The original plan for experimental study was to determine how flow capacity of a shale shaker was affected by
- Vibrator frequency and amplitude.
- Vibrator placement.
- Angle of the screen with respect to horizontal.
- Screen size, type, and area.
- Height above the screen of the fluid weir.
- Fluid properties.
To handle these variables, an experimental vibrating screen (Fig. 1) was constructed, with approximately 4.5 sq/ft (0.418 m²) of active screen surface. A specially designed inline hydraulic vibrator was used that had the ability to impart controlled peak accelerations to the deck and shaker screen cloth varying from 0 to 15 g, with a frequency selectable over a range from 0 to 200 Hz in increments of 1 Hz. As shown in Fig. 1, the position of the vibrator could be varied over the length of the shaker deck, and the vibrator angle could be varied from normal to the screen to parallel with the screen. In addition, a 60-Hz fixed-frequency, electrically operated, unbalanced-rotor vibrator was available that could replace the in-line vibrator.
Shale shaker had the ability to impart approximately 8-g peak acceleration and could be varied in position over the complete deck length. Four elastomeric shear mounts were used at both ends on both sides of the shaker deck to isolate the deck from the supporting structure.
As shown in Fig. 1, provisions were made to vary the deck angle from 0 to 5° below horizontal, and weir height could be varied from 2 to 15 in. (5.08 to 38.1 cm) above the screen cloth. The screen cloth itself could be changed easily, and a variety of mesh sizes and types were available for testing.
To monitor deck motion accurately, three pairs of piezoelectric accelerometers were mounted at approximately screen level on one side of the deck at the top, middle, and bottom as shown in Fig. 1. In each pair, one accelerometer measured the acceleration component normal to the screen, and one measured the component parallel with the screen. The time-varying accelerations from all six sensors were recorded by means of an oscillographic recorder. Drilling fluid, with selected amounts of sand to simulate drilled solids, was mixed continuously with fluid jet mixers in a 75-bbl (11.92-m3) tank below the vibrating screen.
This slurry was fed by a centrifugal pump to the vibrating screen through a flow adjustment valve and a magnetic flow-meter. The distance along the screen to the point where the fluid disappeared through the screen cloth (liquid endpoint, Fig. 1) was controlled by means of the adjustment valve. This distance, then, determined the feed flow rate, which was recorded on the oscillograph with the accelerometer data.
Before an analysis of fluid flow and solid-particle movement can be performed for a shaker screen, it is essential that the screen cloth motion be known. Fig. 2 shows a schematic diagram for dynamic analysis of a generalized vibrating deck using three degrees of freedom: the horizontal and vertical displacement of the deck center of gravity and the rotation of the deck about the center of gravity.
The equations of motion were written assuming small angles of deck rotation and linear deck-mounting springs, such that the system of equations was completely linear. Although a linear analysis might not always hold, especially for elastomeric mounts, it was deemed sufficient for this work. The techniques used in derivation of the equations of motion are standard and can be found in most advanced vibration test books.
Representative results are shown in Figs. 3 and 4. These results used the 60-Hz rotary vibrator at two different positions on the vibrating deck. Position of the vibrator parallel with the screen surface is measured from the center of the middle vertical accelerometer to the center of the rotary vibrator. The position of the vibrator normal to the screen was fixed at approximately 12 in. (30.48 cm) above the screen surface. The plots labeled “top,” “middle,” and “bottom” represent the accelerations at the three accelerometer locations shown in Fig. 1, where “top” refers to the location nearest the fluid tank, and so on. The “top” and “bottom” accelerometer pairs are located at the upper and lower edges of the screen surface, and the “middle” accelerometer pair is located halfway between these. All accelerometers are on a level equal to that of the screen surface. The directions of rotation are clockwise around the elliptical patterns in Figs. 3 and 4.
The closed curves in these figures present computer model results, while the points represent experimentally obtained data. The discrepancies are thought to be due to the linearized analysis used in the model. Observe that when the vibrator position is changed to a location further down the vibrating deck, changing from the position in Fig. 3 to that in Fig. 4, the elliptical patterns all tilt further down the deck, indicating increased conveying speed of particles along the screen. The important point is that for a given deck configuration, vibrator placement is an extremely important consideration in determining screen motion and, thus, fluid and particle motion.
In contrast to the heuristic approach taken in most present practice of vibrating deck design, a suitable dynamic description of the moving screen is essential to understanding the solids-separation process.
The flow of fluid down an inclined screen can be treated as a type of incompressible, spatially varied, open-channel flow.For in-line vibration, these accelerations were taken as averages of the fundamental sinusoidal components of accelerations determined from the signals from the three normal and three parallel accelerometers shown in Fig. 1.
Because any particles removed from the fluid by the screen also must be conveyed off the screen to allow room for more fluid to pass through, it becomes necessary to consider available results from the vibratory conveying literature.
if all terms in the argument for Fare held constant, particle-conveying velocity is inversely proportional to frequency. This is extremely important, because it indicates that the so-called “high-speed” shale shakers are not as effective as lower-speed shakers for moving particles off the screen, other factors being equal. In screening heavy-solids loads, this may mean that at high frequencies solids cannot be moved off the screen fast enough to clear the screen for more feed fluid. Of course, the screen could be tilted downward to increase the conveying speed, but this would decrease the fluid-handling capacity of the screen, as indicated in Figs. 5 and 6.
To visualize the effect, consider the photographs in Fig. 11, which show the effect of varying frequency on the ability of the screen to handle flow. For these results, the in-line vibrator was placed to vibrate through the center of gravity of the screen deck and normal to the screen, the deck angle 0 was 100, the weir height dT was 2 in. (5.08 cm), and the screen was a “layered” screen having a median cut point near that of the sand in the drilling fluid.
The flow rate was adjusted by hand in an attempt to bring the “average” liquid endpoint to the middle pair of studs, or tension bar retainers, shown in the photographs. Observe that as the frequency was decreased from 80 to 20 Hz, the pattern of the discharged sand changed from broad strips to individual agglomerates, thus uncovering the screen for more fluid to pass through. The broad bands of sand form at higher frequencies because the mean conveying speed of the sand particles is low. The accelerations given in each photograph are the averages of the root-mean-square accelerations from each of the three vertical accelerometers shown in Fig. 1. Because of limitations in the in-line vibrator, it was not possible to keep the accelerations the same for all frequencies. However, because particle-conveying speed increases with increasing normal screen acceleration, 25 the flow rate at 80 Hz would have been smaller than 178 gal/min (11.23 dm³ / s) if the acceleration were reduced to that for the other frequencies, and the flow rate at 20 Hz would have been larger than 368 gal/min (23.22 dm³ / s) if the acceleration had been increased.
When a drilling fluid with drilled solids flows through a screen, effects occur in addition to those considered previously. In the first place, those particles considerably larger than the screen pores will tend to cover the openings, thus reducing the effective screening area for the fluid and smaller particles to pass through.
This effect, of course, would increase as the amount of such particles in the fluid increased, as the feed flow rate increased, and as the screen conveying velocity decreased. More problematical, however, is the so-called “blinding” effect, in which particles slightly larger in size than the pores wedge permanently in the openings. English shows that these blinding particles will have an effective diameter up to 10% larger than the pore openings in the screen.
A third effect, explained by Taggart, arises because particles that are only slightly smaller than the screen openings pass through the pores with difficulty because of poor orientation or speed with respect to a given screen aperture. Taggart classifies the particles with this effect, as well as those causing blinding, as critical or near-sized particles and says that they range in size from 25% smaller to 50% larger than the pore openings.
The blinding process is the controlling factor in the mechanics of sieving operations and has developed an extensive mathematical treatment of this problem. It presents results showing (1) increasing mass of blinding material per unit screen area vs. sieving time and (2) increasing percentage undersize in the oversize leaving the screen vs. time of screening. All of these results show that (1) a steady-state condition is reached after a certain amount of sieving or screening time and (2) the changes in reaching the steady state, as the screen blinds, are analogous to exponential changes.
The experimental work done in this study tended to support the results given by English. Fig. 12 shows the effect of blinding vs. screening time using the same fluid mix and screen as used for the results in Fig. 11. The rotary 60-Hz vibrator was used for these tests, with the vibrator mounted to give the acceleration patterns shown in Fig. 3. The deck angle was 0, 10, and 30° , as indicated, and the weir height in Fig. 10 was 4 in. (10.16 cm). The notations Stud 5 and Stud 6 in Fig. 12 refer to the fluid endpoint being held at the top and middle studs, respectively, shown in Fig. 11. These results were obtained by intermittently reducing the feed flow to hold the liquid endpoint initially at Stud 5 as the screen blinded.
After approximately 15 minutes of this type of operation, the feed flow was increased to bring the liquid endpoint down to Stud 6, thus increasing the screen area available to the fluid. Subsequently,the feed flow was adjusted to hold the liquid endpoint at Stud 6. Observe both the exponential-type decrease in flow rate to a steady condition and the fact that the 0° deck angle provides a consistently larger flow rate than the 10 and 30° deck angles. In other words, even though the percentage decrease in flow due to blinding is largest for the 0° deck angle, the total flow capacity is nevertheless the largest.
To check the effect of vibrator frequency on blinding, the in-line vibrator was mounted such that the line of action passed through the center of gravity of the deck at an angle approximately 22.5° down-screen from the position normal to the screen. The deck angle was 00, the weir height dT was 4 in. (10.16 cm), and the screen and mud were as for Figs. 11 and 12. As screening time progressed, the frequency of the vibrator was changed among several different frequencies as indicated in Fig. 13. The acceleration levels indicated are those for the component normal to the screen. Observe that although blinding is evident at all frequencies, the 20- Hz frequency gives consistently higher flow rates than the other frequencies. Again, this is due to the higher particle-conveying rates at 20 Hz. In other words, slow conveying at high frequencies allows particles to pile up on the screen, thus reducing the screen’s capacity to transmit fluid.
The results indicate that optimizing the design of a vibrating screen for drilling fluids must take into account the dynamic motion of the bed, which is affected strongly by vibrator placement, as well as vibration frequency and amplitude. No attempt was made to assess the effect on flow capacity of additives to the drilling mud, such as polymer flocculants, fluid-loss reducers, or bentonite extenders.
Moreover, time did not permit a study of the effect of particles other than sand, such as shale or “gumbo clay.” Accordingly, the conclusions derived from this work must be considered with care. However, it seems reasonable to state that vibrators can be placed to give good conveyance of granular particles off the screen without having to tilt the screen downward. This means that horizontal screens can be used, which, when compared with downward-tilting screens, give the largest flow capacity. Furthermore, lower vibration frequencies give higher shaker capacities than higher frequencies, other factors being equal. Increasing the normal acceleration imparted to the screen cloth gives larger flow capacities, provided, of course, that the parallel acceleration component and phase angle are adjusted appropriately to give adequate particle conveyance. Obviously, the flow capacity of any shaker and screen cloth will depend not only on the rheology of the fluid but also on the amount of near- and oversized particles in the fluid.
Finally, a limited study of particle-size distributions indicated that the separation efficiency of a given screen for sand particles was not affected significantly by any of the parameters included in our study, other than the screen cloth itself. However, it was observed that, in general, steeper deck angles yielded oversized particles that were wetter than particles discharged from flatter decks. Hence, an added advantage of flat screen decks is that less fluid is discharged from the circulating mud system.