CATS – A process-based model for turbulent turbidite systems at the reservoir scale

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CATS – A process-based model for turbulent turbidite

systems at the reservoir scale

Vanessa Teles, Benoit Chauveau, Philippe Joseph, Pierre Weill, Fakher

Maktouf

To cite this version:

Stratigraphy,

Sedimentology

CATS

–

A

process-based

model

for

turbulent

turbidite

systems

at

the

reservoir

scale

Vanessa

Teles

*

,

Benoıˆt

Chauveau,

Philippe

Joseph,

Pierre

Weill

1

,

Fakher

Maktouf

2

IFPE´nergiesnouvelles,1-4,avenuedeBois-Pre´au,92852Rueil-Malmaisoncedex,France

1. Introduction

Several recent oil discoveriesare setin deep-marine reservoirs,andthesearecommonlycomposedofturbidite sandstoneswithverygoodreservoirproperties,butalso withaveryhighdegreeofheterogeneity.Thesereservoirs areusuallyformedbythestackingofdepositsrelatedto severalhundredsofindividualturbidityflowevents.There is a wide range of gravity flow types and several classifications have been proposed in the literature according to flow characteristics such as rheology or density (Mulder and Alexander, 2001; Mulder and

Cochonat, 1996; Shanmugam,2000), sedimentaryfacies ofdeposits(MuttiandRicciLucchi,1975;Pickeringetal., 1989) or sediment transport processes (Lowe, 1979; Middletonand Hampton,1973; Stowet al., 1996). The relationshipbetweenprocessesandresulting architectu-resarestillsubjecttodebate(Mulder,2011;Shanmugam, 2012), particularly because direct observations and characterization of turbidity currents are difficult in reality. They are thescene of several complexphysical processesinteractingina nonlinearway.Evenin recent casessuchas turbiditycurrentsmonitoredin Monterey Canyon(Xuetal.,2004,2013),andthe1929GrandBanks event(Piperetal.,1999)orthe1979Niceevent(Migeon et al., 2001; Mulder et al., 2012), where cable breaks provideconstrainsontimingandassociateddepositscan bestudied,thereisdebateontheflowregime,transport anddepositionprocesses.

Mostofthesereservoirslieindeep-offshorelocations wheredataarescarce.Tobetterunderstandtheirinternal

C.R.Geoscience348(2016)489–498

ARTICLE INFO Articlehistory:

Received19February2016

Acceptedafterrevision15March2016 Availableonline2June2016

HandledbySylvieBourquin Keywords: Turbidite Numericalsimulation Process-basedmodel Reservoir Cellularautomata Rousenumber ABSTRACT

TheCellularAutomataforTurbiditesystems(CATS)modelisintendedtosimulatethefine architectureandfaciesdistributionofturbiditereservoirswithamulti-eventand process-basedapproach.Themainprocessesoflow-densityturbulentturbidityflowaremodeled: downslopesediment-ladenflow,entrainmentofambientwater,erosionanddepositionof severaldistinctlithologies.Thisnumericalmodel,derivedfrom(Salles,2006;Sallesetal., 2007),proposesanewapproachbasedontheRouseconcentrationprofiletoconsiderthe flowcapacitytocarrythesedimentloadinsuspension.InCATS,theflowdistributionona given topography is modeled with local rules between neighboring cells (cellular automata)basedonpotentialandkineticenergybalanceanddiffusionconcepts.Input parametersaretheinitialflowparametersanda3Dtopographyatdepositionaltime.An overviewofCATScapabilitiesindifferentcontextsispresentedanddiscussed. ß2016Acade´miedessciences.PublishedbyElsevierMassonSAS.Thisisanopenaccess

articleundertheCCBY-NC-NDlicense(http://creativecommons.org/licenses/by-nc-nd/ 4.0/).

* Correspondingauthor.

E-mailaddress:vanessa.teles@ifpen.fr(V.Teles).

1_{NowatUniversite´ deCaenNormandie,CNRS,Morphodynamique}

continentaleetcoˆtie`re(M2C),24,ruedesTilleuls,14000Caen,France.

2

NowatGEOREX,7C,placeduDoˆme,immeubleE´lyse´e-LaDe´fense, 92056Paris-LaDe´fensecedex,France.

ContentslistsavailableatScienceDirect

Comptes

Rendus

Geoscience

w ww . sc i e nce d i re ct . co m

http://dx.doi.org/10.1016/j.crte.2016.03.002

architectureandsedimentdistribution,oneapproachisto study the processes, which led to their formation. Numericalmodelingis oneway tostudythesesystems and to link the modeled processes to the associated depositsandresultingarchitecture.Allparameterscanbe easilycontrolled and sensitivity analysiscan becarried out.Thedifficultyliesinmodelingthedifferentprocesses andtheirinteractionscorrectlywhenthereisstilldebate ontheactingprocessesthemselvesandonthedifferent proposed formulations. The most detailed flow models (Basanietal.,2014;Meiburgetal.,2015;Rouzairoletal., 2012)implement3DNavier–Stokesequationsandareable toreproduce thefullcomplexity ofturbulent flow. But, thesedetailednumericalsimulationsrequirehugerunning times,evenwithhighlyparallelizedpowerfulcomputing machines. The most common approximation of the Navier–Stokes equations is the Saint-Venant system of equations(e.g.,Parkeretal.,1986;ZengandLowe,1997)in whichtheflowparametersaredepth-averaged.Evenwith this approximated approach, the application of these modelstoawholeturbiditereservoir,resultingfromthe stackingofmanyfloweventdeposits,remainsachallenge. Furthermore,sinceflowparametersvaryfromoneeventto theotherand are difficulttoinfer fromfield data,it is difficulttoconstrainthemodelwithaccurateparameters. Theapplicationsof suchprocess-basedmodelsfollow a trial-and-errorapproachthatrequiresseveralsimulations andthushighcomputationtime.

Toovercometheseproblems,analternativeapproachis tousesimplifiedmodelsmimickingtheflowwithenough realism to reproduce detailed description of reservoir architectureandheterogeneityofdeep-offshorefieldsand withlowcomputationtimesinordertogenerate multi-eventsimulations.Tothispurpose,theCellularAutomata for Turbidite Systems (CATS) model was developed at IFPEN.CATSisamulti-lithologyprocess-basedmodelfor turbulentturbiditycurrentsandtheirassociated sedimen-tary processes. An overview of CATS capabilities in differentcontextsispresentedanddiscussedinthispaper.

2. Modeldescription

2.1. CATS:amodelforlow-densityturbiditycurrents Among gravity flows, turbidity currents are usually definedassubmarinesediment-ladenflowsinwhichthe transportismainlysupportedbytheflowturbulence,with a distinction between high-density and low-density turbiditycurrents(MiddletonandSouthard,1984;Mulder andAlexander,2001).TheCATSmodelhasbeendeveloped for low-densityturbidity currents where sedimentsare transported essentially in suspension by the fluid and where interactions between particles can be neglected.

MulderandAlexander(2001)giveamaximumthreshold of 9% of volumetric sediment concentration for low-density turbidity currents above which interactions between particles become non-negligible (Bagnold, 1962).Insuchacontext,themainprocessestobemodeled aresediment-ladengravity-drivenflowofturbulentdilute sediment suspensions, ambientwater entrainment into

theflowandsedimentaryprocessessuchaserosionand deposition.

2.2. CellularAutomataprinciples

Thismodelisbasedoncellularautomata(CA)concepts (Salles,2006):

thespaceispartitionedintoidenticalcellscomposinga regularmesh.Eachcellisanautomatonandbearsthe localphysicalpropertiesoftheflowandoftheseafloor; thechosenmodeledprocessesareimplementedthrough locallawseitheraslocalinteractionsbetween neighbor-ing cells through mass and energy transfers; or as internaltransformationsofphysicalandenergetic prop-erties in each cell,which can beperformed indepen-dentlyfromtheneighbors’state.

IntheCATSmodel,flowdistributiondrivenbygravity and bykineticenergyis consideredaslocalinteractions betweenadjacentcells.Sedimenterosion,depositionand water entrainmentofambientwater areinternal trans-formationsessentiallybasedonempiricallaws.

2.3. Theflowmodel 2.3.1. Definitionoftheflow

Theflowisdescribedbyathickness(h)representingthe turbiditic sediment-laden flow thickness, by volumetric mean concentrations (Csedi) of differentchosen discrete lithologies,andbyascalarvelocityU(inm/s)computed fromthekineticenergybalanceinthesystem.Itmeans thatthereisnovectorvelocitythatcoulddrivethefluxes andcoulddefinetheirdirection.Theambientfluidisnot explicitly modeled. Sediments are defined in as many discreteclassesofparticletypes(grain-sizeand composi-tion,referredtoas‘‘lithology’’)asneededtodescribethe sedimentarysystem.Secondaryvariablessuchasparticle settling velocity arecomputedfollowing empirical laws (Dietrich, 1982; Soulsby, 1997). Others, such as critical erosion/deposition shear stress

t

E

cr   i=

t

D cr   i   can be adjustedbytheusertomodeldifferentsedimentbehaviors and changetheir erodibilityordepositionalcapabilities. The seabed is described by a given topography (cell altitudes)andproportionsofthedifferentsediments. 2.3.2. Flowdistribution:alocalalgorithm

TheCATS modelisinspiredby thecellularautomata approachfirstdevelopedbyDiGregorioetal.(1994,1997, 1999)forsubaeriallandslideswheretheflowdistribution iscomputedthroughthelocalalgorithmof‘‘minimization ofheightdifferences’’.Salles(2006)andSallesetal.(2007)

equivalentpotentialenergy.InCATS,therun-upheightisa functionofthescalarflowvelocityU:

hr¼U 2 2g0 where g0_¼g

r

c

r

w 1  

is the reduced gravity for the turbidity current of density

r

c submerged in ambient waterofdensity

r

w.

Thisdistributionisdonebycomputing,withanexplicit scheme, volumes to be output per iteration (called ‘‘outfluxes’’inthetexthereafter)fromeverycelltoeach one of the four neighboring cells. Details of the flow thicknessdistributionalgorithmarepresentedin Supple-mentarymaterial1.

Aftercomputationoftheseoutfluxesforallcellsofthe computational grid, the flow parameters are updated according to overall mass and energy conservation principles,takingintoaccountthetransfersbetweencells, and the transformation between kinetic and potential energies(seedetailsinSupplementarymaterial2).

This algorithm is similarto a local diffusionprocess applied to both kinetic and potential energies. The flow behavior iscontrolled by thetopography,theflow thicknessandkineticenergy.Onhighslopes,theflowwill follow the topography gradient and will propagate downslope. On low-gradient topographies, the flow distribution will tend to spread in all directions as an isotropicdiffusionoftheflowthickness.Theuseofthe run-upheightinthealgorithmallowstheflowtoclimbupward byinertiaaccordingtoitskineticenergy.

2.3.3. Sedimentconcentrationtransfer

Innature,theverticalsedimentconcentrationprofilesin theflowareverydifferent,dependingontheparticlesize distribution and density (Kneller and Buckee, 2000). Moreover, in complex topographies, the distribution of coarseorfinesedimentscarriedinsuspensioncanbequite different(Altinakaretal.,1996;Parkeretal.,1987). Fine-grainedsedimentscaneasilybedistributedthroughoutthe wholewatercolumn,andshowanalmosthomogeneous concentrationalongtheverticaland,thus,willbe distribut-edmoreeasily on topographichighssuch asterracesor leveeswhentheflowspillsover.Conversely,coarse-grained sedimentsaremoreconcentratedtowardthebottomofthe flowandwilltendtoremainintopographiclowssuchas channels.Thesedifferentsedimentdistributionsintheflow areimportanttoconsiderinordertocorrectlyreproducethe resultingdepositedsediments.

Inordertotakeintoaccountthesedifferentbehaviors insedimenttransferwiththeflow,CATScomputesvertical concentrationprofileswithdifferentshapesdependingon the sediment grain-size and density. In the following balanceequationatequilibrium(GlennandGrant,1987; Soulsby,1997),thesettlingofthegrainstowardthebedis counterbalancedbythediffusionofgrainsupward,dueto theturbulentwatermotionsnearthebed:

ws;iCið

h

Þ¼Ks dCið

h

Þ

dz

where:

ws,iisthesettlingvelocityforeachlithologyi,

Ci (

h

) is the suspended-sediment concentration of lithologyiatelevation

h

abovetheseafloorand Ksistheeddydiffusivity.Itdependsontheturbulencein

theflow,throughtheshearvelocityu*,ontheelevation above the seafloor

h

and on the flow thickness h (Rouse,1937):

Ks¼

k

u

h

1

h

h

h i

An analytical solution of the equation gives the followingexpressionoftheverticalsuspended-sediment concentrationprofilefortheith_lithologyC

i(

h

): C_ið

h

Þ¼C_a;i

h

za;i hza;i h

h

 Roui (1) where:

theRousenumberRoui¼ ws;i ku

(

k

isthevonKarman constant=0.40)and

Ca,iisareferencesuspended-sedimentconcentrationat elevation

h

=

h

a (see Smith and McLean (1977) for

details).

Differentconcentration profilescan beobtained asa functionoftheRousenumber(Fig.1).

For small orlight sediments and strong current, the Rousenumberislowandtheverticalconcentrationtends tobeconstantverticallyastheflowturbulencecaneasily maintainthem in suspension.Conversely, for coarse or heavy sediments and weak current, the Rouse number tendstooneandthesedimentsareconcentratedmainly nearthebed.

Sedimenttransfer capacity iscomputed accordingto thecomputed‘‘Rouseprofiles’’.IfthevalueoftheRouse numberissmall,thesedimentconcentrationis homoge-neous over the whole water column and thesediment concentrationofthetransferredwatermasswillbevery close to the mean sediment concentration in theflow.

Fig.1.Normalizedsuspended-sedimentconcentrationprofilesforthree differentRousenumbers.

Inthecaseofaflowdistributiontoahigherneighborcell, onlytheupperpartofthewatercolumnthatspillsoverthe obstacleistransferred.Forcoarsersediments,the concen-trationwillbesignificantlylowerthanthemean concen-trationofthewholewatercolumn(seesection3.1.1foran illustrationofdifferentiatedsedimentdistribution). 2.4. Waterentrainmentprocess

Theturbulentturbidityflow thicknesstendstogrow withdistance downstreamthroughtheincorporationof ambient fluid (Ellison and Turner, 1959). The water entrainment coefficient (ew) is commonly expressed empiricallyasa functionoftheRichardsonnumber(Ri), whichisdefinedastheratiooftheworkdonebygravityto theworkdone byinertia:Ri¼g0_h=u2 _{(Fukushimaetal.,}

1985;Parkeretal.,1987;Turner,1986).TheRinumberis the inverse of the square of the densimetric Froude number.

Inthework,theentrainmentiscomputedaccordingto

Turner’s (1986) law, identified from the laboratory experimentsofEllisonandTurner(1959):

ew¼E00:1 Ri

1þ5 Ri for Ri0:8

whereE0isanempiricalparameterequalto0.08.

Wells et al. (2010) have compiled the available information on the entrainment ratio, extending this previousrange.Theyshowedthat theentrainmentratio asymptotesto0.08forlowvaluesofRi.Waterentrainment leadstoanincreaseintheflowthicknessandadecreasein the flow concentration. In addition, the dissipation of kinetic energy linked to this process is applied and estimatedaccordingtotheentrainmentrateew.

2.5. Sedimentaryprocesses:erosionanddeposition Similarly to water entrainment laws, erosion and depositionlawsareempiricalandoriginatefrom labora-tory studies performed to characterize the physical processes governing turbidity currents (Hiscott, 1994; Partheniades, 1971). All these empirical laws may be controversialastheyarededucedfromdifferentspecific analogue models that have their own experimental protocoland are deducedfromlaboratory scale experi-mentsandappliedonamesoscopicscale(gridspace).

Furthermore, there is still debate on what the flow parameterscontrollingerosionanddepositionlawsare.It iscommontorelateobserveddepositedgrain-sizeswith flowvelocityasthemaincontroloftheflowcompetence fortransportingsediments.Onetypeoflawistocompute erosionanddepositionbycomparingtheflowshearstress tocriticalvaluesoftheshearstressfordifferentlithologies (Krone, 1962). However, Hiscott (1994) proposed that deposition is not controlled by the flow competence (velocity),butratherbythecapacityoftheflowtocarry,in suspension,itssedimentloadcomposedofseveralsizesof particles.Thatwouldexplainthediscrepanciesraisedby

Komar (1985) in the velocity estimates from observed

deposit grain-sizes. Flow competence and transport capacity are two different ways to apprehend erosion anddepositionprocesses.Thisquestionisverysimilarto theonestillindebateinfluvialandlandscapeevolution communitiesbetweentransported-limitedversus detach-ment-limited approaches (Pelletier, 2011). The relative importanceof oneconceptversustheotheris probably case-dependent, according to the flow regime and the sediment types, among other parameters. Thus, both approachesareimplementedintheCATSmodelandcan be used according to the user’s understanding of his studycase.

2.5.1. Erosionanddepositionlawsasafunctionofflowshear stress

Partheniades’ (1971) erosion lawand Krone’s (1962)

depositionlawbothdependonthedifferencebetweenthe flowbasalshearstressandthecriticalshearstressdefined foreachlithology.

In CATS, the bottom shear stress is computed as a functionofthecurrentdensity(

r

c),theflowvelocity(U) andthedragcoefficient(CD103–102)bythequadratic frictionlaw(Soulsby,1997):

t

b¼

r

cCDu2 or

t

b¼

r

cu

Thecriticalshearstressvalueofagivenlithologycanbe eithercomputedaccordingtotheSoulsbyandWhitehouse (1997)laworsetdirectlybytheuser.

TherateoferosionEiscomputedforeachcellandfor eachlithologyusingPartheniades’(1971)lawforcohesive sediments: E¼M

t

b

t

E cr 1  

whereMisanempiricalparameterusuallyrangingfrom 1107_to4107_ms1_{for turbiditycurrents(Ockenden}

etal.,1989).Erosionoccurswhentheflowbottomshear stress

t

bappliedbytheturbiditycurrentonthesediment bedexceedsthecriticalshearstressforgrainmotion

t

E

cr

 

i oftheconsideredlithology.

Deposition occurs when the valueof the flow shear stressonthebed(

t

b)islowerthanthecriticalshearstress

t

D

cr

 

i definedfor eachlithologyi. Itisa functionofthe ‘‘settlingvelocity’’(ws,i)andoftheeffectiveconcentration

Ceff,i computed in the flow bottom layer hdep that can

potentially contribute to deposition during the current computationaltimestep:

Di¼Ceff;i: ws;i 1

t

b

t

D cr   i " #!

2.5.2. Erosionanddepositionlawsasafunctionofflow capacity

computedastheintegraloftheRouseconcentrationprofile described in Section 2.3.3 following the approximated solutionproposedbyHiscott(1994).Thecell concentra-tion value Csed is compared to this flow capacity Ccap (Fig.2).

IftheflowcapacityCcapisgreaterthanthecurrentflow concentrationCsed,the‘‘Rouse’’erosionrateisappliedand more sediment is eroded from the bed and put into suspension in the water column, so that Csed tends to Ccap.Theformulationoftheerosionrateisthenidentical toPartheniades’(1971)law.Noerosionwilloccurifthe flowconcentrationisatitsfullcapacityCcap,evenifthe bottomshearstressismuchhigherthanthecriticalshear stressforgrainmotion.

IftheflowcapacityvalueCcapbecomessmallerthanthe flow concentration Csed, due to a flow deceleration for example,then theexcesssediment canbedeposited so thatthesedimentconcentrationtendstothetheoretical concentrationvalueCcap.Thedefinitionofthedeposition ratedependsontheexcessofsedimentconcentrationto theflowtransportcapacity.Itcanbewrittenasfollows:

Dep¼ Ceff;i:ws;i

Csed;iCcap Csed;i if Csed>Ccap 0 if Csed<Ccap 8 < : 3. Applications

Several applications of CATS are presented in this sectionin ordertoillustratethedifferentcapabilitiesof themodeloncomplextopographies.Alberta˜oetal.(2014)

show an application of CATS to an ancient subsurface caseintheBrazilianoffshore.

3.1. Syntheticsinuouschannelandunconfinedtopography Thefirstseriesof simulationsoftheCATSmodelare performed on a synthetic inclined sinuous channel

openingon anunconfinedflatarea (seeFig.S1, Supple-mentarymaterial3).Thegridis3kmwideand7.5kmlong, with a 5050m resolution. The upstream part of the simulateddomainfeaturesa25-mdeepand400-mwide sinuouschannelwithasinuosityof1.32andaslopeof0.58. The downstream part is a 33-km-flat unconfined topography. The main purpose of this simulation is to showthespatialdistributionofdifferentlithologiesthat can be achieved when using the Rouse profile. A first single-event simulation performed with the Rouse ap-proachisdescribedinSupplementarymaterial3.Itshows a realistic deposit distribution on the topography: the coarserlithologyisconfinedinthechannel,whereasthe fineroneisabletooverspillanddepositonthebanks. 3.1.1. Multi-eventsimulation

Onthesametopography,amulti-eventsimulationwith 50eventswasperformedwithdifferentinitialsediment concentrations in the flows(Maktouf, 2012). Eachflow eventisactiveduring6104s(16h40min)withconstant valuesofflowthicknessandvelocityrespectivelyequalto 10mand2m/s,andvaryingsedimentconcentrations.The scenarioof turbiditycurrent events hasbeenchosenin ordertomimicaprogressivedecreaseofthesandsupply (following a by-pass stage not simulated here), corres-pondingtothefirst40events,thenareactivationofthe sand supply (last 10 events) (values of input flow thickness,velocityandsedimentconcentrationsforeach ofthe50eventsareillustratedinFig.S3,Supplementary material3).

The flow values were calibrated in order to obtain aggradingchanneldepositsandalobeintheunconfined areaatthemouthofthechannel.Sandandsiltlithologies weredefinedasintheprevioussimulation(seeTableS1, Supplementarymaterial3).

Erosionanddepositionprocessesweremodeledwith the shear stress-dependent laws described in Section

2.5.1.Theotherparametersarethesameasintheprevious single-event simulation, except for the concentration

Fig.2. Maximumsedimenttransportcapacity(blueline)andsedimentconcentrationinthewatercolumn(redline).Left:ifsedimenttransportcapacity becomessmallerthantheconcentrationinthewatercolumn,afterflowdecelerationforexample,depositionisactivatedsothatCsedreturnsbacktoCcap

value.Right:ifsedimenttransportcapacitybecomeslargerthantheconcentrationinthewatercolumn,afterflowaccelerationforexample,erosionis activatedsothatCsedtendstoCcap.

profile, which is considered to be constant for all lithologiesinthissimulation.

The first flow stays confined in the channel, its thicknessincreasesupto20mduetowaterentrainment. Ontheunconfinedarea,theflowspreadsout,leadingtoa decreaseoftheflowvelocityandtolobe-shapeddeposits. Inthechannel,oncetheflowinputends,sedimentsare deposited in a relative homogeneous layer, with a thicknessof 0.6m intheupstream partofthechannel, decreasingdownstreamto0.2minthelobe.The param-eterswerechosentosimulatethegraduallyfillinginofthe channel by successive events as in an abandonment process.Thesimulatedflow,firstchannelized,overspills as thesimulation progresses and creates levees on the channel banks. Fig.3 illustrates the simulated deposits throughtime every10 flow events. Sands and silts are depositedinthechannelwithafiningupwardduringthe first 40 flow events due to the fining of the input concentrations in the flow. In the unconfined area, cross-sections show that the simulated deposits of the last10events(whichcorrespondtoanewphaseofsand input) are diverted to the right (Fig. 3, bottom). The previousdepositsontheunconfinedsurfaceatthechannel mouthhavedecreasedthelocalslopeinthechannel’saxis. Theflowisdivertedandfollowsthehigherlateralslope

gradient, in processessimilar tothelobe compensation processproposedbyMuttiandSonnino(1981).

3.2. Makrantopography

Thissecond applicationbasedon a realpresent case illustratestheabilityof theCATSmodeltosimulatethe behavior ofturbiditycurrentsona complextopography and the prediction of the related deposits. In the northwestern partoftheOman basin, theoffshore part oftheMakranaccretionarywedgeiscomposedofseveral accreted ridges and piggyback basins ( Ellouz-Zimmer-mannetal.,2007).Adensesystemofcanyonsandgullies cutsacrosstheMakranprism.Thesesystemshavebeen characterized by Bourget et al. (2011) from the data acquiredduringtheCHAMAKcruise(Ellouz-Zimmermann et al., 2007). Theyfound that these networksconverge downstreaminsevenoutlets,thusdefiningsevencanyon systems.Themodelhasbeenappliedtothedownstream partof thesecondcanyonsystemdescribed byBourget etal.(2011)(FigureS4,inSupplementarymaterial4).The ‘‘Makran’’ topography dimensions are 12.4km in width and 38.4km in length with a grid resolution of 400m400m. Theaverage slope is 1.68.The upstream partofthistopographyshowstheendofawidesinuous

Fig.4.Simulationresultsshowingfromlefttoright:Flowthickness(heightinm),flowvelocity(m/s),erosionofthesubstratum(m),sandandfinesilt deposits(m).(Colorbarsfordepositsareinlogscale,verticalexaggeration7).Differentstagesofthesimulationsareshown.Top:Duringthefirstevent, whentheflowreachesthesecondbasinpassingthelastaccretionaryridge,velocityincreasesandleadstoerosion(visibleonthemiddlepanel).Middle:The flowspreadsoverthewholedomain,sandsaredepositedintheplungepool,finesedimentsstarttodepositonthedownstreambank.Bottom:Atthe beginningofthesecondflow,showingthedifferentdistributionsofthetwotypesofsedimentsoverthetopography.

canyon openinginto a small basinconfinedby thelast accretionary ridge (Bourget et al., 2011). It connects downstreamtoaplungepoolwhichis15kmlong,7km wideand150mdeepthrougha400-m-high‘‘knickpoint’’, definedhereasadisruptionintheequilibriumduetothe lastaccretionaryridge,asinBourgetetal.(2011).

On this realcomplex topography,150-m-thick flows are input at the most upstream point of the canyon availableinthistopography(whitearrowinFig.4).Two types of flow are simulated: the first one has a finer sedimentload(composition:2%offinesiltand1%ofsand), whilethesecondoneissandier(composition:1%offinesilt and3%ofsand).BotharediluteflowsbelowtheBagnold limit of 9% (Middleton and Hampton, 1973). Sediment characteristicsandsimulationparametersaredetailedin

Table S2, Supplementary material 4. The multi-event simulation is composed of 25 events (10 ‘muddy’ flow events,10 ‘sandy’flow events andthen 5‘muddy’ flow events) (see Table S2, Supplementary material 4 for simulationdetails).

Thesimulatedflowisfirstchannelizedbythecanyon walls.Duetotherun-upheightandtheRouseprofile,the flowclimbsalittleonthesideswhereitdecelerates.This leadstothedepositionoffine-grainedsedimentsfirston the sides, whereas the coarse-grained sediments are deposited in themiddle of thecanyon. When theflow spreadsinthefirst basin,its velocitydecreases,leading first tothesedimentation of sand just past thecanyon mouth,andthentothedepositionoffinesiltsfartherinthe basin.Partoftheflowisabletoexitthedomainlaterallyin this unconfined basin. When the flow reaches the knickpoint, it is channelized towards the plunge pool andaccelerates,leadingtoerosionintheslope(Fig.4,top panels).Intheplungepool,sandsdepositfirstinsidethe pool,andsiltsstarttodepositonthedownstreambankof thepool(Fig.4,middlepanels).Withaflowinputactivity of 8000 s, the flow is able to reach the downstream boundaryofthecomputationaldomainover-spillingthe plungepool banks,but atthat time,theflow isalready waning. Flow velocity decreases and, with it, the flow capacity and shearstress reaches thedecantationpoint successivelyforeachlithologyleadingtothe sedimenta-tionoftheremainingsedimentsintheflowcolumn.The bottompanelsofFig.4showthesimulationresultsatthe beginningofthesecondflow:flowheightandvelocityare visibleinthecanyon.Sandandsiltweredepositedbythe firstflow.Theyshowadifferentspatialdistribution,with sandsconfinedwithintheplungepoolandsiltsdeposited

downstream. The difference in deposits between the middle and bottom panels is due to the decantation processattheendoftheflow.

TheCATSmodelisabletosimulatebotherosionofthe initialtopography(erosionpanelsonFig.4)and remobili-zationofthepreviousdeposits.

Fig. 5 shows the sand proportion of the simulated depositsalongtheplungepoolattheendofthe25flow events. No seismic cross-section is available for this specificlocation.However, it ispossibletocomparethe resultingmainsedimentaryfeatureswiththeseismicline acrossaclose-byplungepoolpublishedinBourgetetal. (2011).Theyrecognized‘‘distalplungepooldepositsthat aggradeandmigrate’’inthedownstreamdirection,they ‘‘onlapandformtheplungepoolflanks.’’(Bourgetetal., 2011)Thesefeaturesareverysimilartothedistaldeposit intheplungepoolofthesimulation(Fig.5).Bourgetetal. (2011) also identified mass wasting and locally sharp erosional surfaces in the most proximal banks of the plungepooljust afterthe‘‘knickpoint’’.TheCATSmodel simulates erosionintheslopeand justdownstreamthe accretionaryridge.Notethateachfloweventstartswith erosion and remobilization of previous deposits farther downstream. The last 5 ‘‘muddy’’ events produce a blanketingofthesystem.

4. Discussion

The CATS model is able to simulate several multi-lithologygravity-driven turbidityflowevents associated with sedimentaryprocesses suchas erosion, deposition andwaterentrainmentofambientfluid.Thesimulations showthat themodeledprocessesare abletoreproduce complexdepositsusingsimplelawsthatcontrollocaland internal interactionsofthecells. Theflowis distributed according to an algorithm similar to the diffusion of energy.Onhighslopetopography,thesimulatedbehavior is controlled by the local slopes and matches wellthe expected turbulent flow behavior, which follows the highestslopegradients.Theselocalrules areadaptedto fast computation solutions. The single flow events presentedherearecomputedinafewminutesonseveral processors. Complex behavior and feedback between processesseemtobeaccuratelysimulated.

Astheflowdistributionismainlycontrolledbythelocal slope,themodelisnotabletoreproduceanadvectiveflow on a flator low-slopesurface. In this specificcase, the diffusivebehaviorwillalwaysbedominant,spreadingin

all directions, and will not accurately reproduce the advection part of the flow on low-slope topographies. Thisissueisrelatedtothecomputationoftimestepfor each iteration of the cellular automata approach that infers,followingSalles(2006),thattheprocessvelocitycan be inferred from the kinetic energy V¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2g0 _h

jþhr;j

 

q

, whereas thecomputedoutfluxes arecomputedthrough the more complex flow distribution algorithm (see

SupplementaryMaterial1).Severaltestshaveshownthat thistimestepneedstobeadaptedtothecellularautomata actualfluxcomputation.Developmentsareinprogressto tacklethisissue.

5. Conclusion

TheCATSmodelisaprocess-basedmodelintendedto simulateturbulentlow-densityturbidityflows.Itisbased oncellularautomataconceptsandimplementsanalgorithm oflocaldiffusionofenergiescoupledwithother physically-orempirically-basedprocessessuchassediment concen-tration profiles controlled by the Rouse number, and erosion,depositionandwaterentrainmentlaws.

The objective of such a modeling approach is to reproduce the architecture and spatial distribution of thefacies ofturbidite reservoirswithaphysical consis-tencegivenbythesimulatedsedimentaryprocesses.The secondobjectiveistoperformfastsimulationsthatcanbe integrated in operational workflows of the petroleum industry.Themodelhasbeenappliedtodifferentsettings: syntheticchannelandunconfinedtopographiesand real-worldcomplextopographies.Itshowsrealistictransient behaviorsandtheresultingdistributionofcoarseandfine sedimentdeposits.

Acknowledgments

TheauthorswouldliketothanksponsorsoftheCATSJIP projectinIFPEN(Engie,Petrobras,Statoil,DONGEnergy, BHPBilliton,Total),whosupportedpartofthe develop-mentoftheCATSmodel.TheywouldliketothankalsoBen Kneller(UniversityofAberdeen)andRichardLabourdette (Total)fortheirconstructivereviews,whichhelpedthem toimprovethispaper.

AppendixA. Supplementarymaterial

Supplementarymaterialassociatedwiththisarticlecan befoundintheonlineversionavailableathttp://dx.doi.org/ 10.1016/j.crte.2016.03.002.

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