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Particle-Size-Distribution Measurement Techniques and Their Relevance or Irrelevance to Wire-Wrap-StandaloneScreen Selection for Gradual-FormationFailure Conditions Ke Zhang, Rice University; Rajesh A. Chanpura, Schlumberger; Somnath Mondal1, Chu-Hsiang Wu, and Mukul M. Sharma, University of Texas at Austin; and Joseph A. Ayoub and Mehmet Parlar, Schlumberger

Summary Sand-particle-size distributions (PSDs) are used for various purposes in sand control: for example, decision making between various sand-control techniques and sizing of the filter media (sand screens and/or gravel packs) through either rule of thumb or physical experiments or theoretical models. PSDs of formation-sand samples are also often used to generate “simulated” formation sand for laboratory experiments. The two most commonly used techniques for PSD measurements are sieve and laser. Although some engineers use one technique for no obvious or justifiable reasons, others use both techniques for measurements and do not know what to do with the data when significant differences exist in PSDs obtained from each technique. Although the inherent limitations of (and the differences between), these two techniques as well as other factors affecting the measurements are well-known, a systematic study as to which of these two techniques is relevant to sand-control-screen selection and why is lacking. In this study, we critically review the current practices in PSD determination and the use (and misuse) of the information obtained from these measurements, propose a methodology toward determining what is relevant under gradual-formation-failure conditions for wire-wrap screen, discuss when it should be used and why, and present initial experimental results that support our conclusions. Introduction Particle-size distribution (PSD) of formation sand for reservoirs requiring sand control is the sole information used when applying rules of thumb for sand-control-technique selection (Tiffin et al. 1998; Price-Smith et al. 2003), screen-size selection for standalone-screen (SAS) application (Coberly 1937), and gravel-size selection for gravel-pack application (Saucier 1974). Chanpura et al. (2012, 2013a) and Mondal et al. (2011, 2012) also use PSD of formation sand (and a specified acceptable sand production) for sizing screens for SASs on the basis of numerical and/or analytical models. Such models can result in accurate estimates of sand production in laboratory sand-retention tests (SRTs), provided that both the screen and the sand PSD are well-characterized. Therefore, the importance of an accurate determination of PSD of the formation sand is evident. Any inaccuracy in determining PSD could result in improper sand-control-technique selection and/or screen-/gravel-size selection. Even in cases when SRTs are used for screen sizing for SASs, unless the test is performed with the actual formation sand, inaccurate reporting of PSD could result in 1

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C 2015 Society of Petroleum Engineers Copyright V

This paper (SPE 168152) was accepted for presentation at the SPE International Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, USA, 26–28 February 2014, and revised for publication. Original manuscript received for review 22 March 2014. Revised manuscript received for review 6 January 2015. Paper peer approved 31 March 2015.

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testing simulated sand that is not representative of the original formation sand, thus leading to incorrect screen-size selection. Dry-sieve analysis and laser-particle-size analysis are the two techniques that are most commonly used for determining PSD of formation sand. However, it is well-known that there are differences 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 in PSDs reported from these two techniques and recommend which technique is suitable to use under which conditions. Techniques for Particle-Size-Distribution (PSD) Determination As mentioned earlier in the study, dry-sieve analysis and laser particle-size analysis (LPSA) are currently the two types of particle-sizing techniques that are commonly used in the industry. We provide a brief description of these techniques, followed by a comparison 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 particles are first separated into individual grains and then cleaned, dried, and weighed. They are then passed through a stack of sieves in a shaker, with the coarsest sieve at the top and finest sieve at the bottom. Typically, the smallest sieve that is used in the dry sieve is 400 US mesh (37 lm). Sand particles that pass through the smallest sieve are collected in a pan. From the measured weight of the sand retained in each individual sieve, cumulative weight percent retained by each sieve size is calculated and plotted against sieve size on a semilogarithmic scale. Dry-sieve analysis was performed as per ISO 13503-2 (2006) in this work. LPSA. LPSA determines PSD of sand electronically by measuring the intensity of light scattered as a laser beam passes through a dispersed-particulate sample. The angle of scatter of the laser light is inversely proportional to the particle size. The angular intensity of light scattered is captured by a series of photosensitive detectors. The data are then processed and analyzed through the instrument software to calculate the particle sizes. In LPSA, sample dispersion is controlled by a range of wet- or dry-dispersion units, which ensure that the particles are delivered to the measurement area or the optical bench at the correct concentration and in a stable state. A dry-dispersion unit is ideally suited for measurement of powders, especially moisture-sensitive materials. Wet-sample dispersion units use a liquid dispersant, either aqueous or solvent-based, to disperse the sample. The liquid dispersant chosen has to be able to hold the sample in suspension through stirring. Any settling or floating of the particles will introduce errors in the laser-diffraction measurement. To keep the sample suspended and homogenized, it is recirculated continuously through the measurement zone. A wet-dispersion unit with June 2015 SPE Drilling & Completion

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

deionized water was used for LPSA in this study because samples consisted 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-sieve analysis and LPSA methods is in the way particle sizes are estimated by these techniques. The sieve measures the second-smallest dimension because of the way the particles orient themselves to pass through the opening given sufficient time. As opposed to the smallest dimension, a sieve emphasizes the second-smallest dimension because if the slot opening is the same size as the particle’s smallest dimension, the particle cannot pass through in the direction of its second-smallest dimension. A light-scattering device, such as a laser, measures various dimensions as the particles flow randomly through the light beam. It then calculates the equivalent diameter of a sphere that has the same volume as the particle; 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 LPSA is that in a sieve, a minimum 20 g of sample is used, whereas only a fraction of a gram of sample is used in LPSA. Thus, if the small amount of sample used in LPSA is not representative of the sample 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 larger silica particles, whereas in LPSA, such agglomeration of particles does not occur. This could lead to the dry-sieve analysis reporting larger sizes near the “fine” tail of the PSD, whereas the LPSA would show a longer “fine” tail. If the clay particles in the sample are of swelling or dispersive nature, then the fluid used in LPSA could affect the PSD (i.e., the PSD reported by the LPSA is sensitive to the fluid used for samples containing swelling-/dispersive-type clay particles). Thus, it is important to determine the mineralogy of formation-sand samples. Thus, for perfectly spherical particles, dry-sieve analysis and LPSA should provide exactly the same PSDs as long as the particles are within the applicability range of both techniques, the particles do not react with the fluid used in LPSA, and the smaller sample size used in the laser is representative of the larger sample used in the sieve. However, for nonspherical particles, the PSDs reported from dry-sieve analysis and LPSA would be different and the difference would depend upon the degree of asphericity of the particles. (Sphericity is the ratio of the surface area of a sphere, with the same volume as the given particle, to the surface area of the particle. Degree of asphericity means how far the value of sphericity is from unity.) Note that apart from these differences in PSDs from dry-sieve analysis and LPSA, there could also be differences in PSDs from different LPSA measurements depending on variables such as sonication time and amplitude (Ballard and Beare 2013). Table 1 summarizes some of the differences between drysieve analysis and LPSA. Dynamic Image Analysis. In addition to dry-sieve analysis and LPSA, there is another technique, dynamic image analysis,

which is also used for the determination of PSD. The CAMSIZER (2012) is one of the laboratory instruments for dynamic image analysis that uses the principle of digital-image processing and can measure a size range from 30 lm to 30 mm. It simultaneously determines PSD, particle shape, sphericity, aspect ratio, and other information from powders and granular materials. The sample is transported to the measurement zone by means of a vibratory feeder, where the particles drop between an extended-light source and two cameras. The projected particle shadows 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 longest dimension in each 2D projection is determined. Of all the 2D projections, the shortest (of the longest dimension in each 2D projection), xmin, and the longest, xmax, dimensions are determined. The aspect ratio of that particle is then xmax/xmin. Sphericity is reported as the square of circularity, which is defined as the ratio of the perimeter of the circle (of the same 2D projection area as the particle) to the perimeter of the particle (also in the same 2D projection); that is, sphericity ¼ 4pA/P2, where A is the area and P is the perimeter of the particle in 2D projection. Note that the calculation of sphericity given here is different from how it is normally defined. Sphericity is normally defined as the ratio of the surface area of a sphere (equal volume as 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 of the perimeters. The volume calculation in dynamic image analysis is derived from an assumed particle shape. One of the manufacturers of the dynamic image analyzer uses a prolate-spheroidal model to calculate the volume of the particles from the 2D images, regardless of the actual geometry of the particles. Because of this approximation, the PSD reported matches neither laser nor sieve data unless the particles are either spherical (in which case all three techniques should match subject to comments made upon other potential effects discussed previously) or prolate spheroid (spheroid in which the polar axis is greater than the equatorial diameter, in which case it should match with dry sieve). Particle-Size Distribution (PSD) of Glass Beads As mentioned previously, for perfectly spherical particles, drysieve analysis and laser-particle-size analysis (LPSA) should give exactly the same particle sizes if the particles do not interact with the fluid used in LPSA and the particle sizes are within the range of both techniques: larger than 37 lm and smaller than approximately 1000–2000 lm. The glass beads were inert so they do not swell or disperse when in contact with the fluid used in the laser measurement. So, as a first step to calibrate both instruments and to ensure that everything is working properly and the data collected are indeed accurate, PSDs of synthetic, spherical glass beads (Fig. 1) were obtained by use of both techniques. As expected, dry-sieve analysis and LPSA gave almost-identical PSDs for two different samples of spherical glass beads used (Fig. 2).

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Effect of Particle Shape Of the possible causes for the differences in particle-size distributions (PSDs) reported from dry-sieve analysis and laser particlesize analysis (LPSA) mentioned previously, the effect of sample size is not an issue if a proper sample-splitting method is followed. In addition, if the particles are not of swelling or dispersive type, then there is no dependence of PSD on the fluid used for LPSA. Therefore, the most-important reason for the difference in PSDs from dry-sieve analysis and LPSA is the shape of the particles. Here, we analyze the effect of shape of the particles on PSDs reported from dry-sieve analysis and LPSA. First, we show the effect of shape on the PSD theoretically for a few regularshaped particles. Then, we analyze the PSDs of actual samples of irregular shape.

Fig. 1—Microscopic image of synthetic glass beads, with magnification of approximately 80X.

Effect of Sampling For Laser Particle-Size Analysis (LPSA) With spherical glass beads of the size range selected, even though dry-sieve analysis and LPSA should provide almost-identical particle-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 LPSA is crucial to accurate determination of PSD by laser measurement. If the sample is selected randomly by hand, there is a high chance that the PSD from the LPSA will be different from the dry-sieve analysis (Fig. 3a). However, if a sample splitter is used instead, a representative sample can be obtained for LPSA that will give a PSD almost identical to that of dry-sieve analysis (Fig. 3b). For the PSDs shown in Fig. 2, a sample splitter was used to obtain samples for LPSA.

Theoretical PSDs of Regular-Shaped Particles. For a triaxial ellipsoid, three axes a, b, and c are different from one another; suppose a < b < c. The dry sieve would always take the secondsmallest dimension b as the particle size, whereas LPSA would give a larger, a smaller, or even the same particle p size ﬃﬃﬃﬃﬃ as the dry sieve, depending on the relationship between b and ac: pﬃﬃﬃﬃﬃ • If b < pac ﬃﬃﬃﬃﬃ, LPSA gives a larger size. • If b > pac ﬃﬃﬃﬃﬃ, dry sieve gives a larger size. • If b ¼ ac, dry sieve and LPSA give the same size. For a prolate spheroid (a ¼ 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, square pyramidal, and conical. Given that dry-sieve analysis reports the second-smallest dimension as the particle size and LPSA reports the equivalent diameter of a sphere (of the same volume as the particle) as the particle size, the PSDs are calculated for spheroidal-, cylindrical-, square-pyramidal-, and conical-shaped particles for different aspect ratios (Fig. 4). As mentioned previously, for a prolate spheroid, LPSA always give a larger size than dry-sieve analysis, irrespective of the PSD of Glass Bead Sample B 100

Cumulative Percentage Retained

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Fig. 2—PSD of spherical glass beads: (a) Sample A; (b) Sample B. PSD of Split LPSA Sample Cumulative Percentage Retained

Cumulative Percentage Retained

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10

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Fig. 3—PSD of spherical glass beads: (a) random sample; (b) split sample. 166

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(d) LPSA_L/D = 3

100

10

Particle Size (µm) Dry sieve

LPSA_L/D = 1

LPSA_L/D = 2

LPSA_L/D = 3

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

aspect ratio (Fig. 4a). For the other three shapes, depending on the specific aspect ratio, LPSA gives a larger, a smaller, or the same size as dry sieve. Although this is a theoretical analysis of expected PSDs from sieve and laser for differently shaped particles, Fig. 4 also shows microscopic images of real sand particles that closely resemble the shapes considered (i.e., such shapes indeed exist in real formation particles). Crossover of PSDs From Dry-Sieve Analysis and LPSA. As mentioned previously, if a sample contains a high fraction of fine (e.g., clay) particles, then sticking of fine particles to the surface of larger silica particles could result in dry-sieve analysis reporting larger sizes near the “fine” tail even if LPSA reports larger sizes near the “coarse” tail of the PSD; that is, there could be crossover of PSDs reported from dry-sieve analysis and LPSA for samples containing a relatively high fraction of fine particles. Here, we demonstrate that such crossover of PSDs could also occur strictly because of the shape of the particles. If the aspect ratio of the prolate spheroid is specifically set as 2 and that of square pyramid as 0.5, the PSDs from dry-sieve analysis and LPSA would be as shown in Figs. 5a and 5b. PSD from LPSA is greater than that from dry-sieve analysis for prolate spheroid (Fig. 5a), and PSD from dry-sieve analysis is greater than that from LPSA for square pyramid (Fig. 5b). When these particles are mixed together such that there is a higher concentration of prolate-spheroidal particles near the coarse end and higher concentration of square-pyramidal particles near the fine end, then there is a crossover of PSDs from dry-sieve analysis and LPSA, as shown in Fig. 5c. PSDs of Mixture of Calcium Carbonate and Silica Particles. Here, we analyze the PSDs of real particles that are of irregular shape. The objective was to use samples that have highly aspherical particles so that the PSDs from dry-sieve analysis and LPSA would be significantly different. With PSDs being different, the expected sand production in sand-retention tests (SRTs) would be different. Sand production in SRTs could be estimated by use of the models developed by Chanpura et al.

(2012, 2013a) and by Mondal et al. (2011, 2012) under the conditions of slurry test (representing gradual failure) and prepack test (representing hole collapse), respectively. The next step would be to perform an actual SRT and compare the estimated and experimental sand production and determine whether PSDs from dry-sieve analysis or from LPSA give a better match between predicted and experimental sand production, and thus to conclude which technique is relevant. We first searched for the availability of certain shapes of synthetic particles (e.g., ellipsoidal, pyramidal) in various size ranges applicable for both laser and sieve, much like the spherical glass particles described previously, except with different shapes. Unfortunately, we were not able to find such synthetic particles. We started considering real particles of different mineralogy under a microscope, and identified graded calcium carbonate and certain silica particles as potential candidates to create a mixture. Fig. 6 shows the PSDs obtained from dry-sieve analysis and LPSA for calcium carbonate particles (Fig. 6a), silica particles (Fig. 6b), and a mixture of calcium carbonate (8 mass%) and silica (92 mass%) particles (Fig. 6c). As can be seen from Figs. 6a and 6b, for both calcium carbonate and silica particles, the PSDs reported from LPSA are greater than those from drysieve analysis. Both samples were analyzed under a microscope, and they indeed had a large fraction of aspherical particles. When these particles were mixed, the PSD of the mixture also had a similar trend; specifically, PSD from LPSA is greater than that from dry sieve (Fig. 6c). The calcium carbonate particles were in the 100–500 lm range, and silica particles were in the 75–180 lm range. Although the LPSA and dry-sieve-analysis PSDs of the composite-silica particles shown in Fig. 6b exhibit significant differences, and thus in principle this mixture could be used for an SRT, predicted sand-production numbers for both PSDs were very small when either a 6-gauge (150 lm) or a 7-gauge (175 lm) wire-wrap screen (WWS) is used. Keeping in mind potential experimental error in measurements, we wanted to design the experiment for relatively large sand production in absolute terms for both PSDs and also wanted a case where the predicted sandproduction numbers differ significantly when dry-sieve-analysis

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Square-Pyramid-Shape Particles: Aspect Ratio = 0.5 100 90 80 70 60 50 40 30 20 10 0 100 1000 Particle Size (µm)

Spheroid Particles: Aspect Ratio = 2

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Spheroid + Square-Pyramid-Shape Particles Cumulative Percentage Retained

100 90 80 70 60 50 40 30 20 10 0 1000

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Particle Size (µm) Dry sieve

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

and LPSA PSDs are used in the models. In addition, we wanted to stay away from regions where the two distributions (laser and sieve) overlap as well as stay away from the region where the PSDs from both techniques change sharply. These are the reasons that we decided to add some larger carbonate particles (100–500 lm) to the silica sample to obtain the PSD in Fig. 6c. We then also added some amount of smaller (smaller than 62 lm) 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 than 62 lm) silica particles (15 mass%) are shown in Fig. 7. It can be seen from Fig. 6c that there is no crossover of drysieve-analysis and LPSA PSDs, whereas there is crossover when some amount of smaller (smaller than 62 lm) silica particles were added, as shown in Fig. 7. To analyze the cause of this crossover, PSDs of the mixture of calcium carbonate, larger silica, and smaller silica particles were calculated on the basis of individually measured PSDs (dry-sieve analysis and LPSA) of calcium

PSD of Calcium Carbonate Particles

PSD of Silica Particles

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PSD of Calcium Carbonate and Silica Particles Cumulative Percentage Retained

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Fig. 6—PSDs of: (a) calcium carbonate particles; (b) silica particles; and (c) mixture of calcium carbonate and silica particles. 168

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PSD of Calcium Carbonate, Larger Silica, and Smaller (

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Particle-Size-Distribution Measurement Techniques and Their Relevance or Irrelevance to Wire-Wrap-StandaloneScreen Selection for Gradual-FormationFailure Conditions Ke Zhang, Rice University; Rajesh A. Chanpura, Schlumberger; Somnath Mondal1, Chu-Hsiang Wu, and Mukul M. Sharma, University of Texas at Austin; and Joseph A. Ayoub and Mehmet Parlar, Schlumberger

Summary Sand-particle-size distributions (PSDs) are used for various purposes in sand control: for example, decision making between various sand-control techniques and sizing of the filter media (sand screens and/or gravel packs) through either rule of thumb or physical experiments or theoretical models. PSDs of formation-sand samples are also often used to generate “simulated” formation sand for laboratory experiments. The two most commonly used techniques for PSD measurements are sieve and laser. Although some engineers use one technique for no obvious or justifiable reasons, others use both techniques for measurements and do not know what to do with the data when significant differences exist in PSDs obtained from each technique. Although the inherent limitations of (and the differences between), these two techniques as well as other factors affecting the measurements are well-known, a systematic study as to which of these two techniques is relevant to sand-control-screen selection and why is lacking. In this study, we critically review the current practices in PSD determination and the use (and misuse) of the information obtained from these measurements, propose a methodology toward determining what is relevant under gradual-formation-failure conditions for wire-wrap screen, discuss when it should be used and why, and present initial experimental results that support our conclusions. Introduction Particle-size distribution (PSD) of formation sand for reservoirs requiring sand control is the sole information used when applying rules of thumb for sand-control-technique selection (Tiffin et al. 1998; Price-Smith et al. 2003), screen-size selection for standalone-screen (SAS) application (Coberly 1937), and gravel-size selection for gravel-pack application (Saucier 1974). Chanpura et al. (2012, 2013a) and Mondal et al. (2011, 2012) also use PSD of formation sand (and a specified acceptable sand production) for sizing screens for SASs on the basis of numerical and/or analytical models. Such models can result in accurate estimates of sand production in laboratory sand-retention tests (SRTs), provided that both the screen and the sand PSD are well-characterized. Therefore, the importance of an accurate determination of PSD of the formation sand is evident. Any inaccuracy in determining PSD could result in improper sand-control-technique selection and/or screen-/gravel-size selection. Even in cases when SRTs are used for screen sizing for SASs, unless the test is performed with the actual formation sand, inaccurate reporting of PSD could result in 1

now with Shell

C 2015 Society of Petroleum Engineers Copyright V

This paper (SPE 168152) was accepted for presentation at the SPE International Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, USA, 26–28 February 2014, and revised for publication. Original manuscript received for review 22 March 2014. Revised manuscript received for review 6 January 2015. Paper peer approved 31 March 2015.

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testing simulated sand that is not representative of the original formation sand, thus leading to incorrect screen-size selection. Dry-sieve analysis and laser-particle-size analysis are the two techniques that are most commonly used for determining PSD of formation sand. However, it is well-known that there are differences 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 in PSDs reported from these two techniques and recommend which technique is suitable to use under which conditions. Techniques for Particle-Size-Distribution (PSD) Determination As mentioned earlier in the study, dry-sieve analysis and laser particle-size analysis (LPSA) are currently the two types of particle-sizing techniques that are commonly used in the industry. We provide a brief description of these techniques, followed by a comparison 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 particles are first separated into individual grains and then cleaned, dried, and weighed. They are then passed through a stack of sieves in a shaker, with the coarsest sieve at the top and finest sieve at the bottom. Typically, the smallest sieve that is used in the dry sieve is 400 US mesh (37 lm). Sand particles that pass through the smallest sieve are collected in a pan. From the measured weight of the sand retained in each individual sieve, cumulative weight percent retained by each sieve size is calculated and plotted against sieve size on a semilogarithmic scale. Dry-sieve analysis was performed as per ISO 13503-2 (2006) in this work. LPSA. LPSA determines PSD of sand electronically by measuring the intensity of light scattered as a laser beam passes through a dispersed-particulate sample. The angle of scatter of the laser light is inversely proportional to the particle size. The angular intensity of light scattered is captured by a series of photosensitive detectors. The data are then processed and analyzed through the instrument software to calculate the particle sizes. In LPSA, sample dispersion is controlled by a range of wet- or dry-dispersion units, which ensure that the particles are delivered to the measurement area or the optical bench at the correct concentration and in a stable state. A dry-dispersion unit is ideally suited for measurement of powders, especially moisture-sensitive materials. Wet-sample dispersion units use a liquid dispersant, either aqueous or solvent-based, to disperse the sample. The liquid dispersant chosen has to be able to hold the sample in suspension through stirring. Any settling or floating of the particles will introduce errors in the laser-diffraction measurement. To keep the sample suspended and homogenized, it is recirculated continuously through the measurement zone. A wet-dispersion unit with June 2015 SPE Drilling & Completion

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

deionized water was used for LPSA in this study because samples consisted 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-sieve analysis and LPSA methods is in the way particle sizes are estimated by these techniques. The sieve measures the second-smallest dimension because of the way the particles orient themselves to pass through the opening given sufficient time. As opposed to the smallest dimension, a sieve emphasizes the second-smallest dimension because if the slot opening is the same size as the particle’s smallest dimension, the particle cannot pass through in the direction of its second-smallest dimension. A light-scattering device, such as a laser, measures various dimensions as the particles flow randomly through the light beam. It then calculates the equivalent diameter of a sphere that has the same volume as the particle; 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 LPSA is that in a sieve, a minimum 20 g of sample is used, whereas only a fraction of a gram of sample is used in LPSA. Thus, if the small amount of sample used in LPSA is not representative of the sample 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 larger silica particles, whereas in LPSA, such agglomeration of particles does not occur. This could lead to the dry-sieve analysis reporting larger sizes near the “fine” tail of the PSD, whereas the LPSA would show a longer “fine” tail. If the clay particles in the sample are of swelling or dispersive nature, then the fluid used in LPSA could affect the PSD (i.e., the PSD reported by the LPSA is sensitive to the fluid used for samples containing swelling-/dispersive-type clay particles). Thus, it is important to determine the mineralogy of formation-sand samples. Thus, for perfectly spherical particles, dry-sieve analysis and LPSA should provide exactly the same PSDs as long as the particles are within the applicability range of both techniques, the particles do not react with the fluid used in LPSA, and the smaller sample size used in the laser is representative of the larger sample used in the sieve. However, for nonspherical particles, the PSDs reported from dry-sieve analysis and LPSA would be different and the difference would depend upon the degree of asphericity of the particles. (Sphericity is the ratio of the surface area of a sphere, with the same volume as the given particle, to the surface area of the particle. Degree of asphericity means how far the value of sphericity is from unity.) Note that apart from these differences in PSDs from dry-sieve analysis and LPSA, there could also be differences in PSDs from different LPSA measurements depending on variables such as sonication time and amplitude (Ballard and Beare 2013). Table 1 summarizes some of the differences between drysieve analysis and LPSA. Dynamic Image Analysis. In addition to dry-sieve analysis and LPSA, there is another technique, dynamic image analysis,

which is also used for the determination of PSD. The CAMSIZER (2012) is one of the laboratory instruments for dynamic image analysis that uses the principle of digital-image processing and can measure a size range from 30 lm to 30 mm. It simultaneously determines PSD, particle shape, sphericity, aspect ratio, and other information from powders and granular materials. The sample is transported to the measurement zone by means of a vibratory feeder, where the particles drop between an extended-light source and two cameras. The projected particle shadows 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 longest dimension in each 2D projection is determined. Of all the 2D projections, the shortest (of the longest dimension in each 2D projection), xmin, and the longest, xmax, dimensions are determined. The aspect ratio of that particle is then xmax/xmin. Sphericity is reported as the square of circularity, which is defined as the ratio of the perimeter of the circle (of the same 2D projection area as the particle) to the perimeter of the particle (also in the same 2D projection); that is, sphericity ¼ 4pA/P2, where A is the area and P is the perimeter of the particle in 2D projection. Note that the calculation of sphericity given here is different from how it is normally defined. Sphericity is normally defined as the ratio of the surface area of a sphere (equal volume as 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 of the perimeters. The volume calculation in dynamic image analysis is derived from an assumed particle shape. One of the manufacturers of the dynamic image analyzer uses a prolate-spheroidal model to calculate the volume of the particles from the 2D images, regardless of the actual geometry of the particles. Because of this approximation, the PSD reported matches neither laser nor sieve data unless the particles are either spherical (in which case all three techniques should match subject to comments made upon other potential effects discussed previously) or prolate spheroid (spheroid in which the polar axis is greater than the equatorial diameter, in which case it should match with dry sieve). Particle-Size Distribution (PSD) of Glass Beads As mentioned previously, for perfectly spherical particles, drysieve analysis and laser-particle-size analysis (LPSA) should give exactly the same particle sizes if the particles do not interact with the fluid used in LPSA and the particle sizes are within the range of both techniques: larger than 37 lm and smaller than approximately 1000–2000 lm. The glass beads were inert so they do not swell or disperse when in contact with the fluid used in the laser measurement. So, as a first step to calibrate both instruments and to ensure that everything is working properly and the data collected are indeed accurate, PSDs of synthetic, spherical glass beads (Fig. 1) were obtained by use of both techniques. As expected, dry-sieve analysis and LPSA gave almost-identical PSDs for two different samples of spherical glass beads used (Fig. 2).

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Effect of Particle Shape Of the possible causes for the differences in particle-size distributions (PSDs) reported from dry-sieve analysis and laser particlesize analysis (LPSA) mentioned previously, the effect of sample size is not an issue if a proper sample-splitting method is followed. In addition, if the particles are not of swelling or dispersive type, then there is no dependence of PSD on the fluid used for LPSA. Therefore, the most-important reason for the difference in PSDs from dry-sieve analysis and LPSA is the shape of the particles. Here, we analyze the effect of shape of the particles on PSDs reported from dry-sieve analysis and LPSA. First, we show the effect of shape on the PSD theoretically for a few regularshaped particles. Then, we analyze the PSDs of actual samples of irregular shape.

Fig. 1—Microscopic image of synthetic glass beads, with magnification of approximately 80X.

Effect of Sampling For Laser Particle-Size Analysis (LPSA) With spherical glass beads of the size range selected, even though dry-sieve analysis and LPSA should provide almost-identical particle-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 LPSA is crucial to accurate determination of PSD by laser measurement. If the sample is selected randomly by hand, there is a high chance that the PSD from the LPSA will be different from the dry-sieve analysis (Fig. 3a). However, if a sample splitter is used instead, a representative sample can be obtained for LPSA that will give a PSD almost identical to that of dry-sieve analysis (Fig. 3b). For the PSDs shown in Fig. 2, a sample splitter was used to obtain samples for LPSA.

Theoretical PSDs of Regular-Shaped Particles. For a triaxial ellipsoid, three axes a, b, and c are different from one another; suppose a < b < c. The dry sieve would always take the secondsmallest dimension b as the particle size, whereas LPSA would give a larger, a smaller, or even the same particle p size ﬃﬃﬃﬃﬃ as the dry sieve, depending on the relationship between b and ac: pﬃﬃﬃﬃﬃ • If b < pac ﬃﬃﬃﬃﬃ, LPSA gives a larger size. • If b > pac ﬃﬃﬃﬃﬃ, dry sieve gives a larger size. • If b ¼ ac, dry sieve and LPSA give the same size. For a prolate spheroid (a ¼ 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, square pyramidal, and conical. Given that dry-sieve analysis reports the second-smallest dimension as the particle size and LPSA reports the equivalent diameter of a sphere (of the same volume as the particle) as the particle size, the PSDs are calculated for spheroidal-, cylindrical-, square-pyramidal-, and conical-shaped particles for different aspect ratios (Fig. 4). As mentioned previously, for a prolate spheroid, LPSA always give a larger size than dry-sieve analysis, irrespective of the PSD of Glass Bead Sample B 100

Cumulative Percentage Retained

Cumulative Percentage Retained

PSD of Glass Bead Sample A 100 80 60 40 20 0 1000

100 Particle Size (µm) Dry sieve

80 60 40 20

10

0 1000

LPSA

100 Particle Size (µm) Dry sieve

10

LPSA

Fig. 2—PSD of spherical glass beads: (a) Sample A; (b) Sample B. PSD of Split LPSA Sample Cumulative Percentage Retained

Cumulative Percentage Retained

PSD of Random LPSA Sample 100 90 80 70 60 50 40 30 20 10 0 1000

100 Particle Size (µm) Dry sieve

LPSA

10

100 90 80 70 60 50 40 30 20 10 0 1000

100 Particle Size (µm) Dry sieve

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LPSA

Fig. 3—PSD of spherical glass beads: (a) random sample; (b) split sample. 166

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Cylindrical Particles

100

100

Cumulative Percentage Retained

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Prolate-Spheroid Particles

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80 60 40 20 0 1000

100 Particle Size (µm)

10

(a)

80 60 40 20 0 1000

100 Particle Size (µm)

10

(b) Dry sieve

LPSA_L/D = 2

LPSA_L/D = 3

Dry sieve

Dry sieve

LPSA_L/D = 2

100 90 80 70 60 50 40 30 20 10 0 1000

Cumulative Percentage Retained

Cumulative Percentage Retained

100

10

Particle Size (µm)

(c)

LPSA_L/D = 1

Conical Particles

Square-Pyramid-Shape Particles 100 90 80 70 60 50 40 30 20 10 0 1000

LPSA_L/D = 0.5

LPSA_L/D = 1

LPSA_L/D = 2

(d) LPSA_L/D = 3

100

10

Particle Size (µm) Dry sieve

LPSA_L/D = 1

LPSA_L/D = 2

LPSA_L/D = 3

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

aspect ratio (Fig. 4a). For the other three shapes, depending on the specific aspect ratio, LPSA gives a larger, a smaller, or the same size as dry sieve. Although this is a theoretical analysis of expected PSDs from sieve and laser for differently shaped particles, Fig. 4 also shows microscopic images of real sand particles that closely resemble the shapes considered (i.e., such shapes indeed exist in real formation particles). Crossover of PSDs From Dry-Sieve Analysis and LPSA. As mentioned previously, if a sample contains a high fraction of fine (e.g., clay) particles, then sticking of fine particles to the surface of larger silica particles could result in dry-sieve analysis reporting larger sizes near the “fine” tail even if LPSA reports larger sizes near the “coarse” tail of the PSD; that is, there could be crossover of PSDs reported from dry-sieve analysis and LPSA for samples containing a relatively high fraction of fine particles. Here, we demonstrate that such crossover of PSDs could also occur strictly because of the shape of the particles. If the aspect ratio of the prolate spheroid is specifically set as 2 and that of square pyramid as 0.5, the PSDs from dry-sieve analysis and LPSA would be as shown in Figs. 5a and 5b. PSD from LPSA is greater than that from dry-sieve analysis for prolate spheroid (Fig. 5a), and PSD from dry-sieve analysis is greater than that from LPSA for square pyramid (Fig. 5b). When these particles are mixed together such that there is a higher concentration of prolate-spheroidal particles near the coarse end and higher concentration of square-pyramidal particles near the fine end, then there is a crossover of PSDs from dry-sieve analysis and LPSA, as shown in Fig. 5c. PSDs of Mixture of Calcium Carbonate and Silica Particles. Here, we analyze the PSDs of real particles that are of irregular shape. The objective was to use samples that have highly aspherical particles so that the PSDs from dry-sieve analysis and LPSA would be significantly different. With PSDs being different, the expected sand production in sand-retention tests (SRTs) would be different. Sand production in SRTs could be estimated by use of the models developed by Chanpura et al.

(2012, 2013a) and by Mondal et al. (2011, 2012) under the conditions of slurry test (representing gradual failure) and prepack test (representing hole collapse), respectively. The next step would be to perform an actual SRT and compare the estimated and experimental sand production and determine whether PSDs from dry-sieve analysis or from LPSA give a better match between predicted and experimental sand production, and thus to conclude which technique is relevant. We first searched for the availability of certain shapes of synthetic particles (e.g., ellipsoidal, pyramidal) in various size ranges applicable for both laser and sieve, much like the spherical glass particles described previously, except with different shapes. Unfortunately, we were not able to find such synthetic particles. We started considering real particles of different mineralogy under a microscope, and identified graded calcium carbonate and certain silica particles as potential candidates to create a mixture. Fig. 6 shows the PSDs obtained from dry-sieve analysis and LPSA for calcium carbonate particles (Fig. 6a), silica particles (Fig. 6b), and a mixture of calcium carbonate (8 mass%) and silica (92 mass%) particles (Fig. 6c). As can be seen from Figs. 6a and 6b, for both calcium carbonate and silica particles, the PSDs reported from LPSA are greater than those from drysieve analysis. Both samples were analyzed under a microscope, and they indeed had a large fraction of aspherical particles. When these particles were mixed, the PSD of the mixture also had a similar trend; specifically, PSD from LPSA is greater than that from dry sieve (Fig. 6c). The calcium carbonate particles were in the 100–500 lm range, and silica particles were in the 75–180 lm range. Although the LPSA and dry-sieve-analysis PSDs of the composite-silica particles shown in Fig. 6b exhibit significant differences, and thus in principle this mixture could be used for an SRT, predicted sand-production numbers for both PSDs were very small when either a 6-gauge (150 lm) or a 7-gauge (175 lm) wire-wrap screen (WWS) is used. Keeping in mind potential experimental error in measurements, we wanted to design the experiment for relatively large sand production in absolute terms for both PSDs and also wanted a case where the predicted sandproduction numbers differ significantly when dry-sieve-analysis

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Square-Pyramid-Shape Particles: Aspect Ratio = 0.5 100 90 80 70 60 50 40 30 20 10 0 100 1000 Particle Size (µm)

Spheroid Particles: Aspect Ratio = 2

Cumulative Percentage Retained

Cumulative Percentage Retained

100 90 80 70 60 50 40 30 20 10 0 1000

Stage:

100

10

Particle Size (µm) Dry sieve

Dry sieve

LPSA

10

LPSA

Spheroid + Square-Pyramid-Shape Particles Cumulative Percentage Retained

100 90 80 70 60 50 40 30 20 10 0 1000

100

10

Particle Size (µm) Dry sieve

LPSA

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

and LPSA PSDs are used in the models. In addition, we wanted to stay away from regions where the two distributions (laser and sieve) overlap as well as stay away from the region where the PSDs from both techniques change sharply. These are the reasons that we decided to add some larger carbonate particles (100–500 lm) to the silica sample to obtain the PSD in Fig. 6c. We then also added some amount of smaller (smaller than 62 lm) 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 than 62 lm) silica particles (15 mass%) are shown in Fig. 7. It can be seen from Fig. 6c that there is no crossover of drysieve-analysis and LPSA PSDs, whereas there is crossover when some amount of smaller (smaller than 62 lm) silica particles were added, as shown in Fig. 7. To analyze the cause of this crossover, PSDs of the mixture of calcium carbonate, larger silica, and smaller silica particles were calculated on the basis of individually measured PSDs (dry-sieve analysis and LPSA) of calcium

PSD of Calcium Carbonate Particles

PSD of Silica Particles

(a)

100 90 80 70 60 50 40 30 20 10 0 1000

Cumulative Percentage Retained

Cumulative Percentage Retained

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100 Particle Size (µm) Dry sieve

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(b)

LPSA

100 Particle Size (µm) Dry sieve

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LPSA

PSD of Calcium Carbonate and Silica Particles Cumulative Percentage Retained

100 90 80 70 60 50 40 30 20 10 0 1000

(c)

100 Particle Size (µm) Dry sieve

10

LPSA

Fig. 6—PSDs of: (a) calcium carbonate particles; (b) silica particles; and (c) mixture of calcium carbonate and silica particles. 168

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PSD of Calcium Carbonate, Larger Silica, and Smaller (