Description: The labelling of shaker screens has been a problem. Existing mesh count designations do not adequately describe a shaker screen’s potential separation performance. Consequently, it is difficult to make an informed decision when selecting shaker screens. The establishment of a standardized, performance-based designation system has been hindered largely by the time, expense and difficulty in deriving absolute screen separation efficiencies from full scale laboratory testing.
This topic introduces a technique which overcomes this problem by relating the separation efficiency potential of a shaker screen to a volume-equivalent distribution of its mesh sizes. Magnified, computer-enhanced visual images of screen apertures were measured using a PC-based image analyzer system. An equivalent volume distribution was t.hen derived from this data to yield a curve corresponding to a grade efficiency or percent-separated function. These equivalent volume distributions were compared to experimental percent.-separated values for square, oblong and layered mesh screens to confirm the viability of the image analysis technique.
The separation performance of a given shale shaker is primarily a function of its screen cloth aperture dimensions. Manufacturer commonly designate these shaker screens by mesh count, which is the number of openings per lineal inch of screen cloth. Unfortunat.ely, mesh count does not delineate the actual opening dimensions of the screen since opening size is a function of both mesh count and wire diameter: D = (1/ −)
Layered “sandwich” screens further complicate this matter. The second underlying cloth’s wires may partially block the apertures in the top layer to result 1I1 a myriad of effective apert.ure dimensions. The layered screen is commonly assigned an equivalent U.S. test sieve number by the manufacturer. Separation efficiency measurements for these screens have shown the assigned designations to be predominantly optimistic.
Given the wide variety of screen cloth compositions used in the industry today, the opening size (and the potential particle size a screen may remove) can rarely be assumed from mesh count information alone. Therefore, full-scale testing under controlled conditions has been required to measure the separation performance of our primary solids removal device, the shale shaker. This is a time-consuming, expensive proposition and the facilities available for this type of determination are limited. Further-more, several shaker and feed particle-related factors negatively impact the repeatability of experimental separation measurement.
This topic describes how the separation efficiency potential of shaker screens can be conceptually represented by a volume equivalent distI-ibut.ion of aperture sizes as a solution to this problem. Because only screen apertures are analyzed, these distributions are absolute for a given screen composition, allowing comparisons to be made across the spect.rum of screen compositions used on shale shakers today.
Separation Efficiency of Shaker Screens
The separation efficiency of our solids control devices is defined by the mass or volume percent of particles removed as a function of particle size. The separation efficiency calculated for each particle diameter x yields a curve called the percent-separated, or grade efficiency, function. This curve is independent of any feed particle size distribution and gives the probability of removal for any specific size of particle.
The grade efficiency of a given shaker and screen combination is determined experimentally from the feed, effluent and discharge mass flow rates, and the particle size distributions of these streams. Technically, it is necessary to sample only two of the three streams; the third is usually sampled to verify conservation of mass.
The grade efficiency of the screen for a given size range, Xl > X2, is then computed by:
The point on the percent-separated curve most often quoted is the d50 , or “cut point.” The d50 serves as a single value indicator of a device’s separation performance. This is the size corresponding to a 50% probability of separation; that is, the particle size at which 50 volume percent of the particles of that specific size will likely be removed.
Unfortunately, separation values obtained through experimental tests are not absolute for a given screen. Several factors will alter the percent-separated curve:
- The relationship between the shape of the feed solids and the shape of the screen openings: If the feed particles are uniformly spherical, the size separated by a rectangular screen aperture will be a function of its minor axis dimension. Similar results could not be expected if splinter-shaped particles were presented to the screen.
- The conveyance velocity, contact time and loading rate of the solids on the screen:6 This is primarily a function of shaker dynamics. Consider a screen with a wide distribution of aperture sizes. The probability of a particle finding a hole of sufficient size to pass through will depend on the time spent on the screen and on the amount of interference by other particles.
- The degree of agglomeration with other fine particles and “piggy-backing” of fine solids with coarse solids: In the presence of viscous drilling fluids, surface tension forces tend to cause the wet particles to cling together. When these attractive forces are greater than the vibratory force imparted by the shaker, the massed solids tend to act as a single large particle and may not pass through the screen.
- Sampling technique and particle sizing method: The size of the samples and the location they are taken will affect the accuracy and repeatability of the results. Particle sizes are not measured directly by sieves, but implied by their opening size. Laser diffraction devices use algorithms to compute particle volumes and calculate equivalent spherical diameters of non-spherical particles. Thus, a particle which passes through a sieve may have a spherical diameter larger than the sieve aperture size.
- Blinding or plugging of the screen cloth: A wide distribution of feed particle sizes is necessary to obtain accurate separation data. This creates ideal conditions for plugging by “near-size” particles. The resultant decrease in hole sizes available for subsequent feed particles will yield optimistic separation performance data.
- Grinding of the solids in the pool region of linear motion shakers with high deck angles and low conveyance velocities.
The shape distribution of drill cuttings is not particularly well-represented in the laboratory. Drill cuttings do not conform to a specific particle shape. They are represented in the laboratory by typically spherical sand grains. This results in optimistic separation efficiencies for rectangular screen apertures. Also, shaker dynamics are not constant for all shakers and screen panels are rarely interchangeable. This necessitates testing each shaker and screen combination individually. Multiple replicate samples are normally collected and analyzed during a test of each screen. The high cost in time and resources, the lack of facilities, and the variability of the results has made the establishment of a definitive ranking system for screens based on experimental separation data highly unfeasible.
Relative Separation Efficiency Potential
This problem demands another approach. Since our primary interest is in the relative separation performance of shaker screens, a more appropriate tack would be to characterize the screen by its distribution of hole sizes, independent of shaker and feed particle variables. This relative grade efficiency potential is based on the concept that the probability of particles with an equivalent spherical diameter of x being removed by the screen is directly related to the volume percent of openings of that size or smaller occurring in the screen. Of course, the warp and shute dimensions of a screen aperture cannot be equated to separation efficiency potential on a volume or mass basis until each aperture is adequately represented by an equivalent volume.
Consider a perfectly square aperture with warp and shute openings of La and Lb respectively (Figure 1). Correctly oriented in azimuth, the largest volume of solid which will pass through these dimensions is a cube with a volume given by: Vc = La * Lb * Lh.
Although a square prism (Lh > La= Lb) will possess a larger volume and may pass through a square aperture if correctly oriented, its orientation is unstable with respect to its center of gravity. If it were oriented to produce the lowest center of gravity, it would not pass through the square aperture.
Regardless, perfect azimuthal orientation of a cube is realistically unlikely. A square opening is represented best by a sphere, since it will fit through the opening regardless of orientation (Figure 1). However, screen apertures are rarely square. Given a rectangular aperture (Figure 2), where la is the major axis length and lb is the minor axis length, the maximum volume defined by the aperture dimensions becomes: Vr = La * Lb2
Clearly, a sphere will not adequately represent the maximum volume which may pass through this aperture, since its volume is a function of only the minor axis length, Lb (Figure 2). A more representative shape which may be considered self-orienting with respect to azimuth is an ellipsoid (Figure 3). The volume of the ellipsoid, with respect to aperture dimensions La and Lb, is calculated by:
When La = Lb the equation is the same as that for a sphere. Thus, the ellipsoidal volume equation is valid for both rectangular and square mesh apertures, and more realistically addresses the relationship between aperture shape and separation potential when the feed particle shape is undefined.
Particle volumes are normally represented by an equivalent spherical diameter. Letting Ve = Vs as illustrated in Figure 4, the equation for a sphere can be rearranged to solve for an equivalent spherical diameter:
Each aperture in the screen cloth may now be represented by a spherical diameter corresponding to an equivalent ellipsoidal volume. Once a representative sample of apertures is dimensionally analyzed, a volume distribution curve can be generated to characterize a screen’s separation potential.
Dimensional Analysis of Screens
Each screen aperture must be measured for major and minor axis length. An image analysis system driven by a personal computer is necessary to expedite sampling and dimensional analysis. Image analysis software performs dimensional analyses of raster graphics images produced by a video camera. Output may be stored in ASCII or spreadsheet files.
The shaker screen analyses presented in this paper used a video camera mounted on a microscope to provide magnified images of screen cloth. Magnification is dictated by average aperture size and depth of field requirements. Samples were backlit, to improve contrast between the apertures and wire. Images were collected in a diagonal path across the screen to optimally sample the range of aperture shapes and sizes present in the screen. The change in average radius was checked as the sample size increased. The data set was considered complete and statistically representative once the running average did not change with additional samples. Depending on the variation in aperture size, from 300 to 3500 apertures were analyzed for each screen composition. Layered screens with inherently wide distributions of hole sizes and shapes typically demand a sample size greater than 1000 apertures to be statistically representative.
The Martin’s Radii from each aperture’s center of gravity at 0, 90 , 180, and 270 degrees orientation were measured. The horizontal and vertical dimensions of each aperture are the sum of the 0 and 180 degree radii, and the 90 and 270 degree, respectively. A computer spreadsheet program was used to calculate each aperture’s major and minor axis length, ellipsoidal volume, and equivalent spherical diameter. The aperture dimensional data were then sorted by ascending ellipsoidal volume to generate a curve of cumulative volume percent as a function of equivalent spherical diameter.
The screen aperture dimensions measured by image analysis are strictly a function of the amount of light passing vertically through the screen cloth. For example, Dutch weaves have the parallel wires in one direction touching each other. This type of weave cannot be analyzed since light will not pass vertically through the screen. Image analysis is therefore restricted to the open weave cloth commonly used in oilfield screen compositions.
Because the video image is two-dimensional, there is some inherent discrepancy between the actual opening dimensions and those measured by image analysis in layered screen compositions. Apertures created by interference from the second underlying layer may be larger on the bias than they appear from the plan view. This error could become significant as the resultant aperture dimensions become smaller than the wire diameter of the top screen cloth.
However, the type of cloth used in layered screens mitigates the impact of this error. The performance goal of screen manufacturers is to maximize the liquid throughput capability, or conductance of a screen for a given particle size to be separated. This is accomplished by minimizing wire diameter and increasing mesh count for a given aperture size. The result is a thinner screen with better conductance. Triple layer screen compositions rely on very fine wires in the first two layers to maintain good fluid conductance properties. The second, slightly coarser layer of cloth acts primarily as a buffer between the fine top layer and the third extremely coarse backing cloth to maintain acceptable screen life. A secondary benefit is realized by the reduction in average aperture dimensions and cut point, because the screening layers are assumed to remain in contact.
The dimensional error caused by the bias angle of the aperture created by interference is primarily a function of the top layer’s thickness. As the wire diameter of the top layer is reduced relative to its aperture size, the highly biased apertures created between the top two layers become increasingly insignificant on an equivalent volume basis. The two screening layers effectively act as a single layer of cloth. The bottom backing cloth is eliminated from the analysis of triple layer screens because the interference is infrequent and the standoff created by its large wire diameters will yield highly biased apertures of sufficient size to permit the passage of particles which fit through the resultant apertures of the top two layers. In practice, a screen with relatively large wire diameters for a given aperture size is not used as the top component of triple layer screens because of the detrimental effect on liquid throughput. The insignificance of any dimensional error inherent in the image analysis method for practical screen compositions is substantiated by the comparative results presented in this paper.
Equivalent ellipsoidal volume distribution curves were generated from image analysis data for a range of single mesh screens (Figure 5) and layered screens (Figure 6). The dimensional specifications of these screens appear in Tables 1 and 2. As expected, the single mesh screens exhibit a narrow range of hole sizes; the variation reflects the weaving tolerance of the manufacturing process. Layered screen apertures exhibit a much wider distribution of hole sizes. This distribution is related to the frequency of interference by the adjacent underlying screen cloth.
The image analysis ellipsoidal volume distribution curve is compared to experimental percent-separated curves from sieve analysis and laser diffraction analysis for a market grade 100 x 100 mesh screen in Figure 7 and a layered 210 screen in Figure 8. The experimental measurements were taken in the laboratory using sand in bentonite and water slurry. The difference in separation efficiencies between the two experimental curves in each figure highlights the difficulty in producing an absolute percent-separated curve for a given screen. Despite the narrow hole size distribution present in the market grade 100 x 100 mesh screen, the experimentally measured percent-separated curves display a decreasing slope as percent-separated values approach 0 and 100 percent. This may be explained in part by the inherent measurement inaccuracy manifested by increasingly minute differences in particle size distributions between the feed and discharge streams and the feed and effluent streams as separation efficiencies approach these points. Also, the shaker and particle shape factors discussed previously tend to decrease the slope of the percent-separated curve. The wide distribution of hole sizes present in the layered screen tends to mask this effect. In absolute terms, the hole size distribution curve produced by image analysis characterizes the relative separation potential of the screen more accurately because it is unaffected by these factors.
Figure 9 compares the image analysis d50 values (IA d50) to the range of experimental d50 values collected from laboratory and field tests. The IA d50 values generally fall within the range of the experimental measurement results. Equally significant, the ranking of the screens’ separation performance is also in agreement.
In Figure 10, the percent-separated data from one set of full-scale experimental laboratory measurements are compared to image analysis hole size distributions. Particle sizes were measured by wet sieve analysis. The d50 values from this experimental data set are generally optimistic compared to the range of the doo sizes measured in other tests (Figure 9).
The separation range of each curve is represented by the spherical diameters falling between the dl6 and d84 values. Other solids control devices such as the centrifuge and hydrocyclone exhibit log normal separation efficiency curves. Although no attempt has been made to typify the distribution curves appearing in this paper, the dl6 and d84 are reported to represent the sharpness of the expected cut.
The spread between the d16 and d84 points exhibited by this experimental data for the single mesh screens may be attributed to the viscous effects of the mud on the attraction between the sand grains. With a thinner carrier fluid and/or longer contact time on the shaker, the sand grains would behave more as independent particles; the spread between dl6 and d84 would be reduced, and the d50 size would shift closer to the d84 value.
Again, the screen separation ranking is in close agreement between the two methods. An exception occurs with the 80 x 40 mesh screen. It is explained by the spherical sand grains reflecting only the minor axis dimension of the screen apertures. This is supported by the the similarity between the market grade 80 x 80 and the 80 x 40 experimental separation data.
Applications in Screen Design
The potential for applying the image analysis technique to shaker screen design and selection is readily apparent. Since only the screen cloth is analyzed, hole size distribution curves can be generated quickly and economically from image analysis data. A typical analysis requires less than 20 minutes. The separation potential of new layered screen combinations can be confirmed from small samples of cloth without the expense of fabricating panels, mixing sand slurries, and performing experimental tests.
Table 1-Measured Screen Cloth Dimensions, Single Layer Screens
|NOMINAL DESIGNATION||MESH COUNT(openings/inch)||WIRE DIA.(microns)||OPENING SIZE (microns)|
Table 2-Measured Screen Cloth Dimensions, Layered Screens.
|NOMINAL DESIGNATION||MESH COUNT(openings/inch)||WIRE DIA.(microns)||OPENING SIZE (microns)|
When the separation potential is considered in conjunction with screen conductance the two primary performance specifications of a screen may be predicted to optimize screen compositions. Although screen service life must also be considered, these performance specifications will allow the adjustment of product lines to eliminate poor performers or fill gaps in the separation and conductance combinations covered by the available screens.
Table 3 summarizes the separation efficiency potential and conductance performance of common oilfield screens. Beside each screen designation is a U.S. test sieve number with an average opening size equivalent to the IA d50 value. This provides a simple mesh count scale to rank the mean separation efficiency potential of screens and permits an informed selection of shaker screens to be made at the rig.
Table 3-Performance Characteristics of Selected Screens.
|NOMINAL DESIGNATION||U.S. SIEVE EQUIVALENT||IA d50 (microns)||IA d16 (microns)||IA d84 (microns)||CONDUCTANCE (kD/mm)|
- Ranking shaker screens by separation efficiency values measured by full-scale experimental testing is not practical: Facilities are limited, the tests are time-consuming and expensive, and the results are subject to several uncontrollable factors such as shaker dynamics, feed particle shape and screen blinding.
- Shale shaker screens can be characterized by their equivalent ellipsoidal volume distributions of aperture sizes. Each distribution is absolute for a given screen and is unaffected by shaker dynamics and feed particle variables.
- The d50 values of ellipsoidal volume distribution curves correlate well with experimentally measured grade efficiency d50 values for both single mesh and multilayered screen compositions.
- The relative separation performance of a given shaker screen can be directly related to the equivalent volume distribution of its apertures, all other factors being equal.
- Image analysis provides a viable means of dimensionally analyzing screen apertures quickly and economically. Hole size distribution curves generated through image analysis can be created in a fraction of the time required by full-scale experimental testing.
- The relative separation efficiency potential of new layered screen combinations can be predicted by the image analysis technique before fabrication. The speed and predictive ability of this method are both desirable features in screen design and quality control applications.
- Shaker screen characterization through image analysis provides the absolute separation efficiency potential values necessary to establish a performance-based screen designation system. The manufacturer’s mesh count label can be linked to both separation efficiency and conductance performance.
Nomenclature d = wire diameter, inches D = average opening size, inches d50 = mean particle size removed, μm d16 = particle size with 16% removal, μm d84 = particle size with 84% removal, μm Ex1x2 = separation efficiency of size range, La = major axis length, μm Lb = minor axis length, μm Lh = height of solid, μm Mwd = mass flow rate of wet discard solids, kg/min Mwf = mass flow rate of wet feed solids, kg/min n = number of apertures per inch Va = volume of cube, μm3 Ve = ellipsoidal volume, μm3 Vr = volume of square prism, μm3 Vs = spherical volume, μm3 Wt%ds = weight percent of dry discard solids Wt%fs = weight percent of dry feed solids X= equivalent spherical diameter, μm