Dan Li ,Kai Guo ,*,Jingnan Li ,Yiping Huang ,Junchao Zhou ,Hui Liu ,Chunjiang Liu ,*

1 School of Chemical Engineering and Technology,Tianjin University,Tianjin 300072,China

2 State Key Laboratory of Chemical Engineering,Tianjin University,Tianjin 300072,China

3 China Construction Industrial&Energy Engineering Co.,Ltd.,Nanjing 210000,China

Keywords:Tw o-stage internal loop airlift reactor Hydrodynamics Bubble Multiphase flow

A B S T R A C T Local hydrodynamics of a gas–liquid–solid system,such as bubble circulation regime,gas holdup,liquid velocity and axial profile of solid concentration,are studied in a two-stage internal loop airlift reactor.Empirical correlations for gas holdup and liquid velocity are proposed to ease the reactor design and scale-up.Different bubble circulation regimes were displayed in the first(lower)and second(upper)stages.Increasing superficial gas velocity and solid loading can promote regime transition of the second stage,and the gas holdup of the second stage is higher than that of the lower stage.In addition,the effects of solid loading on bubble behaviour are experimentally investigated for each stage.It is found that bubble size in the downcomer decreases with the presence of solid particles,and bubble size distribution widens under higher superficial gas velocity and lower solid loading.?2018 The Chemical Industry and Engineering Society of China,and Chemical Industry Press.All rights reserved.

1.Introduction

Internal loop airlift reactor(ILALR)is an important class of multiphase reactors,and has been widely applied in chemical/biochemical processes,and wastewater treatment[1–5].Compared with conventional stirred tanks and bubble columns,ILALRs have many advantages,such as simple structure,low energy consumption,low shear rate and excellent interphase contacts[6–9].

Hydrodynamic parameters including phase holdup,liquid velocity,and mixing time are very important for the industrial design and scale-up of ILALR.Researchers have studied the hydrodynamics of ILALR by experimental and numerical simulating methods[10–13].In a novel airlift loop photobioreactor,Guo et al.[14]investigated the effects of the top clearance on hydrodynamics and mass transfer coefficient,and empirical models of these parameters are proposed to control the reactor rationally.Using computational fluid dynamics,Ghasemi and Hosseini[15]simulated the gas holdup in riser and downcomer under different bubble circulation regimes,and found that both the gas holdup differences and ratios between the riser and downcomer change significantly as the regime changes.Bubble circulation regimes can be identified according to changes in the gas holdup or gas holdup ratios.Mendes and Badino[16]experimentally studied the effects of operating conditions and liquid physical propertieson regional gasholdup,and proposed several empirical correlations.As the multiphase process applications of ILALRs increase,researchers have attempted to characterise the hydrodynamics in gas–liquid–solid systems[17–19].Because of the intricate effects of particles,the hydrodynamic characteristics of the gas–liquid–solid three-phase system are significantly more complicated than those of gas–liquid systems.Zhang et al.[20]measured the bubble dynamics with different solid loadings and superficial gas velocities.Their results show that compared with the superficial gas velocity,the solid loading has no significant effect on bubble size and bubble rise velocity.Hong et al.[21]explained the bubble-particle collision processes by measuring the force variation and bubble pressure oscillation during such a collision.Results indicate that,with high solid loading,particle collisions and pressure oscillations can lead to bubble breakage.Thus,tiny bubbles are generated because of the presence of solid,which is inconsistent with the results of Zhang et al.[20].It should be noted that the importance of hydrodynamics in the downcomer region has been emphasized due to its promising application in photosynthetic[22–24]or liquid–solid diffusion controlled catalytic and electrochemical processes[25].ILALRs can provide ordered mixing(light/dark cycles)for photosynthesis[22,26],in which the downcomer is regarded as the illuminated region and deserves more interest than riser area because of spatially various illuminance.Also,for electro-organic synthesis,downcomer can be used as an electrochemical reactor[25],and shows the advantages of uniform current and potential distribution over the riser.Nevertheless,local hydrodynamic parameters investigated on the downcomer region are limited,and more studies should be conducted.

In recent years,based on single-stage ILALRs,multistage ILALRs have been proposed with the advantage of higher efficiency.For example,it has been proved that multistage ILALRs have higher gas holdup[27]and mass transfer rate[28]than single-stage ILALRs.Besides the global characteristics,some local hydrodynamic characteristics have been studied to obtain an in-depth understanding of multi-stage ILALRs.In a 2D two-stage ILALR,Zhang et al.[29]installed screens with different mesh sizes in the riser of each stage,which were aimed to break large bubbles up and narrow the bubble size distribution.The results show that screens can efficiently break bubbles up.Their study also indicates that there are two main bubble circulation flow s in the two-stage ILALR,and the local gas holdup in these two stages is obviously different.A similar conclusion was drawn by Li et al.[30],who measured the gas holdup,bubble behaviour and liquid velocity in a two-phase three stage ILALR.The results show that bubble behaviour and liquid velocity are governed by different rules,which depend on the superficial gas velocity.In addition,empirical correlations of gas holdup and liquid velocity for each stage were proposed separately.Apparently,each stage of multistage ILALRs has different flow patterns so that the overall behavior becomes more complicated.Although many hydrodynamic studies concerning the multistage ILALRs have been conducted,there are no sufficient investigations focused on the local hydrodynamics in gas–liquid–solid systems,especially in the downcomer where the data is relatively scarce.

In this study,the hydrodynamics and bubble behaviour in a gas–liquid–solid system are investigated in a two-stage ILALR.First,the bubble circulation regimes in different stages are identified under different superficial gas velocities and solid loadings.The gas holdup,liquid velocity,and axial profiles of the slurry concentration are measured under different flow regimes.Empirical correlations are then proposed to predict the gas holdup and liquid velocity.Finally,the effects of solid loading on bubble size are investigated using the electrical conductivity technique.

2.Experimental

2.1.Experimental setup

Fig.1.(a)Schematic diagram of two-stage ILALR,A:gas distributor,B:internal,C: first stage riser R1,D:second-stage riser R2,E: first-stage downcomer S1,F:second-stage downcomer S2,G:gas–liquid separator;and(b)Schematic diagram of the test facility,1:two-stage ILALR,2:U tube manometer,3:slurry collector,4:rotameter,5:gas valve,6:compressor,7:data acquisition system,8:solenoid valve,9:injection port of tracer.

The experimental installation is shown schematically in Fig.1.The two-stage ILALR was made of polymethyl methacrylate for easy observation of flow behaviour.As shown in Fig.1(a),the two-stage ILALR comprises six main parts:gas distributor(A), first-stage riser R1(C),second-stage riser R2(D), first-stage downcomer S1(E),second-stage downcomer S2(F),and gas–liquid separator(G).The height of the ILALR is 2.0 m,and the inner diameter is 0.19 m.The height H and inner diameter of each stage are 0.70 m and 0.14 m,respectively.The bottom stage is called the first stage,and the other is the second stage.The vertical distance between the two stages is 0.10 m,and there is an internal(B) fixed in the middle of the ILALR,as shown in Fig.2.The internal is made of alloy,and the horizontal clearance from its lower edge to the inner wall of column is 0.01 m.The vertical clearance between draft tube and the bottom of the reactor is 0.09 m.The gas distributor is a sintered filter made of titanium with 10 μm pores,and its diameter is 0.15 m.

In this work,compressed air and tap water were used as the gas and liquid,respectively.Micron glass beads with a density of 2400 kg·m?3and a diameter of 40–50 μm served as the solid phase.Compressed air was injected into the reactor through the gas distributor.The superficial gas velocity based on the reactor cross-section was adjusted in the range 0.03–0.07 m·s?1by the gas valve.The system can be considered to be stable,when there is no obvious fluctuation in the pressure drop.

2.2.Measurements

2.2.1.Bubble penetration depth

The bubble penetration depth h into the downcomer was measured by visual observation[24].The flow pattern can be classified into three different bubble circulation regimes according to the following criteria:

a.h=0 Bubble-free regime(BFR).

b.0＜h＜H Transition regime(TR).

c.h=H Complete bubble circulation regime(CBCR).w here H is the height of the draft tube in a stage.

The BFR exists under low superficial gas velocities,where the bubbles only exist in the riser.In TR,the bubbles are entrained into and partially fill the downcomer.Thus,the axial profile of the gas holdup in the downcomer is nonuniform[31,32].With increasing superficial gas velocity,the flow regime turns from TR to CBCR,in which the bubbles fully fill the downcomer and the axial profile of gas holdup becomes uniform.

2.2.2.Gas holdup

The gas holdup(εG)of the downcomer in each stage was measured with the pressure drop method[29].The U-tube manometer connections are shown in Fig.1.The relationship between the pressure drop ΔP and gas holdup εGis:

w here ρSLis the slurry density,which can be calculated using:

w here φSis the slurry concentration.Compared with the solid and water densities,the gas density is small,and can be neglected.Thus,εGcan be simplified to:

2.2.3.Local slurry concentration

The local slurry concentration in the downcomer was investigated using the pycnometric technique[33].In the downcomer,slurry taps were installed to gather samples at six different axial positions(0.165 m,0.440 m,0.715 m,0.965 m,1.240 m,1.515 m above the gas distributor),as shown in Fig.1(b).Six taps were used for sampling simultaneously to reduce the detrimental effects of sampling on the bulk flow and the experimental error.The first slurry sample time was 30 min after the introduction of the solid into the reactor.Three samples were taken at 10 min intervals,and the results were averaged as the experimental values.As the densities of water and solid are known,the local slurry concentration(φS)can be calculated as:

Fig.2.Structural details of interstage internals:(a)front view;(b)bottom view.

w here mSLand VSLare the mass and volume,respectively,of the slurry sample,which were obtained from the pycnometric procedure:

2.2.4.Bubble behaviour

The bubble behaviour was measured using a dual-tip electrical conductivity probe and data acquisition system(BVW2,Jiuzhang Chemical Technology,Nanjing,China).A probe consists of two conductive tips fixed by the epoxy resin and supported by a stainless steel tube.The working mechanism of the device is such that different phases induce differentiated voltage signals when they flow through the probes,due to the different conductivities.The measured voltage signals of different phases were recorded during the experiments.In this work,the experimental acquisition frequency was 50 kHz;and 256000 data points were acquired,both of which are sufficient to guarantee precise signals.The values of Lpin Table 1 represent the distance between the upstream and down-stream tips of the dual-tip electrical conductivity probe,as shown in Fig.3.Four probes were installed perpendicular to the direction of bulk flow at different axial locations to measure the bubble behaviour.Their positions(mountiong heights)are given in Table 1.

Table 1Detailed information of probes

To acquire bubble signals,the voltage signals recorded by BVW2 were firstly compared with the critical voltage threshold[34].Bubble signals beyond the measuring range of BVW2(Ub＜ 1 m·s?1and 2 mm＜db＜30 mm)were then filtered out[35,36].Following Ziegenhein et al.[18],the bubble shapes were assumed to be constant in the experiment,so that the chord length along the bulk flow direction represents the bubble diameter.Thus,the bubble diameter dbiwas determined as follow s:

w here t is the total measuring time,Ubis the bubble velocity,which can be calculated as:

where ΔtABis the time difference from the up-stream to down-stream tip of the conductivity probe,and Lpis the distance between the upstream and down-stream tips of the dual-tip electrical conductivity probe.

The mean bubble size can be represented by the Sauter diameter(d32),which was calculated by

Fig.3.Installation and details of the electrical conductivity probe.

2.2.5.Liquid velocity

The liquid velocity(UL)of each stage was analysed using the pulse response technique.A pulse signal(0.5 ml saturated NaCl solution)was introduced to the system after the steady of system has been reached.BVW2 was applied to trap conductivity signals of the tracer in the liquid phase.The original conductivity signals were filtered to eliminate the bubble disturbance.The liquid velocity was calculated as

where Δh is the distance between the measuring heights of two probes and Δt is the response time difference of these two conductivity probes.

The ratio of liquid flow rates in the two stages was monitored to represent the slurry circulation rate GS:

As seen in Eq.(11),GSis the ratio of β2,which represents the fraction of flow rate from S2to S1,and β1,which is the circulation fraction of S1,representing the fraction of flow rate from R1to R2.

When the value of GSapproaches 1,the circulation fractions β1and β2are equivalent.When the value markedly drops from 1,it can be deduced that the circulation in one stage is significant,but insignificant in the other stage.Thus,this index indicates the differences in hydrodynamic behaviour between the two stages.

Fig.4.Axial profiles of slurry concentration φS in downcomer.(C S:●5%;▲10%;▼15%;?20%).

3.Results and Discussion

3.1.Local slurry concentration

For chemical reactions in the multiphase system,it is crucial to ensure the reactants be uniformly mixed in the reactor,especially for three-phase systems in which the particle density is tw ice larger than liquid density.Fig.4 shows axial profiles of the slurry concentration φSunder different operating conditions.At low UG,axial profile of φSis not uniform,and φSin S1is higher than that in S2,especially for CS=5%and 10%.This tendency is attributed to the transition of bubble circulation regime in S2,and detailed explanation can be found in Section 3.2.

3.2.Bubble circulation regime

The flow regime of S1was found to be CBCR under all operating conditions in the UGrange of 0.03–0.07 m·s?1.Flow regime transition occurs in the second stage,as shown in Fig.5.Under low UG,the flow regime of S2is TR,and a transition from TR to CBCR appears as UGincreases.The bubble flow regime substantially depends on the relationship between the liquid circulation velocity and average slip velocity of the bubble swarm in the downcomer[37].In TR,the liquid velocity and slip velocity of the bubble swarm are equal in magnitude,but have opposite directions[38].With an increase in UG,the gas holdup increases in the riser,which can result in an increase in the liquid circulation velocity.When the liquid circulation velocity is greater than the average slip velocity of the bubble swarm,the flow regime becomes CBCR.The same variation trend with respect to UGwas reported by Yu et al.[31]Fig.6 shows the bubble circulation regime of each stage:the first stage is CBCR,whereas the second one is TR.

Fig.5.Effects of U G and C Son bubble penetration depth h in S2.

With an increase in the solid loading,the critical UGfor transition from TR to CBCR decreases(0.10,0.09 and 0.07 m·s?1for CS=0,5%and 10%,respectively).For CS=15%and 20%,the critical UGfor regime transition is less than 0.05 m·s?1.The decrease in the critical UGcan be attributed to the effects of the additional solid on the bubbles near the gas distributor in the riser.According to the study of Yang et al.[39],the bubble size near the gas distribution increases with an increase in solid loading.Larger bubbles have a higher rise velocity and are more likely to enter S2from the riser of S1.In terms of the multiphase reactions,BFR and TR are not desirable because of the unsatisfactory interphase contact[31].Therefore,the bubble circulation regimes in S1and S2are expected to be CBCR.

Fig.6.Bubble circulation regime for U G=0.03 m·s?1(the first stage is CBCR,and the second one is TR):(a)global graph;(b)local graph.

The ununiform distribution of slurry concentration with low UGand CSis because of the TR in S2,in which the liquid velocity is too small to overcome the particle terminal velocity.With an increase in UG,increased liquid velocity restrains the solid settlement,and declines the difference of φSbetween the two stages.When the bubble circulation regimes of S1and S2are both CBCR,the particles are uniformly suspended axially in the downcomers.Similar behaviour was reported by Liu et al.[17]with a higher solid concentration of 40%.

3.3.Gas holdup

The effects of the superficial gas velocity UGand solid loading CSon gas holdup εGof the downcomer in each stage are shown in Fig.7.A dotted line divides the figure into two parts:TR and CBCR;the values of this dotted line are determined based on the bubble penetration depth h in Fig.5.The gas holdup εGof each stage increases with an increase in UG,and the increasing rate(i.e.the slope of εG)in TR is faster than that in CBCR.Similar results were reported by Yu et al.[31].In addition,as the solid loading increases,the gas holdup of each stage decreases,which can be explained by the steric effect[39]and the viscosity effect.Particles take up certain space of multiphase system,and the volume that can be occupied by gas phase decreases correspondingly.Also,with increasing slurry viscosity caused by the addition of particles,bubble size tends to increase near the gas distributor[40]and in riser[41,42].Because of higher rising velocity,bigger bubbles have shorter residence time,which makes overall and local gas holdup reduced.

Comparing εG1and εG2,it can be found that εG2is greater than εG1when both stages are in CBCR.At low UG,φSin S1is higher than that in S2,so that the volume fraction occupied by gas is lower in S1.In addition,affected by recirculation in downcomer,partial circulating slurry flow s from S2into S1,and results in aggrandized liquid velocity in S1[30].Thus,the residence time of bubbles gradually reduced,and the gas holdup of S1becomes relatively lower.

Fig.8 shows the trend of change of εG2/εG1with UGunder different bubble circulation regimes.It can be found that the UGcorresponding to the maximum value of εG2/εG1is equal to the critical UGof flow regime transition from TR to CBCR in S2.

Fig.7.Effects of U G and C S on gas holdup εG(Mean ± SD)in the downcomer.(C S:■0;●5%;▲10%;▼15%;?20%).

Fig.8.Relationship of U G with εG2/εG1 under different bubble circulation regimes.

According to Milivojevic et al.,[43]solid particles change the fluid flow field,and bubbles mainly interact with liquid not solid,especially in multiphase systems where particle size is obviously smaller than bubbles,so that the particle motion is tightly coupled to the fluid motion.Also,particles are not aggregated in the liquid phase.Thus,the influence caused by the presence of particles can be expressed using the changes of slurry viscosity.Slurry viscosity can be easily estimated by Thomas'formula[44]:

where solid holdup(εS)adopts the average value in downcomer of each stage.Empirical correlations for both gas holdup and liquid velocity are of the following form:

Empirical correlations for the gas holdup of three-phase system under CBCR were obtained:

w here subscripts 1 and 2 denote the stage number.

As shown in Fig.9,the predicted εGdata agree well with the experimental data.Moreover,the deviations between the calculated εGand the experimental values are less than 10%.In the empirical correlations of gas holdup,the fitted parameters a and b are similar with the literature[41].

3.4.Liquid velocity

Fig.10 shows the effects of UGand CSon the liquid velocity in S1and S2.UL1increases with UG,but decreases with CS.This result agrees with a previous study,[45]which mainly focused on single-stage ILALRs.The liquid velocity is controlled by the density difference between the riser and downcomer,which is known to decrease with an increase in CS.Furthermore,the dynamic viscosity and density of the slurry increases with CS,which results in an increase in the resistance to liquid circulation.

In S2,with CS=15%and 20%(i.e.under CBCR),the effect of UGon UL2coincides with that of S1.For lower value of the solid loading(TR,CS=0,5%and 10%),UL2increases drastically with UG.The rate of increase slow s after regime transition from TR to CBCR.The effect of CSon UL2is rather complex,precluding a simple rule from being obtained,especially in TR.The influence of CSon UL2depends on two opposing factors.With an increase in CS,the bubble size increases in the riser.Thus,more bubbles entrain into S2from S1and the driving force for liquid circulation increases.In contrast,the flow resistance of circulation increases because of the additional solid and resulting increase in the dynamic viscosity and density[17,19].

The liquid velocity and gas holdup are interdependent and follow similar rules as the superficial gas velocity and solid loading(expressed via increased liquid viscosity)in CBCR.Thus,in gas–liquid–solid systems,empirical correlations for the liquid velocity,which have the same form as εG,can be obtained as:

Fig.9.Comparison between the calculated εG and experimental data.

Fig.10.Liquid velocity U L with different UG and C S.

Fig.11.Comparison between the calculated U L and experimental data.

Fig.12.Slurry circulation rate with different superficial gas velocity and solid loading.

The predicted data agree well with the experimental data,as shown in Fig.11.Note that the empirical correlations can only be used to predict the liquid velocity in CBCR.In TR,the liquid velocity cannot be predicted by such a concise correlation.

The experimental values of GSfor different UGand CSare shown in Fig.12.With low UG,GSis large and significantly deviates from 1.This is because in S1,the slurry mainly circulates into the downcomer from the riser,and less fluid can pass through the internal and enters S2.Under these operating conditions,obvious circulation appears in the first stage.Increasing of UGor CScan reduce the value of GSand lessen the disparity between the two stages.

According to the dependence of ULand GSon UGand CS,it can be determined that,although adding solid decreases the overall liquid velocity,it can reduce the difference between the two stages in the multistage reactors.

3.5.Bubble behaviour

Bubble sizeis one of the main factors determining the hydrodynamic parameters[46,47].In this study,the bubble size was measured in the downcomer at positions 0.600 m(S1)and 1.400 m(S2)above the gas distributor.To avoid the influence of bubble circulation regime transitions,the effect of CSon the bubble size distribution was only investigated under CBCR,as shown in Fig.13.The bubble size distribution is relatively wider when UG=0.07 m·s?1than for 0.06 m·s?1,which is in agreement with the literature[48,49].With an increase in UG,the bubble size distribution becomes less uniform,which means that both bubble coalescence and breakup become more frequent[50].

Fig.13.Effect of solid loading on bubble size distribution with different U G in the downcomer of two stages.

Fig.14.Bubble Sauter diameter along the axial direction at different U G.(C S:■0;●5%;▲10%;?20%).

The bubble Sauter diameter d32along different axial directions for UG=0.06 and 0.07 m·s?1are shown in Fig.14.In each stage,d32is small at low axial positions,and the values in S2are greater than those in S1at the corresponding positions.The bubble size is small in locations near the gas distributor where the bubble coalescence is dominant and increases with axial height until the bubble breakup and coalescence reach a balance[51].In addition,hydrostatic pressure effects may have an influence.With the change in multiphase density and the development of a velocity head,the axial profiles of hydrostatic pressure decrease with height above the gas distributor[52].With the influence of the hydrostatic pressure,d32is small at low axial positions.

Fig.14.shows that d32decreases with increasing C s.Bubbles existing in the downcomer are mainly carried by the downward liquid circulating from riser.ULdecreases with increasing CS,which has been demonstrated in this experiment(see Fig.10).During the experiments,it is observed that with lower UL,big bubbles are more likely to ascend and escape directly from the gas–liquid separator region and difficult to enter the downcomer following the circulating liquid.From Fig.13,this tendency can be demonstrated by the declining amount of large bubbles in higher C s.

4.Conclusions and Perspectives

Local hydrodynamics of downcomer,such as gas holdup,liquid behaviour and solid axial distribution have been studied in a two-stage ILALR.The effects of solid loading on the bubble size in the downcomer were investigated using a dual-tip electrical conductivity probe and data acquisition system.The conclusions can be summarized as follows:

(1)In the two-stage ILALR,the first and second stages show different characteristics in terms of the bubble circulation regime.With low UG,the flow regime is CBCR in S1,but TR in S2.An increase in UGor CScan lead to a transition from TR to CBCR in S2.

(2)In CBCR,the gas holdup and liquid velocity increase with an increase in UGand a decrease in CS.Second-stage gas holdup is higher than that of the first-stage.And no clear trend was found for the influence of CSon liquid velocity in TR.For gas–liquid–solid systems,empirical correlations for the gas holdup and liquid velocity under CBCR were proposed.The slurry circulation rate GS,representing the ratio of circulation fraction between the two stages,decreases with an increase in UGand CS.The appropriate value of GScan be determined according to the practical demands or objectives in various industries.As a parameter reflecting the interrelation between stages,GScan be considered as an optional optimization objective in the industrial design of multistage ILALRs.

(3)In the downcomer,the bubble size distribution widens as an increasing UGand decreasing CS.The bubble Sauter diameter(d32)decreases with the presence of particles,and d32in S2is greater than that in S1at the corresponding positions.

For perspectives,many researchers have demonstrated that gas holdup is related to the bubble circulation regimes,and the regime transition can be related with the variation of gas holdups in different regions.In this experiment,different characteristics of flow regime appear in two stages,and the flow regime transition can be reflected by the maximum value of the curve of εG2/εG1ratio(as shown in Fig.8).However,these curves show different features under different CS.Under low CS(CS=0,5%),the ratio increases regularly and then decreases with UG.By contrast,these curves fluctuate after regime transition under higher CS.This fluctuation of εG2/εG1and how to identify the bubble circulation regimes according to the gas holdups in a two-stage ILALR should be investigated further.

Nomenclature

CSsolid loading

dbbubble diameter,mm

d32Sauter mean diameter,mm

g acceleration of gravity,m·s?2

GSslurry circulation rate

H height of draft tube in one stage,m

h bubble penetration depth,m

Δh distance between two measuring points,m

Lpdistances between up-stream tip and dow n-stream tip of

conductivity probe,m

mSLslurry mass,kg

ΔP pressure drop,Pa

Qdliquid flow rate in downcomer,m3·h?1

t total measuring time,s

Δt response time difference between the two conductivity probes,s

ΔtABtime different between up-stream and down-stream tip of conductivity probe,s

Ubbubble velocity,m·s?1

UGsuperficial gas velocity,m·s?1

ULliquid velocity,m·s?1

V average voltage of the signals

VCcritical voltage threshold

VLliquid volume,m?3

VSLslurry volume,m?3

VSsolid volume,m?3

β circulation fraction

εg1gas holdup in first stage

εG2gas holdup in second stage

εSsolid holdup

ρGgas density,kg·m?3

ρLliquid density,kg·m?3

ρSsolid density,kg·m?3

ρSLslurry density,kg·m?3

φSslurry concentration

σ standard deviation

Subscripts

G gas phase

GSL gas–solid–liquid phase

L liquid phase

S solid phase

SL solid–liquid phase

1 first stage

2 stage