Influences of fluid physical properties,solid particles,and operating conditions on the hydrodynamics in slurry reactors

He Yang,Aqiang Chen,Shujun Geng,Jingcai Cheng,Fei Gao,Qingshan Huang,4,5,*,Chao Yang,4,5,*

1 Key Laboratory of Biofuels,Qingdao Institute of Bioenergy and Bioprocess Technology (QIBEBT),Chinese Academy of Sciences (CAS),Qingdao 266101,China

2 Dalian National Laboratory for Clean Energy (DNL),Dalian 116023,China

3 Synthetic Biology Technology Innovation Center of Shandong Province,Qingdao 266101,China

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

5 School of Chemical Engineering,University of Chinese Academy of Sciences,Beijing 100080,China

6 Petrochemical Research Institute,China National Petroleum Corporation (CNPC),Beijing 100083,China

Keywords:Multiphase reactors Fluid physical properties Particle Operating conditions Bubble column Airlift loop reactor

ABSTRACT Slurry reactors are popular in many industrial processes,involved with numerous chemical and biological mixtures,solid particles with different concentrations and properties,and a wide range of operating conditions.These factors can significantly affect the hydrodynamic in the slurry reactors,having remarkable effects on the design,scale-up,and operation of the slurry reactors.This article reviews the influences of fluid physical properties,solid particles,and operating conditions on the hydrodynamics in slurry reactors.Firstly,the influence of fluid properties,including the density and viscosity of the individual liquid and gas phases and the interfacial tension,has been reviewed.Secondly,the solid particle properties(i.e.,concentration,density,size,wettability,and shape)on the hydrodynamics have been discussed in detail,and some vital but often ignored features,especially the influences of particle wettability and shape,as well as the variation of surface tension because of solid concentration alteration,are highlighted in this work.Thirdly,the variations of physical properties of fluids,hydrodynamics,and bubble behavior resulted from the temperature and pressure variations are also summarized,and the indirect influences of pressure on viscosity and surface tension are addressed systematically.Finally,conclusions and perspectives of these notable influences on the design and scale-up of industrial slurry reactors are presented.

1.Introduction

Gas-liquid–solid three-phase slurry reactors,including bubble column reactor and airlift loop reactors (ALR),have been recommended as industrial contactors with techno-economical advantage,as shown in Fig.1.The airlift loop reactors (internal airlift reactor and external airlift reactor)are a type of multiphase slurry reactors developed from bubble columns,which achieved a directional flow due to the fluid density difference between the riser and the downcomer [1].The slurry reactors have the advantage of high catalytic efficiency,simple design and construction,low power consumption,low shear stresses,and excellent mass/heat transfer performance,which are particularly suitable for the processes with uniform distribution of the reaction components and high mass/heat transfer at low power consumption [2,3].Therefore,they have been increasingly employed in the areas of biochemical wastewater treatment [4] biological fermentation [5]large-scale cultivation of photosynthetic organisms [6–8],petrochemical industry [9] and coal chemical industry [10,11].

Numerous experimental studies on these slurry reactors have been investigated in recent years,and it has been widely accepted that the hydrodynamic characteristics (i.e.,flow regime transition,gas holdup,liquid velocity,bubble size distribution,and bubble rise velocity) and mass/heat transfer performance are mainly dependent on the following factors:Structural parameters (i.e.,column diameter [12],column height [13],downcomer-to-riser cross-sectional area ratio [14],and gas sparger [15]),physical properties of gas–liquid-solid three phases systems (i.e.,the physical properties of gas and liquid phases [16–18],solid concentration [19],particle density [20],particle size [21],wettability of solid particles [22],and particle shape [23]),and operating conditions (i.e.,superficial gas velocity (ug) [24],temperature [25],and pressure [26]).Moreover,in order to predict the hydrodynamic characteristics and transfer properties in these slurry reactors,extensive researchers have deduced some theoretical and empirical correlations based on the experimental data and energy conservation equations [27,28].Although relatively simple in construction,the slurry reactors have some important considerations and challenges on the proper design,scale-up,and operating due to the complexity of multiphase flow and lacking information on hydrodynamics over a wide range of operating conditions of commercial interest [29].

The global hydrodynamic parameters in the slurry reactors behave quite differently due to the presence of solid particles,and in turn the variations of hydrodynamic parameters affect the bubble formation,bubble size and its distribution [30–32].Influences of the particle properties,including solid concentration,solid density,solid particle size,and wettability,on the hydrodynamic characteristics should be taken seriously,especially for the solid concentration because the productivity in a slurry reactor can be markedly promoted by increasing the catalyst loading [33,34].Unfortunately,there is currently a lack of facts and details on slurry reactors’ hydrodynamics with high slurry concentrations.Additionally,the industrial processes are usually conducted under harsh operating conditions (i.e.,high superficial gas velocity even higher than the bubble terminal velocity,high temperature,and high pressure) [35].A high superficial gas velocity would be required to increase the throughput of the gas phase [24,33],and quite a lot of processes with considerable commercial interest are operated under the elevated pressures and temperatures [36–38].However,most investigations were concentrated on the ambient conditions,and relatively little is known regarding the industrial jetting conditions in the high-temperature/pressure systems.Few related reports are scattered in the literature,and some critical parameters of hydrodynamics are seriously underestimated or even reported contradictorily.Therefore,the hydrodynamics in slurry reactors under these severe conditions should be systematically elucidated for industrial applications.

This article is ordered as follows.In Section 2,the influences of fluid physical properties on the bubble behaviors and gas holdup are summarized.In Section 3,the influences of the solid particle on hydrodynamics in slurry reactors are outlined.Additionally,the effects of solid concentration are discussed because of their heavy relevance to the industrial processes.In Section 4,principal operating conditions in the industrial processes,such as the gassing rate,temperature,and pressure on hydrodynamics and their influencing mechanism,are reviewed and analyzed.In Section 5,the specific influences of solid particles and operating conditions on hydrodynamics in the slurry reactors are summarized;some basic design,scale-up,operating considerations and challenges for the industrial design of the slurry reactors are also elaborated.

2.Influence of Fluid Physical Properties

In most industrial processes,the liquid phase and gas phase are consisted of numerous chemical and biological mixtures,which contain some surface tension active substances.The influences of liquid properties (i.e.,viscosity and density),gas properties (i.e.,viscosity and density),and surface tension on the hydrodynamics and bubble behaviors in the multiphase reactors are the matters of considerable practical importance [39,40].There are many investigations on the hydrodynamics and mass/heat transfer performance of gas–liquid or gas–liquid-solid reactors with different kinds of fluid.

2.1.Influence of liquid physical properties

There exists a dual effect of liquid viscosity on hydrodynamic characteristics in slurry reactors.Both an increase and a decrease of the gas holdup were observed with the increased liquid viscosity[16,41].Eissa and Schügerl [42] first inspected the dual effect of liquid viscosity on gas holdup in a bubble column with a diameter of 0.159 m and a height of 3.9 m in a water-glycerol system (ρl=1000–1201 kg?m-3,μl=1.00×10-3–3.941×10-2Pa?s).The experimental results have been shown in Fig.2,which indicated that the gas holdup increased when the liquid viscosity varied from 1.00×10-3Pa?s to 3.00×10-3Pa?s,while the gas holdup showed a decreasing tendency when the liquid viscosity further increased up to 1.1 × 10-2Pa?s.From 1.1 × 10-2Pa?s to 3.941 × 10-2Pa?s,the gas holdup slightly decreased with the liquid viscosity,and the degree of decline became negligible at the low superficial gas velocity (0.002 m?s-1).The authors attributed this phenomenon to the variations of bubble motion resistance in the liquid with different viscosities.The drag force was not large enough to make the bubble coalescence at the relatively low liquid viscosities,resulting in a more uniform bubble distribution.However,a high liquid viscosity could promote the bubble coalescence and get a lower gas holdup.The dual effect was also perceived by Ruzickaet al.[41]who thought that the liquid viscosity had a dual influence on the flow regime transition:When the liquid viscosity was in a lower range(μl=1×10-3–3×10-3Pa?s),the homogeneous flow regime was stabilized and the criticalugfor the flow regime transition increased,while a further increase in the liquid viscosity(μl=3×10-3–2.2×10-2Pa?s)could destabilize the homogeneous flow regime.The detailed dual effect of liquid viscosity on bubble size distribution,gas holdup,and flow regime transition in a large-scale bubble column was also investigated by Besagniet al.[43].However,further researches are still desired to set up a comprehensive theory or a physical model,which can describe the dual effects of liquid viscosity on gas holdup.

Otakeet al.[44] examined the liquid properties,including the frequencies of bubble passing and the coalescence and break-up of bubbles with four kinds of liquid:Ethyl alcohol(ρl=789 kg?m-3,μl=1.20 × 10-3Pa?s),distilled water (ρl=997 kg?m-3,μl=1.01× 10-3Pa?s),62 %(mass) aqueous glycerol solution (ρl=1160 kg?m-3,μl=1.25×10-2Pa?s),and 75%(mass)aqueous glycerol solution (ρl=1190 kg?m-3,μl=3.65 × 10-2Pa?s).As shown in Fig.3,the number of bubbles passing through the column’s crosssection per 10 s was defined as the bubble passage frequency.In other words,this parameter can indicate the degree of bubble coalescence or break-up.Their experimental results indicated that for the aqueous glycerol solutions with a high density and viscosity,it was more favorable to coalescence than to break up,showing a smaller value of the bubble passage frequency.The authors proposed that the bubble coalescence and break-up were affected by the shear force,which was attributed to the distribution of liquid velocity around the bubbles.

The increased liquid viscosity will enhance the resistance to elongation of a bubble,resulting in a long time for bubble breakup and a large maximum stable bubble size [47].?ztürket al.[46] studied the gas holdup and volumetric mass transfer coefficient with 17 pure organic liquids,5 inherently mixed liquids,and 17 adjusted mixtures (ρlranged from 714 to 1593 kg?m-3;μlranged from 0.00033 to 0.02 Pa?s).The relation betweenugand gas holdup showed that the gas holdups in organic liquids(apart from ethylene glycol solutions)are usually higher than that in water.Furthermore,it was indicated that the influence of liquid properties on the volumetric mass transfer coefficient (varied by up to 10 times)was much more apparent than that on gas holdup(varied by up to 2 times).This phenomenon was mainly attributed to the viscosity effect on the diffusion coefficient.In addition,the authors also found that the gas holdup in the mixed liquids showed a higher value compared to that in the pure liquids with similar viscosity,density,and surface tension [46].

2.2.Influence of gas physical properties

The effect of gas density on the bubbles’ break-up has been overlooked in the literature,while it is vital for the scale-up of slurry reactors [47].Wilkinson and van Dierendonck [48] investigated the gas holdup in waterversusthe gas density at four superficial gas velocities.As shown in Fig.4,at a givenug,the gas holdup increased with the increment of gas density by increasing the pressure,and besides,the influence of gas density on the gas holdup was more evident at the highug(>0.08 m?s-1).Moreover,this conclusion was consistent with other kinds of gas (i.e.,argon,helium,CO2,and SF6).The variation of gas holdup with the increased gas density may be due to the change of bubble size distribution.The authors also investigated the influence of gas density on bubble break-up percentage in turbulent pipe flow and found that this impact was especially significant for a relatively high gas density.It should be noted that the increase of pressure leads to the higher gas density,and concurrently the surface tension also changes,which is a crucial factor that cannot be ignored for the distribution of bubble size and gas holdup.?ztürket al.[46]observed that both the gas holdup and the volumetric mass transfer coefficient increased with the increased gas density (nitrogen,helium,CO2,hydrogen,and air;ρgranged from 0.09 to 2.46 kg?m-3;μgranged from 8.8×10-6to 1.94×10-5Pa?s).In fact,the variation of surface tension with different gases was omitted in these investigations,and its contribution to the bubble size reduction should be evaluated.

Unlike the liquid viscosity,the gas viscosity was thought to have a marginal influence on bubbles’breakup.Walter and Blanch[45] evaluated the influence of gas viscosity using nitrogen(μg=2.0 × 10-4Pa?s),hydrogen (μg=8.6 × 10-5Pa?s),argon(μg=2.2 × 10-4Pa?s),and air (μg=1.8 × 10-4Pa?s) in their experiment.It was found that the maximum stable bubble size decreased slightly with the increased gas viscosity.To be specific,the stable bubble size only decreased approximately by about 4.3%as the gas viscosity increased by 1.56 times.Therefore,a negligible impact of gas viscosity was commonly adopted in practice.

2.3.Influence of surface tension

It has been well known that the surface tension is one of the major contributing forces that affected the bubble diameter during the formation and rise[49].The reduction of surface tension leads to a smaller average bubble diameter,and in turn increases the interfacial area between gas and liquid,decreasing bubble rise velocity and promoting the gas holdup and mass transfer performance.Jamialahmadiet al.[50] investigated the bubble formation at different gas flow rates in air-aqueous solutions (potassium chloride and alcohol solutions).As shown in Fig.5,the bubble diameter increased along with the surface tension.Moreover,the impact of surface tension was remarkably decreased as the gas flow rate increased.It is noteworthy that the effect of surface tension on bubble diameter was pronounced for the liquid with low surface tension (less than 0.04 N?m-1).Davidson and Schüler [51]also proposed a similar conclusion and pointed out that the effect of surface tension could be ignored at highug.

Fig.4.Influence of gas density on gas holdup in water by increasing the pressure at different superficial gas velocities [48].

An efficient method to diminish the stable bubble size and enhance the interfacial area between the gas and the liquid is to reduce the surface tension [45].Walter and Blanch [45] examined the effect of surface tension by adding surfactants (i.e.,n-butanol,n-propanol,n-octanol,hexanoic acid,dodecanol,and SDS;the surface tension of these aqueous solutions varied from 0.025 to 0.073 N?m-1).The authors analyzed the effect of surfactants on the bubble break-up mechanism and argued that it depended on the surfactant replenishment rate at the bubble surface.For the surfactants with small molecular weight,a fast replenishment rate could make the surface tension and the maximum stable bubble diameter reduce.On the other hand,large molecular weight surfactants can make the rippling of the bubble surface decrease,stabilizing the bubble surface.Furthermore,the authors proposed a simple model to predict the maximum stable bubble size related to the fluid physical properties:

wheredmis the maximum stable bubble diameter (m);σ denotes the surface tension (N?m-1);P/Vis defined as the power per unit volume (W?m-3);ρ,μe,and μgare density (kg?m-3),extensional viscosity(kg?m-3?s-1)and shear viscosity of gas-phase(kg?m-3?s-1),respectively.It can be seen that the maximum stable bubble diameter could reduce by 34%when the liquid surface tension decreased by 50%.Dargar and Macchi [52] revealed that the gas holdup was very sensitive to the surfactants in multi-component liquids.They measured the gas holdup in various dilute aqueous solutions (i.e.,0.5% ethanol,5% ethanol,0.5% pentanol,0.01% SDS,0.01% HTAB(hexadecyl trimethyl ammonium bromide),and 0.01% Triton X-100 (mass fraction);the surface tension of these aqueous solutions varied from 0.0362 to 0.0723 N?m-1).The experimental data showed that the addition of surfactants could make the gas holdup increase by an average of 41% in the gas–liquid system while the increase was roughly by 37% in the gas–liquid-solid system (with glass beads,dp=2.1 mm,5 mm).

2.4.General remarks

Fig.5.Influence of surface tension on bubble diameter at different gas flow rates[50].

Hydrodynamic characteristics of multiphase reactors are a complex function of physical properties of the fluids.The increased liquid viscosity has a dual effect on the bubble behaviors,and the detailed dual effect of liquid viscosity on bubble size distribution,gas holdup,and flow regime transition in slurry reactors is problem-dependent.The liquid density was proved to have a slight influence on bubble behaviors.On the contrary,the gas holdup could be increased with the increasing gas density,and a different trend in the profile of gas holdupversusthe gas density was observed in different ranges ofug.The higher theugis,the more significant the extent of this impact.However,the influence of gas density on gas holdup should be restudied and suppress the impacts of surface tension variation because of the increased pressure in future investigations.The influence of gas viscosity on the hydrodynamics in the slurry reactor was found to be insignificant.However,it has been widely accepted that the addition of surfactant to the aqueous solution could result in a smaller bubble mean diameter and a significantly higher gas holdup.

3.Influence of Solid Particles

Flow regime transition,gas holdup,liquid velocity,mass/heat transfer performance,bubble size and distribution,bubble rising velocity,and viscosity and surface tension of liquid phase in the slurry reactors are different from those in the counterpart without solid particles[31,53,54].Due to the presence of a solid phase,the gas–liquid mass transfer limitations in the gas–liquid-solid threephase system may cause a notable and complex influence on the reaction conversion,especially at the high solid concentration and highug[55].Moreover,the influence of the solid particle size on hydrodynamics cannot be ignored.When the solid concentration and particle size are beyond some critical values,solid particles’ density and wettability will exert more or less influence on the hydrodynamics in the slurry reactors [12].There also exist some dual influences of solid properties on the hydrodynamic in the previous literature,resulted from the variations of physical properties,bubble formation,bubble coalescence and break-up,and solid spatial distribution with different sizes and loadings in the slurry reactors.

In short,although numerous investigations have been undertaken to investigate the influences of solid particles on the hydrodynamics and mass/heat transfer in the slurry reactors,the underlying mechanisms are still not well understood due to the complexity of multiphase flow and many unclear interactions between involved parameters,such as solid loading,particle size,density,wettability,and shape.

3.1.Influence of solid concentration

In order to obtain a better reactor performance,the slurry reactors should be operated at the highest catalyst concentration compatible with slurry handling ability (e.g.,the capacity of liquid–solid separation) [34] because the processes of continuous solid–liquid separation and solid recycling are the two bottlenecks for promisible extensive application of slurry reactors [56,57].The solid volumetric concentration in the slurry usually ranged from 15%(vol)to 30%(vol),and sometimes even up to 50%(vol)[19,55].

The addition of solid particles could considerably influence the hydrodynamic characteristics.Therefore,it is vital to identify practical operating conditions and the design implications of increasing solid concentrations in the slurry reactors.For example,the influences of high solid concentration on the gas distributor design and the startup procedure of the reactor were realized in the previous literature[33]and it was observed that the deactivation rate of catalysts increased with increasing solid concentration [33].Besides,the high slurry concentrations could result in the accumulation of fine bubbles in the suspension and then lead to a drop in the rise velocity of the smaller bubble fraction [58].

3.1.1.Influence of solid concentration on flow regime transition

The hydrodynamics characteristics,mixing behavior,and mass transfer performance in the slurry reactors are characterized by the typical flow regimes,which are usually dependent on the superficial gas velocity and named homogeneous (bubbly flow),transition flow (bridging flow),and heterogeneous (churnturbulent flow),respectively[59–61].Flow regime plays a crucially important role in the processes of design,operation,control,and scale-up of the slurry reactors,which can be discriminated by the different bubble size distributions [62,63].The slurry is prevailed in a homogeneous flow regime at the lowug,and the bubbles in the slurry phase are similar to those during the bubble formation with relatively smaller diameters (about 1–7 mm)[64,65].The narrow bubble size distribution,the weak bubble interactions,and the uniform radial distribution of gas holdup are usually observed in the low range ofug[66].As a homogeneous and heterogeneous bridge,the transition flow has small bubbles and begins to form large bubbles.With a further increase ofug,the small bubbles become larger bubbles (usually about 20–70 mm in diameter)through coalescence and breakup,and a wide bubble size distribution means the formation of a heterogeneous flow regime in the slurry reactor [64,65].It is noteworthy that the related literature of the flow regime transition in slurry reactors is very scarce,especially for the conditions with high solid loading.It is vital to understand the flow regime transition in the slurry reactors in various solid-phase systems.

Menaet al.[67]studied the effect of solid concentration(Cs=0–0.3)on the homogeneous-heterogeneous flow regime transition in a bubble column reactor in an air–water-calcium alginate bead(dp=2.1 mm,ρp=1023 kg?m-3)system.The flow regime transition was determined with a traditional gas holdupversus ugmethod,and the corresponding results are shown in Fig.6.It can be seen that the homogeneous flow regime is stabilized for a low solid concentration (Cs=0–0.05),and the gas holdup could be promoted with the solid concentration in this range when theugwas higher than 0.04 m?s-1.However,a destabilization of the homogeneous flow regime occurred at a high solid concentration (Cs>0.05),and a notable decrease of gas fraction could be observed with an increase of solid loading in this range,especially whenugwas high than 0.03 m?s-1.

Motaet al.[68] also investigated the influence of the spent grains (dp<2.1 mm,ρp=1037 kg?m-3) on the flow regime transition.It was found that the critical gas holdup decreased with an increased solid mass concentration (Cs=0–0.2).Furthermore,the heterogeneous prevailed at the highest solids mass concentration,which may be caused by the non-uniform distribution of spent grains in the reactor and the interaction of spent grains with bubbles in the interface between the gas and liquid phase.Vanduet al.[69]also noted that the range of operation velocity in the homogeneous flow regime became narrower with the addition of solid particles(porous alumina catalyst,dp:10%<10 μm,50%<16 μm,90%<39 μm;ρp=3900 kg?m-3)because of the formation of large bubbles.As stated above,solid particles’ addition leads to the coalescence of bubbles,and hence the formation of large bubbles triggers a heterogeneous flow regime.

Fig.6.Influence of solid concentration on flow regime transition in a bubble column reactor [67].

3.1.2.Influence of solid concentration on gas holdup

The gas holdup was found to depend onugand liquid velocity[70],solid concentration [71],and solid particle size [21].The effects of solid concentration have been extensively investigated in the literature [56,71],and many researchers reported that the gas holdup decreased with the increasing solid concentration,which resulted from an enhancement of bubble coalescence and a reduction of bubble fragmentation rate [54,72,73].

It should be noted that the effects of bubble coalescence inhibition became negligible at the high solid concentration [33,74].Moreover,there exists a dual effect of solid concentration on gas holdup in previous investigations [21].For example,Wanget al.[75] indicated that the solid concentration has no apparent influence on the gas holdup in the range of solid holdup from 0 to 0.1 in the air–water-glass bead(dp=200 μm,ρp=485 kg?m-3)system in an external loop airlift slurry reactor.On the contrary,Li and Prakash[55]investigated the effects ofug(up to 0.35 m?s-1)and solid concentrations(i.e.,Csup to 0.4)on the gas holdup in an air–waterglass particle (dp=35 μm,ρp=2450 kg?m-3) system and they observed that the gas holdup decreased with increasing solid concentration and the rate of decline was rapid at the highug(>0.24 m?s-1).A similar conclusion was obtained by Gandhiet al.[33] and the corresponding results are shown in Fig.7.

It can be seen from Fig.7 that the gas holdup decreased with the addition of solid particles (glass beads,dp=35 μm,ρp=2450 kg?m-3)and the rate of decrease slowed down at the high slurry concentrations [33].It is noteworthy that a negligible variation of gas holdup with the increased solid concentration was observed when the solid fraction was higher than 0.25.Vanduet al.[69]also measured the gas holdup with the solid concentration(from 0 to 0.25)of porous alumina catalyst (dp:10% <10 μm,50% <16 μm,90% <39 μm;ρp=3900 kg/m-3) and found that the gas holdup decreased to a significant extent,due to the creation of large bubbles when adding the solid particles into the cylindrical bubble columns.Ruthiyaet al.[76]studied the gas holdup againstugin the air–water and air–water-silica particle (dp=35 μm,ρp=2450 kg?m-3) systems in rectangular and cylindrical slurry bubble columns;the results indicated that the influence of silica concentration on the gas holdup in the cylindrical slurry bubble column was more evident compared to that in the rectangular slurry reactor.

Fig.7.Influence of solid concentration on gas holdup [33].

Krishnaet al.[77] found that the total gas holdup was significantly decreased with increasing the solid concentration (silica particle,dp:10% <27 μm,50% <38 μm,90% <47 μm;ρp=2100 kg?m-3) from 0 to 0.36.The authors also observed that the dense-phase gas holdup (small bubble holdup) decreased when the solid concentration increased while the dilute-phase gas holdup(large bubble holdup)was independent of the solid concentration.The gas holdups in these two parts are crucial for estimating the total gas holdup in the slurry reactors by the empirical correlations,whether for a homogeneous or heterogeneous flow regime.Rabhaet al.[31] studied the effects of solid concentration(glass particles,dp=100 μm,ρp=2500 kg?m-3) on gas holdup using an ultrafast electron beam X-ray tomography in a slurry bubble column.They indicated that the reduction of gas holdup with the increased solid concentration was observed to be less at a high solid concentration (fromCs=0.1 to 0.36) compared to that at a low solid loading(Cs=0.05),and proposed that the bubbles started coalescing after the addition of solid particles while with a further addition of solid particles,the bubble break-up regime was dominant.Sadaet al.[78] found that the gas holdup decreased with increasing solid mass concentration (aluminum oxide,dp<3 μm,ρp=3850 kg?m-3;calcium hydroxide,dp=7 μm,ρp=2240 kg?m-3;calcium carbonate) when the added solid particles were larger than 50 μm,and that no appreciable influence on gas holdup at low solid concentration was observed.However,the gas holdup could be increased with the particles smaller than 10 μm when small bubbles were generated.Menaet al.[67] observed that the gas holdup increased with the increased solid concentration (up toCs=0.03) and then decreased with a further addition of solid particles(calcium alginate beads,dp=2.1 mm,ρp=1023 kg?m-3),and a similar result was also obtained by Immichet al.[79] with the solid coal particles (dp=74 μm,ρp=1400 kg?m-3).Therefore,the underlying mechanism of increase or reduction in the gas holdup with the solid increment has not been explained precisely and needs to be further investigated.

A large number of correlations,which covered a wide range of variables such as liquid and gas properties andugto predict the gas holdup,have been proposed in the literature [12].The typical correlations for predicting gas holdup at different solid loadings in the slurry reactors are summarized in Table 1.

Table 1 Correlations for predicting gas holdup at different solid concentrations

It is noteworthy that the empirical correlation proposed by Karaet al.[12] was dependent on the solid particle size (coal and dried mineral ash,dp=10–70 μm,ρp=1300 kg?m-3).Moreover,the authors used dimensionless groups to present the effects ofugand solid mass concentration,and this correlation showed that the gas holdup was almost independent of solid concentration.A similar conclusion can be drawn from another correlation put forward by Sauer and Hempel [80] and the model can reproduce the experimental data with a mean error of less than 30% in a wide range of particle sizes and densities.Koideet al.[81]also proposed an empirical equation for predicting the gas holdup in the transitional and heterogeneous flow regimes;they indicated that the reduction of gas holdup by adding solid particles was high in the transition flow,while the diminution was low in the heterogeneous flow.

3.1.3.Influence of solid concentration on liquid velocity

Liquid velocity is also an essential parameter for the slurry reactors’ design,and relevant with an exchange of momentum and mass/heat transfer [82].The previous investigations showed that the parameters,including the column height and diameter,superficial gas velocity,and the fluid physical and chemical properties(the density,viscosity,and surface tension of fluids),have principal influences on the liquid velocity[83].Dhaouadiet al.[83]proposed that solid particles’existence led to a decrease of driving force and consequently to a decrease in the liquid velocity.Moreover,they argued that the liquid velocity was influenced more by the solid concentration than the gas holdup.Liuet al.[84] carried out the experiments in a slurry airlift reactor at the high solid concentrations (glass beads,dp=53,83,117,149 μm,ρp=2450 kg?m-3,Cs=0–0.40).As shown in Fig.8,the liquid velocity decreased with the increment of solid concentration.The authors proposed two reasons:On the one side,the driving force of liquid velocity decreased due to the decreased differential gas holdup between the riser and downcomer with the presence of solid particles;on the other side,the resistance of liquid circulation increased as a result of the enhanced slurry apparent viscosity caused by increased solid concentration.Furthermore,the rate of liquid velocity decline was rapid at highug.

Jinet al.[85] studied the influence of activated sludge (dp=5–85 μm) both in an internal airlift reactor and an external airlift reactor.Their experimental results showed that the liquid velocity decreased as the sludge loading increased,and the liquid velocity was affected by the flow regime.Milivojevicet al.[19]investigated the hydrodynamic characteristics in an external airlift reactor in an air–water-Ca-alginate bead(dp=（2.5±0.2)mm)three-phase system.The effects of low and high solid concentration on the reactor hydrodynamics (mainly on the liquid velocity) were studied.Sur-prisingly,their results indicated that the liquid velocity increased slightly with the solid loading increment at the low loading(Cs=0–0.075).However,a further increase in solid loading(Cs=0.075–0.5) could decrease the liquid velocity.The concentration of Ca-alginate beads had different effects on the liquid velocity at different superficial gas velocities:The liquid velocity decreased with increasing solid concentration (Cs=0–0.05) at lowug(<0.009 m?s-1);however,at the highug(>0.009 m?s-1),the liquid velocity increased with increasing solid concentration until the concentration of Ca-alginate particles was up to 0.025,and then the liquid velocity decreased with a further increase in solid concentration.The authors explained this phenomenon as follows:The number of bubbles was small and hence the rate of bubble coalescence between them was low,leading to a minor stabilizing effect of the particles at the lowug(<0.009 m?s-1);on the other hand,the apparent viscosity of the suspension increased with the increased solid concentration,which promoted the bubble coalescence and in turn resulted in a lower gas holdup,and correspondingly a lower liquid velocity.

Fig.8.Influence of solid concentration on liquid velocity at different superficial gas velocities [84].

3.1.4.Influence of solid concentration on suspension viscosity

The primary influence of solid concentration on the fluids can be defined as an increase in the continuous slurry phase’s apparent viscosity,affecting the bubble coalescence and break-up [86].Low viscosity can stabilize the uniform bubbly flow,whereas the high viscosity can destabilize the bubbly flow [41].As pointed out by Huanget al.[66],the slurry can be taken as a pseudohomogeneous phase under the conditions that the solid fraction is less than 0.25,the particle diameter is less than 100 μm,andugis high enough,so as to result in a liquid velocity bigger than the terminal slip velocity of the solid particles.In this circumstance,the solid particles are relatively uniform in both axial and radial directions.

It should be noted that the influence of increasing solid concentration and liquid viscosity on hydrodynamics is qualitatively parallel [69,87].Numerous theoretical and empirical correlations of apparent slurry viscosity have already been proposed to predict the impact of solid loading.Some typical and simple empirical models for predicting the apparent slurry viscosity are shown in Table 2.

Table 2 Theoretical and empirical correlations for predicting apparent slurry viscosity with solid concentrations

Einstein firstly proposed a classical correlation related to the solid volumetric concentration to estimate the apparent slurry viscosity,i.e.,μslurry=μl(1+2.5Cs).However,this correlation has some limitations,including the hypothesis of uniform spherical particles with low loading and ignoring hydrodynamic interactions.At the low solid concentration,the relative effective viscosity (i.e.,η∞=-μslurry/μl) of a suspension of spherical particles (silica particles) incyclohexane was investigated by van der Werffet al.[94],and the corresponding experimental data and some typical theoretical predictions using some well-known models are illustrated in Fig.9.It is noteworthy that the predictions with the model proposed by Beenakker [88],who regarded the solid particles as the rigid spheres,agree well with the experimental data,especially when the solid loading is below 0.3.

3.1.5.Influence of solid concentration on bubble behaviors

Bubble size distribution and its corresponding bubble rise velocity play a crucial role in designing the slurry reactor.The bubble size may either increase or decrease with the addition of solid particles;there are conflicting explanations for the underlying mechanisms.Krishnaet al.[77] argued that the increased bubble size in the gas–liquid-solid (porous silica particles,dp:10% <27 μ m,50%<38 μm,90%<47 μm;ρp=2100 kg?m-3)three-phase system compared with that in the gas–liquid two-phase system can be attributed to the increase of apparent suspension viscosity with the increased solid concentration.Rabhaet al.[31] indicated that bubbles start coalescing even at a low solid concentration (spherical glass particles,dp=100 μm,ρp=2500 kg?m-3,Cs=0.05);the bubble coalescence was enhanced and hence large bubble slugs were formed when the solid concentration was up to 0.10,while it was found to break up at a high solid concentration (Cs=0.36).Moreover,they measured the approximate bubble size distribution at a high solid concentration (Cs=0.1) and found that the bubble size was dependent onugand solid concentration.

Sastaravetet al.[23] investigated the bubble size distribution both in a bubble column reactor and an airlift loop reactor with various polypropylene media types (ring:dp=5 mm,ρp=0.950 k g?m-3;sphere:dp=4.5 mm,ρp=0.941 kg?m-3;cylinder:dp=3.5-mm,ρp=1.022 kg?m-3;square:dp=2.5 mm,ρp=0.961 kg?m-3)and solid concentration(Cs=0–0.15),and their results showed that the bubble size distribution became smaller,i.e.,about 22%–27%and 5%–29% reduction on average in the bubble column reactor and the airlift loop reactor with the addition of solid media.They thought that the solid media addition led more likely to a higher breaking rate and a lower bubble rise velocity.On the contrary,Vanduet al.[69]observed that the bubble diameter was practically independent of slurry concentration when the solid concentration(porous alumina catalyst,dp:10% <10 μm,50% <16 μm,90% <3 9 μm;ρp=3900 kg?m-3) was greater than 0.05 by analyzing the video images.Chilekaret al.[95] investigated the effects of slurry concentration on bubble size at different carbon particle concentrations (carbon particles,dp=40 μm,Cs=0–0.0078) and found that the impact on the bubble size was not apparent.

Fig.9.Typical influence of solid concentration on apparent slurry viscosity.

In most industrial processes,the bubble rise velocity in the continuous liquid phase was generally presented as the slip velocity relative to the surrounding moving liquids,which decides the residence time of bubbles and hence the contact time for the interfacial transport between gas and liquid.Therefore,the reactors’performance is also related to the bubble rise velocity [96].Li and Prakash [58] performed the experiments in the air–water-glass particle(dp=35 μm,ρp=2450 kg?m-3)systems to study the bubble population and their rising velocities.Interestingly,their experimental results showed that the rise velocity of large bubbles increased with the increased solid concentration up to 20% (vol)and then reached an asymptotic value at the high solid concentrations,as shown in Fig.10(a).However,the rise velocity of small bubbles first increased and then decreased with the increase of slurry concentration and achieved a maximum at a slurry concentration of about 0.25,as shown in Fig.10(b).

In addition,Li and Prakash [58] also developed a correlation to predict the reduction of small bubble rise velocity at the high slurry concentrations (aboutCs>0.20) as follows:

Hooshyaret al.[97]investigated the bubble behaviors in rectangular and cylindrical slurry reactors in an air–water-glass bead(dp=108 μm,ρp=2450 kg?m-3) system and argued that the increase of solid concentration could widen the distribution of bubble rise velocity and increase the average bubble velocity.The increase of average bubble velocity was decided by the system’s physical properties and liquid velocity.The detailed mechanism needs to be investigated in future work.

3.1.6.Influence of solid concentration on mass/heat transfer coefficient

In general,the gas–liquid volumetric mass transfer coefficient(kLa) describes the interphase mass transfer rate,which is based on the concept that the liquid film is the dominant resistance for mass transfer [46].Also,kLais usually the basis to compare and evaluate the performance of mass transfer with different reactor designs[85,98].The values ofkLawere found to follow the bubble size distribution intimately and decrease dramatically at the high solid concentrations,which might be interpreted as that the high solid concentrations could produce many large gas bubbles with small gas–liquid interfacial areas,leading to smallkLavalues [99].

Liet al.[53] pointed out that the gas–liquid volumetric mass transfer coefficient decreased quickly with the increased solid concentration (Cs=0–0.40) of fine particles (glass beads,dp=11–93 μm),because the solid particles had a profound negative effect on the gas–liquid interfacial area.Quickeret al.[100]also indicated that the suspended solid fines(activated carbon,ρp=1800 kg?m-3;kieselguhr,ρp=2360 kg?m-3;aluminum oxide,ρp=3180 kg?m-3)could significantly affect the gas–liquid interfacial area,particularly at the high solid loadings.However,there was no significant effect of solid loading on the gas–liquid volumetric mass transfer coefficient at the low solids loadings (activated carbon,Cm<46-kg?m-3;kieselguhr,Cm<100 kg?m-3;aluminum oxide,Cm<10-kg?m-3),and this conclusion was also verified by our group[56,57] with the brown alumina particles larger than 66.1 μm.

Fig.10.(a) Influence of solid concentration on large bubble rise velocity [58].(b)Influence of solid concentration on small bubble rise velocity [58].

Koideet al.[81] pointed out that the presence of the solid particles(glass sphere,dp=192 μm,ρp=2500 kg?m-3;bronze sphere,dp=81 μm,ρp=8770 kg?m-3)could reducekLain the reactor,and the reduction ofkLawas also related to the flow regime,which was high in the transition regime and low in the heterogeneous regime.They also proposed an empirical equation for the estimation ofkLa,which was applicable to both the transition and heterogeneous flow regimes.However,an opposite conclusion was proposed by Sastaravetet al.[23] as shown in Fig.11.The experimental results indicated that compared to the values in the non-addition cases,kLacould be enhanced by about 29.65% after supplying the solid sphere media(polypropylene media,dp=5 mm,ρp=0.941 kg?m-3)with a solid concentration of 10% (vol) into the bubble column reactor,whilekLaat the same conditions reduced by about 26.68% in the airlift loop reactor.It was indicated that the solid sphere media were inappropriate for mass transfer enhancement in airlift loop reactors,which resulted from a high terminal velocity of solid particles and high bubble rising velocity,possibly because of its low solid density and high affinity with the bubble interface.A similar conclusion was also obtained by Ferreiraet al.[101]:The solid particle with low density and high affinity to the interface of bubbles could result in a significant decrease in mass transfer rate.However,compared with the airlift loop reactor,this impact can be negligible in the bubble column reactor,maybe due to the higher liquid velocity in the airlift loop reactor with the cross-sectional area divided into two separate regions.

Fig.11.Influence of solid concentration on volumetric mass transfer coefficient[23].

Smith and Skidmore [102] investigated the influence of solid particles (coal particles,dp=74 mm,ρp=1415 kg?m-3) on mass transfer in an airlift loop reactor.The experimental result showed thatkLaincreased as the solid concentration increased at low solid concentrations,reaching a maximum at approximatelyCs=0.014,and then decreased with further solid additions(0.014

UnlikekLa,the heat transfer coefficient was related to the position inside the column[53].The effects of high gas velocities(up to 0.35 m?s-1)and high solid concentrations(glass beads,dp=35 μm,ρp=3900 kg?m-3,Cs=0–0.40)on the heat transfer coefficient were investigated by Li and Prakash [55].It was observed that both the particle size and the slurry concentration have some adverse effects on the heat transfer coefficient at the center of the column.However,the heat transfer coefficient showed no difference at the column wall under different solid particle sizes.Besides,the heat transfer coefficient was always lower at the wall than that in the center.

However,several researchers put forward an opposite conclusion about the influence of solid concentration on the heat transfer coefficient.For example,Saxena and Patel [74] measured the heat transfer coefficient in a baffled bubble column in an air–waterglass bead system.In their experiments,the glass beads of three different sizes(dp:50–143 μm,ρp=3900 kg?m-3)were employed,and the solid mass concentration was up to 30%(mass).The investigation suggested that the heat transfer coefficient could be generally increased by adding solid particles for all sizes.To be specific,the heat transfer coefficient could be increased with the increased solid concentration for the 50 and 90 μm particles,while a marginal difference was observed for the 119 and 143 μm particles.In another work,the experimental results showed that the heat transfer coefficient in the air–water-magnetite system was slightly greater than that in the air–water system,and it had only a weak dependence on solid concentration and particle diameter [105].

Therefore,to determine the dependence of solid particles on heat transfer efficiency in slurry reactors,an in-depth detailed analysis of the heat transfer data based on radial and axial profiles should be performed in the future.

3.1.7.Influence of solid concentration on surface tension

Like suspension viscosity mentioned above,the addition of solid particles into the continuous phase will produce some variations of physical properties in the continuous phase [106,107].The variation of surface tension at different slurry concentrations has often been neglected inadvertently.Thus the investigation on apparent surface tension of the continuous phase with adding solid particles is still lacking.

Generally speaking,increasing the solid concentration will decrease the surface tension between gas phase and continuous phase.Thampi and Pandit[108]studied the rheological properties of concentrated distillery spent wash at different solid mass concentrations (0.13,0.20,0.30,0.40,0.50,and 0.60).The experimental results showed that the surface tension depended on the solid concentration,but the degree of impact was not particularly noticeable.The surface tension changed from 49 N?m-1to 43 N?m-1as the solid mass concentration increased from 0.13 to 0.20.With a further increment of solid concentration (from 0.20 to 0.60),the surface tension showed a slight difference and remained in the region of (42 ± 2) N?m-1.Liuet al.[109] investigated the bubble generation process in a nitrogen-glycerol-water solutions-glass bead (dp=12 μm,ρp=1130 kg?m-3) system in a T-junction microchannel by a high-speed camera.The authors indicated that the surface tension decreased exponentially with the increment of solid mass concentration (Cm=0–0.05),and the relationship between the surface tension and solid mass concentration could be obtained by a simple model as

From this model,it can be seen that the impact of solid loading on surface tension is significant when the solid concentration is small.The reduced surface tension can decrease the bubble diameter during the bubble formation and correspondingly promote the gas holdup in the slurry reactor,which in some sense neutralizes the impact of increment in apparent slurry viscosity because of the addition of solid particles.

The surface tension is a crucial physical property related to the bubble formation and bubble diameter in the slurry reactors,and in turn the bubble behaviors can influence the hydrodynamic characteristics and mass transfer performance.Therefore,it is worth paying more attention to the variation of surface tension at different solid concentrations.Additionally,it is noteworthy that the solid particles’ impacts on the surface tension and apparent slurry viscosity should be strictly distinguished.

3.2.Influence of solid density

The system with a low-density-particle showed a different hydrodynamics characteristic compared to that with the conventional solid particles.Bly and Worden [20] studied the difference between the conventional glass-particle (dp=1.30 mm,3.03 mm,and 5.99 mm)systems and the low-density gel-particle(dp=1.15-mm,2.59 mm,and 3.84 mm) systems through quantitative and qualitative observations;their results indicated that the solid density could significantly influence the degree of coalescence and mode of fluidization.

Weiet al.[110] studied the hydrodynamic characteristics in a rectangular gas–liquid-solid three-phase bubble column,and they argued that the criticalugfor flow regime transition decreased when the particle density increased from 2500 kg?m-3to 4800 kg?m-3.Moreover,the bed expansion height,turbulent structures,and bubble size distributions showed a distinct difference at highugwith changing particle density.Jamialahmadi and Müller-Steinhagen [111] argued that the gas holdup could be increased by reducing the particle density (i.e.,ρpfrom 1360 kg?m-3to 700 kg?m-3) for a constant particle diameter (styrocel particles,dp=1.3 mm),and a slight reduction in gas holdup occurred for the smaller particles (dp=0.813 mm) with a density of 1200 kg?m-3.Most notably,the hydrodynamic characteristics and the degree of bubble coalescence were highly dependent on the system properties.However,detailed information of the effects of low-density particles on the hydrodynamics in the slurry reactors is still lacking.

3.3.Influence of solid particle size

In most slurry reactors,the particle diameters are in a wide range of 20–200 μm [112,113],and it may also be less than 10 μm in some particular situations.The extent of the influence of the additional particles on the hydrodynamics in the slurry reactors is considered to depend on the particle size [78,114].

The influence of solid particle size on flow regime transition in a three-phase bubble column in an air–water-glass bead (or iron powder) system was investigated experimentally by Weiet al.[110],and the experimental results indicated that the solid particle size had little effect on flow regime transition when the solid particles increased from 48 μm to 150 μm.However,when the particle size was increased up to 270 μm,the criticalugfrom the transitional regime to the heterogeneous regime was markedly decreased.

The particle size was found to have a negligible effect on the gas holdup as long as their concentration was low.Kelkaret al.[21]investigated the hydrodynamics and mixing in a three-phase (oil shale particles) bubble column with the solid particle size being varied from 44 μm to 254 μm,and their results indicated that particle size did not exert any significant influence on the gas holdup.Moreover,the addition of 144 μm oil shale particles was found to decrease the gas holdup slightly,which may occur due to the changes in slurry viscosity and density with the addition of solid particles.Saxena and Patel [74] indicated that the gas holdup remained almost the same for the slurries with 50,90,and 143 μm glass beads.However,there also exist some opposite views about the influence of solid particle size.For example,Karaet al.[12] investigated the relationship between particle size and gas holdup in an air–water-coal/dried mineral ash system,and their results are illustrated in Fig.12.It can be seen that there is little difference between the gas holdup in the air–water two-phase system and that in the air–water-solid three-phase system with 10 μm diameter particles,and a negative impact of particle size on gas holdup was observed as the particle size increased.

A similar conclusion was also proposed by Sadaet al.[78],and they observed that the addition of solid particles (i.e.,aluminum oxide,calcium hydroxide,and calcium carbonate) smaller than 10 μm could promote the gas holdup at low solid concentration.Besides,it was found that the solid particle above 50 μm had a negligible effect on the gas holdup as long as the solid mass concentration (Cm<0.001) was low enough.Liet al.[53] also studied the effects of particle size (glass bead,dp=11 μm,35 μm,and 93 μm) on the hydrodynamics in a slurry bubble column,and a smaller bubble rise velocity was observed for the particle with 93 μm in size compared to those with 11 μm and 35 μm in size.

3.4.Influence of wettability of solid

Fig.12.Influence of superficial gas velocity on gas holdup with different diameter particles [12].

The non-wettable particles,with no polar group on surface,cannot form a bond with highly polar liquids like water,and they will remain unwetted in the polar liquid and prone to contact the gas phase.On the contrary,the wettable particles will be entirely wetted due to the formed physical bonds with the polar molecules.

Jamialahmadi and Müller-Steinhagen[111]studied the effect of the solid particle nature on gas holdup in a slurry reactor and found that the gas holdup decreased considerably when small amounts of non-wettable solids (i.e.,polystyrene particles) were added into the air–water system.It is noteworthy that when the solid concentration varied from 0.02 to 0.10,the gas holdup was affected marginally.On the contrary,even for almost identical particle size and density,the addition of a small number of wettable solids (i.e.,nylon and diakon particles with a loading less than 0.05) into the air–water system could prominently promote the gas holdup in the transition and heterogeneous flow regime,as shown in Fig.13.

The particular phenomenon was explained as that the wettability of solid particles would affect the bubble coalescence [111].That is to say,the non-wettable solids could promote the bubble coalescence while the wettable solids could suppress bubble coalescence.They argued that the extent of solid particles dispersed in water was dependent on the balance between the particle cohesion and the adhesion of solid particles to water.The non-wettable particles tended to stick together rather than being dispersed in the water individually.On the contrary,the wettable particles have strong polar groups in their structure,and they would be suspended in the bulk of water without a tendentious migration to the gas–liquid interfaces,which can be verified by the fact that no floated particles were observed when the gas was stopped.Therefore,the polar liquid could not adhere to the surface of non-wettable particles,and the resistance of the liquid film between bubbles related to bubble coalescence will be reduced because of the presence of non-wettable particles in the film.However,the wettable particles,which exist in the liquid film,will lead to a higher resistance for bubble coalescence,making the gas holdup increasing.

However,some contradictory conclusions were also obtained by Kimet al.[22];it was observed that the bed with nonwettable particles tend to expand rather than contract when the gas was injected into the bed,which was interpreted as the free motion of non-wettable particles resulted in the break-up of bubbles,and in turns increasing the gas holdup [22].A similar result was also proposed by Kelkaret al.[21] who studied the effect of solid wettability through two different solid particles,i.e.,oil shale particles and polystyrene beads.They argued that the oil shale particles as a kind of wettability particle could promote bubble coalescence and hence decrease the axial dispersion coefficient.What on earth is the influencing mechanism of the solid particle wettability should be clarified in the future.

Fig.13.Influence of solid wettability on gas holdup [111].

3.5.Influence of particle shape

Unlike the solid physical properties,such as density,size,and wettability,the influences of particle shape on the hydrodynamic characteristics and mass transfer performance in the slurry reactors are lack of detailed investigation.The solid particles added to the slurry reactor varied in shape in the industrial processes.Sastaravetet al.[23] selected four different polypropylene solid particles,including ring,sphere,cylinder,and square (the detailed information of polypropylene solid particles are listed in Table 3),to investigate their effects on the bubble hydrodynamics in a bubble column reactor,and the related results are shown in Fig.14.

Table 3 Detailed information on polypropylene solid particles

In this Fig.14,it can be seen that the mean bubble diameter decreases with the addition of solid particles.In addition,the extent of influence of the particle shape on mean bubble diameter was distinct whenugwas higher than 0.0051 m?s-1,and the ring particles resulted in the smallest bubble diameter and followed in order by the sphere,cylinder,and square particles,which may be due to the different rates of bubble break-up and the ability to maintain the bubble size at the highugfor each particle shape.For the ring shape solid particles,which have a stronger force at the edges than those of the edgeless solids,they can capture the bubbles inside,thus avoiding the bubble coalescence at the highug[23].However,the influence extent of the solid particle size and surface roughness is more influential than that of the particle shape at the normal conditions,and the solid particle with a large diameter and high surface are more effective in diminishing the bubble coalescence [115].

A similar conclusion was also proposed by Wongwailikhitet al.[116],who investigated the particle shape effect on the bubble hydrodynamics and mass transfer rate using the cylinder,sphere,ellipsoid,and ring solid particles.The experimental results indicated that the solid particles with the ring-shape led to a better mass transfer performance at the same conditions in the bubble column reactor and followed in descending order by the sphere,ellipsoid,and cylinder particles,which attributed to the hollows and their surface area of ring-shaped particle that could decrease the liquid circulating velocity in the column.Besides,the particles with sharp edges positively influence the rate of bubble break-up[116].

Fig.14.Influence of particle shape on mean bubble diameter in a bubble column reactor [23].

3.6.General remarks

The hydrodynamic characteristics are different with different solid particles in the slurry reactors,and the concentration of the added solid particles also leads to a notable and complex influence on the performance of the slurry reactors.The variations of solid properties,including density,particle size,wettability,and particle shape,make the multiphase processes more complex.

Generally speaking,the addition of no-wettability solid particles negatively influences the gas holdup,liquid velocity,and mass/heat transfer performance,and the homogeneous flow regime is destabilized at a high solid concentration.Similarly,the distribution of bubble size could be widened with more nonwettable solid particles.It should be noted that the surface tension of the continuous phase will decrease while the slurry viscosity will increase as the increment of solid concentration.Therefore,the effects of adding solid particles on gas holdup can be balanced to some extent by different variations of physical properties (i.e.,the apparent slurry viscosity and surface tension) in the continuous liquid phase,and this dual influence deserved to be investigated separately and systematically in the future.

The mixing and mass transfer properties are more excellent for the system with the low-density-particles,and the particle size did not exert any notable influence on hydrodynamics.Though the effects of solid properties on hydrodynamics have been widely investigated in the past,several underlying mechanisms are still not discernable,especially for the influences of the solid wettability and particle shape.Wettability is usually ignored in many researches,and it should be paid more attention.The influences of particle shape are mainly ascribed to the rate of bubble break-up and the ability to maintain the bubble size at the highug,and the ring-shaped solids with hollows and sharp edges are considered the optimal particles for a better mass transfer performance.However,in practice,the spherical particles are usually employed because of their relatively high mass transfer efficiency and ease of being fluidized.

4.Influence of Operating Conditions

Numerous experimental and theoretical investigations in the gas–liquid and gas–liquid-solid system with different operating conditions have been undertaken,and these investigations are beneficial for a better understanding of the hydrodynamics in the slurry reactor.The prevailing conditions that affected the hydrodynamics and mass/heat transfer behaviors include superficial gas velocity,operational pressure,and operating temperature[77,117,118].Moreover,variations of physical properties,including liquid viscosity,gas density,and surface tension with the pressure and temperature variations,should not be ignored when making comments on the slurry reactors [119].

4.1.Influence of superficial gas velocity

The slurry reactors prevail in different flow regimes at different superficial gas velocities,which lead to different hydrodynamic characteristics (i.e.,gas holdup,liquid velocity,bubble size distribution,and bubble rise velocity).However,most researches focused on a relatively much lowerugthan the operationalugin the industrial slurry reactors [50].Therefore,the hydrodynamics deserves further systematic investigations,especially under the gas jetting conditions for industrial applications [24].

4.1.1.Influence of superficial gas velocity on gas holdup

ugis a crucial factor that influences the gas holdup,and the relation between theugand the gas holdup has been reported in numerous experimental investigations [10,57,87,120,121].Generally speaking,the gas holdup usually increases with the increment ofug.However,there exist different behaviors in the homogeneous and heterogeneous regimes:The gas holdup increases almost linearly with the increment ofugin the homogeneous regime (the slope of gas holdupversus ugis usually greater than 1 s?m-1and the line passes through the origin of coordinates),while in the heterogeneous regime,the increase is less pronounced,i.e.,the slope in the profile of gas voidage againstugis usually less than 1 [62,118,122].

Krishnaet al.[77] measured the gas holdups in the dilute and dense phases by a dynamic gas disengagement method,which indicated that the small bubble gas holdup in the dense-phase was practically independent of the operating gas velocity whenugis above 0.1 m?s-1.Similarly,Hyndmanet al.[120] investigated the flow regime transition using the method of gas holdupversus ug(from 0.037 m?s-1to 0.15 m?s-1);they concluded that the small bubble gas holdup was a constant,which equaled to the total gas holdup of flow regime transition.Wanget al.[75] showed that the gas holdup increased almost linearly with increasingug(0–0.10 m?s-1).Moreover,the radial profile of gas holdup became more uniform whenugexceeded 0.04 m?s-1,which may occur due to the variations of bubble size in the radial direction withug.

However,a contrary conclusion was obtained by Shaikh and Al-Dahhan [118] as shown in Fig.15.A sharp increase in radial gas holdup profile was observed with the increment ofug,especially when theugwas around 0.06 or 0.07 m?s-1.The radial profile of gas holdup showed a noticeable change at the regime transition point between the homogeneous and heterogeneous regimes.Actually,the radial profile of gas holdup was dependent on the flow regime,which was uniform in the homogeneous regime (ugbelow 0.07 m?s-1) and showed a parabola trend in the heterogeneous regime [123,124].

Fig.15.Influence of superficial gas velocity on radial profile of gas holdup [118].

4.1.2.Influence of superficial gas velocity on liquid velocity

Liquid-phase mixing,which governs the liquid residence-time distribution and affects the gas phase behavior,determines the mean driving force for mass transfer [125].The liquid undergoes a circulation in the slurry reactor,which rises with big bubbles in the central region and flows downward in the near-wall region.

Numerous experimental studies have been conducted to provide insight into liquid velocity distribution in the slurry reactors.Generally,the liquid velocity in the central region increases with increasingug[126–128].Krishnaet al.[129]carried out some notable experiments,measuring the liquid velocity profiles along the center-line and in the radial direction at different superficial gas velocities.Their results showed that the liquid velocity increased almost linearly with theugincrement,and the radial distribution of liquid velocity was parabolic.Degaleesanet al.[125] measured the ensemble-averaged liquid velocities using a computer-aided radioactive-particle tracking (CARPT),and the corresponding results are shown in Fig.16.It can be seen that the reversal point in the profile of mean axial liquid velocity was always located at the point ofr/R≈0.65 whenugvaried from 0.024 m?s-1to 0.12 m?s-1In addition,it also showed that the liquid velocity profile was highly dependent on the flow regime (relevant withug)and the column diameter.

Fig.16.Influence of superficial gas velocity on non-dimensional time-averaged axial liquid velocity profiles [125].

It is noteworthy that Wu and Aldahhan[130]proposed a simple correlation to predict the axial liquid velocity profile under a wide range of operating conditions.In their model,onlyug,the physical properties,and the column dimensions were required to input.Merchuk and Stein[131]also proposed a simple exponential function,in which the measured liquid velocity could be adequately correlated tougfor several ratios of opening in the downcomer of an external airlift reactor.These contributions are necessary for the design,optimization,and control of the slurry reactors,and the detailed information about the correlations are listed in Table 4.

4.1.3.Influence of superficial gas velocity on bubble size

Many experimental and theoretical investigations of bubble formation in the gas–liquid or gas–liquid-solid system under different operating conditions have been undertaken [132].Different flow regimes may prevail at different superficial gas velocities in these slurry reactors,leading to different bubble behaviors.Generally speaking,a homogeneous flow regime is usually observed at lowug,and bubbles with a narrow bubble size distribution and weak bubble–bubble interaction are present.However,at highug,there exists a wide bubble size distribution due to bubble break-up and coalescence,making small and large bubbles coexisting in these reactors [133,134].

There also exist several diverse impacts of orificeugon the bubble diameter just formed at orifices[50,135].Xiaoet al.[24]found that the bubble diameter firstly increased monotonously to a specific value and then kept relatively a constant when increasing the orificeugunder the industrial jetting conditions (the orificeugfrom 10 m?s-1to 80 m?s-1).The steady increase of bubble diameter in the low range ofugcan be attributed to the increased bubble coalescence resulted from the increased number of bubbles when the orificeugincrease.However,the relatively constant bubble diameter at high orificeugcan be explained by the force balance(buoyancy and gas momentum act as upward forces;surface tension,drag,and inertial forces generated by acceleration act as downward resistance) during the bubble formation process[136]).Under higher orificeug(the Reynold number is more than 1000),a big slip velocity between the gas and the liquid phase and a prominent drag force due to the invariant drag coefficient are obtained,resulting in the nearly constant bubble diameter[137,138].The results are also consistent with the bubble prediction model proposed by Miyaharaet al.[139],who studied the bubble size and its distribution in a bubble column with a draught tube and a sieve plate at a high orificeug.Jamialahmadiet al.[50]found that the slope of bubble diameterversusgas flow rate was relatively smaller at the high gas flow rate (G>4 × 10-6m3?s-1)than that at the low one in the water-glycerol solutions.Wanget al.[140] also studied the relationship of the bubble volume and the gas volumetric flow rate (the gas pressure of air feed is 4 × 105Pa) and found that the bubble diameter maintained constant until the gas flow rate was up to 4 × 10-7m3?s-1for a given orifice and then increased continuously with the increased gas volume flow rate.Fukumaet al.[141] reported that the bubble size increased slightly with increasingugwhenugwas less than 0.02 m?s-1and then increased considerably whenugwas larger than 0.04 m?s-1in a bubble column using a multi-nozzle gas distributor that had 8 tubes with 2.6 mm in diameter (air–waterglass beads,dp=160/460 μm).

However,a different conclusion was also reported by Wanget al.[75]who investigated the hydrodynamics using a ring gas distributor with 36 holes(1.2 mm in diameter)in an external loop airlift slurry reactor(air–water-glass beads,dp=200 μm).The results indicated that the bubble size decreased noticeably with increasingugin the lowugrange and the reduction of bubble diameter became negligible whenugexceeded 0.05 m?s-1.The decreased bubble diameter may be ascribed to bubble breakage in a violent turbulent environment and the bubble redispersion exerted by the substantial liquid circulation in the external loop airlift slurry reactor.Additionally,it should be noted thatugin these work is too small compared to that in the research of Xiaoet al.[24]leading to difficulties in comparison among these researches.Moreover,these contradictory conclusions about the influence ofugon bubble formation may arise from the differences in gas sparger[142] and pressure.

4.2.Influence of temperature

Most previous investigations in the slurry reactors were operated at the atmospheric temperatures(i.e.,less than 313.1 K).However,elevated temperatures were commonly adopted in the commercial contactors,sometimes even near the boiling points[25].To quantify the hydrodynamic characteristics and bubble behaviors at high temperature,it is necessary to understand the underlying mechanism of temperature influences on the fluid flow.

4.2.1.Influence of temperature on physical properties of fluids

To characterize the hydrodynamic behaviors of the slurry reactors under high temperature conditions,it is crucial to understand the variations of the physical properties of all the fluids.Under the atmospheric pressures,it has been widely accepted that the surface tension decreases approximately linearly with the increasing temperature [143] as shown in Fig.17.

It has been widely accepted that the correlation of σ=a-bt(whereaandbare constant,andTis the temperature) is valid for the large majority of organic liquids.Deam and Maddox [144]found that the surface tension decreased with an increment of temperature under the low-pressure conditions.However,the surface tension showed a slight increase when the pressure was more than 4×106Pa[144].Linet al.[119]indicated that the surface tension decreased with the increased temperature by approximately 4% for every 10 K in the N2-Paratherm NF system.

The influence of temperature on liquid viscosity is more significant than that on surface tension,as shown in Fig.18.When the temperature increased from 293 K to 373 K,the viscosity of Paratherm NF at 2.01×107Pa,1.01×107Pa,and 1.0×105Pa could be decreased 17.89,12.79,9 folds,respectively [119].On the other hand,the gas viscosity almost increases linearly with the increased temperature under the atmospheric pressure.Unlike surface tension and viscosity,the temperature has little effect on the liquid density,which only decreased by approximately 6%when the temperature increased from 293 K to 393 K [119].However,the gasdensity could decrease sharply with the increment of temperature under the specific pressures according to the ideal gas state equation.It should be noted that the influencing mechanisms of temperature on hydrodynamics are mainly attributed to the variations in physical properties of fluids;a typical illustration of the variations in different systems is given in Table 5 [25].

Table 4 The correlations for predicting the liquid velocity

Table 5 Variation of fluids’ physical properties in different working systems [25]

Fig.17.Dependence of surface tension on temperature for several organic liquids[143].

Fig.18.Liquid viscosity as a function of temperature at different pressures [119].

4.2.2.Influence of temperature on gas holdup

The effect of temperature on gas holdup is obscure because of the inadequate data in the literature.The operating temperature may strongly influence the local gas holdup and radial gas holdup profiles,and the detail relations depend on the operating conditions (temperatureTand pressureP) through their influences on the fluid physical properties.According to models of bubble formation [24] the bubble size during the bubble formation would be decreased due to the decreased liquid viscosity,lower surface tension,and smaller gas density.In contrast,the initial bubble size would be raised because of the decreased liquid density,owing to the temperature increase.Therefore,the joint actions of these multiple factors with nonlinear interactions resulted in a complicated influence on gas holdup.

The transitionugfrom the homogeneous to the heterogeneous regime decreased with the increment of temperature.Zouet al.[25] inspected the relation between the gas holdup and temperature,and it can be seen from Fig.19 that the operating temperature could remarkably affect the gas holdup in all the systems.To be specific,the gas holdup in the traditional air–water system could be promoted by about 143%when the temperature increased from 298.15 K to 367.15 K.Additionally,the effect of temperature can be divided into two stages by the increased rate of gas holdup (i.e.,increased slowly and increased remarkably,also shown in Fig.19),and the demarcation temperature points are 348.15 K,338.15 K,and 353.15 K for the air–water,air-alcohol,and air-5%NaCl systems,respectively.Pohoreckiet al.[145] also observed that the gas holdup increased with the increased temperature,and they thought that the reason was probably mainly due to the diminution of the surface tension according to their correlations between the gas holdup and the liquid physical properties.

Deckweret al.[146] studied the hydrodynamics in the bubble column slurry reactors with different diameters (i.e.,4.1 cm and 10 cm).For the reactor with a 4.1 cm column diameter,a remarkable decrease (approximately 66.67%) in the gas holdup was observed as the temperature increased from 453.15 K to 513.15 K,but the gas holdup almost maintained a constant with a further increase in temperature.For the larger diameter column,no significant difference of gas holdup can be distinguished in a wide range of temperatures(from 416.15 K to 558.15 K).A similar decreasing trend with temperature was also observed in an air–water system reported by Groveret al.[147],who carried out the experiments in a bubble column with a diameter of 10 cm.Moreover,in their investigation in the air-electrolyte solution system(i.e.,air-CuCl2-water system and air-NaCl-water system),the gas holdup increased with the increased temperature at lowug,while an opposite phenomenon was observed at a highug.The complex dependence of gas voidage on temperature in these two contributions may be ascribed to the small reactor column diameters employed.The influence of temperature on gas holdup in slurry reactors with large diameter needs further investigations.

Fig.19.Influence of operating temperature on the total gas holdup [25].

4.2.3.Influence of temperature on bubble behaviors

The physical properties of the liquid phase have significant impacts on the bubble size.It has been widely accepted that the gas holdup tends to become higher with the decrease of surface tension,liquid viscosity,and gas density,resulting from the diminished stable bubble size at the increased temperature [148].

Soonget al.[149] investigated the Sauter mean bubble diameters at two different temperatures (293.15 K and 538.15 K) and two different pressures (1.0 × 105Pa and 1.36 × 106Pa).The experiment showed that the bubble size was substantially decreased (approximately from 15 mm to 4 mm) when the temperature increased from 293.15 K to 538.15 K at constant pressure,and the main reason was that the high temperature led to a low surface tension.Linet al.[119] found that the increased temperature led to a small average bubble diameter and a narrow distribution of bubble size.However,they thought that the decrease of bubble size was mainly ascribed to the crucial role of combined reductions in surface tension and liquid viscosity.However,an opposite conclusion was also obtained by Groveret al.[147],whose experiments indicated that the increased temperature led to a significant decrease in gas density instead of the changes of surface tension and liquid viscosity,increasing the bubble size.

Schaferet al.[148] proposed that the increased temperature tended to reduce the bubble diameter on the condition that the operating pressure was higher than the saturation pressure when the evaporation was negligible.Lauet al.[38] also argued that the influence of temperature was generally not notable,only if at the high-pressure conditions (more than 1.48 × 106Pa).

4.3.Influence of pressure

Most slurry reactors’ investigations were conducted under ambient conditions,while the experimental data performed under high pressure is relatively limited.However,many industrial processes of commercial interest (e.g.,methanol synthesis,Fischer-Tropsch synthesis,direct coal liquefaction) are executed under the high pressures[26,150].The bubble dynamics and macroscopic hydrodynamic properties in the high-pressure systems should be offered for better design,scale-up,and operating these multiphase reactors [151].

4.3.1.Influence of pressure on physical properties of fluids

Similar to temperature,it is crucial to know the physical properties of fluids under the high pressure.Except for the influence of pressure on gas density,the influences of pressure on other physical properties,such as the surface tension,viscosities of gas and liquid,and liquid density,are usually ignored.In practice,investigations of the influence of increased pressure on the liquid viscosity and surface tension are very scarce.Thus,the phenomenon that only tiny bubbles(i.e.,about 1 mm with a large straight pipe sparger) in the slurry reactor of direct coal liquefaction [10] were obtained under the condition of 1.9 × 107Pa and 723.15 K could not be well understood.

Slowinskiet al.[152]found that,in general,the surface tension of the liquid phase decreased with increasing operating pressure,which was ascribed to the adsorption of pressurizing gas on the liquid surface.Besides the gas absorption,Rice[153]assumed that this effect could also be attributed in part to the intrinsic decrease in liquid density in the neighborhood of the surface.A typical illustration of the variation of surface tension with operating pressures in many gas–water systems and gas-n-hexane systems is shown in Fig.20(a) and (b).It can be found that except for helium,which shows no effect,the surface tension of water andn-hexane decreased distinctly and almost linearly with increasing pressure for other kinds of gas.The falling slope is dependent on the type of substances.A similar conclusion was also proposed by Massoudi and King [154],who investigated the effects of operating pressure on the surface tension of water with He,H2,O2,N2,Ar,CO,CO2,N2O,CH4,C2H4,C2H6,C3H8,andn-C4H10.

Stephan and Lucas [155] indicated that most organic liquids’viscosity could augment dramatically with increasing pressure.Besides,the relation between pressure and liquid density may be interrelated with the temperature.Linet al.[119] found that the viscosity of Paratherm NF can be increased by about 65% as the pressure increases from 1.0 × 105to 2.01 × 107Pa at a constant temperature of 293 K,as shown in Fig.18.However,the influence of pressure on the liquid density is negligible,which is consistent with that of temperature[119].Therefore,the liquid physical properties should be applied to interpret the flow characteristics in the slurry reactors at the corresponding pressure.

4.3.2.Influence of pressure on gas holdup

A significant pressure effect on gas holdup was observed in the slurry reactors.Shaikh and Al-Dahhan[118]carried out the experiments in a pilot-scale bubble column at atmospheric as well at high operating pressures (i.e.,4 × 105Pa and 1 × 106Pa);their results showed that the cross-sectional averaged gas holdup at the point of flow regime transition increased with the increased operating pressure,demonstrating an increase in operating pressure could delay the regime transition.

Fig.20.(a)Influence of pressure on surface tension between water and some gases[152].(b) Influence of pressure on the relative surface tension between n-hexane and some gases [152].

It was reported that the relationship between the pressure and the gas holdup might show a remarkable difference under various operational conditions (different superficial gas velocities,gas spargers,and solid loadings).The majority of works reported that gas holdup was markedly promoted when the pressure increased[156–158].For example,Fanet al.[159] found that the elevated pressures (1 × 105–5.6 × 106Pa) would lead to a high gas holdup in a wide range ofug(0–0.4 m?s-1) in the gas–liquid and gas–liquid-solid systems.Besides,they also obtained an empirical correlation to estimate the gas holdup under the high-pressure conditions.A similar conclusion was also proposed by Urseanuet al.[117] who performed the experiments in a pressurized environment (1 × 105–5.6 × 106Pa) with high viscous liquid media.The total gas holdup was observed to have a considerable increase with the increment of operating pressure.

Jianget al.[160]reported that the gas holdup could be increased with increasing pressure up to 1.5 × 106Pa,beyond which the influence of pressure was insignificant.A similar trend was also observed by Letzelet al.[60],who carried out the experiments in a bubble column operated under the pressure from 1.0 × 105Pa to 1.3× 106Pa in order to examine the effect of elevated pressure on the stability of the homogeneous flow regime.As shown in Fig.21,a significant influence of operating pressure in favor of high gas fraction was observed.To be specific,the gas voidage atugof 0.2 m?s-1in the nitrogen-water system increased from 0.29 to 0.57 when the pressure increased from 1 × 105Pa to 7 × 105Pa.However,this influence was insignificant when the pressure above 7×105Pa,and its influence can be almost ignored at the pressure of more than 1.1 × 106Pa.

Kojimaet al.[161] studied the influence of pressure on gas holdup using single nozzle spargers of different diameters.The effect became noticeable with the decrease of nozzle diameter;moreover,the gas holdup increased with the increased pressure(from 1 × 105Pa to 1.1 × 106Pa) in the gas–liquid system and independent of pressure when the solid mass concentration was up to 0.3,which might be attributed to the coalescence of bubbles enhanced by the addition of solid particles.Similarly,Luoet al.[162]carried out the experiments of pressure effects on gas holdup in slurry bubble columns at pressures up to 5.6×106Pa andugup to 0.45 m?s-1.They observed that the gas holdup increased with an increase in pressure (from 1 × 105Pa to 5.6 × 106Pa).Besides,at the sameugof 0.3 m?s-1,the gas holdup decreased from 0.55 to 0.48 (about 12%) when the solid concentration increased from 0 to 0.191 at 5.6 × 106Pa,while at the ambient pressure,the counterpart decreased from 0.35 to 0.18 (about 49%).

Fig.21.Influence of system pressure on the total gas holdup [60].

The magnitude of the pressure influence on gas fraction was found dependent onug.Deckweret al.[146]found that little effect of pressure on gas holdup in a Fischer-Tropsch slurry bubble column when the pressure rose from 4.0 × 105Pa to 1.1 × 106Pa.It is noteworthy that this marginal influence may be ascribed to the smallug(lower than 0.034 m?s-1) adopted in their experiments.Oyevaaret al.[163]also proposed an indistinctive influence of pressure on gas holdup at lowugin the range from 0.01 m/s and 0.035 m.s-1.Additionally,it was observed that the influence of pressure gradually weakened when the liquid viscosity increased[117].

4.3.3.Influence of pressure on bubble behaviors

According to numerous researches conducted to investigate the effect of pressure on bubble behaviors,the pressure is a significant factor that affected the mean bubble diameter.Since the pressure mainly affects the gas density[148],surface tension[152],and liquid viscosity [119],the influence of fluid physical properties and operating pressure on bubble diameter is closely conjugated.It has been widely accepted that the elevated pressures could bring about an increment of gas holdup in the slurry reactors,which was mainly attributed to the small bubble size and narrow bubble size distribution produced under high pressures.The combination of three factors(reduced bubble size at the sparger[164],the suppressed bubble coalescence [160],and the enhanced breakup of large bubbles [165]) leads to a complicated relationship between the pressure and the bubble diameter.Meanwhile,the small bubble diameter at elevated pressure will lead to the increased gas holdup in the heterogeneous flow regime due to the longer residence time of bubbles with a smaller diameter [166].

La Nauze and Harris[167]found that a large fraction of smaller bubble was formed when the pressure increased from 1×105Pa to 2 × 106Pa,and this was in agreement with the findings of Kling[168]:The bubbles became more elongated and also significantly smaller at the high pressures.Fanet al.[159]indicated that the rise velocity of single bubbles in liquids and liquid–solid suspensions decreased with an increase in pressure,and the bubble size was drastically reduced as the pressure increased.The most fundamental reason for the bubble size reduction can be attributed to the variations of physical properties of gas and liquid with the pressure[169].

Lemoineet al.[170]proposed that the pressure increase gradually shifted the bubble size distribution toward smaller in the gas–liquid system (two gases:N2and air;four organic liquids:Pure toluene and three mixtures of toluene,benzoic acid,and benzaldehyde).Besides,the small bubble mean diameter seemed to remain constant when the pressure changed from 2.0×105Pa to 8.0×105Pa,whereas the overall Sauter mean bubble diameter decreased.Idogawaet al.[156] also argued that the bubble diameter decreased with increasing pressure,as shown in Fig.22.In addition,the bubbles were of almost uniform size,and a narrower bubble size distribution was obtained with the increased pressure.However,this dependence was weakened as the operating pressure increased and finally disappeared.

It should be noted that the elevated pressure could lead to a reduction of surface tension and the increments of gas density,thus decreasing the size of the bubbles formed at the gas sparger.What’s more,the mean bubble diameter tends to be uniform no matter what type of gas sparger is applied.However,these results were only suitable for gas–water systems.A similar conclusion was also proposed by Luoet al.[171],who analyzed the effect of pressure on the bubble coalescence and break-up in a nitrogen-Paratherm NF-glass bead (dp=2.1 and 3 mm,ρp=2520 kg?m-3)system and found that the average bubble size decreased and the bubble size distribution became more uniform with the increased pressure.However,they thought that the pressure effect was insignificant when it was up to 6 × 106Pa.

4.4.General remarks

Fig.22.Influence of system pressure on mean bubble diameter using different types of gas spargers [156].

The hydrodynamics under various operating conditions in the slurry reactors have been investigated previously.The operating conditions,includingug,temperature,and pressure,play crucial roles in determining the slurry reactor hydrodynamic characteristics.

With the increase ofug,the gas holdup first increases linearly and then becomes obscure,and the radial profile of gas holdup changes from the uniform distribution to a parabolic profile.The liquid velocity increases almost linearly withug,and the radial distribution of liquid velocity becomes parabola-like.Moreover,the liquid velocity also depends on the design of the gas sparger.

The operating pressure and temperature not only could change the gas density and gas viscosity,but also could alter other physical properties of liquid(i.e.,surface tension,liquid viscosity,and liquid density).Hence,they should be employed to interpret the hydrodynamic characteristics in the slurry reactors under the corresponding pressure and temperature conditions.The increased temperature leads to a decrease in surface tension and liquid viscosity.The surface tension decreases while the liquid viscosity and gas density increase with the operating pressure increment,but these variations have been usually ignored by many investigators and deserve some special attention.It has been widely accepted that the gas holdup will increase while the bubble diameter tends to become smaller with the increased temperature and pressure,depending on the sensitivities of the fluid physical properties.

5.Conclusions and Perspectives

The slurry reactors have plenty of excellent benefits,including high catalytic efficiency,low production cost,feasible scale-up,and outstanding mass/heat transfer performance,and hence the slurry reactors were recommended as industrial multiphase reactors [172,173].

The physical properties of fluids have significant influences on the hydrodynamics and mass transfer performance.The increased liquid viscosity has a dual effect on the bubble size distribution,the gas holdup,and the flow regime transition.However,the increment of gas density leads to an increase of gas holdup and shows different rates under different superficial gas velocities.The addition of a surfactant to an aqueous solution can remarkably decrease the surface tension,which results in a smaller mean bubble diameter and a higher gas holdup.The increased gas density could promote the gas holdup because of the enhancement of bubble break-up,while the influence of gas viscosity on hydrodynamics is negligible.

The hydrodynamics in a slurry reactor would be totally different if different kinds of solid catalysts are added.It was found that the solid concentration could directly influence the apparent slurry viscosity.It is noteworthy that the solid loading can also decrease the surface tension,and this neglected impact deserves more attention in the future.It was found that a low solid concentration could stabilize the homogeneous flow regime,and its destabilization usually occurred at a high solid concentration.Besides,the gas holdup in the regime transition point decreases with the increased solid concentration.The liquid circulation velocity decreased with the existence of solid particles because of the reduced driving force.The particle size above 50 μm has been observed to have a negligible effect on the gas holdup as long as their concentration is low.The wettable and non-wettable particles have an opposite effect on the gas holdup in slurry reactors.The influence of particle shape is mainly ascribed to the rate of bubble break-up and the ability to maintain the bubble size at a higherug,and the solid with hollows and sharp edges are considered favorable for mass transfer in the slurry reactors.

Generally speaking,the gas holdup increases with increasedug,and there exist different growth trends in the homogeneous and heterogeneous regimes.The liquid velocity in the central region increased with the increment ofug,and the radial profile of liquid velocity is parabolic.A highugwould produce a wide bubble size distribution due to the break-up and coalescence of bubbles.The temperature affects the fluid physical properties (surface tension,liquid and gas viscosities,liquid and gas densities);the surface tension decreases linearly with temperature in different organic liquids;the liquid viscosity decreases with the increment of temperature,while the liquid density is slightly influenced by temperature.

It has been widely accepted that the bubble diameter tends to become smaller with the decrease of surface tension and liquid viscosity,resulting in an increment of gas holdup at a high temperature.Similar to the influence of temperature on fluid density,the surface tension can decrease linearly with increasing operating pressure in many gas–liquid systems,while the liquid viscosity can also increase slightly with the increased pressure.These variations of liquid physical properties could bring about a small bubble size during the bubble formation and a narrow bubble size distribution.Some investigations are highly desired to reveal the underlying mechanisms due to variations of fluid physical properties,especially evolutions of liquid viscosity and surface tension at the elevated temperature and pressure.Besides,the gas sparger’s influence can be ignored in the gas–water system at the high operating pressures (approximately more than 6 × 106Pa).However,the hydrodynamics deserves further systematic investigations,especially for the operating conditions close to the industrial applications.

It is noteworthy that the variations of hydrodynamics and mass/heat transfer in the slurry reactors are highly dependent on the operating conditions,and there is still a lack of investigations under the operating conditions close to industrial processes.Although enormous merits in the slurry reactors have been revealed in previous investigations,the slurry reactors’technology needs to be developed systematically by the economically and industrially feasible method.

Just as the coin has two sides,there are some defects associated with the slurry reactor.For example,the solid particles usually take part in the chemical reactions as a catalyst,which needs to be recycled continuously.This annoying problem was successfully resolved by our group [55,56,69],who proposed a new kind of slurry reactor to achieve a continuous large-scale production.Additionally,apart from the conventional shortcomings (backmixing in both the continuous and dispersed phases [174] and the liquid–solid separation[175]),the problems of low volumetric solid catalyst loading and non-uniform solid distribution should also be seriously considered,which not only represents the productivity of reactor but also influences the catalyst deactivation rate and attrition.It should be noted that these deficiencies can be well dealt with by process intensification with the help of computational fluid dynamics.

It is noteworthy that although numerous achievements have been made in previous literature,there are still several unclear mechanisms,including the dual effect of liquid viscosity,the influence of solid concentration on surface tension,the impacts of solid wettability,the dependences of the surface tension and the liquid viscosity on the operating temperature and the pressure,and so on.Besides,the limited experimental data over a broad range of operating conditions,the considerable challenges resulted from backmixing in fluids,and difficulty in the liquid–solid separation bring about a great challenge to design,scale-up,and operate the industrial slurry reactors properly.These problems should be further investigated on novel promising slurry reactors integrating mixing and separation in some industrial processes.Moreover,the combination of the CFD with the experimental data is a powerful tool to investigate the hydrodynamic characteristics and mass/heat transfer performance in the novel slurry reactors.

Nomenclature

Cmsolid mass concentration in the slurry,kg?m-3

Cssolid volumetric concentration in the slurry,dimensionless

DTcolumn diameter,m

dBmean bubble diameter,mm

d0orifice diameter,mm

dpsolid particle diameter,μm

GGas flow rate,m3?s-1

kLavolumetric mass transfer coefficient,s-1

Ppressure,Pa

RegReynolds number of gas phase,dimensionless

ReslReynolds number of slurry phase,dimensionless

Ttemperature,K

Ub,Llarge bubble rise velocity,m?s-1

Ub,Ssmall bubble rise velocity,m?s-1

Ugsuperficial gas velocity,m?s-1

Ulliquid velocity,m?s-1

εggas holdup,dimensionless

εlliquid holdup,dimensionless

η∞relative effective viscosity,dimensionless

μeextensional viscosity,Pa?s

μggas viscosity,Pa?s

μlliquid viscosity,Pa?s

μslslurry viscosity,Pa?s

ρggas density,kg?m-3

ρlliquid density,kg?m-3

ρssold density,kg?m-3

σ surface tension,N?m-1

vsuskinematic liquid viscosity,m2?s-1

veff,radradial momentum transfer coefficient,m2?s-1

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (21 878318;21808234),the Dalian National Laboratory for Clean Energy Cooperation Fund,CAS (DNL201902),‘‘Transformational Technologies for Clean Energy and Demonstration”,Strategic Priority Research Program of the Chinese Academy of Sciences (CAS) (XDA21060400),Qingdao Institute of Bioenergy and Bioprocess Technology (QIBEBT) and Dalian National Laboratory for Clean Energy (DNL) of CAS (QIBEBT ZZBS 201803;QIBEBT I201907),Director Innovation Fund of Synthetic Biology Technology Innovation Center of Shandong Province (sdsynbio-2020-ZH-02),and Project of CNPC-DICP Joint Research Center.