Technological and Profitable Analysis of Airlifting in Deep Sea Mining Systems

20 Pages·2017·6.05 MB·English

minerals
Article
Technological and Profitable Analysis of Airlifting in
Deep Sea Mining Systems
WenbinMa*,CeesvanRheeandDingenaSchott
DepartmentofMaritimeandTransportTechnology,DelftUniversityofTechnology,
2628CDDelft,TheNetherlands;[email protected](C.v.R.);[email protected](D.S.)
* Correspondence:[email protected];Tel.:[phone]
Received:16June2017;Accepted:4August2017;Published:10August2017
Abstract: Airliftingtechnologyutilizedindeep-seamining(DSM)industrywasproposedinthe70s
oflastcentury,whichwastriggeredbythediscoveryofvastamountsofmineralresourcesonthe
seabed. Theobjectiveofthispaperistoassessthetechnologicalfeasibilityandprofitabilityanalyses
intermsofsolidproductionrate,energyconsumptionpertonnageofmineral,andprofitabilityper
tonnageofmineral. Theeffectsofsubmergenceratio,pipediameter,particlediameter,miningdepth,
andgasfluxrateareinvestigated. Theanalysisisbasedonanumericalcalculationperformedina
Matlabenvironment. Theresearchreportedinthispapercanassisttoselectanoptimaltransport
planforDSMprojectsdependingonitssolidproductionrate,energyconsumption,andprofitability.
Keywords: energyconsumption;profitability;pipediameter;submergenceratio;solidproduction
rate;technologicalfeasibility
1. Introduction
IntheDSMindustry,airliftingisoneofthemostwidelyresearchedtechnologiesequippedwith
thecorrespondingfacilities,e.g.,collectingmachine(CM)[1]. Airliftingusescompressedgastolift
the liquid-gas or solid-liquid-gas multiphase flow [2]. It is also used in other industries, such as
in chemical industry to transport toxic substances and sewage treatment plants [3]. Although the
airliftingtransportinDSMhasbeenresearchedforalongtime,untilnowthereisnocorresponding
commercialscaledDSMprojectinprogress. Technologicalfeasibilityandprofitabilityanalysesaretwo
ofthemajorconsiderationsforitsindustrialization[4].
AlotofexperimentalandtheoreticalanalysesofairliftingtechnologyutilizedintheDSMindustry
startedinthe70soflastcentury,whichwastriggeredbythediscoveryofvastamountsofmanganese
nodulesontheseabedofdepthrangingfrom4000to6000m[5]. YoshinagaandSato[6]proposed
anumericalmodelingmethodoftheairliftingpumpdependingonmomentumequationanalysis,
which was validated by a vertical pipe lifting system with height of 6.74 m and diameter of 26
and 40 mm, respectively. In Yoshinaga and Sato’s research, the flux rates of solid and gas are
givenparameterstocalculatetheliquidfluxrate, whichdoesnotagreewiththerealisticworking
condition. Actually,thegasfluxrateisthegivenparameterandthefluxratesofsolidandliquidare
calculatedparameters. Additionally,YoshinagaandSato’smodeliscreatedforuniformparticlessize
distribution[3]. Kassabetal.[3]innovatedYoshinagaandSato’smodelbytakingtherelationship
between the liquid and gas flux rates into consideration, which was validated by a vertical pipe
liftingsystemwithheightof3.75manddiameterof25.4mm. Inthenumericalcalculationmodel
proposedbyYoshinagaandSato,thecompressibilityofgasisneglectedbecauseofthesmall-scaled
experiments.Hattaetal.[5]proposedanairliftingnumericalmodeldependingonthesolid-liquidmass
conservationequations,twomomentumequations,andanequationforthesolid-liquidvolumetric
fractions. Additionally, Hatta et al. [7] analyzed a special kind of pipe with an abrupt diameter
Minerals2017,7,143;doi:10.3390/min7080143 www.mdpi.com/journal/minerals
Minerals2017,7,143 2of20
enlargement. Hattaetal.[5,7]utilizedthemultifluidmethodtopredicttheperformancesofairlifting
pumps, which can be used to calculate the gas flux rate up to 45 m/s. However, Hatta et al. [5,7]
admitted that it is quite difficult to establish the transitional situation of the multiphase flow in a
pipesystem. MargarisandPapanikas[8]proposedanairliftingnumericalmethodbyanalyzingthe
fundamentalconservationequationsofflowcontinuityandmomentum. Hongetal.[9]analyzedpipe
inclinationeffectsofairliftingwaterpumpbyexperiments.Theyinvestigatedtheairliftingperformance
asafunctionofthevariationofinclinationangles. Nam-Cheoletal.[10]studiedtheairliftingpump
withairjetnozzleanalyzingitsperformanceinfluencedbysubmergeddepth,liftinghead,andgas
flux rate. Researches of both Hong et al. and Nam-Cheol et al. focused on the experiments and
didnotconsiderthecorrespondingtheoreticalexplanationandanalysisfortheirexperimentaldata.
Fanetal.[11]researchedairliftingpumpperformancesutilizedinanartificialupwelling. Almostall
ofthesetheoreticalandexperimentalinvestigationsarefarawayfromtheindustrialscaledworking
conditionsofDSM.Theserealisticconditionsneedtobeconsideredconcerningthescaleeffectsbetween
theup-scaledmodelanditsindustrialscaledprototype. Additionally,noresearchhasconsideredall
relatedparametersthatcaninfluencetheairliftingperformancesinDSMprojects.
Basedontheliteraturereview,airliftingtechnologicalconsiderationinDSMindustryfocuses
on the transport performances influenced by the submergence ratio which is defined as the ratio
betweensubmergenceandthetotallengthofthepipe,miningdepth,pipediameter,gasfluxrate,and
particlediameter[5–11]. ForthetechnologicalanalysisofverticaltransportinDSMindustry,energy
consumptionliftingpertonnageofmineralandsolidproductionratewereintroducedbyMaetal.[12].
These parameters will also be introduced for the technological analysis of airlifting in this paper.
Additionally,profitabilityisanotherinfluencingfactorforairliftingtechnologyutilizedinDSM,which
is mainly reflected by a high initial capital expenditure to purchase the related facilities and high
operatingcostonthesefacilities,e.g.,productionsupportvessel(PSV),seafloorvehicles,transhipment
vessels, mineral processing plants, and even the tailings treatment facilities in a later stage [4,12].
FortheprofitableanalysisofairliftingtechnologyutilizedinDSM,profitabilityliftingpertonnageof
mineralisresearchedinthispaper. Thenumericalcalculationmethodusedinthispaperisbasedon
theoriginalmodelsofYoshinagaandSato,andKassabetal.,andconsidersthecompressibilityofthe
gas,whichisimportantbecauseofthelargeminingdepthinengineeringconditions. Additionally,the
numericalcalculationmethodconsidersthecompleteparameters,whichconsistsofthesubmergence
ratio,miningdepth,pipediameter,particlediameter,andgasfluxrate.
Theobjectiveofthispaperistoassessthetechnologicalfeasibilityandprofitabilityintermsof
solidproductionrate,energyconsumptionpertonnageofmineral,andprofitabilitypertonnageof
mineral. Theeffectsofsubmergenceratio,pipediameter,particlediameter,miningdepth,andgasflux
rateareinvestigated. ThispaperincombinationwithpaperwrittenbyMaetal.[12]canbeusedasa
referencetoselectapropertransportplanforDSMprojects. Thepaperisarrangedasfollows. The
Section2isthetheoreticalanalysisincludingtheoreticalmodelsofairliftingmomentum,airlifting
energyconsumptionpertonnageofminerals,andprofitabilityofairliftingutilizedinDSMsystems.
IntheSection3,thevalidationsofthenumericalcalculationmethodandcalculationresultsofthesolid
productionrate,airliftingenergyconsumptionpertonnageofminerals,andprofitabilitypertonnage
ofmineralareanalyzedanddiscussed. Finally,inSection4conclusionsoftheconductedresearch
aregiven.
2. TheoreticalAnalysis
2.1. AirliftingMomentumModelling
TheschematicdiagramofairliftingisshowninFigure1[6].Theairliftingpipesystemconsistsofa
solid-liquidtwo-phaseflowhappenedbetweengasinletandseabed,andasolid-liquid-gasthree-phase
flowhappenedbetweenpipeoutletandgasinletasshowninFigure1. InFigure1,thelettersofE, I,
Orepresenttwo-phaseflowentrance,gasinlet,andoutletofmineralmixtures.
Minerals2017,7,143 3of20
Minerals 2017, 7, 143 3 of 20

FigFuigrue r1e. 1T.hTeh sechscehmeamtiact diciadgiaragmra mof oafna aniraliirftliinftgin sgyssytesmte m[6][.6 ].
The momentum equation for airlifting can be written as Equation (1) [3,6].
ThemomentumequationforairliftingcanbewrittenasEquation(1)[3,6].
 n   n 
A(cid:26)J ρ v +AJ∑nlρlvJl,E(+i)i=ρ1J(s(ii))vρs(i)v(si,E)((cid:27)i)−−AA(cid:26)Jg,JOρg,Oρvg,O+vJlρlvl++i=J1ρJs(vi)ρ+s(i)v∑ns(i)J (i)ρ (i)v (i)(cid:27)
l l l,E s s s,E g,O g,O g,O l l l s s s
−πDi=1Iτdz−πDOτdz−AIρ(cid:26)C +n ρ(i)C (i)gdz (cid:27) i=1 (1)
−−πAD(cid:82)Oi(cid:82)(cid:26)EIτρls−CdAzIO−i+EρπglsCρDg,C3i(cid:82)+IOρlCi+τlI3,3d+∑3nzi=n−1ρρsA((iiE))(cid:82)CCEsI,3l(i)l,(ρ2ilg)Cd(cid:27)iz=l1,+g2Ads+{zρi+l∑=ngs,21(ALρ2{s+(ρLi3)g)C}(=sL,20(+i) Lg)d}z=0 (1)
I g g,3 l l,3 s s,3 l 2 3
in which A is the pipe cross sectionai=l 1area (m2), J is the volumetric flux (m/s), ρ is the density
(kign/mw3h),i chv Ais isthteh evpeliopceitcyr o[sms/sse]c, ttihone asluabrsecar(ipmt2s) ,ofJ iss,t hle,v oglu mreeptrreicseflnutx s(omlid/ sp),aρrtiisclteh,e lidqeunisdi,t yan(kdg g/ams3 ),
resvpiesctthiveevleyl,o cτity i[sm t/hse], tshheesaur bsstcrreipssts (oNfs/m,l2,)g, reDpr eisse nthteso lpidippea rdtiicalme,eltiqeru id(m,a)n, dCga sisr esthpee ctvivoelulym,τe is
i
cotnhceenshtreaatriosntr e(-s)s, 2(N, 3/ rmep2)r,eDseinist ttwheo-ppiphaesdei aflmowet earn(dm t)h,rCeei-spthhaesve ofllouwm erecsopneccetnivteralyti,o ni (r-)e,p2r,e3serneptsr ethseen t
tytpwe oo-fp dhiafsfeerflenotw paanrtdictlhesre. e-phaseflowrespectively,irepresentsthetypeofdifferentparticles.
FoFro trhteh seosloidli-dli-qluiqiudi dtwtow-op-hpahsae sfeloflwo,w s,osloidli danadn dliqliuqiudi daraer erergeagradredde dasa sinicnocmomprpersessisbilbel.e F.oFro trhteh e
sosliodli-dli-qliuqiudi-dg-agsa sththrreeee-p-phhaassee flflooww,, asasd ednesintysitayn daflnudx frlautxe orfagtea soafr egeaass ilyarien fleuaesnilcye dinbfyluseunrcroedu ndbyin g
suprrreosusnudrein,gY opsrheisnsaugrae,a nYdosShaitnoapgrao panodse dSattoo dpivroidpeosthede utop -driisveirdpe iptheei nutpo-rNiseelre mpiepnet sin[t6o]. TNh eetlhemirdentetsrm
[6]o.f TEhqeu tahtiirodn t(e1r)mis owf rEiqttuenataiosnE (q1u) aisti ownri(t2te)n[3 a,6s] E. quation (2) [3,6].
ππDD(cid:90)IIττddzz==AAΔ(cid:26)P∆f.lPsfL.ls+LΔ+P ∆P (cid:27) (2) (2)
iiEE llss  Δz∆z2 2 E E
ini wnhwichhic hΔ∆PP /Δ/z∆ zisi sththe efrfircitcitoinon pprersessusruer egrgardaideinetn itni nsosloidli-dli-qliuqiudi dfloflwo w(P(aP/ma/),m Δ),P∆P is itshteh perpersessusruer e
f.lsf.ls E E
dedcerecraesaes aet atthteh eenetnratrnacnec peopsoitsiiotino n(P(aP)a. ) .
ThTeh feofuoruthrt thertemrm ini EnqEuqautaiotino n(1()1 c)acna nbeb reerwewritrtiettne nasa EsqEuqautaiotino n(3()3 [)1[31]3. ].
πDπD(cid:90)IIττddzz==AA(cid:40)N∑NΔP∆f.3P(kf.3)(Δkz)(∆k)z+(kΔ)P+∆ P (cid:41) (3) (3)
i iEE 33 k=k1=1Δz(∆kz)(k) I I
ini wnhwichhic hΔ∆PfP.3f(.k3()k/)Δ/z∆(kz)(k )isi sthteh efrfircitciotino nprpersessusruer gergardaidenietn itni nsosloidli-dli-qluiqiudi-dga-gsa fsloflwo w(Pa(P/ma/),m Δ),P∆I PiIs itshteh e
prpersessusruer deedcerceraesaes aeta tthteh geagsa isnilnelte ptopsoistiiotino n(P(aP)a. ).
In the airlifting numerical calculation process, the velocity relationship of solid particles needs
to be considered. For three-phase flow, the velocity of particles can be calculated as Equation (4) [14].
Minerals2017,7,143 4of20
Intheairliftingnumericalcalculationprocess,thevelocityrelationshipofsolidparticlesneedsto
beconsidered. Forthree-phaseflow,thevelocityofparticlescanbecalculatedasEquation(4)[14].
m
v (i) = c +v (i) (4)
s sw
ρ
A
inwhichcisthedistributioncoefficient(-),misthemassfluxofthethree-phaseflow(kg/m2·s),ρ is
A
theapparentdensityofthethree-phasemixture(kg/m3),v isthewallaffectedsettlingvelocityina
sw
three-phaseflow(m/s).
For solid-liquid two-phase flow, the volume concentration of solid, liquid can be calculated
throughsolvingEquation(5)[15].
(cid:18)−v −J −J (cid:19) J
C2+ sl l s C + l =0 (5)
l v l v
sl sl
inwhichv istheslipvelocity,whichisrelatedtotheparticlediameter,pipediameter,settlingvelocity,
sl
andsolidvolumeconcentration(m/s).
ThevolumeconcentrationofthegascanbecalculatedasEquation(6)[6].
Cg = 1+0.4ρρlsg,3(cid:18)ρmgJg −1(cid:19)+0.6ρρlsg,3(cid:18)ρmgJg −1(cid:19)ρρl1sg,3++0.04.(cid:16)4(cid:16)mρgmJg−−1(cid:17)1(cid:17)0.5−1 (6)
ρgJg
inwhichρ isthemeandensityoftheslurry(kg/m3).
ls,3
ComparedtotheoriginalmodelofYoshinagaandSato,thesignificantdifferenceofgasdensity
andfluxrate,whicharecausedbythelargeminingdepthinengineeringconditions,aretakeninto
consideration,seeEquation(7)[15].
(cid:40) J = Jg_0·P0
g_z Pz (7)
ρ = ρg_0·Pz
g_z P0
inwhichP istheinitialgaspressure(Pa),P isthegaspressureattheverticalpositionofz(Pa),ρ is
0 z g_0
theinitialgasdensity(kg/m3),ρ isthegasdensityattheverticalpositionofz(kg/m3).
g_z
BasedonEquations(1)–(7),theairliftingprocessintheverticalpipesystemcanbecalculated.
After the establishment of airlifting numerical model, the next section will focus on the energy
consumptioncalculation.
2.2. EnergyConsumptionperTonnageofMineralModelling
The energy consumption of airlifting system is closely related to the compressor’s expansion
type,whichisdefinedasanisothermalexpansioninthispaper[11]. Theairliftingefficiencycanbe
calculatedasEquation(8)[15,16].
ρ E
η = (1− l) u (8)
a
ρ E
s t
in which E is the useful energy consumption of the airlifting system (J), E is the total energy
u t
consumptionoftheairliftingsystem(J).
The useful energy consumption of the airlifting system is defined as the anti-gravitational
energy consumption of lifting mineral solids from seabed to pipe outlet. It can be calculated as
Equation(9)[11,15,16].
E = ρ ·A·J ·g·(L +L ) (9)
u s s 2 1
inwhichL andL arelengthsofdifferentsegmentsoftheverticalpipe(m),seeFigure1.
1 2
Minerals2017,7,143 5of20
Thetotalenergyconsumptionoftheairliftingsystemistheisothermalenergyconsumptionofthe
compressor. ItcanbecalculatedasEquation(10)[11,15,16].
P
E = J ·A·ln I (10)
t g_atm
P
atm
inwhich J isthegasfluxunderatmosphericpressure(m/s),P isthepressureattheinlet(Pa),
g_atm I
P istheatmosphericpressure(Pa).
atm
Additionally,theenergyconsumptionpertonnageofmineralsisalsoanimportantparameter,
whichcanbecalculatedasEquation(11)[12].
E
E = t (11)
ton
Q
s
inwhichQ isthemineralsolidsproductionrate(ton).
s
2.3. ProfitabilityperTonnageofMineralModelling
TheprofitabilityanalysisofairliftingutilizedinDSMsystemsfocusesonthedifferencebetween
gross income and total expenditure derived from minerals. The total expenditure of an airlifting
systemisdividedintocapitalexpenditure(CAPEX)andoperationalexpenditure(OPEX)[12,17].
M = M +M (12)
t c o
in which M represents the cost ($), c, o represent the initial capital expenditure and
operationexpenditure.
TheM andM inEquation(12)canbecalculatedasEquation(13)[12,18].
c o
(cid:40)
M = M +M +M
c c_m c_t c_p
(13)
M = M +M +M
o o_m o_t o_p
inwhichm,t, prepresenttheminingsystem,transportsystem,andprocessingplantrespectively. The
initialcapitalexpenditureoftheminingsystemisspentondifferentkindsofseafloorvehicles.
ThepipesystemofairliftingtechnologyinDSMprojectsconsistsofamajorup-riserpipeandan
auxiliaryair-injectionpipe,whichisrequiredtocalculateinitialcapitalcostofpipesystems[12].

 nr = (L1l+prL2) (14)
 nI = lLp1I
inwhichn andn aretheup-riserandair-injectionpipeelementsnumber(-),l andl arethepipe
r I pr pI
elementlengthoftheup-riserpipeandair-injectionpiperespectively(m). Therefore,theinitialcapital
costofthetransportsystemcanbecalculatedasEquation(15)[12].
(cid:110) (cid:16) (cid:17) (cid:16) (cid:17) (cid:111)
M = M +π·ρ ·M ·(1+ε )· l · r2 −r2 ·n +l · r2 −r2 ·n +M (15)
c_t sv p m_p 1 pr r_1 r_2 r pI I_1 I_2 I _ot
inwhich M istheinitialcapitalcostontheshippingvesselincludingproductionsupportvesseland
sv
trans-shipmentvessels($),M isthemanufacturingcostofthepipelinesystem($),ρ isthematerial
m_p p
densityofthepipe(kg/m3),ε isthepipemanufacturingpricefactorwhichmeanstheaddedvalueof
1
materials(-),ristheradiusofpipelines(m),1,2representtheexternalandinternalradiusofpipelines
(m), M istheothertransportcost($).
_ot
Minerals2017,7,143 6of20
Theoperationexpenditureoftheminingsystem,transportsystem,andprocessingsystemcanbe
calculatedasEquation(16)[12].

 Mo_m = Mm_ma+Mm_pe
M = M +M (16)
o_t t_ma t_pe
 M = M +M +M
o_p p_la p_ma p_pe
in which ma, pe, and la represent the maintenance, power and energy consumption, and
laborexpenditures.
The M inEquation(16)canbecalculatedasEquation(17)[12].
p_la
M = ∑N ∑ns W ·(1+a)N (17)
p_la i
j=1i=1
inwhichW isthesalaryforthestaffi($/year),n isthestaffnumber(-),Nistheminingperiod(year),
i s
aistheinflationrate(-).
The maintenance, power, and energy consumption expenditures can be calculated as
Equation(18)[12].

N
 Mj_ma = ∑ 24·s·Qs·Kj_k·(1+a)N
i=1 (18)
N
 Mj_pe = ∑ 24·s·Ek·R·(1+a)N
i=1
inwhich jrepresentstheminingsystem,transportsystem,andtheprocessingsystemrespectively,
Kisthemaintenancefeeeveryyear($/ton),Risthepowerandenergyconsumptionprice($/kWh),
E istheenergyconsumption(kWh/h),sisthemeanworkingdaysperyear.
k
TheincomederivedfrommineralscanbecalculatedasEquation(19)[12].
N (cid:16) (cid:17)
M = ∑ 24·s·Q ·M ·(1+a)N (19)
in s i,mm
i=1
inwhich M isthemineralorepricewhichissettobe95$/ton.
i,mm
TheprofitabilitypertonnageofmineralcanbecalculatedasEquation(20)[12].
M M −M +M
M = be = in t re (20)
ton
N N
∑(24·s·Q ) ∑(24·s·Q )
s s
i=1 i=1
inwhich M isthepurebenefitofDSMproject($), M istheresidualvalue($).
be re
3. ResultsandDiscussions
3.1. Validations
3.1.1. ModelValidatedbyExperimentalDataofYoshinagaandSato
ThenumericalcalculationmodelofEquations(1)–(7)proposedbyYoshinagaandSato[6]isused
inthissection. Additionally,theexperimentaldatafoundinYoshinagaandSato’spapercanbeusedas
thevalidationdata. InYoshinagaandSato’sexperiment[6],sphericalanduniformparticlesareused,
asfollows: C1-Sp-06,whichdensityanddiameterare2540kg/m3and6.1mmrespectively,C1-Sp-10,
whichdensityanddiameterare2540kg/m3 and9.9mmrespectively,andC2-Sp-06,whichdensity
anddiameterare3630kg/m3and9.5mmrespectively. InFigure2,ninetypesofairliftingconditions
areshownwithsolidfluxraterangingfrom0.014to0.095m/s. Axisxrepresentstheexperimental
dataofliquidfluxratefrom0to1m/s. Axisyrepresentsthecalculationdataofliquidfluxratefrom0
Minerals2017,7,143 7of20
Minerals 2017, 7, 143 7 of 20
tofl1umx /ras.teT hfreocmlo s0e rtoth 1e dma/tsa. pTohien tcslaorseert oththee ddaiatag opnoailn,ttsh earme otroe tahcec udraiatgeothnealc, atlhcue lamtioorne raecscuultrsa.tTe htehe
mcaajolcruitlyatoiofnd aretasuplotsin. tTshaer emlaojcoartietyd oinf tdhaetaa rpeoaiwntist hairne 1l0o%catdeedv iinat itohne oafretha ewdiitahgino n1a0l%,w dheivchiatiniodni coaft etshe
thdaitatghoenmalo, dwehliicshs uinfdfiicciaentetsly thaactc uthrae tme.odel is sufficiently accurate.

FiFgiugruere2 .2V. Valaidliadtaiotinonre rseuslutsltbs ybyex epxepreimrimenetnatladl adtaatfar ofrmomY oYsohsinhaingaagaan adnSda Stoat[o6 ][.6].
3.1.2. Model Validated by Experimental Data of Kassab et al.
3.1.2. ModelValidatedbyExperimentalDataofKassabetal.
In Yoshinaga and Sato’s model of simulating a solid-liquid-gas airlifting system, the flux rates
InYoshinagaandSato’smodelofsimulatingasolid-liquid-gasairliftingsystem,thefluxratesof
of gas and solid are designated as a pair of original values. Then based on momentum balance
gasandsolidaredesignatedasapairoforiginalvalues. Thenbasedonmomentumbalanceequation,
equation, the flux rate of liquid is determined [6]. Kassab et al. utilize the Stenning and Martin
thefluxrateofliquidisdetermined[6]. Kassabetal. utilizetheStenningandMartinequation,see
equation, see Equation (21), combining with momentum method to solve the flux rates of solid and
Equation(21),combiningwithmomentummethodtosolvethefluxratesofsolidandliquiddirectly
liquid directly from gas flux rate [19].
fromgasfluxrate[19].
LL3 − 1LL+13 −(cid:0)1V+/(1V(gs/1·(Vsl⋅)V(cid:1)l)=) =2g2Jg·Jl2Ll⋅2L1(cid:20)((KKcc++11))++(K(Kc +c+2)2VV)glVVg (cid:21) ((2211))
1 g l l 1 l
in which V , V are the volume flow rate of gas and liquid (m3/s), s is the slip factor (-), K is the
in which V ,gV alre the volume flow rate of gas and liquid (m3/s), slis the slip factor (-), K cis the
g l l c
friction factor (-).
frictionfactor(-).
ThTehes isnl Einqu Eaqtuioanti(o2n1 )(2c1a)n cbaen cbael ccuallactueldatwedit hwEitqhu Eaqtiuoanti(o2n2 )(2[220) ][.20].
l
V 0.35(cid:112)⋅ g⋅D
sl =s1l.=21+.20+.20VV.2glV+gl +0.35· JJllg·Dii ((2222))
The K in Equation (21) can be calculated with Equation (23) [19].
TheKc inc Equation(21)canbecalculatedwithEquation(23)[19].
4⋅ f ⋅L
KcK=c 4=· f ·DL11 ((2233))
Di i
in which f is the friction coefficient calculated by Colebrook-White equation, which can be
inwhich f isthefrictioncoefficientcalculatedbyColebrook-Whiteequation,whichcanbecalculated
ascaElqcuualatitoedn (a2s4 E)q[2u1a]t.ion (24) [21].
f =0.25·(cid:34)log(cid:32) Dεiε+ 5.74 (cid:33)(cid:35)−−22 (24)
f =0.25⋅log3.7 DiR+e50..974  (24)
  3.7 Re0.9 
inwhichεisthepipewallroughness(m),ReistheliquidReynoldsnumber(-).
in which ε is the pipe wall roughness (m), Re is the liquid Reynolds number (-).
Based on Equations (21)–(24), the innovated numerical method of airlifting by Kassab et al. is
validated in Figure 3. Kassab et al. investigated airlifting performances influenced by submergence
Minerals2017,7,143 8of20
BasedonEquations(21)–(24),theinnovatednumericalmethodofairliftingbyKassabetal. is
Minerals 2017, 7, 143 8 of 20
validatedinFigure3. Kassabetal. investigatedairliftingperformancesinfluencedbysubmergence
rartaiotioa ndanpda rtipcalertidcilaem edtiearm[3e]te.r In[3F]i.g uIrne 3,Fipgaurrteic le3,d iapmarettiecrles ofdi4a.m75e,te7r.1s 0,oafn d49.7.550, m7.m10,, anadnd
su9b.5m0e mrgmen, caendra stuiobmofe0rg.5e0n,c0e. 7r2a,tiaon odf 00..5708,, 0a.r7e2,c aanlcdu l0a.7te8d, .arAe lciaklecuthlaetevda.l iAdlaiktieo nthpe rvinalciidpaletiodne spcrriinbceidple
indFeisgcurirbee2d, tihn eFciglousreer 2th, ethdea ctlaopseori nthtse tdoatthae pdoiiangtos ntaol ,ththee dmiaogroenaacl,c uthrea tmetohree caaclccuurlaatteio tnher ecsaullctuslaartieo.n
Asremsuolstts oafred. aAtas pmooinstt soaf rdealtoac aptoeidntisn atrhee laorceaatewd iitnh itnhe1 0a%read ewviitahtiino n10o%ft hdeevdiiaatgioonn aolf, tthhee dcaialcguolnaatilo, nthe
sycsatelcmuluatsieodn isnytshteismp uapseedr iisns tuhfifis cpieanptelry iasc scuufrfaicteie.ntly accurate.

FiFgiugruer3e. 3V. aVliadliadtiaotniorne sruesltusltbsy beyx epxepriemriemnetanltadla dtaatfaro fmromKa Kssaasbsaebt eatl a[3l ][.3].
3.1.3. Scale Effect
3.1.3. ScaleEffect
Scale effect arises due to differences between an up-scaled model and its industrial scaled
Scale effect arises due to differences between an up-scaled model and its industrial scaled
prototype, which leads to some deviations between the simulation results [22]. The scale ratio
prototype,whichleadstosomedeviationsbetweenthesimulationresults[22]. Thescaleratiobetween
between the general up-scaled model and industrial scaled prototype of airlifting model in DSM
thegeneralup-scaledmodelandindustrialscaledprototypeofairliftingmodelinDSMprojectscanbe
projects can be up to 500~600, which is much larger than that in normal mechanical and hydraulic
upto500~600,whichismuchlargerthanthatinnormalmechanicalandhydraulicsimulations[3,6,23].
simulations [3,6,23]. Additionally, most parameters of the experimental and theoretical airlifting
Additionally,mostparametersoftheexperimentalandtheoreticalairliftingmodelingresearchesare
modeling researches are smaller than the industrial scaled airlifting parameters in DSM projects
smallerthantheindustrialscaledairliftingparametersinDSMprojects[3,6]. Themostfrequently
[3,6]. The most frequently used method to compensate scale effect is to distort model geometry by
usedmethodtocompensatescaleeffectistodistortmodelgeometrybygivingupexactgeometric
giving up exact geometric similarities or change the related parameter appropriately, e.g., model
similaritiesorchangetherelatedparameterappropriately,e.g.,modelroughness[22]. Inthissection,
roughness [22]. In this section, flow regime conditions both in the experiments of Yoshinaga and
flow regime conditions both in the experiments of Yoshinaga and Sato and Kassab et al., and the
Sato and Kassab et al., and the following large-scale calculation case are taken into consideration.
followinglarge-scalecalculationcasearetakenintoconsideration. Becauseofthelackoftheoretical
Because of the lack of theoretical research on solid-liquid-gas three-phase flow regimes in a vertical
researchonsolid-liquid-gasthree-phaseflowregimesinaverticalpipesystem,theflowregimeof
pipe system, the flow regime of gas-liquid flow in a vertical pipe system is used. In the airlifting
gas-liquid flow in a vertical pipe system is used. In the airlifting vertical pipe system, there exist
vertical pipe system, there exist five different type flow regimes including bubble, slug, froth,
fivedifferenttypeflowregimesincludingbubble,slug,froth,annular,andfinelydispersedbubbles
annular, and finely dispersed bubbles depending on the velocity and geometry of the lifting
dependingonthevelocityandgeometryoftheliftingcomponents[15,24]. Thisthoughthasalready
components [15,24]. This thought has already been used by the other researchers in the DSM field
beenusedbytheotherresearchersintheDSMfield[25]. Theflowregimetransitionsarecalculatedas
[25]. The flow regime transitions are calculated as Equations (25)–(29) [15,24].
Equations(25)–(29)[15,24].
J =J3l.0=·3J.0⋅−Jg1.−115.1·5(cid:104)σ⋅σ·g⋅·g(cid:0)⋅ρ(ρ−l −ρρg(cid:1))//ρρ2(cid:105)l20.02.525 ((2255))
l g l g l
Jl+JgJ=l +4J.0g·=(cid:40)4(cid:34).0D⋅i0.42D9i0·.4(cid:18)29⋅ρσ(cid:19)ρσl0.008.098/9 /Jl0J.0l07.0272(cid:35)·⋅(cid:2)gg⋅·((cid:0)ρρll−−ρρgg)(cid:1)//ρρll(cid:3)00.4.44646(cid:41) ((2266))
l
J = J (27)
g l
J =−J +α ⋅ g⋅D (28)
g l sf i
Minerals2017,7,143 9of20
J = J (27)
Minerals 2017, 7, 143 g l 9 of 20
(cid:112)
J = −J +α · g·D (28)
g l sf i
J ⋅ρ0.5 =3.1⋅σ⋅g⋅(ρ−ρ)0.25 (29)
J ·ρ0g.5 =g3.1·(cid:2)σ·g·(cid:0)ρ −l ρ (cid:1)g(cid:3)0.25 (29)
g g l g
ininw hwihchichσ iσs t hise tshuer fsaucrefatceen steionnsioonf tohfe thlieq uliiqdu(idN /(Nm/2m),2)α, sαf sifs ais faa cftaocrtowr hwichhicihs iisn flinufelunecnedcedby btyh tehe
airaliirfltiifntigngg egoemometreitersie.s.E Eququataitoinon( 2(52)5)d edpeipcitcstst hteher ergeigmimeetr atrnasnitsiiotinonfr ofrmomb ubbubblbeleto tosl usgluflg ofwlo.wT. hTehe
folfloolwloiwnginEgq uEaqtuioantiso(n2s6 )–(2(269)–)(a2r9e) coarrere scpoornredsipnogntdoibnugb btoly btoubdbislpy ertose ddibsupbebrslyedfl obwu,bfbrolyth ftloowdi,s pfreorsthed to
budbibsplyerflsoewd, bsulubgbltyo ffrloowth, flslouwg, taon dfrofrtoht hflotowa, nannudl afrroflthow to. Faingnuurela4r dfleopwic. tFsitghuercea 4lc duelaptiicotns trheseu clatslcouflathtieon
florwesureltgsi mofe t.he flow regime.

Figure 4. Flow regime figure combining the experimental results of Yoshinaga and Sato and Kassab
Figure 4. Flow regime figure combining the experimental results of Yoshinaga and Sato and
et al. [3,6].
Kassabetal.[3,6].
Analyzing Figure 4, most of the flow regimes in Yoshinaga and Sato, and Kassab’s experiments
AnalyzingFigure4,mostoftheflowregimesinYoshinagaandSato,andKassab’sexperiments
are froth flows, which is limited by the small-scaled gas flux rate. However, for the case studies in
arefrothflows,whichislimitedbythesmall-scaledgasfluxrate. However,forthecasestudiesinthis
this paper, as the gas flux rates change from 30 to 180 m/s, all the flow regimes in the following
paper,asthegasfluxrateschangefrom30to180m/s,alltheflowregimesinthefollowingcalculation
calculation system are annular flows. Therefore, besides the scale effects between the up-scaled
systemareannularflows. Therefore,besidesthescaleeffectsbetweentheup-scaledmodelandan
model and an industrial scaled prototype of airlifting model, flow pattern differences should also be
industrialscaledprototypeofairliftingmodel,flowpatterndifferencesshouldalsobeconsideredin
considered in the future research.
thefutureresearch.
3.2. Solid Production Rate Analysis
3.2. SolidProductionRateAnalysis
Solid production rate is an important parameter in DSM, which determines the gross income
SolidproductionrateisanimportantparameterinDSM,whichdeterminesthegrossincome
directly; see Equation (19). In this section, the relationships between solid production rate and
directly; see Equation (19). In this section, the relationships between solid production rate and
submergence ratio, mining depth, pipe diameter, particle diameter, and gas flux rate are researched.
submergenceratio,miningdepth,pipediameter,particlediameter,andgasfluxrateareresearched.
The parameter changing ranges of airlifting in DSM systems are given as Table 1.
TheparameterchangingrangesofairliftinginDSMsystemsaregivenasTable1.
Table 1. The parameters of the airlifting system in DSM.
Table1.TheparametersoftheairliftingsysteminDSM.

Parameters S (-) d (mm) D (m) Jg (m/s) H (m)
r s i
Parameters RSanrg(-e) 0.985–1d.0s0(0m m)1.0–50.0 0D.2i5(m–0).40 30–18J0g (m/5s0)0–6000 H(m)
Range 0.985–1.000 1.0–50.0 0.25–0.40 30–180 500–6000
Figure 5 depicts the relationship between the solid production rate and submergence ratio at
different mining depth and gas flux rate with pipe diameter of 0.40 m and particle diameter of 5.0
mm. Analyzing Figure 5a–d, it is obvious that with the same gas flux rate the solid production rate of
airlifting decreases with the increase of mining depth on the whole. Additionally, when the
submergence ratio is set to be 1.000, 0.995, 0.990, and 0.985 respectively, there are not so many
differences between these calculating conditions. Although with a small changing amplitude, by
Minerals2017,7,143 10of20
Figure 5 depicts the relationship between the solid production rate and submergence ratio at
different mining depth and gas flux rate with pipe diameter of 0.40 m and particle diameter of
5.0mm. AnalyzingFigure5a–d,itisobviousthatwiththesamegasfluxratethesolidproduction
rate of airlifting decreases with the increase of mining depth on the whole. Additionally, when
Minerals 2017, 7, 143 10 of 20
thesubmergenceratioissettobe1.000, 0.995, 0.990, and0.985respectively, therearenotsomany
dainffaelryeznincegs tbheet wdeaetna, thite spercoavlceus lathtiantg lcaorngderi tisounbsm. Aerlgthenocueg hrawtiiot hmaasym aallsloc hraenpgriensgenatm lparligteurd es,obliyd
apnraoldyuzicntigotnh eradtea twa,iitthp trhoev essamthea tglaasr gfelurxs urabtme.e Irtg ecnance brea teioxpmlaaiyneadls oasr etpharet sae nlatrlgaregr esrusbomliderpgreondcue crtaiotino
raaltseo wmiethanths elifstainmge ag raeslafltuivxe rsamtea.llIetrc vanerbtiecaelx dpilsatiannecde awshtehna tthael amrgineirnsgu dbempethrg iesn tchee rsaatmioea. lTsohemreefaonres,
laifnti naigrlaifrtienlagt isvyestsemma lclaenr vlieftr tmicaolred imstiannecrealws hweintht hae lamrgineirn sgudbempetrhgiesntchee rsaatmioe. .ATsh seurbefmoreer,gaenncaei rrlaifttiion gis
sayns tiemmpcoarntalniftt pmaorarmemetienre irna lasiwrliiftthinagl asrygsetermsu, bthmee crgalecnucleatriaotnio h.eAres sisu bcomnedrguecntecde troa thioavisea anni minpsiogrhtat notf
pitasr aimnfeluteernicninagi rloinft iningdsuyssttreiaml ,stchaelecda lcDuSlaMti ownohrekriengis ccoonnddiuticotends. toHhoawveevaenr, intaskiginhgt oifnittos iancflcouuenntc itnhge
oanctuinadl uwstorrikailnsgc acloenddDitSioMnsw, tohrek ivnagluceosn odfi tsiuonbms.eHrgoewnceev erar,titoa ksihnogulidn tonoatc bcoe utnoto tshmeaalcl,t uwahliwcho rrkainngge
cforonmdi t0io.9n8s5, tthoe 1v.0a0l0u.e Fsuorftshuebrmmoerreg,e wncheerna ttihoes mhoinuilndgn dotepbteht oiso ssemt tahlle, wsahmiceh, ara lnarggeefrr ogmas 0f.l9u8x5 rtaote1 .m00a0y.
Fnuortt hperormduocree ,aw lharegnetrh seomlidin pinrogdduecptitohni srasteet. tFhoers ianmstea,nacela, rigne Friggausrefl u5xa rwahteenm tahyen motinpirnogd duecpetah laisr g5e0r0
saonlidd 1p0r0o0d umct iroenspraetcet.ivFeolry,i ntshtea nacier,liifntinFgig usyrest5eamw wheitnht hgeasm filnuixn gradteep othf i7s05 0a0ndan 9d01 m00/0s mtrarnessppeocrttisv ethlye,
tmheaxaiimrliuftmin mgsinyesrteamls owf i4t9h7g.9a sanfldu 4x2r8a.t0e toofn7/h0 raensdpe9c0timve/lys. tHraonwspeovretrs, ath learmgearx gimasu fmluxm rianteer malasyo fal4w97a.y9s
arnedpr4e2s8e.n0t toan l/ahrgreers preacntgivee loyf. Hapopwliecvaebrl,ea mlairngienrgg adseflptuhx. rFaoter minasytaanlcwea, yisn reFpigruesreen 5tca, lathrge emrraaxnigmeuomf
aapppplliiccaabblelem mininininggd depeptht.hFs oorf ignastsa fnlcuex, irnatFei gouf r3e05, c5,0t,h 9e0m aanxdim 1u50m map/sp alircea b1l0e0m0, i2n0in0g0,d 3e5p0t0h sanofdg 4a5s0fl0u mx
rraetsepoefct3i0v,e5ly0., F9o0ra tnhde a1i5r0lifmti/ngs asryest1e0m00 w,2it0h0 g0,a3s 5fl0u0xa rnadte4 o5f0 108m0 mre/ssp aetc mtivineilny.g Fdoerptthhe oaf i1rl0i0ft0i nmg, styhsetreem is
wa itshudgdasenfl udxercarteeasoef 1o8f0 smol/ids aptrmodinuicntgiodne rpatthe.o fIt1 0co00ulmd ,bthe eerxepislaainseudd daesn tdhaect rseoalsiedo pfrsoodliudcptiroond uracttieo nis
riantfelu. Ietnccoeudl dbyb eboexthp ltahien eindcaresatsheadt saoirlildiftpinrogd euffcitciioenncrya taenisd itnhfleu meninceindgb dyebpotthh wthheicihn chreaavsee dthaei rcloifntfinligct
eefffifecicetn ocny tahned ptehrefomrminainngcedse opft haiwrlihfitcinhgh sayvsetethme. c onflicteffectontheperformancesofairliftingsystem.
Figure 5. Figure of solid production rate Qs influenced by submergence ratio S at different
Figure5. FigureofsolidproductionrateQsinfluencedbysubmergenceratioSratdiffrerentmining
dmepinthinHg daenpdthg asHfl uaxnrda tgeaJsg f.luTxh erastuebJmge. rTghene cseurbamtioerogfe(nac–ed r)aatrieo 1o.f0 0(a0–,d0.)9 a9r5e, 01..909000,, 00..998955,,r 0e.s9p9e0c,t i0v.9e8ly5.,
respectively.
Figure 6 depicts the relationship between the solid production rate and pipe diameter at
different mining depths and gas flux rate with the submergence ratio of 0.990 and particle diameter
of 5.0 mm. Analyzing Figure 6a–d, a larger pipe diameter can increase the solid production rate
significantly. For instance, when the mining depth is 500 m and gas flux rate is 70 m/s, the solid
production rate is 487.6 ton/h in Figure 6a with a pipe diameter of 0.40 m and 143.8 ton/h in Figure
6d with a pipe diameter of 0.25 m. Additionally, a larger pipe diameter may also represent a larger