight packing of the catalyst should be used to eliminate the flow maldistribution. Effects of the Ratio of the Center Pipe to the Annular Channel Cross-Sectional Area. The effects of the ratio of the cross-sectional areas of the center pipe and the annular channel were investigated theoretically and experimentally for the CF-π configuration by Genkin et al.5 It was found that increasing this ratio will improve the flow distribution in a CF-π configuration. Chang and Calo7 found that, at a ratio of one, π-flow configurations will have the most uniform flow distribution. Mu et al.13 found that there is an optimum ratio at which the CP-π configuration has the most uniform flow distribution. The effects of this ratio on all four radial flow configurations are investigated in the present work. Figure 17 and Table 7 show that a CF-π configuration has the best flow distribution at a ratio of 0.21 (less than one). When this ratio is increased to one, a more uniform flow distribution was achieved by all configurations. Increasing the ratio was achieved by increasing the center pipe cross-sectional area. The annular channel and bed cross-sectional areas and the reactor height were kept the same as those in Table 1. At a ratio of one, π-flow configurations have the most uniform flow distribution, as shown in Table 7. At a ratio of 1.8 (greater than one), a CP-π configuration has the best flow distribution.

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Figure 22. Effects of setting the center pipe porosity lower than the porosity of the annular channel perforated plate on the flow distribution. Table 7. Nonuniformities at Different Ratios of Cross-Sectional Areas nonuniformity

Figure 23. Effects of setting the center pipe porosity lower than the porosity of the annular channel perforated plate on the reactor radial pressure profile.

Figure 24. Effects of the bed porosity on the flow distribution in radial flow reactor.

It seems that both or one of the π-flow configurations will always have the most uniform flow distribution. The sign of the nonuniformity values for the CF-π and the CP-π configurations changes as the ratio increases. This change of the sign of the nonuniformity indicates that an optimum value is passed. The optimum ratio for a CF-π configuration is between 0.21 and 1, and that for CP-π is between 1 and 1.8. A high ratio produces a low reactor pressure drop and, hence, a low reactor operating cost. Therefore, the CP-π configuration is the superior configuration for the radial flow reactor.

radial flow configuration

ratio (0.21) < 1

ratio ) 1

ratio (1.8) > 1


0.084 -0.089 0.036 0.044

0.013 -0.006 -0.006 0.014

0.010 0.001 -0.013 0.017

Increasing the ratio of the cross-sectional areas improves the flow distribution and at the same time reduces the reactor pressure drop. However, improving the flow distribution by the center pipe porosity produces a higher reactor pressure drop. Therefore, in designing a radial flow reactor, it is preferred to first find the optimum ratio that produces the most uniform flow and to then manipulate the center pipe porosity to improve the uniformity. Effects of Partially Blocking the Center Pipe Top Part. The previous parametric studies are applicable to both RFBRs and RFMBRs. A partial blockage of the center pipe perforated wall mainly occurs in an RFMBR. In an RFMBR, the process catalyst is circulated between the reactor system and the regeneration system. Catalyst dust and chips are produced by this circulation. If the catalyst dust and chips reach the reactor system, they can plug the reactor perforated holes. In a CP-π configuration, since the flow is toward the center pipe, it usually suffers from blockage. The CFD model was used to simulate the blockage of the top part of the center pipe. Figures 25-27 show the radial velocity profiles for a CP-π configuration under different conditions of the center pipe. With a clean center pipe, the radial velocity shows some deviation along the bed height. More flow is coming through the top part of the bed. The maximum radial velocity is 0.22 m/s. At low blockage of the top part of the center pipe, the deviation between the radial velocity profiles is increased. The maximum radial velocity increases to more than 0.23 m/s. At severe blockage of top part of the center pipe, less flow comes through the top part of the bed and the maximum radial velocity increases to 0.26 m/s. Therefore, blockage of the center pipe increases the deviation from uniform flow and, in addition to that, the increase in the maximum radial velocity may initiate pinning phenomena.


Figure 25. CP-π radial velocity profiles at a clean center pipe.

Figure 26. CP-π radial velocity profiles at low blockage of the top part of the center pipe.

Figure 27. CP-π radial velocity profiles at severe blockage of the top section of the center pipe.

Designing a reactor with uniform flow distribution can be achieved by adjusting the reactor dimensions and center pipe porosity. In the RFBR, the clean condition for the perforated plates may not be impacted during operation. However, in the RFMBR, it may be impacted by the operation due to catalyst circulation. To keep the perforated plates in the RFMBR as clean as possible, a dust removal system can be installed before the reactor system. Conclusions Flow in an RFBR is simulated using computational fluid dynamics. All four RFBR flow configurations, namely, CP-z, CP-π, CF-z, and CF-π, were investigated. When the ratio of the center pipe cross-sectional area to the annular channel cross-

sectional area is less than one, the CF-π configuration was found to have the lowest flow maldistribution. A reactor with uniform flow has a lower pressure drop than a reactor with flow maldistribution. The numerical model was quantitatively validated against the published results of Heggs et al.,11 and the CFD simulation results were in good agreement with the experimental results. The simulation results were also in qualitative agreement with the experimental results of an RFMBR carried out by Song et al.9 The flow uniformity can be enhanced by lowering the center pipe porosity and the bed porosity. However, this will increase the operating cost due to a high reactor pressure drop. Making the center pipe porosity higher than that of the annular perforated plate increases the flow maldistribution. However, an advantage of this is the achievement of a low reactor pressure drop. The ratio of the center pipe cross-sectional area to the annular channel cross-sectional area has a major impact on the reactor uniformity. At a ratio less than one, CF-flow configurations show the best flow distribution and the CF-π configuration produces the most uniform flow distribution. At a ratio of one, both π-flow configurations produce the most uniform flow distribution. At a ratio larger than one, CP-flow configurations show the best flow distribution and the CP-π configuration produces the most uniform flow distribution. It was shown that one of the π-flow types always has the most uniform flow distribution. From an energy saving point of view, the CP-π configuration is the best configuration for a radial flow reactor since it can have uniform flow distribution at a low reactor pressure drop. In the design stage, the optimum ratio should be found first and then the center pipe porosity can be used to improve the flow uniformity. For a reactor that is in operation, simple solutions to improve the uniformity include a reduction in the center pipe porosity and maintaining a tight packing of the catalyst. If changing the ratio is applicable from a mechanical point view, then the impact on the catalyst bed volume will be a bottleneck for such a change. Changing the catalyst activity may be a solution for this bottleneck. If the change in the ratio reduces the bed volume, then using a high catalyst activity can compensate for the volume reduction. On the other hand, using a low catalyst activity can compensate for the increase in the bed volume. The CFD model shed significant light on the operation of an RFMBR. Center pipe blockage in an RFMBR increases the flow maldistribution, and it can contribute to pinning phenomena. Installing a dust removal system before the reactor system will minimize the blockage rate of the center pipe and the annular perforated plate in the CP and CF configurations, respectively. Acknowledgment The authors would like to acknowledge the support of KFUPM and Saudi ARAMCO during the course of this work and the preparation of this paper. Literature Cited (1) Little, D. M. Catalytic Reforming; PennWell: Tulsa, OK, 1985. (2) Hlavacek, V.; Kubicek, M. Modeling of Chemical Reactors-XXV: Cylindrical and Spherical Reactor with Radial Flow. Chem. Eng. Sci. 1972, 27, 177. (3) Calo, J. M. Cell Model Studies of Radial Flow, Fixed Bed Reactors. ACS Symp. Ser. 1978, 65, 550. (4) Balakotaiah, V.; Luss, D. Effect of Flow Direction on Conversion in Isothermal Radial Flow-Bed Reactors. AIChE J. 1981, 27, 442.

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(5) Genkin, V. S.; Dil’man, V. V.; Sergeev, S. P. The Distribution of a Gas Stream over a Radial Contact Apparatus. Int. Chem. Eng. 1973, 13, 24. (6) Ponzi, P. R.; Kaye, L. A. Effects of Flow Maldistribution on Conversion and Selectivity in Radial Flow Fixed-Bed Reactors. AIChE J. 1979, 25, 100. (7) Chang, H. C.; Calo, J. M. An Analysis of Radial Flow Packed Bed ReactorssHow Are They Different. ACS Symp. Ser. 1981, 168, 305. (8) Lobanov, E. L.; Skipin, Y. A. Increasing the Operating Efficiency of Radial Reactors in Reforming. Chem. Technol. Fuels Oil 1986, 22, 275. (9) Song, X.; Wang, Z.; Jin, Y.; Gong, M. Investigations on Hydrodynamics of Radial Flow Moving Bed Reactors. Chem. Eng. Technol. 1993, 16, 383. (10) Heggs, P. J.; Ellis, D. I.; Ismail, M. S. The Modeling of FluidFlow Distributions in annular Packed Beds. Gas Sep. Purif. 1994, 8, 257. (11) Heggs, P. J.; Ellis, D. I.; Ismail, M. S. Prediction of Flow Distributions and Pressure Changes in Multi-Layered Annular Packed Beds. Gas Sep. Purif. 1995, 9, 243. (12) Bolton, G. T.; Hooper, C. W.; Mann, R.; Stitt, E. H. Flow Distribution and Velocity Measurement in a Radial Flow Fixed Bed Reactor Using Electrical Resistance Tomography. Chem. Eng. Sci. 2004, 59, 1989. (13) Mu, Z.; Wang, J.; Wang, T.; Jin, Y. Optimum Design of Radial Flow Moving-Bed Reactors Based on a Mathematical Hydrodynamic Model. Chem. Eng. Process. 1952, 42, 409.

(14) Song, X.; Jin, Y.; Yu, Z. Influence of Outward Radial Gas Flow on Particle Movement in an Annular Moving Bed. Powder Technol. 1994, 79, 247. (15) Ginestra, J. C.; Jackson, R. Pinning of a Bed of Particles in a Vertical Channel by a Cross Flow of Gas. Ind. Eng. Fundam. 1985, 24, 121. (16) Doyle, F. J.; Jackson, R.; Ginestra, J. C. The Phenomenon of Pinning in an Annular Moving Bed Reactor with Cross-flow of Gas. Chem. Eng. Sci. 1986, 41, 1485. (17) Pilcher, K. A.; Bridgwater, J. Pinning in a Rectangular Bed Reactor with Gas Cross-Flow. Chem. Eng. Sci. 1990, 45, 2535. (18) Suter, D.; Bartroli, A.; Schneider, F.; Rippin, D. W. T.; Newson, E. J. Radial Flow Reactor Optimization for Highly Exothermic Selective Oxidation Reactions. Chem. Eng. Sci. 1990, 45, 2169. (19) Chang, H. C.; Saucier, M.; Calo, J. M. Design Criterion for Radial Flow Fixed-Bed Reactors. AIChE J. 1983, 29, 1039. (20) Perry, R. H.; Green, D. Chemical Engineer’s Handbook, 7th ed.; McGraw-Hill: New York, USA. 1997; Section 6. (21) Ergun, S. Fluid Flow through Packed Columns. Chem. Eng. Prog. 1952, 48, 89. (22) FLUENT 6.1 Manual; Fluent Inc.: Lebanon, NH, 1998.

ReceiVed for reView January 10, 2005 ReVised manuscript receiVed February 13, 2006 Accepted February 27, 2006 IE050027X

Simulation of Flow Distribution in Radial Flow Reactors - Industrial

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