- Email: [email protected]
Tracer dispersion in trickle beds under tilts and roll motions – CFD study and experimental validation
Journal Pre-proofs Tracer Dispersion in Trickle Beds Under Tilts and Roll Motions - CFD Study and Experimental Validation Amir Motamed Dashliborun, Faï çal Larachi PII: DOI: Reference:
S1385-8947(19)32255-7 https://doi.org/10.1016/j.cej.2019.122845 CEJ 122845
To appear in:
Chemical Engineering Journal
Please cite this article as: A.M. Dashliborun, F. Larachi, Tracer Dispersion in Trickle Beds Under Tilts and Roll Motions - CFD Study and Experimental Validation, Chemical Engineering Journal (2019), doi: https://doi.org/ 10.1016/j.cej.2019.122845
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
Tracer Dispersion in Trickle Beds Under Tilts and Roll Motions - CFD Study and Experimental Validation Amir Motamed Dashliborun and Faïçal Larachi* Department of Chemical Engineering, Laval University, Québec, QC, Canada G1V 0A6 *Corresponding author. Tel.: +1 (418) 656-3566, Fax: +1 (418) 656-5993 E-mail address: [email protected] (F. Larachi) Abstract A wire-mesh sensor was used to measure the liquid residence time distribution (RTD) and tracer dispersion in trickle beds subjected to stationary tilts and roll motions. The measured tracer characteristics were confronted to three-dimensional transient Euler-Euler CFD simulations to expose the role of inclined and oscillating porous media. The simulation results satisfactorily reproduced the widening tracer signals with increased bed inclination reflecting in asymmetric RTDs prompted by permanent gravity-driven stratified flow zone through the packing. Similarly, tracer dispersion was predicted to increase for rolling beds by increasing tilt angle and motion period. While an increase of tilt angle shortened RTD breakthrough time due to the faster tracer stream evolving in the liquid-rich lower-most zones, tracer elution tended to slow-down with increasing the rolling period. In addition, it was revealed that with altering the column angular position during roll motions the fluid flow structures inevitably varied inside the packing leading to different mixing behaviors and residence time distributions. Keywords Residence time distribution; tracer dispersion; Eulerian porous media model; experimental validation; CFD simulation; tilt and roll motion
1.
1. Introduction Oil and gas production units on mobile sea platforms such as floating production, storage and offloading (FPSO) commonly employ multiphase fixed beds for onboard treatment and refining of offshore hydrocarbon streams [1,2]. Trickle bed reactor is a particular configuration of the fixed bed where the gas and liquid phases flow co-currently in the direction of gravity over randomly filled solid particles, thereby allowing high flexibility in throughput demands for industrial applications [3,4]. Recent experimental investigations revealed that ship tilts and oscillations stemming from sea conditions could affect the operation and performances of trickle beds onboard offshore floating platforms [5–10]. Hydrodynamic studies using imaging techniques such as electrical capacitance tomography (ECT) and capacitance wire-mesh sensor (WMS) demonstrated remarkable gas-liquid disengagement and significant variations of the fluid flow paths in porous media due to bed tilts and vessel motions [5–7,9–14]. Imaging of the gas-liquid flow showed that permanent tilts of the trickle bed caused accumulation of the liquid phase in the lower-wall zones, whereas roll motions resulted in periodic transverse displacements of fluids across the packing. Beside experimental works, computational fluid dynamic (CFD) simulations helped shape an understanding of trickle bed reactors subjected to ship tilts and oscillations [15–18]. For resolving the local fluid distributions and velocity fields in trickle beds, the Eulerian CFD method in which all phases are treated mathematically as interpenetrating continua has been widely used [19,20]. In this approach, closure equations are often applied for coupling of fluid phases through momentum exchange coefficients [19,21]. Using a transient two-fluid Eulerian CFD model within the porous media approach, numerical simulations were recently carried out to describe the hydrodynamic behavior of trickle beds under ship tilts and roll motions [18]. The model consisted of closure laws 2.
for porous resistances (i.e., fluid-solid interactions) and gas-liquid interaction as well as capillary and mechanical dispersion forces. The simulation results were validated against experimental data of liquid saturation and pressure drop provided by a capacitance wire-mesh sensor and a differential pressure transmitter, respectively. It was realized from the numerical results that incorporation of capillary and mechanical dispersion terms in the CFD model was essential to accurately capture the transient hydrodynamics of trickle beds under moving conditions; otherwise, it caused severe loss of temporal stability and an erratic behavior in the computed liquid saturation and pressure drop. In virtue of the validated CFD model, it was found that an increase of rolling angle and period resulted in a decrease of liquid saturation, bed pressure drop, and uniformity degree of the fluid distribution. A traditional approach for investigation of the hydrodynamics inside trickle bed reactors relies on Residence Time Distribution (RTD) determination whereby measurement or simulation of the dynamic tracer concentration signal at desired locations of the reactor is carried out [22]. This method is a powerful tool for characterization of the fluid maldistribution and the extent of deviations from ideal plug flow in packed-bed reactors. Thanks to new tomography techniques either invasive or non-invasive, the experimental study of phase distribution and RTD tracing in multiphase reactors has been noticeably facilitated [20]. Recent RTD experiments mimicking offshore floating packed beds using wire-mesh sensors (WMS) revealed that the liquid flow became more dispersive during column motions causing liquid maldistribution and more deviations to plug flow behavior of the liquid phase with increasing the tilt angle and motion period [7,13,23]. The tracer tests showed that tracer migration in the lowermost liquid-rich region outpaced the one slowly drifting in the uppermost gas-rich region on account of the gas-liquid disengagement in tilted beds [7]. From spatial- and time-resolved WMS measurements, it was also 3.
realized that column roll motions prompted secondary transverse zigzag motion of tracer across the bed [7]. Such transverse movement of tracer inflated the signal variance. Furthermore, with increasing the roll motion period the signal variance inflated more and tracer elution to be completed was much longer due to increased axial dispersion [7,13,23]. The inflated signal variances suggested drastic departures from liquid plug flow, reflecting lower Péclet numbers. The bed oscillations and their influences on the tracer behavior have been thoroughly discussed in our previous works [7,13,23]. Despite recent progress concerning the modeling and simulation of gas-liquid flow dynamics inside offshore floating packed beds, application of validated CFD-based Eulerian model was limited to track local fluid distributions and prediction of parameters such as bed overall pressure drop and liquid holdup [16–18]. CFD simulation studies on the liquid RTD in stationary tilted and oscillating trickle beds have not been yet addressed, though there are few works on the conventional stationary vertical bed configuration [22,24,25]. Hence, the present study aims at conducting CFD simulations of trickle bed under column stationary tilts and roll motions with specific focus on simulating the liquid residence time distribution of a tracer pulse. For validation of the simulation results, wire-mesh sensors (WMS) were employed to experimentally capture the time evolution of tracer concentration signals in the course of bed tilts and motions. The effect of stationary tilt angles and roll motion parameters (i.e., amplitude and period) on the tracer response was thoroughly investigated. Moreover, a comprehensive analysis was performed with aid of the CFD model to highlight the influence of fluid flow structures on the tracer response curves at different angular positions of the rolling bed.
4.
2. Experimental A schematic diagram of the laboratory-scale setup used for the determination of liquid residence time distributions and validation of the CFD simulations is shown in Figure 1. The Plexiglas column (ID = 57 mm) was filled with 3 mm glass beads up to a height of 1000 mm resulting in an average packing porosity of ca. 0.40. Retaining stainless steel screens were placed at the top and bottom of the packed bed to avert inter-particle movements during column tilts and rolling. The packed column instrumented with a pair of wire-mesh sensors (WMS1 and WMS2) for tracer pulse detection was bound to a NOTUS hexapod ship motion emulator allowing six-degree-offreedom motions (Figure 1). Tracer experiments were performed at room temperature and atmospheric pressure by forcing air and water to flow through the bed in cocurrent downflow. The gas and liquid throughputs corresponded to the trickle flow regime. The desired gas flow rate was adjusted by means of a calibrated flowmeter, while two peristaltic pumps were, respectively, used for the supply of the continuous liquid stream and for tracer injection. Prior to RTD experiments, column operation was kept under pulse flow regime for at least 30 min to ensure complete prewetting of the packing according to the Kan and Greenfield procedure [26]. Since roll motion has been reported in literature as the most influential oscillation on the hydrodynamic performance of multiphase packed beds [6–9,12], in this study roll motions with 5° and 10° amplitudes and periods of 5-40 s, covering typical conditions of ships subjected to marine swells [27,28], were imposed to the trickle bed. It is noteworthy to mention that during the roll motion the bed periodically evolves between the vertical and tilted modes. This type of column tested motion can be observed from the video clip illustrated in our previous works [6,7]. For comparative purposes, the limiting cases of stationary vertical (0°) and stationary tilted (5°-10°) bed configurations were included as well.
5.
Aqueous sodium chloride solutions were briefly injected for 5 s upstream the liquid feeding line and two wire-mesh sensor grids, inserted 100 mm and 600 mm downstream in the bed (Figure 1), registered the evolution due to liquid back-mixing of the travelling tracer pulses. A sampling frequency of 100 Hz was deemed sufficient to track the temporal evolution of tracer pulses in the stationary and rolling trickle bed. Since the setup was operated in a recycle mode for the liquid phase, an electrical conductivity meter monitored liquid conductivity in the feed tank after tracer injection so that signal baseline drifts due to accumulation of the tracer were prevented by regular replacements of the liquid with fresh deionized water. Furthermore, an appropriate filter was used to reduce random noise present in tracer signals to acceptable levels [29]. More information about the configuration, the operating principle and calibration of the wire-mesh sensors, data processing, and application to multiphase flow measurements for RTD studies can be found in our group’s previous studies [7,30–32].
3. Description of CFD model The CFD model used in the present study is based on our previous work [18], where a 3D twofluid Eulerian model was applied in porous media approach to predict the hydrodynamic behavior of a gas-liquid cocurrent downflow trickle bed under column inclinations and roll motions. Notwithstanding that exhaustive numerical investigations on hydrodynamic characteristics of trickle beds in terms of liquid saturation, pressure drop, fluid distribution and velocity in the context of offshore floating applications were carried out in our previous work [18], there is still a lack of numerical research work to address the important problem of tracer dispersion under column tilts and roll motions. Thus, the implemented CFD model is briefly described here. The macroscopic volume-averaged forms of mass and momentum balance equations for each flowing phase are summarized in Table 1. Since momentum balances for flowing fluids are derived from 6.
averaging pore-scale Navier-Stokes equations, the system of equations requires closure laws [33]. Hence, porous resistances (i.e., fluid-solid interactions) and gas-liquid interaction together with fluid dispersion mechanisms were considered in the form of closure laws [18]. The Ergun-like model, containing viscous and inertial contributions, developed by Attou et al. [34] was used to account for porous resistances and gas-liquid interaction (Eqs. 10-14). In order to account momentum dispersion in the porous medium, namely the capillary pressure and the mechanical dispersion, the correlation developed by Attou and Ferschneider [35] was applied to account for the former (Eqs. 15-18), whereas the model developed by Lappalainen et al. [36] and Fourati et al. [37] was considered to describe the latter in both gas and liquid phases (Eqs. 19-22). Since the two-fluid Eulerian method solves a unique averaged pressure field for the gas phase, a capillary pressure model (Eq. 15) is required to consider the pressure jump at the gas–liquid interface due to capillarity [32,36]. Thus, the gradient of this expression (Eq. 18) was added to the momentum conservation equation of the liquid phase as a capillary dispersive force term to account for the capillary pressure in the CFD model [33,36]. For simulation of the age distribution of a scalar quantity in the trickle bed reactor, a User Defined Scalar (UDS) transport equation involving diffusion and convection terms (Eq. 23) has to be solved along with the momentum transport equations. The global diffusion coefficient (Dtr) in porous media results from the sum of molecular diffusion and mainly dispersion due to the porous structure [22]. In this work, the dispersion coefficient defined as a function of the liquid axial velocity (νʹl,ax) and the tracer spreading factor (Str) was applied (Eq. 24), which is an appropriate parameter for taking into account geometrical liquid distribution in packed beds [25,38]. Moreover, the inlet boundary condition was similar to the experimental condition where a pulse of the tracer concentration with 5 s duration is injected at the bed inlet. More details about fluid-solid and gas-liquid interaction forces, the capillary and
7.
mechanical dispersion forces as well as their theoretical justifications can be found elsewhere [34,36,37]. The influence of roll motions in a computational domain is realized commonly through the implementation of moving reference frame (MRF) and sliding mesh techniques. The MRF method modifies the momentum equation to incorporate the additional acceleration/deceleration force terms due to the transformation of the inertial reference frame to the non-inertial frame, whereas the sliding mesh approach retains the momentum equation in the stationary reference but allows all of the boundaries and the cells to move together in a rigid-body motion [39]. For detailed information about the MRF and sliding mesh techniques and their theoretical backgrounds, the reader is directed to ANSYS FLUENT user’s guide (2015) [39]. Our previous CFD simulation work on the trickle bed hydrodynamics under roll motions showed no difference in the simulation results obtained from these two techniques [18]. Therefore, all simulations of the rolling bed were performed using the MRF approach due to its quite low computational burden and CPU time compared to the sliding mesh method. The transformation of fluid velocities from the inertial frame to the non-inertial frame was made using the relative velocities as dependent variables (Eq. 4), whereby four additional acceleration terms appeared in the momentum equations. The Coriolis acceleration (2𝜔 ⃗ ×𝑣ʹq), the centripetal acceleration (𝜔 ⃗ ×(𝜔 ⃗ ×𝑟)), and the accelerations due to unsteady variation of the rotational (d𝜔 ⃗ /dt×𝑟) and translational (d𝑣t/dt) velocities (Eq. 3) appeared in the momentum balance as a result of translational and rotational movements of the non-inertial reference frame relative to the inertial reference frame. Figure 2a illustrates the established computational domain with respect to the moving frame. The pressure-based unsteady state solver in double precision mode within ANSYS® FLUENT 18.1 CFD software was used to solve the set of equations in Table 1. The closure laws and roll motions 8.
of the trickle bed were implemented in the software using user-defined functions. Figure 2b shows the typical meshing used for the 3D computational domain along with representatives of injected inlet tracer pulse and computed outlet tracer pulse. The impact of grid resolution, numerical scheme selection, and boundary conditions on model results was examined according to a methodology similar to the one exposed in our previous studies [17,18]. A mesh number of 12,750 on the domain with the minimum and maximum cell volume of, respectively, ca. 2.015e-07 and 4.83e-07 m3 was found sufficient for all bed configurations to ensure grid-independent solutions with an acceptable computational time. Solution convergence for each time step was assumed as all residuals fell below 10-3 during the maximum iteration number of 100. Since the column-toparticle diameter ratio (D/dp = 19) was large enough, we assumed a uniform porosity distribution across the bed [40,41]. A stable solution obtained under the stationary vertical configuration was considered as an initial condition for simulation of rolling trickle beds. In addition, the momentum equations were first solved using an unsteady approach to achieve a converged-periodic solution for the hydrodynamics. The fluid flow and UDS equation were then solved simultaneously. The area-weighted averaged concentration of the tracer at any desired location was monitored with time to obtain the RTD curves. Further details on applied boundary conditions, assumptions, and numerical simulation procedure can be found in our previous work [18].
4. Results and discussion 4.1. Experimental validation In our group’s previous numerical studies [17,18], the capability of the developed CFD model was assessed through analyzing time series of the bed overall pressure drop and the instantaneous variations of local and cross-sectional averaged liquid saturations across the bed obtained from the simulation results and experimental data. Predictions of the model for the pressure drop and liquid 9.
saturation values as well as wave morphology in the course of column roll motions were in good agreement with the experimental results for all tested conditions. Hence, the CFD model was extended here to simulate mixing and RTD in the trickle bed under column tilts and roll motions. The RTD obtained numerically under different bed configurations was compared against experimental data to evaluate accuracy of the CFD model prediction. Prior to performing the simulations of rolling trickle beds, the RTD was calculated for the stationary bed positioned at different tilt angles. To quickly capture the tracer behavior for the various non-conventional packed bed modalities, an overall picture of tracer dispersion and backmixing of the liquid can be grasped from comparisons of the simulation with the experiment for the vertical column. Furthermore, comprehensive experiments using wire-mesh sensors to investigate the tracer migration over the bed crosswise plane due to fluid flows under ship tilts and roll motions are provided elsewhere [7]. However, for the sake of skipping repetitions, since the experimental results concerning how the tracer is maldistributed and how the tilting and rolling affects packed bed uniformity were already detailed in our previous works [7,18], readers can refer to those specific works. Figure 3a-c reveals good agreement between numerical and experimental values between 0° (vertical) and 10°, despite the slight overestimation of the dispersion at the high tilting angle (10°). The main reason behind this lack of fit for RTD curves at the high tilt angle can be attributed to the correlation of dispersion coefficient (Eq. 24) employed in the UDS equation (Eq. 23). In porous media, the global diffusion coefficient (Dtr) results from the sum of molecular diffusion and mainly dispersion due to the porous structure [22]. It should be indicated that here the applied correlation was originally derived for the vertical packed bed configuration, where it was a function of the tracer spreading factor and liquid axial velocity. Hence, for sake of high level of 10.
accuracy in CFD simulations of tracer dispersion at high tilt angles of the trickle bed, a new correlation for the dispersion coefficient based on operation conditions and geometrical tracer distribution in tilted beds ought to be developed. Meanwhile, the simulation results were reasonably close to experimental RTD measurements for different oscillation amplitudes and periods of the rolling trickle bed for which representative results are illustrated in Figure 4a-c with Θ = 5° and T = 20 s, Θ = 10° and T = 20 s, Θ = 10° and T = 5 s, respectively. Thus, in the following section, the developed CFD model is applied to further examine the influence of different motion parameters on the tracer response. 4.2. Effect of column tilts and roll motions on tracer response The influence of stationary tilt angles and roll motion parameters (i.e., amplitude and period) on the tracer response was examined under identical gas and liquid flow rates (Figure 5). Here, as representative results, tracer concentration curves at two bed heights of H = 5 cm and H = 85 cm are monitored for stationary tilted beds (Figure 5a) as well as for rolling beds with varying amplitudes at a constant motion period (Figure 5b) and with varying oscillation periods at a constant amplitude (Figure 5c). The simulation results are illustrated as time series of scalar concentration (i.e., signal) averaged in the cross section and normalized to the total amount of scalar. A significant impact of column stationary tilts on the liquid dispersion is evident from a widened distribution of tracer age at H = 85 cm (Figure 5a). Furthermore, breakdown of symmetry in the tracer age distribution became more pronounced with incrementing the tilt angle. Bed deviations from the vertical position (0°) prompted gravity-driven stratified flow zones in the porous medium whereby a twofold phenomenon appeared: (1) relatively fast migration of tracer in the lower liquid-rich zone, (2) increase of tracer exit age due to spreading a part of it by the slower liquid 11.
flow in the upper gas-rich zone. The former phenomenon defines the breakthrough time of tracer age distribution, whereas the later one determines the time needed to complete the tracer elution. Therefore, the age distribution of tracer in tilted packed beds highly depends on dominance of these phenomena. From Figure 5a, it can be seen that emergence of severe segregated flow pattern at high tilting angles was reflected in widened asymmetric tracer signals with lower breakthrough times and long tails, thereby a more dispersive behavior for the liquid flow. Tracer responses for the bed submitted to different oscillation angles and periods of the roll motion are shown in Figures 5b and c, respectively. It is perceivable from this set of figures that an increase of rolling angle and period caused more liquid dispersion as reflected in widened tracer signals at the expense of temporary evolving gas-rich and liquid-rich regions. Time-dependent gravitational and inertial forces prompted in the course of hexapod roll motions caused, respectively, liquid accumulations in the lower-wall zones and secondary transverse displacements of the liquid across the bed whereby liquid back-mixing became severe. It is worthy of notice that an increase of the oscillation amplitude resulted in lower breakthrough time for the fastest liquid tracer stream due to redirection of part of the tracer towards the lowermost liquid-rich zones and thus facilitating its passage through the packing (Figures 5b). On the other hand, tracer elution to be completed became longer with increasing the motion period, which was interpreted as resulting from poor mixing in gentler roll motions with decreased inertial forces (Figures 5c). To evidence the role of inertial forces in tracer responses, Figures 6a and b compare the age distribution of tracer for the rolling bed, respectively, subject to 5° and 10° oscillation angles under 20 s and 40 s periods with the corresponding distribution curve for the limiting case of stationary tilted beds. As clearly seen, a permanent tilt (red lines) of the bed worsened liquid dispersion in comparison with those of rolling bed configurations due to exacerbated gravity-driven force and 12.
the absence of inertial force. In fact, column angular excitation induced secondary transverse displacements of the fluid in the radial and circumferential directions, which in turn tended to disperse the accumulated liquid over the bed cross section and provide more uniformity in the crosswise liquid distribution. Nevertheless, with increasing the motion period the tracer response curve became wider prone to approach that of the stationary tilted bed (Figure 6b). This is due to the fact that the gravity-driven stratification tended to outpace the opposing column inertial forces as the motion period was slowed down. This observation underlines an important contribution of the column acceleration/deceleration on diminishing segregated fluid regions. Meanwhile, a marginal influence of the motion period was found on the distribution curve during the 5°amplitude oscillations where the gravity-driven stratification remained rather low (Figure 6a). From the observations made earlier, it was found that the fluid flow structures behind the tracer mixing and residence time distribution inside rolling porous media differ entirely from those in stationary tilted beds. Hence, further CFD simulations were carried out to examine the influence of fluid flow structures at different angular positions of the rolling bed (Θ = 10°, T = 20 s) on the tracer response. For this purpose, five angular positions were targeted over one-half period of the roll motion as shown in Figure 7a. Under the rolling motion condition, the fluid flow equations were first solved at any desired position and then each one saved as a separate simulation file. Having had the fluid flow structures for each angular position, the UDS equations were then solved while the roll motion was disabled within the solver. This method allowed obtaining the tracer age distribution at each desired position without interfering in the RTD response of other positions. Figure 7b monitors the tracer response curves at different angular positions over onehalf period of the roll motion. It can bee seen that each angular position represented its own age distribution curve, except for the extreme angular positions of +10° and -10° whose curves almost 13.
overlapped. The reason for the difference between the curves of +5° and -5° angular positions rests mainly on a difference in their flow structures. While altering the column angular position from +10° to +5° (Figure 7a) led to a persistent memory of fluid maldistribution, tilting the column from 0° to -5° showed a marginal effect on the flow structure owing to the memory of a relatively uniform fluid distribution. Consequently, a more widened distribution of tracer signal was found for +5° in comparison with that of -5° (Figure 7b). On the other hand, the overlap of curves for the angular positions of +10° and -10° can be ascribed to the fact that these angular positions were the extreme tilt angles that the column experienced during the roll motion. Hence, any memory of fluid distribution stemming from previous lower angular positions was lost due to a dominant gasliquid segregation, leading to identical distribution curves. This observation highlights the fact that during column roll motions the fluid flow structures significantly changed inside the porous medium by altering the position leading to various behaviors in tracer mixing and residence time distribution. As expected, the broadening of tracer response curve and loss of symmetric distribution became more pronounced at high angular positions as a consequence of the progressive development of a segregated flow pattern.
5. Conclusion An Eulerian two-fluid CFD model was extended to describe the tracer mixing and residence time distribution (RTD) in a trickle bed reactor subjected to stationary tilts and roll motions. Experimental data obtained from wire-mesh sensors using a tracer injection method and RTD tools were employed to validate the simulation results. The CFD model was capable of reproducing the dominant features of the RTD curves measured experimentally where the incidence of dispersive phenomena and mixing in the course of column tilts and oscillations was predicted satisfactorily via the model. The simulation results indicated that the bed deviations from vertical configuration 14.
led to gravity-driven stratified flow zones in the packing which contributed to widen the asymmetric tracer signals giving rise to lower breakthrough times and long tails. Likewise, liquid back-mixing became more severe for rolling beds by increasing the column tilt angle and the motion period on account of the temporary evolving segregated fluid regions. From CFD simulations, it was also found that by altering positions during roll motions the fluid flow structures significantly changed inside the packing resulting in different mixing behaviors and residence time distributions. The developed CFD model and results presented in this work could be utilized for further investigations about radial mixing behaviors and chemical reaction performance of the trickle bed reactor under offshore conditions. For example, future works focusing on CFD-validated backmixing data could serve for developing Pe-number correlations applicable to sea conditions where the different motion degrees of freedom could be included as additional independent variables. Robustness of these correlations for design purposes could combine CFD simulations to save tedious experimentations with a few validated experimentations rather than relying only on extensive measurements as classically practiced.
Acknowledgments The authors gratefully acknowledge the Natural Sciences and Engineering Research Council of Canada and the Canada Research Chair on Sustainable Energy Processes and Materials for their financial support.
Nomenclature 𝑎̂
unit direction vector for the axis of rotation (-)
𝐶̿ q
inertial resistance tensor (1/m)
15.
dmin
minimum equivalent diameter of the area between three contacting spheres
dp
particle diameter (m)
D
column diameter (m)
̿q 𝐷
viscous resistance tensor (1/m2)
Dtr
tracer dispersion coefficient (m2/s)
E(θ)
residence time distribution
𝐹 D,q
total dispersion force exerted on phase q (N/m3)
𝐹 D,mech,q
mechanical dispersion force exerted on phase q (N/m3)
𝐹 gl
gas-liquid interaction force (N/m3)
𝐹q
total force term exerted on phase q (N/m3)
𝐹 qs
fluid-solid interaction forces, 𝐹 ls and 𝐹 gs, (N/m3)
g
acceleration due to gravity (m/s2)
H
distance from bed inlet (m)
Kgl
gas-liquid interaction coefficient (kg/ m3/s)
Kqs
momentum exchange coefficient of phase q (kg/ m3/s)
P
pressure (Pa)
𝑟
position vector (m)
16.
Sm
spread factor (m)
Str
tracer spread factor (m)
t
time (s)
𝑡̅
mean residence time (s)
T
motion period (s)
⃗⃗⃗ 𝑢′
velocity of the moving frame (m/s)
U
superficial velocity (m/s)
𝑣D
drift velocity (m/s)
𝑣q
phase velocity viewed from the stationary frame (m/s)
⃗⃗⃗ 𝑣′q
phase velocity viewed from the moving frame (m/s)
⃗⃗⃗ l,ax 𝑣′
liquid axial velocity (m/s)
𝑣𝑡 ⃗⃗⃗
translational frame velocity (m/s)
||.||
absolute value of a vector
Greek letters βq
saturation of phase q (-)
dimensionless time (t/𝑡̅)
rolling angle function (radian)
17.
amp
tilt angle amplitude (radian)
ɛ
bed porosity (-)
ɛq = βq× ɛ
volume fraction of phase q (-)
Μ
viscosity (kg/m.s)
Ρ
density (kg/m3)
Σ
surface tension (N/m)
scalar
Τ
stress tensor (Pa)
𝜔 ⃗
angular velocity (radian/s)
Subscripts D
dispersion
g
gas
l
liquid
mech
mechanical
p
particle
s
solid
References [1]
J.T. Cullinane, N. Yeh, E. Grave, Effects of tower motion on packing efficiency, 14376618.
MS SPE Conference Paper, Macae, Brazil, 2011. [2]
R.H. Weiland, N.A. Hatcher, J. Seagraves, Choosing Tower Internals for LNG, Shale Gas, and Tail Gas Treating. Paper presented at: SOGAT, Abu Dhabi, UAE, 2013.
[3]
F.S. Mederos, J. Ancheyta, J. Chen, Review on criteria to ensure ideal behaviors in tricklebed reactors, Appl. Catal. A Gen. 355 (2009) 1–19.
[4]
V. V Ranade, R. Chaudhari, P.R. Gunjal, Trickle bed reactors: reactor engineering & applications, Elsevier, 2011.
[5]
M. Schubert, M. Hamidipour, C. Duchesne, F. Larachi, Hydrodynamics of cocurrent twophase flows in slanted porous media—Modulation of pulse flow via bed obliquity, AIChE J. 56 (2010) 3189–3205.
[6]
A. Motamed Dashliborun, F. Larachi, Hydrodynamics of gas–liquid cocurrent downflow in floating packed beds, Chem. Eng. Sci. 137 (2015) 665–676.
[7]
G.P. Assima, A. Motamed-Dashliborun, F. Larachi, Emulation of gas-liquid flow in packed beds for offshore floating applications using a swell simulation hexapod, AIChE J. 61 (2015) 2354–2367.
[8]
A. Motamed Dashliborun, F. Larachi, M. Hamidipour, Cyclic operation strategies in inclined and moving packed beds—Potential marine applications for floating systems, AIChE J. 62 (2016) 4157–4172.
[9]
A. Motamed Dashliborun, F. Larachi, M. Schubert, Offshore Floating Packed‐ Bed Reactors: Key Challenges and Potential Solutions, Chem. Eng. Technol. 40 (2017) 1975– 1984. 19.
[10] A. Motamed Dashliborun, J. Zhang, S.M. Taghavi, F. Larachi, 110th Anniversary: Marinization of Multiphase Reactors through the Prism of Chemical Engineers, Ind. Eng. Chem. Res. 58 (2019) 2607-2630. [11] H. Bouteldja, M. Hamidipour, F. Larachi, Hydrodynamics of an inclined gas–liquid cocurrent upflow packed bed, Chem. Eng. Sci. 102 (2013) 397–404. [12] P. Gauthier, S. Clément, C. Vincent, P.S. Claire, M. Thomas, A. Pascal, F. Manel, B. Philippe, W. Graeme, Hexapod Pilot Tests Determine the Influence of 3D Motions on the Performance of an Amine-Based Acid Gas Removal Unit Installed on a Floating Support. 18743-MS IIPTC Conference Paper, Bangkok, Thailand, 2016. [13] A.M. Dashliborun, F. Larachi, M. Schubert, Hydrodynamics of gas-liquid cocurrent upflow in oscillating packed beds for offshore marine applications, Chem. Eng. Sci. 170 (2017) 583–596. [14] A. Wongkia, F. Larachi, S. Assabumrungrat, Hydrodynamics of countercurrent gas-liquid flow in inclined packed beds–A prospect for stretching flooding capacity with small packings, Chem. Eng. Sci. 138 (2015) 256–265. [15] I. Iliuta, F. Larachi, Hydrocarbon hydrodesulfurization in vertical, inclined and oscillating trickle beds–Hydrodynamics & reactor performance for offshore petroleum marine applications, Fuel. 186 (2016) 35–49. [16] I. Iliuta, F. Larachi, Three–dimensional simulations of gas–liquid cocurrent downflow in vertical, inclined and oscillating packed beds, AIChE J. 62 (2016) 916–927. [17] A. Motamed Dashliborun, M. Hamidipour, F. Larachi, Hydrodynamics of inclined packed
20.
beds under flow modulation – CFD simulation and experimental validation, AIChE J. 63 (2017) 4161–4176. [18] A. Motamed Dashliborun, F. Larachi, CFD Study and Experimental Validation of Multiphase Packed Bed Hydrodynamics in the Context of Rolling Sea Conditions, AIChE J. 65 (2019) 385–397. [19] Y. Wang, J. Chen, F. Larachi, Modelling and simulation of trickle‐bed reactors using computational fluid dynamics: A state‐of‐the‐art review, Can. J. Chem. Eng. 91 (2013) 136–180. [20] M.P. Dudukovic, Ž. V Kuzeljevic, D.P. Combest, Three‐Phase Trickle‐Bed Reactors, Ullmann's Encyclopedia of Industrial Chemistry. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA, 2014: 1-40. [21] A. Atta, S. Roy, K.D.P. Nigam, Prediction of pressure drop and liquid holdup in trickle bed reactor using relative permeability concept in CFD, Chem. Eng. Sci. 62 (2007) 5870–5879. [22] F. Augier, M. Fourati, Y. Haroun, Characterization and modelling of a maldistributed Trickle Bed Reactor, Can. J. Chem. Eng. 95 (2017) 222–230. [23] A. Motamed Dashliborun, A. Füssel, F. Larachi, Prospect of open-cell solid foams for floating-platform multiphase reactor applications – Maldistribution susceptibility and hydrodynamic behavior, Chem. Eng. J. 332 (2018) 596-607. [24] P.R. Gunjal, V. V Ranade, R. V Chaudhari, Liquid distribution and RTD in trickle bed reactors: experiments and CFD simulations, Can. J. Chem. Eng. 81 (2003) 821–830. [25] K. Lappalainen, E. Gorshkova, M. Manninen, V. Alopaeus, Characteristics of liquid and 21.
tracer dispersion in trickle-bed reactors: Effect on CFD modeling and experimental analyses, Comput. Chem. Eng. 35 (2011) 41–49. [26] K.M. Kan, P.F. Greenfield, Multiple hydrodynamic states in concurrent two phase down flow through packed beds, Ind. Eng. Chem. Process Desigen Dev. 17 (1978) 482–485. [27] L. Moskowitz, Estimates of the power spectrums for fully developed seas for wind speeds of 20 to 40 knots, J. Geophys. Res. 69 (1964) 5161–5179. [28] J.M.J. Journée, W.W. Massie, Offshore hydromechanics, Delft University of Technology, Delft (the Netherlands), 2000. [29] P. L. Mills, M.P. Dudukovic, Convolution and deconvolution of nonideal tracer response data with application to three-phase packed-beds, Comput. Chem. Eng. 13 (1989) 881–898. [30] M. Schubert, A. Khetan, M.J. Da Silva, H. Kryk, Spatially resolved inline measurement of liquid velocity in trickle bed reactors, Chem. Eng. J. 158 (2010) 623–632. [31] A. Motamed Dashliborun, H. Härting, M. Schubert, F. Larachi, Process intensification of gas–liquid downflow and upflow packed beds by a new low‐shear rotating reactor concept, AIChE J. 63 (2017) 283–294. [32] M.J. Da Silva, E. Schleicher, U. Hampel, Capacitance wire-mesh sensor for fast measurement of phase fraction distributions, Meas. Sci. Technol. 18 (2007) 2245-2251. [33] Z. Solomenko, Y. Haroun, M. Fourati, F. Larachi, C. Boyer, F. Augier, Liquid spreading in trickle-bed reactors: Experiments and numerical simulations using Eulerian–Eulerian twofluid approach, Chem. Eng. Sci. 126 (2015) 698–710. [34] A. Attou, C. Boyer, G. Ferschneider, Modelling of the hydrodynamics of the cocurrent gas– 22.
liquid trickle flow through a trickle-bed reactor, Chem. Eng. Sci. 54 (1999) 785–802. [35] A. Attou, G. Ferschneider, A two-fluid hydrodynamic model for the transition between trickle and pulse flow in a cocurrent gas–liquid packed-bed reactor, Chem. Eng. Sci. 55 (2000) 491–511. [36] K. Lappalainen, M. Manninen, V. Alopaeus, CFD modeling of radial spreading of flow in trickle-bed reactors due to mechanical and capillary dispersion, Chem. Eng. Sci. 64 (2009) 207–218. [37] M. Fourati, V. Roig, L. Raynal, Liquid dispersion in packed columns: experiments and numerical modeling, Chem. Eng. Sci. 100 (2013) 266–278. [38] P. Marchot, D. Toye, M. Crine, A.-M. Pelsser, G. L’homme, Investigation of Liquid Maldistribution in Packed Columns by X-Ray Tomography, Chem. Eng. Res. Des. 77 (1999) 511–518. [39] A. Fluent, ANSYS fluent theory guide 15.0, Inc, Canonsburg, PA. (2013). [40] A. Atta, M. Hamidipour, S. Roy, K.D.P. Nigam, F. Larachi, Propagation of slow/fast-mode solitary liquid waves in trickle beds via electrical capacitance tomography and computational fluid dynamics, Chem. Eng. Sci. 65 (2010) 1144–1150. [41] M. Hamidipour, J. Chen, F. Larachi, CFD study and experimental validation of trickle bed hydrodynamics under gas, liquid and gas/liquid alternating cyclic operations, Chem. Eng. Sci. 89 (2013) 158–170. Table Captions Table 1
Equations of Eulerian two-fluid porous media and scalar transport in CFD model employed for simulations of stationary tilted (angles of 0°-15°) and rolling 23.
(amplitudes of 0°-15° and periods of 5-40 s) trickle beds. Figure captions Figure 1
Schematic diagram of the experimental setup for gas-liquid cocurrent downflow trickle bed embarked on a hexapod robot and instrumented with WMSs.
Figure 2
(a) Roll motion of the hexapod robot and coordinate systems in computational domain, (b) axial and radial sections of the used mesh structure in the 3D geometry along with representatives of injected inlet tracer pulse and computed outlet tracer pulse.
Figure 3
Comparison of experimental and numerical RTD responses for three stationary tilted bed configurations with (a) 0°, (b) 5°, and (c) 10° angles (Ug = 0.138 m/s, Ul = 0.0024 m/s).
Figure 4
Comparison of experimental and numerical RTD responses for rolling beds with (a) 5°, T = 20 s; (b) 10°, T = 20 s; (c) 10°, T = 5 s (Ug = 0.138 m/s, Ul = 0.0024 m/s).
Figure 5
Simulation results of the evolution of dynamic tracer signals at two bed heights in response to (a) stationary tilted configurations, (b) 20 s-period roll motion with different amplitudes, and (c) 10°-amplitude roll motion with different periods (Ug = 0.138 m/s, Ul = 0.0024 m/s).
Figure 6
Comparison of the computed tracer signal for static tilted beds and rolling beds under the same amplitude of (a) 5° and (b) 10° at H = 50 cm (Ug = 0.138 m/s, Ul = 0.0024 m/s).
Figure 7
Comparison of the tracer signal for different instances of a rolling bed with 10° and T =20 s, (a) sinusoidal path of column roll motion and (b) computed tracer signals at H = 50 cm (Ug = 0.138 m/s, Ul = 0.0024 m/s).
24.
Table 1 Continuity equation
Momentum equation
q q q q vq 0 , (q = l, g) t
(1)
g l
(2)
dv d q q vq q q vq vq q q (2 vq ( r ) r t ) t dt dt
(3)
q P q q q g Fq
vq vq u , u vt r amp cos(
(4)
2 t ) T 2
(5)
d 2 2 amp ( ) sin t , dt T 2 T
aˆ
(6)
q q q vq vqT q q q .vq I
(7)
Fg Fgl Fgs FD, g
(8)
Fl Fgl Fls FD,l
(9)
1 Fqs q Dq vq q vq Cq vq Kqs vq , (q = l, g) 2
(10)
Porous resistances
Kls 180l
(1 )2 (1 ) 1.8l vl 2 2 l d p l d p
(1 g )2 1 K gs 180 g g d p2 1 g
Gas-liquid interaction
2 3
2/3
1 g 1 1.8 g d p 1 g
(11) 1/3
vg
Fgl K gl vg - vl (1 g )2 1 K gl 180 g g d p2 1 g
(12)
(13)
2/3
1 g 1 1.8 g d p 1 g
1/3
vg - vl
(14)
25.
Capillary pressure
g 1 1 1 Pc Pg Pl 2 l ( )F d p d min l 1 l
1/3
(15)
1
d min
3 1 2 d p 2
g F l
g 1 88.1 l
(16)
(17)
Capillary dispersion
g 1 2 1 1 Pc l ( )( )F 3 1 d p d min l 1 l
Mechanical dispersions
FD,mech,l Kls vD ,l K gl (vD ,l vD , g )
(19)
FD, mech, g K gs vD , g K gl (vD , g vD ,l )
(20)
vD , q
Sm
q
( vq q (vq . q )
vq vq
) , (q = l, g)
4/3
l
(18)
(21)
Sm 0.015 d p
(22)
UDS transport equation
l ll l l vll l l Dtr l t
(23)
Dispersion coefficient
Dtr Str vl, ax , Str Sm
(24)
26.
Figure 1
27.
Figure 2 a
b Yʹ
Xʹ
Yʹ
Xʹ
Inlet pulse
Zʹ
Zʹ
-Θ
+Θ Xʹ Z' Y'
Y
Outlet pulse
28.
Figure 3 a
b 0.15
0.15
Θamp = 0
0.12
EXP
Θamp = 5
0.12
EXP
CFD
E (θ)
E (θ)
CFD
0.09
0.09
0.06
0.06
0.03
0.03
0
0 0.5
1
1.5
2
θ (-)
2.5
3
0
0.5
1
1.5
θ (-)
2
2.5
3
c 0.15
Θamp = 10
0.12
EXP
CFD
E (θ)
0
0.09 0.06
0.03 0 0
0.5
1
1.5
θ (-)
2
2.5
3
29.
Figure 4 b
a 0.15
0.15
Θamp = 5 , T = 20 s
0.12
EXP
Θamp = 10 , T = 20 s
0.12
EXP
CFD
E (θ)
E (θ)
CFD
0.09
0.09
0.06
0.06
0.03
0.03
0
0 0.5
1
1.5
2
θ (-) c
0.15
2.5
3
0
0.5
1
1.5
θ (-)
2
2.5
3
Θamp = 10 , T = 5 s
0.12
Exp
CFD
E (θ)
0
0.09 0.06 0.03 0 0
0.5
1
1.5
θ (-)
2
2.5
3
30.
Figure 5 a 0.2
Inlet 5° 15°
H = 5 cm
Normalized signal (-)
Stationary
0.16
0° 10°
0.12 0.08 H = 85 cm
0.04 0 0
20
40
60
Time (s)
b
100
c H = 5 cm Roll motion (T = 20 s)
0.16
0.2 Inlet
5°
10°
15°
Normalized signal (-)
0.2
Normalized signal (-)
80
0.12 H = 85 cm
0.08 0.04 0
H = 5 cm Roll motion (Θamp = 10 )
0.16
Inlet
5s
10 s
20 s
0.12 H = 85 cm
0.08 0.04 0
0
20
40
Time (s)
60
80
0
20
40
Time (s)
60
80
31.
Figure 6 a
b 0.15
0.15
0.12
Static tilted bed (10 ) Θamp = 10 , T = 20 s Θamp = 10 , T = 40 s
Normalized signal (-)
Normalized signal (-)
Static tilted bed (5 ) Θamp = 5 , T = 20 s Θamp = 5 , T = 40 s
0.12
0.09
0.09
0.06
0.06
0.03
0.03
0
0 0
20
40
Time (s)
60
80
0
20
40
Time (s)
60
80
32.
Figure 7 b
a
0.15 +10
Θ( )
10 5
+5
0
0
0
10
20
30
40
-5
-5
50 -10
-10
60
Normalized signal (-)
15
+ 10° 0° - 10°
0.12
+ 5° - 5°
0.09 0.06 0.03
0
-15
Time (s)
0
20
40
Time (s)
60
80
33.
Research Highlights ►Tracer dispersion in trickle beds was studied numerically under marine conditions. ►Eulerian two-fluid CFD model was able to describe tracer mixing and RTD. ►Column tilts and roll motions were responsible for widening of tracer signals. ►Variation of flow structures with roll motion caused different mixing behaviors.
34.
S1385-8947(19)32255-7 https://doi.org/10.1016/j.cej.2019.122845 CEJ 122845
To appear in:
Chemical Engineering Journal
Please cite this article as: A.M. Dashliborun, F. Larachi, Tracer Dispersion in Trickle Beds Under Tilts and Roll Motions - CFD Study and Experimental Validation, Chemical Engineering Journal (2019), doi: https://doi.org/ 10.1016/j.cej.2019.122845
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
Tracer Dispersion in Trickle Beds Under Tilts and Roll Motions - CFD Study and Experimental Validation Amir Motamed Dashliborun and Faïçal Larachi* Department of Chemical Engineering, Laval University, Québec, QC, Canada G1V 0A6 *Corresponding author. Tel.: +1 (418) 656-3566, Fax: +1 (418) 656-5993 E-mail address: [email protected] (F. Larachi) Abstract A wire-mesh sensor was used to measure the liquid residence time distribution (RTD) and tracer dispersion in trickle beds subjected to stationary tilts and roll motions. The measured tracer characteristics were confronted to three-dimensional transient Euler-Euler CFD simulations to expose the role of inclined and oscillating porous media. The simulation results satisfactorily reproduced the widening tracer signals with increased bed inclination reflecting in asymmetric RTDs prompted by permanent gravity-driven stratified flow zone through the packing. Similarly, tracer dispersion was predicted to increase for rolling beds by increasing tilt angle and motion period. While an increase of tilt angle shortened RTD breakthrough time due to the faster tracer stream evolving in the liquid-rich lower-most zones, tracer elution tended to slow-down with increasing the rolling period. In addition, it was revealed that with altering the column angular position during roll motions the fluid flow structures inevitably varied inside the packing leading to different mixing behaviors and residence time distributions. Keywords Residence time distribution; tracer dispersion; Eulerian porous media model; experimental validation; CFD simulation; tilt and roll motion
1.
1. Introduction Oil and gas production units on mobile sea platforms such as floating production, storage and offloading (FPSO) commonly employ multiphase fixed beds for onboard treatment and refining of offshore hydrocarbon streams [1,2]. Trickle bed reactor is a particular configuration of the fixed bed where the gas and liquid phases flow co-currently in the direction of gravity over randomly filled solid particles, thereby allowing high flexibility in throughput demands for industrial applications [3,4]. Recent experimental investigations revealed that ship tilts and oscillations stemming from sea conditions could affect the operation and performances of trickle beds onboard offshore floating platforms [5–10]. Hydrodynamic studies using imaging techniques such as electrical capacitance tomography (ECT) and capacitance wire-mesh sensor (WMS) demonstrated remarkable gas-liquid disengagement and significant variations of the fluid flow paths in porous media due to bed tilts and vessel motions [5–7,9–14]. Imaging of the gas-liquid flow showed that permanent tilts of the trickle bed caused accumulation of the liquid phase in the lower-wall zones, whereas roll motions resulted in periodic transverse displacements of fluids across the packing. Beside experimental works, computational fluid dynamic (CFD) simulations helped shape an understanding of trickle bed reactors subjected to ship tilts and oscillations [15–18]. For resolving the local fluid distributions and velocity fields in trickle beds, the Eulerian CFD method in which all phases are treated mathematically as interpenetrating continua has been widely used [19,20]. In this approach, closure equations are often applied for coupling of fluid phases through momentum exchange coefficients [19,21]. Using a transient two-fluid Eulerian CFD model within the porous media approach, numerical simulations were recently carried out to describe the hydrodynamic behavior of trickle beds under ship tilts and roll motions [18]. The model consisted of closure laws 2.
for porous resistances (i.e., fluid-solid interactions) and gas-liquid interaction as well as capillary and mechanical dispersion forces. The simulation results were validated against experimental data of liquid saturation and pressure drop provided by a capacitance wire-mesh sensor and a differential pressure transmitter, respectively. It was realized from the numerical results that incorporation of capillary and mechanical dispersion terms in the CFD model was essential to accurately capture the transient hydrodynamics of trickle beds under moving conditions; otherwise, it caused severe loss of temporal stability and an erratic behavior in the computed liquid saturation and pressure drop. In virtue of the validated CFD model, it was found that an increase of rolling angle and period resulted in a decrease of liquid saturation, bed pressure drop, and uniformity degree of the fluid distribution. A traditional approach for investigation of the hydrodynamics inside trickle bed reactors relies on Residence Time Distribution (RTD) determination whereby measurement or simulation of the dynamic tracer concentration signal at desired locations of the reactor is carried out [22]. This method is a powerful tool for characterization of the fluid maldistribution and the extent of deviations from ideal plug flow in packed-bed reactors. Thanks to new tomography techniques either invasive or non-invasive, the experimental study of phase distribution and RTD tracing in multiphase reactors has been noticeably facilitated [20]. Recent RTD experiments mimicking offshore floating packed beds using wire-mesh sensors (WMS) revealed that the liquid flow became more dispersive during column motions causing liquid maldistribution and more deviations to plug flow behavior of the liquid phase with increasing the tilt angle and motion period [7,13,23]. The tracer tests showed that tracer migration in the lowermost liquid-rich region outpaced the one slowly drifting in the uppermost gas-rich region on account of the gas-liquid disengagement in tilted beds [7]. From spatial- and time-resolved WMS measurements, it was also 3.
realized that column roll motions prompted secondary transverse zigzag motion of tracer across the bed [7]. Such transverse movement of tracer inflated the signal variance. Furthermore, with increasing the roll motion period the signal variance inflated more and tracer elution to be completed was much longer due to increased axial dispersion [7,13,23]. The inflated signal variances suggested drastic departures from liquid plug flow, reflecting lower Péclet numbers. The bed oscillations and their influences on the tracer behavior have been thoroughly discussed in our previous works [7,13,23]. Despite recent progress concerning the modeling and simulation of gas-liquid flow dynamics inside offshore floating packed beds, application of validated CFD-based Eulerian model was limited to track local fluid distributions and prediction of parameters such as bed overall pressure drop and liquid holdup [16–18]. CFD simulation studies on the liquid RTD in stationary tilted and oscillating trickle beds have not been yet addressed, though there are few works on the conventional stationary vertical bed configuration [22,24,25]. Hence, the present study aims at conducting CFD simulations of trickle bed under column stationary tilts and roll motions with specific focus on simulating the liquid residence time distribution of a tracer pulse. For validation of the simulation results, wire-mesh sensors (WMS) were employed to experimentally capture the time evolution of tracer concentration signals in the course of bed tilts and motions. The effect of stationary tilt angles and roll motion parameters (i.e., amplitude and period) on the tracer response was thoroughly investigated. Moreover, a comprehensive analysis was performed with aid of the CFD model to highlight the influence of fluid flow structures on the tracer response curves at different angular positions of the rolling bed.
4.
2. Experimental A schematic diagram of the laboratory-scale setup used for the determination of liquid residence time distributions and validation of the CFD simulations is shown in Figure 1. The Plexiglas column (ID = 57 mm) was filled with 3 mm glass beads up to a height of 1000 mm resulting in an average packing porosity of ca. 0.40. Retaining stainless steel screens were placed at the top and bottom of the packed bed to avert inter-particle movements during column tilts and rolling. The packed column instrumented with a pair of wire-mesh sensors (WMS1 and WMS2) for tracer pulse detection was bound to a NOTUS hexapod ship motion emulator allowing six-degree-offreedom motions (Figure 1). Tracer experiments were performed at room temperature and atmospheric pressure by forcing air and water to flow through the bed in cocurrent downflow. The gas and liquid throughputs corresponded to the trickle flow regime. The desired gas flow rate was adjusted by means of a calibrated flowmeter, while two peristaltic pumps were, respectively, used for the supply of the continuous liquid stream and for tracer injection. Prior to RTD experiments, column operation was kept under pulse flow regime for at least 30 min to ensure complete prewetting of the packing according to the Kan and Greenfield procedure [26]. Since roll motion has been reported in literature as the most influential oscillation on the hydrodynamic performance of multiphase packed beds [6–9,12], in this study roll motions with 5° and 10° amplitudes and periods of 5-40 s, covering typical conditions of ships subjected to marine swells [27,28], were imposed to the trickle bed. It is noteworthy to mention that during the roll motion the bed periodically evolves between the vertical and tilted modes. This type of column tested motion can be observed from the video clip illustrated in our previous works [6,7]. For comparative purposes, the limiting cases of stationary vertical (0°) and stationary tilted (5°-10°) bed configurations were included as well.
5.
Aqueous sodium chloride solutions were briefly injected for 5 s upstream the liquid feeding line and two wire-mesh sensor grids, inserted 100 mm and 600 mm downstream in the bed (Figure 1), registered the evolution due to liquid back-mixing of the travelling tracer pulses. A sampling frequency of 100 Hz was deemed sufficient to track the temporal evolution of tracer pulses in the stationary and rolling trickle bed. Since the setup was operated in a recycle mode for the liquid phase, an electrical conductivity meter monitored liquid conductivity in the feed tank after tracer injection so that signal baseline drifts due to accumulation of the tracer were prevented by regular replacements of the liquid with fresh deionized water. Furthermore, an appropriate filter was used to reduce random noise present in tracer signals to acceptable levels [29]. More information about the configuration, the operating principle and calibration of the wire-mesh sensors, data processing, and application to multiphase flow measurements for RTD studies can be found in our group’s previous studies [7,30–32].
3. Description of CFD model The CFD model used in the present study is based on our previous work [18], where a 3D twofluid Eulerian model was applied in porous media approach to predict the hydrodynamic behavior of a gas-liquid cocurrent downflow trickle bed under column inclinations and roll motions. Notwithstanding that exhaustive numerical investigations on hydrodynamic characteristics of trickle beds in terms of liquid saturation, pressure drop, fluid distribution and velocity in the context of offshore floating applications were carried out in our previous work [18], there is still a lack of numerical research work to address the important problem of tracer dispersion under column tilts and roll motions. Thus, the implemented CFD model is briefly described here. The macroscopic volume-averaged forms of mass and momentum balance equations for each flowing phase are summarized in Table 1. Since momentum balances for flowing fluids are derived from 6.
averaging pore-scale Navier-Stokes equations, the system of equations requires closure laws [33]. Hence, porous resistances (i.e., fluid-solid interactions) and gas-liquid interaction together with fluid dispersion mechanisms were considered in the form of closure laws [18]. The Ergun-like model, containing viscous and inertial contributions, developed by Attou et al. [34] was used to account for porous resistances and gas-liquid interaction (Eqs. 10-14). In order to account momentum dispersion in the porous medium, namely the capillary pressure and the mechanical dispersion, the correlation developed by Attou and Ferschneider [35] was applied to account for the former (Eqs. 15-18), whereas the model developed by Lappalainen et al. [36] and Fourati et al. [37] was considered to describe the latter in both gas and liquid phases (Eqs. 19-22). Since the two-fluid Eulerian method solves a unique averaged pressure field for the gas phase, a capillary pressure model (Eq. 15) is required to consider the pressure jump at the gas–liquid interface due to capillarity [32,36]. Thus, the gradient of this expression (Eq. 18) was added to the momentum conservation equation of the liquid phase as a capillary dispersive force term to account for the capillary pressure in the CFD model [33,36]. For simulation of the age distribution of a scalar quantity in the trickle bed reactor, a User Defined Scalar (UDS) transport equation involving diffusion and convection terms (Eq. 23) has to be solved along with the momentum transport equations. The global diffusion coefficient (Dtr) in porous media results from the sum of molecular diffusion and mainly dispersion due to the porous structure [22]. In this work, the dispersion coefficient defined as a function of the liquid axial velocity (νʹl,ax) and the tracer spreading factor (Str) was applied (Eq. 24), which is an appropriate parameter for taking into account geometrical liquid distribution in packed beds [25,38]. Moreover, the inlet boundary condition was similar to the experimental condition where a pulse of the tracer concentration with 5 s duration is injected at the bed inlet. More details about fluid-solid and gas-liquid interaction forces, the capillary and
7.
mechanical dispersion forces as well as their theoretical justifications can be found elsewhere [34,36,37]. The influence of roll motions in a computational domain is realized commonly through the implementation of moving reference frame (MRF) and sliding mesh techniques. The MRF method modifies the momentum equation to incorporate the additional acceleration/deceleration force terms due to the transformation of the inertial reference frame to the non-inertial frame, whereas the sliding mesh approach retains the momentum equation in the stationary reference but allows all of the boundaries and the cells to move together in a rigid-body motion [39]. For detailed information about the MRF and sliding mesh techniques and their theoretical backgrounds, the reader is directed to ANSYS FLUENT user’s guide (2015) [39]. Our previous CFD simulation work on the trickle bed hydrodynamics under roll motions showed no difference in the simulation results obtained from these two techniques [18]. Therefore, all simulations of the rolling bed were performed using the MRF approach due to its quite low computational burden and CPU time compared to the sliding mesh method. The transformation of fluid velocities from the inertial frame to the non-inertial frame was made using the relative velocities as dependent variables (Eq. 4), whereby four additional acceleration terms appeared in the momentum equations. The Coriolis acceleration (2𝜔 ⃗ ×𝑣ʹq), the centripetal acceleration (𝜔 ⃗ ×(𝜔 ⃗ ×𝑟)), and the accelerations due to unsteady variation of the rotational (d𝜔 ⃗ /dt×𝑟) and translational (d𝑣t/dt) velocities (Eq. 3) appeared in the momentum balance as a result of translational and rotational movements of the non-inertial reference frame relative to the inertial reference frame. Figure 2a illustrates the established computational domain with respect to the moving frame. The pressure-based unsteady state solver in double precision mode within ANSYS® FLUENT 18.1 CFD software was used to solve the set of equations in Table 1. The closure laws and roll motions 8.
of the trickle bed were implemented in the software using user-defined functions. Figure 2b shows the typical meshing used for the 3D computational domain along with representatives of injected inlet tracer pulse and computed outlet tracer pulse. The impact of grid resolution, numerical scheme selection, and boundary conditions on model results was examined according to a methodology similar to the one exposed in our previous studies [17,18]. A mesh number of 12,750 on the domain with the minimum and maximum cell volume of, respectively, ca. 2.015e-07 and 4.83e-07 m3 was found sufficient for all bed configurations to ensure grid-independent solutions with an acceptable computational time. Solution convergence for each time step was assumed as all residuals fell below 10-3 during the maximum iteration number of 100. Since the column-toparticle diameter ratio (D/dp = 19) was large enough, we assumed a uniform porosity distribution across the bed [40,41]. A stable solution obtained under the stationary vertical configuration was considered as an initial condition for simulation of rolling trickle beds. In addition, the momentum equations were first solved using an unsteady approach to achieve a converged-periodic solution for the hydrodynamics. The fluid flow and UDS equation were then solved simultaneously. The area-weighted averaged concentration of the tracer at any desired location was monitored with time to obtain the RTD curves. Further details on applied boundary conditions, assumptions, and numerical simulation procedure can be found in our previous work [18].
4. Results and discussion 4.1. Experimental validation In our group’s previous numerical studies [17,18], the capability of the developed CFD model was assessed through analyzing time series of the bed overall pressure drop and the instantaneous variations of local and cross-sectional averaged liquid saturations across the bed obtained from the simulation results and experimental data. Predictions of the model for the pressure drop and liquid 9.
saturation values as well as wave morphology in the course of column roll motions were in good agreement with the experimental results for all tested conditions. Hence, the CFD model was extended here to simulate mixing and RTD in the trickle bed under column tilts and roll motions. The RTD obtained numerically under different bed configurations was compared against experimental data to evaluate accuracy of the CFD model prediction. Prior to performing the simulations of rolling trickle beds, the RTD was calculated for the stationary bed positioned at different tilt angles. To quickly capture the tracer behavior for the various non-conventional packed bed modalities, an overall picture of tracer dispersion and backmixing of the liquid can be grasped from comparisons of the simulation with the experiment for the vertical column. Furthermore, comprehensive experiments using wire-mesh sensors to investigate the tracer migration over the bed crosswise plane due to fluid flows under ship tilts and roll motions are provided elsewhere [7]. However, for the sake of skipping repetitions, since the experimental results concerning how the tracer is maldistributed and how the tilting and rolling affects packed bed uniformity were already detailed in our previous works [7,18], readers can refer to those specific works. Figure 3a-c reveals good agreement between numerical and experimental values between 0° (vertical) and 10°, despite the slight overestimation of the dispersion at the high tilting angle (10°). The main reason behind this lack of fit for RTD curves at the high tilt angle can be attributed to the correlation of dispersion coefficient (Eq. 24) employed in the UDS equation (Eq. 23). In porous media, the global diffusion coefficient (Dtr) results from the sum of molecular diffusion and mainly dispersion due to the porous structure [22]. It should be indicated that here the applied correlation was originally derived for the vertical packed bed configuration, where it was a function of the tracer spreading factor and liquid axial velocity. Hence, for sake of high level of 10.
accuracy in CFD simulations of tracer dispersion at high tilt angles of the trickle bed, a new correlation for the dispersion coefficient based on operation conditions and geometrical tracer distribution in tilted beds ought to be developed. Meanwhile, the simulation results were reasonably close to experimental RTD measurements for different oscillation amplitudes and periods of the rolling trickle bed for which representative results are illustrated in Figure 4a-c with Θ = 5° and T = 20 s, Θ = 10° and T = 20 s, Θ = 10° and T = 5 s, respectively. Thus, in the following section, the developed CFD model is applied to further examine the influence of different motion parameters on the tracer response. 4.2. Effect of column tilts and roll motions on tracer response The influence of stationary tilt angles and roll motion parameters (i.e., amplitude and period) on the tracer response was examined under identical gas and liquid flow rates (Figure 5). Here, as representative results, tracer concentration curves at two bed heights of H = 5 cm and H = 85 cm are monitored for stationary tilted beds (Figure 5a) as well as for rolling beds with varying amplitudes at a constant motion period (Figure 5b) and with varying oscillation periods at a constant amplitude (Figure 5c). The simulation results are illustrated as time series of scalar concentration (i.e., signal) averaged in the cross section and normalized to the total amount of scalar. A significant impact of column stationary tilts on the liquid dispersion is evident from a widened distribution of tracer age at H = 85 cm (Figure 5a). Furthermore, breakdown of symmetry in the tracer age distribution became more pronounced with incrementing the tilt angle. Bed deviations from the vertical position (0°) prompted gravity-driven stratified flow zones in the porous medium whereby a twofold phenomenon appeared: (1) relatively fast migration of tracer in the lower liquid-rich zone, (2) increase of tracer exit age due to spreading a part of it by the slower liquid 11.
flow in the upper gas-rich zone. The former phenomenon defines the breakthrough time of tracer age distribution, whereas the later one determines the time needed to complete the tracer elution. Therefore, the age distribution of tracer in tilted packed beds highly depends on dominance of these phenomena. From Figure 5a, it can be seen that emergence of severe segregated flow pattern at high tilting angles was reflected in widened asymmetric tracer signals with lower breakthrough times and long tails, thereby a more dispersive behavior for the liquid flow. Tracer responses for the bed submitted to different oscillation angles and periods of the roll motion are shown in Figures 5b and c, respectively. It is perceivable from this set of figures that an increase of rolling angle and period caused more liquid dispersion as reflected in widened tracer signals at the expense of temporary evolving gas-rich and liquid-rich regions. Time-dependent gravitational and inertial forces prompted in the course of hexapod roll motions caused, respectively, liquid accumulations in the lower-wall zones and secondary transverse displacements of the liquid across the bed whereby liquid back-mixing became severe. It is worthy of notice that an increase of the oscillation amplitude resulted in lower breakthrough time for the fastest liquid tracer stream due to redirection of part of the tracer towards the lowermost liquid-rich zones and thus facilitating its passage through the packing (Figures 5b). On the other hand, tracer elution to be completed became longer with increasing the motion period, which was interpreted as resulting from poor mixing in gentler roll motions with decreased inertial forces (Figures 5c). To evidence the role of inertial forces in tracer responses, Figures 6a and b compare the age distribution of tracer for the rolling bed, respectively, subject to 5° and 10° oscillation angles under 20 s and 40 s periods with the corresponding distribution curve for the limiting case of stationary tilted beds. As clearly seen, a permanent tilt (red lines) of the bed worsened liquid dispersion in comparison with those of rolling bed configurations due to exacerbated gravity-driven force and 12.
the absence of inertial force. In fact, column angular excitation induced secondary transverse displacements of the fluid in the radial and circumferential directions, which in turn tended to disperse the accumulated liquid over the bed cross section and provide more uniformity in the crosswise liquid distribution. Nevertheless, with increasing the motion period the tracer response curve became wider prone to approach that of the stationary tilted bed (Figure 6b). This is due to the fact that the gravity-driven stratification tended to outpace the opposing column inertial forces as the motion period was slowed down. This observation underlines an important contribution of the column acceleration/deceleration on diminishing segregated fluid regions. Meanwhile, a marginal influence of the motion period was found on the distribution curve during the 5°amplitude oscillations where the gravity-driven stratification remained rather low (Figure 6a). From the observations made earlier, it was found that the fluid flow structures behind the tracer mixing and residence time distribution inside rolling porous media differ entirely from those in stationary tilted beds. Hence, further CFD simulations were carried out to examine the influence of fluid flow structures at different angular positions of the rolling bed (Θ = 10°, T = 20 s) on the tracer response. For this purpose, five angular positions were targeted over one-half period of the roll motion as shown in Figure 7a. Under the rolling motion condition, the fluid flow equations were first solved at any desired position and then each one saved as a separate simulation file. Having had the fluid flow structures for each angular position, the UDS equations were then solved while the roll motion was disabled within the solver. This method allowed obtaining the tracer age distribution at each desired position without interfering in the RTD response of other positions. Figure 7b monitors the tracer response curves at different angular positions over onehalf period of the roll motion. It can bee seen that each angular position represented its own age distribution curve, except for the extreme angular positions of +10° and -10° whose curves almost 13.
overlapped. The reason for the difference between the curves of +5° and -5° angular positions rests mainly on a difference in their flow structures. While altering the column angular position from +10° to +5° (Figure 7a) led to a persistent memory of fluid maldistribution, tilting the column from 0° to -5° showed a marginal effect on the flow structure owing to the memory of a relatively uniform fluid distribution. Consequently, a more widened distribution of tracer signal was found for +5° in comparison with that of -5° (Figure 7b). On the other hand, the overlap of curves for the angular positions of +10° and -10° can be ascribed to the fact that these angular positions were the extreme tilt angles that the column experienced during the roll motion. Hence, any memory of fluid distribution stemming from previous lower angular positions was lost due to a dominant gasliquid segregation, leading to identical distribution curves. This observation highlights the fact that during column roll motions the fluid flow structures significantly changed inside the porous medium by altering the position leading to various behaviors in tracer mixing and residence time distribution. As expected, the broadening of tracer response curve and loss of symmetric distribution became more pronounced at high angular positions as a consequence of the progressive development of a segregated flow pattern.
5. Conclusion An Eulerian two-fluid CFD model was extended to describe the tracer mixing and residence time distribution (RTD) in a trickle bed reactor subjected to stationary tilts and roll motions. Experimental data obtained from wire-mesh sensors using a tracer injection method and RTD tools were employed to validate the simulation results. The CFD model was capable of reproducing the dominant features of the RTD curves measured experimentally where the incidence of dispersive phenomena and mixing in the course of column tilts and oscillations was predicted satisfactorily via the model. The simulation results indicated that the bed deviations from vertical configuration 14.
led to gravity-driven stratified flow zones in the packing which contributed to widen the asymmetric tracer signals giving rise to lower breakthrough times and long tails. Likewise, liquid back-mixing became more severe for rolling beds by increasing the column tilt angle and the motion period on account of the temporary evolving segregated fluid regions. From CFD simulations, it was also found that by altering positions during roll motions the fluid flow structures significantly changed inside the packing resulting in different mixing behaviors and residence time distributions. The developed CFD model and results presented in this work could be utilized for further investigations about radial mixing behaviors and chemical reaction performance of the trickle bed reactor under offshore conditions. For example, future works focusing on CFD-validated backmixing data could serve for developing Pe-number correlations applicable to sea conditions where the different motion degrees of freedom could be included as additional independent variables. Robustness of these correlations for design purposes could combine CFD simulations to save tedious experimentations with a few validated experimentations rather than relying only on extensive measurements as classically practiced.
Acknowledgments The authors gratefully acknowledge the Natural Sciences and Engineering Research Council of Canada and the Canada Research Chair on Sustainable Energy Processes and Materials for their financial support.
Nomenclature 𝑎̂
unit direction vector for the axis of rotation (-)
𝐶̿ q
inertial resistance tensor (1/m)
15.
dmin
minimum equivalent diameter of the area between three contacting spheres
dp
particle diameter (m)
D
column diameter (m)
̿q 𝐷
viscous resistance tensor (1/m2)
Dtr
tracer dispersion coefficient (m2/s)
E(θ)
residence time distribution
𝐹 D,q
total dispersion force exerted on phase q (N/m3)
𝐹 D,mech,q
mechanical dispersion force exerted on phase q (N/m3)
𝐹 gl
gas-liquid interaction force (N/m3)
𝐹q
total force term exerted on phase q (N/m3)
𝐹 qs
fluid-solid interaction forces, 𝐹 ls and 𝐹 gs, (N/m3)
g
acceleration due to gravity (m/s2)
H
distance from bed inlet (m)
Kgl
gas-liquid interaction coefficient (kg/ m3/s)
Kqs
momentum exchange coefficient of phase q (kg/ m3/s)
P
pressure (Pa)
𝑟
position vector (m)
16.
Sm
spread factor (m)
Str
tracer spread factor (m)
t
time (s)
𝑡̅
mean residence time (s)
T
motion period (s)
⃗⃗⃗ 𝑢′
velocity of the moving frame (m/s)
U
superficial velocity (m/s)
𝑣D
drift velocity (m/s)
𝑣q
phase velocity viewed from the stationary frame (m/s)
⃗⃗⃗ 𝑣′q
phase velocity viewed from the moving frame (m/s)
⃗⃗⃗ l,ax 𝑣′
liquid axial velocity (m/s)
𝑣𝑡 ⃗⃗⃗
translational frame velocity (m/s)
||.||
absolute value of a vector
Greek letters βq
saturation of phase q (-)
dimensionless time (t/𝑡̅)
rolling angle function (radian)
17.
amp
tilt angle amplitude (radian)
ɛ
bed porosity (-)
ɛq = βq× ɛ
volume fraction of phase q (-)
Μ
viscosity (kg/m.s)
Ρ
density (kg/m3)
Σ
surface tension (N/m)
scalar
Τ
stress tensor (Pa)
𝜔 ⃗
angular velocity (radian/s)
Subscripts D
dispersion
g
gas
l
liquid
mech
mechanical
p
particle
s
solid
References [1]
J.T. Cullinane, N. Yeh, E. Grave, Effects of tower motion on packing efficiency, 14376618.
MS SPE Conference Paper, Macae, Brazil, 2011. [2]
R.H. Weiland, N.A. Hatcher, J. Seagraves, Choosing Tower Internals for LNG, Shale Gas, and Tail Gas Treating. Paper presented at: SOGAT, Abu Dhabi, UAE, 2013.
[3]
F.S. Mederos, J. Ancheyta, J. Chen, Review on criteria to ensure ideal behaviors in tricklebed reactors, Appl. Catal. A Gen. 355 (2009) 1–19.
[4]
V. V Ranade, R. Chaudhari, P.R. Gunjal, Trickle bed reactors: reactor engineering & applications, Elsevier, 2011.
[5]
M. Schubert, M. Hamidipour, C. Duchesne, F. Larachi, Hydrodynamics of cocurrent twophase flows in slanted porous media—Modulation of pulse flow via bed obliquity, AIChE J. 56 (2010) 3189–3205.
[6]
A. Motamed Dashliborun, F. Larachi, Hydrodynamics of gas–liquid cocurrent downflow in floating packed beds, Chem. Eng. Sci. 137 (2015) 665–676.
[7]
G.P. Assima, A. Motamed-Dashliborun, F. Larachi, Emulation of gas-liquid flow in packed beds for offshore floating applications using a swell simulation hexapod, AIChE J. 61 (2015) 2354–2367.
[8]
A. Motamed Dashliborun, F. Larachi, M. Hamidipour, Cyclic operation strategies in inclined and moving packed beds—Potential marine applications for floating systems, AIChE J. 62 (2016) 4157–4172.
[9]
A. Motamed Dashliborun, F. Larachi, M. Schubert, Offshore Floating Packed‐ Bed Reactors: Key Challenges and Potential Solutions, Chem. Eng. Technol. 40 (2017) 1975– 1984. 19.
[10] A. Motamed Dashliborun, J. Zhang, S.M. Taghavi, F. Larachi, 110th Anniversary: Marinization of Multiphase Reactors through the Prism of Chemical Engineers, Ind. Eng. Chem. Res. 58 (2019) 2607-2630. [11] H. Bouteldja, M. Hamidipour, F. Larachi, Hydrodynamics of an inclined gas–liquid cocurrent upflow packed bed, Chem. Eng. Sci. 102 (2013) 397–404. [12] P. Gauthier, S. Clément, C. Vincent, P.S. Claire, M. Thomas, A. Pascal, F. Manel, B. Philippe, W. Graeme, Hexapod Pilot Tests Determine the Influence of 3D Motions on the Performance of an Amine-Based Acid Gas Removal Unit Installed on a Floating Support. 18743-MS IIPTC Conference Paper, Bangkok, Thailand, 2016. [13] A.M. Dashliborun, F. Larachi, M. Schubert, Hydrodynamics of gas-liquid cocurrent upflow in oscillating packed beds for offshore marine applications, Chem. Eng. Sci. 170 (2017) 583–596. [14] A. Wongkia, F. Larachi, S. Assabumrungrat, Hydrodynamics of countercurrent gas-liquid flow in inclined packed beds–A prospect for stretching flooding capacity with small packings, Chem. Eng. Sci. 138 (2015) 256–265. [15] I. Iliuta, F. Larachi, Hydrocarbon hydrodesulfurization in vertical, inclined and oscillating trickle beds–Hydrodynamics & reactor performance for offshore petroleum marine applications, Fuel. 186 (2016) 35–49. [16] I. Iliuta, F. Larachi, Three–dimensional simulations of gas–liquid cocurrent downflow in vertical, inclined and oscillating packed beds, AIChE J. 62 (2016) 916–927. [17] A. Motamed Dashliborun, M. Hamidipour, F. Larachi, Hydrodynamics of inclined packed
20.
beds under flow modulation – CFD simulation and experimental validation, AIChE J. 63 (2017) 4161–4176. [18] A. Motamed Dashliborun, F. Larachi, CFD Study and Experimental Validation of Multiphase Packed Bed Hydrodynamics in the Context of Rolling Sea Conditions, AIChE J. 65 (2019) 385–397. [19] Y. Wang, J. Chen, F. Larachi, Modelling and simulation of trickle‐bed reactors using computational fluid dynamics: A state‐of‐the‐art review, Can. J. Chem. Eng. 91 (2013) 136–180. [20] M.P. Dudukovic, Ž. V Kuzeljevic, D.P. Combest, Three‐Phase Trickle‐Bed Reactors, Ullmann's Encyclopedia of Industrial Chemistry. Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA, 2014: 1-40. [21] A. Atta, S. Roy, K.D.P. Nigam, Prediction of pressure drop and liquid holdup in trickle bed reactor using relative permeability concept in CFD, Chem. Eng. Sci. 62 (2007) 5870–5879. [22] F. Augier, M. Fourati, Y. Haroun, Characterization and modelling of a maldistributed Trickle Bed Reactor, Can. J. Chem. Eng. 95 (2017) 222–230. [23] A. Motamed Dashliborun, A. Füssel, F. Larachi, Prospect of open-cell solid foams for floating-platform multiphase reactor applications – Maldistribution susceptibility and hydrodynamic behavior, Chem. Eng. J. 332 (2018) 596-607. [24] P.R. Gunjal, V. V Ranade, R. V Chaudhari, Liquid distribution and RTD in trickle bed reactors: experiments and CFD simulations, Can. J. Chem. Eng. 81 (2003) 821–830. [25] K. Lappalainen, E. Gorshkova, M. Manninen, V. Alopaeus, Characteristics of liquid and 21.
tracer dispersion in trickle-bed reactors: Effect on CFD modeling and experimental analyses, Comput. Chem. Eng. 35 (2011) 41–49. [26] K.M. Kan, P.F. Greenfield, Multiple hydrodynamic states in concurrent two phase down flow through packed beds, Ind. Eng. Chem. Process Desigen Dev. 17 (1978) 482–485. [27] L. Moskowitz, Estimates of the power spectrums for fully developed seas for wind speeds of 20 to 40 knots, J. Geophys. Res. 69 (1964) 5161–5179. [28] J.M.J. Journée, W.W. Massie, Offshore hydromechanics, Delft University of Technology, Delft (the Netherlands), 2000. [29] P. L. Mills, M.P. Dudukovic, Convolution and deconvolution of nonideal tracer response data with application to three-phase packed-beds, Comput. Chem. Eng. 13 (1989) 881–898. [30] M. Schubert, A. Khetan, M.J. Da Silva, H. Kryk, Spatially resolved inline measurement of liquid velocity in trickle bed reactors, Chem. Eng. J. 158 (2010) 623–632. [31] A. Motamed Dashliborun, H. Härting, M. Schubert, F. Larachi, Process intensification of gas–liquid downflow and upflow packed beds by a new low‐shear rotating reactor concept, AIChE J. 63 (2017) 283–294. [32] M.J. Da Silva, E. Schleicher, U. Hampel, Capacitance wire-mesh sensor for fast measurement of phase fraction distributions, Meas. Sci. Technol. 18 (2007) 2245-2251. [33] Z. Solomenko, Y. Haroun, M. Fourati, F. Larachi, C. Boyer, F. Augier, Liquid spreading in trickle-bed reactors: Experiments and numerical simulations using Eulerian–Eulerian twofluid approach, Chem. Eng. Sci. 126 (2015) 698–710. [34] A. Attou, C. Boyer, G. Ferschneider, Modelling of the hydrodynamics of the cocurrent gas– 22.
liquid trickle flow through a trickle-bed reactor, Chem. Eng. Sci. 54 (1999) 785–802. [35] A. Attou, G. Ferschneider, A two-fluid hydrodynamic model for the transition between trickle and pulse flow in a cocurrent gas–liquid packed-bed reactor, Chem. Eng. Sci. 55 (2000) 491–511. [36] K. Lappalainen, M. Manninen, V. Alopaeus, CFD modeling of radial spreading of flow in trickle-bed reactors due to mechanical and capillary dispersion, Chem. Eng. Sci. 64 (2009) 207–218. [37] M. Fourati, V. Roig, L. Raynal, Liquid dispersion in packed columns: experiments and numerical modeling, Chem. Eng. Sci. 100 (2013) 266–278. [38] P. Marchot, D. Toye, M. Crine, A.-M. Pelsser, G. L’homme, Investigation of Liquid Maldistribution in Packed Columns by X-Ray Tomography, Chem. Eng. Res. Des. 77 (1999) 511–518. [39] A. Fluent, ANSYS fluent theory guide 15.0, Inc, Canonsburg, PA. (2013). [40] A. Atta, M. Hamidipour, S. Roy, K.D.P. Nigam, F. Larachi, Propagation of slow/fast-mode solitary liquid waves in trickle beds via electrical capacitance tomography and computational fluid dynamics, Chem. Eng. Sci. 65 (2010) 1144–1150. [41] M. Hamidipour, J. Chen, F. Larachi, CFD study and experimental validation of trickle bed hydrodynamics under gas, liquid and gas/liquid alternating cyclic operations, Chem. Eng. Sci. 89 (2013) 158–170. Table Captions Table 1
Equations of Eulerian two-fluid porous media and scalar transport in CFD model employed for simulations of stationary tilted (angles of 0°-15°) and rolling 23.
(amplitudes of 0°-15° and periods of 5-40 s) trickle beds. Figure captions Figure 1
Schematic diagram of the experimental setup for gas-liquid cocurrent downflow trickle bed embarked on a hexapod robot and instrumented with WMSs.
Figure 2
(a) Roll motion of the hexapod robot and coordinate systems in computational domain, (b) axial and radial sections of the used mesh structure in the 3D geometry along with representatives of injected inlet tracer pulse and computed outlet tracer pulse.
Figure 3
Comparison of experimental and numerical RTD responses for three stationary tilted bed configurations with (a) 0°, (b) 5°, and (c) 10° angles (Ug = 0.138 m/s, Ul = 0.0024 m/s).
Figure 4
Comparison of experimental and numerical RTD responses for rolling beds with (a) 5°, T = 20 s; (b) 10°, T = 20 s; (c) 10°, T = 5 s (Ug = 0.138 m/s, Ul = 0.0024 m/s).
Figure 5
Simulation results of the evolution of dynamic tracer signals at two bed heights in response to (a) stationary tilted configurations, (b) 20 s-period roll motion with different amplitudes, and (c) 10°-amplitude roll motion with different periods (Ug = 0.138 m/s, Ul = 0.0024 m/s).
Figure 6
Comparison of the computed tracer signal for static tilted beds and rolling beds under the same amplitude of (a) 5° and (b) 10° at H = 50 cm (Ug = 0.138 m/s, Ul = 0.0024 m/s).
Figure 7
Comparison of the tracer signal for different instances of a rolling bed with 10° and T =20 s, (a) sinusoidal path of column roll motion and (b) computed tracer signals at H = 50 cm (Ug = 0.138 m/s, Ul = 0.0024 m/s).
24.
Table 1 Continuity equation
Momentum equation
q q q q vq 0 , (q = l, g) t
(1)
g l
(2)
dv d q q vq q q vq vq q q (2 vq ( r ) r t ) t dt dt
(3)
q P q q q g Fq
vq vq u , u vt r amp cos(
(4)
2 t ) T 2
(5)
d 2 2 amp ( ) sin t , dt T 2 T
aˆ
(6)
q q q vq vqT q q q .vq I
(7)
Fg Fgl Fgs FD, g
(8)
Fl Fgl Fls FD,l
(9)
1 Fqs q Dq vq q vq Cq vq Kqs vq , (q = l, g) 2
(10)
Porous resistances
Kls 180l
(1 )2 (1 ) 1.8l vl 2 2 l d p l d p
(1 g )2 1 K gs 180 g g d p2 1 g
Gas-liquid interaction
2 3
2/3
1 g 1 1.8 g d p 1 g
(11) 1/3
vg
Fgl K gl vg - vl (1 g )2 1 K gl 180 g g d p2 1 g
(12)
(13)
2/3
1 g 1 1.8 g d p 1 g
1/3
vg - vl
(14)
25.
Capillary pressure
g 1 1 1 Pc Pg Pl 2 l ( )F d p d min l 1 l
1/3
(15)
1
d min
3 1 2 d p 2
g F l
g 1 88.1 l
(16)
(17)
Capillary dispersion
g 1 2 1 1 Pc l ( )( )F 3 1 d p d min l 1 l
Mechanical dispersions
FD,mech,l Kls vD ,l K gl (vD ,l vD , g )
(19)
FD, mech, g K gs vD , g K gl (vD , g vD ,l )
(20)
vD , q
Sm
q
( vq q (vq . q )
vq vq
) , (q = l, g)
4/3
l
(18)
(21)
Sm 0.015 d p
(22)
UDS transport equation
l ll l l vll l l Dtr l t
(23)
Dispersion coefficient
Dtr Str vl, ax , Str Sm
(24)
26.
Figure 1
27.
Figure 2 a
b Yʹ
Xʹ
Yʹ
Xʹ
Inlet pulse
Zʹ
Zʹ
-Θ
+Θ Xʹ Z' Y'
Y
Outlet pulse
28.
Figure 3 a
b 0.15
0.15
Θamp = 0
0.12
EXP
Θamp = 5
0.12
EXP
CFD
E (θ)
E (θ)
CFD
0.09
0.09
0.06
0.06
0.03
0.03
0
0 0.5
1
1.5
2
θ (-)
2.5
3
0
0.5
1
1.5
θ (-)
2
2.5
3
c 0.15
Θamp = 10
0.12
EXP
CFD
E (θ)
0
0.09 0.06
0.03 0 0
0.5
1
1.5
θ (-)
2
2.5
3
29.
Figure 4 b
a 0.15
0.15
Θamp = 5 , T = 20 s
0.12
EXP
Θamp = 10 , T = 20 s
0.12
EXP
CFD
E (θ)
E (θ)
CFD
0.09
0.09
0.06
0.06
0.03
0.03
0
0 0.5
1
1.5
2
θ (-) c
0.15
2.5
3
0
0.5
1
1.5
θ (-)
2
2.5
3
Θamp = 10 , T = 5 s
0.12
Exp
CFD
E (θ)
0
0.09 0.06 0.03 0 0
0.5
1
1.5
θ (-)
2
2.5
3
30.
Figure 5 a 0.2
Inlet 5° 15°
H = 5 cm
Normalized signal (-)
Stationary
0.16
0° 10°
0.12 0.08 H = 85 cm
0.04 0 0
20
40
60
Time (s)
b
100
c H = 5 cm Roll motion (T = 20 s)
0.16
0.2 Inlet
5°
10°
15°
Normalized signal (-)
0.2
Normalized signal (-)
80
0.12 H = 85 cm
0.08 0.04 0
H = 5 cm Roll motion (Θamp = 10 )
0.16
Inlet
5s
10 s
20 s
0.12 H = 85 cm
0.08 0.04 0
0
20
40
Time (s)
60
80
0
20
40
Time (s)
60
80
31.
Figure 6 a
b 0.15
0.15
0.12
Static tilted bed (10 ) Θamp = 10 , T = 20 s Θamp = 10 , T = 40 s
Normalized signal (-)
Normalized signal (-)
Static tilted bed (5 ) Θamp = 5 , T = 20 s Θamp = 5 , T = 40 s
0.12
0.09
0.09
0.06
0.06
0.03
0.03
0
0 0
20
40
Time (s)
60
80
0
20
40
Time (s)
60
80
32.
Figure 7 b
a
0.15 +10
Θ( )
10 5
+5
0
0
0
10
20
30
40
-5
-5
50 -10
-10
60
Normalized signal (-)
15
+ 10° 0° - 10°
0.12
+ 5° - 5°
0.09 0.06 0.03
0
-15
Time (s)
0
20
40
Time (s)
60
80
33.
Research Highlights ►Tracer dispersion in trickle beds was studied numerically under marine conditions. ►Eulerian two-fluid CFD model was able to describe tracer mixing and RTD. ►Column tilts and roll motions were responsible for widening of tracer signals. ►Variation of flow structures with roll motion caused different mixing behaviors.
34.