## June 2017

## Special Focus: Process/Plant Optimization

# CFD study of mixing performance of redistribution systems for packed columns

The maldistribution of liquid flow within long packed beds is a well-known phenomenon in distillation and absorption columns. In a packed column, the maldistribution of liquid results in differences in liquid concentration across the column.

The maldistribution of liquid flow within long packed beds is a well-known phenomenon in distillation and absorption columns. In a packed column, the maldistribution of liquid results in differences in liquid concentration across the column. Therefore, a liquid redistribution system used within a long packed bed must serve two primary functions: the equalization of liquid flow, and the equalization of liquid concentration. **FIG. 1** shows a standard redistribution system, which consists of a packing support, a liquid collector and a liquid distributor. In addition, a downpipe with a ring channel, or sometimes a dedicated mixing drum, is used between the collector and the liquid distributor to ensure that any concentration difference of collected liquid is fully eliminated.

Within the cryogenic air separation unit (ASU), the crude argon (CAR) column contains up to 190 theoretical stages to reduce oxygen (O_{2}) concentrations to ppm levels at the top of the column. Due to safety regulations, the column is usually split into two parts to reduce its height. Industry experience dictates that a redistributor should be added to eliminate liquid maldistribution that has developed along the packing bed if a packing bed is too long (e.g., > 5 m), or if the number of theoretical stages (NTS) of a bed is too large (e.g., more than 20 NTS). For a CAR column, redistribution systems alone may reach 15 m in column height.

The ASU industry has been searching for a short redistribution system to reduce column height and subsequent investment costs. In the past decade, a short system has been developed—this solution (**FIG. 2A**) is principally a pan-type liquid distributor. The rectangular caps of vapor risers are reinforced mechanically to serve as a support to the packing bed above, and the collector and downpipe found in a standard system are removed to save system height. As such, liquid from the bed above rains down directly to the pan distributor. Since the distributor remains in this solution, equalization of liquid flow is not a concern. However, the forced mixing of liquid is eliminated with the removed collector, downpipe and ring channel. To fulfill market demands, a short redistribution system^{a} was recently developed (**FIG. 2B**).^{1} This three-in-one solution integrates the support, collector and distributor into one piece. During development, efforts were made to maintain and verify the function of liquid mixing.

## Simulation models

The extent to which the lack of liquid mixing within a redistribution system influences column performance depends heavily on the specific application and separation requirements. Experimental quantification of a lack of liquid mixing faces difficulty in commercial columns, as it is challenging to find identical cases where the only difference is the mixing of liquid, while lab tests may not produce relevant results due to limited column height. Alternatively, simulation can shed some light on the matter.

A two-column simulation model^{2} was established in 1982 to evaluate the impact of liquid maldistribution. This model assumed that the column was split into two equal parts and that the feed streams to the two columns were unevenly split, resulting in a deviation of the liquid-to-vapor (L/V) ratio in each column. Consequently, the concentrations of product streams from the two columns were different. Mixing the bottom or top product streams, respectively, resulted in reduced performance. By comparing this model to a single-column simulation, the sensitivity of the reduced column performance-to-liquid maldistribution ratio could be established for a specific separation task. However, this model cannot evaluate a redistribution system with, or without, a mixing function.

Literature^{3} suggests that a derived two-column simulation procedure can be tailored to evaluate mixing impact. In Schultes’ work (**FIG. 3**), each of three long parallel columns were further divided into short columns in series. Deviations of liquid flow were assumed at the top columns, and liquid streams from three parallel columns were removed from the bottom of the upper columns, mixed and returned to the lower columns at the same deviation. Vapor streams were also mixed, but zero deviation of vapor flow was assumed for three parallel columns. That simulation more appropriately represents a redistribution system with mixing function, if the deviation of liquid flow is kept relatively low (to reflect an even flow of liquid achieved by the redistribution system).

Comparatively, simulation of three parallel columns without further division into sub-columns can represent deteriorating concentration differences along long columns, if a redistribution system without liquid mixing function is utilized in reality. **FIG. 4** illustrates the different NTS required for a specific separation task in various scenarios.^{3} If a flow deviation of 5% is assumed, adding three sets of redistribution systems in rectification and stripping sections can reduce the required NTS by more than 30%, which is significant.

To simplify matters and make this study independent of application and separation requirements, evaluations were limited to the uniformity of liquid flow and concentration after the two redistribution systems by artificially generating non-uniformity of flow and concentration above each system. The computational fluid dynamics (CFD) results provide a basis for process engineers to further investigate the eventual influence of mixing on column performance in their particular process.

# METHODOLOGY

## Multiphase flow modeling

Empirical correlations have long been the basis of design and evaluation of liquid distributors in industrial applications. Various formulations with different levels of complexity and accuracy have been developed to assess the discharge velocity of liquid via orifices in a wide range of industrial applications.^{4,5,6,7,8,9} While many of these correlations are successfully applied to traditional designs and standard operating conditions, they often fail to capture the complex flow physics present in nontraditional designs operating under suboptimal loads and regimes. With significant advances in numerical methods and continuous growth in computational resources, multiphase CFD has been increasingly used as an alternative powerful design tool.^{10} Various authors have demonstrated CFD capabilities to predict flow within orifice-type liquid distributors by comparing results with measurements.^{11,12,13}

Heggemann *et al.* reported a systematic comparison of simulation and measurement within a single channel equipped with a predistributor. An agreement between simulation and measurement was reported for all cases, including real representative operational design.^{11} Luehong *et al.* reported multiphase simulations with free surface models for different predistributor designs. The study further reported the impact of inflow rate, location and orientation of the orifices on overall outflow distribution.^{12} Gomes *et al.* applied CFD for the development of a new liquid distributor. A prototype that was constructed and tested experimentally confirmed the general outcome of the CFD result.^{13}

Despite the increased use of CFD for assessment of design in liquid distributors,^{14,15,16,17,18} aspects of flow remain to be studied. Many studies are limited to single orifice in simplified setups, or only solve the liquid phase, neglecting the complex influence of the free surface and the vapor phase on distribution quality. In this study, CFD simulations were used for the first time (to the authors’ knowledge) to assess the mixing of liquid within two real-size liquid distributors, including all orifices. The hydraulic and mixing performance of two designs under uniform and non-uniform inflow was investigated.

## Governing equations

CFD simulations of two redistribution systems were performed under representative operating conditions of a CAR column in an ASU to assess performance in terms of concentration and hydraulic equalization. The simulations were performed assuming a non-homogeneous Eulerian mixture of V/L where the velocity of the vapor phase is neglected. Since resolving liquid stream and droplets downstream of a packed bed is computationally expensive and somewhat impractical, an alternative approach was used in this study. A non-homogeneous, multiphase and free-surface model was applied to resolve the liquid flow falling through the vapor. In this approach, liquid was resolved as dispersed phase within the vapor, accounting for interphase drag. Simultaneously, an interface was tracked between two phases where liquid was collected on the deck. The main part of the computational domain was occupied by one phase only. The general phase averaged continuity and momentum equations in an Eulerian approach for *k* phase.^{19}

(1)

(2)

In Eq. 1 and Eq. 2, subscript *k* is replaced by *c* to account for the continuous phase, and *d* for the disperse phase. The stress-strain tensor includes both laminar and turbulent terms. The tilde denotes phase-averaged variables, while the overbar refers to time-averaged values. The only momentum exchange force considered here is the drag force between the continuous and dispersed phases, and it is defined in Eq. 3 as:

(3)

where *K _{dc}* is a coefficient representing a characteristic density multiplied by an inverse time scale of the disperse phase.

Nearly all definitions of this coefficient include a drag coefficient. The value of 0.44 was used for the drag coefficient in this study. The time-averaged terms represented turbulence dispersion in the momentum equations. Several terms in these equations must be modeled to close the phase-averaged momentum equations. A full description of all modeling assumptions can be found in literature.^{20} Even though the flow field was modeled as an Eulerian mixture, an interface tracking approach was activated once the volume fraction of the dispersed phase exceeded a certain limit.

## Turbulence modeling

To close the Reynolds-averaged Navier–Stokes (RANS) equations, the turbulent shear-strain tensor (STT) was modeled using a two-equation turbulence model. Turbulence was resolved as a homogeneous field using the SST turbulence model and assuming that all phases share the same turbulence field. This is considered a valid simplifying assumption, knowing that the turbulence in vapor phase does not play a significant role in mixing within the liquid phase in the distributor. The SST model is known to improve the prediction of the separation and recirculation zone by taking account for transport of shear stresses.^{21} Eq. 4 and Eq. 5 are the governing equations for turbulent kinetic energy and turbulent eddy frequency:

(4)

(5)

where *P* is the shear production of turbulence, and *F* represents the blending function between *k-ω* and *k-ε* inside and outside of the boundary layer. The value for all constants can be found in literature.^{21} Ultimately, the turbulence eddy viscosity was calculated using Eq. 6:

(6)

where *S* is the invariant measure of the strain rate and *F*’ is the second blending function.

## Computational setup

Simulations were performed using a commercial solver. The computational domains for the pan-type system and the three-in-one system were constructed using in-house tools. The height and diameter were specified for both systems as 0.8 m and 2 m, respectively. To reflect commercial designs, the bottom plate of the system was assumed to be 2 mm thick for the former system, and 1.5 mm thick for the latter system. In addition, the pan type contained 204 orifices with a 6.8-mm diameter, and the three-in-one contained 146 orifices with an 8-mm diameter. **FIG. 5 **depicts the top views of orifice arrangements. To capture the flow through the orifices, an ambient domain was constructed around each orifice, ensuring an accurate assessment of the flowrate through the orifices. The ambient domains for the three-in-one system are illustrated in **FIG. 6.**

A hybrid hex-dominant tet/hex was generated for both systems with local refinements in the orifices. To accurately capture the boundary layer close to the walls, multiple prism layers were generated on the internal no-slip walls. **FIG. 7 **shows the computational grids at different locations of the domains—the size of the grid was 7 MM and 8 MM for the two systems, respectively.

To quantify the redistribution in both systems, in addition to RANS equations, a transport equation was solved for a scalar variable released from two particular locations of the inlet area. The performance of the systems was demonstrated by an air-separation column under representative operating conditions (e.g., 88K operating temperature and 1.2 bar operating pressure). The initial liquid level above the orifices was 0.13 in both systems. The liquid and vapor properties are summarized in **TABLE 1.** The volume flowrate of 30 m^{3} h^{–1} was specified, and the ambient domain was modeled as an opening with a specified averaged pressure.

# RESULTS AND DISCUSSIONS

## Hydraulic equalization

As described herein, non-uniformity in composition or concentration was the direct outcome of non-uniformity of liquid flow within the packed bed. Therefore, prior to the assessment of liquid mixing, both systems were first evaluated in terms of hydraulic equalization.

Steady-state uniform liquid inflow was first released above the systems, and then outflow through each orifice was simulated. A coefficient of variation (COV) of 2.5% among 204 orifices was obtained for the pan-type system, and 2% was derived among 148 orifices for the three-in-one system.

To create non-uniformity, 7% of the inlet area above the two systems released inflow with 10% higher mass flowrate than the rest of the inlet area. Due to the symmetry of the systems, as shown in **FIGs. 8, 9, 10** and **11,** two inlet configurations were selected. The two configurations differed in how close non-uniformity inflow occurred to the shortest vapor riser, or the shortest distributor arm. For both configurations, the simulation results showed less than 0.05% difference in the COV values compared to uniform inflow cases, confirming the satisfactory performance of both systems in terms of hydraulic equalization.

## Concentration equalization

Next, the mixing performance was assessed. As shown in **FIGS. 8, 9, 10** and **11,** a scalar variable released from the highlighted inlet areas represented a liquid concentration of 1; conversely, the concentration of the liquid released from the rest inlet area was set as 0. The flowrate at the highlighted inlet areas remained 10% higher than the rest of the inflow. The results of the simulations are summarized here.

The iso-surface of a concentration between 0 and 1 showed the extent to which the high-concentration fluid can reach all orifices in a system. **FIG. 8** shows an iso-surface with a concentration of 0.05 (red) for the first configuration. In the pan-type system, the influence region of mixing was slightly larger than the footprint of the non-uniformity generated at the inlet. The mixing in this system was largely due to turbulent diffusion rather than convection. In the three-in-one system, however, the high-concentration liquid seemed to reach most of the orifices, except for the region at the far end of the main trough. **TABLE 2** shows the COV of concentration among the orifices in both systems. Based on COV values, the three-in-one system was five times more effective in mixing the high- and low-concentration liquid introduced in Configuration 1. In **FIG. 9,** the contour plot of concentration was drawn at a plane of 0.02 m above the orifices, supporting the same findings.

The second configuration was subsequently investigated and viewed as representing a more difficult mixing task, as high-concentration liquid must travel a greater distance to reach all orifices, compared with Configuration 1. Similarly, **FIG. 10** shows the iso-surface with a concentration of 0.05, and **FIG. 11** shows the contour plot of concentration at a plane of 0.02 m above the orifices. As previously seen, the pan system failed to transport the high-concentration liquid, while the three-in-one system performed much better. **TABLE 3 **summarizes the COV values for Configuration 2. For the three-in-one system, the COV with Configuration 1 is smaller than that of the second configuration, confirming earlier predictions. It is worth mentioning that, for a better visual effect, a liquid concentration above 0.5 is not illustrated in **FIGS. 9** and **11.**

## Key takeaways

Two redistribution systems were assessed using steady-state multiphase simulations of vapor and liquid flow in connection with a transport equation for a scalar variable. The results show that both systems perform well in terms of hydraulic equalization with a COV of flowrate of less than 2.5% under both uniform and non-uniform inflow. In addition, the mixing performance was assessed by releasing the scalar concentration at two different inlet locations (Configurations 1 and 2). Based on computational results for Configuration 1, the COV of concentration at orifices in the three-in-one system was five times smaller than that of the pan-type system. For Configuration 2, mixing of the three-in-one also improved by a factor of 2.5. The study demonstrated that the three-in-one system provided excellent mixing compared to the pan-type system. **HP**

**NOTE**

^{a} Short redistribution system by Sulzer Chemtech.

**NOMENCLATURES**

*F* External body force*g* Gravitational acceleration*k* Turbulent kinetic energy*P* Turbulence production*S* Shear strain rate*t* Time*Ũ* Phase-averaged velocity*α* Phase fraction*ρ* Phase-averaged density*τ* Shear stress tensor*ω* Turbulent eddy frequency*ν* Eddy viscosity*υ _{t}* Turbulent eddy viscosity

COV Coefficient of variation

*Index for species*

_{k}*Disperse phase*

_{d}*Continuous phase*

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