Kang Yu,Weijie Wang,Tao Zhang,Yumei Yong*,Chao Yang,**

1 CAS Key Laboratory of Green Process and Engineering,Institute of Process Engineering,Chinese Academy of Sciences,Beijing 100190,China

2 School of Chemical Engineering,University of Chinese Academy of Sciences,Beijing 100049,China

3 PetroChina Petrochemical Research Institute,Beijing 102206,China

Keywords:Internals Phase holdup Backmixing Slightly-expanded-bed reactor Multiphase flow Hydrodynamics

ABSTRACT Five different internals were designed,and their effects on phase holdup and backmixing were investigated in a gasliquid concurrent upflow reactor where the spherical alumina packing particles of three diameters(3.0,4.5 and 6.0 mm)were slightly expanded under the conditions of varied superficial gas velocities(6.77×10-2-3.61×10-1 m·s-1)and superficial liquid velocities(9.47×10-4-2.17×10-3 m·s-1).The experimental results show that the gas holdup increases with the superficial gas velocity and particle size,opposite to the variational trend of liquid holdup.When an internal component is installed amid the upflow reactor,a higher gas holdup,a less liquid holdup and a larger Peclet number characterizing the weaker backmixing are obtained compared to those in the bed without internals under the same operating conditions.Additionally,the minimal backmixing is observed in the reactor equipped with the internals with a novel multi-step design.Finally,empirical correlations were proposed for estimating gas holdup,liquid holdup and Peclet number with the relative deviations within 11%,12%and 25%,respectively.

1.Introduction

The slightly-expanded-bed reactor with gas and liquid flowing upwards is a new type of gas-liquid-solid three-phase reactors,in which the liquid phase acts as a continuous phase and the gas phase flows through the catalyst granular bed as dispersed bubbles[1].Compared to the conventional residue hydrogenation using fixed beds,the upflow slightly-expanded-bed reactor has been attracting widespread attention due to its slower rising pressure drop,longer operating cycles and more effective contact between reactants and catalysts[2-5].However,some deficiencies of unstable hydrodynamic performance and severe backmixing[4,5]still exist and have been observed in industrial operations.In response to these problems,installing a gas-liquid redistributor as the internal component in an upflow reactor is considered to be the most straightforward and effective solution,which is conducive to promote a more homogeneous radial distribution of gas and liquid,further improving their mixing and mass transfer efficiency.

Undoubtedly,the existence of internals has an important influence on the multiphase flow and mixing in a reactor,and at the same time,the hydrodynamics that we often focus on is also implicated in changing under this influence.For instance,Hadi et al.[6]reported that installing internals in their square gas-solid fluidized bed brought about slight decrease in bubble size,significant reduction in bubble holdup,and noticeable disturbance to the bubble flow pathways.In addition,the shape and structure of an internal component can affect its performance distinctly.Taking gas-liquid distributors as an example,the industrial gas-liquid distributors are generally classified into four types[7]:perforated plate,multiport chimney,bubble cap and gas-lift distributors,with respective advantages and disadvantages.In order to compare the distribution performance of three types of distributors at the inlet of a trickle bed,Bazer-Bachi et al.[8]introduced a gamma-ray tomography to visualize the gas-liquid distribution,and their results showed that the multi-aperture chimney trays performed better than gas-lift and bubble cap systems in terms of the uniformity and sensitivity.After the importance of internals and the impact of their structures have been fully recognized,the internals can be designed and manufactured scientifically to improve the performance and hydrodynamic characteristics of upflow reactors.U.S.patent No.6554994 B1[9]described a gas-liquid redistributor consisting of a multi-hole distribution plate and a plurality of risers with air inlet holes connected to the plate,which achieved uniform distribution for hydrogen and heavy feedstock flowing upwards through a fixed bed.A lot of reactor space was occupied by this redistributor,and the small holes on the riser side were easily plugged by particles.

Gas and liquid holdups have been extensively studied in fluidized beds[10-12],packed beds[13-26]and expanded beds[26,27]with various measurement methods.In recent years,some advanced photographic and measuring techniques such as ultrafast electron beam Xray tomography[11],electrical capacitance tomography[13],magnetic resonance imaging[25],and gas dynamic tracer technique[26]have been increasingly applied in multiphase reactors to facilitate visualization of multiphase flow fields,simplify data processing and improve measurement precision.Furthermore,it is meaningful to set up a hydrodynamic correlation or model[13,15,17,18,21,28]for a class of reactors,and after that the researchers can continue to optimize and take advantage of them to forecast the hydrodynamic characteristics of the reactors.Attou and Ferschneider[28]developed a simple hydrodynamic model taking into account the interphase interaction forces to estimate the pressure drop and liquid holdup in packed-bed reactors,and the estimated values given by this model were consistent with the experimental data,whether the concurrent flow of gas and liquid was upward or downward.However,this model has yet to be perfected in regard to the prediction of bubble diameter.

Backmixing directly affects the concentration distribution and residence time distribution(RTD)of the fluid in a reactor,and it is considered an important factor when designing multiphase flow reactors.For a complex reaction process,the effects of backmixing cannot be underestimated,and the change of reactant concentration induced by backmixing is closely correlated with the efficiency and selectivity of the reaction.In the mid-1970s,it was reported by Montagna and Shah[29]that the increase of effective residence time and the aggravation of backmixing of the liquid contributed to the decrease of reactant conversion when the gas and liquid flow rates increased in a concurrent upflow hydrodesulfurization reactor.Similarly but not the identical reaction process,Burkhardt et al.[30]compared with the influence of gas-liquid flow directions on the axial dispersion of liquid phase in a hydrotreating bench scale plant by the RTD experiments.The axial dispersion coefficient was found to be distinctly higher in the downflow mode than that in the upflow mode,which proves the superiority of the upflow mode in the hydrotreating reactor.

As reviewed above,the researches of phase holdup and backmixing in reactors are mainly focused on fixed beds and fluidized beds,and the reports are rather rare in the upflow slightly-expanded-bed reactor.In particular,the studies about the influence of different internals on flow and backmixing in the upflow three-phase reactor have not yet been found.In view of the current deficiencies in the literatures and the problems exposed in industrial upflow reactors,our present work is devoted to the development of new types of internals and their performance tests by systematic experiments,and to the investigation of the dependence of gas holdup,liquid holdup and backmixing on different internals and other operating conditions in the upflow reactor.In the end,the informative reference data are provided in the form of correlations for easing the operation and production of industrial reactors.

2.Experimental

2.1.Experimental setup

Fig.1 depicts the schematic diagram of the experimental setup.The entire reactor is made of transparent plexiglass with an inner diameter of 280 mm and a packing height between 760 mm and 1030 mm(the height-to-diameter ratio of 2.7-3.7).The packing is spherical alumina particles;they are classified into three groups according to the mean particle diameter(3.0,4.5 and 6.0 mm),and their detailed physical properties are listed in Table 1.A layer of wire screen with 2 mm×2 mm meshes was installed at a certain distance above the packing section in order to prevent particles from flying off the bed and control the expansion rate of particles within 5%[5].Below the packing section there were two gas-liquid distributing layers stacked with 5-mm and 11-mm glass beads respectively to homogenize the flow of gas and liquid near the inlet,and a perforated plate and a metal wire mesh were installed between the packing section and the distributing layers to separate alumina particles and glass beads.The pressure drop of packing section and other relevant parts can be acquired by the pressure measurements of several pressure sensors mounted on the upper and lower ends of packing section and internals.The tracer injection device and conductivity probes were inserted into the liquid at the inlet and outlet respectively to measure the RTD of the tracer.

The operating pressure of the slightly-expanded-bed reactor applied in industrial residue hydrogenation processes is approximately 18.0 MPa,and the reaction temperature is generally in the range of 370-385°C.Under such high temperature and pressure operating conditions,residual oil behaves as a Newtonian fluid,and its density is between 760 and 1080 kg·m-3;kinematic viscosity ranges from 0.7 to 3.1 mm2·s-1,which are exactly in line with the density and kinematic viscosity of water at normal temperature and pressure.Hence,water was utilized to simulate residual oil in our cold model experimental study.On the other hand,for the sake of experimental safety,economy and convenience,compressed air was selected to substitute hydrogen used in residuehydrogenation.Inourexperiment,air andwaterwere introduced into the bottom of the reactor separately through a compressor and a pump.The superficial air velocities varied from 6.77×10-2to 3.61×10-1m·s-1and the superficial water velocities ranged from 9.47×10-4to 2.17×10-3m·s-1,which were selected based on the gas-liquid volume ratio in the range of 30 to 380 in industrial operations.

As a kind of extremely essential internals,the gas-liquid redistributor has been the key consideration for regulating the uniformity of gas-liquid flow and ameliorating the backmixing characteristics in the current work.Fig.2 shows the structural schematic diagrams of five gas-liquid redistributors designed and applied in our experiments.From overall view,redistributors I,II and III are of flat plate type while redistributors IV and V belong to the raised multi-step type that are divided into three steps by short cylindrical baffles from the periphery to the center.Their effective operating area is the total cross section of the bed;the total opening fractions are all 0.125;the thickness of redistributors is 10 mm,but their hole size,shape and distribution are quite different.It can also be seen from Fig.2 that redistributor I has uniform larger circular holes,and redistributor II is equipped with uniform rhombic holes formed by the 45°crossing of the grooves on the upper and lower sides of the flat plate.The smaller circular holes of redistributor III become gradually sparse in three regions with the radial intervals of 110-140 mm,43-110 mm and 0-43 mm respectively from outside to inside,which are same as the radial intervals of the three steps of redistributors IV and V from the periphery to the center.The hole distribution and opening fraction of redistributors IV are identical with that of redistributor III.Oppositely,redistributor V has the smallest opening fraction(0.0950)in the peripheral step but the largest(0.169)in the central step.Furthermore,these redistributors were all installed at 450-mm height of the bed in the respective experiment.More structural characteristics and geometric parameters of five redistributors are presented in Table 2 in detail.

2.2.Determination of gas and liquid holdups

In order to eliminate the effects of particle micropores on the measurement of gas and liquid holdups,the particles needed to be immersed in water for at least 24 h before each experiment to ensure that the entire space of the micropores was occupied by water.

Fig.1.Schematic diagram of the experimental setup.

Gas holdup was measured by a simple and feasible flow monitoring method put forward by Maldonado et al.[16].While the gas and liquid were flowing upward smoothly and steadily,the gas inlet valve was suddenly shut off,but the liquid flow continued,and the time interval from this moment until the liquid spilled over the outlet again was accurately recorded.Thus,the gas holdup under this operating condition can be derived from the ratio of the gas volume to the total volume of the bed except particle volume,where the gas volume is determined by multiplying the liquid volumetric flow rate over the recorded time,and the formula for gas holdup can be expressed as

Here,Vgrepresents the measured gas volume;Vtand ε0respectively represent the total volume and bulk voidage of the stationary packing bed before the fluid is introduced;φ means the expansion percentage of the bed with gas-liquid steady flow;Vadenotes the volume of the gas-liquid two-phase flow region above the packing section,and Vbis the void volume of the gas-liquid distributor below the packing section.

The liquid holdup studied in our work refers to the dynamic liquid holdup,which was usually measured by the drainage method[17].Unlike the measurement of gas holdup,gas and liquid inlet valves were required to be switched off simultaneously after the flow in the bed had reached a steady state,and the water was then collected by a graduated container for 30 min discharged from the drain valve at the bottom of the reactor.Then the liquid holdup here is defined as the volume fraction of the collected liquid occupying the entire bed except particles,and its expression is as follows:where Vlrepresents the total volume of the collected liquid in the above experiment.

What needs to be emphasized is that the sum of gas and liquid holdups here should satisfy the following relationship theoretically:

Table 1 Physical properties of packing

Fig.2.Structural schematic diagram of redistributors(a)I,(b)II,(c)III,(d)IV and(e)V(dimension unit:mm).

Table 2 Structural characteristics of five gas-liquid redistributors①

2.3.Determination of Peclet number

In this study,the conventional method of the stimulus-response technique was applied in the determination of RTD and the calculation of Peclet number.After the gas-liquid flow rate was adjusted to the set condition and the flow in the bed was stabilized,a certain amount of 4.0 mol·L-1KCl solution was injected into the bottom of the reactor by the tracer injection device.Then voltage signal values at the outlet over time was collected through a conductivity meter,which can be converted into tracer concentration data by a calibration curve prepared in advance,whereby the RTD of the tracer in the reactor was gained.

The axial dispersion model is adopted to describe the axial dispersion of liquid in the upflow reactor,and the mathematical expression for a one-dimensional axial dispersion model is written as[31].

where ulis the superficial flow velocity of liquid,and Dais the axial dispersion coefficient.

The boundary conditions here are given by[32]

where c0is the initial concentration of tracer,and L is the height of the reactor.

In order to acquire the numerical solution of Eq.(4),the average residence time tmand variance σt2are introduced.Among them,the average residence time is the first moment of the RTD function E(t)to the origin,that is

Variance represents the second moment of RTD to the average residence time,which can be used to measure the deviation of E(t)from its centroid.It can be expressed as

The relationship between dimensionless varianceof the RTD curve and Peclet number can be obtained by applying the Laplace transform[33]:

The average residence time tmand varianceare determined by the RTD that is gained experimentally,and the Peclet number can be calculated according to Eq.(10)subsequently.Peclet number is defined as the ratio of convective transport rate and diffusive transport rate,which is accustomed to characterize the degree of backmixing in the reactor,and a greater Peclet number indicates a weaker degree of backmixing.

3.Results and Discussion

3.1.Gas holdup

Variation of gas holdup with the superficial gas and liquid velocities in the upflow reactor without internals is depicted in Fig.3.The relative error of each gas holdup measurement is within 5.6%.We can see that the gas holdup shows an obvious rise as the superficial gas velocity increases,which is similar to the results from the fixed bed studies conducted by Chen et al.[13],Sivakumar et al.[18],Therning and Rasmuson[19],Collins et al.[25],and Alexander et al.[26].This can be attributed to the increased gas-liquid drag force that brings about the resistance to gas flow and increased retention.However,unlike the certain descending trend observed in the fixed-bed reactors with the increase of liquid velocity[13,18,19,25,26],gas holdup shows a fluctuating trend for the change of superficial liquid velocity in our study,and it is in agreement with the work on the expanded bed by Alexander et al.[26].

Fig.4 demonstrates the dependence of gas holdup on particle diameter at ul=1.76×10-3m·s-1with superficial gas velocities ranging between 0.0902 and 0.3158 m·s-1,from which a higher gas holdup is obtained in the bed packed with the larger particles compared to the bed with smaller packing,as was also observed in the fixed beds with gas-liquid concurrent upflow[13,18].It can be explained that the wider interstices between the larger particles are more conducive to the formation of larger bubbles[34]with faster rising velocities,but they are prone to frequent collisions and breakups in the tortuous packing channels,so more gas is accumulated in the bed to form a higher gas holdup.In contrast,the smaller bubbles between smaller particles can run out of the bed with less resistance at the same liquid flow rate,which results in a lower gas holdup.

Fig.3.Effect of superficial gas and liquid velocities on gas holdup(dp=3 mm,H/D=3.7,without internals).

Fig.4.Effect of particle diameter on gas holdup(ul=1.76×10-3 m·s-1,H/D=2.7,without internals).

Fig.5 reveals the effect of internals on gas holdup.After comparing the cases equipped with redistributor V to those without redistributor,the gas holdup is found to be slightly higher when the internal component is applied.This is mainly due to the crushing and blocking effects of the internals on the growing and rising bubbles,whence the residence time of the bubbles becomes longer.

At present,the research of gas holdup is mainly focused on the fluidized bed and fixed bed,but there are few reports about gas holdup in the slightly-expanded-bed reactor.In our work,an empirical correlation for calculating the gas holdup in an upflow slightly-expanded-bed reactor was proposed by dimensionless processing of experimental data and with reference to the form of the correlation made by Sivakumar et al.[18]:

Fig.5.Effect of internals(redistributor V)on gas holdup(ul=1.76×10-3 m·s-1,dp=3 mm,H/D=3.7).

Fig.6.Comparison of the experimental and calculated βgvalues using Eq.(11).

where the superficial gas velocity ugand liquid velocity ulappear in the dimensionless gas-phase Reynolds number(Reg)and liquid-phase Reynolds number(Rel),respectively.The third dimensionless term on the right hand side of Eq.(11)represents the ratio of void volume to solid volume in the reactor,which is distinguished from the gas holdup correlation in the packed bed study of Sivakumar et al.[18].The comparison between calculated gas holdup values based on this correlation and measured data in the experiment is illustrated in Fig.6,and the maximum relative deviation within 11%suggests that this correlation can predict gas holdup satisfactorily.

3.2.Liquid holdup

The effect of the superficial flow velocities of gas and liquid on liquid holdup is shown in Fig.7(a)and(b).The measurement error of each liquid holdup is within 11.2%.It is observed that the liquid holdup decreases dramatically with increasing superficial gas velocity,while increases slightly with the increase of superficial liquid velocity,and this result is in compliance with the work of fixed beds finished by Anter et al.[14],Cassanello et al.[15],Larachi et al.[20],Sindhu et al.[21],Saroha et al.[22]and Molga and Westerterp[23,24].In the gas-liquid concurrent upflow reactor,the liquid considered as the continuous phase completely moistens the particles and produces liquid films on the outer surface of the particles,which prevents the flow resistance of liquid phase from becoming so large that the liquid retention volume grows too fast under the increscent liquid flow velocity.However,as a dispersed phase,when the superficial velocity of gas increases,the increasing drag force of gas on liquid contributes the liquid to leave the bed faster.Consequently,the variation of gas velocity has a more crucial influence on liquid holdup.In addition,it can be inferred that the sum of βgand βlunder the same operating conditions does not always satisfy Eq.(3),which is attributed to the errors in the measurement and calculation methods of gas and liquid holdups,but the relative errors of their sum never exceed 8%.

At a constant superficial liquid velocity,the liquid holdup is found to be larger in the bed packed with smaller sized particles in Fig.8,which is consistent with the regularity of a fixed bed reported by Moreira et al.[17].One reason for this is that the narrower pore channels formed between the smaller particles result in greater flow resistance and more liquid retention.Additionally,in the bed packed with smaller particles,the specific surface area of particles and the liquid-solid contact area are obviously larger.Since the thickness of the liquid film covering the particles is mainly determined by local gravity,the surface of the particles is covered with more liquid,and thereby leading to a rise in liquid holdup.

Fig.7.Effect of superficial(a)gas velocity and(b)liquid velocity on liquid holdup(dp=3 mm,H/D=3.7,without internals).

Fig.9 exhibits the differences in liquid holdup caused by the internals(redistributor V).Compared with the bed without internals,a little smaller liquid holdup can be acquired in the bed where the internal component is installed.The presence of internals contributes to the breakup of large bubbles into more small bubbles that can escape more easily from the bed so that the liquid is more likely to be taken out of the bed by gas.Moreover,a more homogeneous distribution of liquid provided by internals also plays a role in the marginal decrease of liquid holdup to a certain extent.

In order to achieve the convenient prediction of liquid holdup in an upflow slightly-expanded-bed reactor,a correlation for estimating liquid holdup was formulated by dimension analysis method taking into account the superficial flow velocities of gas and liquid,the particle diameter,the bed expansion percentage and the voidage as the particles were stationary:

The physical meaning of each item in the above correlation refers to Eq.(11).Fig.10 gives a comparison between experimental and calculated values,from which it can be seen that the above correlation for estimating liquid holdup is in good agreement with the experimental data with a maximum relative deviation of less than 12%.

Fig.8.Effect of particle diameter on liquid holdup(ul=1.76×10-3 m·s-1,H/D=2.7,without internals).

3.3.Backmixing characteristics

Obviously,the increase of superficial gas velocity has an exacerbating effect on backmixing accompanied by a decrease in the Peclet number as shown in Fig.11,which is in line with the findings of Cassanello et al.[15]and Saroha et al.[22]in fixed beds and Al-Dahhan et al.[35]in expanded beds.On the other hand,the addition of internals has a significant effect on the backmixing characteristics in the upflow reactor.For more convenient and targeted comparisons,only the backmixing characteristics of internals I,II,and V are given here.It can be found that installing the internals helps to suppress backmixing effectively,and the degree of suppression of backmixing is different with different internals further that redistributor V exhibits better results than the other two redistributors in this respect.This is because redistributor V with a suitable multi-step design contributes to a more uniform distribution of gas and liquid,which makes all liquid packages have roughly the same residence time.Besides,along with an increasing superficial gas velocity,the reduction in Peclet number implies an exacerbation of axial backmixing due to the enhanced perturbation and collision of liquid and particles by the bubbles.

Fig.9.Effect of internals(redistributor V)on liquid holdup(ul=1.76×10-3 m·s-1,dp=3 mm,H/D=3.7).

Fig.10.Comparison of the experimental and calculated βlvalues using Eq.(12).

Fig.12 shows three RTD curves obtained from a set of repeated experiments at ul=1.76×10-3m·s-1and ug=0.135 m·s-1,and the average residence time of these three measurements is 557.31 s,554.16 s and 552.96 s,respectively.The high degree of coincidence indicates that the measurement errors of the RTD experiments are satisfactory and the above experimental results are reliable.

Based on the format of formulas in the relevant literatures[15,36],an empirical correlation for calculating the Peclet number was obtained by fitting and analyzing the experimental data using MATLAB R2016b software,which considered the influencing factors such as the superficial flow velocities of gas and liquid,the particle properties,the voidage of static bed and the expansion percentage.Specifically,what is worth mentioning is that the opening fraction of the internals are also considered in the correlation formula innovatively:

Fig.11.Effect of superficial gas velocity on Peclet number at(a)ul=1.76×10-3 m·s-1 and(b)ul=2.17×10-3 m·s-1(dp=3 mm,H/D=3.7).

Fig.12.RTD from repeated measurements(dp=3 mm,H/D=3.7,with redistributor V).

The comparison between experimental and calculated Peclet numbers is presented in Fig.13.A maximum relative deviation of 25%is caused because the structural differences between the five redistributors cannot be expressed uniformly using physical parameters.There is still a lack of terms in Eq.(13),which can specifically quantify the effects of different redistributors on backmixing.Therefore,the estimated values from the fitted correlation naturally exhibit a deviation compared with the experimental values.Further,more experimental studies on redistributors with different structures are needed in order to clarify the specific effects of different redistributors on backmixing and further refine the Peclet number correlation.However,although the present Peclet number correlation has a large relative deviation,it reflects the trend of variation of Pe with the relevant physical parameters and is of some reference value to the design and development of upflow reactors with redistributors in the industrial hydrotreating of residue oil fraction.

3.4.Comparison of the performance of different internals

Redistributor III(flat plate type)and redistributor IV(multi-step type)have the same opening fraction and hole distribution,but difference in configuration will affect the performance of redistributors and the flow and mixing characteristics in the reactor when they are installed as internals at the same location in the bed.It can be noticed by contrast in Figs.14(a),(b)and(c)that the bed pressure drop is lower,the average residence time of liquid is shorter and the degree of backmixing is less in the bed equipped with a redistributor IV under the same operating conditions.As can be seen through the comprehensive evaluation,the performance of redistributor IV is more remarkable than that of redistributor III.Qualitatively,the stepped internals can better regulate the radial non-uniformity of the gas-liquid two-phase flow,strengthen the mixture of gas and liquid phase and ameliorate the axial backmixing.

Fig.13.Comparison of the experimental and calculated Peclet number using Eq.(13).

Both redistributors IV and V are designed with three steps,and what makes them different is that the opening fraction of redistributor IV decreases sequentially from the outside to the inside while redistributor V is exactly the opposite.Fig.15 provides a comparison of the performance of redistributors IV and V indicating that the bed pressure drop and the Peclet number of the bed equipped with redistributor V are both larger than those of the bed with redistributor IV,but their average residence time is roughly equal.This consequence means that redistributor V can perform better in alleviating the axial backmixing of the bed than redistributor IV.The main reason for the consequence we speculate is that the maldistribution of fluid makes more gas assemble at the near wall after passing through a section of bed,while the low opening fraction at the periphery of redistributor V generates higher flow resistance and promotes more gas to flow toward the middle.As a result,the radial distribution of gas phase becomes more homogeneous and the degree of backmixing is relieved.In another aspect,the shorter step height of redistributor V determines that less reactor space is occupied,which makes the advantages of redistributor V more prominent.

Fig.14.Effect of internals III and IV on(a)bed pressure drop,(b)average residence time and(c)Peclet number(ul=1.76×10-3 m·s-1,dp=3 mm,H/D=3.7).

Fig.15.Effect of internals IV and V on(a)bed pressure drop,(b)average residence time and(c)Peclet number(ul=1.76×10-3 m·s-1,dp=3 mm,H/D=3.7).

4.Conclusions

In this work,a series of experiments were completed to measure gas holdup,liquid holdup and Peclet number under various operating conditions in a slightly-expanded bed with concurrent gas and liquid upflow that were regulated and redistributed by different types of internals.The results show that gas holdup presents an upward trend when the superficial gas velocity and the particle diameter increase contrary to the obvious decline in liquid holdup.The increased superficial liquid velocity can cause the liquid holdup to rise slowly while it does not have an obvious effect on gas holdup.Furthermore,from the perspective of internals,smaller liquid holdup,higher gas holdup and larger Peclet number are observed in the presence of internals,indicating that the internals can effectively mitigate axial backmixing in the bed.Subsequently,the degree of suppression on backmixing by the five redistributors is derived:V＞IV＞II＞I＞III,hence the performance of redistributor V in view of backmixing is the best at present.More significantly,three correlations are separately proposed for estimating gas holdup,liquid holdup and Peclet number by nonlinear regression,and they are all found to provide low relative deviations relative to the experimental data.To some degree,it is of practical significance to the industrial upflow reactor for residue hydrotreating.

Nomenclature

c tracer concentration,mol·L-1

dpmean particle diameter,mm

D inner diameter of the reactor,mm

Daaxial dispersion coefficient,m2·s-1

H height of the bed packed with particles,mm

L reactor height,m

ΔP pressure drop of the bed packed with particles,Pa

Pe Peclet number

Re Reynolds number(Re=ρudp/μ)

t residence time of tracer in the reactor,s

tmaverage residence time of tracer,s

u superficial flow velocity,m·s-1

V volume,m3

x axial direction of the reactor

βggas holdup

βlliquid holdup

φ expansion percentage of the bed

Ф opening fraction of redistributors

μ dynamic viscosity,Pa·s

ρ density,kg·m-3

ε0bulk voidage of the stationary stacking bed

Subscripts

0 initial

a above

b below

B bulk

Cal calculated value

Exp experimental value

g gas phase

l liquid phase

m average

max maximal

p particle

s solid phase

t total