02 SPE-134326-PA-P

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1/12472 December 2011 SPE Drilling & Completion

Numerical Simulations of Sand-ScreenPerformance in Standalone ApplicationsSomnath Mondal, SPE, and Mukul M. Sharma, SPE, University of Texas at Austin; and Rajesh A. Chanpura, SPE,

Mehmet Parlar, SPE, and Joseph A. Ayoub, SPE, Schlumberger

Copyright © 2011 Society of Petroleum Engineers

This paper (SPE 134326) was accepted for presentation at the SPE Annual TechnicalConference and Exhibition, Florence, Italy, 20–22 September 2010, and revised for

publication. Original manuscript received for review 5 October 2010. Revised manuscriptreceived for review 24 January 2011. Paper peer approved 15 February 2011.

Summary

The selection of optimum screens for standalone screen (SAS)applications has historically been based on experimental data, rulesof thumb, or correlations. Recent sand-retention tests conducted invarious laboratories offer empirical screen-selection criteria on thebasis of different sand-size-distribution parameters. Unfortunately,these experiments have their own limitations. They provide substan-tially different results, depending on how the tests are conducted andinterpreted, leading to significant differences in the recommendedscreen type and screen-opening size for any given sand sample.To resolve these inconsistencies and to understand the physics ofthe problem better, this paper presents 3D numerical simulationsto evaluate the performance of wire-wrapped sand screens andultimately to develop systematic screen-selection criteria.

In this paper, a new method is presented to estimate the massand size distribution of the solids produced through wire-wrapscreens. The method uses the entire particle size distribution ofthe formation sand and is validated with experimental and numeri-cal data. The new method allows us to evaluate the performanceof different screens without running expensive and sometimesinconclusive experiments, enhances our understanding of screenperformance, and helps to design sand screens better to meet per-formance criteria under a wide variety of conditions.

We first present results from 3D, discrete-element computersimulations of sand screens placed in contact with granular sand-packs of approximately 100,000 particles. The numerical modelcomputes the mass and the size distribution of the solids produced.The effect of the most important parameters, such as friction coef-ficient, fluid viscosity, pressure gradient, and ratio of screen-open-ing size to sand size, on the mechanism of bridge formation andamount of sand produced is studied using both monodispersed andpolydispersed systems.

The results have helped resolve some key questions aboutthe physics of sand bridge formation. Numerous simulations areconducted to replicate the experimental conditions over a widerange of screen-opening/sand-size ratios for wire-wrap screens.Good agreement is observed between laboratory experiments andthe simulations.

Introduction

Many deepwater sandstone reservoirs are weakly consolidated andrequire some form of sand control. Many of the producers in theseenvironments are completed openhole, and gravel packing is one of

the widely used techniques. However, SASs in open hole can alsoprovide highly reliable sand-control completions when applied in the“right environment” with the “right procedures.” Under these condi-tions, SASs result in lower cost with less operational complexity andcomparable productivity performance, compared to gravel packs.

Various criteria exist in the industry for screen sizing andselection for SASs. These are based on experimental data, rulesof thumb, or correlations developed through sand-retention experi-ments. However, there are considerable differences in the waythese experiments are conducted and in the way the data are

analyzed. There is no standard procedure to perform these sand-retention tests and to analyze the data. Accordingly, the screenrecommendations are also different from different test procedures.To address this issue and to understand the physics of the problembetter, a study was initiated using a numerical-simulation approachto evaluate the performance of sand screens and ultimately todevelop systematic screen-selection criteria.

Numerous 3D, discrete-element computer simulations havebeen conducted of sand screens placed in contact with granularsandpacks of approximately 100,000 particles. The numericalmodel computes the mass and the size distribution of the producedsolids and allows us to identify the key controlling parameters. Thisresults in better prediction capabilities.

The effect of the most important parameters on the amount of

sand produced was studied for both monodisperse (all particles havethe same size) and polydisperse (particles have a size distribution)systems using the simplest screen geometry: wire-wrap screens.Numerical simulations replicating the experimental conditions overa wide range of screen-opening/sand-size ratios were shown to pre-dict reasonably well the amount of sand production observed in thelaboratory tests. This process led to the development of simplifiedcorrelations relating total sand production and size distribution ofthe produced solids to the particle-size distribution (PSD) of forma-tion sand and the size of the screen slot openings.

In this paper, we• Critically review the state of the art in screen selection for

SAS applications• Detail the numerical-simulation approach and explain the

effect of different physical and model parameters

• Simulate idealized (monodispersed and polydispersed) sandsto understand the physics of bridge formation

• Simulate typical field sand samples retained by wire-wrapscreens

• Compare numerical and laboratory-test results and presentimportant new correlations for wire-wrap screens

• Present a new method for sand-screen selection and design

Past Work on Screen Selection for SAS Applications. Sizing ofsand-control media for oilfield applications has been the subject ofmany laboratory studies dating back to the early 1900s (Coberly1937; Suman et al. 1985; Markestad et al. 1996; Tiffin et al. 1998;Malbrel et al. 1999; Ballard et al. 1999; Underdown et al. 1999; Gil-lespie et al. 2000; Hodge et al. 2002; Ballard and Beare 2003; Con-stien and Skidmore 2006; Williams et al. 2006; Ballard and Beare2006; Mathisen et al. 2007; Underdown and Hopkins 2008).

Chanpura et al. (2010) provide a thorough review of the pastwork on screen selection for SAS applications. As can be seen fromtheir discussion, almost all the screen-sizing criteria that exist inthe literature for SASs are (a) based on a few points (e.g., d 10, d 50)of the PSD, (b) based on relative ranking of screen performances,or (c) have implicit assumptions on acceptable sand production.As proposed by Chanpura et al. (2010), an ideal screen-selectionmethodology should take into account the entire PSD of the forma-tion sand and be able to predict sand production (along with PSD ofthe produced solids) and retained screen (plus near-screen) perme-ability and also give users the choice to define an acceptable sand-production volume (along with size of the produced solids) andretained screen (plus near-screen) permeability. Then, for a given

screen type and size and given PSD and using the model results/ correlations and an acceptability criterion, the user can make an

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2/12December 2011 SPE Drilling & Completion 473

informed decision on screen/completion selection. An approachusing numerical simulations could be a viable method to achievethis. With this goal in mind, a study was initiated using numericalsimulations matching experimental data to understand and relatePSD/screen combinations and correlate sand production alongwith PSD of produced solids until sand production either stops orbecomes only fines production (the latter would be expected onlyin a bimodal PSD). As a first step, we initiated this study with thesimplest screen geometry (i.e., wire-wrap screens).

Model Formulation

We present simulations using the discrete-element method (DEM)

in three dimensions on systems of N monodispersed or polydis-persed, cohesionless, frictional spheres of fixed density . In theDEM, information about each particle (e.g., mass, velocity, force,angular momentum) lying within the computational domain (simu-lation box) is individually tracked in a Lagrangian frame (Cundalland Strack 1979). The Large-Scale Atomic/Molecular MassivelyParallel Simulator (LAMMPS) is a classical molecular-dynamics(MD) simulator, which, because of the physical and algorithmicanalogies between DEM and MD, offers a very fast and efficientgranular package for conducting DEM simulations (Kloss andGoniva 2010). LAMMPS is available as an open-source code(Plimpton 1995; Sandia National Laboratories 2010) and wasused for all the simulations. The goal was to simulate prepackexperiments by first generating a packing of polydisperse granularspheres over a wire-wrap-screen geometry and then flowing a fluidat a given pressure gradient through the pack. The mass of sandproduced per unit area of screen for various screen sizes and PSDswas computed.

The number of particles N in the system was varied fromapproximately 4,000 for monodispersed systems to approximately100,000 for polydispersed systems. The simulation box was a 3Dunit cell of 50d ×50d bounded by fixed granular walls in the x–yplane, where d is the diameter of a particle. In the z direction, thebox was bounded at the bottom by a wall with an open slot parallelto the y axis, representing the screen, and an open top. Initially, theslot was kept closed and a prepack of particles was generated beforeopening the slot and allowing particles to be produced through theslot. Two different methods were used to populate the box withparticles and generate the initial configuration of packed spheres.

The monodispersed packs with approximately 4,000 particleswere prepared by generating particles in a face-center cubic

lattice structure within the simulation box. The particles weresubsequently imparted at initial random velocity, allowed to settleunder gravity, and compacted by applying large body forces. Thismethod of particle-pack construction mimics sedimentation. Thepolydispersed systems with approximately 100,000 particles wereconstructed by arranging the particles within a region of the simu-lation box as randomly positioned nonoverlapping spheres andthen allowing them to settle under gravity, followed by compaction.This method of construction mimics the pouring of granular par-ticles within a box. The different methods of generating the initialconfiguration were chosen on the basis of their computational effi-ciency (i.e., the minimum time required to reach static equilibrium

for a certain simulation). The different particle sizes and numberof particles of each size were obtained from the measured PSDof the formation-sand sample used for the corresponding experi-ment. Fig. 1a shows the simulation box with approximately 10,000particles in it. The layer of blue particles at the bottom representsthe screen with the slot. The slot is closed by a layer of particlesto generate the initial prepack configuration.

The spherical particles interact only on contact through aspring/dashpot interaction law that models forces acting in thedirections normal and tangential to their lines of centers. Contact-ing Spheres i and j with Radius Ri and R j positioned at ri and r j experience a relative normal compression = |rij – d|, where rij =ri – r j and d = Ri+R j , which results in the force

F F Fij n t = + . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

The Hertzian contact model was used in this study where thenormal pushback force between two overlapping spheres is propor-tional to the area of overlap of the two particles and is, therefore,a nonlinear function of the overlap distance. The normal (Fn) andtangential (Ft ) contact forces are given by (Brilliantov et al. 1996;Silbert et al. 2001; Zhang and Makse 2005)

F n vni j

i j

n ij

i j

i j

n n

R R

R Rk

m m

m m=

+−

+

. . . . . . . . . . . . (2)

and

F s vt i j

i jt t

i j

i jt t

R R

R R k

m m

m m= + − − +

, . . . . . . . . . . . (3)

(a) (b)

y

x z

Fig. 1—(a) Simulation box with initial particle configuration. (b) Bridging of particles.

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where nij = rij /|rij |; vn and vt are the normal and tangential compo-nents of the surface relative velocity of the two particles, respec-tively, k n, k t and n,, t , are the elastic and viscoelastic dampingconstants for normal and tangential contact; respectively, and mi and m j are the mass of the contacting particles.st is the tangentialdisplacement vector that is obtained by integrating the surface rela-tive velocities during the elastic deformation of the contact. Themagnitude of st is truncated as necessary to satisfy a local fric-tional yield criterion, |Ft |≤ |Fn |, where is the particle/particlefriction coefficient. Particle/wall interactions are treated similarly,with the wall behaving as a particle with infinite radius and mass.Though LAMMPS does not have an explicit fluid component, thepresence of a viscous fluid was modeled implicitly by applying aviscous drag force on each particle. The viscous drag force ( Fv)is given by

F vv i id = 3 , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)

where is the dynamic viscosity of the fluid and d i and vi are thediameter and the velocity of the particle, respectively. The normalforce on each particle caused by the pressure gradient (P) of thefluid was modeled as a body force (Fb) given by

Fb iP

zd =

∆∆

4

3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5)

All physical quantities in the simulation were used in dimen-sionless units by normalizing with the following: length ≈ d , time ≈

d g / , velocity ≈ dg , force ≈ mg, stress ≈ mg d 2, where d forthe monodispersed cases was 100 µm and g is the accelerationbecause of gravity. The polydispersed cases were normalized usingdiameter d and mass m of the smallest particle in the simulationbox, which depends on the PSD of the formation sand used in theexperiment. The simulations were run with density of the particles = 2650 kg/m3. In general, according to Hertz’ theory, normalizedstiffness constants depend on the elastic moduli and diameter of theparticles, and for quartz grains, k n and k t are ≈ 1010 mg/d2 (Johnson1985; Zhang and Makse 2005). However, granular simulationsreported in the literature suggest that the results are not particularlysensitive to the values of k n and k t as long as they are close to thek n→ ∞ limit of small deformations (Erta et. al. 2001). In addition,the results are not sensitive to the particular values of n,t or thek k

t nratio as long as they are not too different (Silbert et. al. 2001;

Schäfer et. al. 1996). Therefore, all simulations were run with both

k n and k t ≈ 1010 mg/d2 and n = t = 50 g d 3 .

The simulations were performed using the Texas AdvancedComputing Center (TACC) High-Performance Computing (HPC)resource. The polydispersed simulations (approximately 100,000particles) took approximately 24 hours to run on 48 processors ofa Dell Linux cluster. This is equivalent to approximately 48 days ofcentral-processing-unit (CPU) time or computer time on a desktop

computer with a single processor. Fig. 1b shows the bridging ofparticles near the end of a polydispersed simulation.

Results and Discussion

Effect of Model Physics. The effect of various model parameterson the cumulative number of particles produced before formationof sand bridges was studied using simulations of approximately4,000 monodispersed particles with 100-µm diameter. The slotwidth for the simulations was 200 µm. The pressure gradient ofthe flow was assumed to be 2,200 psi/ft, the viscosity of the fluid

was taken as 1 cp, and the particle/particle or particle/wall frictioncoefficient was assumed to be 0.5. These are the default parametersunless otherwise stated. The most important factors that influencethe simulation results have been summarized in this section.

Shear Forces and Bridge Formation. Fig. 2 shows the bridgingof sand particles over a slot opening indicated by the cumulativenumber of particles produced reaching a plateau (Case 1, bluecurve). Fig. 2 also demonstrates the necessity of shear forces inbridging of particles. Shear forces were turned off for Case 2 (redcurve), the no-bridging case, by assigning k t = 0 and t = 0 in thesimulations. It is clear from these results that if no frictional forcesexist between sand grains, no bridging occurs.

Stiffness Constant. The effect of the stiffness constant (k n) wasstudied with respect to the bridging behavior of particles. Fig. 3shows that the results are insensitive for k n ≥ 2×107 mg/d

2, in agree-

ment with Ertaş et al. (2001). Angular Momentum. In general, for granular simulations

with spherical particles, rotational motion of individual particlesis allowed and angular momentum is also tracked in a Lagrang-ian frame (along with position and velocity, the angular velocityof particles is updated at each timestep). We found that simula-tions that allowed rotational motion of particles showed muchhigher sand production than experiments. In reality, sand grainsare severely aspherical in shape and bridging of sand grains overscreens may be largely attributed to interlocking of grains. BecauseDEM models cannot handle aspherical particles for granular simu-lations, one way to incorporate asphericity is to prevent particlesfrom freely rolling over each other. Therefore, for all simulations,angular velocity of particles was constrained and not updated ateach timestep.

Box Geometry. The real screen geometry consists of slot open-ings of various sizes typically separated by wires 2000–3000 µmwide. An identical simulation box representation of this geometrywould require periodic walls at a distance of 1000–1500 µm fromthe slot opening on each side. For polydispersed cases, in the nor-malized LAMMPS units, this would result in a large simulation box(approximately 200d ×200d for some cases) and would require avery large number of particles to populate and create the initial con-figuration. Hence, fixed granular walls were selected over periodicones. Because particle/wall interactions are modeled in the sameway as to particle/particle interactions, fixed granular walls areanalogous to static blocks of particles. It was also observed thatfixed walls at a distance greater than approximately 15 d from theslot had little or no effect on the number of particles produced,

which implied that bridging was affected only by the arrange-ment of particles close to the opening. Therefore, the simulation

10

100

1,000

0.01 0.1 1 10

C u m u l a t i v e N u m b e r o f

P a r t i c l e s P r o d u c e d

Dimensionless Time

k t =1010 mg/d2,

γ t =50 √(g/d3 )

k t =0,

γ t =0

Fig. 2—Bridging of particles and effect of shear forces.

10

100

1,000

0.01 0.1 1 10



Dimensionless Time

k n =2×105

k n =2×106

k n =2×107

k n =2×108

k n =2×109

Fig. 3—Effect of stiffness constant.

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box geometry was chosen to be a cuboid with a base of 50d ×50d bounded by fixed granular walls in the x – y plane.

Friction Coefficient. As mentioned earlier, shear forces arenecessary to form bridges, and the magnitude of shear forces act-ing on the particles is determined by the friction coefficient. Fig. 4shows the effect of friction coefficient and, as may be expected,shows that the cumulative number of particles produced decreaseswith an increasing friction coefficient. No bridge formation was

observed below a friction factor of 0.3. A friction factor of 0.5,standard for granular simulations (Silbert et al. 2002a; Landryet al. 2004), was chosen for further simulations.

Initial Particle Configuration. Dissimilar packing arrange-ments were formed using different random seeds for the initialvelocity assigned to the particles. In the Hertz contact model,tangential forces are a function of the loading history of thecontact. Therefore, there is variability in the cumulative numberof particles produced for different packings, as shown by Fig. 5. The error bars show one standard deviation from the mean num-ber of particles produced for five different packings. Simulationsof frictional sphere packings by Silbert et al. (2002b) also showthat static granular packings do not have a unique force networkdetermined by the packing or the loadings on particles but that the

force network is a function of the construction history. However,the variability seen in repeat runs (with different initial particlepackings) is small relative to the effect of slot width, the variableparameter in the experiments. For all simulation results shown inthis study, error bars are shown that reflect this variability (± onestandard deviation from the mean).

Results for Monodispersed Particles. After the various questionsabout the model physics were resolved, several simulations wereconducted on monodispersed packings to understand differentaspects of the model and to study the effect of key operational orgeometric parameters.

Pressure Gradient. Fig. 6 shows the cumulative number of par-ticles produced for a wide range of pressure gradients. At low pres-sure gradients (< 100 psi/ft), an increasing trend can be observed,while there is no clear dependence at high pressure gradients. Theresults were generated for five different packing arrangements.

Fluid Viscosity. The effect of the fluid viscosity on the cumu-lative number of particles produced was studied using monodis-persed particles. Fig. 7 shows that a larger number of particles

was produced at low viscosities. This is because, at higher vis-cosities, particles have lower kinetic energy and lower velocities.It can be argued intuitively that this favors the formation of stablebridges. However, polydispersed simulations with a fluid viscos-ity of approximately 500 cp (the viscosity of the fluid used in theexperiments) were extremely slow because, with low velocities, itrequired significantly longer simulation time to produce enoughparticles before bridging occurred. It also can be observed fromFig. 7 that there is not a significant difference in the number ofparticles produced at viscosities greater than 10 cp. Hence, poly-dispersed simulations were conducted with fluid viscosities of10 cp to reduce computation times significantly while not affectingthe number of particles produced to a great extent.

Slot-Width/Particle-Diameter Ratio. Finally, the slot width was

varied while keeping the particle diameters constant, as shownin Fig. 8. This is the most important factor affecting the numberof particles produced, and no bridging was observed for slot-width/particle-diameter ratios greater than three, as also noted byMcCormack (1988).

Effect of PSD. To facilitate our understanding of the effect of PSDon the mass of sand produced per unit area of screen, we conductedsimulations using synthetic PSDs, as shown in Fig. 9a. The d 50 forall the assumed distributions was kept constant at 100 µm whileincreasing the uniformity coefficient (UC = d 40 / d 90). The slot widthand all other parameters were also kept constant. For these linear

0

5

10

15

20

25

30

0111.0



Dimensionless Time

Fig. 5—Effect of initial particle configuration.

(a) (b)

0

20

40

60

80

0 50 100 150



Pressure Gradient, psi/ft

0

20

40

60

80

100

0 5,000 10,000 15,000 20,000

C u m u l a t i v e

N u m b e r o f


Pressure Gradient, psi/ft

Fig. 6—Effect of pressure gradient at (a) low gradients and (b) high gradients.

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1



Friction Coefficient

Fig. 4—Effect of friction coefficient.

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PSDs, Fig. 10 shows that the mass of sand produced goes through amaximum as UC is increased. The reason for this maximum can beinferred from Fig. 9b, which shows that fines production increaseswith increasing UC (i.e., the size and mass of the particles in thesample are decreasing but a larger number of particles is beingproduced). It is because of this opposing effect that the total massof sand produced goes through a maximum at UC ≈ 4 for the linearPSD shown in Fig. 9a. At lower values of UC , the mass of sand pro-duced increases with UC because the number of (relatively large)particles produced increases. At higher values of UC , the mass ofsand produced decreases with UC , as the decreasing mass of theproduced sand particles becomes the dominating factor. However,this behavior of produced mass vs. UC needs to be verified withmore-realistic PSDs before drawing further conclusions.

The effect of initial particle configurations for polydispersedcases was also studied using these PSDs. The variability observedin the mass of sand produced was < 10%. This is because, thoughthere is variation in the amount of particles produced of each size,overall these variations cancel each other out and the total mass ofsand produced is affected less.

Comparison With Experiments. Thirty prepack tests on wire-wrap screens from 6 to16 gauge reported by Chanpura et al. (2010)were simulated using the model described. The test setup and theexperimental procedure used by these investigators were the sameas that described by Constien and Skidmore (2006). In the experi-ments, a Newtonian test oil of approximately 500-cp viscosity wasflowed through a prepack of formation sand over wire-wrap screen

0

20

40

60

80

100

0.01 0.1 1 10 100 1000



Viscosity, cp

Fig. 7—Effect of fluid viscosity.

0

20

40

60

80

100

120

140

1 1.5 2 2.5 3 3.5



Slot Width/Particle Diameter

Fig. 8—Effect of slot-width/grain-size ratio (w /d ).

(a)

(b)

0

20

40

60

80

100

0 50 100 150 200

% C o a r s e

r b y W e i g h t

Grain Size, µm

UC=1

UC=1.1867

UC=1.5121

UC=2.5314

UC=6

UC=8.8415

UC=12.25

1

10

1×102

1×103

1×104

1×105

0 50 100 150 200 C u m u l a t i v e N u m b e r o f P r o d u c e d

P a r t i c l e s

Grain Size, µm

UC=1

UC=1.1867

UC=1.5121

UC=2.5314

UC=6

UC=8.8415

UC=12.25

Fines

Fig. 9—(a) PSD of formation sand. (b) PSD of produced sand.

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at a pressure gradient of 4,800 psi/ft. Effluent samples with theproduced solids were collected at regular intervals, and mass ofthe formation sand produced per unit screen area was measured.Our numerical simulations replicate this procedure as closely aspossible and simulate particle production through screens at thegrain scale.

The experimental PSDs by weight were divided into 7–8 binsand were converted into PSDs by number in order to generate theinitial packing. The simulations were conducted as described ear-lier. The size distribution of the produced particle can be calculatedby simply counting the number of produced particles of each sizeand converting it into a mass-based distribution. Fig. 11 summa-rizes the simulation results and shows an overall comparison withthe experimental results. We saw evidence of bridge formationin most cases except those where d 10 of formation sand was lessthan the slot-opening width (i.e., d 10 < w). These cases showedcontinued sand production at the end of the experiments as wellas the simulations. Thus, the mass of sand produced reported inthese cases is not final and would increase if these experimentswere continued further. This was observed in the simulations, too,

because there was no sand retention by either bridging or sizeexclusion (single particle blocking the screen opening). Therefore,the approximately 100,000 particles used for the simulations wasnot enough and, with a larger number of particles and longerrun time, the mass of sand produced from the simulations wouldincrease as well. However, because of computational constraints,the simulations were not performed with greater than approxi-mately 100,000 particles. Because these cases do not represent

a fixed mass of sand produced, we have excluded them from thecorrelations developed in this paper.

Figs. 12a and 12b present two conventional plots used toascertain screen performance. Though the simulations follow thesame trend as seen in the experiments, there is no strong correla-tion observed in either the experimental data or the simulation

results.

Simplified Correlations. We looked at various dimensionlessgroups for the x axis. However, no strong correlation was observedfor any x-axis group. Only imprecise criteria for whether to adoptsand control could be suggested [e.g., d 10 / w ≤ 1, (d 50 / UC )/ w < 0.1].Most conventional methods used to predict screen performanceattempt to correlate a dimensional y axis (which is a function ofthe absolute particle diameter) to a dimensionless x axis (which isa function of the relative particle diameter). In our opinion, suchinconsistent axes accentuate the scatter, as shown in Fig. 12. There-fore, we propose a dimensionless y axis M D , defined as

M MA

D UC

D=

3 , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (6)

where M D is the dimensionless mass, M is the experimentally ornumerically determined mass of sand produced per unit area, A isunit area, is density, D is a representative diameter (d 10 or d 50), and UC is the uniformity coefficient of the formation sand. Figs. 13aand 13b show the plots of M D vs. d 10UC/w and d 50UC/w, respec-tively. The agreement of the numerical results with the experiments

11.1867

1.5121

2.5314

6

8.8415

12.25

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 2 4 6 8 10 12 14

M a

s s o f S a n d P r o d u c e d , k g / m 2

UC

Fig. 10—Effect of PSD.

0.01

0.1

1

10

0.01 0.1 1 10

S i m u l a t i o n M a s s o f S a n d P r o

d u c e d , k g / m 2

Experimental Mass of Sand Produced, kg/m2

Fig. 11—Comparison of simulation vs. experimental mass of sand produced.

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is also demonstrated. It should be noted that M D should always becalculated with the D that has been used for the x axis. Thus, fromthe fit lines, simple correlations for mass of sand produced may bewritten in dimensionless form as

M A d UC

w

D

b

10 110

1

= ( )−

. . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)

and

M A d UC w D

b

50 350

3

= ( )−

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . (8)

Hereafter, all correlations have been specified in the generalform y = An x

bn, where An and bn are the respective constants inthe correlations.

As can be seen from the plots, better correlations and more-obvious trends (for both the experimental data and the simulationresults based on 23 experimental data sets) are obtained when bothaxes are made dimensionless, as proposed here. It is expected thatthis simple new correlation can be used to assist in screen selectionand design for a given sand size distribution under a variety ofconditions.

The M-S Method. Even though making both axes dimensionless inFig. 13 helped to improve the correlation, it does not provide the PSDof produced solids and is still based on only three points from theentire formation PSD (a representative diameter, d 10 or d 50, and the uni-formity coefficient, UC , which is defined in terms of d 40 and d 90). Thenew method proposed in the following uses the entire formation PSDto determine the mass of sand produced and its PSD. The backbone

of this method is a correlation between the numbers of particles ofdiameter DP produced through a screen of slot opening w (Eq. 9):

N A D

w p p

b

= ( )−

5

5

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (9)

From every simulation, the number of particles of each sizethat were produced through the screen was counted and plottedagainst DP /w. A schematic of the procedure has been illustratedin Fig. 14. The formation-sand size distributions were binned into7–8 sizes to generate the number-based size distributions used inthe simulations. Let us assume that we have two formation-sandPSDs, A (blue) and B (red) (Fig. 14), and we divided them intofive bins (for simplicity) as shown by the dark horizontal lines. Thedashed lines in respective colors represent the particle diameters(e.g., D1 A – D5 A for PSD A) from each bin that was used to populatethe simulation box. The number of produced particles for D1 A (if D1 A

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% C u m u l a t i v e b y W e i g h t

100

80

60

40

20

0

Diameter, microns

PSD A

PSD B

1000 100 10 1D 5A

D 2A

D 3A

D 4A

D 1A

Fig. 14—Schematic to illustrate the effect of formation sand size distribution on the number and distribution of produced solids.

11.010.0

N u m b e r o f P a r t i c l e s P r o d u c e d / m 2

f o r 1 0 % O

F A

D p /w

1×1010

1×1011

1×1012

1×

106

1×107

1×108

1×109

y =A5x–b 5

R ²=0.8998

Fig. 15—Number of particles produced vs. particle-/slot-size ratio (from simulations).

11.010.0100.0

N u m b e r o f P a r t i c l e s P r o d u

c e d , N P

D P /w

1×103

1×104

1×105

1×106

1×107

1×108

1×109

y =A6 x–b 6

R ²=0.9531

10

1

1×102

Fig. 16—Number of particles produced vs. particle-/slot-size ratio (from experiments).

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configurations are much less important compared to the ratio ofparticle diameter to slot width. It should be noted that the producedPSDs used to generate Fig. 16 were measured during the initialphase of the experiments and not throughout the tests. However,the strong dependence on size ratio is unmistakable.

The correlations obtained in Figs. 15 and 16 do not imply thatthe number of particles produced (of a particular size) dependsonly on the ratio of the particle size to the slot width. In fact, thenumber of particles produced depends both on the DP /w ratio andon the number of particles of that size present in the original sand(i.e., on the entire PSD of the original sand). For example, it canbe seen from Fig. 15 that d 10 of Formation Sand B is the samesize as d 90 of Formation Sand A. Because we have divided bothformation PSDs into nearly equal sized bins (approximately 20%)by mass, it means that d 10 of Formation Sand B represents 20%of Formation B by mass or 20% by volume (because density is

constant and assuming a constant porosity in the initial pack). Onthe other hand, d 90 of Formation Sand A also constitutes 20% bymass and volume. The probability of any particle lying inside thesimulation box (or any unit volume for that matter) of seeing theslot is the volume fraction occupied by that particle in the box.Because d 10 of Formation Sand B and d 90 of Formation Sand Aoccupy the same volume fraction in the box, their probability ofseeing the slot is the same. Hence, the fact that one diameter is d 10 and the other is d 90 does not make a difference.

The M-S method calculates the mass of sand produced byusing this correlation (Eq. 9) and the available size distributions offormation particles (for example, one could use d 5, d 10, d 25, d 40, d 50,d

60, d 75, d 90, and d 95). The method is independent of the bins chosen.The algorithm for the M-S method is presented here.

Step 1: Calculate the number of produced particles per square

meter of screen with 10% OFA ( NPi) of size d i as

If then , elsd

w NP p A d

wi

i ii

b

≤ = × ( )

−

1 55

, ee NPi= 0, . . . (10)

where pi is the bin size for d i (i.e., p5 = 0.075, p10 = 0.1, p25 = 0.15, p40 = 0.125, p50 = 0.1, p60 = 0.125, p75 = 0.15, p90 = 0.1, and p95 =0.075).

Step 2: Calculate the normalized mass of sand produced ford i-sized particles with respect to the mass of one particle of size,d

50, ( M D50,i) as follows. The screen has x % OFA.

M

d

d NP

x

D i

i

i5050

3

10,%

%=

×

OFA

OFA. . . . . . . . . . . . . . . . . . . (11)

Step 3: Repeat Steps 1 and 2 for i = 5, 10, 25, 40, 50, 60, 75,90, and 95. The total normalized mass of sand produced ( M D50)is given by

M M D D i50 50= ( )∑ , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (12)

The mass fraction of produced solids with size d i is

f M

M i

D i

D

= 5050

, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (13)

f i could then be used to calculate size distribution of the producedparticles.

Fig. 17 shows the plot of dimensionless mass of sand pro-duced obtained from the experiments ( M D50) vs. M D50 calculatedusing only the correlation as outlined in Steps 1 through 3. Thedimensionless mass of sand produced M D50 is defined as before butwithout UC (but with the /6 term to account for the volume of aspherical particle of size d 50), as follows:

M MA

d D50

50

3

6

=

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (14)

Step 4: Using the correlation in Fig. 17, the dimensionlessmass of sand produced calculated from Eq. 12 is revised to obtainRev M D50 as

Rev M A M D Db

50 7 50

7= ( ) , . . . . . . . . . . . . . . . . . . . . . . . . . . . (15)

from which the mass of sand produced in kg/m2 ( M ) can beobtained as

M

M d

A

D

=×Rev 50 50

3

6

, . . . . . . . . . . . . . . . . . . . . . . . . . . (16)

where is 2650 kg/m3, A is 1 m2, and d 50 is in meters.Please note that d 10 may also be used as the representative

diameter in Step 2 to obtain the equivalent number of (d 10-sized)particles produced. However, in that case, d 50 in Eqs. 11 through16 should be replaced by d 10.

Figs. 18 and 19 show the comparison of the dimensionlessmass ( M D50) and the dimensional mass ( M ) of sand produced

M D 5 0 - E x p e r i m e n t

M D 50 - Correlation

y =A7 x–b 7

R ²=0.72098

1×105

1×105

1×106

1×106

1×107

1×107

1×108

1×108

1×109

1×109

Fig. 17—Correlation to calculate dimensionless mass of sand produced.

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M D 5 0 - E x p e r i m e n t

RevM D 50 - Correlation

1×105

1×105

1×106

1×106

1×107

1×107

1×108

1×108

1×109

1×109

Fig. 18—Comparison of dimensionless mass of sand produced from correlation with experimental data.

Fig. 19—Comparison of mass of sand produced from correlation with experimental data.

0.01

0.1

1

10

0111.010.0

M a s s - E x p e r i m e n t , k g / m 2

Mass - Correlation, kg/m2

calculated using the M-S method with the experimental data,respectively.

Conclusions

A new method (the M-S method) is presented to estimate boththe mass and size distribution of the produced solids for wirewrapscreens using the entire PSD of the formation sand. On the basis ofcomparisons with experiments, this method is found to provide much-more-accurate predictions of screen performance compared with pastmethods that are based on d 10, d 50, or UC and can be used for system-atic screen-size selection in the absence of experimental data.

We have presented a numerical-simulation tool to evaluate theperformance of wire-wrapped sand screens. The simulations canbe used to estimate the mass of the sand produced and the PSDof the produced sand. The effects of various parameters in themodel have been tested and validated systematically to provide an

accurate representation of the physics of the problem. The mostimportant findings from the model are• As expected, friction and shear forces are necessary to form stable

bridges, whereas the slot-width/particle-diameter ratio is the mostcritical parameter affecting the number of particles produced.

• High fluid viscosities and lower pressure gradients facilitatebridging of particles. The number of particles produced increases

with the fluid pressure gradient at typical field values (< 100psi/ft), but, at higher fluid pressure gradients corresponding to

many of the experiments reported in the literature, there is noclear dependence.The numerical results have been compared with experimental

results. After normalization to the dimensionless parameter M D , good quantitative agreement and very consistent trends wereobserved in both the experiments and the model results whendisplayed logarithmically. Two simple correlations are presentedto predict the dimensionless mass ( M D) of sand produced, using arepresentative diameter (d 10 or d 50) and UC . These correlations areshown to be approximate because they rely on only two parametersin the sand size distribution (d 10 or d 50 and the UC ).

Nomenclature

A = area, L2, m2

An, bn = constant coefficients in correlations d = diameter, L, m [m]

d i = diameter of Particle i, diameter of particle representingi percentile by mass, L, m [m]

DP = particle diameter, L, m [m]

D1 A – D5 A = particle diameters representing bins, L, m [m]

f i = mass fraction of produced solids with size d i

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Fb = normal body force vector from pressure gradient,mL/t2, N

Fn = normal contact force vector, mL/t2, N

Ft = tangential contact force vector, mL/t2, N

Fv = viscous drag force vector, mL/t2, N

g = acceleration because of gravity, L/t2, m/s2

k n = elastic constant for normal contact, m/Lt2, Pa

k t = elastic constant for tangential contact, m/Lt2, Pa

m = mass, m, kg

mi, m j = mass of Contacting Particles i and j, m, kg

M = mass produced per unit area, m/L2, kg/m2

M D = dimensionless mass of sand produced M D10 = dimensionless mass of sand produced with respect to d 10 M D50 = dimensionless mass of sand produced with respect to d 50 nij = unit vector joining the centers of Particles i and j

N = number of particles in simulation box

N P = number of particles produced

NP D = equivalent number of particles produced

p = bin size

P = pressure, m/Lt2, Pa [psi]

ri, r j = position vector of Contacting Particles i and j, L, m

rij = position vector joining the centers of Particles i and j,L, m

Rev M D50 = revised M D50

Ri, R j = radius of Contacting Particles i and j, L, m UC = uniformity coefficient

vi = velocity vector of Particle i, L/t, m/s

vn = normal velocity vector, L/t, m/s

vt = tangential velocity vector, L/t, m/s

w = slot opening, L, m [m]

x = screen OFA

n = viscoelastic damping constant for normal contact, 1/Lt,1/ms

t = viscoelastic damping constant for tangential contact,1/Lt, 1/ms

= relative normal compression, L, m

P/ z = pressure gradient, m/t2, Pa/m [psi/ft]

st

= tangential displacement vector, L, m

= dynamic viscosity, m/Lt, Pa·s [cp]

= friction coefficient

= density, m/L3, kg/m3

Acknowledgment

The authors wish to acknowledge the financial support providedby Schlumberger and Schlumberger Sand Control Client AdvisoryBoard members, BG-Group, BP, Chevron, ConocoPhillips, Statoil,and Total, that made this work possible. We would also like tothank the TACC at The University of Texas at Austin for providingHPC resources for the research.

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Somnath Mondal is a PhD candidate in the Department ofPetroleum and Geosystems Engineering at The University ofTexas at Austin. His current research is focused on particulate

flow modeling and the numerical simulation of sand-retentiontests to develop better screen-selection guidelines. Mondalholds a bachelor of engineering degree in chemical engi-neering from Birla Institute of Technology and Science, Pilani,India, and an MS degree in petroleum engineering from TheUniversity of Texas at Austin. Mukul M. Sharma is a profes-sor and holds the “Tex” Moncrief Chair in the Department ofPetroleum and Geosystems Engineering at The University ofTexas at Austin, where he has been for the past 23 years. Heserved as chairman of the department from 2001 to 2005. Hiscurrent research interests include improved oil recovery, injec-tion-water management, hydraulic fracturing, formation dam-age, and petrophysics. He has published more than 200 journalarticles and conference proceedings and holds nine patents.Sharma holds a bachelor of technology degree in chemicalengineering from the Indian Institute of Technology and MS

and PhD degrees in chemical and petroleum engineering from

the University of Southern California. Among his many awards,Sharma is the recipient of the 2009 Lucas Gold Medal, the2004 SPE Faculty Distinguished Achievement Award, the 2002Lester C. Uren Award, and the 1998 SPE Formation EvaluationAward. He served as an SPE Distinguished Lecturer in 2002, hasserved on the Editorial Boards of many journals, and taughtand consulted for the industry worldwide. Rajesh A. Chanpura is a product-development engineer with Schlumberger basedin Houston. He has been with Schlumberger for 10 years. Inhis current position, Chanpura is working on developing anin-house methodology and software product for comple-tion and screen selection for openhole completions. In hisprevious position with Schlumberger, he was involved in the

development of Schlumberger’s gravel-packing simulator(SandCADE). Chanpura holds an undergraduate degree inconstruction engineering from The University of Mumbai (1993),a master’s degree in civil engineering from the Indian Instituteof Technology, Mumbai, and a PhD degree in civil engineeringfrom the Georgia Institute of Technology. Mehmet Parlar is atechnical advisor at Schlumberger, based in Rosharon, Texas,USA. He holds a BS degree from Istanbul Technical Universityand MS and PhD degrees from the University of SouthernCalifornia, all in petroleum engineering. He has 22 years ofindustry experience, with 7 years in product developmentand the remainder in sand control. He authored more than50 papers and holds 19 US patents. He was a distinguishedauthor in 2000, elected a distinguished member in 2007, a dis-tinguished lecturer in 2007–08, and served in various organiz-ing committees for SPE ATWs, forums, and conferences. Joseph

Ayoub is the reservoir and production and completion engi-neering domain career leader for Schlumberger. Before that,he held many engineering and operations posts in the US,Europe, Africa, and the Middle East. Ayoub has taught numer-ous industry seminars and published more 30 papers, mainlyin the areas of well testing, hydraulic fracturing, and frac andpack. His involvement was instrumental for introducing thepressure derivative method in the early 1980s and for launch-ing the frac and pack technique in the Gulf of Mexico in theearly 1990s. More recently, Ayoub led the formation of industryconsortiums to investigate many technical challenges in theareas of stimulation and sand control. He holds an engineer-ing degree and a DEA (master’s) from the Ecole Centrale deParis. He was named a Schlumberger Advisor in 1999 and anSPE Distinguished Member in 2005. Ayoub served on numer-ous SPE committees, including as chairman, and served as SPE

Distinguished Lecturer in 1998–99 and in 2009–010.

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