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Particle-Size-Distribution MeasurementTechniques and Their Relevance or

Irrelevance to Wire-Wrap-Standalone-Screen Selection for Gradual-Formation-

Failure ConditionsKe Zhang,Rice University;Rajesh A. Chanpura,Schlumberger;Somnath Mondal1, Chu-Hsiang Wu,and

Mukul M. Sharma,University of Texas at Austin; and Joseph A. AyoubandMehmet Parlar,Schlumberger

Summary

Sand-particle-size distributions (PSDs) are used for various pur-poses in sand control: for example, decision making between vari-ous sand-control techniques and sizing of the filter media (sandscreens and/or gravel packs) through either rule of thumb or phys-ical experiments or theoretical models. PSDs of formation-sandsamples are also often used to generate simulated formation

sand for laboratory experiments. The two most commonly usedtechniques for PSD measurements are sieve and laser. Althoughsome engineers use one technique for no obvious or justifiablereasons, others use both techniques for measurements and do notknow what to do with the data when significant differences existin PSDs obtained from each technique. Although the inherent lim-itations of (and the differences between), these two techniques aswell as other factors affecting the measurements are well-known,a systematic study as to which of these two techniques is relevantto sand-control-screen selection and why is lacking.

In this study, we critically review the current practices in PSDdetermination and the use (and misuse) of the informationobtained from these measurements, propose a methodology to-ward determining what is relevant under gradual-formation-fail-

ure conditions for wire-wrap screen, discuss when it should beused and why, and present initial experimental results that supportour conclusions.

Introduction

Particle-size distribution (PSD) of formation sand for reservoirsrequiring sand control is the sole information used when applyingrules of thumb for sand-control-technique selection (Tiffin et al.1998; Price-Smith et al. 2003), screen-size selection for stand-alone-screen (SAS) application (Coberly 1937), and gravel-sizeselection for gravel-pack application (Saucier 1974). Chanpuraet al. (2012, 2013a) and Mondal et al. (2011, 2012) also use PSDof formation sand (and a specified acceptable sand production) forsizing screens for SASs on the basis of numerical and/or analytical

models. Such models can result in accurate estimates of sand pro-duction in laboratory sand-retention tests (SRTs), provided thatboth the screen and the sand PSD are well-characterized. There-fore, the importance of an accurate determination of PSD of theformation sand is evident. Any inaccuracy in determining PSDcould result in improper sand-control-technique selection and/orscreen-/gravel-size selection. Even in cases when SRTs are usedfor screen sizing for SASs, unless the test is performed with theactual formation sand, inaccurate reporting of PSD could result in

testing simulated sand that is not representative of the original for-mation sand, thus leading to incorrect screen-size selection.

Dry-sieve analysis and laser-particle-size analysis are the twotechniques that are most commonly used for determining PSD offormation sand. However, it is well-known that there are differen-ces in PSDs reported from these two techniques (Ballard et al.1999; Ballard and Beare 2003; Slayter et al. 2008). In this study,

we critically review the possible causes for the differences inPSDs reported from these two techniques and recommend whichtechnique is suitable to use under which conditions.

Techniques for Particle-Size-Distribution (PSD)

Determination

As mentioned earlier in the study, dry-sieve analysis and laserparticle-size analysis (LPSA) are currently the two types of parti-cle-sizing techniques that are commonly used in the industry. Weprovide a brief description of these techniques, followed by acomparison that highlights the advantages and limitations.

Dry-Sieve Analysis. In a dry-sieve analysis, PSD of sand is

determined by mechanical separation of particles. Sand particlesare first separated into individual grains and then cleaned, dried,and weighed. They are then passed through a stack of sieves in ashaker, with the coarsest sieve at the top and finest sieve at thebottom. Typically, the smallest sieve that is used in the dry sieveis 400 US mesh (37 lm). Sand particles that pass through thesmallest sieve are collected in a pan. From the measured weightof the sand retained in each individual sieve, cumulative weightpercent retained by each sieve size is calculated and plottedagainst sieve size on a semilogarithmic scale. Dry-sieve analysiswas performed as per ISO 13503-2 (2006) in this work.

LPSA. LPSA determines PSD of sand electronically by meas-uring the intensity of light scattered as a laser beam passesthrough a dispersed-particulate sample. The angle of scatter of thelaser light is inversely proportional to the particle size. The angu-lar intensity of light scattered is captured by a series of photosen-sitive detectors. The data are then processed and analyzed throughthe instrument software to calculate the particle sizes.

In LPSA, sample dispersion is controlled by a range of wet- ordry-dispersion units, which ensure that the particles are deliveredto the measurement area or the optical bench at the correct con-centration and in a stable state. A dry-dispersion unit is ideallysuited for measurement of powders, especially moisture-sensitivematerials. Wet-sample dispersion units use a liquid dispersant, ei-ther aqueous or solvent-based, to disperse the sample. The liquiddispersant chosen has to be able to hold the sample in suspensionthrough stirring. Any settling or floating of the particles will intro-duce errors in the laser-diffraction measurement. To keep the

sample suspended and homogenized, it is recirculated continu-ously through the measurement zone. A wet-dispersion unit with

CopyrightVC 2015 Society of Petroleum Engineers

This paper (SPE 168152) was accepted for presentation at the SPE InternationalSymposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, USA, 2628February 2014, and revised for publication. Original manuscript received for review 22 March2014. Revised manuscript received for review 6 January 2015. Paper peer approved 31March 2015.

1now with Shell

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deionized water was used for LPSA in this study because samplesconsisted of sand particles that were insoluble in water.

Possible Causes for the Differences in PSDs From Dry-Sieve

Analysis and LPSA. The main difference between the dry-sieveanalysis and LPSA methods is in the way particle sizes are esti-mated by these techniques. The sieve measures the second-small-est dimension because of the way the particles orient themselvesto pass through the opening given sufficient time. As opposed tothe smallest dimension, a sieve emphasizes the second-smallest

dimension because if the slot opening is the same size as the par-ticles smallest dimension, the particle cannot pass through in thedirection of its second-smallest dimension. A light-scattering de-vice, such as a laser, measures various dimensions as the particlesflow randomly through the light beam. It then calculates theequivalent diameter of a sphere that has the same volume as theparticle; that is, the laser assumes every particle to be a sphere,and reports the value of some equivalent diameter.

Another difference between the dry-sieve analysis and LPSAis that in a sieve, a minimum 20 g of sample is used, whereas onlya fraction of a gram of sample is used in LPSA. Thus, if the smallamount of sample used in LPSA is not representative of the sam-ple used in dry-sieve analysis, it would result in a different PSD.

If a sample contains a high fraction of clay particles, then in a

dry sieve these clay particles could adhere to the surface of largersilica particles, whereas in LPSA, such agglomeration of particlesdoes not occur. This could lead to the dry-sieve analysis reportinglarger sizes near the fine tail of the PSD, whereas the LPSAwould show a longer fine tail.

If the clay particles in the sample are of swelling or dispersivenature, then the fluid used in LPSA could affect the PSD (i.e., thePSD reported by the LPSA is sensitive to the fluid used for sam-ples containing swelling-/dispersive-type clay particles). Thus, it isimportant to determine the mineralogy of formation-sand samples.

Thus, for perfectly spherical particles, dry-sieve analysis andLPSA should provide exactly the same PSDs as long as the par-ticles are within the applicability range of both techniques, theparticles do not react with the fluid used in LPSA, and the smallersample size used in the laser is representative of the larger sample

used in the sieve. However, for nonspherical particles, the PSDsreported from dry-sieve analysis and LPSA would be differentand the difference would depend upon the degree of asphericity ofthe particles. (Sphericity is the ratio of the surface area of asphere, with the same volume as the given particle, to the surfacearea of the particle. Degree of asphericity means how far the valueof sphericity is from unity.)

Note that apart from these differences in PSDs from dry-sieveanalysis and LPSA, there could also be differences in PSDs fromdifferent LPSA measurements depending on variables such assonication time and amplitude (Ballard and Beare 2013).

Table 1 summarizes some of the differences between dry-sieve analysis and LPSA.

Dynamic Image Analysis. In addition to dry-sieve analysis andLPSA, there is another technique, dynamic image analysis,

which is also used for the determination of PSD. TheCAMSIZER (2012) is one of the laboratory instruments fordynamic image analysis that uses the principle of digital-imageprocessing and can measure a size range from 30 lm to 30 mm.It simultaneously determines PSD, particle shape, sphericity, as-pect ratio, and other information from powders and granularmaterials. The sample is transported to the measurement zone bymeans of a vibratory feeder, where the particles drop between anextended-light source and two cameras. The projected particleshadows are recorded at a rate of 60 images per second, with

more than 780,000 pixels each.The particle is scanned in multiple directions, and the longestdimension in each 2D projection is determined. Of all the 2D pro-

jections, the shortest (of the longest dimension in each 2D projec-tion),xmin, and the longest, xmax, dimensions are determined. Theaspect ratio of that particle is thenxmax/xmin.

Sphericity is reported as the square of circularity, which isdefined as the ratio of the perimeter of the circle (of the same 2Dprojection area as the particle) to the perimeter of the particle(also in the same 2D projection); that is, sphericity 4pA/P2,where A is the area and P is the perimeter of the particle in 2Dprojection. Note that the calculation of sphericity given here isdifferent from how it is normally defined. Sphericity is normallydefined as the ratio of the surface area of a sphere (equal volumeas the particle) to the surface area of the particle. However,

because the dynamic image analyzer can only record 2D images,the ratio of surface areas is reduced to the square of the ratio ofthe perimeters.

The volume calculation in dynamic image analysis is derivedfrom an assumed particle shape. One of the manufacturers of thedynamic image analyzer uses a prolate-spheroidal model to calcu-late the volume of the particles from the 2D images, regardless ofthe actual geometry of the particles. Because of this approxima-tion, the PSD reported matches neither laser nor sieve data unlessthe particles are either spherical (in which case all three techni-ques should match subject to comments made upon other poten-tial effects discussed previously) or prolate spheroid (spheroid inwhich the polar axis is greater than the equatorial diameter, inwhich case it should match with dry sieve).

Particle-Size Distribution (PSD) of Glass Beads

As mentioned previously, for perfectly spherical particles, dry-sieve analysis and laser-particle-size analysis (LPSA) shouldgive exactly the same particle sizes if the particles do not interactwith the fluid used in LPSA and the particle sizes are within therange of both techniques: larger than 37lm and smaller thanapproximately 10002000 lm. The glass beads were inert so theydo not swell or disperse when in contact with the fluid used in thelaser measurement. So, as a first step to calibrate both instru-ments and to ensure that everything is working properly and thedata collected are indeed accurate, PSDs of synthetic, sphericalglass beads (Fig. 1)were obtained by use of both techniques. Asexpected, dry-sieve analysis and LPSA gave almost-identical

PSDs for two different samples of spherical glass beads used(Fig. 2).

Table 1Comparison between dry-sieve analysis and LPSA for sand-control applications.

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Effectof Sampling ForLaserParticle-Size

Analysis (LPSA)

With spherical glass beads of the size range selected, even thoughdry-sieve analysis and LPSA should provide almost-identical par-ticle-size distributions (PSDs), depending on how the sample for

LPSA is obtained, some differences in PSDs may be observed.Determining a representative small fraction of sample for LPSAis crucial to accurate determination of PSD by laser measurement.If the sample is selected randomly by hand, there is a high chancethat the PSD from the LPSA will be different from the dry-sieveanalysis(Fig. 3a).However, if a sample splitter is used instead, arepresentative sample can be obtained for LPSA that will give aPSD almost identical to that of dry-sieve analysis (Fig. 3b). Forthe PSDs shown in Fig. 2, a sample splitter was used to obtainsamples for LPSA.

Effect of Particle Shape

Of the possible causes for the differences in particle-size distribu-tions (PSDs) reported from dry-sieve analysis and laser particle-size analysis (LPSA) mentioned previously, the effect of samplesize is not an issue if a proper sample-splitting method is fol-lowed. In addition, if the particles are not of swelling or dispersivetype, then there is no dependence of PSD on the fluid used forLPSA. Therefore, the most-important reason for the difference inPSDs from dry-sieve analysis and LPSA is the shape of the par-ticles. Here, we analyze the effect of shape of the particles onPSDs reported from dry-sieve analysis and LPSA. First, we show

the effect of shape on the PSD theoretically for a few regular-shaped particles. Then, we analyze the PSDs of actual samples ofirregular shape.

Theoretical PSDs of Regular-Shaped Particles. For a triaxialellipsoid, three axes a, b, and c are different from one another;suppose a< b< c. The dry sieve would always take the second-smallest dimension b as the particle size, whereas LPSA wouldgive a larger, a smaller, or even the same particle size as the drysieve, depending on the relationship between band

ffiffiffiffiffiac

p :

Ifb ffiffiffiffiffiac

p , dry sieve gives a larger size.

Ifb ffiffiffiffiffiacp , dry sieve and LPSA give the same size.For a prolate spheroid (a

b< c), LPSA would always give a

larger particle size than dry sieve. Besides the ellipsoidal shape,we also analyzed several other regular shapes: cylindrical, squarepyramidal, and conical. Given that dry-sieve analysis reports thesecond-smallest dimension as the particle size and LPSA reportsthe equivalent diameter of a sphere (of the same volume as theparticle) as the particle size, the PSDs are calculated for spheroi-dal-, cylindrical-, square-pyramidal-, and conical-shaped particlesfor different aspect ratios(Fig. 4).

As mentioned previously, for a prolate spheroid, LPSA alwaysgive a larger size than dry-sieve analysis, irrespective of the

Fig. 1Microscopic image of synthetic glass beads, with mag-nification of approximately 80X.

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Fig. 3PSD of spherical glass beads: (a) random sample; (b) split sample.


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aspect ratio (Fig. 4a). For the other three shapes, depending on thespecific aspect ratio, LPSA gives a larger, a smaller, or the samesize as dry sieve. Although this is a theoretical analysis ofexpected PSDs from sieve and laser for differently shaped par-ticles, Fig. 4 also shows microscopic images of real sand particlesthat closely resemble the shapes considered (i.e., such shapesindeed exist in real formation particles).

Crossover of PSDs From Dry-Sieve Analysis and LPSA. Asmentioned previously, if a sample contains a high fraction of fine(e.g., clay) particles, then sticking of fine particles to the surfaceof larger silica particles could result in dry-sieve analysis report-ing larger sizes near the fine tail even if LPSA reports largersizes near the coarse tail of the PSD; that is, there could becrossover of PSDs reported from dry-sieve analysis and LPSA forsamples containing a relatively high fraction of fine particles.Here, we demonstrate that such crossover of PSDs could alsooccur strictly because of the shape of the particles.

If the aspect ratio of the prolate spheroid is specifically set as 2and that of square pyramid as 0.5, the PSDs from dry-sieve analy-sis and LPSA would be as shown in Figs. 5a and 5b. PSD fromLPSA is greater than that from dry-sieve analysis for prolate sphe-

roid (Fig. 5a), and PSD from dry-sieve analysis is greater thanthat from LPSA for square pyramid (Fig. 5b). When these par-ticles are mixed together such that there is a higher concentrationof prolate-spheroidal particles near the coarse end and higher con-centration of square-pyramidal particles near the fine end, thenthere is a crossover of PSDs from dry-sieve analysis and LPSA, asshown in Fig. 5c.

PSDs of Mixture of Calcium Carbonate and Silica

Particles. Here, we analyze the PSDs of real particles that are ofirregular shape. The objective was to use samples that havehighly aspherical particles so that the PSDs from dry-sieve analy-sis and LPSA would be significantly different. With PSDs beingdifferent, the expected sand production in sand-retention tests

(SRTs) would be different. Sand production in SRTs could beestimated by use of the models developed by Chanpura et al.

(2012, 2013a) and by Mondal et al. (2011, 2012) under the condi-tions of slurry test (representing gradual failure) and prepack test(representing hole collapse), respectively. The next step wouldbe to perform an actual SRT and compare the estimated and ex-perimental sand production and determine whether PSDs fromdry-sieve analysis or from LPSA give a better match betweenpredicted and experimental sand production, and thus to concludewhich technique is relevant.

We first searched for the availability of certain shapes of syn-thetic particles (e.g., ellipsoidal, pyramidal) in various sizeranges applicable for both laser and sieve, much like the spheri-cal glass particles described previously, except with differentshapes. Unfortunately, we were not able to find such syntheticparticles. We started considering real particles of different miner-alogy under a microscope, and identified graded calcium carbon-ate and certain silica particles as potential candidates to create amixture. Fig. 6 shows the PSDs obtained from dry-sieve analysisand LPSA for calcium carbonate particles (Fig. 6a), silica par-ticles (Fig. 6b), and a mixture of calcium carbonate (8 mass%)and silica (92 mass%) particles (Fig. 6c). As can be seen fromFigs. 6a and 6b, for both calcium carbonate and silica particles,the PSDs reported from LPSA are greater than those from dry-sieve analysis. Both samples were analyzed under a microscope,and they indeed had a large fraction of aspherical particles. Whenthese particles were mixed, the PSD of the mixture also had asimilar trend; specifically, PSD from LPSA is greater than thatfrom dry sieve (Fig. 6c). The calcium carbonate particles were inthe 100500lm range, and silica particles were in the75180 lm range.

Although the LPSA and dry-sieve-analysis PSDs of the com-posite-silica particles shown in Fig. 6b exhibit significant differ-ences, and thus in principle this mixture could be used for anSRT, predicted sand-production numbers for both PSDs werevery small when either a 6-gauge (150 lm) or a 7-gauge (175 lm)wire-wrap screen (WWS) is used. Keeping in mind potential ex-perimental error in measurements, we wanted to design theexperiment for relatively large sand production in absolute terms

for both PSDs and also wanted a case where the predicted sand-production numbers differ significantly when dry-sieve-analysis

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Fig. 4Theoretical PSDs from dry-sieve analysis and LPSA for different regular-shaped particles.L/D= aspect ratio.


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and LPSA PSDs are used in the models. In addition, we wanted tostay away from regions where the two distributions (laser andsieve) overlap as well as stay away from the region where thePSDs from both techniques change sharply. These are the reasonsthat we decided to add some larger carbonate particles(100500lm) to the silica sample to obtain the PSD in Fig. 6c.We then also added some amount of smaller (smaller than 62lm)silica particles to include fine particles as well in the mixture.The PSDs of the combined mixture of calcium carbonate (8

mass%), larger silica (77 mass%), and smaller (smaller than62lm) silica particles (15 mass%) are shown in Fig. 7.

It can be seen from Fig. 6c that there is no crossover of dry-sieve-analysis and LPSA PSDs, whereas there is crossover whensome amount of smaller (smaller than 62 lm) silica particles wereadded, as shown in Fig. 7. To analyze the cause of this crossover,PSDs of the mixture of calcium carbonate, larger silica, andsmaller silica particles were calculated on the basis of individuallymeasured PSDs (dry-sieve analysis and LPSA) of calcium

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Fig. 6PSDs of: (a) calcium carbonate particles; (b) silica particles; and (c) mixture of calcium carbonate and silica particles.

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Fig. 5Crossover of PSDs from dry-sieve analysis and LPSA.


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carbonate (Fig. 6a) and larger silica (Fig. 6b) particles. The esti-mated PSDs are compared with the measured PSDs from dry-sieve analysis(Fig. 8a)and LPSA (Fig. 8b).

It can be seen from Fig. 8a that there is a very-good matchbetween the calculated and measured PSDs for dry-sieve analysisdown to 62 lm. However, for LPSA PSDs (Fig. 8b), we see thatthe measured PSD is less than the calculated PSD in the size rangeof 60200lm. Note that there is no crossover of calculated PSDsfrom dry sieve and LPSA, as shown in Fig. 9. If the calculatedand the measured PSDs from LPSA had also matched, then thecrossover that we see in Fig. 7 would not have existed. The fact

that the calculated and measured dry-sieve-analysis PSDs matchconfirms that the reason for the crossover has nothing to do withsieve measurements, as we had originally suspected on the basisof Ballard and Beare (2003) and Slayter et al. (2008), who dis-cussed potential sticking of finer particles on coarser particles.The reason for the crossover of measured dry-sieve-analysis andLPSA PSDs in Fig. 7 clearly has something to do with laser meas-urements. Although this could be caused by various factors, dif-ferent obscuration levels (percentage of light scattered out of thebeam by the particles) used in laser measurements (e.g., in ourtests for calcium carbonate/larger silica particles and for calciumcarbonate/larger silica/smaller silica particles) leading to differentsize distributions have been reported in the literature (Stori andBalsamo 2010; Sperazza et al. 2004). It is worth noting that wewere not able to find any studies that discuss the effect of obscura-tion levels on LPSA PSD measurements for samples containing awide range of particle sizes. Although LPSA is certainly a usefultool, it is important to understand many sources of potential errorsand thus misleading results. Without systematic studies to identifythe proper pumping speed, obscuration levels, or solvent type fora given mineralogy, accuracy of the results obtained from LPSAmay be questionable.

Note that even though there are some questions on the accu-racy of the LPSA PSD in the size range smaller than the WWSslot size that we will be using in the SRT, this will have no effecton experimental sand production in slurry tests. This is because,as stated in previous publications, it is the particles that are largerthan the screen openings that dictate the amount of sand pro-

duced in three out of four cases of interest, with the exceptionbeing prepack SRTs (simulating hole collapse) on mesh-type

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screens (Chanpura et al. 2013b). Therefore, the only case wherePSD in the small size range will have an impact is when the mod-els are used for predicting sand production for prepack SRTs onmesh screens.

Sand-Retention Tests (SRTs)

There are two types of SRTs that are generally performed forsand-screen selection: slurry tests (Gillespie et al. 2000; Under-down et al. 2001; Ballard and Beare 2006; Williams et al. 2006;Mathisen et al. 2007) and prepack tests (Markestad et al. 1996;Ballard and Beare 2003; Constien and Skidmore 2006; Williamset al. 2006). In a slurry test, which represents gradual rock failurearound the borehole, low-concentration sand slurry (typically lessthan 1 vol%) is pumped at a constant rate and a sandpack formson the screen during the test. In a prepack test that representscomplete hole collapse, a sandpack is placed on the screen andclean fluid is pumped through the sandpack and the screen. In aslurry test, the mechanism of sand retention is size exclusion only

(i.e., only the particles that exceed the screen opening are retainedby the screen because of the low sand concentration in the testedslurry), and, as a first approach, which requires further validation,briding can be neglected (Valdes and Santamarina 2006). In con-trast, in a prepack test, sand retention is achieved by size exclu-sion and by bridging (when two or more particles meet at anopening, at least one particle that is smaller than the screen open-ing will not be able to go through the opening).

Models have been developed to estimate sand production inprepack tests through a wire-wrap screen (WWS) (Mondal et al.2011), through a plain-square-mesh (PSM) screen (Mondal et al.2012), and in slurry tests through WWS (Chanpura et al. 2012)and through PSM (Chanpura et al. 2013a). Here, we estimate sandproduction by use of the particle-size distributions (PSDs) fromdry-sieve analysis and laser-particle-size analysis (LPSA) (Fig. 7)

for WWS and compare it with experimental sand production.

Sand Production in Slurry Tests of WWS. A slurry test wasperformed with the mixture of calcium carbonate, silica, andsmaller (smaller than 62 lm) silica particles by use of a WWScoupon. A slot size of 250lm (vertical solid line in Fig. 7) wasselected for the reasons discussed previously.

The estimated sand productions for the PSDs from dry-sieveanalysis and LPSA shown in Fig. 7 through WWS with slot sizeof 250lm were 0.197 lbm/ft2 and 0.030 lbm/ft2, respectively. Ex-perimental sand production was 0.172 lbm/ft2. It is clear that theestimated sand production for the PSD from dry-sieve analysis ismuch closer to the experimental sand production compared withthat from LPSA PSD. This was actually anticipated because themechanism of sand retention in a slurry test is similar to the waythe particles are retained in a dry sieve; that is, particles orientthemselves with the second-smallest dimension to pass throughthe opening in a unidirectional flow (Rusnak 1957). This was fur-ther confirmed with this test. Thus, the PSD from dry-sieve analy-sis is the relevant one to estimate sand production in slurry testing(representing gradual failure). In fact, apart from cases where theparticles are near-spherical (needs to be quantified), PSDsobtained from LPSA seem to have no relevance to sand retention/production at all because LPSA gives a nonphysical dimensionfor a nonspherical particle.

One thing to note is that the sand production was estimated byuse of the analytical model (Chanpura et al. 2012), which assumesall spherical particles. However, in reality the particles are notspherical. If we assume that the particles are all square pyramidalin shape, then the estimated sand production is 0.175 lbm/ft2 and0.027 lbm/ft2 (for dry-sieve-analysis and LPSA PSDs, respec-tively), and for conical-shaped particles, the estimated sand pro-duction is 0.137 lbm/ft2 and 0.021 lbm/ft2 (for dry-sieve-analysis

and LPSA PSDs, respectively). For estimating sand productionfor square-pyramidal- and conical-shaped particles, an aspect ra-tio of 1.39 (estimated from dynamic image analyzer for particleslarger than the slot size) was used. It can be seen that estimatedsand production for square-pyramidal shape is very close to theexperimental sand production.

The calcium carbonate, silica, and small particles were alsoexamined under a microscope (Fig. 10). It can be seen from Fig.10 that there are indeed particles that can be approximated bythese shapes (square pyramidal and conical). Further, the samplemixture was also analyzed by dynamic image analysis, and an as-pect ratio of 1.39 was determined from the instrument for the frac-tion of particles larger than the slot size (250 lm).Table 2 showsthe experimental sand production compared with estimated sandproduction for the two PSDs for differently shaped particles.

The results presented here show that PSD from dry-sieveanalysis already gives a close-enough estimate of sand produc-tion even if we assume all the particles are sphericalcertainlya much closer estimate than laser PSD gives. If we analyze thesample further by use of dynamic image analysis, then we candetermine an estimate of the aspect ratio of the particles. Then,by assigning a specific shape to the particles (through a micro-scope), we can get an even-closer match to the experimentalsand production.

If the WWS selection will be performed on the basis of anactual SRT rather than model-estimated sand production, then theSRT should be performed with the original formation sand. If thetest is performed with a synthetic sample generated on the basisof a specified PSD, then it is important to know how the PSD of

the original formation was obtained as well as how the syntheticsample was generated. For example, for slurry tests, the PSD ofthe original formation sand should be obtained from dry-sieveanalysis and the synthetic sample should be generated throughdry-sieve analysis as well. Even in this case, the experimentalsand production with a synthetic sample may not be exactly thesame as it would be with actual formation sand because it wouldbe impossible to have exactly the same shape of the particles in a

Fig. 10Mixture of calcium carbonate, silica, and smaller(smaller than 62 lm) silica particles under a microscope (mag-nification of approximately 80X).

Table 2Experimental vs. estimated sand production (Chanpura et al. 2012) (lbm/ft2) in slurry test.


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synthetic sample as in the original formation sand. If the PSD ofthe original formation sand and that of the synthetic sample are

generated from LPSA, then the difference or the error in experi-mental sand production from a slurry test by use of a syntheticsample can be expected to be even larger. This is because, withdry-sieve analysis, as a minimum the second-smallest dimensionsof the particles (which are what matter in slurry testing) arematched (formation sand vs. synthetic sample), whereas withLPSA the average dimensions of the particles (which are less rele-vant) are being matched.

Sand Production in Prepack Tests of WWS. Mondal et al.(2011, 2012) presented discrete-element-method simulations ofprepack tests. A probabilistic model was also developed by Mon-dal (2013) to predict the sand production in prepack tests and wasvalidated against the numerical simulations and experimental data

from Mondal et al. (2011). In this model, it is assumed that thereis a volume Vnear the outlet of a screen of opening size Do andparticles can only bridge when they are present in this volume.Particles are produced through several discharges, and each of thedischarges contains particles of different sizes derived from theformation sand PSD. LetNi,sbe a set of particles present in a dis-

charges at any given step i and di,maxbe the maximum particle di-ameter in this set. The near-screen volume at step i is defined asViDo d2i,max, and Vi satisfies the following condition at everytimestep:

Xim1

p

6d3m 1 /Vi, where/ is the porosity of the

sandpack. At each step, a particle randomly selected from thePSD is imported into Vi and the total cumulative probability of

jamming is calculated on the basis of PJX

s

XkP

i; sk , where

Pi; sk is the probability to form a bridge withk (k 1, 2, ) par-

ticles present in Ni,s at a given step i and discharge s. The occur-rence of screen jamming or particle discharge is then determined

according to whether PJ> 1 at step i while the conditionXim1

p

6d3m 1 /Vi is met. The jamming probability used

here is calculated by use of the experimental data of Mondal et al.(2011). The reader is urged to refer to Mondal (2013) for a fulldescription of this model.

Table 3shows the analytical results of estimated sand produc-tion in WWS prepack tests for dry-sieve-analysis and LPSA PSD.It is noteworthy that the model predicts LPSA PSD to producemore sand when using 250-lm WWS and dry-sieve-analysis PSDto produce more sand when using 400-lm WWS.Figs. 11 and 12demonstrate the percentage of retention mechanism (bridging andsize exclusion) that causes the screen jamming in each of the fourdifferent cases.

We may explain the results obtained here by looking at the

PSD shown in Fig. 7. For the 250-lm-WWS case, the major frac-tion of dry-sieve-analysis PSD is of particles with size of approxi-mately 100200lm, which makes bridging the dominantmechanism. On the contrary, LPSA PSD has higher size-exclu-sion probability and lower bridging probability because of its por-tion of particles larger than the opening size. Therefore, size-

Table 3Estimated sand production (Mondal 2013) (lbm/ft2) in

prepack test.

100

PercentageofRetentionby

Mechanism

80

60

40

20

00 5 10 15

Bridging

Size-Exclusion

20 25 30

Number of Runs(a) (b)

100


Mechanism

80

60

40

20

00 5 10 15

Bridging

Size-Exclusion

20 25 30

Number of Runs

Fig. 11Estimated percentage of retention mechanism in prepack tests of 250-lm WWS for (a) dry-sieve PSD and (b) LPSA PSD.

100


Mechanism

80

60

40

20

00 5 10 15

Bridging

Size-Exclusion

20 25 30

Number of Runs(a) (b)

100


Mechanism

80

60

40

20

00 5 10 15

Bridging

Size-Exclusion

20 25 30

Number of Runs

Fig. 12Estimated percentage of retention mechanism in prepack tests of 400-lm WWS for (a) dry-sieve PSD and (b) LPSA PSD.


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exclusion occupies a considerable fraction of all the retentioncases in LPSA PSD. With a small opening size of 250 lm, bridg-ing is easier and hence produces less sand when modeling withdry-sieve-analysis PSD. For the 400-lm-WWS case, the probabil-ity of size-exclusion and bridging both drop because of the largeropening size. Because more particles are required to form a bridgein this case, the probability of bridging drops more and becomeslower than that of size-exclusion. This leads to the result ofincreased sand production and more sand being produced in dry-sieve-analysis PSD.

Although one can explain the results of the analytical modelfrom the differences between the two PSDs, it is still nontrivial toconclude which PSD will give a more-accurate result by compar-ing the experiments. This is because in prepack tests, unlike slurrytests, particles do not necessarily orient themselves to the screenopenings because of their high concentration. Therefore, not onlythe smaller particle dimension but also its entire volume plays animportant role in deciding the occurrence of jamming, especiallyparticle bridging, which directly influences the result of sand pro-duction. Hence, further experiments are needed for prepack testsbefore concluding which method captures the PSD better withrespect to the competing jamming mechanisms of size exclusionand bridging. However, it can be expected that in the case of pre-pack tests, the difference in prediction during use of dry-sieve-analysis PSD and LPSA PSD will be lower than that in slurrytests. This is planned to be part of our future work in this area.

ProposedMethodology

The first task that should be performed before a thorough particle-size-distribution (PSD) analysis is to visually observe the sampleunder the microscope to determine the approximate particleshapes, particle-size range, and mineralogy of the particles (cleanvs. dirty sand). This information would indicate whether dry-sieveanalysis or laser particle-size analysis (LPSA) is a feasible tech-nique for PSD determination.

Dry-sieve analysis should be the preferred technique to obtainthe PSD for sand control unless not enough sand is available tosample. Once the PSD from dry-sieve analysis is obtained, it canbe used in the models to estimate sand production in sand-reten-tion tests (SRTs). If the information obtained from microscopic

inspection indicates that the particles are highly aspherical, thendynamic image analysis should be performed to determine the as-pect ratio of the particles. By use of the aspect ratio, sand-produc-tion estimates from the models can be refined, taking into accountthe shape of the particles.

If dry-sieve analysis is not feasible (i.e., if enough sample isnot available), then LPSA could be used. First, detailed mineral-ogy of the particles should be determined by use of X-ray diffrac-tion. This would help to decide the fluid to be used in LPSA sothat it does not interact with the particles. Once the PSD fromLPSA is obtained, it can be used in the models to estimate sandproduction in SRTs. However, if the particles are highly aspheri-cal (as inferred from microscope), then the PSD and, therefore,the sand-production estimate would not be accurate.

ConclusionsOn the basis of the simulations and experimental observationsreported in this study, the following conclusions can be made: Differences in particle-size distributions (PSDs) from dry-sieve

analysis and laser particle-size analysis (LPSA) (including thecrossover) can be caused by the aspherical shape of the par-ticles, particle sampling for LPSA, fluid used in LPSA, and dif-ferent obscuration levels used in LPSA* Differences from particle sampling could be eliminated or

minimized by proper use of a sample splitter to generate sam-ples for LPSA.

* The effect of particle shape was analyzed in detail. For slurrytests representing a gradual-failure condition in the field, dry-sieve analysis gives the relevant PSD of formation sand for

sand-production estimates through wire-wrap screens by useof the models developed previously.

If slurry tests are performed by use of a synthetic sample gener-ated on the basis of specified PSD of formation sand, then thePSD of the formation sand should be obtained from dry-sieveanalysis and the synthetic sample should be generated on thebasis of the dry-sieve analysis. Even in this case, there wouldbe some error in experimental sand production because the syn-thetic sample and the original formation may not have exactlythe same particle shapes.

For prepack tests, size exclusion and particle bridging are bothinfluenced by the particles shape and volume because of thelimited space for particle orientation in the near-screen region.Further experiments have to be performed before concludingwhich method provides the PSD that better captures the effectof particle/particle interactions.

Before selecting a sand-control method or before designing asand-control screen, more research needs to be performed thanobtaining a PSD analysis by use of a sieve or laser apparatus.Observation of the sand sample under a microscope should beperformed for an initial evaluation of approximate particleshapes, particle-size range (to determine whether the particleswill be in the measurement range of one technique or the other),and a gross idea of mineralogy; a more-detailed analysis of par-ticle shape should be performed by use of dynamic image anal-ysis (to determine an average aspect ratio and sphericity); and amore-detailed analysis of mineralogy through X-ray-diffractionanalysis, particularly for LPSA, should be performed in addi-

tion to PSD measurements only.* If LPSA is being considered for PSD measurements, it is im-

portant to understand any sources of potential errors and thusmisleading results from LPSA. Without systematic studies toidentify the proper pumping speed, obscuration levels, or sol-vent type for a given mineralogy, accuracy of the resultsobtained from LPSA may be questionable.

Acknowledgments

The authors would like to thank Schlumberger for permission topublish the results of this work. The authors also acknowledge thefinancial support provided by Schlumberger and SchlumbergerSand Control Client Advisory Board members BG Group, BP,Chevron, ConocoPhillips, Statoil, and Total. The authors would

also like to thank the Texas Advanced Computing Center at theUniversity of Texas at Austin for providing high-performance-computing resources for this work.

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Ke (Cathy) Zhang is a masters degree student in the Depart-ment of Energy Resources Engineering at Stanford University.She has interned with Schlumberger twice as an undergradu-ate student and worked on projects related to sand controland high-temperature hydraulic-fracturing-fluid stabilizer.Zhangs current research interests include experimental inves-tigation of oil recovery from Bakken shale by miscible carbondioxide injection, and tomographic imaging of multiphaseflow in porous media. She holds a bachelors degree in chemi-cal engineering from Rice University.

Rajesh A. Chanpura is a product champion for Screens andInflow-Control Devices (ICDs) in Schlumberger Sand Manage-ment Services, based in Houston. He is responsible for definingthe key requirements and introducing new products devel-oped under the Screens and ICDs portfolio to the field. Chan-pura has been with Schlumberger for more than 14 years. Inhis previous role, Chanpura developed an in-house methodol-ogy and answer product for screen selection for openholecompletions. Before that, he was involved in the developmentof Schlumbergers gravel-packing simulator. Chanpura holdsa bachelors degree in construction engineering from the Uni-versity of Mumbai; a masters degree in civil engineering fromthe Indian Institute of Technology, Mumbai; and a PhD degreein civil engineering from Georgia Institute of Technology.

Somnath Mondal is a production technologist at Shell. His cur-rent research interests include hydraulic fracturing, comple-tions effectiveness, near-wellbore pressure transients, and flowof particulate systems. Mondal holds a bachelors degree inchemical engineering from Birla Institute of Technology and

Science, India, and masters and PhD degrees in petroleumengineering from the University of Texas at Austin.

Chu-Hsiang Wuis a PhD degree candidate in the Departmentof Petroleum and Geosystems Engineering at the University ofTexas at Austin. His current research focuses on modeling partic-ulate-flow behavior and sand-retention tests for evaluating andimproving screen designs. Wu holds bachelors and mastersdegrees in mechanical engineering from National Tsing Hua Uni-versity, Taiwan, and National Taiwan University, respectively.

Mukul M. Sharma is a professor and holds the Tex MoncriefChair in the Department of Petroleum and Geosystems Engi-neering at the University of Texas at Austin, where he has beenfor the past 30 years. Sharma served as chair of the depart-ment from 2001 to 2005. He has made contributions in theareas of hydraulic fracturing, injection-water management,

formation damage, improved oil recovery, and petrophysics.Sharma has published more than 300 journal articles and con-ference-proceedings articles and holds 15 patents. Among hismany awards, Sharma is the recipient of the 2009 Lucas GoldMedal, the highest technical award from SPE, the 2004 SPEFaculty Distinguished Achievement Award; the 2002 SPE LesterC. Uren Award; and the 1998 SPE Formation Evaluation Award.He served as an SPE Distinguished Lecturer in 2002, has servedon the editorial boards of many journals, and has taught andconsulted for more than 50 companies worldwide. Sharmahas also cofounded two private exploration-and-productioncompanies and a consulting company. He holds a bachelorsdegree in chemical engineering from the Indian Institute ofTechnology, Kanpur, and masters and PhD degrees in chemi-cal and petroleum engineering, respectively, from the Univer-sity of Southern California.

Joseph A. Ayoub is the production and completion engi-neering discipline manager with Schlumberger. He holds

http://dx.doi.org/10.2118/151637-PAhttp://dx.doi.org/10.2118/151637-PAhttp://dx.doi.org/10.2118/158922-PAhttp://dx.doi.org/10.2118/98363-MShttp://dx.doi.org/10.2118/98363-MShttp://dx.doi.org/10.2118/64398-MShttp://www.iso.org/iso/catalogue_detail.htm?csnumber=36976http://www.iso.org/iso/catalogue_detail.htm?csnumber=36976http://dx.doi.org/10.2118/31087-MShttp://dx.doi.org/10.2118/107539-MShttp://dx.doi.org/10.2118/107539-MShttp://dx.doi.org/10.2118/134326-PAhttp://dx.doi.org/10.2118/134326-PAhttp://dx.doi.org/10.2118/146656-PAhttp://dx.doi.org/10.2118/146656-PAhttp://dx.doi.org/10.2118/85504-PAhttp://www.jstor.org/stable/30058984http://www.jstor.org/stable/30058984http://dx.doi.org/10.2118/4030-PAhttp://dx.doi.org/10.2118/114781-MShttp://dx.doi.org/10.1306/031104740736http://dx.doi.org/10.5194/se-1-25-2010http://dx.doi.org/10.5194/se-1-25-2010http://dx.doi.org/10.2118/39437-MShttp://dx.doi.org/10.2118/75326-PAhttp://dx.doi.org/10.2118/75326-PAhttp://dx.doi.org/10.2118/88819-PAhttp://dx.doi.org/10.2118/98235-MShttp://dx.doi.org/10.2118/98235-MShttp://dx.doi.org/10.2118/88819-PAhttp://dx.doi.org/10.2118/75326-PAhttp://dx.doi.org/10.2118/75326-PAhttp://dx.doi.org/10.2118/39437-MShttp://dx.doi.org/10.5194/se-1-25-2010http://dx.doi.org/10.5194/se-1-25-2010http://dx.doi.org/10.1306/031104740736http://dx.doi.org/10.2118/114781-MShttp://dx.doi.org/10.2118/4030-PAhttp://www.jstor.org/stable/30058984http://www.jstor.org/stable/30058984http://dx.doi.org/10.2118/85504-PAhttp://dx.doi.org/10.2118/146656-PAhttp://dx.doi.org/10.2118/146656-PAhttp://dx.doi.org/10.2118/134326-PAhttp://dx.doi.org/10.2118/134326-PAhttp://dx.doi.org/10.2118/107539-MShttp://dx.doi.org/10.2118/107539-MShttp://dx.doi.org/10.2118/31087-MShttp://www.iso.org/iso/catalogue_detail.htm?csnumber=36976http://www.iso.org/iso/catalogue_detail.htm?csnumber=36976http://dx.doi.org/10.2118/64398-MShttp://dx.doi.org/10.2118/98363-MShttp://dx.doi.org/10.2118/98363-MShttp://dx.doi.org/10.2118/158922-PAhttp://dx.doi.org/10.2118/151637-PAhttp://dx.doi.org/10.2118/151637-PA

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more than 12 patents and has published more than 35papers, mainly in the areas of well testing, hydraulic fractur-ing, and frac packs. Ayoubs involvement was instrumentalfor introducing the pressure-derivative method and forlaunching the frac-pack technique in the Gulf of Mexico inthe early 1990s. More recently, he led the formation of indus-try consortiums to investigate technical challenges in theareas of stimulation and sand control. Ayoub has served onnumerous SPE committees and served as an SPE Distin-guished Lecturer in 19981999 on Improving Productivity ofSand Control Completions and in 20092010 on Realizing FullPotential of Hydraulic Fracturing. He was named a Schlum-berger Adviser in 1999 and an SPE Distinguished Member in

2005, and served as technical director forSPE Drilling & Com-pletion from 2010 to 2013. Ayoub holds an engineering

degree and a masters degree from Ecole Centrale de Paris,France.

Mehmet Parlar is currently a technical adviser for Schlum-berger Sand Management Services, based in Houston. He has25 years of industry experience, with 7 years in product devel-opment and 18 years in sand control, all with Schlumberger.Parlar is a contributor to more than 55 technical papers andholds 27 US patents. He is an SPE Distinguished Member, wasan SPE Distinguished Lecturer (20072008 and 20112012), wasan SPE Distinguished Author (2000), and has been activelyinvolved in many SPE events. Parlar holds a bachelors degreefrom Istanbul Technical University and masters and PhD

degrees from the University of Southern California, all in petro-leum engineering.

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