Hydrodynamics of gas-liquid counter-current flow in solid foam packings

Solid foam materials combine high voidage and high surface area. These two properties are advantageous for use in chemical reactors due to the low frictional pressure drop and relatively high surface area that may be used for catalyst deposition. Hydrodynamic parameters such as liquid holdup, pressure drop, and flow regimes similar to those for packed beds, have been obtained for the gas and liquid flows through these solid foam packings. The open-celled solid foam packings used were in the range of 5-40 pores per linear inch (ppi). The regimes studied are two high liquid holdup regimes and a low liquid holdup regime (trickle flow regime). Also the flooding points for counter-current flow have been determined.     

Trickle bed hydrodynamics and flow regime transition at elevated temperature for a Newtonian and a non-Newtonian liquid

Despite the hydrodynamics of trickle beds experiencing high pressures has become largely documented in the recent literature, trickle bed hydrodynamic behavior at elevated temperatures, on the contrary, largely remains terra incognita. This study's aim was to demonstrate experimentally the temperature shift of trickle-to-pulse flow regime transition, pulse velocity, two-phase pressure drop, liquid holdup and liquid axial dispersion coefficient. These parameters were determined for Newtonian (air-water) and non-Newtonian (air-0.25% Carboxymethylcellulose (CMC)) liquids, and the various experimental results were compared to available literature models and correlations for confrontation and recommendations. The trickle-to-pulse flow transition boundary shifted towards higher gas and liquid superficial velocities with increasingly temperatures, aligning with the findings on pressure effects which likewise were confirmed to broaden the trickle flow domain. The Larachi-Charpentier-Favier diagram [Larachi et al., 1993, The Canadian Journal of Chemical Engineering 71, 319-321] provided good predictions of the transition locus at elevated temperature for Newtonian liquids. Conversely, everything else being kept identical, increasingly temperatures occasioned a decrease in both two-phase pressure drop and liquid holdup; whereas pulse velocity was observed to increase with temperature. The Iliuta and Larachi slit model for non-Newtonian fluids [Iliuta and Larachi, 2002, Chemical Engineering Science 46, 1233-1246] predicted with very good accuracy both the pressure drops and the liquid holdups regardless of pressure and temperature without requiring any adjustable parameter. The Burghardt et al. [2004, Industrial and Engineering Chemistry Research 43, 4511-4521] pulse velocity correlation can be recommended for preliminary engineering calculations of pulse velocity at elevated temperature, pressure, Newtonian and non-Newtonian liquids. The liquid axial dispersion coefficient (D_ax) extracted from the axial dispersion RTD model revealed that temperatures did not affect in a substantial manner this parameter. Both Newtonian and power-law non-Newtonian fluids behaved qualitatively similarly regarding the effect of temperature.     

Pressure drop hysteresis in trickle bed reactors

An understanding of the hydrodynamics of trickle bed reactors (TBR) is essential for their design and prediction of their performance. Flow variables, packing characteristics, physical properties of fluids and operation modes influence the behavior of the TBR. The existence of multiple hydrodynamic states or hysteresis (pressure drop, liquid holdup, catalyst wetting, gas-liquid mass transfer) is due to the different flow structures in the packed bed and can be attained by a set of different operating procedures. Experiments were performed to study the effect of liquid and gas velocity, liquid surface tension, liquid viscosity and the particle diameter of the packing on two-phase pressure drop hysteresis. The parallel zone model for pressure drop hysteresis in the trickling flow was used for analysis of experimental data and flow structure. Theoretically predicted pressure drop hysteresis loop is in satisfactory agreement with experimental data.     

Numerical and Experimental Study of Catalyst Loading and Body Effects on a Gas‐Liquid Trickle‐Flow Bed

The influence of tortuosity and fluid volume fractions on trickle‐flow bed performance was analyzed. Hydrodynamics of the gas‐liquid downward flow through trickle beds, filled with industrial trilobe catalysts, were investigated experimentally and numerically. The pressure drop and liquid holdup were measured at different gas and liquid velocities and in two different loading methods, namely, sock and dense catalyst loading. The effect of sharp corners on hydrodynamic parameters was considered in a bed with rectangular cross section. The reactor was simulated, considering a three‐phase model, appropriate porosity function, and interfacial forces based on the Eulerian‐Eulerian approach. Computational fluid dynamics (CFD) simulation results for pressure drop and liquid holdup agreed well with experimental data. Finally, the velocity distribution in two types of loading and the effect of bed geometry in CFD results demonstrated that pressure drop and liquid holdup were reduced compared to a cylindrical one due to high voidage at sharp corners.     

Hydrodynamics in a pilot‐scale cocurrent trickle‐bed reactor at low gas velocities

Hydrodynamic data obtained from laboratory‐scale trickle‐beds often fail to accurately represent industrial‐scale systems with high packing aspect ratios and column‐to‐particle diameter ratios. In this study, pressure drop, liquid holdup, and flow regime transition were investigated in a pilot‐scale trickle‐bed column of 33 cm ID and 2.45 m bed height packed with 1.6 mm × 8.4 ± 1.4 mm cylindrical extrudates for air‐water mass superficial velocities of 0.0023 – 0.094 kg/m²s and 4.5 – 45 kg/m²s, respectively, at atmospheric pressure. Significant deviation was observed from pressure drop and liquid holdup correlations at low liquid flows rates, corresponding to gravity‐driven flow limit. Likewise, liquid saturation is overestimated by correlations at high liquid flow rates, owing to significantly reduced wall effects. Lastly, trickle‐to‐dispersed bubble flow and trickle‐to‐pulsing flow regime transitions are reported using a combination of visual observations and analysis of the magnitude of local pressure fluctuations within the column. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2560–2569, 2018     

Magnetohydrodynamics of trickle bed reactors: Mechanistic model, experimental validation and simulations

An isothermal one-dimensional two-fluid magnetohydrodynamic (MHD) model based on the volume average mass, charge, and momentum balance equations and the Maxwell's equations coupled via the Lorentz force and Ohm's law was developed for the prediction of the two-phase pressure drop and the total liquid holdup in trickle bed reactors experiencing a homogeneous transverse magnetic field. The slit model approximation and the drift flux Kozeny-Carman approach were extended for the derivation of appropriate drag force closures required in the conservation equations, respectively, in the trickle flow regime and in the dispersed bubble flow regime. The expression of liquid-solid drag was adapted to take into account the influence of the magnetic field on the laminar term and the damping of turbulent/inertial term via the Hartman number and the liquid-to-bed electrical resistance ratio. Associating these drag forces with the proposed model resulted in a fully predictive MHD approach for trickle beds. Several model limiting formulations were derived for an electrically conducting fluid flowing downwards with a stagnant gas (pure trickle flow) to yield liquid holdup, as well as for single-phase upward conditions to yield the single-phase pressure drops.     

Power-law fluids flow through multiparticle system

A study on the flow of power-law fluids through a multi-particle system including both fixed bed and fluidized bed is presented. Equations for the pressure drop, the minimum fluidization velocity, and the bed expansion are obtained by extending the Blake-Kozeny's equation for the pressure drop through packed beds to power-law fluids. Bed expansion equations are also obtained by extending the Richard-son-Zaki's theory for the drag force in a multiparticle suspension to power-law fluids. These equations are compared with experimental data.     

An investigation of liquid maldistribution in trickle beds

The influence of liquid maldistribution at the top of the packing on flow characteristics in packed beds of gas and liquid cocurrent downflow (trickle beds) is experimentally investigated. Particular attention is paid to the effect of gas and liquid flow rates on flow development. Tests are made in the trickling and pulsing flow regimes. A uniform, a half-blocked and a quarter-blocked liquid distributor is tested. Packings of various sizes and shapes are employed. Data are presented on pressure drop and liquid holdup as well as trickling to pulsing flow transition. Diagnosis of radial and axial liquid distribution is made by means of conductance probes. The effects of liquid foaming, bed pre-wetting, top-bed material, and blockage midway the bed on liquid distribution are also examined. Overall, liquid waves in the pulsing flow regime have a beneficial effect, promoting uniform liquid distribution in the bed cross section.     

Hydrodynamics of gas–liquid flow in micropacked beds: Pressure drop,liquid holdup,and two‐phase model

Hydrodynamics of gas–liquid two‐phase flow in micropacked beds are studied with a new experimental setup. The pressure drop, residence time distribution, and liquid holdup are measured with gas and liquid flow rates varying from 4 to 14 sccm and 0.1 to 1 mL/min, respectively. Key parameters are identified to control the experimentally observed hydrodynamics, including transient start‐up procedure, gas and liquid superficial velocities, particle and packed bed diameters, and physical properties of the liquids. Contrary to conventional large packed beds, our results demonstrate that in these microsystems, capillary forces have a large effect on pressure drop and liquid holdup, while gravity can be neglected. A mathematical model describes the hydrodynamics in the micropacked beds by considering the contribution of capillary forces, and its predictions are in good agreement with experimental data. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4694–4704, 2017     

Bed structure and its impact on liquid distribution in a trickle bed reactor

Trickle bed reactors, which has been a workhorse for the process and refining industry for many decades, are progressively being challenged to provide solutions to deep processing of feedstocks. It is known that the structure of the packed bed which is formed with a certain arrangement of catalyst particles in the three-dimensional space within the reactor modulates in an unknown fashion the flow of fluids in the trickle bed, and in turn affects the conversion and selectivity in the trickle bed. Under deep processing conditions, the impact of the bed structure in modulating the overall reactor performance in a trickle bed is not as yet established. The question begets three sequential studies: estimating and quantifying the bed structure, measuring the liquid distribution, and estimating transport parameters (that are dependent on the bed structure and liquid distribution) so that the overall performance metrics as a reactor may be quantified. This contribution relates to the second of these questions, the first being already addressed to some extent by our earlier work. The current investigation aims at quantifying the effect of structure of the packed bed on hydrodynamics of the reactor. The impact of various packing techniques is discussed along with the development of correlations for two-phase pressure drop and dynamic liquid holdup. Liquid distribution is studied in depth for various operating parameters such as gas and liquid superficial velocities and column aspect ratio for uniform and non-uniform packing methods. The packing devices consist of various inserts attached to a hopper which can generate packing structures having void fraction in the range of 37.2%–46.4%. The maldistribution factor and flow maps for various aspect ratio of column suggest that maldistribution rises along with the increased channeling effect along the height of the column. Uniformly packed bed were measurably less prone to maldistribution along the length than the non-uniformly packed beds.     

Role of gas phase in the deposition dynamics of fine particles in trickle-bed reactors

Experiments were conducted to study the role of gas velocity in the capture of fine particles from non-aqueous suspensions circulated in co-current down-flow trickle flow reactors. The rate of filtration and pressure drop in the trickle bed were investigated using surfactant-stabilized kaolin-containing kerosene suspensions. It was determined that the filter coefficient was sensitive to liquid holdup and specific deposit. The initial collection efficiencies were compared with predictions based on existing theories. Agreement was generally not good with the exception for the limit of low superficial gas velocity. A general correlation establishing the relationship between the filtration rate and the liquid holdup in trickle beds was proposed to reconcile the experimental data with existing filtration theories.     

Structure of trickle-to-pulse flow regime transition and pulse dynamics at elevated temperature in slow-mode cyclic operation

The effects of temperature and pressure on the structure of the trickle-to-pulse flow regime transition in slow-mode cyclic operation in trickle-bed reactors were reported. The relationship between liquid holdup and liquid velocities at the trickle-to-pulse flow transition in cyclic operation, the shock wave behavior as a function of bed depth, as well as the pulsing flow regime properties were investigated for Newtonian (air-water) and non-Newtonian (air-0.25% carboxymethylcellulose (CMC)) liquids. At a given temperature, the breakthrough, plateau and decay times of the shock wave were found to decrease with bed depth. The pulse velocity and pulse frequency for pulsing flow regime both in cyclic operation and in natural pulsing (constant-throughput operation) were observed to increase with temperature. However, increasing the reactor pressure led to increased pulse frequency and decreased pulse velocity. Analysis of the transition liquid holdups for natural pulse flow and cyclic operation revealed that the liquid holdup decreased with temperature and pressure. The transition liquid holdups and superficial liquid pulse velocities in symmetric peak-base cyclic operation surpassed those in constant-throughput operation for given temperature, pressure and gas velocity, giving rise to wider trickle flow regime area in cyclic operation. The behavior of both Newtonian and power-law non-Newtonian fluids was similar regarding the effect of temperature, pressure and gas velocity.     

Nonequilibrium thermomechanical modeling of liquid drainage/imbibition in trickle beds

We extend the macroscopic nonequilibrium thermomechanical multiphase flow theory proposed by Hassanizadeh and Gray for porous media to analyze a set of drainage and imbibition experiments in trickle beds. The nonequilibrium model rests on inclusion of mass and momentum conservations for the gas‐liquid interface, nonequilibrium capillary pressure, Helmholtz free energy gradients in the body supply of momentum for fluid bulk phases and gas‐liquid interface, and mass exchange rates between interface and fluid bulks accounting for production and destruction of gas‐liquid interfacial area. To solve the nonequilibrium model, entropy‐consistent constitutive relationships are derived and calibrated using liquid holdup and bed pressure drop measurements in drainage and imbibition. The model captures very well the decay (drainage), and breakthrough (imbibition) curvatures of liquid holdup and pressure drop kinetics, while model closer inspection allows assessing the role of nonequilibrium capillary pressure and of dynamic interfacial mass exchanges for the production/destruction of interfacial area. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3123–3134, 2012     

Pressure buildup in gas‐liquid flow through packed beds due to deposition of fine particles

In order to understand the increase in pressure drop in hydrotreating reactors due to deposition of fine solids, experiments were conducted with a model suspension of kaolin clay in kerosene. The suspension was circulated through packed beds of catalyst pellets in the trickle‐flow and pulse‐flow regimes, and the increase in pressure drop measured as a function of particle concentration in the bed. The increase in pressure drop was linear with particle concentrations over the range 0–60 kg.m^?3. A consistent approach to modeling the pressure drop behavior was to determine an effective porosity of the packed bed as a function of the concentration of fine particles, then use this porosity in the Ergun equation as a basis for calculating the two‐phase pressure drop.     

INTERPRETATION OF FLOW NONUNIFORMITY AND HYSTERESIS WITH A CAPILLARY ARRAY MODEL

A novel capillary array model is proposed to shed light on the development of themaldistribution of cocurrent downward gas-liquid flow and the hysteretic performance behavior in apacked column.The model is based on the principle of nonequilibrium thermodynamics and incombination with lateral random walk of elemental liquid rivulets.The liquid distribution over aone-dimensional array of capillaries is simulated and the basic features of gas-liquid flow in packedbeds are demonstrated.With proper correspondence of hysteresis branches with nonuniformity of flowdistribution assumed,the experimentally observed hysteresis in pressure drop,liquid holdup and masstransfer rate can be qualitatively simulated.Strenuous efforts are still required for further developingthis model into a predictive tool for the evaluation of performance of packed-bed type devices.     

Hydrodynamics of inclined packed beds under flow modulation ‐ CFD simulation and experimental validation

A three‐dimensional unsteady‐state Eulerian multi‐fluid CFD model was developed to simulate the hydrodynamic behavior of inclined gas‐liquid cocurrent downflow packed beds under ON‐OFF liquid, ON‐OFF gas, and gas/liquid alternating cyclic operations. Validation of the CFD simulation results was performed with experimental data provided by electrical capacitance tomography imaging. Incorporation in the Eulerian multifluid CFD model of capillary pressure and mechanical dispersion force was essential to accurately capture the transient spatial heterogeneities arising in tilted packed beds under different cyclic modulation strategies. The applied CFD model was able to satisfactorily predict the values of liquid holdup and pressure drop as well as the morphological characteristics of the traveling waves inside the bed for the examined flow modulations. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4161–4176, 2017     

纤维填充滴流反应器的流体力学

<正> 1 引言 近期的研究表明,无机纤维催化剂(玻璃纤维、碳纤维、氧化铝纤维等)具有较高的活性、选择性和稳定性,如氧化铝纤维为载体的裂解汽油加氢。但到目前为止,有关纤维滴流床的化工数据几乎未见报道。本工作的目的是对纤维滴流床进行流体力学研究,考察操作条件、填料性质、填充方式变化时流体流动性质如压降、持液量等的变化规律,以求建立计算压降和持液量的关联式,为纤维滴流床反应器的设计和放大提供基础数据。     

Cocurrent gas—liquid flow in packed columns

A model is proposed for cocurrent gas liquid flow through a packed bed. For a given packing, gas and liquid flow rates, we proposed that (i) liquid holdup is a function only of pressure gradient and liquid flow rate and (ii) pressure gradient is only a function of liquid holdup and gas flow rate. Equations are presented which permit the prediction of pressure gradient and liquid holdup for cocurrent upflow and cocurrent downflow in a packed bed. Predictions from the model are shown to be in reasonable agreement with the experimental observations of Turpin and Huntington.     

低、高压滴流床中压降和持液量计算的统一关系式

基于对滴流床中气液两相流动特征尺度的分析,提出以修正的相摩擦系数对相Reynolds数进行关联,获取低、高压滴流床中压降和持液量计算的统一关联式的方法.对于滴流床中单相不饱和流（液体流动,气体静止）情形,以及低压和高压滴流床中两相流、高气液作用情形,收集了文献报道的不同大小颗粒、不同物系的大量实验数据,以相摩擦系数对相Reynolds数进行关联,得到新的压降和持液量计算式,其物理意义明确,计算精度得以提高.