Liquid mean residence time (MRT) in rotating packed bed (RPB) by empirical correlation and residence time distribution (RTD) method using computational fluid dynamics (CFD) simulation

. Rotating packed bed (RPB) belongs to a HIGee technology, a process intensification device that can provide better mass transfer rate due to the generation of hyper-gravity under the influence of centrifugal force. While determining the efficiency of the RPB, the MRT of the liquid plays a vital role. The MRT of the RPB is very small and can be tuned in accordance with the mass transfer rate of the solvent to achieve the required outlet concentration of the absorbed gas. There exist two methods, i.e., empirical correlation and the residence time distribution (RTD) method. The applicability of both methods still needs to be investigated for better prediction of MRT in RPB. The current study compares the MRT of the two of the most widely employed techniques, i.e., MRT by empirical correlation and the RTD approach using the Computational Fluid Dynamics (CFD). The difference between the MRT by both methods lies between 30-38%. The results show that the RTD better predicts the MRT in the RPB as compared to the Burns empirical correlation. (cid:883)(cid:484)(cid:3)(cid:3)


Introduction
Rotating packed bed (RPB) is an advanced process intensification device that has paved its way into various chemical industries such as distillation [1], nanoparticle synthesis [2] and gas purification [3] [4]. The centrifugal force, which tends to cause the rotational motion in the RPB, enhances the mass transfer efficiency up to 1-2 orders of magnitude due to intensified mixing at the gas-liquid interface as compared to the packed bed reactor [5]. The energy demand has increased dramatically in the last two decades due to industrialization advancements [6]. To fulfil those energy requirements, fossil fuel incineration is being used to serve this purpose [7]. However, the emission of CO2 as a result of this incineration affects the global carbon cycle and is, therefore, considered one of the major causes of global warming [8]. Various remedial actions have been proposed to cope with this concern by adopting different techniques such as adsorption [9], membrane separation [10], absorption [11] and cryogenics [12]. Among all the proposed techniques, absorption is one of the most reliable, economical, effective and mature carboncapturing techniques [13].
In order to utilize the potential of RPB for CO2 absorption, the mean residence time (MRT) in the RPB is crucial. The MRT of the solvent in the RPB is very small and therefore, it must be synchronized with the mass transfer rate in the RPB [14]. Thus, an accurate prediction of the MRT is one of the critical factors while designing the RPB and optimizing the operational parameters for CO2 absorption. The MRT of the solvent can be calculated by using experimental methods using sensors or engineering devices. However, the experimental approach is expensive and the placement of sensors and the engineering devices in the RPB is challenging due to the complex packing structure of the RPB [15]. Computational Fluid Dynamics (CFD) is an advanced computational tool to study the hydrodynamics of the RPB. To accurately predict the hydrodynamics of the RPB, selecting the appropriate turbulence model is essential. Among various turbulence models, the SST k-omega turbulence model is the most effective model as compared to the other two-equation turbulence models [16]. To the best of our knowledge, no data exists in the scientific literature that compares the MRT by empirical correlation and RTD method using the CFD technique.
The current investigation aims to compare the MRT of the solvents, i.e., MEA and KPZ in the RPB by employing the Burns empirical correlation and the RTD method using the CFD. The flow of the liquid in the RPB was solved by employing the Reference Frame Model (RFM). The MRT was determined by for two different solvents, i.e., Monoethanolamine (MEA) and Piperazine (7.5% by weight of K2CO3) promoted potassium carbonate (KPZ) having different solution properties such as dynamic viscosity, density and surface tension.

Geometric model
The MRT study was performed using the RPB used in Yang et al. [17] experiments. Due to the unavailability of the packing details, i.e., packing type and structure, the generation of the exact same packing was practically not possible. The 2D geometric model was built by considering only the coaxial wires in the packing. The dimensional parameters of the 2D geometry are tabulated in Table 1.

Boundary conditions
The relative movement of the inlet with respect to the packing was controlled using the in-house developed User Defined Function (UDF) and the width of the inlet nozzle was set to 1mm. There were total of 10 pressure outlets and the width of each pressure outlet was 3mm. Each simulation was performed with no-slip boundary condition for the packing walls. The RPB was initialized and patched with the solvent's volume fraction of 0 to ensure that there was only CO2 in the RPB before the solvent was injected. The details of the boundary conditions are presented in Table 2.

Solution procedure
All the simulation studies were performed as the transient simulation using Ansys Fluent (2020R1). The pressure-velocity coupling was solved by the PISO algorithm. The volume fraction was computed by the Geo-Reconstruct discritization method. The CFD simulations were run for 5 × 10 4 time steps with a time step size of 1 × 10 −5 . A maximum of 30 iterations per time step were performed to ensure the solution convergence.

Computational Grid
Computational grid number is very important and can affect the simulated results' accuracy. The effect of the boundary layers on the liquid flow was encountered by creating a dense mesh around the packing surface. Using the Ansys meshing software, different mesh numbers ranging from 0.12-0.94M were generated in the computational domain. The liquid holdup at different mesh sizes was calculated and compared, as shown in Figure 1. As the Figure 1 portrays that, the liquid holdup increases up to 28% when the mesh number increased from 0.12M to 0.42M. However, no significant change in the liquid holdup can be observed when the cell count for computational grid was further increased from 0.42M cells which reveals that 0.42M cells are fine enough to predict the liquid holdup in the RPB.

Model validation
The model validation of the 2D CFD model was done using water as the secondary phase and air as the primary phase. The liquid holdup at three different rotational speeds, i.e., 500, 1000 and 1500 RPMs at 1.53 m/s solvent inlet velocity and 30° liquid-packing contact angle were calculated. The simulated results were compared with the experimental data of Yang et al. [17] and the empirical correlation proposed by Burns et al. [18], which can be expressed as follow.  (2) Where, is the liquid holdup, and are the area of the liquid in the RPB and the total area of the RPB, respectively, is the inlet velocity of solvent, i.e., MEA and KPZ, (mm) is the width of the injection nozzle, and are the inner and outer radius of the packing, respectively.

Residence Time Distribution (RTD).
Once the pseudo-steady state was achieved, the tracer having the same solution properties as of the solvent was injected into the RPB for a very short interval of time, i.e., 0.001s by changing the volume fraction of the tracer at the inlet to unity. After 0.001s, the volume fraction of the tracer was reset to 0 and the solvent was reinjected immediately and the concentration of the tracer at the outlet was monitored until the complete tracer came out of the RPB. The MRT was calculated using the following formula [19] Where, is the dimensionless concentration of the solvent, i.e., MEA and KPZ and is the flow time.

Model Validation
As can be seen in Figure 2, the simulated results show a better prediction of the liquid holdup as compared to the Burn empirical correlation. This is because the Burns empirical correlation was developed using the conductivity measurements and therefore, the droplets which reside freely within the vicinity of the packing were ignored during the correlation development. Moreover, the error in the CFD simulated results is because the liquid droplets entrapped at the junction point of coaxial and concentric wires are not considered in the 2D model of the geometry.

Liquid Mean Residence Time (MRT)
The RTD plot of both MEA and KPZ are shown in Figure 3 and the results of MRT by the empirical correlation and RTD are presented in Figure 3: Residence Time Distribution (RTD) plot of MEA and KPZ Table 3. As can be seen in Figure 3: Residence Time Distribution (RTD) plot of MEA and KPZ Table 3 the MRT of MEA is less than the KPZ. This low MRT value of MEA is due to the relatively low frictional forces between MEA molecules which increases the deformation rate compared to the KPZ when the RPB packing exerts the shear force. It can also be observed that with the decrease in the solvent concentration, the MRT of both MEA and KPZ decreases. This reduction in the MRT is also associated with the low viscosity values as compared to the high concentrations. While at low ° the surface of the packing become hydrophilic and the wettability of the packing decreases which also reduces the adhesion of solvents with the packing and thus shows a low MRT.     Table 3 that the low MRT values by the empirical correlation are due to the employment of the 2D geometry of RPB for the CFD simulations which do not consider the concentric wires in the packing structure and therefore, the liquid entrapped between the intersection of axial and concentric wires cannot be predicted using the 2D geometry. Another reason which might be the cause of this difference is the assumptions that Burns et al. [18] made during the correlation development.

Conclusion
The comparison of liquid MRT by empirical correlation and the Residence Time Distribution (RTD) method has been performed using the Computational Fluid Dynamics (CFD) simulation. Both MTREC and MTRRTD follow the same trend under the same operational conditions. However, the Burns correlation for the MTREC is based on assumptions that limit its prediction accuracy for the MRT. The results reveal that the MTRRTD by RTD method using CFD simulation can predict the MRT of the RPB more accurately than the empirical correlation. However, the RTD method requires more computational time as compared to the Burns correlation. The outcomes of this research can be applied to the industrial RPB using the 3D CFD model for tuning mean residence time (MRT) in accordance with the mass transfer rate of the solvent.