dimensionalanalysisofgasholdupofventuricarbonation...

Research ArticleDimensional Analysis of Gas Holdup of Venturi CarbonationReactor for Red Mud Processing

Yibin Xiao1 Yan Liu 1 Zhibin Zhao2 Tingrsquoan Zhang1 and Ruibing Li 3

1School of Metallurgy Northeastern University Shenyang 110819 China2Shenyang Aluminium and Magnesium Engineering and Research Institute (SAMI) Shenyang 110001 China3School of Mechanical and Power Engineering Shenyang University of Chemical Technology Shenyang 110142 China

Correspondence should be addressed to Ruibing Li lrb07163com

Received 17 December 2019 Revised 25 February 2020 Accepted 2 April 2020 Published 30 June 2020

Academic Editor Yannis Dimakopoulos

Copyright copy 2020 Yibin Xiao et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Gas holdup is an important parameter in the carbonation reaction for processing red mud In this paper for estimating the gasholdup of Venturi carbonation reactor water model experiments were performed +e effects of superficial gas velocitiessuperficial liquid velocities and liquid-to-solid and height-to-diameter ratio on the gas holdup are investigated +rough di-mensional analysis using Buckingham π principle a derivation of the empirical correlation is also proposed +e results indicatethat gas holdup increases with the increase in gas velocity with the decrease in liquid velocity with the increase in liquid-to-solidratio and with the increase in height-to-diameter ratio +e calculated results from the empirical correlation agree well with theexperimental data which is important for designing a highly efficient Venturi reactor with a high temperature high pressure andthree phases of gas liquid and solid

1 Introduction

Red mud is a solid residue which is generated duringalumina extraction from bauxite According to the prop-erties of bauxite and alumina production conditions 06ndash25tons of residue were generated for every ton of Al2O3 duringalumina production [1] Approximately 120 million tons ofBayer red mud were generated every year worldwide andsubstantial reserves of over 27 billion tons have accumulated[2] Every alumina plant allocates a large yard for stackingthe Bayer red mud +e industrial solid waste encroaches agreat amount of land causes air pollution contaminates soilor groundwater and results in serious environmentalproblems because of the tiny particles and alkaline slurry+e utilization and recycling of red mud is currently acritical issue and needs to be addressed as soon as possible

Researchers have made significant efforts to explore theutilization of red mud in aluminum industry Some of theminvolve the extraction of valuable materials from red mudsuch as the recovery of alumina soda ferric oxide andtitanium oxide [3ndash5] Most of the red mud is still stacked in

yard although a significant amount of red mud is utilized assubgrade materials [6 7] and additive for cement [8] andceramics [9] and for various other industrial uses [10 11]+e biggest hurdle in the use of red mud is the compositionof soda in red mud slurry Soda needs to be removed prior toutilizing the red mud in industrial processes

Although many processes have been proposed for theutilization of red mud only a few have been applied inindustrial processes due to unfavorable local economic andmarket conditions It is worth mentioning that most of theseprocesses suffer from high costs and low yields For fullyusing the Bayer process residue the team of NortheasternUniversity China proposed a novel approach called thecalcification-carbonation method [12 13] +e methodmainly involves two steps of calcification and carbonationIn the first step of calcification lime is added to red mudslurry in an autoclave at the temperature of 180ndash240degCwhereas the calcification reaction occurs in the solutionduring which the silicon phase is transformed into hydro-garnet (3CaOmiddotAl2O3middotxSiO2middot(6minus 2x)H2O) As a result soda inred mud is extracted

HindawiMathematical Problems in EngineeringVolume 2020 Article ID 6973165 9 pageshttpsdoiorg10115520206973165

x

2Al2O3 middot 2SiO2 middot 2H2O( 1113857 + 3Ca(OH)2 +(2 minus x)Al(OH)3

3CaO middot Al2O3 middot xSiO2(6 minus 2x)H2O +3x

2H2O

Na2O middot Al2O3 middot xSiO2(6 minus 2x)H2O + 3Ca(OH)2

3CaO middot Al2O3 middot xSiO2(6 minus 2x)H2O + 2NaOH + 2H2O(1)

In the second step of carbonation carbon dioxide (CO2)is bubbled into the calcified red mud slurry in the car-bonation reactor at 80ndash120degC under a CO2 partial pressure of05ndash12MPa +e hydrogarnet is decomposed into calciumsilicate calcium carbonate and aluminum hydroxidewhereas alumina is recovered during the process

Based on this method 49 of alumina and 968 of sodaare extracted from red mud +e new-phase red mud whichmainly consists of calcium carbonate calcium silicate andtrace amounts of Na2O is obtained +e new-phase red mudsatisfies the requirements for the production of Portlandcement and therefore can be used fully

+e main unit operation for the process is the carbon-ation reactor A Venturi carbonation reactor was adopted forthe carbonation reaction which is a type of self-stirringreactor with a cylindrical vertical cross section and a conicalbottom equipped with a Venturi tube (Figure 1) +e car-bonation reaction is a three-phase reaction consisting of gasliquid and solid +e ascending CO2 gas which is laterallyintroduced near the bottom disperses into the red mudslurry within the reactor +e carbonation reaction is per-formed during the rising of gas and slurry +e efficiency ofthe carbonation reaction is governed by the concentration ofgas in liquid and the contact surface of bubbles with solidGenerally speaking in gas-liquid-solid flow systems thiscontact mainly depends on several factors including thebubble sizes and their distributions [14 15] gas holdup[16 17] and bubble rise velocity [18 19]

Gas holdup (ε) is an important parameter in hydrody-namics which is widely used to determine the characteristicsof gas-liquid-solid phase in fluidized beds and bubble col-umns [20 21]+e gas holdup is the volume fraction of gas inthe reactor indicating the size of the contact area of gas withliquid +e gas holdup significantly affects the efficiencies ofmass transfer heat transfer and microrate of reaction +egas holdup distribution is mainly related to the superficialgas velocity solidsrsquo concentration pressure distributiondensity of each phase and the physical properties of theliquid [22]

+is is particularly important for the reactor proposed inthis study where the gas holdup characteristics are not yetclear especially at a quantitative level Various measuringtechniques such as pressure difference techniques [23 24]high-speed camera [25] double optical probe [26 27]particle image velocimetry (PIV) technology [28 29] andtomography techniques [30 31] have been proposed tostudy the hydrodynamic behaviors of gas-liquid flowsNumerical modeling and simulations were proposed to

predict the distribution of a radial gas holdup global gasholdup and the two-phase flow field [32ndash34] +ese tech-niques provide useful information to better understand thegas-liquid flows under different conditions However thesetechniques may have certain limitations For example themeasurement of gas holdup in the transient flow which isrelated to fluid velocities dimensions of the equipment andthe properties of the fluid is generally difficult and in manycases involves high costs However such detailed infor-mation is highly desirable for the present new reactor

In this paper based on the water model experiments forthe Venturi carbonation reactor the gas holdup and therelationship between the gas holdup and various parametersin the carbonation process are studied and an empiricalcorrelation is derived for gas holdup as a function of su-perficial gas velocities superficial liquid velocities andliquid-to-solid and height-to-diameter ratio +e applica-bility of the correlation is validated following which theeffects of various parameters on the gas holdup of theVenturi carbonation reactor can be quantified that benefitsthe performance of the novel reactor

2 Experimental

21 Principles For the simulation of carbonation reactorthe geometric and dynamic similarities are necessary Awater model with geometric similarity in which the main

Gas

d5 d6

Gas and liquid

h1

h3

h2

d2

d1

Gasd3d4

Liquid

Figure 1 Venturi carbonation reactor

2 Mathematical Problems in Engineering

geometrical sizes are proportional to the prototype on a scaleof 1 6 is established Meanwhile the dynamic similarityfollows the rule that themodified Froud numbers (Fr) for themodel and prototype are equal +e modified Froud numberis defined using

Frprime ρg middot u2

ρl middot g middot H (2)

where u is the characteristic velocity (ms) H is the depthof pool (m) ρl and ρg are the densities of liquid and gas(kgm3) respectively and g is the acceleration due togravity (ms2)

+e characteristic velocity can be expressed using

u 4Q

π middot d2(3)

where Q is the flow rate of fluid (m3h) d is the throatdiameter of the jet reactor (m) and π is the circular constantCombining equations (2) and (3) the modified Froudnumber is obtained which is given by

Frprime 1621ρg middot Q2

ρl middot g middot H middot d4(4)

From Frmprime Frpprime the quantity of fluid injected into the

model can be calculated

Qm ρgp

ρgm

middotρlm

ρlp

middotd4

m

d4p

middotHm

Hp

⎛⎝ ⎞⎠

12

middot Qp (5)

where the subscripts p m l and g stand for prototypemodel liquid and gas respectively

22 Apparatus +e water model used in the experimentrefers to the design for industrial implementation of redmud process which includes a main reactor a fluid cir-culation system and an observation system +e newlydesigned Venturi jet flow device used for the calcified slagcarbonation is a prototype in which the Venturi tube is usedas a liquid entry point at the bottom +is part helps ingenerating a negative pressure relative to the ambient at-mospheric pressure which sucks gas into the reactorthrough gas inlet +e gas mainly escapes from the outlet atthe top whereas liquid and bubbles are removed from theright side of the outlet (Figure 1) +e geometrical param-eters for the reactor are listed in Table 1

In the water model system materials made up of organicglass were used to ensure a steady movement of the fluid andobserve the mixing of fluid circulation stream and bubblebehavior (Figure 2) +e size and the distribution of gasbubbles and their movements were directly observable

23 Methodology +e pressure-difference method was usedto measure the gas holdup in the reactor According toBernoulli principle the pressure difference between the twocross sections of fluidized bed in the reactor was measuredFor the gas-liquid system the density of the mixture of gasand liquid is given by

ρmix ρgεg + ρl 1 minus εg1113872 1113873 (6)

+e pressure difference between the two cross sections isgiven by

P ρmixgh (7)

+e gas density ρg is very small as compared to the liquiddensity ρl and therefore can be ignored From equations (6)and (7) the gas holdup can be calculated using

εg 1 minusP

ρlgh (8)

where εg is the gas holdup g is the acceleration due to gravity(ms2) ρmix is the density of gas-liquid mixture in the reactor(kgm3) ρl is the density of liquid in the reactor (kgm3) h isthe altitude difference between the two measuring sections ofa fluidized bed in a reactor (m) and P is the pressure dif-ference between the two cross sections (kPa)

24DimensionalAnalysis Dimensional analysis is a methodfor reducing complex physical problems to their simplestform by studying the dimensions of variables that describethe physical phenomenon +e principal use of dimensionalanalysis is to make the physical equation dimensionallyhomogeneous +e method is of great generality andmathematical simplicity In engineering empirical corre-lation among various parameters can be derived from ex-perimental data using the method of dimensional analysiswhich also enables weighing the magnitude of each oper-ating parameter

Table 1 Geometric parameters of the Venturi Carbonation reactor

Parameters Symbol Value(mm)

Length of cylindrical section h1 675Length of spread section h2 240Length of carbonation reactor h3 1183Diameter of the gas inlet d1 10Diameter of throat of the carbonationreactor d2 30

Diameter of the throat of liquid inlet d3 147Diameter of the liquid inlet d4 42Diameter of the cylindrical section d5 240Diameter of the liquid outlet d6 100

Figure 2 Water model system

Mathematical Problems in Engineering 3

3 Dimensional Analysis of Gas Holdup

Based upon the water model experiments the gas holdup(εg) in the reactor is mainly related to superficial gasvelocity (Ug) superficial liquid velocity (Ul) liquid-to-solid ratio (Rls) and height-to-diameter ratio (Rhd) [23]Based on the dimensional analysis the influence ofvarious factors on the gas holdup in the reactor isstudied According to Buckinghamrsquos theorem (π -principle) a general functional form of the independentvariables was obtained and is given in the followingequations [35ndash37]

εg f Ug Ul Rls Rhd d1 d2 d5 H μg ρg μl ρl1113872 1113873 (9)

or

f εg Ug Ul Rls Rhd d1 d2 d5 H μg ρg μl ρl1113872 1113873 0

(10)

where εg is the gas holdup Ug and Ul are the superficialvelocities of gas and liquid (ms) respectively Rls is theliquid-to-solid ratio Rhd is the height-to-diameter ratioand d1 d2 and d5 are the diameter of gas inlet of the jetreactor (m) diameter of the throat of the jet reactor (m)and diameter of the reactor (m) respectively FurthermoreH is the height of liquid level in the reactor (m) μg and μlare the viscosities of gas and liquid (Pamiddots) respectively andρg and ρl are the densities of gas and liquid (kgm3) re-spectively +e dimensions of the variables are listed inTable 2

Based on π-principle the total number of variables (n) is13 and the number of independent variables (k) is 5 so thatnminus k 8 which is the number of dimensionless quantitiesthat can be set up Furthermore ρg μg ρl μl and d5 wereselected as the independent variables whereas εg Rls andRhd were selected as the dimensionless values +enaccording to the π-principle the dimensionless forms of theremaining nminus k independent variables were defined asfollows [35ndash37]

Π0 εg (11)

Π1 Rls (12)

Π2 Rhd (13)

Π3 Ugρgd1

μg

(14)

Π4 Ulρld2

μl

(15)

Π5 d1

d5 (16)

Π6 d2

d5 (17)

Π7 H

d5 (18)

+is way a dimensionless functional form is obtained asfollows

f εg Rls RhdUgρgd1

μg

Ulρld2

μl

d1

d5d2

d5H

d51113888 1113889 0 (19)

An explicit functional form is given by

εg f Rls RhdUgρgd1

μg

Ulρld2

μl

d1

d5

d2

d5

H

d51113888 1113889 (20)

In addition d1 d2 and H are quantitative in nature+erefore equation (20) can be expressed as


μg

Ulρld2

μl

1113888 1113889 (21)

4 Derivation of the Empirical Correlation

Generally the criterion equation can be expressed in the formof power function with the independent variable being undercertain conditions+erefore equation (21) can be rewritten as

εg a0Ra1ls R

a2hd

Ugρgd1

μg

1113888 1113889

a3 Ulρld2

μl

1113888 1113889

a4

(22)

where a0 a1 a2 a3 and a4 are the fitting coefficients Aftertaking the logarithm on both sides of equations (22)equation (23) is obtained

ln εg ln a0 + a1 lnRls + a2 lnRhd + a3 lnUgρgd1

μg

+ a4 lnUlρld2

μl

(23)

Based on the linear relationship of equation (23) thefitting coefficients a1 a2 a3 and a4 are obtained by plottingthe experimental data in Origin 86 (See Figure S1 in theSupplementary Material) whereas a0 is optimized using theQuasi-Newton method

a0 141 times 10minus5

a1 0270

a2 1185

a3 0998

a4 minus0266

(24)

Table 2 Dimensions of the variables

εg Ug Ul Rls Rhd d1 d2 d5 H ρg μg ρl μlM 0 0 0 0 0 0 0 0 0 1 1 1 1L 0 1 1 0 0 1 1 1 1 minus3 minus1 minus3 minus1T 0 minus1 minus1 0 0 0 0 0 0 0 minus1 0 minus1


+e values of the coefficients are the mean values of theslopes in their respective graphs +e fitting equation can beexpressed using

εg 141 times 10minus5R0270ls R

1185hd

Ugρgd1

μg

1113888 1113889

0998Ulρld2

μl

1113888 1113889

minus0266

(25)

+e results obtained using equation (25) are consistentwith the experimental results +e mean statistical varianceis 097 (See Table S2 in the Supplementary Material) whilethe mean relative error is within 87 (See Table S3 in theSupplementary Material) Furthermore equation (25) isvalid within a range of the following parameters Ug of708ndash2123mmiddotsminus1 Ul of 089ndash177mmiddotsminus1 Rls of 10ndash20 Rhd of3ndash5 Figure 3 shows that the calculated results obtained fromthe fitting equation agree well with the experiment dataEquation (25) is significant for designing a highly efficientVenturi reactor involving high temperature high pressureand three phases of gas liquid and solid

5 Discussion

51 Compatibility of the Similarity Criteria +e establish-ment of the criteria model is very simple However theabsence of the physical analysis leads to incorrect results[38] In this study thirteen physical quantities involved withthe gas holdup were analyzed (equation (9)) +ese quan-tities are the determinants which significantly affect the sizeamount and residence time of gas bubbles in the fluid Somephysical quantities involved with the gas holdup includetemperature and surface tension +ese parameters arerelatively stable in fluid flow and do not have a considerableeffect on the gas holdup and therefore are not included inthe model In fact the densities of gas and liquid (ρg and ρl)and viscosities of gas and liquid (μg and μl) are stable +eirdimensions can be used to make dimensionless complexesaccording to π-theorem which requires that both sides of thephysical equation must be dimensionally homogeneousEight dimensionless complexes were made (see equations(11)ndash(18)) wherein Π3 and Π4 represent the Reynoldsnumbers which often appear in the analysis of heat andmass transfer in fluid flow

Re1 Ugρgd1

μg

Re2 Ulρld2

μl

(26)

+e Reynolds numbers are the main similarity criteriacharacterizing the similarities of inertia force and viscosityforce in fluid flowΠ2Π5 andΠ6 characterize the geometricsimilarities of apparatus and Π0 Π1 and Π7 assure thesimilarities of magnitude of gas solid and liquid +e cri-terion model for estimating the gas holdup of the jet reactoris constructed in the case of a serious physical analysis andunderstanding of its physical background Incompatiblesimilarity criteria are not found in the dimensionless

complexes +erefore it is available in the process of mul-tiphase flow

+e data used in the dimensional analysis was obtainedfrom water model experiments which were based on thegeometric and dynamic similarities Froude number wasused as the dynamic similarity criteria to construct the watermodel Using the throat diameter of the jet reactor as alength scale the Froude number characterizes the similar-ities of inertia force and gravity in fluid which assure thedynamic similarity of the water model with the prototype(see Section 21)

Figure 4 shows a comparison of the results of theproposed correlation with those of the water experiments Itcan be seen that the calculated results are in good agreementwith the experimental results +erefore the proposedcorrelation can be used for predicting the gas holdup in thenovel reactor

52 Effect of Various Parameters on Gas Holdup +e watermodel experiments showed that the gas holdup in theVenturi reactor is mainly affected by the superficial gasvelocity superficial liquid velocity liquid-to-solid ratio (Rls)and height-to-diameter ratio (Rhd) Among them the su-perficial gas velocity showed an obvious impact on gasholdup As shown in Figure 3(a) when Rls 20 Rhd 4 andUl 133mmiddotsminus1 gas holdup increased with the increase insuperficial gas velocity Notably the increase in gas velocityincreased the number of gas bubbles With the increase inthe superficial gas velocity the strength of stirring alsointensified Larger gas bubbles were disintegrated intosmaller bubbles whereas the rising velocity of small gasbubbles became slower due to which the gas holdupincreased

+e superficial liquid velocities showed a weaker effecton gas holdup With the increase in the superficial liquidvelocity the gas holdup decreased (Figure 3(b)) Fan et al[39] reported that the bubble rise velocity (Ug) can beexpressed in terms of a bubble slip velocity (Us) and thelinear liquid velocity (Ul) using

Ug

εg

Us +Ul

εl

(27)

Equation (27) shows that the gas holdup has an inverserelationship with the liquid velocity In air-water systemsthe slip velocity is the major contributor to bubble risevelocity (Ugεg) [39] However the bubble rise velocityincreases with the increase in liquid velocity which de-creases the gas holdup

When solid particles are added in the solution theproperties of liquid such as viscosity change +e existenceof solid particles and the increase in viscosity prevented thedisintegration of large bubbles into small bubbles and in-creased the coalescence of smaller bubbles into larger onesFurthermore the residence time of bubbles in the solutiondecreased +e increase in liquid-to-solid ratio means thatthe solid particles decreased due to which the gas holdupincreased (Figure 3(c))


+e ratio of the height to diameter of the reactor (Rhd) isan important parameter for the equipment +e experi-mental conditions were set to be as follows Rhd 3 4 and 5Ul 133mmiddotsminus1 and Rls 20 As shown in Figure 3(d) for lowsuperficial gas velocity and high height-to-diameter ratiothe results show a significant difference between the cal-culated and experimental values However with the increasein the value of Rhd the gas holdup increased

+e increase in temperature led to an expansion of thevolume of bubbles due to which the gas density decreasedAccording to eqaution (6) the decreased gas density isnegligible as compared to the liquid density+is change wastaken into consideration in the dynamic similarity wherethe flow rate of the gas and gas density were included in themodel (equation (4)) +erefore the gas density and liquid

density in equation (25) should be considered when de-signing industrial unit operations Similarly the viscosity ofred mud slurry is affected by temperature and is also con-sidered in the model

+e surface tension of bubbles may affect the gas holdupin fluid Liu et al [40] discussed the applicability of waterexperimental results to the hot metal ladle in plant andreported that the differences in the surface tension in molteniron were 35 times that of water Mach [41] reported that thesurface tension had a significant effect on gas holdup andhydrodynamics in a three-phase fluidized bed while vis-cosity had only a slight impact Lower liquid surface tensionfacilitates the formation of smaller bubbles and promotes anoncoalescing tendency in the rising gas bubbles thus re-ducing the growth of bubbles Surfactants can increase drag

Rls = 20Rhd = 4

Ul = 137 mmiddotsndash1

10 15 205Ug (mmiddotsndash1)

005

010

015ε

020

025

ExperimentCalculated

(a)

Rls = 20Rhd = 4

Ug = 1062 mmiddotsndash1

08 10 12 14 16 18Ul (mmiddotsndash1)

ε


006

008

010

012

014

016

018

020

022

024

(b)

Rhd = 4Ul = 133 mmiddotsndash1

10 15 20Rls

ε

005

010

015

020

025

Experiment (mmiddotsndash1)Ug = 707Ug = 1062Ug = 1415Ug = 1769Ug = 2123

Calculated (mmiddotsndash1)Ug = 707Ug = 1062Ug = 1415Ug = 1769Ug = 2123

(c)

Rls = 20Ul = 133 mmiddotsndash1

Rhd

3 54 6

ε



005

010

015

020

025

030

035

(d)

Figure 3 Comparison between the experimental and calculated results (a) εg vs Ug (b) εg vs Ul (c) εg vs Rls (d) εg vs Rhd


on gas bubbles due to the formation of a surface tensiongradient on the bubble surface [39] A higher drag results inlower bubble rise velocities which in turn results in a highergas holdup

6 Conclusions

Based upon water model experiments the effects of su-perficial gas velocities superficial liquid velocities andliquid-to-solid and height-to-diameter ratios on gas holdupof the Venturi carbonation reactor were studied Based upondimensional analysis and Buckinghamrsquos theorem an em-pirical correlation was proposed

Superficial gas velocity is primarily the major influencingfactor for gas holdup of the Venturi carbonation reactorWith the increase in superficial gas velocity the bubbles inthe solution and gas holdup increased +e superficial liquidvelocity and the values of Rls and Rhd significantly impactedthe gas holdup in the reactor +ere is a negative correlationbetween the superficial liquid velocity and gas holdup of thereactor

+e results obtained using the empirical correlation areconsistent with the experimental results and produce astatistical variance of 097 and mean relative error of lessthan 87 +e results are significant for designing a highlyefficient Venturi reactor having high temperature highpressure and three phases of gas liquid and solid

Notations

a0 a1 a2 a3and a4

Undetermined constants

d Characteristic diameter of pipe md1 Gas inlet diameter of the reactor md2 +roat diameter of the reactor md5 Diameter of the reactor mFrprime Modified Froud numberg Acceleration due to gravity ms2h Altitude difference between the two

measuring sections of a fluidized bed m

H Height of liquid level in the reactor mRls Liquid-to-solid ratioRhd Height-to-diameter ratioQ Flow rate of fluid cm3minu Characteristic velocity msU Superficial velocity msP Pressure difference between the two

measuring sections Paρ Density of fluid kgm3

ρmix Density of the mixture of gas and liquidkgm3

μ Viscosity of the fluid Pamiddotsε Gas holdupπ Circular constantSubscriptsp m l s andg

+e prototype model liquid solid and gasrespectively

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare that they have no conflicts of interest

Acknowledgments

+e authors are grateful to the National Natural ScienceFoundation of China and National 863 Plan of China for thefinancial support (Grant no U1202274 and Grant no51204040)

Supplementary Materials

Figure S1 fitting coefficients a1 a2 a3 and a4 as obtainedaccording to the slopes (a) a1 (b) a2 (c d) a3 (e) a4 TableS2 mean statistical variance of the results presented inFigure S1 the first and second columns are obtained fromFigure S1 (a) first and third columns are obtained fromFigure S1 (b) fourth and fifth columns are obtained fromFigure S1 (c) sixth and seventh columns are obtained fromFigure S1 (d) eighth column is obtained from Figure S1 (e)Table S3 relative error between the calculated and experi-mental results +e relative error δ (Xi minusXc)Xt times 100where Xi is the experimental value and Xc is the calculated

value +e mean relative error σ

1113936ni1 δ

2n1113969

whereσ 87 (Supplementary Materials)

References

[1] W Liu J Yang and B Xiao ldquoReview on treatment andutilization of bauxite residues in Chinardquo International Journalof Mineral Processing vol 93 no 3-4 pp 220ndash231 2009

[2] C Klauber M Grafe and G Power ldquoBauxite residue issuesII options for residue utilizationrdquo Hydrometallurgy vol 108no 1-2 pp 11ndash32 2011

[3] W Liu S Sun L Zhang S Jahanshahi and J Yang ldquoEx-perimental and simulative study on phase transformation in

010 015 020 025 030005 035ε (exe)

005

010

015

020

025

030

035

ε (ca

l)

Figure 4 Comparison between the experimental and calculatedresults


Bayer red mud soda-lime roasting system and recovery of AlNa and Ferdquo Minerals Engineering vol 39 pp 213ndash218 2012

[4] S Agatzini-Leonardou P Oustadakis P E Tsakiridis andC Markopoulos ldquoTitanium leaching from red mud by dilutedsulfuric acid at atmospheric pressurerdquo Journal of HazardousMaterials vol 157 no 2-3 pp 579ndash586 2008

[5] S Agrawal V Rayapudi and N Dhawan ldquoExtraction of ironvalues from red mudrdquo Materials Today Proceedings vol 5no 9 pp 17064ndash17072 2018

[6] E Mukiza L Zhang X Liu and N Zhang ldquoUtilization of redmud in road base and subgrade materials a reviewrdquo Re-sources Conservation and Recycling vol 141 pp 187ndash1992019

[7] Y Li X Min Y Ke D Liu and C Tang ldquoPreparation of redmud-based geopolymer materials from MSWI fly ash and redmud by mechanical activationrdquo Waste Management vol 83pp 202ndash208 2019

[8] P E Tsakiridis S Agatzini-Leonardou and P OustadakisldquoRed mud addition in the raw meal for the production ofPortland cement clinkerrdquo Journal of Hazardous Materialsvol 116 no 1-2 pp 103ndash110 2004

[9] X Xu J Song Y Li J Wu X Liu and C Zhang ldquo+emicrostructure and properties of ceramic tiles from solidwastes of Bayer red mudsrdquo Construction and Building Ma-terials vol 212 pp 266ndash274 2019

[10] M A Khairul J Zanganeh and B Moghtaderi ldquo+e com-position recycling and utilisation of Bayer red mudrdquo Re-sources Conservation and Recycling vol 141 pp 483ndash4982018

[11] S Vigneshwaran M Uthayakumar and V ArumugaprabuldquoDevelopment and sustainability of industrial waste-based redmud hybrid compositesrdquo Journal of Cleaner Productionvol 230 pp 862ndash868 2019

[12] R Li T Zhang Y Liu G Lv and L Xie ldquoCalcification-carbonation method for red mud processingrdquo Journal ofHazardous Materials vol 316 pp 94ndash101 2016

[13] G Lu T Zhang F Guo et al ldquoClean and efficient utilizationof low-grade high-iron sedimentary bauxite via calcification-carbonationmethodrdquoHydrometallurgy vol 187 pp 195ndash2022019

[14] R Rakoczy and S Masiuk ldquoExperimental study of bubble sizedistribution in a liquid column exposed to a rotating magneticfieldrdquo Chemical Engineering and Processing Process Intensi-fication vol 48 no 7 pp 1229ndash1240 2009

[15] A Gordiychuk M Svanera S Benini and P Poesio ldquoSizedistribution and Sauter mean diameter of micro bubbles for aVenturi type bubble generatorrdquo Experimental Dermal andFluid Science vol 70 pp 51ndash60 2016

[16] A Mowla T Treeratanaphitak H M BudmanN M Abukhdeir and M A Ioannidis ldquoA meta-analysis ofempirical correlations for average gas hold-up in three-phasefluidized bedsrdquo Powder Technology vol 301 pp 590ndash5952016

[17] M Rasanen T Eerikainen and H Ojamo ldquoCharacterizationand hydrodynamics of a novel helix airlift reactorrdquo ChemicalEngineering and Processing Process Intensification vol 108pp 44ndash57 2016

[18] A S Mohamed M A Herrada J M Lopez-Herrera andA M Gantildean-Calvo ldquoIsothermal dissolution of small risingbubbles in a low viscosity liquidrdquo Chemical Engineering andProcessing Process Intensification vol 85 pp 136ndash144 2014

[19] S Maurer M Rudisuli S L Teske et al ldquoTransformation oflocal bubble rise velocity measurements to global resultsshown by a Monte Carlo simulation of a fluidized bedrdquo

International Journal of Multiphase Flow vol 70 pp 89ndash952015

[20] S C Saxena and N S Rao ldquoEstimation of gas holdup in aslurry bubble column with internals nitrogen-therminol-magnetite systemrdquo Powder Technology vol 75 no 2pp 153ndash158 1993

[21] N P Franka and T J Heindel ldquoLocal time-averaged gasholdup in a fluidized bed with side air injection using X-raycomputed tomographyrdquo Powder Technology vol 193 no 1pp 69ndash78 2009

[22] K Raghunathan S Kumar and L-S Fan ldquoPressure distri-bution and vortical structure in the wake behind gas bubblesin liquid and liquid-solid systemsrdquo International Journal ofMultiphase Flow vol 18 no 1 pp 41ndash50 1992

[23] R Li T A Zhang Y Liu J Zhou R Zou and S KuangldquoCharacteristics of red mud slurry flow in carbonation re-actorrdquo Powder Technology vol 311 pp 66ndash76 2017

[24] Y H Tan A A Rafiei A Elmahdy and J A Finch ldquoBubblesize gas holdup and bubble velocity profile of some alcoholsand commercial frothersrdquo International Journal of MineralProcessing vol 119 pp 1ndash5 2013

[25] W M Verde J L Biazussi N A Sassim and A C BannwartldquoExperimental study of gas-liquid two-phase flow patternswithin centrifugal pumps impellersrdquo Experimental Dermaland Fluid Science vol 85 pp 37ndash51 2017

[26] P Tyagi and V V Buwa ldquoExperimental characterization ofdense gas-liquid flow in a bubble column using voidageprobesrdquo Chemical Engineering Journal vol 308 pp 912ndash9282017

[27] G Besagni and F Inzoli ldquoComprehensive experimental in-vestigation of counter-current bubble column hydrodynam-ics holdup flow regime transition bubble size distributionsand local flow propertiesrdquo Chemical Engineering Sciencevol 146 pp 259ndash290 2016

[28] K H K Chung M J H Simmons andM Barigou ldquoLocal gasand liquid phase velocity measurement in a miniature stirredvessel using PIV combined with a new image processingalgorithmrdquo Experimental Dermal and Fluid Science vol 33no 4 pp 743ndash753 2009

[29] J Sossa-Echeverria and F Taghipour ldquoComputational sim-ulation of mixing flow of shear thinning non-Newtonianfluids with various impellers in a stirred tankrdquo ChemicalEngineering and Processing Process Intensification vol 93pp 66ndash78 2015

[30] A Kazemzadeh F Ein-Mozaffari A Lohi and L PakzadldquoIntensification of mixing of shear-thinning fluids possessingyield stress with the coaxial mixers composed of two differentcentral impellers and an anchorrdquo Chemical Engineering andProcessing Process Intensification vol 111 pp 101ndash114 2017

[31] G P Assima A Hamitouche M Schubert and F LarachildquoLiquid drainage in inclined packed beds-accelerating liquiddraining time via column tiltrdquo Chemical Engineering andProcessing Process Intensification vol 95 pp 249ndash255 2015

[32] N Yang Z Wu J Chen Y Wang and J Li ldquoMulti-scaleanalysis of gas-liquid interaction and CFD simulation of gas-liquid flow in bubble columnsrdquo Chemical Engineering Sciencevol 66 no 14 pp 3212ndash3222 2011

[33] R Zhou N Yang and J Li ldquoCFD simulation of gas-liquid-solid flow in slurry bubble columns with EMMS drag modelrdquoPowder Technology vol 314 pp 466ndash479 2017

[34] R Li S Kuang T Zhang Y Liu and A Yu ldquoNumericalinvestigation of gas-liquid flow in a newly developed car-bonation reactorrdquo Industrial amp Engineering Chemistry Re-search vol 57 no 1 pp 380ndash391 2018


[35] A A Sonin De Physical Basis of Dimensional Analysispp 1ndash57 Dep Mech Eng MIT Cambridge MA USA 2001

[36] D Wang Y Liu Z Zhang P Shao and T A Zhang ldquoDi-mensional analysis of average diameter of bubbles for bottomblown oxygen copper furnacerdquo Mathematical Problems inEngineering vol 2016 Article ID 4170371 8 pages 2016

[37] G Garcıa-Ros I Alhama M Canovas and F AlhamaldquoDerivation of universal curves for nonlinear soil consoli-dation with potential constitutive dependencesrdquo Mathemat-ical Problems in Engineering vol 2018 Article ID 583759215 pages 2018

[38] C BoyadjievDeoretical Chemical Engineering Modeling andSimulation Springer-Verlag Berlin Germany 2010

[39] L-S Fan F Bavarian R L Gorowara B E KreischerR D Buttke and L B Peck ldquoHydrodynamics of gas-liquid-solid fluidization under high gas hold-up conditionsrdquo PowderTechnology vol 53 no 3 pp 285ndash293 1987

[40] Y Liu M Sano T Zhang Q Wang and J He ldquoIntensifi-cation of bubble disintegration and dispersion by mechanicalstirring in gas injection refiningrdquo ISIJ International vol 49no 1 pp 17ndash23 2009

[41] W Mach ldquoSuspendierung fester Korper im turbulenten GasFlussigkeitsstromrdquo Chemie Ingenieur Technik vol 42 no 5pp 311ndash316 1970


x

2Al2O3 middot 2SiO2 middot 2H2O( 1113857 + 3Ca(OH)2 +(2 minus x)Al(OH)3

3CaO middot Al2O3 middot xSiO2(6 minus 2x)H2O +3x

2H2O

Na2O middot Al2O3 middot xSiO2(6 minus 2x)H2O + 3Ca(OH)2

3CaO middot Al2O3 middot xSiO2(6 minus 2x)H2O + 2NaOH + 2H2O(1)

In the second step of carbonation carbon dioxide (CO2)is bubbled into the calcified red mud slurry in the car-bonation reactor at 80ndash120degC under a CO2 partial pressure of05ndash12MPa +e hydrogarnet is decomposed into calciumsilicate calcium carbonate and aluminum hydroxidewhereas alumina is recovered during the process

Based on this method 49 of alumina and 968 of sodaare extracted from red mud +e new-phase red mud whichmainly consists of calcium carbonate calcium silicate andtrace amounts of Na2O is obtained +e new-phase red mudsatisfies the requirements for the production of Portlandcement and therefore can be used fully

+e main unit operation for the process is the carbon-ation reactor A Venturi carbonation reactor was adopted forthe carbonation reaction which is a type of self-stirringreactor with a cylindrical vertical cross section and a conicalbottom equipped with a Venturi tube (Figure 1) +e car-bonation reaction is a three-phase reaction consisting of gasliquid and solid +e ascending CO2 gas which is laterallyintroduced near the bottom disperses into the red mudslurry within the reactor +e carbonation reaction is per-formed during the rising of gas and slurry +e efficiency ofthe carbonation reaction is governed by the concentration ofgas in liquid and the contact surface of bubbles with solidGenerally speaking in gas-liquid-solid flow systems thiscontact mainly depends on several factors including thebubble sizes and their distributions [14 15] gas holdup[16 17] and bubble rise velocity [18 19]

Gas holdup (ε) is an important parameter in hydrody-namics which is widely used to determine the characteristicsof gas-liquid-solid phase in fluidized beds and bubble col-umns [20 21]+e gas holdup is the volume fraction of gas inthe reactor indicating the size of the contact area of gas withliquid +e gas holdup significantly affects the efficiencies ofmass transfer heat transfer and microrate of reaction +egas holdup distribution is mainly related to the superficialgas velocity solidsrsquo concentration pressure distributiondensity of each phase and the physical properties of theliquid [22]

+is is particularly important for the reactor proposed inthis study where the gas holdup characteristics are not yetclear especially at a quantitative level Various measuringtechniques such as pressure difference techniques [23 24]high-speed camera [25] double optical probe [26 27]particle image velocimetry (PIV) technology [28 29] andtomography techniques [30 31] have been proposed tostudy the hydrodynamic behaviors of gas-liquid flowsNumerical modeling and simulations were proposed to

predict the distribution of a radial gas holdup global gasholdup and the two-phase flow field [32ndash34] +ese tech-niques provide useful information to better understand thegas-liquid flows under different conditions However thesetechniques may have certain limitations For example themeasurement of gas holdup in the transient flow which isrelated to fluid velocities dimensions of the equipment andthe properties of the fluid is generally difficult and in manycases involves high costs However such detailed infor-mation is highly desirable for the present new reactor

In this paper based on the water model experiments forthe Venturi carbonation reactor the gas holdup and therelationship between the gas holdup and various parametersin the carbonation process are studied and an empiricalcorrelation is derived for gas holdup as a function of su-perficial gas velocities superficial liquid velocities andliquid-to-solid and height-to-diameter ratio +e applica-bility of the correlation is validated following which theeffects of various parameters on the gas holdup of theVenturi carbonation reactor can be quantified that benefitsthe performance of the novel reactor

2 Experimental

21 Principles For the simulation of carbonation reactorthe geometric and dynamic similarities are necessary Awater model with geometric similarity in which the main

Gas

d5 d6

Gas and liquid

h1

h3

h2

d2

d1

Gasd3d4

Liquid

Figure 1 Venturi carbonation reactor







u 4Q

π middot d2(3)






Qm ρgp

ρgm

middotρlm

ρlp

middotd4

m

d4p

middotHm

Hp

⎛⎝ ⎞⎠

12

middot Qp (5)







P ρmixgh (7)


εg 1 minusP

ρlgh (8)












or


(10)



Π0 εg (11)

Π1 Rls (12)

Π2 Rhd (13)

Π3 Ugρgd1

μg

(14)

Π4 Ulρld2

μl

(15)

Π5 d1

d5 (16)

Π6 d2

d5 (17)

Π7 H

d5 (18)



μg

Ulρld2

μl

d1

d5d2

d5H

d51113888 1113889 0 (19)



μg

Ulρld2

μl

d1

d5

d2

d5

H

d51113888 1113889 (20)



μg

Ulρld2

μl

1113888 1113889 (21)



εg a0Ra1ls R

a2hd

Ugρgd1

μg

1113888 1113889

a3 Ulρld2

μl

1113888 1113889

a4

(22)



μg

+ a4 lnUlρld2

μl

(23)



a1 0270

a2 1185

a3 0998

a4 minus0266

(24)






1185hd

Ugρgd1

μg

1113888 1113889

0998Ulρld2

μl

1113888 1113889

minus0266

(25)


5 Discussion


Re1 Ugρgd1

μg

Re2 Ulρld2

μl

(26)







Ug

εg

Us +Ul

εl

(27)








Rls = 20Rhd = 4



005

010

015ε

020

025


(a)

Rls = 20Rhd = 4



ε


006

008

010

012

014

016

018

020

022

024

(b)


10 15 20Rls

ε

005

010

015

020

025



(c)


Rhd

3 54 6

ε



005

010

015

020

025

030

035

(d)




6 Conclusions




Notations

a0 a1 a2 a3and a4









Data Availability




Acknowledgments





1113936ni1 δ

2n1113969


References




010 015 020 025 030005 035ε (exe)

005

010

015

020

025

030

035

ε (ca

l)


















































u 4Q

π middot d2(3)






Qm ρgp

ρgm

middotρlm

ρlp

middotd4

m

d4p

middotHm

Hp

⎛⎝ ⎞⎠

12

middot Qp (5)







P ρmixgh (7)


εg 1 minusP

ρlgh (8)












or


(10)



Π0 εg (11)

Π1 Rls (12)

Π2 Rhd (13)

Π3 Ugρgd1

μg

(14)

Π4 Ulρld2

μl

(15)

Π5 d1

d5 (16)

Π6 d2

d5 (17)

Π7 H

d5 (18)



μg

Ulρld2

μl

d1

d5d2

d5H

d51113888 1113889 0 (19)



μg

Ulρld2

μl

d1

d5

d2

d5

H

d51113888 1113889 (20)



μg

Ulρld2

μl

1113888 1113889 (21)



εg a0Ra1ls R

a2hd

Ugρgd1

μg

1113888 1113889

a3 Ulρld2

μl

1113888 1113889

a4

(22)



μg

+ a4 lnUlρld2

μl

(23)



a1 0270

a2 1185

a3 0998

a4 minus0266

(24)






1185hd

Ugρgd1

μg

1113888 1113889

0998Ulρld2

μl

1113888 1113889

minus0266

(25)


5 Discussion


Re1 Ugρgd1

μg

Re2 Ulρld2

μl

(26)







Ug

εg

Us +Ul

εl

(27)








Rls = 20Rhd = 4



005

010

015ε

020

025


(a)

Rls = 20Rhd = 4



ε


006

008

010

012

014

016

018

020

022

024

(b)


10 15 20Rls

ε

005

010

015

020

025



(c)


Rhd

3 54 6

ε



005

010

015

020

025

030

035

(d)




6 Conclusions




Notations

a0 a1 a2 a3and a4









Data Availability




Acknowledgments





1113936ni1 δ

2n1113969


References




010 015 020 025 030005 035ε (exe)

005

010

015

020

025

030

035

ε (ca

l)
















































or


(10)



Π0 εg (11)

Π1 Rls (12)

Π2 Rhd (13)

Π3 Ugρgd1

μg

(14)

Π4 Ulρld2

μl

(15)

Π5 d1

d5 (16)

Π6 d2

d5 (17)

Π7 H

d5 (18)



μg

Ulρld2

μl

d1

d5d2

d5H

d51113888 1113889 0 (19)



μg

Ulρld2

μl

d1

d5

d2

d5

H

d51113888 1113889 (20)



μg

Ulρld2

μl

1113888 1113889 (21)



εg a0Ra1ls R

a2hd

Ugρgd1

μg

1113888 1113889

a3 Ulρld2

μl

1113888 1113889

a4

(22)



μg

+ a4 lnUlρld2

μl

(23)



a1 0270

a2 1185

a3 0998

a4 minus0266

(24)






1185hd

Ugρgd1

μg

1113888 1113889

0998Ulρld2

μl

1113888 1113889

minus0266

(25)


5 Discussion


Re1 Ugρgd1

μg

Re2 Ulρld2

μl

(26)







Ug

εg

Us +Ul

εl

(27)








Rls = 20Rhd = 4



005

010

015ε

020

025


(a)

Rls = 20Rhd = 4



ε


006

008

010

012

014

016

018

020

022

024

(b)


10 15 20Rls

ε

005

010

015

020

025



(c)


Rhd

3 54 6

ε



005

010

015

020

025

030

035

(d)




6 Conclusions




Notations

a0 a1 a2 a3and a4









Data Availability




Acknowledgments





1113936ni1 δ

2n1113969


References




010 015 020 025 030005 035ε (exe)

005

010

015

020

025

030

035

ε (ca

l)















































1185hd

Ugρgd1

μg

1113888 1113889

0998Ulρld2

μl

1113888 1113889

minus0266

(25)


5 Discussion


Re1 Ugρgd1

μg

Re2 Ulρld2

μl

(26)







Ug

εg

Us +Ul

εl

(27)








Rls = 20Rhd = 4



005

010

015ε

020

025


(a)

Rls = 20Rhd = 4



ε


006

008

010

012

014

016

018

020

022

024

(b)


10 15 20Rls

ε

005

010

015

020

025



(c)


Rhd

3 54 6

ε



005

010

015

020

025

030

035

(d)




6 Conclusions




Notations

a0 a1 a2 a3and a4









Data Availability




Acknowledgments





1113936ni1 δ

2n1113969


References




010 015 020 025 030005 035ε (exe)

005

010

015

020

025

030

035

ε (ca

l)

















































Rls = 20Rhd = 4



005

010

015ε

020

025


(a)

Rls = 20Rhd = 4



ε


006

008

010

012

014

016

018

020

022

024

(b)


10 15 20Rls

ε

005

010

015

020

025



(c)


Rhd

3 54 6

ε



005

010

015

020

025

030

035

(d)




6 Conclusions




Notations

a0 a1 a2 a3and a4









Data Availability




Acknowledgments





1113936ni1 δ

2n1113969


References




010 015 020 025 030005 035ε (exe)

005

010

015

020

025

030

035

ε (ca

l)














































6 Conclusions




Notations

a0 a1 a2 a3and a4









Data Availability




Acknowledgments





1113936ni1 δ

2n1113969


References




010 015 020 025 030005 035ε (exe)

005

010

015

020

025

030

035

ε (ca

l)













































dimensionalanalysisofgasholdupofventuricarbonation...

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