numerical evaluation of cfd-dem coupling applied to lost...

Research ArticleNumerical Evaluation of CFD-DEM Coupling Applied to LostCirculation Control Effects of Particle and Flow Inertia

Marcos V Barbosa Fernando C De Lai and Silvio L M Junqueira

Federal University of Technology-ParanamdashUTFPR Postgraduate Program in Mechanical and Materials EngineeringmdashPPGEMResearch Center for Rheology and Non-Newtonian FluidsmdashCERNN 81280-340 R Deputado Heitor Alencar Furtado5000-Bloco N-Ecoville Curitiba PR Brazil

Correspondence should be addressed to Silvio L M Junqueira silvioutfpredubr

Received 3 May 2019 Accepted 11 September 2019 Published 20 October 2019

Guest Editor Qijun Zheng

Copyright copy 2019 Marcos V Barbosa et al is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

In the present study the transport and deposition of solid particles to mitigate the loss circulation of fluid through a fracturetransversely placed to a vertical channel is numerically investigatedese solid particles (commonly known in the industry as lostcirculation materialsmdashLCMs) are injected into the flow during the drilling operation in the petroleum industry in hopes tocontrol the fluid loss e numerical simulation of the process follows a two-stage process the first characterizes the lostcirculation flow and the second the particle injectione numerical model comprises an EulerianndashLagrangian approach in whichthe dense discrete phase model (DDPM) is combined with the discrete element method (DEM) A parametric analysis is done byvarying the vertical channel Reynolds number the particle-to-fluid density ratio and the particle diameter Results are shown interms of the particlersquos bed geometric characteristics focusing on the location inside the fracture where the particles deposit andthe particle bed length height and time spent to fill the fracture Also monitored are the fluid loss reduction over time and thefractured channel bottom pressure (which can be related to the fracture pressure) Results indicate that using a slowintermediateflow velocity associated with heavy particles with small diameters provides the best combination for the efficient mitigation of thefluid loss process

1 Introduction

e fundamentals of flow of fluid and solid particles orfluid-solid two-phase flow are of great interest because ofseveral important engineering applications such as sedi-ment transport hydrocyclones fluidized beds filtrationprocesses sedimentation cuttings removal and wellborestability [1]

Singular among the existing practical problems of two-phase fluid-solid flows is the loss of drilling fluid through theporous formation during the drilling process of oil explo-ration e loss occurs by the leakage of drilling fluidthrough pores or discontinuities (such as fractures) [2] of therock formation in the wellbore as drilling progresses Lostcirculation events have always been a significant cause ofnonproductive drilling time increasing well construction

costs Overall such events could be classified as ldquolightrdquo losswhen loss rates are below 50 bblh moderate for losses thatrange between 50 and 150 bblh and severe for losses over150 bbh e industry spends millions of dollars a year tocombat lost circulation and its detrimental effects such asstuck pipe and kicks [3 4] Commonly related to formationswith high permeability (caves and vugs) the loss of circu-lation is intensified in the presence of fractured zones whoseeffects are notably more dramatic when the fractures areconnected to a network of natural fissures [5]

Historically materials to combat the lost circulation so-called LCM (lost circulation material) have been used by theoil industry to minimize drilling fluid losses Such materialsare typically classified as flakes fibers and granulars (cal-cium carbonate mica etc) Recent strategies list a range ofapplications such as graphite cross-linked pills high fluid

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 6742371 13 pageshttpsdoiorg10115520196742371

loss compression or a blending of these materials in differentconcentrations [6 7] Because of the high cost of drillingfluids oil companies resort to a ldquosealing flowrdquo technique byadding particles of selected granulometry to the drilling fluiditself in hopes that the particles will settle along the fractureand eventually seal the leaking path stopping the loss ofdrilling fluid [4 8ndash10]

e study of this sealing flow is complex and frequentlydifficult to perform experimentally particularly due tolimitations of available equipment (harsh flow conditions)and difficulty in performing flow visualization (opacity ofthe medium) Nevertheless the alternative of performingnumerical modeling and simulations of sealing flow issue tobe addressed in the present work is not without challengesof its own e main limitation of a numerical approach hasbeen the large computational power necessary to resolve theflow and interactions of all the individual particles flowingalong with the fluid Notwithstanding numerical simula-tions of sealing flow have recently been brought to theforefront (ie they became practical) due to the recentadvances in the available hardware and software

When modeling fluid-particle flow in sealing prob-lems the model needs to be able to address not only fluidmotion itself but also the particle-fluid and the particle-particle interactions in an efficient fashion [11] In thisrespect the combination of computational fluid dynamics(CFD) and discrete element method (DEM) is recognizedas one of the most powerful combinations for the nu-merical study of fluid-particle interactions especiallywhen a four-way coupling is paramount to obtainingsimulation results that are realistic and accurate

e DEM accounts for particle motion including col-lisions among the particles by solving Newtonrsquos second lawof motion for each individual particle [12] e methodconsiders a soft-sphere approach in which the collisionsamong several particles can be easily addressed in the sametime step making it a preferable choice for dense flowswhether the particles are spherical or not [13]

e capability and use of the CFD-DEM combinationhave been reported recently in the literature for a wide rangeof applications including fluidized beds [14ndash19] filtrationprocesses [20ndash24] hole cleaning and sediment transport inthe oil and gas industry [25ndash28] hydrocyclones vortex flowand instabilities [29ndash31] and bed-load transport [32 33]Specifics of the CFD-DEM coupling have also been docu-mented including studies of different types of DEM cou-pling [34] numerical errors involved in the models [35]requirements for the coupling with distinct fluid mechanicsnumerical models [36ndash38] and the use of nonsphericalparticles [39]

In the present work a CFD-DEM combination is used tosimulate the transport of particles along a simplified verticaland fractured wellbore e objective is to learn how theparticles behave along the fracture and how they deposit andeventually seal a leaking path of the drilling fluid or at leastreduce its loss Of great interest is the determination vianumerical simulations of the amount of fluid being lostthrough the fracture considering different flow configura-tions characterized by the distinct flow Reynolds number

particle-to-fluid density ratio and particle diameter eoutcome of such parametric exercise is a prediction of whenthe addition of the particles will yield the sealing of theleaking path making the sealing flow of practical interest

2 Problem Characterization

e drilling operation consists in a very simplified view ofthe partial removal of a substrate material in order to reachan oil and gas reservoir e substrate is removed by theaction of a drilling column which carries a drill bit at the endDue to the friction effect against the substrate the drill bittends to overheat when in operation to keep it within anacceptable working temperature range the bit is cooled bythe action of a drilling fluid injected at the top of the drillingcolumn is fluid flows down the drilling column and itreturns to the surface through the annular space comprisedbetween the column and the formation

During drilling the operator must observe among otherfactors the so-called operational window and the equivalentcirculating density e operational window is a combina-tion of two pressures inside the wellbore the pore pressureand the formation pressure e pore pressure is defined asthe pressure of fluids within the pores of a reservoir theformation pressure is the pressure at which the formation ismechanically fractured e equivalent circulating density(ECD) is the effective density of the circulating (drilling)fluid taking into account the pressure drop in the annulus[40]

Observing the operational window and the ECD thedrilling process may be classified as underbalanced oroverbalanced (see Figure 1) Underbalanced drilling occurswhen ECD is lower than the pore pressure Conversely anoperation is overbalanced when the ECD is higher than thepore pressure erefore the lost circulation tends to be-come more prevalent during overbalanced drilling becauseof the tendency of the drilling process in this case to causefractures in the formation It is important to notice that thelost circulation phenomenon may be intensified in thepresence of fractures already present in the formation(natural fractures) in addition to those caused by the drillingprocess (when ECD is higher than the formation pressure)[41 42]

When facing lost circulation in overbalanced drilling theoperator may attempt to mitigate the losses by addingparticles to the circulating fluid as mentioned previouslyRemarkably such process is feasible during operation es-pecially in the cases of seepage or partial losses is is sobecause the particles are transported to the fluid loss regionby the drilling fluid itself depositing accumulating andclogging the flow path

In the present study the fluid loss region is repre-sented by a discrete fracture which mimics a naturallyoccurring fracture or even induced by the drilling process[43 44] Figure 2 shows a 2D representation of thewellbore formation with a horizontal fracture of a typicalvertical drilling operation e figure shows a longitudinal(top) and a transversal cutting plane (bottom) the frac-ture aperture (eFR) and its depth (zFR) and also the fluid

2 Mathematical Problems in Engineering

flow direction in each region of the wellbore-fracture-formation

e geometric representation of the idealized fracture ispresented in Figure 3(a) Notice that zFR is significantlylarger than eFR providing a symmetric inlet at the fractureregion In Figure 3(b) the red region marked as (1) is theinlet section of the fluid (2) represents the end of thefracture (3) symbolizes the wellbore top region and (4)indicates the injection surface from which the particles arereleased e annulus is represented by half of its hydraulicdiameter (hCH) which is the space between the drillingcolumn and the wellbore wall In relation to the fracturewhose aperture is eFR the figure also shows the upstream andthe downstream lengths lUP and lDW respectively

Another simplification adopted in this study is to con-sider the formation (including the fracture surfaces) im-permeable erefore the lost circulation analysis is limitedto the fracture flow region Consequently the fracture fillingprocess is analyzed without the percolation effect thattypically occurs in porous reservoirs As the porosity can bevery small in these regions the simplification effect isconsideredminor in respect to the flow and deposition of theparticles

To characterize the fluid loss a two-step procedure isproposed by changing the boundary conditions applied inthe problem whose goal is to observe a predetermined flowcondition inside the wellbore e flow is represented by aReynolds number (equation (1)) defined in terms of thevelocity at the wellbore inlet UβCHi set at surface (1) inFigure 3(b)

UβCHi ReμβρβhCH

(1)

where the subscripts β CH and i refer to the fluid phase thewellbore and the inlet region respectively e circulatingfluid density is indicated by ρ and the viscosity by μ

A special procedure is necessary for determining the flowboundary conditions in the domain because the fluid loss in

a real wellbore is due to the pressure difference between theannulus and the formation as explained earlier by theoperational window and these pressures are usually un-known Hence a specific amount of fluid loss is first set at thefracture outlet qloss at surface (2) while the remainder of thecirculating fluid returns to the surface with qreturn set atsurface (3) of Figure 3(b) With all boundary conditions setthe problem is simulated until a fully developed flow con-dition is obtained at the annulus

When this state is reached the pressure at the wellboreinlet pβinlet and the respective pressures at surfaces (2) and(3) are collected respectively ploss and preturn e secondstep is implemented by maintaining the velocity inletboundary condition at surface (1) and changing theboundary conditions of surfaces (2) and (3) to the relatedpressures collected in the first step Once the flow con-sidering the fluid loss reaches a steady regime the particlesare released from the injection surface (4) at the same flowvelocity as that of the circulating fluid to minimize anyeffect they might otherwise have over the fluid loss velocityfield

3 Numerical Model

e analysis of the particle transport in a fluid can beperformed according to two approaches e first one theso-called Eulerian approach consists of treating the par-ticles as a continuum solid phase is method is usuallypreferred when the tracking of the particles can beneglected meaning that the particle concentration field isenough to describe the particle motion Alternatively inthe Lagrangian approach the particles are tracked in-dividually throughout the domain with their trajectoriescomputed using Newtonrsquos second law of motion [45 46]

AnnulusDrillingcolumn

Wellborewall

Fracturewall

ZFR

Formation

eFR

Annulus outletDrilling

column inlet

Figure 2 Representation of a wellbore with discrete fracture cutplanes longitudinal (top) and transversal (bottom)

Pressure ECD

Depth

ECD

Porepressure

Fracturepressure

Underbalancedregion

Overbalancedregion

Operationalwindow

Figure 1 Representation of the operational window its upper andlower limits and ECD

Mathematical Problems in Engineering 3

In the study presented hereby the fluid and the particlesare described according to respectively the Eulerian andLagrangian approaches via the dense discrete phase model(DDPM) of Ansys Fluentreg software e basics of the nu-merical model are presented here with a more thorough anddetailed analysis found in [47] For the continuous phase(fluid) the mass and momentum conservation equations aredescribed by equations (2) and (3)

zρβρβzt

+ nabla middot εβρβuβ1113872 1113873 0 (2)

z εβρβuβ1113872 1113873

zt+ nabla middot εβpβuβuβ1113872 1113873 minus εβnablaρβ + nabla middot εβμβnabla middot uβ1113872 1113873

+ εβρβg + FDPM + SDPM

(3)

where t is the time εβ represents the continuous phasevolume fraction uβ is the velocity vector pβ is the pressuregradient g refers to the gravity acceleration vector FDPMrefers to the coupling force between the phases and SDPM isthe source term due to the displacement of fluid caused bythe particle entering a control volume

Particle movement is determined using both the defi-nition of velocity and Newtonrsquos second law of motion givenby equations (4) and (5) respectively

dxp

dt up (4)

mpdupdt

Fd + Fgb + Fpg + Fvm + Fls + FDEM (5)

where xp and up represent the particle position and ve-locity respectively and the particle mass is given bymp By

applying a Lagrangian approach to the particles severalforces can be included in the analysis of particle motion Asummary of the expressions for determining the afore-mentioned forces is presented in Table 1 where drag (Fd)gravitational and buoyancy (Fgb) pressure gradient (Fpg)virtual (added) mass (Fvm) and Saffmanrsquos lift (Fls) forcesare considered

Regarding equation (5) a four-way coupling accountsfor the particle collisions [48] As such FDEM Fn + Ft wherethe last two terms represent respectively the normal and thetangential components [49] In this sense the particles areable to collide with each other as well as with any solidsurface on the numerical domain be it a fracture or achannel surface is means that once a particle reaches theboundary of the numerical domain two situations mayoccur if the boundary is a solid surface the collision force iscalculated using FDEM in case of an open flow region such asthe fracture or channel outlet (surfaces 2 and 3 in Figure 1)the particle will simply exit (be eliminated from) the domainas it happens in practical situations

While the drag coefficientCD is obtained fromMorsi andAlexanderrsquos [50] correlation Saffmanrsquos constant Cls is cal-culated using Li and Ahmadirsquos [51] model being the virtualmass coefficient obtained from [52]

e tangential component of the collision force is usuallyobtained from Coulombrsquos law in which μa is the frictioncoefficient and ζ12 represents the tangential direction Forthe proposed problem the tangential force is neglected

e normal force is evaluated by a spring-dashpotmodel [53] by means of several numerical parameters Inthe spring part of the model the overlap δ is calculatedwith two collision partners according to their position xrelated to their radius δ |x2 ndash x1| ndash (r1 ndash r2) e particlestiffness constant is a numerical parameter calculated byk π|u12|

2dpρp3σ2d where σd represents the fraction of the

ZFR

eFR

(a)

hFR

zFR

lDW

lUP

hCH

xy z

(1)

(2)

(3)

(4)

eFR

Flow direction

(b)

Figure 3 3D domain representation and scale of the fracture plane related to the wellbore (a) fractured wellbore simplified representation (b)


particle diameter that is allowed to overlap with the col-lision partner and u12 is the relative velocity between thecollision partners λ12 indicates the normal direction ofcollision

Similarly the dashpot part modeling employs thedamping coefficient c [54] calculated from the reducedmassm12 2m1m2(m1 +m2) the coefficient of restitution (η) andfrom the collision time (tcol) as follows c minus 2m12ln (η)tcol

For the simulations presented here an extensive sensi-tivity analysis was performed to ensure the correct char-acterization of fluid motion as well as particle transport andcollision e main numerical parameters applied on themodel are summarized as follows fluid time stepΔtβ 2 middot10minus 2 s particle time step Δtp 2 middot10minus 4 s and parti-clersquos stiffness constant k 20Nm Also the coefficient ofrestitution η 09 is applied for both particle-particle andparticle-wall collisions Other numerical details of theDDPM model such as pressure-velocity coupling pressurecorrection spatial discretization and transient formulationare detailed in [47]

4 Results and Discussion

41 Verification of DDPM-DEM Capability In order toevaluate the capability of the model to accurately predict theinteraction between the solid and fluid phases as well as tocorrectly determine the collision forces amongst the parti-cles two verification tests were carried out the settlingvelocity of a single particle released in a fluid and thebouncing motion of a single particle against a static solidsurface

e settling velocity problem consists of abandoning asingle sphere from a resting position inside a container offluid and measuring its velocity up to a constant valuenamed terminal or settling velocity e collision problemconsists at first of the same settling velocity problem exceptthat this time the particle will collide with a static wall andbounce on it until the particle achieves a zero-velocitycondition Interacting problems of one two or four particlesare often applied in the literature to evaluate the capacity ofnumerical models [55ndash60]

e settling velocity of a single spherical particlepresented in Figure 4(a) was simulated and comparedwith the numerical and experimental results of [61] eresults correspond to a particle density and diameter of

ρp 7710 kgm3 and Dp 08mm respectively settling inwater (ρβ 9982 kgm3 and μβ 1003 10minus 3 Pamiddots)

e results presented in Figure 4(a) show a goodagreement with both the numerical model and the experi-mental results presented by Mordant and Pinton [61] evenat the final stages of the settling process For the settlingvelocity the relative difference is less than 1 0316ms forthe experimental results and 0313ms for the numericalsimulationus one can conclude that the DDPMmodel isindeed able to calculate the interaction forces between thefluid and a particle with the inclusion of the selected forcesshown at Table 1

As the particle deposition process occurs within thefracture particle collisions become more important Con-sequently in order to ascertain the capability of the DDPM-DEM models outcomes from the bouncing motion of aspherical particle are compared with the experimental re-sults from [62] as depicted in Figure 4(b) In this case aparticle withDp 08mm and ρp 7800 kgm3 is moving in afluid composed of a water-glycerin mixture (737 water involume) with properties ρβ 935 kgm3 and μβ 10minus 2 PamiddotsPrior to the first collision the particle attains a settlingvelocity of roughly 06ms

Observe the DEMmodel is capable to represent the wall-particle interactions since after the first collision only aslightly lower value of the maximum velocity is observedWhen the second collision happens a time shift in thenumerical simulation of roughly 01 s is noticed whichpersists for the remaining collisions causing a delay in thetime demanded to cease the particle motion However it isimportant to notice that the speeds at each collision as well asthe number of collisions were predicted correctly by thesimulations

As the particles are mostly carried in the horizontaldirection of the fluid motion that occurs inside the fractureinstead of being exclusively moved in the vertical directionless interest is dedicated to the repetitive collision of aparticle against a wall erefore the first collision thatoccurs when the particle reaches the surface of the fracturedemands special attention From the analysis presented inthis section it is possible to assure that the DDPM-DEMmodel is indeed a good approach for the problem in-vestigated here

42 Filling a Horizontal Fracture In the simulations to bepresented the fluid loss occurring at the end of the fracturewas set as qloss 10 of the total mass flow rate As the lostcirculation phenomenon is established the particles arereleased in the numerical domain from an injection surfaceas shown in Figure 5 with the maximum velocity attainedfrom the fluid flow velocity profile As the momentumexchange from particle to fluid along time occurs theparticles tend to assume the velocity of the fluid nearby As aconsequence at a steady state a parabolic velocity profile isverified (the color of the particle is associated to itsvelocitymdashred means faster particles) At each time step atotal of 30 particles are injected For instance considering

Table 1 Forces considered in the numerical model

Force EquationGravitational andbuoyancy Fgb mp((ρp minus ρβ)ρp)g

Drag Fd (34)(mpμβρpd2p)CDRep(uβ minus up)

Saffman lift Fls Clsmp(ρβρp)(nabla times uβ) times (uβ minus up)

Virtual mass Fvm Cvmmp(ρβρp)(DDt)(uβ minus up)

Pressure gradient Fpg mp(ρβρp)(uβnabla middot uβ)

CollisionNormal Fn [kδ + c(u12 middot λ12)]λ12Tangential Ft minus μa|Fn|ζ12


175 seconds of injection for a time step of 2 middot10minus 2 seconds262500 particles will be injected into the domain

Before choosing the particle time step size one must becertain that no particle will be released inside each other sothat the overlap parameter δ is not incorrectly calculatedis is guaranteed by associating the particle velocity withthe fluid time step size in a manner that the distance coveredby the particle is sufficiently larger than the particle di-ameter By observing this simple procedure an incorrectparticle injection can be avoided

It is also important to understand that not all particleswill enter the fracture and contribute to the filling process Infact depending on the particlesrsquo properties fluid and flowconditions only 2 to 5 of all injected particles will ever getinto the fracture Also as the fluid loss is reduced throughoutthe process fewer particles will enter the fracture issituation is presented in Figure 6

e channel geometric characteristic presents an up-stream length of lUP 18m a downstream length oflDW 0225m and a width of hCH 0045m e fracturewas considered as impermeable with hFR 0720m in lengthand width eFR 001m e fluid considered in the simu-lations was a water-glycerin mixture with ρβ 11876 kgm3and μβ 27973 10minus 3 Pamiddots

e flow Reynolds number written in terms of fluidrsquosmean velocity (UβCHi) equation (1) set at the channelinlet controls the flow rate e particle-to-fluid densityratio (ρpβ) and the particle diameter (Dp) are also the mainparameters of the present study

A numerical grid test where the fluid loss stabili-zation was taken as the main parameter to determinemesh independence showed that for a relative differenceof 1 no significant changes on the flow conditions andon the particle transportdeposition rate were observed

Injection surface

1 time step

2 time steps

3 time steps8 time steps

Figure 5 Particle injection process for several time steps

t (s)0 01 02 03 04

0

01

02

03

Present studyMP (2000)-simulationMP (2000)-experimental

u p (m

s)

(a)

u p (m

s)

04 05 06 07ndash06

ndash04

ndash02

0

02

04

06

Present studyGLP (2002)

t (s)

(b)

Figure 4 Comparison between the data from [61] (MP) (a) and [62] (GLP) (b)


Additionally a grid refinement to ensure a suitable walleffect evaluation was applied specifically for each con-figuration us a channel with 18000 20000 and 22000control volumes and respective Reynolds numbers of250 500 and 750 were considered In Figure 7 a meshdetail at the fracture inlet region is shown

Initially the influence of the Reynolds number over theparticle bed formation as well as the fluid loss through thefracture is investigated e simulations were accomplishedfor three configurations namely Re 250 500 and 750corresponding to a channel inlet velocity of UβCHi 01310262 and 0393ms respectively For each flow time step1500 particles (ρpβ 225 andDp 05mm) are injected intothe domain from the particle injection surface Figure 8shows the particle bed formed inside the fracture at themoment the particles cease to enter the fracture Δtfill

One can notice a strong influence of the Reynoldsnumber especially in the particle bed position (hbedi)measured as the distance from the fracture inlet to thebeginning of the particle bed Clearly the bed position isinfluenced by the flow quantity of movement which in turnalso impacts the particle bed extension (hbed) As expectedfor low Re the particles start to deposit closer to the fractureentrance forming a more compact bed which also leads toan increase in the particle bed height represented here interms of the fracture vertical filling percentage (eFR) aspresented in Table 2

As related to Re the flow velocity will be different for allthree conditions even if the initial percentage of fluid loss(qloss 10) is the same for all the cases simulated us alow Re indicates a low fluid velocity in the fracture and thereverse is also true In this way the flow presents more or lessmomentum to carry particles along the fracture as theReynolds number is respectively higher or lower Conse-quently the smaller the Re is the closer to the fractureentrance (reduction on hbedi) and also more compact is theparticle bed implying in a shorter length (hbed) and in alarger height (eFR)

Given the flow inability to maintain particles suspendedfor a long period of time it is possible to see in Table 2 thatthe time required to the particle deposition process (Δtfill) issmaller for lower Reynolds number Hence to reduce thefluid loss in an impermeable fracture the flow rate has to be

reduced to provide a faster particle deposition in thefracture

Assuming that the understanding on how the particleinjection process acts on the fluid loss through the fracture isparamount for the present study the influence ofQloss (qlosstqloss)times 100 defined as the ratio between thefluid lost along the particle injection (qlosst) and the initialfluid loss (qloss) is investigated for different Re erefore asshown in Figure 9(a) for a fluid loss of 100 as the particledeposition process takes place a reduction in the fluid es-caping through the fracture is expected

Another monitor defined as Pinlet (pinlettpβinlet)times

100 has been configured at the inlet of the main channelwith the aim to mimic the downhole pressure In such amonitor presented in Figure 9(b) pinlett and pβinlet arerespectively the pressure at the fracture entrance along theparticle injection and the initial pressure

Figure 9(a) shows that the fluid loss is reduced to roughly42 of the original loss for both Re 500 and 750 Howeverthe time spent in the particle deposition process (which isindicated when the fluid loss reaches a plateau) is muchhigher for Re 750 as described previously By reducing theReynolds number to 250 and consequently the flow strengththe fluid loss reaches 38 indicating a reduction of 62 ofthe original fluid loss

e downside of choosing a lower velocity for the fluid isa dramatic increase in the pressure measured at the channelinlet as can be observed in Figure 9(b)e particles injected

Instant when particles start toenter the fracture

Instant when particles start todeposit inside the fracture

Instant when particlesstop entering the fracture

Figure 6 Fracture inlet region for several instants showing the variation on the amount of particle entering the fracture

y

x

Figure 7 Mesh display for the fracture inlet region for Re 500


at the channel contribute to the increase in pressure due todifferences in the particle-to-fluid density ratio For lowervelocities more particles are expected to accumulate onthe main (vertical) channel which causes a prompt in-crease of Pinlet for Re 250 As the particles move morerapidly throughout the domain the increase in the pres-sure is less prominent

In the second set of simulations the influence of theparticle-to-fluid density ratio (ρpβ) is investigated For thisthe case Re 500 is set as the reference flow configurationand all the particles have diameter Dp 05mm e mainobjective is to observe the effect of changes in the particledensity over the fracture filling process Further on theeffect of changes in the particle diameter will be presented

Re (ndash) up (ms)0207 0145 0072 0000

2500386 0270 0135 0000

5000577 0404 0202 0000

750hFR = 0 hFR = 90mm hFR = 180mm hFR = 270mm

Figure 8 Particle bed formed inside the fracture at Δtfill for Reynolds number (Re) variations (ρpβ 250 Dp 05mm)

Table 2 Particle bed geometric characteristics in terms of Reynolds number

Re (ndash) hbedi(mm) hbed(mm) eFR() Δtfill(s)

250 15 108 64 76500 64 131 54 82750 102 196 45 136

Qlo

ss (

)

0 25 50 75 100 125 150 17530

60

90

120

150

250500750

Re

tip (s)

(a)

250500750

Re

tip (s)

P inl

et (

)

0 25 50 75 100 125 150 175100

140

180

220

260

300

(b)

Figure 9 Monitoring for the fluid loss (Qloss) by the fracture (a) and dimensionless pressure (Pinlet) at the bottom of the fractured channel(b) for Reynolds number variations (ρpβ 250 Dp 05mm)


as well e final condition for the particles to be packedinside the fracture is presented in Figure 10 Informationon size extension and position of each bed is presented inTable 3

Whilst changes in Reynolds number influence theflow strength modifications in the particle density alterthe particle quantity of movement Consequently theflow has more difficulty to carry heavier particles Asshown in Figure 10 the lighter the particles the greaterthe hbed values (see the ρpβ 150 case in Table 3) On thecontrary as the particles get heavier (case ρpβ 250) thefluid does not have enough momentum to carry themaway With that a tendency of the particles to accumulatenear the entrance is observed and a more compact bed isformed

e observations concerning the influence of theparticle mass shown in Figure 10 are also related to theparticle bed length which gets larger for lighter particlesFor the ρpβ values analyzed it seems there is a stabilizationprocess regarding the particle bed length because no sig-nificant difference was observed between cases ρpβ 225and ρpβ 250 except for a shift on the particle bed initialposition hbedi which is related to particle quantity ofmovement

Regarding the fluid loss reduction shown inFigure 11(a) which is the main objective of this study aslight difference when using heavier particles is noticedsince the final reduction of loss circulation ranges from39 (ρpβ 150) to 47 (ρpβ 250) e use of heavierparticles provides a significant reduction of the time re-quired to fill the fracture Nevertheless they are not aseffective as using the lighter particles to reduce the loss offluid Notice that the difference on the fluid loss reductionfor ρpβ 150 and ρpβ 250 is only of 4 while the timefor the filling process is cut by 50

Concerning the pressure monitor at the fracturedchannel inlet presented in Figure 11(b) the use of heavierparticles has the drawback of increasing the pressure in thisregion by roughly 60 Different from the change in fluidvelocity here the increase in pressure between the limitcases ie ρpβ 150 and ρpβ 250 is only about 31 Suchbehavior indicates that a technician for instance is better offchoosing heavier particles for the filling process since in thiscase the pressure does not represent any significant re-striction for the operation with respect to the particledensity

Finally an alternative analysis of the particle inertia byconsidering different particle diameters (Dp 04 05 and06mm) is presented in Figure 12 As pointed out earlier theReynolds number is fixed as 500 while the particle-to-fluiddensity ratio is kept as ρpβ 250 Again due to the sameflow conditions it is possible to see that the increase ofparticle mass due to the increase in its diameter is re-sponsible for changing the fixed bed position along thefracture as particle gets heavier the fluid flow gets less ca-pable of transporting them

Results from Figure 12 show that the particle bed lengthincreases with the particle diameter From the geometriccharacteristics of each bed presented in Table 4 one can

notice that there is an apparent stability on the fracturefilling time when Dp 05 and 06mm

As occurred in the particle-to-fluid density ratio analysisit is possible to see from Figure 13(a) that particles with lessquantity of movement (lighter due to a smaller diameter)have the ability to more effectively reduce the fluid loss Inthe case presented here this is also related to the porosity ofthe bed As a matter of fact a more cohesive and less porousbed is formed when the particles are smaller which in turnhelps to reduce the fluid loss

Still the increase in Pinlet in Figure 13(b) is directlylinked to the particle mass variation as the flow char-acteristics remain the same for the three simulationserefore the higher the particle mass the higher Pinlete relative difference of 32 in Pinlet for the limit cases(Dp = 04 and 06 mm) may not be as significant for thedrilling operation Otherwise when a comparison be-tween Dp = 05 and 06 mm cases is drawn the formerpresents not only a better fluid loss reduction (roughly54) but also a lower increase in Pinlet and a similar Δtfillsuggesting that it would be wiser to employ particles withDp = 05 mm

5 Final Remarks

In this work the reduction of the lost circulation in ahorizontal fracture branching from a vertical channel em-ulating a fractured oil well was investigated A numericalmodeling accounting for the transport and deposition ofsolid particles inside the fracture was proposed Numericalresults obtained using the coupling of DDPM-DEM modelsproved to be a good alternative not only to represent thetwo-phase flow but also to characterize the particle bedlength height and position is study provided a betterunderstanding of using particles to seal a fracture especiallyconcerning to the oil and gas industry

Several observations can be pointed out from the re-sults When injecting a fixed type of particles an increase inthe flow velocity usually increases the time spent on thefilling process because the particles tend to be carried by theflow in the fracture region for longer distances is isreflected in the particle bed formation whose length isinversely proportional to its height Increasing the particle-to-fluid density ratio the particles get heavier thereforethey tend to accumulate closer to the fracture inlet esame behavior is verified when the particle diameter isincreased the particles also accumulate closer to the inletregion of the fracture In both cases the time spent to fillthe fracture is reduced Clearly this is related to the weightof the particle since density and diameter are directly linkedto particle mass

On the contrary particle density and diameter affect bedlength and height in an opposite manner while the particlebed length is reduced as the particle density is increased thereverse is true for the particle diameter is happens due tothe increase in the particle mass at the annulus providing ahigher pressure and resulting in a longer particle bed

Remarkably the effects presented here are competi-tive and one can choose to increase particle inertia by


increasing its density or diameter Also the same effectmay be achieved by decreasing flow velocity for instanceBearing in mind the operational window the operatormay alter one or more parameters to achieve a specific

effect which can be represented by reducing the lostcirculation to acceptable levels in the least amount oftime or if possible curtail all losses without taking timeinto account

Table 3 Particle bed geometric characteristics in terms of the particle-to-fluid density ratio

ρpβ hbedi(mm) hbed(mm) eFR() Δtfill(s)

150 150 284 43 147175 101 183 50 111200 79 161 52 94225 64 131 54 82250 53 131 57 77

ρpβ

up (ms)0379 0265 0133 0000

150

175

200

225

250hFR = 0 hFR = 90mm hFR = 180mm hFR = 270mm hFR = 360mm

Figure 10 Particle bed formed inside the fracture at Δtfill for particle-to-fluid density ratio (ρpβ) variations (Re 500 Dp 05mm)

35

50

65

80

95

110

225250

150175200

ρpβ

Qlo

ss (

)

0 25 50 75 100 125 150 175 200tip (s)

(a)

0 25 50 75 100 125 150 175 200100

113

126

139

152

165

225250

150175200

ρpβ

P inl

et (

)

tip (s)

(b)

Figure 11 Monitoring for the fluid loss (Qloss) by the fracture (a) and dimensionless pressure Pinlet at the fractured channel inlet (b) forparticle-to-fluid density ratio variations (Re 500 Dp 05mm)


epresent study represents a development of a robust andcomplete methodology that can help Petrobras to optimize itsdrilling operations in severe loss of circulation scenarios

Data Availability

e data used to support the findings of this study areincluded within the article

Conflicts of Interest

e authors declare that they have no conflicts of interest

Acknowledgments

e authors would like to express their gratitude to theNational Council for Scientific and Technological

Qlo

ss (

)

40

60

80

100

120

040506

Dp (mm)

tip (s)0 20 40 60 80 100 120 140

(a)

040506

Dp (mm)

tip (s)

P inl

et (

)

0 20 40 60 80 100 120 140100

120

140

160

180

200

(b)

Figure 13 Monitoring for the fluid loss (Qloss) by the fracture (a) and dimensionless pressure (Pinlet) at the fractured channel inlet (b) forparticle diameter variations (Re 500 ρpβ 250)

Dp (mm)

up (ms)0386 0270 0135 0000

04

05

06

hFR = 0 hFR = 90mm hFR = 180mm

Figure 12 Particle bed formed inside the fracture at Δtfill for particle diameter (Dp) variations (Re 500 ρpβ 250)

Table 4 Particle bed geometric characteristics as a function of the particle diameter Dp

Dp(mm) hbedi(mm) hbed(mm) eFR() Δtfill(s)

04 77 111 59 11105 53 131 57 7706 44 169 48 77


Development (CNPq) and Petrobras (which also providedtechnical assistance) for the financial support and to Pro-fessor Jose L Lage from Southern Methodist University forhis contribution and pertinent discussions in the develop-ment and conclusion of this work

References

[1] H P Zhu Z Y Zhou R Y Yang and a B Yu ldquoDiscreteparticle simulation of particulate systems a review of majorapplications and findingsrdquo Chemical Engineering Sciencevol 63 no 23 pp 5728ndash5770 2008

[2] N Morita A D Black and G-F Guh ldquoeory of lost cir-culation pressurerdquo in Proceedings of the SPE Annual TechnicalConference and Exhibition pp 43ndash60 New Orleans LA USASeptember 1990

[3] J Bruton C Ivan and T Heinz ldquoLost circulation controlevolving techniques and strategies to reduce downhole mudlossesrdquo in Proceedings of the SPEIADC Drilling Conferencepp 1ndash9 Amsterdam Netherlands February 2001

[4] Y Feng and K E Gray ldquoReview of fundamental studies onlost circulation and wellbore strengtheningrdquo Journal of Pe-troleum Science and Engineering vol 152 pp 511ndash522 2017

[5] J A A Oliveira J Zago C E Fontes A T AWaldmann andA L Martins ldquoModeling drilling fluid losses in fracturedreservoirsrdquo in Proceedings of the SPE Latin America andCaribbean Petroleum Engineering Conference SPE 151021-PPMexico City Mexico April 2012

[6] D K Clapper J J Szabo S P Spence et al ldquoOne sack rapidmix and pump solution to severe lost circulationrdquo in Pro-ceedings of the SPEIADC Drilling Conference and ExhibitionSPEIADC 139817 Amsterdam Netherlands March 2011

[7] W W Sanders R N Williamson C D Ivan and D PowellldquoLost circulation assessment and planning program evolvingstrategy to control severe losses in deepwater projectsrdquo inProceedings of the SPEIADC Drilling Conference SPEIADC79836 Amsterdam Netherlands February 2003

[8] G Wang and X Pu ldquoDiscrete element simulation of granularlost circulation material plugging a fracturerdquo ParticulateScience and Technology vol 32 no 2 pp 112ndash117 2014

[9] H Wang R Sweatman B Engelman W D Halliburton andD Whitfill ldquoe key to successfully applying todayrsquos lostcirculation solutionsrdquo in Proceedings of the SPE AnnualTechnical Conference and Exhibition SPE 95895 Dallas TXUSA October 2005

[10] D Whitfill ldquoLost circulation material selection particle sizedistribution and fracture modeling with fracture simulationsoftwarerdquo in Proceedings of the IADCSPE Asia Pacific DrillingTechnology Conference and Exhibition pp 1ndash12 JakartaIndonesia August 2008

[11] R Silva F A P Garcia P M G M Faia and M G RasteiroldquoSettling suspensions flow modelling a reviewrdquo KONAPowder and Particle Journal vol 32 pp 41ndash56 2015

[12] Y Tsuji T Kawaguchi and T Tanaka ldquoDiscrete particlesimulation of two-dimensional fluidized bedrdquo Powder Tech-nology vol 77 no 1 pp 79ndash87 1993

[13] H Kruggel-Emden E Simsek S Rickelt S Wirtz andV Scherer ldquoReview and extension of normal force models forthe discrete element methodrdquo Powder Technology vol 171no 3 pp 157ndash173 2007

[14] Z G Luo H Zhou T Zhang et al ldquoDEM study of blockagebehaviour of cohesive fine particles in a packed structure oflarge particlesrdquo Powder Technology vol 314 pp 102ndash1092016

[15] S Al-Arkawazi C Marie K Benhabib and P CoorevitsldquoModeling the hydrodynamic forces between fluid-granularmedium by coupling DEM-CFDrdquo Chemical EngineeringResearch and Design vol 117 pp 439ndash447 2017

[16] M Karimi N Mostoufi R Zarghami and R Sotudeh-Gharebagh ldquoA new method for validation of a CFD-DEMmodel of gas-solid fluidized bedrdquo International Journal ofMultiphase Flow vol 47 pp 133ndash140 2012

[17] A Esteghamatian M Bernard M Lance A Hammouti andA Wachs ldquoMicromeso simulation of a fluidized bed in ahomogeneous bubbling regimerdquo International Journal ofMultiphase Flow vol 92 pp 93ndash111 2017

[18] R Sun and H Xiao ldquoDiffusion-based coarse graining inhybrid continuum-discrete solvers theoretical formulationand a priori testsrdquo International Journal of Multiphase Flowvol 77 pp 142ndash157 2015

[19] N G Deen M Van Sint Annaland M A Van der Hoef andJ A M Kuipers ldquoReview of discrete particle modeling offluidized bedsrdquo Chemical Engineering Science vol 62 no 1-2pp 28ndash44 2007

[20] L A Ni A B Yu G Q Lu and T Howes ldquoSimulation of thecake formation and growth in cake filtrationrdquo Minerals En-gineering vol 19 no 10 pp 1084ndash1097 2006

[21] F Qian N Huang J Lu and Y Han ldquoCFD-DEM simulationof the filtration performance for fibrous media based on themimic structurerdquo Computers amp Chemical Engineering vol 71pp 478ndash488 2014

[22] F Qian N Huang X Zhu and J Lu ldquoNumerical study of thegas-solid flow characteristic of fibrous media based on SEMusing CFD-DEMrdquo Powder Technology vol 249 pp 63ndash702013

[23] W Li S Shen and H Li ldquoStudy and optimization of thefiltration performance of multi-fiber filterrdquo Advanced PowderTechnology vol 27 no 2 pp 638ndash645 2016

[24] K J Dong R P Zou R Y Yang A B Yu and G RoachldquoDEM simulation of cake formation in sedimentation andfiltrationrdquo Minerals Engineering vol 22 no 11 pp 921ndash9302009

[25] S Akhshik M Behzad andM Rajabi ldquoCFD-DEM simulationof the hole cleaning process in a deviated well drilling theeffects of particle shaperdquo Particuology vol 25 pp 72ndash822016

[26] S Akhshik M Behzad and M Rajabi ldquoCFD-DEM approachto investigate the effect of drill pipe rotation on cuttingstransport behaviorrdquo Journal of Petroleum Science and Engi-neering vol 127 pp 229ndash244 2015

[27] S Akhshik and M Rajabi ldquoCFD-DEM modeling of cuttingstransport in underbalanced drilling considering aerated mudeffects and downhole conditionsrdquo Journal of Petroleum Sci-ence and Engineering vol 160 pp 229ndash246 2018

[28] B Pang S Wang Q Wang et al ldquoNumerical prediction ofcuttings transport behavior in well drilling using kinetictheory of granular flowrdquo Journal of Petroleum Science andEngineering vol 161 pp 190ndash203 2018

[29] J Chen K Chu R Zou et al ldquoSystematic study of the effect ofparticle density distribution on the flow and performance of adense medium cyclonerdquo Powder Technology vol 314pp 510ndash523 2016

[30] X Ku J Lin M van Sint Annaland and R HagmeijerldquoNumerical simulation of the accumulation of heavy particlesin a circular bounded vortex flowrdquo International Journal ofMultiphase Flow vol 87 pp 80ndash89 2016

[31] Z Y Yu C L Wu A S Berrouk and K NandakumarldquoDiscrete particle modeling of granular Rayleigh-Taylor


instabilityrdquo International Journal of Multiphase Flow vol 77pp 260ndash270 2015

[32] A G Kidanemariam and M Uhlmann ldquoInterface-resolveddirect numerical simulation of the erosion of a sediment bedsheared by laminar channel flowrdquo International Journal ofMultiphase Flow vol 67 pp 174ndash188 2014

[33] G Mallouppas and B van Wachem ldquoLarge eddy simulationsof turbulent particle-laden channel flowrdquo InternationalJournal of Multiphase Flow vol 54 pp 65ndash75 2013

[34] Y Guo and X Yu ldquoComparison of the implementation ofthree common types of coupled CFD-DEM model for sim-ulating soil surface erosionrdquo International Journal of Multi-phase Flow vol 91 pp 89ndash100 2017

[35] A Volk U Ghia and C Stoltz ldquoEffect of grid type and re-finement method on CFD-DEM solution trend with gridsizerdquo Powder Technology vol 311 pp 137ndash146 2017

[36] M Robinson and M Ramaioli ldquoMesoscale fluid-particleinteraction using two-way coupled SPH and the DiscreteElement Methodrdquo in Proceedings of the 6th InternationalSPHERIC Workshop Hamburg Germany June 2011

[37] K Washino E L Chan K Miyazaki T Tsuji and T TanakaldquoTime step criteria in DEM simulation of wet particles inviscosity dominant systemsrdquo Powder Technology vol 302pp 100ndash107 2016

[38] H P Zhu Z Y Zhou R Y Yang and A B Yu ldquoDiscreteparticle simulation of particulate systems theoretical de-velopmentsrdquo Chemical Engineering Science vol 62 no 13pp 3378ndash3396 2007

[39] W Zhong A Yu X Liu Z Tong and H Zhang ldquoDEMCFD-DEM modelling of non-spherical particulate systems theo-retical developments and applicationsrdquo Powder Technologyvol 302 pp 108ndash152 2016

[40] V Dokhani Y Ma and M Yu ldquoDetermination of equivalentcirculating density of drilling fluids in deepwater drillingrdquoJournal of Natural Gas Science and Engineering vol 34pp 1096ndash1105 2016

[41] M Zamora P N Broussard and M P Stephens ldquoe top 10mud-related concerns in deepwater drilling operationsrdquo inProceedings of the SPE International Petroleum Conferenceand Exhibition in Mexico Villahermosa Mexico February2000

[42] R Caenn and G V Chillingar ldquoDrilling fluids state of theartrdquo Journal of Petroleum Science and Engineering vol 14no 3-4 pp 221ndash230 1996

[43] M R P Tingay J Reinecker and B Muller ldquoBoreholebreakout and drilling-induced fracture analysis from imagelogsrdquoWorld StressMap Project Guidelines Image Logs 2008

[44] M Brudy and M D Zoback ldquoDrilling-induced tensile wall-fractures implications for determination of in-situ stressorientation and magnituderdquo International Journal of RockMechanics and Mining Sciences vol 36 no 2 pp 191ndash2151999

[45] Z Zhang and Q Chen ldquoComparison of the Eulerian andLagrangian methods for predicting particle transport inenclosed spacesrdquo Atmospheric Environment vol 41 no 25pp 5236ndash5248 2007

[46] G Gouesbet and a Berlemont ldquoEulerian and Lagrangianapproaches for predicting the behaviour of discrete particlesin turbulent flowsrdquo Progress in Energy and Combustion Sci-ence vol 25 no 2 pp 133ndash159 1998

[47] B Popoff and M Braun ldquoA Lagrangian approach to denseparticulate flowsrdquo in Proceedings of the ICMF 2007 6th In-ternational Conference on Multiphase Flow p 11 LeipzigGermany July 2007

[48] S Elghobashi ldquoOn predicting particle-laden turbulent flowsrdquoApplied Scientific Research vol 52 no 4 pp 309ndash329 1994

[49] P A Cundall and O D L Strack ldquoA discrete numericalmodel for granular assembliesrdquo Geotechnique vol 29 no 1pp 47ndash65 1979

[50] S A Morsi and A J Alexander ldquoAn investigation of particletrajectories in two-phase flow systemsrdquo Journal of FluidMechanics vol 55 no 2 p 193 1972

[51] A Li and G Ahmadi ldquoDispersion and deposition of sphericalparticles from point sources in a turbulent channel flowrdquoAerosol Science and Technology vol 16 no 4 pp 209ndash2261992

[52] A A Kendoush A H Sulaymon and S A M MohammedldquoExperimental evaluation of the virtual mass of two solidspheres accelerating in fluidsrdquo Experimental Kermal andFluid Science vol 31 no 7 pp 813ndash823 2007

[53] S Luding ldquoCollisions amp contacts between two particlesrdquo inPhysics of Dry Granular Media H J Herrmann J-P Hoviand S Luding Eds Springer Dordrecht Netherlandspp 285ndash304 1998

[54] G Kuwabara and K Kono ldquoRestitution coefficient in acollision between two spheresrdquo Japanese Journal of AppliedPhysics vol 26 no 8 pp 1230ndash1233 1987

[55] A Hager C Kloss S Pirker and C Goniva ldquoParallel resolvedopen source CFD-DEM method validation and applicationrdquoKe Journal of Computational Multiphase Flows vol 6 no 1pp 13ndash27 2014

[56] S Ma Z Wei and X Chen ldquoCFD-DEM combined the fic-titious domain method with Monte Carlo method forstudying particle sediment in fluidrdquo Particulate Science andTechnology vol 36 no 8 pp 920ndash933 2018

[57] G Pozzetti H Jasak X Besseron A Rousset and B PetersldquoA parallel dual-grid multiscale approach to CFDndashDEMcouplingsrdquo Journal of Computational Physics vol 378pp 708ndash722 2019

[58] B Vowinckel J Withers P Luzzatto-Fegiz and E MeiburgldquoSettling of cohesive sediment particle-resolved simulationsrdquoJournal of Fluid Mechanics vol 858 pp 5ndash44 2019

[59] Z Wang Y Teng and M Liu ldquoA semi-resolved CFD-DEMapproach for particulate flows with kernel based approxi-mation and Hilbert curve based searching strategyrdquo Journal ofComputational Physics vol 384 pp 151ndash169 2019

[60] Y Wang L Zhou and Q Yang ldquoHydro-mechanical analysisof calcareous sand with a new shape-dependent fluid-particledrag model integrated into CFD-DEM coupling programrdquoPowder Technology vol 344 pp 108ndash120 2019

[61] N Mordant and J-F Pinton ldquoVelocity measurement of asettling sphererdquo Ke European Physical Journal B vol 18no 2 pp 343ndash352 2000

[62] P Gondret M Lance and L Petit ldquoBouncing motion ofspherical particles in fluidsrdquo Physics of Fluids vol 14 no 2pp 643ndash652 2002


Hindawiwwwhindawicom Volume 2018

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Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Submit your manuscripts atwwwhindawicom

loss compression or a blending of these materials in differentconcentrations [6 7] Because of the high cost of drillingfluids oil companies resort to a ldquosealing flowrdquo technique byadding particles of selected granulometry to the drilling fluiditself in hopes that the particles will settle along the fractureand eventually seal the leaking path stopping the loss ofdrilling fluid [4 8ndash10]

e study of this sealing flow is complex and frequentlydifficult to perform experimentally particularly due tolimitations of available equipment (harsh flow conditions)and difficulty in performing flow visualization (opacity ofthe medium) Nevertheless the alternative of performingnumerical modeling and simulations of sealing flow issue tobe addressed in the present work is not without challengesof its own e main limitation of a numerical approach hasbeen the large computational power necessary to resolve theflow and interactions of all the individual particles flowingalong with the fluid Notwithstanding numerical simula-tions of sealing flow have recently been brought to theforefront (ie they became practical) due to the recentadvances in the available hardware and software

When modeling fluid-particle flow in sealing prob-lems the model needs to be able to address not only fluidmotion itself but also the particle-fluid and the particle-particle interactions in an efficient fashion [11] In thisrespect the combination of computational fluid dynamics(CFD) and discrete element method (DEM) is recognizedas one of the most powerful combinations for the nu-merical study of fluid-particle interactions especiallywhen a four-way coupling is paramount to obtainingsimulation results that are realistic and accurate

e DEM accounts for particle motion including col-lisions among the particles by solving Newtonrsquos second lawof motion for each individual particle [12] e methodconsiders a soft-sphere approach in which the collisionsamong several particles can be easily addressed in the sametime step making it a preferable choice for dense flowswhether the particles are spherical or not [13]

e capability and use of the CFD-DEM combinationhave been reported recently in the literature for a wide rangeof applications including fluidized beds [14ndash19] filtrationprocesses [20ndash24] hole cleaning and sediment transport inthe oil and gas industry [25ndash28] hydrocyclones vortex flowand instabilities [29ndash31] and bed-load transport [32 33]Specifics of the CFD-DEM coupling have also been docu-mented including studies of different types of DEM cou-pling [34] numerical errors involved in the models [35]requirements for the coupling with distinct fluid mechanicsnumerical models [36ndash38] and the use of nonsphericalparticles [39]

In the present work a CFD-DEM combination is used tosimulate the transport of particles along a simplified verticaland fractured wellbore e objective is to learn how theparticles behave along the fracture and how they deposit andeventually seal a leaking path of the drilling fluid or at leastreduce its loss Of great interest is the determination vianumerical simulations of the amount of fluid being lostthrough the fracture considering different flow configura-tions characterized by the distinct flow Reynolds number

particle-to-fluid density ratio and particle diameter eoutcome of such parametric exercise is a prediction of whenthe addition of the particles will yield the sealing of theleaking path making the sealing flow of practical interest

2 Problem Characterization

e drilling operation consists in a very simplified view ofthe partial removal of a substrate material in order to reachan oil and gas reservoir e substrate is removed by theaction of a drilling column which carries a drill bit at the endDue to the friction effect against the substrate the drill bittends to overheat when in operation to keep it within anacceptable working temperature range the bit is cooled bythe action of a drilling fluid injected at the top of the drillingcolumn is fluid flows down the drilling column and itreturns to the surface through the annular space comprisedbetween the column and the formation

During drilling the operator must observe among otherfactors the so-called operational window and the equivalentcirculating density e operational window is a combina-tion of two pressures inside the wellbore the pore pressureand the formation pressure e pore pressure is defined asthe pressure of fluids within the pores of a reservoir theformation pressure is the pressure at which the formation ismechanically fractured e equivalent circulating density(ECD) is the effective density of the circulating (drilling)fluid taking into account the pressure drop in the annulus[40]

Observing the operational window and the ECD thedrilling process may be classified as underbalanced oroverbalanced (see Figure 1) Underbalanced drilling occurswhen ECD is lower than the pore pressure Conversely anoperation is overbalanced when the ECD is higher than thepore pressure erefore the lost circulation tends to be-come more prevalent during overbalanced drilling becauseof the tendency of the drilling process in this case to causefractures in the formation It is important to notice that thelost circulation phenomenon may be intensified in thepresence of fractures already present in the formation(natural fractures) in addition to those caused by the drillingprocess (when ECD is higher than the formation pressure)[41 42]

When facing lost circulation in overbalanced drilling theoperator may attempt to mitigate the losses by addingparticles to the circulating fluid as mentioned previouslyRemarkably such process is feasible during operation es-pecially in the cases of seepage or partial losses is is sobecause the particles are transported to the fluid loss regionby the drilling fluid itself depositing accumulating andclogging the flow path

In the present study the fluid loss region is repre-sented by a discrete fracture which mimics a naturallyoccurring fracture or even induced by the drilling process[43 44] Figure 2 shows a 2D representation of thewellbore formation with a horizontal fracture of a typicalvertical drilling operation e figure shows a longitudinal(top) and a transversal cutting plane (bottom) the frac-ture aperture (eFR) and its depth (zFR) and also the fluid







(1)





3 Numerical Model



Wellborewall

Fracturewall

ZFR

Formation

eFR


column inlet


Pressure ECD

Depth

ECD

Porepressure

Fracturepressure

Underbalancedregion

Overbalancedregion

Operationalwindow




zρβρβzt


z εβρβuβ1113872 1113873



(3)



dxp

dt up (4)

mpdupdt









ZFR

eFR

(a)

hFR

zFR

lDW

lUP

hCH

xy z

(1)

(2)

(3)

(4)

eFR

Flow direction

(b)






























Injection surface

1 time step

2 time steps



t (s)0 01 02 03 04

0

01

02

03


u p (m

s)

(a)

u p (m

s)

04 05 06 07ndash06

ndash04

ndash02

0

02

04

06


t (s)

(b)


















y

x





Re (ndash) up (ms)0207 0145 0072 0000

2500386 0270 0135 0000

5000577 0404 0202 0000





250 15 108 64 76500 64 131 54 82750 102 196 45 136

Qlo

ss (

)

0 25 50 75 100 125 150 17530

60

90

120

150

250500750

Re

tip (s)

(a)

250500750

Re

tip (s)

P inl

et (

)

0 25 50 75 100 125 150 175100

140

180

220

260

300

(b)













5 Final Remarks










150 150 284 43 147175 101 183 50 111200 79 161 52 94225 64 131 54 82250 53 131 57 77

ρpβ

up (ms)0379 0265 0133 0000

150

175

200

225



35

50

65

80

95

110

225250

150175200

ρpβ

Qlo

ss (

)

0 25 50 75 100 125 150 175 200tip (s)

(a)

0 25 50 75 100 125 150 175 200100

113

126

139

152

165

225250

150175200

ρpβ

P inl

et (

)

tip (s)

(b)




Data Availability




Acknowledgments


Qlo

ss (

)

40

60

80

100

120

040506

Dp (mm)

tip (s)0 20 40 60 80 100 120 140

(a)

040506

Dp (mm)

tip (s)

P inl

et (

)

0 20 40 60 80 100 120 140100

120

140

160

180

200

(b)


Dp (mm)

up (ms)0386 0270 0135 0000

04

05

06





04 77 111 59 11105 53 131 57 7706 44 169 48 77



References









































































Journal of












Journal of







Volume 2018






Volume 2018













(1)





3 Numerical Model



Wellborewall

Fracturewall

ZFR

Formation

eFR


column inlet


Pressure ECD

Depth

ECD

Porepressure

Fracturepressure

Underbalancedregion

Overbalancedregion

Operationalwindow




zρβρβzt


z εβρβuβ1113872 1113873



(3)



dxp

dt up (4)

mpdupdt









ZFR

eFR

(a)

hFR

zFR

lDW

lUP

hCH

xy z

(1)

(2)

(3)

(4)

eFR

Flow direction

(b)






























Injection surface

1 time step

2 time steps



t (s)0 01 02 03 04

0

01

02

03


u p (m

s)

(a)

u p (m

s)

04 05 06 07ndash06

ndash04

ndash02

0

02

04

06


t (s)

(b)


















y

x





Re (ndash) up (ms)0207 0145 0072 0000

2500386 0270 0135 0000

5000577 0404 0202 0000





250 15 108 64 76500 64 131 54 82750 102 196 45 136

Qlo

ss (

)

0 25 50 75 100 125 150 17530

60

90

120

150

250500750

Re

tip (s)

(a)

250500750

Re

tip (s)

P inl

et (

)

0 25 50 75 100 125 150 175100

140

180

220

260

300

(b)













5 Final Remarks










150 150 284 43 147175 101 183 50 111200 79 161 52 94225 64 131 54 82250 53 131 57 77

ρpβ

up (ms)0379 0265 0133 0000

150

175

200

225



35

50

65

80

95

110

225250

150175200

ρpβ

Qlo

ss (

)

0 25 50 75 100 125 150 175 200tip (s)

(a)

0 25 50 75 100 125 150 175 200100

113

126

139

152

165

225250

150175200

ρpβ

P inl

et (

)

tip (s)

(b)




Data Availability




Acknowledgments


Qlo

ss (

)

40

60

80

100

120

040506

Dp (mm)

tip (s)0 20 40 60 80 100 120 140

(a)

040506

Dp (mm)

tip (s)

P inl

et (

)

0 20 40 60 80 100 120 140100

120

140

160

180

200

(b)


Dp (mm)

up (ms)0386 0270 0135 0000

04

05

06





04 77 111 59 11105 53 131 57 7706 44 169 48 77



References









































































Journal of












Journal of







Volume 2018






Volume 2018









zρβρβzt


z εβρβuβ1113872 1113873



(3)



dxp

dt up (4)

mpdupdt









ZFR

eFR

(a)

hFR

zFR

lDW

lUP

hCH

xy z

(1)

(2)

(3)

(4)

eFR

Flow direction

(b)






























Injection surface

1 time step

2 time steps



t (s)0 01 02 03 04

0

01

02

03


u p (m

s)

(a)

u p (m

s)

04 05 06 07ndash06

ndash04

ndash02

0

02

04

06


t (s)

(b)


















y

x





Re (ndash) up (ms)0207 0145 0072 0000

2500386 0270 0135 0000

5000577 0404 0202 0000





250 15 108 64 76500 64 131 54 82750 102 196 45 136

Qlo

ss (

)

0 25 50 75 100 125 150 17530

60

90

120

150

250500750

Re

tip (s)

(a)

250500750

Re

tip (s)

P inl

et (

)

0 25 50 75 100 125 150 175100

140

180

220

260

300

(b)













5 Final Remarks










150 150 284 43 147175 101 183 50 111200 79 161 52 94225 64 131 54 82250 53 131 57 77

ρpβ

up (ms)0379 0265 0133 0000

150

175

200

225



35

50

65

80

95

110

225250

150175200

ρpβ

Qlo

ss (

)

0 25 50 75 100 125 150 175 200tip (s)

(a)

0 25 50 75 100 125 150 175 200100

113

126

139

152

165

225250

150175200

ρpβ

P inl

et (

)

tip (s)

(b)




Data Availability




Acknowledgments


Qlo

ss (

)

40

60

80

100

120

040506

Dp (mm)

tip (s)0 20 40 60 80 100 120 140

(a)

040506

Dp (mm)

tip (s)

P inl

et (

)

0 20 40 60 80 100 120 140100

120

140

160

180

200

(b)


Dp (mm)

up (ms)0386 0270 0135 0000

04

05

06





04 77 111 59 11105 53 131 57 7706 44 169 48 77



References









































































Journal of












Journal of







Volume 2018






Volume 2018



































Injection surface

1 time step

2 time steps



t (s)0 01 02 03 04

0

01

02

03


u p (m

s)

(a)

u p (m

s)

04 05 06 07ndash06

ndash04

ndash02

0

02

04

06


t (s)

(b)


















y

x





Re (ndash) up (ms)0207 0145 0072 0000

2500386 0270 0135 0000

5000577 0404 0202 0000





250 15 108 64 76500 64 131 54 82750 102 196 45 136

Qlo

ss (

)

0 25 50 75 100 125 150 17530

60

90

120

150

250500750

Re

tip (s)

(a)

250500750

Re

tip (s)

P inl

et (

)

0 25 50 75 100 125 150 175100

140

180

220

260

300

(b)













5 Final Remarks










150 150 284 43 147175 101 183 50 111200 79 161 52 94225 64 131 54 82250 53 131 57 77

ρpβ

up (ms)0379 0265 0133 0000

150

175

200

225



35

50

65

80

95

110

225250

150175200

ρpβ

Qlo

ss (

)

0 25 50 75 100 125 150 175 200tip (s)

(a)

0 25 50 75 100 125 150 175 200100

113

126

139

152

165

225250

150175200

ρpβ

P inl

et (

)

tip (s)

(b)




Data Availability




Acknowledgments


Qlo

ss (

)

40

60

80

100

120

040506

Dp (mm)

tip (s)0 20 40 60 80 100 120 140

(a)

040506

Dp (mm)

tip (s)

P inl

et (

)

0 20 40 60 80 100 120 140100

120

140

160

180

200

(b)


Dp (mm)

up (ms)0386 0270 0135 0000

04

05

06





04 77 111 59 11105 53 131 57 7706 44 169 48 77



References









































































Journal of












Journal of







Volume 2018






Volume 2018























y

x





Re (ndash) up (ms)0207 0145 0072 0000

2500386 0270 0135 0000

5000577 0404 0202 0000





250 15 108 64 76500 64 131 54 82750 102 196 45 136

Qlo

ss (

)

0 25 50 75 100 125 150 17530

60

90

120

150

250500750

Re

tip (s)

(a)

250500750

Re

tip (s)

P inl

et (

)

0 25 50 75 100 125 150 175100

140

180

220

260

300

(b)













5 Final Remarks










150 150 284 43 147175 101 183 50 111200 79 161 52 94225 64 131 54 82250 53 131 57 77

ρpβ

up (ms)0379 0265 0133 0000

150

175

200

225



35

50

65

80

95

110

225250

150175200

ρpβ

Qlo

ss (

)

0 25 50 75 100 125 150 175 200tip (s)

(a)

0 25 50 75 100 125 150 175 200100

113

126

139

152

165

225250

150175200

ρpβ

P inl

et (

)

tip (s)

(b)




Data Availability




Acknowledgments


Qlo

ss (

)

40

60

80

100

120

040506

Dp (mm)

tip (s)0 20 40 60 80 100 120 140

(a)

040506

Dp (mm)

tip (s)

P inl

et (

)

0 20 40 60 80 100 120 140100

120

140

160

180

200

(b)


Dp (mm)

up (ms)0386 0270 0135 0000

04

05

06





04 77 111 59 11105 53 131 57 7706 44 169 48 77



References









































































Journal of












Journal of







Volume 2018






Volume 2018










Re (ndash) up (ms)0207 0145 0072 0000

2500386 0270 0135 0000

5000577 0404 0202 0000





250 15 108 64 76500 64 131 54 82750 102 196 45 136

Qlo

ss (

)

0 25 50 75 100 125 150 17530

60

90

120

150

250500750

Re

tip (s)

(a)

250500750

Re

tip (s)

P inl

et (

)

0 25 50 75 100 125 150 175100

140

180

220

260

300

(b)













5 Final Remarks










150 150 284 43 147175 101 183 50 111200 79 161 52 94225 64 131 54 82250 53 131 57 77

ρpβ

up (ms)0379 0265 0133 0000

150

175

200

225



35

50

65

80

95

110

225250

150175200

ρpβ

Qlo

ss (

)

0 25 50 75 100 125 150 175 200tip (s)

(a)

0 25 50 75 100 125 150 175 200100

113

126

139

152

165

225250

150175200

ρpβ

P inl

et (

)

tip (s)

(b)




Data Availability




Acknowledgments


Qlo

ss (

)

40

60

80

100

120

040506

Dp (mm)

tip (s)0 20 40 60 80 100 120 140

(a)

040506

Dp (mm)

tip (s)

P inl

et (

)

0 20 40 60 80 100 120 140100

120

140

160

180

200

(b)


Dp (mm)

up (ms)0386 0270 0135 0000

04

05

06





04 77 111 59 11105 53 131 57 7706 44 169 48 77



References









































































Journal of












Journal of







Volume 2018






Volume 2018


















5 Final Remarks










150 150 284 43 147175 101 183 50 111200 79 161 52 94225 64 131 54 82250 53 131 57 77

ρpβ

up (ms)0379 0265 0133 0000

150

175

200

225



35

50

65

80

95

110

225250

150175200

ρpβ

Qlo

ss (

)

0 25 50 75 100 125 150 175 200tip (s)

(a)

0 25 50 75 100 125 150 175 200100

113

126

139

152

165

225250

150175200

ρpβ

P inl

et (

)

tip (s)

(b)




Data Availability




Acknowledgments


Qlo

ss (

)

40

60

80

100

120

040506

Dp (mm)

tip (s)0 20 40 60 80 100 120 140

(a)

040506

Dp (mm)

tip (s)

P inl

et (

)

0 20 40 60 80 100 120 140100

120

140

160

180

200

(b)


Dp (mm)

up (ms)0386 0270 0135 0000

04

05

06





04 77 111 59 11105 53 131 57 7706 44 169 48 77



References









































































Journal of












Journal of







Volume 2018






Volume 2018












150 150 284 43 147175 101 183 50 111200 79 161 52 94225 64 131 54 82250 53 131 57 77

ρpβ

up (ms)0379 0265 0133 0000

150

175

200

225



35

50

65

80

95

110

225250

150175200

ρpβ

Qlo

ss (

)

0 25 50 75 100 125 150 175 200tip (s)

(a)

0 25 50 75 100 125 150 175 200100

113

126

139

152

165

225250

150175200

ρpβ

P inl

et (

)

tip (s)

(b)




Data Availability




Acknowledgments


Qlo

ss (

)

40

60

80

100

120

040506

Dp (mm)

tip (s)0 20 40 60 80 100 120 140

(a)

040506

Dp (mm)

tip (s)

P inl

et (

)

0 20 40 60 80 100 120 140100

120

140

160

180

200

(b)


Dp (mm)

up (ms)0386 0270 0135 0000

04

05

06





04 77 111 59 11105 53 131 57 7706 44 169 48 77



References









































































Journal of












Journal of







Volume 2018






Volume 2018









Data Availability




Acknowledgments


Qlo

ss (

)

40

60

80

100

120

040506

Dp (mm)

tip (s)0 20 40 60 80 100 120 140

(a)

040506

Dp (mm)

tip (s)

P inl

et (

)

0 20 40 60 80 100 120 140100

120

140

160

180

200

(b)


Dp (mm)

up (ms)0386 0270 0135 0000

04

05

06





04 77 111 59 11105 53 131 57 7706 44 169 48 77



References









































































Journal of












Journal of







Volume 2018






Volume 2018









References









































































Journal of












Journal of







Volume 2018






Volume 2018
















































Journal of












Journal of







Volume 2018






Volume 2018








numerical evaluation of cfd-dem coupling applied to lost...

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